%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU355+2 : TPTP v9.2.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n001.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 : 300s
% DateTime : Tue May 5 05:11:35 PM UTC 2026
% Result : Theorem 17.83s 10.87s
% Output : CNFRefutation 48.82s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_681)
% Comments :
%------------------------------------------------------------------------------
fof(s1_tarski__e10_24__wellord2__2,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('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e10_24__wellord2__2) ).
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(t69_enumset1,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(s1_xboole_0__e10_24__wellord2__1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e10_24__wellord2__1) ).
fof(s1_funct_1__e10_24__wellord2__1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_funct_1__e10_24__wellord2__1) ).
fof(s1_tarski__e10_24__wellord2__1,axiom,
! [X1,X2] :
( ( ~ empty(X1)
& relation(X2) )
=> ( ! [X3,X4,X5] :
( ( in(X3,X1)
& ? [X6] :
( X3 = X6
& in(X4,X6)
& ! [X7] :
( in(X7,X6)
=> in(ordered_pair(X4,X7),X2) ) )
& in(X3,X1)
& ? [X8] :
( X3 = X8
& in(X5,X8)
& ! [X9] :
( in(X9,X8)
=> in(ordered_pair(X5,X9),X2) ) ) )
=> X4 = X5 )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(X5,X1)
& in(X5,X1)
& ? [X10] :
( X5 = X10
& in(X4,X10)
& ! [X11] :
( in(X11,X10)
=> in(ordered_pair(X4,X11),X2) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e10_24__wellord2__1) ).
fof(t23_relset_1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_relset_1) ).
fof(s2_funct_1__e10_24__wellord2,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('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_funct_1__e10_24__wellord2) ).
fof(t22_relset_1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_relset_1) ).
fof(s1_funct_1__e4_7_1__tops_2__1,lemma,
! [X1,X2] :
( ( one_sorted_str(X1)
& element(X2,powerset(powerset(the_carrier(X1)))) )
=> ( ! [X3,X4,X5] :
( ( in(X3,complements_of_subsets(the_carrier(X1),X2))
& ! [X6] :
( element(X6,powerset(the_carrier(X1)))
=> ( X6 = X3
=> X4 = subset_complement(the_carrier(X1),X6) ) )
& in(X3,complements_of_subsets(the_carrier(X1),X2))
& ! [X7] :
( element(X7,powerset(the_carrier(X1)))
=> ( X7 = X3
=> X5 = subset_complement(the_carrier(X1),X7) ) ) )
=> X4 = X5 )
=> ? [X3] :
( relation(X3)
& function(X3)
& ! [X4,X5] :
( in(ordered_pair(X4,X5),X3)
<=> ( in(X4,complements_of_subsets(the_carrier(X1),X2))
& in(X4,complements_of_subsets(the_carrier(X1),X2))
& ! [X8] :
( element(X8,powerset(the_carrier(X1)))
=> ( X8 = X4
=> X5 = subset_complement(the_carrier(X1),X8) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_funct_1__e4_7_1__tops_2__1) ).
fof(s1_funct_1__e4_7_2__tops_2__1,lemma,
! [X1,X2] :
( ( one_sorted_str(X1)
& element(X2,powerset(powerset(the_carrier(X1)))) )
=> ( ! [X3,X4,X5] :
( ( in(X3,X2)
& ! [X6] :
( element(X6,powerset(the_carrier(X1)))
=> ( X6 = X3
=> X4 = subset_complement(the_carrier(X1),X6) ) )
& in(X3,X2)
& ! [X7] :
( element(X7,powerset(the_carrier(X1)))
=> ( X7 = X3
=> X5 = subset_complement(the_carrier(X1),X7) ) ) )
=> X4 = X5 )
=> ? [X3] :
( relation(X3)
& function(X3)
& ! [X4,X5] :
( in(ordered_pair(X4,X5),X3)
<=> ( in(X4,X2)
& in(X4,X2)
& ! [X8] :
( element(X8,powerset(the_carrier(X1)))
=> ( X8 = X4
=> X5 = subset_complement(the_carrier(X1),X8) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_funct_1__e4_7_2__tops_2__1) ).
fof(s1_tarski__e18_27__finset_1__1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e18_27__finset_1__1) ).
fof(d1_ordinal1,axiom,
! [X1] : succ(X1) = set_union2(X1,singleton(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_ordinal1) ).
fof(d6_relat_2,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('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_relat_2) ).
fof(redefinition_k10_filter_1,axiom,
! [X1,X2,X3,X4] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1)
& ~ empty_carrier(X2)
& lattice(X2)
& latt_str(X2)
& element(X3,the_carrier(X1))
& element(X4,the_carrier(X2)) )
=> k10_filter_1(X1,X2,X3,X4) = ordered_pair(X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k10_filter_1) ).
fof(d21_lattice3,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& latt_str(X1) )
=> ( ( ~ empty_carrier(X1)
& lattice(X1)
& complete_latt_str(X1)
& latt_str(X1) )
=> ! [X2,X3] :
( element(X3,the_carrier(X1))
=> ( X3 = join_of_latt_set(X1,X2)
<=> ( latt_element_smaller(X1,X3,X2)
& ! [X4] :
( element(X4,the_carrier(X1))
=> ( latt_element_smaller(X1,X4,X2)
=> below(X1,X3,X4) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d21_lattice3) ).
fof(l4_wellord1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',l4_wellord1) ).
fof(redefinition_k1_domain_1,axiom,
! [X1,X2,X3,X4] :
( ( ~ empty(X1)
& ~ empty(X2)
& element(X3,X1)
& element(X4,X2) )
=> ordered_pair_as_product_element(X1,X2,X3,X4) = ordered_pair(X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_domain_1) ).
fof(d4_funct_1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_funct_1) ).
fof(s1_funct_1__e16_22__wellord2__1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_funct_1__e16_22__wellord2__1) ).
fof(t56_relat_1,lemma,
! [X1] :
( relation(X1)
=> ( ! [X2,X3] : ~ in(ordered_pair(X2,X3),X1)
=> X1 = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_relat_1) ).
fof(fc1_zfmisc_1,axiom,
! [X1,X2] : ~ empty(ordered_pair(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
fof(t4_xboole_0,lemma,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
& ~ ( ? [X3] : in(X3,set_intersection2(X1,X2))
& disjoint(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).
fof(fc2_arytm_3,axiom,
! [X1] :
( ( ordinal(X1)
& natural(X1) )
=> ( ~ empty(succ(X1))
& epsilon_transitive(succ(X1))
& epsilon_connected(succ(X1))
& ordinal(succ(X1))
& natural(succ(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_arytm_3) ).
fof(fc3_ordinal1,axiom,
! [X1] :
( ordinal(X1)
=> ( ~ empty(succ(X1))
& epsilon_transitive(succ(X1))
& epsilon_connected(succ(X1))
& ordinal(succ(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_ordinal1) ).
fof(s1_tarski__e16_22__wellord2__1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e16_22__wellord2__1) ).
fof(fc1_ordinal1,axiom,
! [X1] : ~ empty(succ(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_ordinal1) ).
fof(t65_zfmisc_1,lemma,
! [X1,X2] :
( set_difference(X1,singleton(X2)) = X1
<=> ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_zfmisc_1) ).
fof(t42_ordinal1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_ordinal1) ).
fof(l28_zfmisc_1,lemma,
! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l28_zfmisc_1) ).
fof(fc2_subset_1,axiom,
! [X1] : ~ empty(singleton(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).
fof(fc1_finset_1,axiom,
! [X1] :
( ~ empty(singleton(X1))
& finite(singleton(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_finset_1) ).
fof(d8_relat_1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_relat_1) ).
fof(s1_tarski__e6_21__wellord2__1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e6_21__wellord2__1) ).
fof(s1_tarski__e4_7_1__tops_2__2,axiom,
! [X1,X2] :
( ( one_sorted_str(X1)
& element(X2,powerset(powerset(the_carrier(X1)))) )
=> ! [X3] :
( ! [X4,X5,X6] :
( ( X4 = X5
& ? [X7,X8] :
( ordered_pair(X7,X8) = X5
& in(X7,complements_of_subsets(the_carrier(X1),X2))
& ! [X9] :
( element(X9,powerset(the_carrier(X1)))
=> ( X9 = X7
=> X8 = subset_complement(the_carrier(X1),X9) ) ) )
& X4 = X6
& ? [X10,X11] :
( ordered_pair(X10,X11) = X6
& in(X10,complements_of_subsets(the_carrier(X1),X2))
& ! [X12] :
( element(X12,powerset(the_carrier(X1)))
=> ( X12 = X10
=> X11 = subset_complement(the_carrier(X1),X12) ) ) ) )
=> X5 = X6 )
=> ? [X4] :
! [X5] :
( in(X5,X4)
<=> ? [X6] :
( in(X6,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
& X6 = X5
& ? [X13,X14] :
( ordered_pair(X13,X14) = X5
& in(X13,complements_of_subsets(the_carrier(X1),X2))
& ! [X15] :
( element(X15,powerset(the_carrier(X1)))
=> ( X15 = X13
=> X14 = subset_complement(the_carrier(X1),X15) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e4_7_1__tops_2__2) ).
fof(s1_tarski__e4_7_2__tops_2__2,axiom,
! [X1,X2] :
( ( one_sorted_str(X1)
& element(X2,powerset(powerset(the_carrier(X1)))) )
=> ! [X3] :
( ! [X4,X5,X6] :
( ( X4 = X5
& ? [X7,X8] :
( ordered_pair(X7,X8) = X5
& in(X7,X2)
& ! [X9] :
( element(X9,powerset(the_carrier(X1)))
=> ( X9 = X7
=> X8 = subset_complement(the_carrier(X1),X9) ) ) )
& X4 = X6
& ? [X10,X11] :
( ordered_pair(X10,X11) = X6
& in(X10,X2)
& ! [X12] :
( element(X12,powerset(the_carrier(X1)))
=> ( X12 = X10
=> X11 = subset_complement(the_carrier(X1),X12) ) ) ) )
=> X5 = X6 )
=> ? [X4] :
! [X5] :
( in(X5,X4)
<=> ? [X6] :
( in(X6,cartesian_product2(X2,X3))
& X6 = X5
& ? [X13,X14] :
( ordered_pair(X13,X14) = X5
& in(X13,X2)
& ! [X15] :
( element(X15,powerset(the_carrier(X1)))
=> ( X15 = X13
=> X14 = subset_complement(the_carrier(X1),X15) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e4_7_2__tops_2__2) ).
fof(s1_xboole_0__e4_7_1__tops_2__1,lemma,
! [X1,X2] :
( ( one_sorted_str(X1)
& element(X2,powerset(powerset(the_carrier(X1)))) )
=> ! [X3] :
? [X4] :
! [X5] :
( in(X5,X4)
<=> ( in(X5,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
& ? [X6,X7] :
( ordered_pair(X6,X7) = X5
& in(X6,complements_of_subsets(the_carrier(X1),X2))
& ! [X8] :
( element(X8,powerset(the_carrier(X1)))
=> ( X8 = X6
=> X7 = subset_complement(the_carrier(X1),X8) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e4_7_1__tops_2__1) ).
fof(s1_xboole_0__e4_7_2__tops_2__1,lemma,
! [X1,X2] :
( ( one_sorted_str(X1)
& element(X2,powerset(powerset(the_carrier(X1)))) )
=> ! [X3] :
? [X4] :
! [X5] :
( in(X5,X4)
<=> ( in(X5,cartesian_product2(X2,X3))
& ? [X6,X7] :
( ordered_pair(X6,X7) = X5
& in(X6,X2)
& ! [X8] :
( element(X8,powerset(the_carrier(X1)))
=> ( X8 = X6
=> X7 = subset_complement(the_carrier(X1),X8) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e4_7_2__tops_2__1) ).
fof(s1_xboole_0__e6_21__wellord2__1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e6_21__wellord2__1) ).
fof(dt_k2_binop_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('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_binop_1) ).
fof(d7_wellord1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_wellord1) ).
fof(redefinition_k2_binop_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) )
=> apply_binary_as_element(X1,X2,X3,X4,X5,X6) = apply_binary(X4,X5,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_binop_1) ).
fof(d1_lattices,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('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_lattices) ).
fof(d2_lattices,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('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_lattices) ).
fof(d13_relat_1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_relat_1) ).
fof(d12_relat_1,axiom,
! [X1,X2] :
( relation(X2)
=> ! [X3] :
( relation(X3)
=> ( X3 = relation_rng_restriction(X1,X2)
<=> ! [X4,X5] :
( in(ordered_pair(X4,X5),X3)
<=> ( in(X5,X1)
& in(ordered_pair(X4,X5),X2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_relat_1) ).
fof(d11_relat_1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_relat_1) ).
fof(d2_zfmisc_1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_zfmisc_1) ).
fof(d1_wellord1,axiom,
! [X1] :
( relation(X1)
=> ! [X2,X3] :
( X3 = fiber(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 != X2
& in(ordered_pair(X4,X2),X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_wellord1) ).
fof(d14_relat_1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_relat_1) ).
fof(d7_relat_1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_relat_1) ).
fof(d2_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( X1 = X2
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X1)
<=> in(ordered_pair(X3,X4),X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_relat_1) ).
fof(t143_relat_1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',t143_relat_1) ).
fof(d5_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_rng(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X4,X3),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).
fof(s1_relat_1__e6_21__wellord2,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('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_relat_1__e6_21__wellord2) ).
fof(s1_tarski__e4_7_1__tops_2__1,axiom,
! [X1,X2] :
( ( one_sorted_str(X1)
& element(X2,powerset(powerset(the_carrier(X1)))) )
=> ( ! [X3,X4,X5] :
( ( in(X3,complements_of_subsets(the_carrier(X1),X2))
& ! [X6] :
( element(X6,powerset(the_carrier(X1)))
=> ( X6 = X3
=> X4 = subset_complement(the_carrier(X1),X6) ) )
& in(X3,complements_of_subsets(the_carrier(X1),X2))
& ! [X7] :
( element(X7,powerset(the_carrier(X1)))
=> ( X7 = X3
=> X5 = subset_complement(the_carrier(X1),X7) ) ) )
=> X4 = X5 )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(X5,complements_of_subsets(the_carrier(X1),X2))
& in(X5,complements_of_subsets(the_carrier(X1),X2))
& ! [X8] :
( element(X8,powerset(the_carrier(X1)))
=> ( X8 = X5
=> X4 = subset_complement(the_carrier(X1),X8) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e4_7_1__tops_2__1) ).
fof(s1_tarski__e16_22__wellord2__2,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('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e16_22__wellord2__2) ).
fof(s1_tarski__e4_7_2__tops_2__1,axiom,
! [X1,X2] :
( ( one_sorted_str(X1)
& element(X2,powerset(powerset(the_carrier(X1)))) )
=> ( ! [X3,X4,X5] :
( ( in(X3,X2)
& ! [X6] :
( element(X6,powerset(the_carrier(X1)))
=> ( X6 = X3
=> X4 = subset_complement(the_carrier(X1),X6) ) )
& in(X3,X2)
& ! [X7] :
( element(X7,powerset(the_carrier(X1)))
=> ( X7 = X3
=> X5 = subset_complement(the_carrier(X1),X7) ) ) )
=> X4 = X5 )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(X5,X2)
& in(X5,X2)
& ! [X8] :
( element(X8,powerset(the_carrier(X1)))
=> ( X8 = X5
=> X4 = subset_complement(the_carrier(X1),X8) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e4_7_2__tops_2__1) ).
fof(d1_wellord2,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('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_wellord2) ).
fof(d10_relat_1,axiom,
! [X1,X2] :
( relation(X2)
=> ( X2 = identity_relation(X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(X3,X1)
& X3 = X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_relat_1) ).
fof(s1_xboole_0__e18_27__finset_1__1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e18_27__finset_1__1) ).
fof(s1_xboole_0__e16_22__wellord2__1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e16_22__wellord2__1) ).
fof(t32_filter_1,lemma,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( in(ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3),relation_of_lattice(X1))
<=> below_refl(X1,X2,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_filter_1) ).
fof(d3_relat_1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_relat_1) ).
fof(d1_relat_2,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( is_reflexive_in(X1,X2)
<=> ! [X3] :
( in(X3,X2)
=> in(ordered_pair(X3,X3),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relat_2) ).
fof(d8_relat_2,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('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_relat_2) ).
fof(s1_tarski__e4_27_3_1__finset_1__1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e4_27_3_1__finset_1__1) ).
fof(d4_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_dom(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X3,X4),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
fof(s1_xboole_0__e4_27_3_1__finset_1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e4_27_3_1__finset_1) ).
fof(dt_k8_funct_2,axiom,
! [X1,X2,X3,X4] :
( ( ~ empty(X1)
& function(X3)
& quasi_total(X3,X1,X2)
& relation_of2(X3,X1,X2)
& element(X4,X1) )
=> element(apply_as_element(X1,X2,X3,X4),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_funct_2) ).
fof(fc3_lattices,axiom,
! [X1,X2,X3] :
( ( ~ empty(X1)
& function(X2)
& quasi_total(X2,cartesian_product2(X1,X1),X1)
& relation_of2(X2,cartesian_product2(X1,X1),X1)
& function(X3)
& quasi_total(X3,cartesian_product2(X1,X1),X1)
& relation_of2(X3,cartesian_product2(X1,X1),X1) )
=> ( ~ empty_carrier(latt_str_of(X1,X2,X3))
& strict_latt_str(latt_str_of(X1,X2,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_lattices) ).
fof(dt_k10_filter_1,axiom,
! [X1,X2,X3,X4] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1)
& ~ empty_carrier(X2)
& lattice(X2)
& latt_str(X2)
& element(X3,the_carrier(X1))
& element(X4,the_carrier(X2)) )
=> element(k10_filter_1(X1,X2,X3,X4),the_carrier(k8_filter_1(X1,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_filter_1) ).
fof(t166_relat_1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',t166_relat_1) ).
fof(d3_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_intersection2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& in(X4,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(t48_xboole_1,lemma,
! [X1,X2] : set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_xboole_1) ).
fof(l2_wellord1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_wellord1) ).
fof(fraenkel_a_1_0_filter_1,axiom,
! [X1,X2] :
( ( ~ empty_carrier(X2)
& lattice(X2)
& latt_str(X2) )
=> ( in(X1,a_1_0_filter_1(X2))
<=> ? [X3,X4] :
( element(X3,the_carrier(X2))
& element(X4,the_carrier(X2))
& X1 = ordered_pair_as_product_element(the_carrier(X2),the_carrier(X2),X3,X4)
& below_refl(X2,X3,X4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_0_filter_1) ).
fof(dt_k1_domain_1,axiom,
! [X1,X2,X3,X4] :
( ( ~ empty(X1)
& ~ empty(X2)
& element(X3,X1)
& element(X4,X2) )
=> element(ordered_pair_as_product_element(X1,X2,X3,X4),cartesian_product2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_domain_1) ).
fof(d4_relat_2,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('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_2) ).
fof(t68_funct_1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_funct_1) ).
fof(d4_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(l3_wellord1,lemma,
! [X1] :
( relation(X1)
=> ( antisymmetric(X1)
<=> ! [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
& in(ordered_pair(X3,X2),X1) )
=> X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_wellord1) ).
fof(redefinition_k8_funct_2,axiom,
! [X1,X2,X3,X4] :
( ( ~ empty(X1)
& function(X3)
& quasi_total(X3,X1,X2)
& relation_of2(X3,X1,X2)
& element(X4,X1) )
=> apply_as_element(X1,X2,X3,X4) = apply(X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k8_funct_2) ).
fof(d1_funct_1,axiom,
! [X1] :
( function(X1)
<=> ! [X2,X3,X4] :
( ( in(ordered_pair(X2,X3),X1)
& in(ordered_pair(X2,X4),X1) )
=> X3 = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_funct_1) ).
fof(t74_relat_1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_relat_1) ).
fof(t34_lattice3,lemma,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& complete_latt_str(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( X2 = meet_of_latt_set(X1,X3)
<=> ( latt_set_smaller(X1,X2,X3)
& ! [X4] :
( element(X4,the_carrier(X1))
=> ( latt_set_smaller(X1,X4,X3)
=> below_refl(X1,X4,X2) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_lattice3) ).
fof(l1_wellord1,lemma,
! [X1] :
( relation(X1)
=> ( reflexive(X1)
<=> ! [X2] :
( in(X2,relation_field(X1))
=> in(ordered_pair(X2,X2),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_wellord1) ).
fof(s1_ordinal2__e18_27__finset_1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_ordinal2__e18_27__finset_1) ).
fof(d2_mcart_1,axiom,
! [X1] :
( ? [X2,X3] : X1 = ordered_pair(X2,X3)
=> ! [X2] :
( X2 = pair_second(X1)
<=> ! [X3,X4] :
( X1 = ordered_pair(X3,X4)
=> X2 = X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_mcart_1) ).
fof(d1_mcart_1,axiom,
! [X1] :
( ? [X2,X3] : X1 = ordered_pair(X2,X3)
=> ! [X2] :
( X2 = pair_first(X1)
<=> ! [X3,X4] :
( X1 = ordered_pair(X3,X4)
=> X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_mcart_1) ).
fof(d9_orders_2,axiom,
! [X1] :
( rel_str(X1)
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( related(X1,X2,X3)
<=> in(ordered_pair(X2,X3),the_InternalRel(X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_orders_2) ).
fof(d17_lattice3,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( latt_element_smaller(X1,X2,X3)
<=> ! [X4] :
( element(X4,the_carrier(X1))
=> ( in(X4,X3)
=> below(X1,X4,X2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d17_lattice3) ).
fof(d16_lattice3,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( latt_set_smaller(X1,X2,X3)
<=> ! [X4] :
( element(X4,the_carrier(X1))
=> ( in(X4,X3)
=> below(X1,X2,X4) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d16_lattice3) ).
fof(d8_lattices,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('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_lattices) ).
fof(t7_lattice3,lemma,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( below_refl(X1,X2,X3)
<=> related_reflexive(poset_of_lattice(X1),cast_to_el_of_LattPOSet(X1,X2),cast_to_el_of_LattPOSet(X1,X3)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_lattice3) ).
fof(s1_tarski__e8_6__wellord2__1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e8_6__wellord2__1) ).
fof(d16_lattices,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& meet_semilatt_str(X1) )
=> ( lower_bounded_semilattstr(X1)
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ( X2 = bottom_of_semilattstr(X1)
<=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( meet(X1,X2,X3) = X2
& meet(X1,X3,X2) = X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d16_lattices) ).
fof(t91_tmap_1,lemma,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> apply_as_element(the_carrier(X1),the_carrier(X1),identity_on_carrier(X1),X2) = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t91_tmap_1) ).
fof(d13_lattices,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& meet_semilatt_str(X1) )
=> ( lower_bounded_semilattstr(X1)
<=> ? [X2] :
( element(X2,the_carrier(X1))
& ! [X3] :
( element(X3,the_carrier(X1))
=> ( meet(X1,X2,X3) = X2
& meet(X1,X3,X2) = X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_lattices) ).
fof(d1_relat_1,axiom,
! [X1] :
( relation(X1)
<=> ! [X2] :
~ ( in(X2,X1)
& ! [X3,X4] : X2 != ordered_pair(X3,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relat_1) ).
fof(t106_zfmisc_1,lemma,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X1,X3)
& in(X2,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t106_zfmisc_1) ).
fof(l55_zfmisc_1,lemma,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X1,X3)
& in(X2,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l55_zfmisc_1) ).
fof(t8_funct_1,lemma,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(ordered_pair(X1,X2),X3)
<=> ( in(X1,relation_dom(X3))
& X2 = apply(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_funct_1) ).
fof(t26_lattices,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('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_lattices) ).
fof(t31_lattice3,lemma,
! [X1,X2] :
( ( ~ empty_carrier(X2)
& lattice(X2)
& latt_str(X2) )
=> ! [X3] :
( element(X3,the_carrier(poset_of_lattice(X2)))
=> ( relstr_set_smaller(poset_of_lattice(X2),X1,X3)
<=> latt_element_smaller(X2,cast_to_el_of_lattice(X2,X3),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_lattice3) ).
fof(t29_lattice3,lemma,
! [X1,X2] :
( ( ~ empty_carrier(X2)
& lattice(X2)
& latt_str(X2) )
=> ! [X3] :
( element(X3,the_carrier(poset_of_lattice(X2)))
=> ( relstr_element_smaller(poset_of_lattice(X2),X1,X3)
<=> latt_set_smaller(X2,cast_to_el_of_lattice(X2,X3),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_lattice3) ).
fof(t20_relat_1,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X1,X2),X3)
=> ( in(X1,relation_dom(X3))
& in(X2,relation_rng(X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_relat_1) ).
fof(t30_relat_1,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X1,X2),X3)
=> ( in(X1,relation_field(X3))
& in(X2,relation_field(X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_relat_1) ).
fof(t41_ordinal1,lemma,
! [X1] :
( ordinal(X1)
=> ( being_limit_ordinal(X1)
<=> ! [X2] :
( ordinal(X2)
=> ( in(X2,X1)
=> in(succ(X2),X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_ordinal1) ).
fof(t23_lattices,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('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_lattices) ).
fof(fraenkel_a_2_3_lattice3,axiom,
! [X1,X2,X3] :
( ( ~ empty_carrier(X2)
& lattice(X2)
& complete_latt_str(X2)
& latt_str(X2) )
=> ( in(X1,a_2_3_lattice3(X2,X3))
<=> ? [X4] :
( element(X4,the_carrier(X2))
& X1 = X4
& latt_set_smaller(X2,X4,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_3_lattice3) ).
fof(cc6_funct_2,axiom,
! [X1,X2] :
( ( ~ empty(X1)
& ~ empty(X2) )
=> ! [X3] :
( relation_of2(X3,X1,X2)
=> ( ( function(X3)
& quasi_total(X3,X1,X2) )
=> ( function(X3)
& ~ empty(X3)
& v1_partfun1(X3,X1,X2)
& quasi_total(X3,X1,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc6_funct_2) ).
fof(t30_lattice3,lemma,
! [X1,X2] :
( ( ~ empty_carrier(X2)
& lattice(X2)
& latt_str(X2) )
=> ! [X3] :
( element(X3,the_carrier(X2))
=> ( latt_element_smaller(X2,X3,X1)
<=> relstr_set_smaller(poset_of_lattice(X2),X1,cast_to_el_of_LattPOSet(X2,X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_lattice3) ).
fof(t28_lattice3,lemma,
! [X1,X2] :
( ( ~ empty_carrier(X2)
& lattice(X2)
& latt_str(X2) )
=> ! [X3] :
( element(X3,the_carrier(X2))
=> ( latt_set_smaller(X2,X3,X1)
<=> relstr_element_smaller(poset_of_lattice(X2),X1,cast_to_el_of_LattPOSet(X2,X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_lattice3) ).
fof(redefinition_r3_lattices,axiom,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& meet_commutative(X1)
& meet_absorbing(X1)
& join_absorbing(X1)
& latt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> ( below_refl(X1,X2,X3)
<=> below(X1,X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r3_lattices) ).
fof(cc5_funct_2,axiom,
! [X1,X2] :
( ~ empty(X2)
=> ! [X3] :
( relation_of2(X3,X1,X2)
=> ( ( function(X3)
& quasi_total(X3,X1,X2) )
=> ( function(X3)
& v1_partfun1(X3,X1,X2)
& quasi_total(X3,X1,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc5_funct_2) ).
fof(fraenkel_a_2_2_lattice3,axiom,
! [X1,X2,X3] :
( ( ~ empty_carrier(X2)
& latt_str(X2) )
=> ( in(X1,a_2_2_lattice3(X2,X3))
<=> ? [X4] :
( element(X4,the_carrier(X2))
& X1 = X4
& latt_set_smaller(X2,X4,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_2_lattice3) ).
fof(d1_connsp_2,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,powerset(the_carrier(X1)))
=> ( point_neighbourhood(X3,X1,X2)
<=> in(X2,interior(X1,X3)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_connsp_2) ).
fof(s1_xboole_0__e8_6__wellord2__1,lemma,
! [X1,X2] :
( ordinal(X2)
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ( in(X4,succ(X2))
& ? [X5] :
( ordinal(X5)
& X4 = X5
& in(X5,X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e8_6__wellord2__1) ).
fof(redefinition_r3_orders_2,axiom,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& reflexive_relstr(X1)
& rel_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> ( related_reflexive(X1,X2,X3)
<=> related(X1,X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r3_orders_2) ).
fof(d3_lattices,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('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_lattices) ).
fof(d1_binop_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2,X3] : apply_binary(X1,X2,X3) = apply(X1,ordered_pair(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_binop_1) ).
fof(dt_k4_lattices,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('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_lattices) ).
fof(dt_k3_lattices,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('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_lattices) ).
fof(t33_zfmisc_1,lemma,
! [X1,X2,X3,X4] :
( ordered_pair(X1,X2) = ordered_pair(X3,X4)
=> ( X1 = X3
& X2 = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_zfmisc_1) ).
fof(dt_k1_lattices,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('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_lattices) ).
fof(dt_k2_lattices,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('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_lattices) ).
fof(t1_lattice3,lemma,
! [X1,X2] :
( element(X2,the_carrier(boole_lattice(X1)))
=> ! [X3] :
( element(X3,the_carrier(boole_lattice(X1)))
=> ( join(boole_lattice(X1),X2,X3) = set_union2(X2,X3)
& meet(boole_lattice(X1),X2,X3) = set_intersection2(X2,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_lattice3) ).
fof(t5_connsp_2,lemma,
! [X1] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( ( open_subset(X2,X1)
& in(X3,X2) )
=> point_neighbourhood(X2,X1,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_connsp_2) ).
fof(l40_tops_1,lemma,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( in(X3,subset_complement(the_carrier(X1),X2))
<=> ~ in(X3,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l40_tops_1) ).
fof(t26_xboole_1,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_intersection2(X1,X3),set_intersection2(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_xboole_1) ).
fof(redefinition_k3_lattices,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('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k3_lattices) ).
fof(redefinition_k4_lattices,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('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_lattices) ).
fof(commutativity_k4_lattices,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('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k4_lattices) ).
fof(commutativity_k3_lattices,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('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_lattices) ).
fof(t13_compts_1,lemma,
! [X1] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1) )
=> ( compact_top_space(X1)
<=> ! [X2] :
( element(X2,powerset(powerset(the_carrier(X1))))
=> ~ ( centered(X2)
& closed_subsets(X2,X1)
& meet_of_subsets(the_carrier(X1),X2) = empty_set ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_compts_1) ).
fof(t33_ordinal1,lemma,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ( in(X1,X2)
<=> ordinal_subset(succ(X1),X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_ordinal1) ).
fof(t47_setfam_1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_setfam_1) ).
fof(d4_subset_1,axiom,
! [X1] : cast_to_subset(X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_subset_1) ).
fof(t48_setfam_1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_setfam_1) ).
fof(dt_m1_connsp_2,axiom,
! [X1,X2] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1)
& element(X2,the_carrier(X1)) )
=> ! [X3] :
( point_neighbourhood(X3,X1,X2)
=> element(X3,powerset(the_carrier(X1))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_connsp_2) ).
fof(redefinition_k5_subset_1,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> subset_intersection2(X1,X2,X3) = set_intersection2(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_subset_1) ).
fof(t6_yellow_0,conjecture,
! [X1] :
( rel_str(X1)
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ( relstr_set_smaller(X1,empty_set,X2)
& relstr_element_smaller(X1,empty_set,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_yellow_0) ).
fof(reflexivity_r3_lattices,axiom,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& meet_commutative(X1)
& meet_absorbing(X1)
& join_absorbing(X1)
& latt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> below_refl(X1,X2,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r3_lattices) ).
fof(t145_relat_1,lemma,
! [X1,X2] :
( relation(X2)
=> relation_image(X2,X1) = relation_image(X2,set_intersection2(relation_dom(X2),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t145_relat_1) ).
fof(fc1_orders_2,axiom,
! [X1,X2] :
( ( ~ empty(X1)
& relation_of2(X2,X1,X1) )
=> ( ~ empty_carrier(rel_str_of(X1,X2))
& strict_rel_str(rel_str_of(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_orders_2) ).
fof(reflexivity_r3_orders_2,axiom,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& reflexive_relstr(X1)
& rel_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> related_reflexive(X1,X2,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r3_orders_2) ).
fof(t19_xboole_1,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X1,X3) )
=> subset(X1,set_intersection2(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_xboole_1) ).
fof(fc5_lattice2,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& meet_associative(X1)
& meet_semilatt_str(X1) )
=> ( relation(the_L_meet(X1))
& function(the_L_meet(X1))
& quasi_total(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
& v2_binop_1(the_L_meet(X1),the_carrier(X1))
& v1_partfun1(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_lattice2) ).
fof(fc4_lattice2,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& meet_commutative(X1)
& meet_semilatt_str(X1) )
=> ( relation(the_L_meet(X1))
& function(the_L_meet(X1))
& quasi_total(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
& v1_binop_1(the_L_meet(X1),the_carrier(X1))
& v1_partfun1(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_lattice2) ).
fof(fc3_lattice2,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& join_associative(X1)
& join_semilatt_str(X1) )
=> ( relation(the_L_join(X1))
& function(the_L_join(X1))
& quasi_total(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
& v2_binop_1(the_L_join(X1),the_carrier(X1))
& v1_partfun1(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_lattice2) ).
fof(fc2_lattice2,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& join_commutative(X1)
& join_semilatt_str(X1) )
=> ( relation(the_L_join(X1))
& function(the_L_join(X1))
& quasi_total(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
& v1_binop_1(the_L_join(X1),the_carrier(X1))
& v1_partfun1(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_lattice2) ).
fof(t7_mcart_1,lemma,
! [X1,X2] :
( pair_first(ordered_pair(X1,X2)) = X1
& pair_second(ordered_pair(X1,X2)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_mcart_1) ).
fof(existence_m1_connsp_2,axiom,
! [X1,X2] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1)
& element(X2,the_carrier(X1)) )
=> ? [X3] : point_neighbourhood(X3,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_connsp_2) ).
fof(s2_funct_1__e16_22__wellord2__1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_funct_1__e16_22__wellord2__1) ).
fof(t53_wellord1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_wellord1) ).
fof(l3_zfmisc_1,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> ( in(X3,X1)
| subset(X1,set_difference(X2,singleton(X3))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_zfmisc_1) ).
fof(t5_tops_2,lemma,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( element(X2,powerset(powerset(the_carrier(X1))))
=> ~ ( is_a_cover_of_carrier(X1,X2)
& X2 = empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_tops_2) ).
fof(dt_k5_lattice3,axiom,
! [X1,X2] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1)
& element(X2,the_carrier(poset_of_lattice(X1))) )
=> element(cast_to_el_of_lattice(X1,X2),the_carrier(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_lattice3) ).
fof(d6_wellord1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] : relation_restriction(X1,X2) = set_intersection2(X1,cartesian_product2(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_wellord1) ).
fof(t50_subset_1,lemma,
! [X1] :
( X1 != empty_set
=> ! [X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( element(X3,X1)
=> ( ~ in(X3,X2)
=> in(X3,subset_complement(X1,X2)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_subset_1) ).
fof(dt_k4_lattice3,axiom,
! [X1,X2] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1)
& element(X2,the_carrier(X1)) )
=> element(cast_to_el_of_LattPOSet(X1,X2),the_carrier(poset_of_lattice(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_lattice3) ).
fof(t6_zfmisc_1,lemma,
! [X1,X2] :
( subset(singleton(X1),singleton(X2))
=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_zfmisc_1) ).
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(t28_wellord2,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('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_wellord2) ).
fof(fc1_relat_1,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(set_intersection2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_relat_1) ).
fof(t119_relat_1,lemma,
! [X1,X2] :
( relation(X2)
=> relation_rng(relation_rng_restriction(X1,X2)) = set_intersection2(relation_rng(X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t119_relat_1) ).
fof(t90_relat_1,lemma,
! [X1,X2] :
( relation(X2)
=> relation_dom(relation_dom_restriction(X2,X1)) = set_intersection2(relation_dom(X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t90_relat_1) ).
fof(t9_tarski,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('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_tarski) ).
fof(t17_xboole_1,lemma,
! [X1,X2] : subset(set_intersection2(X1,X2),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).
fof(t10_ordinal1,lemma,
! [X1] : in(X1,succ(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_ordinal1) ).
fof(dt_k2_lattice3,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ( reflexive(k2_lattice3(X1))
& antisymmetric(k2_lattice3(X1))
& transitive(k2_lattice3(X1))
& v1_partfun1(k2_lattice3(X1),the_carrier(X1),the_carrier(X1))
& relation_of2_as_subset(k2_lattice3(X1),the_carrier(X1),the_carrier(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_lattice3) ).
fof(t15_finset_1,lemma,
! [X1,X2] :
( finite(X1)
=> finite(set_intersection2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_finset_1) ).
fof(fc11_finset_1,axiom,
! [X1,X2] :
( finite(X1)
=> finite(set_intersection2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc11_finset_1) ).
fof(fc10_finset_1,axiom,
! [X1,X2] :
( finite(X2)
=> finite(set_intersection2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc10_finset_1) ).
fof(fc35_membered,axiom,
! [X1,X2] :
( v5_membered(X1)
=> ( v1_membered(set_intersection2(X1,X2))
& v2_membered(set_intersection2(X1,X2))
& v3_membered(set_intersection2(X1,X2))
& v4_membered(set_intersection2(X1,X2))
& v5_membered(set_intersection2(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc35_membered) ).
fof(fc36_membered,axiom,
! [X1,X2] :
( v5_membered(X1)
=> ( v1_membered(set_intersection2(X2,X1))
& v2_membered(set_intersection2(X2,X1))
& v3_membered(set_intersection2(X2,X1))
& v4_membered(set_intersection2(X2,X1))
& v5_membered(set_intersection2(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc36_membered) ).
fof(fc33_membered,axiom,
! [X1,X2] :
( v4_membered(X1)
=> ( v1_membered(set_intersection2(X1,X2))
& v2_membered(set_intersection2(X1,X2))
& v3_membered(set_intersection2(X1,X2))
& v4_membered(set_intersection2(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc33_membered) ).
fof(fc34_membered,axiom,
! [X1,X2] :
( v4_membered(X1)
=> ( v1_membered(set_intersection2(X2,X1))
& v2_membered(set_intersection2(X2,X1))
& v3_membered(set_intersection2(X2,X1))
& v4_membered(set_intersection2(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc34_membered) ).
fof(fc31_membered,axiom,
! [X1,X2] :
( v3_membered(X1)
=> ( v1_membered(set_intersection2(X1,X2))
& v2_membered(set_intersection2(X1,X2))
& v3_membered(set_intersection2(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc31_membered) ).
fof(fc32_membered,axiom,
! [X1,X2] :
( v3_membered(X1)
=> ( v1_membered(set_intersection2(X2,X1))
& v2_membered(set_intersection2(X2,X1))
& v3_membered(set_intersection2(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc32_membered) ).
fof(fc29_membered,axiom,
! [X1,X2] :
( v2_membered(X1)
=> ( v1_membered(set_intersection2(X1,X2))
& v2_membered(set_intersection2(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc29_membered) ).
fof(fc30_membered,axiom,
! [X1,X2] :
( v2_membered(X1)
=> ( v1_membered(set_intersection2(X2,X1))
& v2_membered(set_intersection2(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc30_membered) ).
fof(fc27_membered,axiom,
! [X1,X2] :
( v1_membered(X1)
=> v1_membered(set_intersection2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc27_membered) ).
fof(fc28_membered,axiom,
! [X1,X2] :
( v1_membered(X1)
=> v1_membered(set_intersection2(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc28_membered) ).
fof(l30_wellord2,lemma,
! [X1,X2] :
( relation(X2)
=> ~ ( well_ordering(X2)
& equipotent(X1,relation_field(X2))
& ! [X3] :
( relation(X3)
=> ~ well_orders(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l30_wellord2) ).
fof(l25_zfmisc_1,lemma,
! [X1,X2] :
~ ( disjoint(singleton(X1),X2)
& in(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l25_zfmisc_1) ).
fof(d4_lattice3,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(poset_of_lattice(X1)))
=> cast_to_el_of_lattice(X1,X2) = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_lattice3) ).
fof(d3_ordinal1,axiom,
! [X1] :
( epsilon_connected(X1)
<=> ! [X2,X3] :
~ ( in(X2,X1)
& in(X3,X1)
& ~ in(X2,X3)
& X2 != X3
& ~ in(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_ordinal1) ).
fof(t39_zfmisc_1,lemma,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_zfmisc_1) ).
fof(l4_zfmisc_1,lemma,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4_zfmisc_1) ).
fof(commutativity_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(t37_zfmisc_1,lemma,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_zfmisc_1) ).
fof(l2_zfmisc_1,lemma,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_zfmisc_1) ).
fof(d7_xboole_0,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_intersection2(X1,X2) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(t136_zfmisc_1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',t136_zfmisc_1) ).
fof(t3_xboole_0,lemma,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] :
~ ( in(X3,X1)
& in(X3,X2) ) )
& ~ ( ? [X3] :
( in(X3,X1)
& in(X3,X2) )
& disjoint(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_0) ).
fof(d3_lattice3,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> cast_to_el_of_LattPOSet(X1,X2) = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_lattice3) ).
fof(d22_lattice3,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& latt_str(X1) )
=> ! [X2] : meet_of_latt_set(X1,X2) = join_of_latt_set(X1,a_2_2_lattice3(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d22_lattice3) ).
fof(t46_zfmisc_1,lemma,
! [X1,X2] :
( in(X1,X2)
=> set_union2(singleton(X1),X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_zfmisc_1) ).
fof(l23_zfmisc_1,lemma,
! [X1,X2] :
( in(X1,X2)
=> set_union2(singleton(X1),X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l23_zfmisc_1) ).
fof(t28_xboole_1,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_intersection2(X1,X2) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).
fof(dt_k6_partfun1,axiom,
! [X1] :
( v1_partfun1(identity_as_relation_of(X1),X1,X1)
& relation_of2_as_subset(identity_as_relation_of(X1),X1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_partfun1) ).
fof(redefinition_k6_partfun1,axiom,
! [X1] : identity_as_relation_of(X1) = identity_relation(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_partfun1) ).
fof(cc2_lattices,axiom,
! [X1] :
( latt_str(X1)
=> ( ( ~ empty_carrier(X1)
& join_commutative(X1)
& join_associative(X1)
& meet_commutative(X1)
& meet_associative(X1)
& meet_absorbing(X1)
& join_absorbing(X1) )
=> ( ~ empty_carrier(X1)
& lattice(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_lattices) ).
fof(dt_k16_lattice3,axiom,
! [X1,X2] :
( ( ~ empty_carrier(X1)
& latt_str(X1) )
=> element(meet_of_latt_set(X1,X2),the_carrier(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k16_lattice3) ).
fof(dt_k15_lattice3,axiom,
! [X1,X2] :
( ( ~ empty_carrier(X1)
& latt_str(X1) )
=> element(join_of_latt_set(X1,X2),the_carrier(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k15_lattice3) ).
fof(rc7_pre_topc,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1) )
=> ? [X2] :
( element(X2,powerset(the_carrier(X1)))
& ~ empty(X2)
& closed_subset(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc7_pre_topc) ).
fof(fc4_subset_1,axiom,
! [X1,X2] :
( ( ~ empty(X1)
& ~ empty(X2) )
=> ~ empty(cartesian_product2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_subset_1) ).
fof(s3_funct_1__e16_22__wellord2,lemma,
! [X1] :
? [X2] :
( relation(X2)
& function(X2)
& relation_dom(X2) = X1
& ! [X3] :
( in(X3,X1)
=> apply(X2,X3) = singleton(X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_funct_1__e16_22__wellord2) ).
fof(dt_k8_filter_1,axiom,
! [X1,X2] :
( ( ~ empty_carrier(X1)
& latt_str(X1)
& ~ empty_carrier(X2)
& latt_str(X2) )
=> ( strict_latt_str(k8_filter_1(X1,X2))
& latt_str(k8_filter_1(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_filter_1) ).
fof(fc2_xboole_0,axiom,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_xboole_0) ).
fof(fc3_xboole_0,axiom,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_xboole_0) ).
fof(rc5_struct_0,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ? [X2] :
( element(X2,powerset(the_carrier(X1)))
& ~ empty(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_struct_0) ).
fof(d2_lattice3,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> poset_of_lattice(X1) = rel_str_of(the_carrier(X1),k2_lattice3(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_lattice3) ).
fof(fc3_subset_1,axiom,
! [X1,X2] : ~ empty(unordered_pair(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_subset_1) ).
fof(t8_zfmisc_1,lemma,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_zfmisc_1) ).
fof(t9_zfmisc_1,lemma,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X2 = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_zfmisc_1) ).
fof(t24_ordinal1,lemma,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ~ ( ~ in(X1,X2)
& X1 != X2
& ~ in(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_ordinal1) ).
fof(antisymmetry_r2_xboole_0,axiom,
! [X1,X2] :
( proper_subset(X1,X2)
=> ~ proper_subset(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_xboole_0) ).
fof(antisymmetry_r2_hidden,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(t50_lattice3,lemma,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& complete_latt_str(X1)
& latt_str(X1) )
=> ( ~ empty_carrier(X1)
& lattice(X1)
& lower_bounded_semilattstr(X1)
& latt_str(X1)
& bottom_of_semilattstr(X1) = join_of_latt_set(X1,empty_set) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_lattice3) ).
fof(rc2_tex_2,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& ~ proper_element(X2,powerset(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_tex_2) ).
fof(d2_subset_1,axiom,
! [X1,X2] :
( ( ~ empty(X1)
=> ( element(X2,X1)
<=> in(X2,X1) ) )
& ( empty(X1)
=> ( element(X2,X1)
<=> empty(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_subset_1) ).
fof(idempotence_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
fof(dt_k1_pcomps_1,axiom,
! [X1] : element(k1_pcomps_1(X1),powerset(powerset(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_pcomps_1) ).
fof(redefinition_k1_pcomps_1,axiom,
! [X1] : k1_pcomps_1(X1) = powerset(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_pcomps_1) ).
fof(dt_k5_lattices,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& meet_semilatt_str(X1) )
=> element(bottom_of_semilattstr(X1),the_carrier(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_lattices) ).
fof(t2_boole,axiom,
! [X1] : set_intersection2(X1,empty_set) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_boole) ).
fof(fc4_lattice3,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ( ~ empty_carrier(poset_of_lattice(X1))
& strict_rel_str(poset_of_lattice(X1))
& reflexive_relstr(poset_of_lattice(X1))
& transitive_relstr(poset_of_lattice(X1))
& antisymmetric_relstr(poset_of_lattice(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_lattice3) ).
fof(rc4_finset_1,axiom,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2)
& finite(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_finset_1) ).
fof(rc3_finset_1,axiom,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2)
& finite(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_finset_1) ).
fof(rc1_subset_1,axiom,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(dt_k3_lattice3,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ( strict_rel_str(poset_of_lattice(X1))
& reflexive_relstr(poset_of_lattice(X1))
& transitive_relstr(poset_of_lattice(X1))
& antisymmetric_relstr(poset_of_lattice(X1))
& rel_str(poset_of_lattice(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_lattice3) ).
fof(dt_k9_filter_1,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> relation(relation_of_lattice(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_filter_1) ).
fof(fc2_pre_topc,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ~ empty(cast_as_carrier_subset(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_pre_topc) ).
fof(fc1_struct_0,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ~ empty(the_carrier(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(fc6_relat_1,axiom,
! [X1] :
( ( ~ empty(X1)
& relation(X1) )
=> ~ empty(relation_rng(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).
fof(fc5_relat_1,axiom,
! [X1] :
( ( ~ empty(X1)
& relation(X1) )
=> ~ empty(relation_dom(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(d8_filter_1,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> relation_of_lattice(X1) = a_1_0_filter_1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_filter_1) ).
fof(redefinition_k2_lattice3,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> k2_lattice3(X1) = relation_of_lattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_lattice3) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(cc1_lattices,axiom,
! [X1] :
( latt_str(X1)
=> ( ( ~ empty_carrier(X1)
& lattice(X1) )
=> ( ~ empty_carrier(X1)
& join_commutative(X1)
& join_associative(X1)
& meet_commutative(X1)
& meet_associative(X1)
& meet_absorbing(X1)
& join_absorbing(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_lattices) ).
fof(irreflexivity_r2_xboole_0,axiom,
! [X1,X2] : ~ proper_subset(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',irreflexivity_r2_xboole_0) ).
fof(l1_zfmisc_1,lemma,
! [X1] : singleton(X1) != empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_zfmisc_1) ).
fof(d11_grcat_1,axiom,
! [X1] :
( one_sorted_str(X1)
=> identity_on_carrier(X1) = identity_as_relation_of(the_carrier(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_grcat_1) ).
fof(dt_k2_subset_1,axiom,
! [X1] : element(cast_to_subset(X1),powerset(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_subset_1) ).
fof(fc2_lattice3,axiom,
! [X1] :
( ~ empty_carrier(boole_lattice(X1))
& strict_latt_str(boole_lattice(X1))
& join_commutative(boole_lattice(X1))
& join_associative(boole_lattice(X1))
& meet_commutative(boole_lattice(X1))
& meet_associative(boole_lattice(X1))
& meet_absorbing(boole_lattice(X1))
& join_absorbing(boole_lattice(X1))
& lattice(boole_lattice(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_lattice3) ).
fof(fc1_lattice3,axiom,
! [X1] :
( ~ empty_carrier(boole_lattice(X1))
& strict_latt_str(boole_lattice(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_lattice3) ).
fof(fc1_subset_1,axiom,
! [X1] : ~ empty(powerset(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(fc1_finsub_1,axiom,
! [X1] :
( ~ empty(powerset(X1))
& cup_closed(powerset(X1))
& diff_closed(powerset(X1))
& preboolean(powerset(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_finsub_1) ).
fof(rc9_lattices,axiom,
? [X1] :
( latt_str(X1)
& ~ empty_carrier(X1)
& strict_latt_str(X1)
& join_commutative(X1)
& join_associative(X1)
& meet_commutative(X1)
& meet_associative(X1)
& meet_absorbing(X1)
& join_absorbing(X1)
& lattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc9_lattices) ).
fof(rc6_lattices,axiom,
? [X1] :
( latt_str(X1)
& ~ empty_carrier(X1)
& strict_latt_str(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc6_lattices) ).
fof(rc3_struct_0,axiom,
? [X1] :
( one_sorted_str(X1)
& ~ empty_carrier(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_struct_0) ).
fof(rc2_orders_2,axiom,
? [X1] :
( rel_str(X1)
& ~ empty_carrier(X1)
& strict_rel_str(X1)
& reflexive_relstr(X1)
& transitive_relstr(X1)
& antisymmetric_relstr(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_orders_2) ).
fof(rc3_ordinal1,axiom,
? [X1] :
( ~ empty(X1)
& epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_ordinal1) ).
fof(rc2_xboole_0,axiom,
? [X1] : ~ empty(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(rc2_relat_1,axiom,
? [X1] :
( ~ empty(X1)
& relation(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(rc1_membered,axiom,
? [X1] :
( ~ empty(X1)
& v1_membered(X1)
& v2_membered(X1)
& v3_membered(X1)
& v4_membered(X1)
& v5_membered(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_membered) ).
fof(rc1_finset_1,axiom,
? [X1] :
( ~ empty(X1)
& finite(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finset_1) ).
fof(rc1_arytm_3,axiom,
? [X1] :
( ~ empty(X1)
& epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1)
& natural(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_arytm_3) ).
fof(d1_enumset1,axiom,
! [X1,X2,X3,X4] :
( X4 = unordered_triple(X1,X2,X3)
<=> ! [X5] :
( in(X5,X4)
<=> ~ ( X5 != X1
& X5 != X2
& X5 != X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_enumset1) ).
fof(s1_tarski__e6_27__finset_1__1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e6_27__finset_1__1) ).
fof(d13_funct_1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_funct_1) ).
fof(d1_lattice3,axiom,
! [X1,X2] :
( ( strict_latt_str(X2)
& latt_str(X2) )
=> ( X2 = boole_lattice(X1)
<=> ( the_carrier(X2) = powerset(X1)
& ! [X3] :
( element(X3,powerset(X1))
=> ! [X4] :
( element(X4,powerset(X1))
=> ( apply_binary(the_L_join(X2),X3,X4) = subset_union2(X1,X3,X4)
& apply_binary(the_L_meet(X2),X3,X4) = subset_intersection2(X1,X3,X4) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_lattice3) ).
fof(d8_setfam_1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_setfam_1) ).
fof(d13_pre_topc,axiom,
! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ! [X3] :
( element(X3,powerset(the_carrier(X1)))
=> ( X3 = topstr_closure(X1,X2)
<=> ! [X4] :
( in(X4,the_carrier(X1))
=> ( in(X4,X3)
<=> ! [X5] :
( element(X5,powerset(the_carrier(X1)))
=> ~ ( open_subset(X5,X1)
& in(X4,X5)
& disjoint(X2,X5) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_pre_topc) ).
fof(free_g3_lattices,axiom,
! [X1,X2,X3] :
( ( function(X2)
& quasi_total(X2,cartesian_product2(X1,X1),X1)
& relation_of2(X2,cartesian_product2(X1,X1),X1)
& function(X3)
& quasi_total(X3,cartesian_product2(X1,X1),X1)
& relation_of2(X3,cartesian_product2(X1,X1),X1) )
=> ! [X4,X5,X6] :
( latt_str_of(X1,X2,X3) = latt_str_of(X4,X5,X6)
=> ( X1 = X4
& X2 = X5
& X3 = X6 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g3_lattices) ).
fof(dt_g3_lattices,axiom,
! [X1,X2,X3] :
( ( function(X2)
& quasi_total(X2,cartesian_product2(X1,X1),X1)
& relation_of2(X2,cartesian_product2(X1,X1),X1)
& function(X3)
& quasi_total(X3,cartesian_product2(X1,X1),X1)
& relation_of2(X3,cartesian_product2(X1,X1),X1) )
=> ( strict_latt_str(latt_str_of(X1,X2,X3))
& latt_str(latt_str_of(X1,X2,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_g3_lattices) ).
fof(s2_funct_1__e4_7_1__tops_2,lemma,
! [X1,X2] :
( ( one_sorted_str(X1)
& element(X2,powerset(powerset(the_carrier(X1)))) )
=> ( ( ! [X3,X4,X5] :
( ( in(X3,complements_of_subsets(the_carrier(X1),X2))
& ! [X6] :
( element(X6,powerset(the_carrier(X1)))
=> ( X6 = X3
=> X4 = subset_complement(the_carrier(X1),X6) ) )
& ! [X7] :
( element(X7,powerset(the_carrier(X1)))
=> ( X7 = X3
=> X5 = subset_complement(the_carrier(X1),X7) ) ) )
=> X4 = X5 )
& ! [X3] :
~ ( in(X3,complements_of_subsets(the_carrier(X1),X2))
& ! [X4] :
~ ! [X8] :
( element(X8,powerset(the_carrier(X1)))
=> ( X8 = X3
=> X4 = subset_complement(the_carrier(X1),X8) ) ) ) )
=> ? [X3] :
( relation(X3)
& function(X3)
& relation_dom(X3) = complements_of_subsets(the_carrier(X1),X2)
& ! [X4] :
( in(X4,complements_of_subsets(the_carrier(X1),X2))
=> ! [X9] :
( element(X9,powerset(the_carrier(X1)))
=> ( X9 = X4
=> apply(X3,X4) = subset_complement(the_carrier(X1),X9) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_funct_1__e4_7_1__tops_2) ).
fof(d12_funct_1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_funct_1) ).
fof(s2_funct_1__e4_7_2__tops_2,lemma,
! [X1,X2] :
( ( one_sorted_str(X1)
& element(X2,powerset(powerset(the_carrier(X1)))) )
=> ( ( ! [X3,X4,X5] :
( ( in(X3,X2)
& ! [X6] :
( element(X6,powerset(the_carrier(X1)))
=> ( X6 = X3
=> X4 = subset_complement(the_carrier(X1),X6) ) )
& ! [X7] :
( element(X7,powerset(the_carrier(X1)))
=> ( X7 = X3
=> X5 = subset_complement(the_carrier(X1),X7) ) ) )
=> X4 = X5 )
& ! [X3] :
~ ( in(X3,X2)
& ! [X4] :
~ ! [X8] :
( element(X8,powerset(the_carrier(X1)))
=> ( X8 = X3
=> X4 = subset_complement(the_carrier(X1),X8) ) ) ) )
=> ? [X3] :
( relation(X3)
& function(X3)
& relation_dom(X3) = X2
& ! [X4] :
( in(X4,X2)
=> ! [X9] :
( element(X9,powerset(the_carrier(X1)))
=> ( X9 = X4
=> apply(X3,X4) = subset_complement(the_carrier(X1),X9) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_funct_1__e4_7_2__tops_2) ).
fof(d1_pre_topc,axiom,
! [X1] :
( top_str(X1)
=> ( topological_space(X1)
<=> ( in(the_carrier(X1),the_topology(X1))
& ! [X2] :
( element(X2,powerset(powerset(the_carrier(X1))))
=> ( subset(X2,the_topology(X1))
=> in(union_of_subsets(the_carrier(X1),X2),the_topology(X1)) ) )
& ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ! [X3] :
( element(X3,powerset(the_carrier(X1)))
=> ( ( in(X2,the_topology(X1))
& in(X3,the_topology(X1)) )
=> in(subset_intersection2(the_carrier(X1),X2,X3),the_topology(X1)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_pre_topc) ).
fof(s1_tarski__e2_37_1_1__pre_topc__1,axiom,
! [X1,X2] :
( ( topological_space(X1)
& top_str(X1)
& element(X2,powerset(powerset(the_carrier(X1)))) )
=> ( ! [X3,X4,X5] :
( ( X3 = X4
& in(set_difference(cast_as_carrier_subset(X1),X4),X2)
& X3 = X5
& in(set_difference(cast_as_carrier_subset(X1),X5),X2) )
=> X4 = X5 )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(X5,powerset(the_carrier(X1)))
& X5 = X4
& in(set_difference(cast_as_carrier_subset(X1),X4),X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e2_37_1_1__pre_topc__1) ).
fof(d2_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_union2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
| in(X4,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(s2_ordinal1__e18_27__finset_1__1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_ordinal1__e18_27__finset_1__1) ).
fof(t54_funct_1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_funct_1) ).
fof(d9_lattice3,axiom,
! [X1] :
( rel_str(X1)
=> ! [X2,X3] :
( element(X3,the_carrier(X1))
=> ( relstr_set_smaller(X1,X2,X3)
<=> ! [X4] :
( element(X4,the_carrier(X1))
=> ( in(X4,X2)
=> related(X1,X4,X3) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_lattice3) ).
fof(d8_lattice3,axiom,
! [X1] :
( rel_str(X1)
=> ! [X2,X3] :
( element(X3,the_carrier(X1))
=> ( relstr_element_smaller(X1,X2,X3)
<=> ! [X4] :
( element(X4,the_carrier(X1))
=> ( in(X4,X2)
=> related(X1,X3,X4) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_lattice3) ).
fof(t26_orders_2,lemma,
! [X1] :
( ( transitive_relstr(X1)
& rel_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ! [X4] :
( element(X4,the_carrier(X1))
=> ( ( related(X1,X2,X3)
& related(X1,X3,X4) )
=> related(X1,X2,X4) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_orders_2) ).
fof(cc4_funct_2,axiom,
! [X1,X2] :
( relation_of2(X2,X1,X1)
=> ( ( function(X2)
& v1_partfun1(X2,X1,X1)
& reflexive(X2)
& quasi_total(X2,X1,X1) )
=> ( function(X2)
& one_to_one(X2)
& quasi_total(X2,X1,X1)
& onto(X2,X1,X1)
& bijective(X2,X1,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_funct_2) ).
fof(cc3_funct_2,axiom,
! [X1,X2,X3] :
( relation_of2(X3,X1,X2)
=> ( ( function(X3)
& one_to_one(X3)
& quasi_total(X3,X1,X2)
& onto(X3,X1,X2) )
=> ( function(X3)
& quasi_total(X3,X1,X2)
& bijective(X3,X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_funct_2) ).
fof(s1_tarski__e1_40__pre_topc__1,axiom,
! [X1,X2] :
( ( topological_space(X1)
& top_str(X1)
& element(X2,powerset(the_carrier(X1))) )
=> ( ! [X3,X4,X5] :
( ( X3 = X4
& ? [X6] :
( element(X6,powerset(the_carrier(X1)))
& X6 = X4
& closed_subset(X6,X1)
& subset(X2,X4) )
& X3 = X5
& ? [X7] :
( element(X7,powerset(the_carrier(X1)))
& X7 = X5
& closed_subset(X7,X1)
& subset(X2,X5) ) )
=> X4 = X5 )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(X5,powerset(the_carrier(X1)))
& X5 = X4
& ? [X8] :
( element(X8,powerset(the_carrier(X1)))
& X8 = X4
& closed_subset(X8,X1)
& subset(X2,X4) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e1_40__pre_topc__1) ).
fof(t45_pre_topc,lemma,
! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ! [X3] :
( in(X3,the_carrier(X1))
=> ( in(X3,topstr_closure(X1,X2))
<=> ! [X4] :
( element(X4,powerset(the_carrier(X1)))
=> ( ( closed_subset(X4,X1)
& subset(X2,X4) )
=> in(X3,X4) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_pre_topc) ).
fof(cc2_funct_2,axiom,
! [X1,X2,X3] :
( relation_of2(X3,X1,X2)
=> ( ( function(X3)
& quasi_total(X3,X1,X2)
& bijective(X3,X1,X2) )
=> ( function(X3)
& one_to_one(X3)
& quasi_total(X3,X1,X2)
& onto(X3,X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_funct_2) ).
fof(s3_subset_1__e1_40__pre_topc,lemma,
! [X1,X2] :
( ( topological_space(X1)
& top_str(X1)
& element(X2,powerset(the_carrier(X1))) )
=> ? [X3] :
( element(X3,powerset(powerset(the_carrier(X1))))
& ! [X4] :
( element(X4,powerset(the_carrier(X1)))
=> ( in(X4,X3)
<=> ? [X5] :
( element(X5,powerset(the_carrier(X1)))
& X5 = X4
& closed_subset(X5,X1)
& subset(X2,X4) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_subset_1__e1_40__pre_topc) ).
fof(d3_wellord1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_wellord1) ).
fof(t46_funct_2,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('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_funct_2) ).
fof(s1_xboole_0__e6_27__finset_1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e6_27__finset_1) ).
fof(d6_pre_topc,axiom,
! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ( closed_subset(X2,X1)
<=> open_subset(subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),X2),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_pre_topc) ).
fof(t21_funct_2,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('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_funct_2) ).
fof(d2_tarski,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
fof(s1_xboole_0__e2_37_1_1__pre_topc__1,lemma,
! [X1,X2] :
( ( topological_space(X1)
& top_str(X1)
& element(X2,powerset(powerset(the_carrier(X1)))) )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ( in(X4,powerset(the_carrier(X1)))
& in(set_difference(cast_as_carrier_subset(X1),X4),X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e2_37_1_1__pre_topc__1) ).
fof(s3_subset_1__e2_37_1_1__pre_topc,lemma,
! [X1,X2] :
( ( topological_space(X1)
& top_str(X1)
& element(X2,powerset(powerset(the_carrier(X1)))) )
=> ? [X3] :
( element(X3,powerset(powerset(the_carrier(X1))))
& ! [X4] :
( element(X4,powerset(the_carrier(X1)))
=> ( in(X4,X3)
<=> in(set_difference(cast_as_carrier_subset(X1),X4),X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_subset_1__e2_37_1_1__pre_topc) ).
fof(s1_xboole_0__e1_40__pre_topc__1,lemma,
! [X1,X2] :
( ( topological_space(X1)
& top_str(X1)
& element(X2,powerset(the_carrier(X1))) )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ( in(X4,powerset(the_carrier(X1)))
& ? [X5] :
( element(X5,powerset(the_carrier(X1)))
& X5 = X4
& closed_subset(X5,X1)
& subset(X2,X4) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e1_40__pre_topc__1) ).
fof(t9_funct_2,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('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_funct_2) ).
fof(t22_pre_topc,lemma,
! [X1] :
( one_sorted_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),X2)) = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_pre_topc) ).
fof(t25_orders_2,lemma,
! [X1] :
( ( antisymmetric_relstr(X1)
& rel_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( ( related(X1,X2,X3)
& related(X1,X3,X2) )
=> X2 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_orders_2) ).
fof(t6_funct_2,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('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_funct_2) ).
fof(cc1_funct_2,axiom,
! [X1,X2,X3] :
( relation_of2(X3,X1,X2)
=> ( ( function(X3)
& v1_partfun1(X3,X1,X2) )
=> ( function(X3)
& quasi_total(X3,X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_2) ).
fof(d3_compts_1,axiom,
! [X1] :
( top_str(X1)
=> ( compact_top_space(X1)
<=> ! [X2] :
( element(X2,powerset(powerset(the_carrier(X1))))
=> ~ ( is_a_cover_of_carrier(X1,X2)
& open_subsets(X2,X1)
& ! [X3] :
( element(X3,powerset(powerset(the_carrier(X1))))
=> ~ ( subset(X3,X2)
& is_a_cover_of_carrier(X1,X3)
& finite(X3) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_compts_1) ).
fof(d1_funct_2,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('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_funct_2) ).
fof(fc3_orders_2,axiom,
! [X1,X2] :
( ( reflexive(X2)
& antisymmetric(X2)
& transitive(X2)
& v1_partfun1(X2,X1,X1)
& relation_of2(X2,X1,X1) )
=> ( strict_rel_str(rel_str_of(X1,X2))
& reflexive_relstr(rel_str_of(X1,X2))
& transitive_relstr(rel_str_of(X1,X2))
& antisymmetric_relstr(rel_str_of(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_orders_2) ).
fof(t22_funct_1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_funct_1) ).
fof(t44_pre_topc,lemma,
! [X1] :
( ( topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( element(X2,powerset(powerset(the_carrier(X1))))
=> ( ! [X3] :
( element(X3,powerset(the_carrier(X1)))
=> ( in(X3,X2)
=> closed_subset(X3,X1) ) )
=> closed_subset(meet_of_subsets(the_carrier(X1),X2),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_pre_topc) ).
fof(d1_setfam_1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_setfam_1) ).
fof(dt_k5_relset_1,axiom,
! [X1,X2,X3] :
( relation_of2(X3,X1,X2)
=> element(relation_rng_as_subset(X1,X2,X3),powerset(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relset_1) ).
fof(dt_k4_relset_1,axiom,
! [X1,X2,X3] :
( relation_of2(X3,X1,X2)
=> element(relation_dom_as_subset(X1,X2,X3),powerset(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_relset_1) ).
fof(t2_lattice3,lemma,
! [X1,X2] :
( element(X2,the_carrier(boole_lattice(X1)))
=> ! [X3] :
( element(X3,the_carrier(boole_lattice(X1)))
=> ( below(boole_lattice(X1),X2,X3)
<=> subset(X2,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_lattice3) ).
fof(d2_tops_2,axiom,
! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(powerset(the_carrier(X1))))
=> ( closed_subsets(X2,X1)
<=> ! [X3] :
( element(X3,powerset(the_carrier(X1)))
=> ( in(X3,X2)
=> closed_subset(X3,X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tops_2) ).
fof(d1_tops_2,axiom,
! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(powerset(the_carrier(X1))))
=> ( open_subsets(X2,X1)
<=> ! [X3] :
( element(X3,powerset(the_carrier(X1)))
=> ( in(X3,X2)
=> open_subset(X3,X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tops_2) ).
fof(t21_funct_1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_funct_1) ).
fof(t46_pre_topc,lemma,
! [X1] :
( ( topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ? [X3] :
( element(X3,powerset(powerset(the_carrier(X1))))
& ! [X4] :
( element(X4,powerset(the_carrier(X1)))
=> ( in(X4,X3)
<=> ( closed_subset(X4,X1)
& subset(X2,X4) ) ) )
& topstr_closure(X1,X2) = meet_of_subsets(the_carrier(X1),X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_pre_topc) ).
fof(d1_tops_1,axiom,
! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> interior(X1,X2) = subset_complement(the_carrier(X1),topstr_closure(X1,subset_complement(the_carrier(X1),X2))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tops_1) ).
fof(t16_tops_2,lemma,
! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(powerset(the_carrier(X1))))
=> ( closed_subsets(X2,X1)
<=> open_subsets(complements_of_subsets(the_carrier(X1),X2),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_tops_2) ).
fof(t17_tops_2,lemma,
! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(powerset(the_carrier(X1))))
=> ( open_subsets(X2,X1)
<=> closed_subsets(complements_of_subsets(the_carrier(X1),X2),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_tops_2) ).
fof(dt_k6_subset_1,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> element(subset_difference(X1,X2,X3),powerset(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_subset_1) ).
fof(dt_k5_subset_1,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> element(subset_intersection2(X1,X2,X3),powerset(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_subset_1) ).
fof(dt_k4_subset_1,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> element(subset_union2(X1,X2,X3),powerset(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_subset_1) ).
fof(t70_funct_1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_funct_1) ).
fof(t49_wellord1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_wellord1) ).
fof(commutativity_k5_subset_1,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> subset_intersection2(X1,X2,X3) = subset_intersection2(X1,X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k5_subset_1) ).
fof(commutativity_k4_subset_1,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> subset_union2(X1,X2,X3) = subset_union2(X1,X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k4_subset_1) ).
fof(t14_relset_1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_relset_1) ).
fof(d5_funct_1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_funct_1) ).
fof(t13_tops_2,lemma,
! [X1] :
( one_sorted_str(X1)
=> ! [X2] :
( element(X2,powerset(powerset(the_carrier(X1))))
=> ( finite(complements_of_subsets(the_carrier(X1),X2))
<=> finite(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_tops_2) ).
fof(t16_relset_1,lemma,
! [X1,X2,X3,X4] :
( relation_of2_as_subset(X4,X3,X1)
=> ( subset(X1,X2)
=> relation_of2_as_subset(X4,X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_relset_1) ).
fof(t55_tops_1,lemma,
! [X1] :
( ( topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( top_str(X2)
=> ! [X3] :
( element(X3,powerset(the_carrier(X1)))
=> ! [X4] :
( element(X4,powerset(the_carrier(X2)))
=> ( ( open_subset(X4,X2)
=> interior(X2,X4) = X4 )
& ( interior(X1,X3) = X3
=> open_subset(X3,X1) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_tops_1) ).
fof(t18_finset_1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_finset_1) ).
fof(dt_m2_relset_1,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
=> element(X3,powerset(cartesian_product2(X1,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(t29_tops_1,lemma,
! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ( closed_subset(X2,X1)
<=> open_subset(subset_complement(the_carrier(X1),X2),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_tops_1) ).
fof(t30_tops_1,lemma,
! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ( open_subset(X2,X1)
<=> closed_subset(subset_complement(the_carrier(X1),X2),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_tops_1) ).
fof(d4_tarski,axiom,
! [X1,X2] :
( X2 = union(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X3,X4)
& in(X4,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
fof(d8_pre_topc,axiom,
! [X1] :
( one_sorted_str(X1)
=> ! [X2] :
( element(X2,powerset(powerset(the_carrier(X1))))
=> ( is_a_cover_of_carrier(X1,X2)
<=> cast_as_carrier_subset(X1) = union_of_subsets(the_carrier(X1),X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_pre_topc) ).
fof(l82_funct_1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',l82_funct_1) ).
fof(t17_pre_topc,lemma,
! [X1] :
( one_sorted_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> subset_complement(the_carrier(X1),X2) = subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_pre_topc) ).
fof(redefinition_k5_relset_1,axiom,
! [X1,X2,X3] :
( relation_of2(X3,X1,X2)
=> relation_rng_as_subset(X1,X2,X3) = relation_rng(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_relset_1) ).
fof(redefinition_k4_relset_1,axiom,
! [X1,X2,X3] :
( relation_of2(X3,X1,X2)
=> relation_dom_as_subset(X1,X2,X3) = relation_dom(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_relset_1) ).
fof(t43_subset_1,lemma,
! [X1,X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( element(X3,powerset(X1))
=> ( disjoint(X2,X3)
<=> subset(X2,subset_complement(X1,X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_subset_1) ).
fof(t115_relat_1,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_rng(relation_rng_restriction(X2,X3)))
<=> ( in(X1,X2)
& in(X1,relation_rng(X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t115_relat_1) ).
fof(t19_wellord1,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_field(relation_restriction(X3,X2)))
=> ( in(X1,relation_field(X3))
& in(X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_wellord1) ).
fof(t86_relat_1,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_dom(relation_dom_restriction(X3,X2)))
<=> ( in(X1,X2)
& in(X1,relation_dom(X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_relat_1) ).
fof(fc4_tops_1,axiom,
! [X1,X2] :
( ( topological_space(X1)
& top_str(X1)
& open_subset(X2,X1)
& element(X2,powerset(the_carrier(X1))) )
=> closed_subset(subset_complement(the_carrier(X1),X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_tops_1) ).
fof(fc3_tops_1,axiom,
! [X1,X2] :
( ( topological_space(X1)
& top_str(X1)
& closed_subset(X2,X1)
& element(X2,powerset(the_carrier(X1))) )
=> open_subset(subset_complement(the_carrier(X1),X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_tops_1) ).
fof(t23_funct_1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funct_1) ).
fof(redefinition_m2_relset_1,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
<=> relation_of2(X3,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(d2_wellord1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_wellord1) ).
fof(d5_wellord1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_wellord1) ).
fof(t16_wellord1,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_restriction(X3,X2))
<=> ( in(X1,X3)
& in(X1,cartesian_product2(X2,X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_wellord1) ).
fof(redefinition_k6_subset_1,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> subset_difference(X1,X2,X3) = set_difference(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
fof(redefinition_k4_subset_1,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> subset_union2(X1,X2,X3) = set_union2(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_subset_1) ).
fof(t11_tops_2,lemma,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ( X2 != empty_set
=> meet_of_subsets(X1,complements_of_subsets(X1,X2)) = subset_complement(X1,union_of_subsets(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_tops_2) ).
fof(t12_tops_2,lemma,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ( X2 != empty_set
=> union_of_subsets(X1,complements_of_subsets(X1,X2)) = subset_complement(X1,meet_of_subsets(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_tops_2) ).
fof(d8_funct_1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_funct_1) ).
fof(free_g1_orders_2,axiom,
! [X1,X2] :
( relation_of2(X2,X1,X1)
=> ! [X3,X4] :
( rel_str_of(X1,X2) = rel_str_of(X3,X4)
=> ( X1 = X3
& X2 = X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g1_orders_2) ).
fof(d1_zfmisc_1,axiom,
! [X1,X2] :
( X2 = powerset(X1)
<=> ! [X3] :
( in(X3,X2)
<=> subset(X3,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(t146_funct_1,lemma,
! [X1,X2] :
( relation(X2)
=> ( subset(X1,relation_dom(X2))
=> subset(X1,relation_inverse_image(X2,relation_image(X2,X1))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t146_funct_1) ).
fof(t2_tarski,axiom,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
<=> in(X3,X2) )
=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
fof(t54_wellord1,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( ( well_ordering(X1)
& relation_isomorphism(X1,X2,X3) )
=> well_ordering(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_wellord1) ).
fof(d1_relset_1,axiom,
! [X1,X2,X3] :
( relation_of2(X3,X1,X2)
<=> subset(X3,cartesian_product2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relset_1) ).
fof(t15_pre_topc,lemma,
! [X1] :
( one_sorted_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> subset_intersection2(the_carrier(X1),X2,cast_as_carrier_subset(X1)) = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_pre_topc) ).
fof(t21_wellord1,lemma,
! [X1,X2,X3] :
( relation(X3)
=> subset(fiber(relation_restriction(X3,X1),X2),fiber(X3,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_wellord1) ).
fof(dt_u1_lattices,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('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_lattices) ).
fof(dt_u2_lattices,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('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u2_lattices) ).
fof(idempotence_k5_subset_1,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> subset_intersection2(X1,X2,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k5_subset_1) ).
fof(idempotence_k4_subset_1,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> subset_union2(X1,X2,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k4_subset_1) ).
fof(t54_subset_1,lemma,
! [X1,X2,X3] :
( element(X3,powerset(X1))
=> ~ ( in(X2,subset_complement(X1,X3))
& in(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_subset_1) ).
fof(cc1_relset_1,axiom,
! [X1,X2,X3] :
( element(X3,powerset(cartesian_product2(X1,X2)))
=> relation(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(dt_k1_tops_1,axiom,
! [X1,X2] :
( ( top_str(X1)
& element(X2,powerset(the_carrier(X1))) )
=> element(interior(X1,X2),powerset(the_carrier(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_tops_1) ).
fof(dt_k6_pre_topc,axiom,
! [X1,X2] :
( ( top_str(X1)
& element(X2,powerset(the_carrier(X1))) )
=> element(topstr_closure(X1,X2),powerset(the_carrier(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_pre_topc) ).
fof(dt_g1_orders_2,axiom,
! [X1,X2] :
( relation_of2(X2,X1,X1)
=> ( strict_rel_str(rel_str_of(X1,X2))
& rel_str(rel_str_of(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_g1_orders_2) ).
fof(t34_funct_1,lemma,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( X2 = identity_relation(X1)
<=> ( relation_dom(X2) = X1
& ! [X3] :
( in(X3,X1)
=> apply(X2,X3) = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_funct_1) ).
fof(t119_zfmisc_1,lemma,
! [X1,X2,X3,X4] :
( ( subset(X1,X2)
& subset(X3,X4) )
=> subset(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t119_zfmisc_1) ).
fof(dt_k7_setfam_1,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> element(complements_of_subsets(X1,X2),powerset(powerset(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_setfam_1) ).
fof(t7_tarski,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& ! [X3] :
~ ( in(X3,X2)
& ! [X4] :
~ ( in(X4,X2)
& in(X4,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_tarski) ).
fof(t57_funct_1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_funct_1) ).
fof(t12_relset_1,lemma,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
=> ( subset(relation_dom(X3),X1)
& subset(relation_rng(X3),X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_relset_1) ).
fof(t145_funct_1,lemma,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> subset(relation_image(X2,relation_inverse_image(X2,X1)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t145_funct_1) ).
fof(fc2_tops_1,axiom,
! [X1,X2] :
( ( topological_space(X1)
& top_str(X1)
& element(X2,powerset(the_carrier(X1))) )
=> closed_subset(topstr_closure(X1,X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_tops_1) ).
fof(t51_tops_1,lemma,
! [X1] :
( ( topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> open_subset(interior(X1,X2),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_tops_1) ).
fof(fc6_tops_1,axiom,
! [X1,X2] :
( ( topological_space(X1)
& top_str(X1)
& element(X2,powerset(the_carrier(X1))) )
=> open_subset(interior(X1,X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_tops_1) ).
fof(d5_pre_topc,axiom,
! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ( open_subset(X2,X1)
<=> in(X2,the_topology(X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_pre_topc) ).
fof(t52_pre_topc,lemma,
! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ( ( closed_subset(X2,X1)
=> topstr_closure(X1,X2) = X2 )
& ( ( topological_space(X1)
& topstr_closure(X1,X2) = X2 )
=> closed_subset(X2,X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_pre_topc) ).
fof(fc2_orders_2,axiom,
! [X1] :
( ( reflexive_relstr(X1)
& transitive_relstr(X1)
& antisymmetric_relstr(X1)
& rel_str(X1) )
=> ( relation(the_InternalRel(X1))
& reflexive(the_InternalRel(X1))
& antisymmetric(the_InternalRel(X1))
& transitive(the_InternalRel(X1))
& v1_partfun1(the_InternalRel(X1),the_carrier(X1),the_carrier(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_orders_2) ).
fof(t32_ordinal1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_ordinal1) ).
fof(t44_tops_1,lemma,
! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> subset(interior(X1,X2),X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_tops_1) ).
fof(t48_pre_topc,lemma,
! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> subset(X2,topstr_closure(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_pre_topc) ).
fof(dt_k6_setfam_1,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> element(meet_of_subsets(X1,X2),powerset(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_setfam_1) ).
fof(dt_k5_setfam_1,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> element(union_of_subsets(X1,X2),powerset(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_setfam_1) ).
fof(t178_relat_1,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( subset(X1,X2)
=> subset(relation_inverse_image(X3,X1),relation_inverse_image(X3,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t178_relat_1) ).
fof(t45_relat_1,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> subset(relation_rng(relation_composition(X1,X2)),relation_rng(X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_relat_1) ).
fof(t44_relat_1,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> subset(relation_dom(relation_composition(X1,X2)),relation_dom(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_relat_1) ).
fof(involutiveness_k7_setfam_1,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k7_setfam_1) ).
fof(t72_funct_1,lemma,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X2,X1)
=> apply(relation_dom_restriction(X3,X1),X2) = apply(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_funct_1) ).
fof(t47_relat_1,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( subset(relation_dom(X1),relation_rng(X2))
=> relation_rng(relation_composition(X2,X1)) = relation_rng(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_relat_1) ).
fof(t46_relat_1,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( subset(relation_rng(X1),relation_dom(X2))
=> relation_dom(relation_composition(X1,X2)) = relation_dom(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_relat_1) ).
fof(t33_xboole_1,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_difference(X1,X3),set_difference(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_xboole_1) ).
fof(t118_zfmisc_1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',t118_zfmisc_1) ).
fof(abstractness_v3_lattices,axiom,
! [X1] :
( latt_str(X1)
=> ( strict_latt_str(X1)
=> X1 = latt_str_of(the_carrier(X1),the_L_join(X1),the_L_meet(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstractness_v3_lattices) ).
fof(t147_funct_1,lemma,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( subset(X1,relation_rng(X2))
=> relation_image(X2,relation_inverse_image(X2,X1)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t147_funct_1) ).
fof(t140_relat_1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',t140_relat_1) ).
fof(t8_xboole_1,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X3,X2) )
=> subset(set_union2(X1,X3),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_xboole_1) ).
fof(t38_zfmisc_1,lemma,
! [X1,X2,X3] :
( subset(unordered_pair(X1,X2),X3)
<=> ( in(X1,X3)
& in(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_zfmisc_1) ).
fof(t118_relat_1,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_rng(relation_rng_restriction(X1,X2)),relation_rng(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t118_relat_1) ).
fof(t99_relat_1,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_rng(relation_dom_restriction(X2,X1)),relation_rng(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_relat_1) ).
fof(t20_wellord1,lemma,
! [X1,X2] :
( relation(X2)
=> ( subset(relation_field(relation_restriction(X2,X1)),relation_field(X2))
& subset(relation_field(relation_restriction(X2,X1)),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_wellord1) ).
fof(l29_wellord1,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_dom(relation_rng_restriction(X1,X2)),relation_dom(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l29_wellord1) ).
fof(l71_subset_1,lemma,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
=> in(X3,X2) )
=> element(X1,powerset(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l71_subset_1) ).
fof(existence_m2_relset_1,axiom,
! [X1,X2] :
? [X3] : relation_of2_as_subset(X3,X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_relset_1) ).
fof(rc1_funct_2,axiom,
! [X1,X2] :
? [X3] :
( relation_of2(X3,X1,X2)
& relation(X3)
& function(X3)
& quasi_total(X3,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_2) ).
fof(rc2_partfun1,axiom,
! [X1,X2] :
? [X3] :
( relation_of2(X3,X1,X2)
& relation(X3)
& function(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_partfun1) ).
fof(existence_m1_relset_1,axiom,
! [X1,X2] :
? [X3] : relation_of2(X3,X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_relset_1) ).
fof(s1_ordinal1__e8_6__wellord2,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('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_ordinal1__e8_6__wellord2) ).
fof(dt_k7_grcat_1,axiom,
! [X1] :
( one_sorted_str(X1)
=> ( function(identity_on_carrier(X1))
& quasi_total(identity_on_carrier(X1),the_carrier(X1),the_carrier(X1))
& relation_of2_as_subset(identity_on_carrier(X1),the_carrier(X1),the_carrier(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_grcat_1) ).
fof(dt_u1_orders_2,axiom,
! [X1] :
( rel_str(X1)
=> relation_of2_as_subset(the_InternalRel(X1),the_carrier(X1),the_carrier(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_orders_2) ).
fof(t116_relat_1,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_rng(relation_rng_restriction(X1,X2)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t116_relat_1) ).
fof(dt_k3_subset_1,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> element(subset_complement(X1,X2),powerset(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_subset_1) ).
fof(t39_wellord1,lemma,
! [X1,X2] :
( relation(X2)
=> ( ( well_ordering(X2)
& subset(X1,relation_field(X2)) )
=> relation_field(relation_restriction(X2,X1)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_wellord1) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(t46_setfam_1,lemma,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ~ ( X2 != empty_set
& complements_of_subsets(X1,X2) = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_setfam_1) ).
fof(t10_tops_2,lemma,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ( ~ ( X2 != empty_set
& complements_of_subsets(X1,X2) = empty_set )
& ~ ( complements_of_subsets(X1,X2) != empty_set
& X2 = empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_tops_2) ).
fof(s1_tarski__e6_22__wellord2__1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e6_22__wellord2__1) ).
fof(involutiveness_k3_subset_1,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,subset_complement(X1,X2)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
fof(t21_relat_1,lemma,
! [X1] :
( relation(X1)
=> subset(X1,cartesian_product2(relation_dom(X1),relation_rng(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_relat_1) ).
fof(dt_u1_pre_topc,axiom,
! [X1] :
( top_str(X1)
=> element(the_topology(X1),powerset(powerset(the_carrier(X1)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_pre_topc) ).
fof(redefinition_k6_setfam_1,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> meet_of_subsets(X1,X2) = set_meet(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_setfam_1) ).
fof(redefinition_k5_setfam_1,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> union_of_subsets(X1,X2) = union(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_setfam_1) ).
fof(t4_subset,axiom,
! [X1,X2,X3] :
( ( in(X1,X2)
& element(X2,powerset(X3)) )
=> element(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(l3_subset_1,lemma,
! [X1,X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( in(X3,X2)
=> in(X3,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_subset_1) ).
fof(d5_ordinal2,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('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_ordinal2) ).
fof(t3_ordinal1,lemma,
! [X1,X2,X3] :
~ ( in(X1,X2)
& in(X2,X3)
& in(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_ordinal1) ).
fof(t5_tex_2,lemma,
! [X1,X2] :
( element(X2,powerset(X1))
=> ( proper_element(X2,powerset(X1))
<=> X2 != X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_tex_2) ).
fof(t160_relat_1,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> relation_rng(relation_composition(X1,X2)) = relation_image(X2,relation_rng(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t160_relat_1) ).
fof(t45_xboole_1,lemma,
! [X1,X2] :
( subset(X1,X2)
=> X2 = set_union2(X1,set_difference(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_xboole_1) ).
fof(t25_relat_1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_relat_1) ).
fof(t174_relat_1,lemma,
! [X1,X2] :
( relation(X2)
=> ~ ( X1 != empty_set
& subset(X1,relation_rng(X2))
& relation_inverse_image(X2,X1) = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t174_relat_1) ).
fof(t5_subset,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(t17_wellord1,lemma,
! [X1,X2] :
( relation(X2)
=> relation_restriction(X2,X1) = relation_dom_restriction(relation_rng_restriction(X1,X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_wellord1) ).
fof(t18_wellord1,lemma,
! [X1,X2] :
( relation(X2)
=> relation_restriction(X2,X1) = relation_rng_restriction(X1,relation_dom_restriction(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_wellord1) ).
fof(t25_wellord2,lemma,
! [X1,X2] :
( relation(X2)
=> ( well_orders(X2,X1)
=> ( relation_field(relation_restriction(X2,X1)) = X1
& well_ordering(relation_restriction(X2,X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_wellord2) ).
fof(rc2_funct_2,axiom,
! [X1] :
? [X2] :
( relation_of2(X2,X1,X1)
& relation(X2)
& function(X2)
& one_to_one(X2)
& quasi_total(X2,X1,X1)
& onto(X2,X1,X1)
& bijective(X2,X1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_2) ).
fof(rc3_partfun1,axiom,
! [X1] :
? [X2] :
( relation_of2(X2,X1,X1)
& relation(X2)
& reflexive(X2)
& symmetric(X2)
& antisymmetric(X2)
& transitive(X2)
& v1_partfun1(X2,X1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_partfun1) ).
fof(d5_subset_1,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,X2) = set_difference(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_subset_1) ).
fof(t63_xboole_1,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& disjoint(X2,X3) )
=> disjoint(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_xboole_1) ).
fof(t1_xboole_1,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(fc1_funct_1,axiom,
! [X1,X2] :
( ( relation(X1)
& function(X1)
& relation(X2)
& function(X2) )
=> ( relation(relation_composition(X1,X2))
& function(relation_composition(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_1) ).
fof(d1_finset_1,axiom,
! [X1] :
( finite(X1)
<=> ? [X2] :
( relation(X2)
& function(X2)
& relation_rng(X2) = X1
& in(relation_dom(X2),omega) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_finset_1) ).
fof(t40_xboole_1,lemma,
! [X1,X2] : set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_xboole_1) ).
fof(t39_xboole_1,lemma,
! [X1,X2] : set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_xboole_1) ).
fof(d4_wellord2,axiom,
! [X1,X2] :
( equipotent(X1,X2)
<=> ? [X3] :
( relation(X3)
& function(X3)
& one_to_one(X3)
& relation_dom(X3) = X1
& relation_rng(X3) = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_wellord2) ).
fof(d2_tex_2,axiom,
! [X1,X2] :
( element(X2,X1)
=> ( proper_element(X2,X1)
<=> X2 != union(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tex_2) ).
fof(t31_ordinal1,lemma,
! [X1] :
( ! [X2] :
( in(X2,X1)
=> ( ordinal(X2)
& subset(X2,X1) ) )
=> ordinal(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_ordinal1) ).
fof(d6_orders_2,axiom,
! [X1] :
( rel_str(X1)
=> ( antisymmetric_relstr(X1)
<=> is_antisymmetric_in(the_InternalRel(X1),the_carrier(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_orders_2) ).
fof(d5_orders_2,axiom,
! [X1] :
( rel_str(X1)
=> ( transitive_relstr(X1)
<=> is_transitive_in(the_InternalRel(X1),the_carrier(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_orders_2) ).
fof(t167_relat_1,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_inverse_image(X2,X1),relation_dom(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t167_relat_1) ).
fof(t144_relat_1,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_image(X2,X1),relation_rng(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t144_relat_1) ).
fof(rc6_pre_topc,axiom,
! [X1] :
( ( topological_space(X1)
& top_str(X1) )
=> ? [X2] :
( element(X2,powerset(the_carrier(X1)))
& closed_subset(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc6_pre_topc) ).
fof(rc2_tops_1,axiom,
! [X1] :
( ( topological_space(X1)
& top_str(X1) )
=> ? [X2] :
( element(X2,powerset(the_carrier(X1)))
& open_subset(X2,X1)
& closed_subset(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_tops_1) ).
fof(rc1_tops_1,axiom,
! [X1] :
( ( topological_space(X1)
& top_str(X1) )
=> ? [X2] :
( element(X2,powerset(the_carrier(X1)))
& open_subset(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_tops_1) ).
fof(t17_finset_1,lemma,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( finite(X1)
=> finite(relation_image(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_finset_1) ).
fof(fc13_finset_1,axiom,
! [X1,X2] :
( ( relation(X1)
& function(X1)
& finite(X2) )
=> finite(relation_image(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc13_finset_1) ).
fof(redefinition_r1_ordinal1,axiom,
! [X1,X2] :
( ( ordinal(X1)
& ordinal(X2) )
=> ( ordinal_subset(X1,X2)
<=> subset(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
fof(t21_ordinal1,lemma,
! [X1] :
( epsilon_transitive(X1)
=> ! [X2] :
( ordinal(X2)
=> ( proper_subset(X1,X2)
=> in(X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_ordinal1) ).
fof(s1_xboole_0__e6_22__wellord2,lemma,
! [X1] :
? [X2] :
! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& ordinal(X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e6_22__wellord2) ).
fof(t10_zfmisc_1,lemma,
! [X1,X2,X3,X4] :
~ ( unordered_pair(X1,X2) = unordered_pair(X3,X4)
& X1 != X3
& X1 != X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_zfmisc_1) ).
fof(d10_xboole_0,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(d4_wellord1,axiom,
! [X1] :
( relation(X1)
=> ( well_ordering(X1)
<=> ( reflexive(X1)
& transitive(X1)
& antisymmetric(X1)
& connected(X1)
& well_founded_relation(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_wellord1) ).
fof(t117_relat_1,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_rng_restriction(X1,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t117_relat_1) ).
fof(t88_relat_1,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_dom_restriction(X2,X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t88_relat_1) ).
fof(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(dt_k2_pre_topc,axiom,
! [X1] :
( one_sorted_str(X1)
=> element(cast_as_carrier_subset(X1),powerset(the_carrier(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_pre_topc) ).
fof(dt_k1_pre_topc,axiom,
! [X1] :
( one_sorted_str(X1)
=> element(empty_carrier_subset(X1),powerset(the_carrier(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_pre_topc) ).
fof(d2_compts_1,axiom,
! [X1] :
( centered(X1)
<=> ( X1 != empty_set
& ! [X2] :
~ ( X2 != empty_set
& subset(X2,X1)
& finite(X2)
& set_meet(X2) = empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_compts_1) ).
fof(t60_xboole_1,lemma,
! [X1,X2] :
~ ( subset(X1,X2)
& proper_subset(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_xboole_1) ).
fof(fc13_relat_1,axiom,
! [X1,X2] :
( ( relation(X1)
& relation_empty_yielding(X1) )
=> ( relation(relation_dom_restriction(X1,X2))
& relation_empty_yielding(relation_dom_restriction(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc13_relat_1) ).
fof(t32_wellord1,lemma,
! [X1,X2] :
( relation(X2)
=> ( well_ordering(X2)
=> well_ordering(relation_restriction(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_wellord1) ).
fof(t31_wellord1,lemma,
! [X1,X2] :
( relation(X2)
=> ( well_founded_relation(X2)
=> well_founded_relation(relation_restriction(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_wellord1) ).
fof(t23_wellord1,lemma,
! [X1,X2] :
( relation(X2)
=> ( connected(X2)
=> connected(relation_restriction(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_wellord1) ).
fof(t25_wellord1,lemma,
! [X1,X2] :
( relation(X2)
=> ( antisymmetric(X2)
=> antisymmetric(relation_restriction(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_wellord1) ).
fof(t22_wellord1,lemma,
! [X1,X2] :
( relation(X2)
=> ( reflexive(X2)
=> reflexive(relation_restriction(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_wellord1) ).
fof(t24_wellord1,lemma,
! [X1,X2] :
( relation(X2)
=> ( transitive(X2)
=> transitive(relation_restriction(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_wellord1) ).
fof(dt_k5_relat_1,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(relation_composition(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(fc9_relat_1,axiom,
! [X1,X2] :
( ( empty(X1)
& relation(X2) )
=> ( empty(relation_composition(X1,X2))
& relation(relation_composition(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc9_relat_1) ).
fof(fc10_relat_1,axiom,
! [X1,X2] :
( ( empty(X1)
& relation(X2) )
=> ( empty(relation_composition(X2,X1))
& relation(relation_composition(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc10_relat_1) ).
fof(fc3_relat_1,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(set_difference(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_relat_1) ).
fof(fc5_funct_1,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( relation(relation_rng_restriction(X1,X2))
& function(relation_rng_restriction(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_funct_1) ).
fof(fc4_funct_1,axiom,
! [X1,X2] :
( ( relation(X1)
& function(X1) )
=> ( relation(relation_dom_restriction(X1,X2))
& function(relation_dom_restriction(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_funct_1) ).
fof(fc2_relat_1,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(set_union2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_relat_1) ).
fof(fc9_finset_1,axiom,
! [X1,X2] :
( ( finite(X1)
& finite(X2) )
=> finite(set_union2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc9_finset_1) ).
fof(d2_ordinal1,axiom,
! [X1] :
( epsilon_transitive(X1)
<=> ! [X2] :
( in(X2,X1)
=> subset(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(t8_wellord1,lemma,
! [X1] :
( relation(X1)
=> ( well_orders(X1,relation_field(X1))
<=> well_ordering(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_wellord1) ).
fof(t5_wellord1,lemma,
! [X1] :
( relation(X1)
=> ( well_founded_relation(X1)
<=> is_well_founded_in(X1,relation_field(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_wellord1) ).
fof(d14_relat_2,axiom,
! [X1] :
( relation(X1)
=> ( connected(X1)
<=> is_connected_in(X1,relation_field(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_relat_2) ).
fof(d12_relat_2,axiom,
! [X1] :
( relation(X1)
=> ( antisymmetric(X1)
<=> is_antisymmetric_in(X1,relation_field(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_relat_2) ).
fof(d9_relat_2,axiom,
! [X1] :
( relation(X1)
=> ( reflexive(X1)
<=> is_reflexive_in(X1,relation_field(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_relat_2) ).
fof(d16_relat_2,axiom,
! [X1] :
( relation(X1)
=> ( transitive(X1)
<=> is_transitive_in(X1,relation_field(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d16_relat_2) ).
fof(cc2_finset_1,axiom,
! [X1] :
( finite(X1)
=> ! [X2] :
( element(X2,powerset(X1))
=> finite(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_finset_1) ).
fof(cc20_membered,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('/export/starexec/sandbox/benchmark/theBenchmark.p',cc20_membered) ).
fof(cc19_membered,axiom,
! [X1] :
( v4_membered(X1)
=> ! [X2] :
( element(X2,powerset(X1))
=> ( v1_membered(X2)
& v2_membered(X2)
& v3_membered(X2)
& v4_membered(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc19_membered) ).
fof(cc18_membered,axiom,
! [X1] :
( v3_membered(X1)
=> ! [X2] :
( element(X2,powerset(X1))
=> ( v1_membered(X2)
& v2_membered(X2)
& v3_membered(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc18_membered) ).
fof(cc17_membered,axiom,
! [X1] :
( v2_membered(X1)
=> ! [X2] :
( element(X2,powerset(X1))
=> ( v1_membered(X2)
& v2_membered(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc17_membered) ).
fof(cc16_membered,axiom,
! [X1] :
( v1_membered(X1)
=> ! [X2] :
( element(X2,powerset(X1))
=> v1_membered(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc16_membered) ).
fof(t35_funct_1,lemma,
! [X1,X2] :
( in(X2,X1)
=> apply(identity_relation(X1),X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_funct_1) ).
fof(connectedness_r1_ordinal1,axiom,
! [X1,X2] :
( ( ordinal(X1)
& ordinal(X2) )
=> ( ordinal_subset(X1,X2)
| ordinal_subset(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',connectedness_r1_ordinal1) ).
fof(t92_zfmisc_1,lemma,
! [X1,X2] :
( in(X1,X2)
=> subset(X1,union(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_zfmisc_1) ).
fof(l50_zfmisc_1,lemma,
! [X1,X2] :
( in(X1,X2)
=> subset(X1,union(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l50_zfmisc_1) ).
fof(t26_finset_1,lemma,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( finite(relation_dom(X1))
=> finite(relation_rng(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_finset_1) ).
fof(abstractness_v1_orders_2,axiom,
! [X1] :
( rel_str(X1)
=> ( strict_rel_str(X1)
=> X1 = rel_str_of(the_carrier(X1),the_InternalRel(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstractness_v1_orders_2) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(t94_relat_1,lemma,
! [X1,X2] :
( relation(X2)
=> relation_dom_restriction(X2,X1) = relation_composition(identity_relation(X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t94_relat_1) ).
fof(t36_xboole_1,lemma,
! [X1,X2] : subset(set_difference(X1,X2),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).
fof(t7_xboole_1,lemma,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(d8_xboole_0,axiom,
! [X1,X2] :
( proper_subset(X1,X2)
<=> ( subset(X1,X2)
& X1 != X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_xboole_0) ).
fof(t83_xboole_1,lemma,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_difference(X1,X2) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_xboole_1) ).
fof(t12_xboole_1,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_union2(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(d6_relat_1,axiom,
! [X1] :
( relation(X1)
=> relation_field(X1) = set_union2(relation_dom(X1),relation_rng(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_relat_1) ).
fof(dt_k2_wellord1,axiom,
! [X1,X2] :
( relation(X1)
=> relation(relation_restriction(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_wellord1) ).
fof(dt_k8_relat_1,axiom,
! [X1,X2] :
( relation(X2)
=> relation(relation_rng_restriction(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_relat_1) ).
fof(dt_k7_relat_1,axiom,
! [X1,X2] :
( relation(X1)
=> relation(relation_dom_restriction(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_relat_1) ).
fof(fc12_finset_1,axiom,
! [X1,X2] :
( finite(X1)
=> finite(set_difference(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_finset_1) ).
fof(fc41_membered,axiom,
! [X1,X2] :
( v5_membered(X1)
=> ( v1_membered(set_difference(X1,X2))
& v2_membered(set_difference(X1,X2))
& v3_membered(set_difference(X1,X2))
& v4_membered(set_difference(X1,X2))
& v5_membered(set_difference(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc41_membered) ).
fof(fc40_membered,axiom,
! [X1,X2] :
( v4_membered(X1)
=> ( v1_membered(set_difference(X1,X2))
& v2_membered(set_difference(X1,X2))
& v3_membered(set_difference(X1,X2))
& v4_membered(set_difference(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc40_membered) ).
fof(fc39_membered,axiom,
! [X1,X2] :
( v3_membered(X1)
=> ( v1_membered(set_difference(X1,X2))
& v2_membered(set_difference(X1,X2))
& v3_membered(set_difference(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc39_membered) ).
fof(fc38_membered,axiom,
! [X1,X2] :
( v2_membered(X1)
=> ( v1_membered(set_difference(X1,X2))
& v2_membered(set_difference(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc38_membered) ).
fof(fc37_membered,axiom,
! [X1,X2] :
( v1_membered(X1)
=> v1_membered(set_difference(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc37_membered) ).
fof(redefinition_r2_wellord2,axiom,
! [X1,X2] :
( equipotent(X1,X2)
<=> are_equipotent(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r2_wellord2) ).
fof(symmetry_r2_wellord2,axiom,
! [X1,X2] :
( equipotent(X1,X2)
=> equipotent(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r2_wellord2) ).
fof(symmetry_r1_xboole_0,axiom,
! [X1,X2] :
( disjoint(X1,X2)
=> disjoint(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(t1_subset,axiom,
! [X1,X2] :
( in(X1,X2)
=> element(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(t37_xboole_1,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).
fof(l32_xboole_1,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l32_xboole_1) ).
fof(t55_funct_1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_funct_1) ).
fof(fc5_pre_topc,axiom,
! [X1] :
( ( topological_space(X1)
& top_str(X1) )
=> closed_subset(cast_as_carrier_subset(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_pre_topc) ).
fof(t13_finset_1,lemma,
! [X1,X2] :
( ( subset(X1,X2)
& finite(X2) )
=> finite(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_finset_1) ).
fof(cc1_arytm_3,axiom,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( element(X2,X1)
=> ( epsilon_transitive(X2)
& epsilon_connected(X2)
& ordinal(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_arytm_3) ).
fof(t23_ordinal1,lemma,
! [X1,X2] :
( ordinal(X2)
=> ( in(X1,X2)
=> ordinal(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_ordinal1) ).
fof(cc14_membered,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('/export/starexec/sandbox/benchmark/theBenchmark.p',cc14_membered) ).
fof(cc13_membered,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('/export/starexec/sandbox/benchmark/theBenchmark.p',cc13_membered) ).
fof(cc12_membered,axiom,
! [X1] :
( v3_membered(X1)
=> ! [X2] :
( element(X2,X1)
=> ( v1_xcmplx_0(X2)
& v1_xreal_0(X2)
& v1_rat_1(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc12_membered) ).
fof(cc11_membered,axiom,
! [X1] :
( v2_membered(X1)
=> ! [X2] :
( element(X2,X1)
=> ( v1_xcmplx_0(X2)
& v1_xreal_0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc11_membered) ).
fof(cc10_membered,axiom,
! [X1] :
( v1_membered(X1)
=> ! [X2] :
( element(X2,X1)
=> v1_xcmplx_0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc10_membered) ).
fof(t62_funct_1,lemma,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> one_to_one(function_inverse(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_funct_1) ).
fof(fc3_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1)
& one_to_one(X1) )
=> ( relation(relation_inverse(X1))
& function(relation_inverse(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_funct_1) ).
fof(t146_relat_1,lemma,
! [X1] :
( relation(X1)
=> relation_image(X1,relation_dom(X1)) = relation_rng(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t146_relat_1) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(d9_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> function_inverse(X1) = relation_inverse(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_funct_1) ).
fof(reflexivity_r1_ordinal1,axiom,
! [X1,X2] :
( ( ordinal(X1)
& ordinal(X2) )
=> ordinal_subset(X1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_ordinal1) ).
fof(d1_struct_0,axiom,
! [X1] :
( one_sorted_str(X1)
=> ( empty_carrier(X1)
<=> empty(the_carrier(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_struct_0) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(rc2_subset_1,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(rc2_finset_1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_finset_1) ).
fof(cc2_funct_1,axiom,
! [X1] :
( ( relation(X1)
& empty(X1)
& function(X1) )
=> ( relation(X1)
& function(X1)
& one_to_one(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_funct_1) ).
fof(cc1_partfun1,axiom,
! [X1] :
( ( relation(X1)
& symmetric(X1)
& transitive(X1) )
=> ( relation(X1)
& reflexive(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_partfun1) ).
fof(dt_k2_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( relation(function_inverse(X1))
& function(function_inverse(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_funct_1) ).
fof(cc3_arytm_3,axiom,
! [X1] :
( element(X1,omega)
=> ( epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1)
& natural(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_arytm_3) ).
fof(t3_xboole_1,lemma,
! [X1] :
( subset(X1,empty_set)
=> X1 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
fof(t37_relat_1,lemma,
! [X1] :
( relation(X1)
=> ( relation_rng(X1) = relation_dom(relation_inverse(X1))
& relation_dom(X1) = relation_rng(relation_inverse(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_relat_1) ).
fof(t26_wellord2,lemma,
! [X1] :
? [X2] :
( relation(X2)
& well_orders(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_wellord2) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(cc2_finsub_1,axiom,
! [X1] :
( ( cup_closed(X1)
& diff_closed(X1) )
=> preboolean(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_finsub_1) ).
fof(cc2_arytm_3,axiom,
! [X1] :
( ( empty(X1)
& ordinal(X1) )
=> ( epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1)
& natural(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_arytm_3) ).
fof(d4_ordinal1,axiom,
! [X1] :
( ordinal(X1)
<=> ( epsilon_transitive(X1)
& epsilon_connected(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_ordinal1) ).
fof(cc2_ordinal1,axiom,
! [X1] :
( ( epsilon_transitive(X1)
& epsilon_connected(X1) )
=> ordinal(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_ordinal1) ).
fof(t65_relat_1,lemma,
! [X1] :
( relation(X1)
=> ( relation_dom(X1) = empty_set
<=> relation_rng(X1) = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_relat_1) ).
fof(involutiveness_k4_relat_1,axiom,
! [X1] :
( relation(X1)
=> relation_inverse(relation_inverse(X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k4_relat_1) ).
fof(t7_wellord2,lemma,
! [X1] :
( ordinal(X1)
=> well_ordering(inclusion_relation(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_wellord2) ).
fof(t6_wellord2,lemma,
! [X1] :
( ordinal(X1)
=> well_founded_relation(inclusion_relation(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_wellord2) ).
fof(t4_wellord2,lemma,
! [X1] :
( ordinal(X1)
=> connected(inclusion_relation(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_wellord2) ).
fof(dt_k4_relat_1,axiom,
! [X1] :
( relation(X1)
=> relation(relation_inverse(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_relat_1) ).
fof(fc11_relat_1,axiom,
! [X1] :
( empty(X1)
=> ( empty(relation_inverse(X1))
& relation(relation_inverse(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc11_relat_1) ).
fof(fc8_relat_1,axiom,
! [X1] :
( empty(X1)
=> ( empty(relation_rng(X1))
& relation(relation_rng(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).
fof(fc7_relat_1,axiom,
! [X1] :
( empty(X1)
=> ( empty(relation_dom(X1))
& relation(relation_dom(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(fc4_ordinal1,axiom,
! [X1] :
( ordinal(X1)
=> ( epsilon_transitive(union(X1))
& epsilon_connected(union(X1))
& ordinal(union(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_ordinal1) ).
fof(fc1_pre_topc,axiom,
! [X1] :
( one_sorted_str(X1)
=> ( empty(empty_carrier_subset(X1))
& v1_membered(empty_carrier_subset(X1))
& v2_membered(empty_carrier_subset(X1))
& v3_membered(empty_carrier_subset(X1))
& v4_membered(empty_carrier_subset(X1))
& v5_membered(empty_carrier_subset(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_pre_topc) ).
fof(t8_boole,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
fof(t64_relat_1,lemma,
! [X1] :
( relation(X1)
=> ( ( relation_dom(X1) = empty_set
| relation_rng(X1) = empty_set )
=> X1 = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_relat_1) ).
fof(t12_pre_topc,lemma,
! [X1] :
( one_sorted_str(X1)
=> cast_as_carrier_subset(X1) = the_carrier(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_pre_topc) ).
fof(d3_pre_topc,axiom,
! [X1] :
( one_sorted_str(X1)
=> cast_as_carrier_subset(X1) = the_carrier(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_pre_topc) ).
fof(idempotence_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(reflexivity_r2_wellord2,axiom,
! [X1,X2] : equipotent(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r2_wellord2) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(t1_zfmisc_1,lemma,
powerset(empty_set) = singleton(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_zfmisc_1) ).
fof(t3_boole,axiom,
! [X1] : set_difference(X1,empty_set) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
fof(t1_boole,axiom,
! [X1] : set_union2(X1,empty_set) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_boole) ).
fof(d6_ordinal1,axiom,
! [X1] :
( being_limit_ordinal(X1)
<=> X1 = union(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_ordinal1) ).
fof(t2_xboole_1,lemma,
! [X1] : subset(empty_set,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(t4_boole,axiom,
! [X1] : set_difference(empty_set,X1) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
fof(dt_l1_pre_topc,axiom,
! [X1] :
( top_str(X1)
=> one_sorted_str(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
fof(dt_l1_lattices,axiom,
! [X1] :
( meet_semilatt_str(X1)
=> one_sorted_str(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_lattices) ).
fof(dt_l2_lattices,axiom,
! [X1] :
( join_semilatt_str(X1)
=> one_sorted_str(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l2_lattices) ).
fof(dt_l1_orders_2,axiom,
! [X1] :
( rel_str(X1)
=> one_sorted_str(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_orders_2) ).
fof(dt_l3_lattices,axiom,
! [X1] :
( latt_str(X1)
=> ( meet_semilatt_str(X1)
& join_semilatt_str(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l3_lattices) ).
fof(cc1_relat_1,axiom,
! [X1] :
( empty(X1)
=> relation(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(cc1_funct_1,axiom,
! [X1] :
( empty(X1)
=> function(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
fof(cc1_finsub_1,axiom,
! [X1] :
( preboolean(X1)
=> ( cup_closed(X1)
& diff_closed(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finsub_1) ).
fof(cc1_finset_1,axiom,
! [X1] :
( empty(X1)
=> finite(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finset_1) ).
fof(cc1_ordinal1,axiom,
! [X1] :
( ordinal(X1)
=> ( epsilon_transitive(X1)
& epsilon_connected(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_ordinal1) ).
fof(cc3_ordinal1,axiom,
! [X1] :
( empty(X1)
=> ( epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_ordinal1) ).
fof(cc15_membered,axiom,
! [X1] :
( empty(X1)
=> ( v1_membered(X1)
& v2_membered(X1)
& v3_membered(X1)
& v4_membered(X1)
& v5_membered(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc15_membered) ).
fof(cc1_membered,axiom,
! [X1] :
( v5_membered(X1)
=> v4_membered(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_membered) ).
fof(cc2_membered,axiom,
! [X1] :
( v4_membered(X1)
=> v3_membered(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_membered) ).
fof(cc3_membered,axiom,
! [X1] :
( v3_membered(X1)
=> v2_membered(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_membered) ).
fof(cc4_membered,axiom,
! [X1] :
( v2_membered(X1)
=> v1_membered(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_membered) ).
fof(d2_pre_topc,axiom,
! [X1] :
( one_sorted_str(X1)
=> empty_carrier_subset(X1) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_pre_topc) ).
fof(t99_zfmisc_1,lemma,
! [X1] : union(powerset(X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_zfmisc_1) ).
fof(t71_relat_1,lemma,
! [X1] :
( relation_dom(identity_relation(X1)) = X1
& relation_rng(identity_relation(X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_relat_1) ).
fof(t3_lattice3,lemma,
! [X1] :
( lower_bounded_semilattstr(boole_lattice(X1))
& bottom_of_semilattstr(boole_lattice(X1)) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_lattice3) ).
fof(t5_wellord2,lemma,
! [X1] : antisymmetric(inclusion_relation(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_wellord2) ).
fof(fc2_partfun1,axiom,
! [X1] :
( relation(identity_relation(X1))
& function(identity_relation(X1))
& reflexive(identity_relation(X1))
& symmetric(identity_relation(X1))
& antisymmetric(identity_relation(X1))
& transitive(identity_relation(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_partfun1) ).
fof(t2_wellord2,lemma,
! [X1] : reflexive(inclusion_relation(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_wellord2) ).
fof(t3_wellord2,lemma,
! [X1] : transitive(inclusion_relation(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_wellord2) ).
fof(dt_k1_wellord2,axiom,
! [X1] : relation(inclusion_relation(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_wellord2) ).
fof(fc2_funct_1,axiom,
! [X1] :
( relation(identity_relation(X1))
& function(identity_relation(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(dt_k6_relat_1,axiom,
! [X1] : relation(identity_relation(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relat_1) ).
fof(dt_k1_lattice3,axiom,
! [X1] :
( strict_latt_str(boole_lattice(X1))
& latt_str(boole_lattice(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_lattice3) ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(fc1_ordinal2,axiom,
( epsilon_transitive(omega)
& epsilon_connected(omega)
& ordinal(omega)
& ~ empty(omega) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_ordinal2) ).
fof(rc4_funct_1,axiom,
? [X1] :
( relation(X1)
& relation_empty_yielding(X1)
& function(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_funct_1) ).
fof(rc3_relat_1,axiom,
? [X1] :
( relation(X1)
& relation_empty_yielding(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_relat_1) ).
fof(rc1_ordinal2,axiom,
? [X1] :
( epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1)
& being_limit_ordinal(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_ordinal2) ).
fof(existence_l1_pre_topc,axiom,
? [X1] : top_str(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_pre_topc) ).
fof(existence_l1_struct_0,axiom,
? [X1] : one_sorted_str(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_struct_0) ).
fof(existence_l1_lattices,axiom,
? [X1] : meet_semilatt_str(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_lattices) ).
fof(existence_l2_lattices,axiom,
? [X1] : join_semilatt_str(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l2_lattices) ).
fof(rc3_funct_1,axiom,
? [X1] :
( relation(X1)
& function(X1)
& one_to_one(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).
fof(rc2_ordinal1,axiom,
? [X1] :
( relation(X1)
& function(X1)
& one_to_one(X1)
& empty(X1)
& epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_ordinal1) ).
fof(rc1_partfun1,axiom,
? [X1] :
( relation(X1)
& function(X1)
& one_to_one(X1)
& empty(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_partfun1) ).
fof(rc2_funct_1,axiom,
? [X1] :
( relation(X1)
& empty(X1)
& function(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(rc1_relat_1,axiom,
? [X1] :
( empty(X1)
& relation(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(rc1_funct_1,axiom,
? [X1] :
( relation(X1)
& function(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
fof(rc1_ordinal1,axiom,
? [X1] :
( epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_ordinal1) ).
fof(rc1_xboole_0,axiom,
? [X1] : empty(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(rc3_lattices,axiom,
? [X1] :
( latt_str(X1)
& strict_latt_str(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_lattices) ).
fof(existence_l3_lattices,axiom,
? [X1] : latt_str(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l3_lattices) ).
fof(rc1_orders_2,axiom,
? [X1] :
( rel_str(X1)
& strict_rel_str(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_orders_2) ).
fof(existence_l1_orders_2,axiom,
? [X1] : rel_str(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_orders_2) ).
fof(fc2_ordinal1,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_ordinal1) ).
fof(fc12_relat_1,axiom,
( empty(empty_set)
& relation(empty_set)
& relation_empty_yielding(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_relat_1) ).
fof(fc4_relat_1,axiom,
( empty(empty_set)
& relation(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(fc6_membered,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_membered) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(t60_relat_1,lemma,
( relation_dom(empty_set) = empty_set
& relation_rng(empty_set) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_relat_1) ).
fof(i_0_643,plain,
! [X2,X3,X4] :
( epred2_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(i_0_644,plain,
( epred1_0
<=> ( ( 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 ) ) ) ) ) ) ) ) ),
introduced(definition) ).
fof(i_0_645,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)],[s1_tarski__e10_24__wellord2__2]) ).
fof(i_0_646,plain,
! [X2339,X2340] : ordered_pair(X2339,X2340) = unordered_pair(unordered_pair(X2339,X2340),singleton(X2339)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(i_0_647,lemma,
! [X3854] : unordered_pair(X3854,X3854) = singleton(X3854),
inference(variable_rename,[status(thm)],[t69_enumset1]) ).
fof(i_0_648,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)],[s1_xboole_0__e10_24__wellord2__1]) ).
fof(i_0_649,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)
& ? [X10] :
( X4 = X10
& in(X5,X10)
& ! [X11] :
( in(X11,X10)
=> in(ordered_pair(X5,X11),X2) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[s1_funct_1__e10_24__wellord2__1]) ).
fof(i_0_650,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)
& ? [X10] :
( X5 = X10
& in(X4,X10)
& ! [X11] :
( in(X11,X10)
=> in(ordered_pair(X4,X11),X2) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[s1_tarski__e10_24__wellord2__1]) ).
fof(i_0_651,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)],[t23_relset_1]) ).
fof(i_0_652,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)],[s2_funct_1__e10_24__wellord2]) ).
fof(i_0_653,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)],[t22_relset_1]) ).
fof(i_0_654,lemma,
! [X1,X2] :
( ( one_sorted_str(X1)
& element(X2,powerset(powerset(the_carrier(X1)))) )
=> ( ! [X3,X4,X5] :
( ( in(X3,complements_of_subsets(the_carrier(X1),X2))
& ! [X6] :
( element(X6,powerset(the_carrier(X1)))
=> ( X6 = X3
=> X4 = subset_complement(the_carrier(X1),X6) ) )
& in(X3,complements_of_subsets(the_carrier(X1),X2))
& ! [X7] :
( element(X7,powerset(the_carrier(X1)))
=> ( X7 = X3
=> X5 = subset_complement(the_carrier(X1),X7) ) ) )
=> X4 = X5 )
=> ? [X3] :
( relation(X3)
& function(X3)
& ! [X4,X5] :
( in(ordered_pair(X4,X5),X3)
<=> ( in(X4,complements_of_subsets(the_carrier(X1),X2))
& ! [X8] :
( element(X8,powerset(the_carrier(X1)))
=> ( X8 = X4
=> X5 = subset_complement(the_carrier(X1),X8) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[s1_funct_1__e4_7_1__tops_2__1]) ).
fof(i_0_655,lemma,
! [X1,X2] :
( ( one_sorted_str(X1)
& element(X2,powerset(powerset(the_carrier(X1)))) )
=> ( ! [X3,X4,X5] :
( ( in(X3,X2)
& ! [X6] :
( element(X6,powerset(the_carrier(X1)))
=> ( X6 = X3
=> X4 = subset_complement(the_carrier(X1),X6) ) )
& in(X3,X2)
& ! [X7] :
( element(X7,powerset(the_carrier(X1)))
=> ( X7 = X3
=> X5 = subset_complement(the_carrier(X1),X7) ) ) )
=> X4 = X5 )
=> ? [X3] :
( relation(X3)
& function(X3)
& ! [X4,X5] :
( in(ordered_pair(X4,X5),X3)
<=> ( in(X4,X2)
& ! [X8] :
( element(X8,powerset(the_carrier(X1)))
=> ( X8 = X4
=> X5 = subset_complement(the_carrier(X1),X8) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[s1_funct_1__e4_7_2__tops_2__1]) ).
fof(i_0_656,axiom,
! [X1] :
( ordinal(X1)
=> ( ! [X2,X3,X4] :
( epred2_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)],[s1_tarski__e18_27__finset_1__1,c_0_643]) ).
fof(i_0_657,plain,
! [X2053] : succ(X2053) = set_union2(X2053,singleton(X2053)),
inference(variable_rename,[status(thm)],[d1_ordinal1]) ).
fof(i_0_658,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)],[d6_relat_2]) ).
fof(i_0_659,plain,
! [X1,X2,X3,X4] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1)
& ~ empty_carrier(X2)
& lattice(X2)
& latt_str(X2)
& element(X3,the_carrier(X1))
& element(X4,the_carrier(X2)) )
=> k10_filter_1(X1,X2,X3,X4) = ordered_pair(X3,X4) ),
inference(fof_simplification,[status(thm)],[redefinition_k10_filter_1]) ).
fof(i_0_660,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& latt_str(X1) )
=> ( ( ~ empty_carrier(X1)
& lattice(X1)
& complete_latt_str(X1)
& latt_str(X1) )
=> ! [X2,X3] :
( element(X3,the_carrier(X1))
=> ( X3 = join_of_latt_set(X1,X2)
<=> ( latt_element_smaller(X1,X3,X2)
& ! [X4] :
( element(X4,the_carrier(X1))
=> ( latt_element_smaller(X1,X4,X2)
=> below(X1,X3,X4) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[d21_lattice3]) ).
fof(i_0_661,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)],[l4_wellord1]) ).
fof(i_0_662,plain,
! [X1,X2,X3,X4] :
( ( ~ empty(X1)
& ~ empty(X2)
& element(X3,X1)
& element(X4,X2) )
=> ordered_pair_as_product_element(X1,X2,X3,X4) = ordered_pair(X3,X4) ),
inference(fof_simplification,[status(thm)],[redefinition_k1_domain_1]) ).
fof(i_0_663,plain,
( ( ( 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 ) ) ) ) ) ) ) )
=> epred1_0 ),
inference(split_equiv,[status(thm)],[i_0_644]) ).
fof(i_0_664,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)],[d4_funct_1]) ).
fof(i_0_665,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)
& X4 = singleton(X3) ) ) ) ),
inference(fof_simplification,[status(thm)],[s1_funct_1__e16_22__wellord2__1]) ).
fof(i_0_666,lemma,
! [X1] :
( relation(X1)
=> ( ! [X2,X3] : ~ in(ordered_pair(X2,X3),X1)
=> X1 = empty_set ) ),
inference(fof_simplification,[status(thm)],[t56_relat_1]) ).
fof(i_0_667,plain,
! [X1,X2] : ~ empty(ordered_pair(X1,X2)),
inference(fof_simplification,[status(thm)],[fc1_zfmisc_1]) ).
fof(i_0_668,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)],[t4_xboole_0]) ).
fof(i_0_669,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)],[fc2_arytm_3]) ).
fof(i_0_670,plain,
! [X1] :
( ordinal(X1)
=> ( ~ empty(succ(X1))
& epsilon_transitive(succ(X1))
& epsilon_connected(succ(X1))
& ordinal(succ(X1)) ) ),
inference(fof_simplification,[status(thm)],[fc3_ordinal1]) ).
fof(i_0_671,plain,
! [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)
& X3 = singleton(X4) ) ) ),
inference(fof_simplification,[status(thm)],[s1_tarski__e16_22__wellord2__1]) ).
fof(i_0_672,plain,
! [X1,X2] :
( epred3_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(i_0_673,plain,
! [X1] : ~ empty(succ(X1)),
inference(fof_simplification,[status(thm)],[fc1_ordinal1]) ).
fof(i_0_674,lemma,
! [X1,X2] :
( set_difference(X1,singleton(X2)) = X1
<=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[t65_zfmisc_1]) ).
fof(i_0_675,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)],[t42_ordinal1]) ).
fof(i_0_676,lemma,
! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
inference(fof_simplification,[status(thm)],[l28_zfmisc_1]) ).
fof(i_0_677,plain,
! [X1] : ~ empty(singleton(X1)),
inference(fof_simplification,[status(thm)],[fc2_subset_1]) ).
fof(i_0_678,plain,
! [X1] :
( ~ empty(singleton(X1))
& finite(singleton(X1)) ),
inference(fof_simplification,[status(thm)],[fc1_finset_1]) ).
fof(i_0_679,plain,
! [X2993,X2994,X3001,X3005,X3006,X3008,X3013,X3014,X3015,X3016,X3017,X3018] :
( ( in(esk225_4(X2993,X2994,X3006,X3008),cartesian_product2(X2993,X3006))
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| esk215_2(X2993,X2994) = esk216_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( esk225_4(X2993,X2994,X3006,X3008) = X3008
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| esk215_2(X2993,X2994) = esk216_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( ordered_pair(esk226_4(X2993,X2994,X3006,X3008),esk227_4(X2993,X2994,X3006,X3008)) = X3008
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| esk215_2(X2993,X2994) = esk216_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( in(esk226_4(X2993,X2994,X3006,X3008),X2993)
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| esk215_2(X2993,X2994) = esk216_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( esk226_4(X2993,X2994,X3006,X3008) = esk228_4(X2993,X2994,X3006,X3008)
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| esk215_2(X2993,X2994) = esk216_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( in(esk227_4(X2993,X2994,X3006,X3008),esk228_4(X2993,X2994,X3006,X3008))
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| esk215_2(X2993,X2994) = esk216_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( ~ in(X3013,esk228_4(X2993,X2994,X3006,X3008))
| in(ordered_pair(esk227_4(X2993,X2994,X3006,X3008),X3013),X2994)
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| esk215_2(X2993,X2994) = esk216_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( in(esk229_7(X2993,X2994,X3006,X3014,X3016,X3017,X3018),X3018)
| X3016 != X3018
| ~ in(X3017,X3018)
| ordered_pair(X3016,X3017) != X3014
| ~ in(X3016,X2993)
| ~ in(X3015,cartesian_product2(X2993,X3006))
| X3015 != X3014
| in(X3014,esk224_3(X2993,X2994,X3006))
| esk215_2(X2993,X2994) = esk216_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( ~ in(ordered_pair(X3017,esk229_7(X2993,X2994,X3006,X3014,X3016,X3017,X3018)),X2994)
| X3016 != X3018
| ~ in(X3017,X3018)
| ordered_pair(X3016,X3017) != X3014
| ~ in(X3016,X2993)
| ~ in(X3015,cartesian_product2(X2993,X3006))
| X3015 != X3014
| in(X3014,esk224_3(X2993,X2994,X3006))
| esk215_2(X2993,X2994) = esk216_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( in(esk225_4(X2993,X2994,X3006,X3008),cartesian_product2(X2993,X3006))
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| ordered_pair(esk218_2(X2993,X2994),esk219_2(X2993,X2994)) = esk216_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( esk225_4(X2993,X2994,X3006,X3008) = X3008
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| ordered_pair(esk218_2(X2993,X2994),esk219_2(X2993,X2994)) = esk216_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( ordered_pair(esk226_4(X2993,X2994,X3006,X3008),esk227_4(X2993,X2994,X3006,X3008)) = X3008
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| ordered_pair(esk218_2(X2993,X2994),esk219_2(X2993,X2994)) = esk216_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( in(esk226_4(X2993,X2994,X3006,X3008),X2993)
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| ordered_pair(esk218_2(X2993,X2994),esk219_2(X2993,X2994)) = esk216_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( esk226_4(X2993,X2994,X3006,X3008) = esk228_4(X2993,X2994,X3006,X3008)
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| ordered_pair(esk218_2(X2993,X2994),esk219_2(X2993,X2994)) = esk216_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( in(esk227_4(X2993,X2994,X3006,X3008),esk228_4(X2993,X2994,X3006,X3008))
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| ordered_pair(esk218_2(X2993,X2994),esk219_2(X2993,X2994)) = esk216_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( ~ in(X3013,esk228_4(X2993,X2994,X3006,X3008))
| in(ordered_pair(esk227_4(X2993,X2994,X3006,X3008),X3013),X2994)
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| ordered_pair(esk218_2(X2993,X2994),esk219_2(X2993,X2994)) = esk216_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( in(esk229_7(X2993,X2994,X3006,X3014,X3016,X3017,X3018),X3018)
| X3016 != X3018
| ~ in(X3017,X3018)
| ordered_pair(X3016,X3017) != X3014
| ~ in(X3016,X2993)
| ~ in(X3015,cartesian_product2(X2993,X3006))
| X3015 != X3014
| in(X3014,esk224_3(X2993,X2994,X3006))
| ordered_pair(esk218_2(X2993,X2994),esk219_2(X2993,X2994)) = esk216_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( ~ in(ordered_pair(X3017,esk229_7(X2993,X2994,X3006,X3014,X3016,X3017,X3018)),X2994)
| X3016 != X3018
| ~ in(X3017,X3018)
| ordered_pair(X3016,X3017) != X3014
| ~ in(X3016,X2993)
| ~ in(X3015,cartesian_product2(X2993,X3006))
| X3015 != X3014
| in(X3014,esk224_3(X2993,X2994,X3006))
| ordered_pair(esk218_2(X2993,X2994),esk219_2(X2993,X2994)) = esk216_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( in(esk225_4(X2993,X2994,X3006,X3008),cartesian_product2(X2993,X3006))
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| in(esk218_2(X2993,X2994),X2993)
| empty(X2993)
| ~ relation(X2994) )
& ( esk225_4(X2993,X2994,X3006,X3008) = X3008
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| in(esk218_2(X2993,X2994),X2993)
| empty(X2993)
| ~ relation(X2994) )
& ( ordered_pair(esk226_4(X2993,X2994,X3006,X3008),esk227_4(X2993,X2994,X3006,X3008)) = X3008
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| in(esk218_2(X2993,X2994),X2993)
| empty(X2993)
| ~ relation(X2994) )
& ( in(esk226_4(X2993,X2994,X3006,X3008),X2993)
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| in(esk218_2(X2993,X2994),X2993)
| empty(X2993)
| ~ relation(X2994) )
& ( esk226_4(X2993,X2994,X3006,X3008) = esk228_4(X2993,X2994,X3006,X3008)
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| in(esk218_2(X2993,X2994),X2993)
| empty(X2993)
| ~ relation(X2994) )
& ( in(esk227_4(X2993,X2994,X3006,X3008),esk228_4(X2993,X2994,X3006,X3008))
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| in(esk218_2(X2993,X2994),X2993)
| empty(X2993)
| ~ relation(X2994) )
& ( ~ in(X3013,esk228_4(X2993,X2994,X3006,X3008))
| in(ordered_pair(esk227_4(X2993,X2994,X3006,X3008),X3013),X2994)
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| in(esk218_2(X2993,X2994),X2993)
| empty(X2993)
| ~ relation(X2994) )
& ( in(esk229_7(X2993,X2994,X3006,X3014,X3016,X3017,X3018),X3018)
| X3016 != X3018
| ~ in(X3017,X3018)
| ordered_pair(X3016,X3017) != X3014
| ~ in(X3016,X2993)
| ~ in(X3015,cartesian_product2(X2993,X3006))
| X3015 != X3014
| in(X3014,esk224_3(X2993,X2994,X3006))
| in(esk218_2(X2993,X2994),X2993)
| empty(X2993)
| ~ relation(X2994) )
& ( ~ in(ordered_pair(X3017,esk229_7(X2993,X2994,X3006,X3014,X3016,X3017,X3018)),X2994)
| X3016 != X3018
| ~ in(X3017,X3018)
| ordered_pair(X3016,X3017) != X3014
| ~ in(X3016,X2993)
| ~ in(X3015,cartesian_product2(X2993,X3006))
| X3015 != X3014
| in(X3014,esk224_3(X2993,X2994,X3006))
| in(esk218_2(X2993,X2994),X2993)
| empty(X2993)
| ~ relation(X2994) )
& ( in(esk225_4(X2993,X2994,X3006,X3008),cartesian_product2(X2993,X3006))
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| esk218_2(X2993,X2994) = esk220_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( esk225_4(X2993,X2994,X3006,X3008) = X3008
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| esk218_2(X2993,X2994) = esk220_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( ordered_pair(esk226_4(X2993,X2994,X3006,X3008),esk227_4(X2993,X2994,X3006,X3008)) = X3008
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| esk218_2(X2993,X2994) = esk220_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( in(esk226_4(X2993,X2994,X3006,X3008),X2993)
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| esk218_2(X2993,X2994) = esk220_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( esk226_4(X2993,X2994,X3006,X3008) = esk228_4(X2993,X2994,X3006,X3008)
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| esk218_2(X2993,X2994) = esk220_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( in(esk227_4(X2993,X2994,X3006,X3008),esk228_4(X2993,X2994,X3006,X3008))
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| esk218_2(X2993,X2994) = esk220_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( ~ in(X3013,esk228_4(X2993,X2994,X3006,X3008))
| in(ordered_pair(esk227_4(X2993,X2994,X3006,X3008),X3013),X2994)
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| esk218_2(X2993,X2994) = esk220_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( in(esk229_7(X2993,X2994,X3006,X3014,X3016,X3017,X3018),X3018)
| X3016 != X3018
| ~ in(X3017,X3018)
| ordered_pair(X3016,X3017) != X3014
| ~ in(X3016,X2993)
| ~ in(X3015,cartesian_product2(X2993,X3006))
| X3015 != X3014
| in(X3014,esk224_3(X2993,X2994,X3006))
| esk218_2(X2993,X2994) = esk220_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( ~ in(ordered_pair(X3017,esk229_7(X2993,X2994,X3006,X3014,X3016,X3017,X3018)),X2994)
| X3016 != X3018
| ~ in(X3017,X3018)
| ordered_pair(X3016,X3017) != X3014
| ~ in(X3016,X2993)
| ~ in(X3015,cartesian_product2(X2993,X3006))
| X3015 != X3014
| in(X3014,esk224_3(X2993,X2994,X3006))
| esk218_2(X2993,X2994) = esk220_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( in(esk225_4(X2993,X2994,X3006,X3008),cartesian_product2(X2993,X3006))
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| in(esk219_2(X2993,X2994),esk220_2(X2993,X2994))
| empty(X2993)
| ~ relation(X2994) )
& ( esk225_4(X2993,X2994,X3006,X3008) = X3008
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| in(esk219_2(X2993,X2994),esk220_2(X2993,X2994))
| empty(X2993)
| ~ relation(X2994) )
& ( ordered_pair(esk226_4(X2993,X2994,X3006,X3008),esk227_4(X2993,X2994,X3006,X3008)) = X3008
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| in(esk219_2(X2993,X2994),esk220_2(X2993,X2994))
| empty(X2993)
| ~ relation(X2994) )
& ( in(esk226_4(X2993,X2994,X3006,X3008),X2993)
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| in(esk219_2(X2993,X2994),esk220_2(X2993,X2994))
| empty(X2993)
| ~ relation(X2994) )
& ( esk226_4(X2993,X2994,X3006,X3008) = esk228_4(X2993,X2994,X3006,X3008)
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| in(esk219_2(X2993,X2994),esk220_2(X2993,X2994))
| empty(X2993)
| ~ relation(X2994) )
& ( in(esk227_4(X2993,X2994,X3006,X3008),esk228_4(X2993,X2994,X3006,X3008))
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| in(esk219_2(X2993,X2994),esk220_2(X2993,X2994))
| empty(X2993)
| ~ relation(X2994) )
& ( ~ in(X3013,esk228_4(X2993,X2994,X3006,X3008))
| in(ordered_pair(esk227_4(X2993,X2994,X3006,X3008),X3013),X2994)
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| in(esk219_2(X2993,X2994),esk220_2(X2993,X2994))
| empty(X2993)
| ~ relation(X2994) )
& ( in(esk229_7(X2993,X2994,X3006,X3014,X3016,X3017,X3018),X3018)
| X3016 != X3018
| ~ in(X3017,X3018)
| ordered_pair(X3016,X3017) != X3014
| ~ in(X3016,X2993)
| ~ in(X3015,cartesian_product2(X2993,X3006))
| X3015 != X3014
| in(X3014,esk224_3(X2993,X2994,X3006))
| in(esk219_2(X2993,X2994),esk220_2(X2993,X2994))
| empty(X2993)
| ~ relation(X2994) )
& ( ~ in(ordered_pair(X3017,esk229_7(X2993,X2994,X3006,X3014,X3016,X3017,X3018)),X2994)
| X3016 != X3018
| ~ in(X3017,X3018)
| ordered_pair(X3016,X3017) != X3014
| ~ in(X3016,X2993)
| ~ in(X3015,cartesian_product2(X2993,X3006))
| X3015 != X3014
| in(X3014,esk224_3(X2993,X2994,X3006))
| in(esk219_2(X2993,X2994),esk220_2(X2993,X2994))
| empty(X2993)
| ~ relation(X2994) )
& ( in(esk225_4(X2993,X2994,X3006,X3008),cartesian_product2(X2993,X3006))
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| ~ in(X3001,esk220_2(X2993,X2994))
| in(ordered_pair(esk219_2(X2993,X2994),X3001),X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( esk225_4(X2993,X2994,X3006,X3008) = X3008
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| ~ in(X3001,esk220_2(X2993,X2994))
| in(ordered_pair(esk219_2(X2993,X2994),X3001),X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( ordered_pair(esk226_4(X2993,X2994,X3006,X3008),esk227_4(X2993,X2994,X3006,X3008)) = X3008
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| ~ in(X3001,esk220_2(X2993,X2994))
| in(ordered_pair(esk219_2(X2993,X2994),X3001),X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( in(esk226_4(X2993,X2994,X3006,X3008),X2993)
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| ~ in(X3001,esk220_2(X2993,X2994))
| in(ordered_pair(esk219_2(X2993,X2994),X3001),X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( esk226_4(X2993,X2994,X3006,X3008) = esk228_4(X2993,X2994,X3006,X3008)
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| ~ in(X3001,esk220_2(X2993,X2994))
| in(ordered_pair(esk219_2(X2993,X2994),X3001),X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( in(esk227_4(X2993,X2994,X3006,X3008),esk228_4(X2993,X2994,X3006,X3008))
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| ~ in(X3001,esk220_2(X2993,X2994))
| in(ordered_pair(esk219_2(X2993,X2994),X3001),X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( ~ in(X3013,esk228_4(X2993,X2994,X3006,X3008))
| in(ordered_pair(esk227_4(X2993,X2994,X3006,X3008),X3013),X2994)
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| ~ in(X3001,esk220_2(X2993,X2994))
| in(ordered_pair(esk219_2(X2993,X2994),X3001),X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( in(esk229_7(X2993,X2994,X3006,X3014,X3016,X3017,X3018),X3018)
| X3016 != X3018
| ~ in(X3017,X3018)
| ordered_pair(X3016,X3017) != X3014
| ~ in(X3016,X2993)
| ~ in(X3015,cartesian_product2(X2993,X3006))
| X3015 != X3014
| in(X3014,esk224_3(X2993,X2994,X3006))
| ~ in(X3001,esk220_2(X2993,X2994))
| in(ordered_pair(esk219_2(X2993,X2994),X3001),X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( ~ in(ordered_pair(X3017,esk229_7(X2993,X2994,X3006,X3014,X3016,X3017,X3018)),X2994)
| X3016 != X3018
| ~ in(X3017,X3018)
| ordered_pair(X3016,X3017) != X3014
| ~ in(X3016,X2993)
| ~ in(X3015,cartesian_product2(X2993,X3006))
| X3015 != X3014
| in(X3014,esk224_3(X2993,X2994,X3006))
| ~ in(X3001,esk220_2(X2993,X2994))
| in(ordered_pair(esk219_2(X2993,X2994),X3001),X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( in(esk225_4(X2993,X2994,X3006,X3008),cartesian_product2(X2993,X3006))
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| esk215_2(X2993,X2994) = esk217_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( esk225_4(X2993,X2994,X3006,X3008) = X3008
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| esk215_2(X2993,X2994) = esk217_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( ordered_pair(esk226_4(X2993,X2994,X3006,X3008),esk227_4(X2993,X2994,X3006,X3008)) = X3008
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| esk215_2(X2993,X2994) = esk217_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( in(esk226_4(X2993,X2994,X3006,X3008),X2993)
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| esk215_2(X2993,X2994) = esk217_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( esk226_4(X2993,X2994,X3006,X3008) = esk228_4(X2993,X2994,X3006,X3008)
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| esk215_2(X2993,X2994) = esk217_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( in(esk227_4(X2993,X2994,X3006,X3008),esk228_4(X2993,X2994,X3006,X3008))
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| esk215_2(X2993,X2994) = esk217_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( ~ in(X3013,esk228_4(X2993,X2994,X3006,X3008))
| in(ordered_pair(esk227_4(X2993,X2994,X3006,X3008),X3013),X2994)
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| esk215_2(X2993,X2994) = esk217_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( in(esk229_7(X2993,X2994,X3006,X3014,X3016,X3017,X3018),X3018)
| X3016 != X3018
| ~ in(X3017,X3018)
| ordered_pair(X3016,X3017) != X3014
| ~ in(X3016,X2993)
| ~ in(X3015,cartesian_product2(X2993,X3006))
| X3015 != X3014
| in(X3014,esk224_3(X2993,X2994,X3006))
| esk215_2(X2993,X2994) = esk217_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( ~ in(ordered_pair(X3017,esk229_7(X2993,X2994,X3006,X3014,X3016,X3017,X3018)),X2994)
| X3016 != X3018
| ~ in(X3017,X3018)
| ordered_pair(X3016,X3017) != X3014
| ~ in(X3016,X2993)
| ~ in(X3015,cartesian_product2(X2993,X3006))
| X3015 != X3014
| in(X3014,esk224_3(X2993,X2994,X3006))
| esk215_2(X2993,X2994) = esk217_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( in(esk225_4(X2993,X2994,X3006,X3008),cartesian_product2(X2993,X3006))
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| ordered_pair(esk221_2(X2993,X2994),esk222_2(X2993,X2994)) = esk217_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( esk225_4(X2993,X2994,X3006,X3008) = X3008
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| ordered_pair(esk221_2(X2993,X2994),esk222_2(X2993,X2994)) = esk217_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( ordered_pair(esk226_4(X2993,X2994,X3006,X3008),esk227_4(X2993,X2994,X3006,X3008)) = X3008
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| ordered_pair(esk221_2(X2993,X2994),esk222_2(X2993,X2994)) = esk217_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( in(esk226_4(X2993,X2994,X3006,X3008),X2993)
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| ordered_pair(esk221_2(X2993,X2994),esk222_2(X2993,X2994)) = esk217_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( esk226_4(X2993,X2994,X3006,X3008) = esk228_4(X2993,X2994,X3006,X3008)
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| ordered_pair(esk221_2(X2993,X2994),esk222_2(X2993,X2994)) = esk217_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( in(esk227_4(X2993,X2994,X3006,X3008),esk228_4(X2993,X2994,X3006,X3008))
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| ordered_pair(esk221_2(X2993,X2994),esk222_2(X2993,X2994)) = esk217_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( ~ in(X3013,esk228_4(X2993,X2994,X3006,X3008))
| in(ordered_pair(esk227_4(X2993,X2994,X3006,X3008),X3013),X2994)
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| ordered_pair(esk221_2(X2993,X2994),esk222_2(X2993,X2994)) = esk217_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( in(esk229_7(X2993,X2994,X3006,X3014,X3016,X3017,X3018),X3018)
| X3016 != X3018
| ~ in(X3017,X3018)
| ordered_pair(X3016,X3017) != X3014
| ~ in(X3016,X2993)
| ~ in(X3015,cartesian_product2(X2993,X3006))
| X3015 != X3014
| in(X3014,esk224_3(X2993,X2994,X3006))
| ordered_pair(esk221_2(X2993,X2994),esk222_2(X2993,X2994)) = esk217_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( ~ in(ordered_pair(X3017,esk229_7(X2993,X2994,X3006,X3014,X3016,X3017,X3018)),X2994)
| X3016 != X3018
| ~ in(X3017,X3018)
| ordered_pair(X3016,X3017) != X3014
| ~ in(X3016,X2993)
| ~ in(X3015,cartesian_product2(X2993,X3006))
| X3015 != X3014
| in(X3014,esk224_3(X2993,X2994,X3006))
| ordered_pair(esk221_2(X2993,X2994),esk222_2(X2993,X2994)) = esk217_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( in(esk225_4(X2993,X2994,X3006,X3008),cartesian_product2(X2993,X3006))
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| in(esk221_2(X2993,X2994),X2993)
| empty(X2993)
| ~ relation(X2994) )
& ( esk225_4(X2993,X2994,X3006,X3008) = X3008
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| in(esk221_2(X2993,X2994),X2993)
| empty(X2993)
| ~ relation(X2994) )
& ( ordered_pair(esk226_4(X2993,X2994,X3006,X3008),esk227_4(X2993,X2994,X3006,X3008)) = X3008
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| in(esk221_2(X2993,X2994),X2993)
| empty(X2993)
| ~ relation(X2994) )
& ( in(esk226_4(X2993,X2994,X3006,X3008),X2993)
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| in(esk221_2(X2993,X2994),X2993)
| empty(X2993)
| ~ relation(X2994) )
& ( esk226_4(X2993,X2994,X3006,X3008) = esk228_4(X2993,X2994,X3006,X3008)
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| in(esk221_2(X2993,X2994),X2993)
| empty(X2993)
| ~ relation(X2994) )
& ( in(esk227_4(X2993,X2994,X3006,X3008),esk228_4(X2993,X2994,X3006,X3008))
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| in(esk221_2(X2993,X2994),X2993)
| empty(X2993)
| ~ relation(X2994) )
& ( ~ in(X3013,esk228_4(X2993,X2994,X3006,X3008))
| in(ordered_pair(esk227_4(X2993,X2994,X3006,X3008),X3013),X2994)
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| in(esk221_2(X2993,X2994),X2993)
| empty(X2993)
| ~ relation(X2994) )
& ( in(esk229_7(X2993,X2994,X3006,X3014,X3016,X3017,X3018),X3018)
| X3016 != X3018
| ~ in(X3017,X3018)
| ordered_pair(X3016,X3017) != X3014
| ~ in(X3016,X2993)
| ~ in(X3015,cartesian_product2(X2993,X3006))
| X3015 != X3014
| in(X3014,esk224_3(X2993,X2994,X3006))
| in(esk221_2(X2993,X2994),X2993)
| empty(X2993)
| ~ relation(X2994) )
& ( ~ in(ordered_pair(X3017,esk229_7(X2993,X2994,X3006,X3014,X3016,X3017,X3018)),X2994)
| X3016 != X3018
| ~ in(X3017,X3018)
| ordered_pair(X3016,X3017) != X3014
| ~ in(X3016,X2993)
| ~ in(X3015,cartesian_product2(X2993,X3006))
| X3015 != X3014
| in(X3014,esk224_3(X2993,X2994,X3006))
| in(esk221_2(X2993,X2994),X2993)
| empty(X2993)
| ~ relation(X2994) )
& ( in(esk225_4(X2993,X2994,X3006,X3008),cartesian_product2(X2993,X3006))
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| esk221_2(X2993,X2994) = esk223_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( esk225_4(X2993,X2994,X3006,X3008) = X3008
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| esk221_2(X2993,X2994) = esk223_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( ordered_pair(esk226_4(X2993,X2994,X3006,X3008),esk227_4(X2993,X2994,X3006,X3008)) = X3008
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| esk221_2(X2993,X2994) = esk223_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( in(esk226_4(X2993,X2994,X3006,X3008),X2993)
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| esk221_2(X2993,X2994) = esk223_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( esk226_4(X2993,X2994,X3006,X3008) = esk228_4(X2993,X2994,X3006,X3008)
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| esk221_2(X2993,X2994) = esk223_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( in(esk227_4(X2993,X2994,X3006,X3008),esk228_4(X2993,X2994,X3006,X3008))
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| esk221_2(X2993,X2994) = esk223_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( ~ in(X3013,esk228_4(X2993,X2994,X3006,X3008))
| in(ordered_pair(esk227_4(X2993,X2994,X3006,X3008),X3013),X2994)
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| esk221_2(X2993,X2994) = esk223_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( in(esk229_7(X2993,X2994,X3006,X3014,X3016,X3017,X3018),X3018)
| X3016 != X3018
| ~ in(X3017,X3018)
| ordered_pair(X3016,X3017) != X3014
| ~ in(X3016,X2993)
| ~ in(X3015,cartesian_product2(X2993,X3006))
| X3015 != X3014
| in(X3014,esk224_3(X2993,X2994,X3006))
| esk221_2(X2993,X2994) = esk223_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( ~ in(ordered_pair(X3017,esk229_7(X2993,X2994,X3006,X3014,X3016,X3017,X3018)),X2994)
| X3016 != X3018
| ~ in(X3017,X3018)
| ordered_pair(X3016,X3017) != X3014
| ~ in(X3016,X2993)
| ~ in(X3015,cartesian_product2(X2993,X3006))
| X3015 != X3014
| in(X3014,esk224_3(X2993,X2994,X3006))
| esk221_2(X2993,X2994) = esk223_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( in(esk225_4(X2993,X2994,X3006,X3008),cartesian_product2(X2993,X3006))
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| in(esk222_2(X2993,X2994),esk223_2(X2993,X2994))
| empty(X2993)
| ~ relation(X2994) )
& ( esk225_4(X2993,X2994,X3006,X3008) = X3008
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| in(esk222_2(X2993,X2994),esk223_2(X2993,X2994))
| empty(X2993)
| ~ relation(X2994) )
& ( ordered_pair(esk226_4(X2993,X2994,X3006,X3008),esk227_4(X2993,X2994,X3006,X3008)) = X3008
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| in(esk222_2(X2993,X2994),esk223_2(X2993,X2994))
| empty(X2993)
| ~ relation(X2994) )
& ( in(esk226_4(X2993,X2994,X3006,X3008),X2993)
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| in(esk222_2(X2993,X2994),esk223_2(X2993,X2994))
| empty(X2993)
| ~ relation(X2994) )
& ( esk226_4(X2993,X2994,X3006,X3008) = esk228_4(X2993,X2994,X3006,X3008)
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| in(esk222_2(X2993,X2994),esk223_2(X2993,X2994))
| empty(X2993)
| ~ relation(X2994) )
& ( in(esk227_4(X2993,X2994,X3006,X3008),esk228_4(X2993,X2994,X3006,X3008))
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| in(esk222_2(X2993,X2994),esk223_2(X2993,X2994))
| empty(X2993)
| ~ relation(X2994) )
& ( ~ in(X3013,esk228_4(X2993,X2994,X3006,X3008))
| in(ordered_pair(esk227_4(X2993,X2994,X3006,X3008),X3013),X2994)
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| in(esk222_2(X2993,X2994),esk223_2(X2993,X2994))
| empty(X2993)
| ~ relation(X2994) )
& ( in(esk229_7(X2993,X2994,X3006,X3014,X3016,X3017,X3018),X3018)
| X3016 != X3018
| ~ in(X3017,X3018)
| ordered_pair(X3016,X3017) != X3014
| ~ in(X3016,X2993)
| ~ in(X3015,cartesian_product2(X2993,X3006))
| X3015 != X3014
| in(X3014,esk224_3(X2993,X2994,X3006))
| in(esk222_2(X2993,X2994),esk223_2(X2993,X2994))
| empty(X2993)
| ~ relation(X2994) )
& ( ~ in(ordered_pair(X3017,esk229_7(X2993,X2994,X3006,X3014,X3016,X3017,X3018)),X2994)
| X3016 != X3018
| ~ in(X3017,X3018)
| ordered_pair(X3016,X3017) != X3014
| ~ in(X3016,X2993)
| ~ in(X3015,cartesian_product2(X2993,X3006))
| X3015 != X3014
| in(X3014,esk224_3(X2993,X2994,X3006))
| in(esk222_2(X2993,X2994),esk223_2(X2993,X2994))
| empty(X2993)
| ~ relation(X2994) )
& ( in(esk225_4(X2993,X2994,X3006,X3008),cartesian_product2(X2993,X3006))
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| ~ in(X3005,esk223_2(X2993,X2994))
| in(ordered_pair(esk222_2(X2993,X2994),X3005),X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( esk225_4(X2993,X2994,X3006,X3008) = X3008
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| ~ in(X3005,esk223_2(X2993,X2994))
| in(ordered_pair(esk222_2(X2993,X2994),X3005),X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( ordered_pair(esk226_4(X2993,X2994,X3006,X3008),esk227_4(X2993,X2994,X3006,X3008)) = X3008
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| ~ in(X3005,esk223_2(X2993,X2994))
| in(ordered_pair(esk222_2(X2993,X2994),X3005),X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( in(esk226_4(X2993,X2994,X3006,X3008),X2993)
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| ~ in(X3005,esk223_2(X2993,X2994))
| in(ordered_pair(esk222_2(X2993,X2994),X3005),X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( esk226_4(X2993,X2994,X3006,X3008) = esk228_4(X2993,X2994,X3006,X3008)
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| ~ in(X3005,esk223_2(X2993,X2994))
| in(ordered_pair(esk222_2(X2993,X2994),X3005),X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( in(esk227_4(X2993,X2994,X3006,X3008),esk228_4(X2993,X2994,X3006,X3008))
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| ~ in(X3005,esk223_2(X2993,X2994))
| in(ordered_pair(esk222_2(X2993,X2994),X3005),X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( ~ in(X3013,esk228_4(X2993,X2994,X3006,X3008))
| in(ordered_pair(esk227_4(X2993,X2994,X3006,X3008),X3013),X2994)
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| ~ in(X3005,esk223_2(X2993,X2994))
| in(ordered_pair(esk222_2(X2993,X2994),X3005),X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( in(esk229_7(X2993,X2994,X3006,X3014,X3016,X3017,X3018),X3018)
| X3016 != X3018
| ~ in(X3017,X3018)
| ordered_pair(X3016,X3017) != X3014
| ~ in(X3016,X2993)
| ~ in(X3015,cartesian_product2(X2993,X3006))
| X3015 != X3014
| in(X3014,esk224_3(X2993,X2994,X3006))
| ~ in(X3005,esk223_2(X2993,X2994))
| in(ordered_pair(esk222_2(X2993,X2994),X3005),X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( ~ in(ordered_pair(X3017,esk229_7(X2993,X2994,X3006,X3014,X3016,X3017,X3018)),X2994)
| X3016 != X3018
| ~ in(X3017,X3018)
| ordered_pair(X3016,X3017) != X3014
| ~ in(X3016,X2993)
| ~ in(X3015,cartesian_product2(X2993,X3006))
| X3015 != X3014
| in(X3014,esk224_3(X2993,X2994,X3006))
| ~ in(X3005,esk223_2(X2993,X2994))
| in(ordered_pair(esk222_2(X2993,X2994),X3005),X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( in(esk225_4(X2993,X2994,X3006,X3008),cartesian_product2(X2993,X3006))
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| esk216_2(X2993,X2994) != esk217_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( esk225_4(X2993,X2994,X3006,X3008) = X3008
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| esk216_2(X2993,X2994) != esk217_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( ordered_pair(esk226_4(X2993,X2994,X3006,X3008),esk227_4(X2993,X2994,X3006,X3008)) = X3008
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| esk216_2(X2993,X2994) != esk217_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( in(esk226_4(X2993,X2994,X3006,X3008),X2993)
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| esk216_2(X2993,X2994) != esk217_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( esk226_4(X2993,X2994,X3006,X3008) = esk228_4(X2993,X2994,X3006,X3008)
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| esk216_2(X2993,X2994) != esk217_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( in(esk227_4(X2993,X2994,X3006,X3008),esk228_4(X2993,X2994,X3006,X3008))
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| esk216_2(X2993,X2994) != esk217_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( ~ in(X3013,esk228_4(X2993,X2994,X3006,X3008))
| in(ordered_pair(esk227_4(X2993,X2994,X3006,X3008),X3013),X2994)
| ~ in(X3008,esk224_3(X2993,X2994,X3006))
| esk216_2(X2993,X2994) != esk217_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( in(esk229_7(X2993,X2994,X3006,X3014,X3016,X3017,X3018),X3018)
| X3016 != X3018
| ~ in(X3017,X3018)
| ordered_pair(X3016,X3017) != X3014
| ~ in(X3016,X2993)
| ~ in(X3015,cartesian_product2(X2993,X3006))
| X3015 != X3014
| in(X3014,esk224_3(X2993,X2994,X3006))
| esk216_2(X2993,X2994) != esk217_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) )
& ( ~ in(ordered_pair(X3017,esk229_7(X2993,X2994,X3006,X3014,X3016,X3017,X3018)),X2994)
| X3016 != X3018
| ~ in(X3017,X3018)
| ordered_pair(X3016,X3017) != X3014
| ~ in(X3016,X2993)
| ~ in(X3015,cartesian_product2(X2993,X3006))
| X3015 != X3014
| in(X3014,esk224_3(X2993,X2994,X3006))
| esk216_2(X2993,X2994) != esk217_2(X2993,X2994)
| empty(X2993)
| ~ relation(X2994) ) ),
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)],[i_0_645])])])])])]) ).
cnf(i_0_680,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[i_0_646]) ).
cnf(i_0_681,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[i_0_647]) ).
fof(i_0_682,lemma,
! [X3229,X3230,X3231,X3233,X3237,X3238,X3239,X3240,X3241] :
( ( in(X3233,cartesian_product2(X3229,X3231))
| ~ in(X3233,esk341_3(X3229,X3230,X3231))
| empty(X3229)
| ~ relation(X3230) )
& ( ordered_pair(esk342_4(X3229,X3230,X3231,X3233),esk343_4(X3229,X3230,X3231,X3233)) = X3233
| ~ in(X3233,esk341_3(X3229,X3230,X3231))
| empty(X3229)
| ~ relation(X3230) )
& ( in(esk342_4(X3229,X3230,X3231,X3233),X3229)
| ~ in(X3233,esk341_3(X3229,X3230,X3231))
| empty(X3229)
| ~ relation(X3230) )
& ( esk342_4(X3229,X3230,X3231,X3233) = esk344_4(X3229,X3230,X3231,X3233)
| ~ in(X3233,esk341_3(X3229,X3230,X3231))
| empty(X3229)
| ~ relation(X3230) )
& ( in(esk343_4(X3229,X3230,X3231,X3233),esk344_4(X3229,X3230,X3231,X3233))
| ~ in(X3233,esk341_3(X3229,X3230,X3231))
| empty(X3229)
| ~ relation(X3230) )
& ( ~ in(X3237,esk344_4(X3229,X3230,X3231,X3233))
| in(ordered_pair(esk343_4(X3229,X3230,X3231,X3233),X3237),X3230)
| ~ in(X3233,esk341_3(X3229,X3230,X3231))
| empty(X3229)
| ~ relation(X3230) )
& ( in(esk345_7(X3229,X3230,X3231,X3238,X3239,X3240,X3241),X3241)
| X3239 != X3241
| ~ in(X3240,X3241)
| ordered_pair(X3239,X3240) != X3238
| ~ in(X3239,X3229)
| ~ in(X3238,cartesian_product2(X3229,X3231))
| in(X3238,esk341_3(X3229,X3230,X3231))
| empty(X3229)
| ~ relation(X3230) )
& ( ~ in(ordered_pair(X3240,esk345_7(X3229,X3230,X3231,X3238,X3239,X3240,X3241)),X3230)
| X3239 != X3241
| ~ in(X3240,X3241)
| ordered_pair(X3239,X3240) != X3238
| ~ in(X3239,X3229)
| ~ in(X3238,cartesian_product2(X3229,X3231))
| in(X3238,esk341_3(X3229,X3230,X3231))
| empty(X3229)
| ~ relation(X3230) ) ),
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)],[i_0_648])])])])])]) ).
fof(i_0_683,plain,
! [X2394,X2395,X2396,X2397,X2398,X2400,X2401,X2402,X2405] :
( ( in(ordered_pair(X2397,esk106_5(X2394,X2395,X2396,X2397,X2398)),X2394)
| ~ in(ordered_pair(X2397,X2398),X2396)
| X2396 != relation_composition(X2394,X2395)
| ~ relation(X2396)
| ~ relation(X2395)
| ~ relation(X2394) )
& ( in(ordered_pair(esk106_5(X2394,X2395,X2396,X2397,X2398),X2398),X2395)
| ~ in(ordered_pair(X2397,X2398),X2396)
| X2396 != relation_composition(X2394,X2395)
| ~ relation(X2396)
| ~ relation(X2395)
| ~ relation(X2394) )
& ( ~ in(ordered_pair(X2400,X2402),X2394)
| ~ in(ordered_pair(X2402,X2401),X2395)
| in(ordered_pair(X2400,X2401),X2396)
| X2396 != relation_composition(X2394,X2395)
| ~ relation(X2396)
| ~ relation(X2395)
| ~ relation(X2394) )
& ( ~ in(ordered_pair(esk107_3(X2394,X2395,X2396),esk108_3(X2394,X2395,X2396)),X2396)
| ~ in(ordered_pair(esk107_3(X2394,X2395,X2396),X2405),X2394)
| ~ in(ordered_pair(X2405,esk108_3(X2394,X2395,X2396)),X2395)
| X2396 = relation_composition(X2394,X2395)
| ~ relation(X2396)
| ~ relation(X2395)
| ~ relation(X2394) )
& ( in(ordered_pair(esk107_3(X2394,X2395,X2396),esk109_3(X2394,X2395,X2396)),X2394)
| in(ordered_pair(esk107_3(X2394,X2395,X2396),esk108_3(X2394,X2395,X2396)),X2396)
| X2396 = relation_composition(X2394,X2395)
| ~ relation(X2396)
| ~ relation(X2395)
| ~ relation(X2394) )
& ( in(ordered_pair(esk109_3(X2394,X2395,X2396),esk108_3(X2394,X2395,X2396)),X2395)
| in(ordered_pair(esk107_3(X2394,X2395,X2396),esk108_3(X2394,X2395,X2396)),X2396)
| X2396 = relation_composition(X2394,X2395)
| ~ relation(X2396)
| ~ relation(X2395)
| ~ relation(X2394) ) ),
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)],[d8_relat_1])])])])])]) ).
fof(i_0_684,plain,
! [X3176,X3177,X3178,X3187,X3191,X3192,X3193,X3194] :
( ( in(esk320_4(X3176,X3177,X3178,X3187),cartesian_product2(X3176,X3176))
| ~ in(X3187,esk319_3(X3176,X3177,X3178))
| esk312_3(X3176,X3177,X3178) = esk313_3(X3176,X3177,X3178)
| ~ relation(X3177)
| ~ relation(X3178)
| ~ function(X3178) )
& ( esk320_4(X3176,X3177,X3178,X3187) = X3187
| ~ in(X3187,esk319_3(X3176,X3177,X3178))
| esk312_3(X3176,X3177,X3178) = esk313_3(X3176,X3177,X3178)
| ~ relation(X3177)
| ~ relation(X3178)
| ~ function(X3178) )
& ( X3187 = ordered_pair(esk321_4(X3176,X3177,X3178,X3187),esk322_4(X3176,X3177,X3178,X3187))
| ~ in(X3187,esk319_3(X3176,X3177,X3178))
| esk312_3(X3176,X3177,X3178) = esk313_3(X3176,X3177,X3178)
| ~ relation(X3177)
| ~ relation(X3178)
| ~ function(X3178) )
& ( in(ordered_pair(apply(X3178,esk321_4(X3176,X3177,X3178,X3187)),apply(X3178,esk322_4(X3176,X3177,X3178,X3187))),X3177)
| ~ in(X3187,esk319_3(X3176,X3177,X3178))
| esk312_3(X3176,X3177,X3178) = esk313_3(X3176,X3177,X3178)
| ~ relation(X3177)
| ~ relation(X3178)
| ~ function(X3178) )
& ( ~ in(X3192,cartesian_product2(X3176,X3176))
| X3192 != X3191
| X3191 != ordered_pair(X3193,X3194)
| ~ in(ordered_pair(apply(X3178,X3193),apply(X3178,X3194)),X3177)
| in(X3191,esk319_3(X3176,X3177,X3178))
| esk312_3(X3176,X3177,X3178) = esk313_3(X3176,X3177,X3178)
| ~ relation(X3177)
| ~ relation(X3178)
| ~ function(X3178) )
& ( in(esk320_4(X3176,X3177,X3178,X3187),cartesian_product2(X3176,X3176))
| ~ in(X3187,esk319_3(X3176,X3177,X3178))
| esk313_3(X3176,X3177,X3178) = ordered_pair(esk315_3(X3176,X3177,X3178),esk316_3(X3176,X3177,X3178))
| ~ relation(X3177)
| ~ relation(X3178)
| ~ function(X3178) )
& ( esk320_4(X3176,X3177,X3178,X3187) = X3187
| ~ in(X3187,esk319_3(X3176,X3177,X3178))
| esk313_3(X3176,X3177,X3178) = ordered_pair(esk315_3(X3176,X3177,X3178),esk316_3(X3176,X3177,X3178))
| ~ relation(X3177)
| ~ relation(X3178)
| ~ function(X3178) )
& ( X3187 = ordered_pair(esk321_4(X3176,X3177,X3178,X3187),esk322_4(X3176,X3177,X3178,X3187))
| ~ in(X3187,esk319_3(X3176,X3177,X3178))
| esk313_3(X3176,X3177,X3178) = ordered_pair(esk315_3(X3176,X3177,X3178),esk316_3(X3176,X3177,X3178))
| ~ relation(X3177)
| ~ relation(X3178)
| ~ function(X3178) )
& ( in(ordered_pair(apply(X3178,esk321_4(X3176,X3177,X3178,X3187)),apply(X3178,esk322_4(X3176,X3177,X3178,X3187))),X3177)
| ~ in(X3187,esk319_3(X3176,X3177,X3178))
| esk313_3(X3176,X3177,X3178) = ordered_pair(esk315_3(X3176,X3177,X3178),esk316_3(X3176,X3177,X3178))
| ~ relation(X3177)
| ~ relation(X3178)
| ~ function(X3178) )
& ( ~ in(X3192,cartesian_product2(X3176,X3176))
| X3192 != X3191
| X3191 != ordered_pair(X3193,X3194)
| ~ in(ordered_pair(apply(X3178,X3193),apply(X3178,X3194)),X3177)
| in(X3191,esk319_3(X3176,X3177,X3178))
| esk313_3(X3176,X3177,X3178) = ordered_pair(esk315_3(X3176,X3177,X3178),esk316_3(X3176,X3177,X3178))
| ~ relation(X3177)
| ~ relation(X3178)
| ~ function(X3178) )
& ( in(esk320_4(X3176,X3177,X3178,X3187),cartesian_product2(X3176,X3176))
| ~ in(X3187,esk319_3(X3176,X3177,X3178))
| in(ordered_pair(apply(X3178,esk315_3(X3176,X3177,X3178)),apply(X3178,esk316_3(X3176,X3177,X3178))),X3177)
| ~ relation(X3177)
| ~ relation(X3178)
| ~ function(X3178) )
& ( esk320_4(X3176,X3177,X3178,X3187) = X3187
| ~ in(X3187,esk319_3(X3176,X3177,X3178))
| in(ordered_pair(apply(X3178,esk315_3(X3176,X3177,X3178)),apply(X3178,esk316_3(X3176,X3177,X3178))),X3177)
| ~ relation(X3177)
| ~ relation(X3178)
| ~ function(X3178) )
& ( X3187 = ordered_pair(esk321_4(X3176,X3177,X3178,X3187),esk322_4(X3176,X3177,X3178,X3187))
| ~ in(X3187,esk319_3(X3176,X3177,X3178))
| in(ordered_pair(apply(X3178,esk315_3(X3176,X3177,X3178)),apply(X3178,esk316_3(X3176,X3177,X3178))),X3177)
| ~ relation(X3177)
| ~ relation(X3178)
| ~ function(X3178) )
& ( in(ordered_pair(apply(X3178,esk321_4(X3176,X3177,X3178,X3187)),apply(X3178,esk322_4(X3176,X3177,X3178,X3187))),X3177)
| ~ in(X3187,esk319_3(X3176,X3177,X3178))
| in(ordered_pair(apply(X3178,esk315_3(X3176,X3177,X3178)),apply(X3178,esk316_3(X3176,X3177,X3178))),X3177)
| ~ relation(X3177)
| ~ relation(X3178)
| ~ function(X3178) )
& ( ~ in(X3192,cartesian_product2(X3176,X3176))
| X3192 != X3191
| X3191 != ordered_pair(X3193,X3194)
| ~ in(ordered_pair(apply(X3178,X3193),apply(X3178,X3194)),X3177)
| in(X3191,esk319_3(X3176,X3177,X3178))
| in(ordered_pair(apply(X3178,esk315_3(X3176,X3177,X3178)),apply(X3178,esk316_3(X3176,X3177,X3178))),X3177)
| ~ relation(X3177)
| ~ relation(X3178)
| ~ function(X3178) )
& ( in(esk320_4(X3176,X3177,X3178,X3187),cartesian_product2(X3176,X3176))
| ~ in(X3187,esk319_3(X3176,X3177,X3178))
| esk312_3(X3176,X3177,X3178) = esk314_3(X3176,X3177,X3178)
| ~ relation(X3177)
| ~ relation(X3178)
| ~ function(X3178) )
& ( esk320_4(X3176,X3177,X3178,X3187) = X3187
| ~ in(X3187,esk319_3(X3176,X3177,X3178))
| esk312_3(X3176,X3177,X3178) = esk314_3(X3176,X3177,X3178)
| ~ relation(X3177)
| ~ relation(X3178)
| ~ function(X3178) )
& ( X3187 = ordered_pair(esk321_4(X3176,X3177,X3178,X3187),esk322_4(X3176,X3177,X3178,X3187))
| ~ in(X3187,esk319_3(X3176,X3177,X3178))
| esk312_3(X3176,X3177,X3178) = esk314_3(X3176,X3177,X3178)
| ~ relation(X3177)
| ~ relation(X3178)
| ~ function(X3178) )
& ( in(ordered_pair(apply(X3178,esk321_4(X3176,X3177,X3178,X3187)),apply(X3178,esk322_4(X3176,X3177,X3178,X3187))),X3177)
| ~ in(X3187,esk319_3(X3176,X3177,X3178))
| esk312_3(X3176,X3177,X3178) = esk314_3(X3176,X3177,X3178)
| ~ relation(X3177)
| ~ relation(X3178)
| ~ function(X3178) )
& ( ~ in(X3192,cartesian_product2(X3176,X3176))
| X3192 != X3191
| X3191 != ordered_pair(X3193,X3194)
| ~ in(ordered_pair(apply(X3178,X3193),apply(X3178,X3194)),X3177)
| in(X3191,esk319_3(X3176,X3177,X3178))
| esk312_3(X3176,X3177,X3178) = esk314_3(X3176,X3177,X3178)
| ~ relation(X3177)
| ~ relation(X3178)
| ~ function(X3178) )
& ( in(esk320_4(X3176,X3177,X3178,X3187),cartesian_product2(X3176,X3176))
| ~ in(X3187,esk319_3(X3176,X3177,X3178))
| esk314_3(X3176,X3177,X3178) = ordered_pair(esk317_3(X3176,X3177,X3178),esk318_3(X3176,X3177,X3178))
| ~ relation(X3177)
| ~ relation(X3178)
| ~ function(X3178) )
& ( esk320_4(X3176,X3177,X3178,X3187) = X3187
| ~ in(X3187,esk319_3(X3176,X3177,X3178))
| esk314_3(X3176,X3177,X3178) = ordered_pair(esk317_3(X3176,X3177,X3178),esk318_3(X3176,X3177,X3178))
| ~ relation(X3177)
| ~ relation(X3178)
| ~ function(X3178) )
& ( X3187 = ordered_pair(esk321_4(X3176,X3177,X3178,X3187),esk322_4(X3176,X3177,X3178,X3187))
| ~ in(X3187,esk319_3(X3176,X3177,X3178))
| esk314_3(X3176,X3177,X3178) = ordered_pair(esk317_3(X3176,X3177,X3178),esk318_3(X3176,X3177,X3178))
| ~ relation(X3177)
| ~ relation(X3178)
| ~ function(X3178) )
& ( in(ordered_pair(apply(X3178,esk321_4(X3176,X3177,X3178,X3187)),apply(X3178,esk322_4(X3176,X3177,X3178,X3187))),X3177)
| ~ in(X3187,esk319_3(X3176,X3177,X3178))
| esk314_3(X3176,X3177,X3178) = ordered_pair(esk317_3(X3176,X3177,X3178),esk318_3(X3176,X3177,X3178))
| ~ relation(X3177)
| ~ relation(X3178)
| ~ function(X3178) )
& ( ~ in(X3192,cartesian_product2(X3176,X3176))
| X3192 != X3191
| X3191 != ordered_pair(X3193,X3194)
| ~ in(ordered_pair(apply(X3178,X3193),apply(X3178,X3194)),X3177)
| in(X3191,esk319_3(X3176,X3177,X3178))
| esk314_3(X3176,X3177,X3178) = ordered_pair(esk317_3(X3176,X3177,X3178),esk318_3(X3176,X3177,X3178))
| ~ relation(X3177)
| ~ relation(X3178)
| ~ function(X3178) )
& ( in(esk320_4(X3176,X3177,X3178,X3187),cartesian_product2(X3176,X3176))
| ~ in(X3187,esk319_3(X3176,X3177,X3178))
| in(ordered_pair(apply(X3178,esk317_3(X3176,X3177,X3178)),apply(X3178,esk318_3(X3176,X3177,X3178))),X3177)
| ~ relation(X3177)
| ~ relation(X3178)
| ~ function(X3178) )
& ( esk320_4(X3176,X3177,X3178,X3187) = X3187
| ~ in(X3187,esk319_3(X3176,X3177,X3178))
| in(ordered_pair(apply(X3178,esk317_3(X3176,X3177,X3178)),apply(X3178,esk318_3(X3176,X3177,X3178))),X3177)
| ~ relation(X3177)
| ~ relation(X3178)
| ~ function(X3178) )
& ( X3187 = ordered_pair(esk321_4(X3176,X3177,X3178,X3187),esk322_4(X3176,X3177,X3178,X3187))
| ~ in(X3187,esk319_3(X3176,X3177,X3178))
| in(ordered_pair(apply(X3178,esk317_3(X3176,X3177,X3178)),apply(X3178,esk318_3(X3176,X3177,X3178))),X3177)
| ~ relation(X3177)
| ~ relation(X3178)
| ~ function(X3178) )
& ( in(ordered_pair(apply(X3178,esk321_4(X3176,X3177,X3178,X3187)),apply(X3178,esk322_4(X3176,X3177,X3178,X3187))),X3177)
| ~ in(X3187,esk319_3(X3176,X3177,X3178))
| in(ordered_pair(apply(X3178,esk317_3(X3176,X3177,X3178)),apply(X3178,esk318_3(X3176,X3177,X3178))),X3177)
| ~ relation(X3177)
| ~ relation(X3178)
| ~ function(X3178) )
& ( ~ in(X3192,cartesian_product2(X3176,X3176))
| X3192 != X3191
| X3191 != ordered_pair(X3193,X3194)
| ~ in(ordered_pair(apply(X3178,X3193),apply(X3178,X3194)),X3177)
| in(X3191,esk319_3(X3176,X3177,X3178))
| in(ordered_pair(apply(X3178,esk317_3(X3176,X3177,X3178)),apply(X3178,esk318_3(X3176,X3177,X3178))),X3177)
| ~ relation(X3177)
| ~ relation(X3178)
| ~ function(X3178) )
& ( in(esk320_4(X3176,X3177,X3178,X3187),cartesian_product2(X3176,X3176))
| ~ in(X3187,esk319_3(X3176,X3177,X3178))
| esk313_3(X3176,X3177,X3178) != esk314_3(X3176,X3177,X3178)
| ~ relation(X3177)
| ~ relation(X3178)
| ~ function(X3178) )
& ( esk320_4(X3176,X3177,X3178,X3187) = X3187
| ~ in(X3187,esk319_3(X3176,X3177,X3178))
| esk313_3(X3176,X3177,X3178) != esk314_3(X3176,X3177,X3178)
| ~ relation(X3177)
| ~ relation(X3178)
| ~ function(X3178) )
& ( X3187 = ordered_pair(esk321_4(X3176,X3177,X3178,X3187),esk322_4(X3176,X3177,X3178,X3187))
| ~ in(X3187,esk319_3(X3176,X3177,X3178))
| esk313_3(X3176,X3177,X3178) != esk314_3(X3176,X3177,X3178)
| ~ relation(X3177)
| ~ relation(X3178)
| ~ function(X3178) )
& ( in(ordered_pair(apply(X3178,esk321_4(X3176,X3177,X3178,X3187)),apply(X3178,esk322_4(X3176,X3177,X3178,X3187))),X3177)
| ~ in(X3187,esk319_3(X3176,X3177,X3178))
| esk313_3(X3176,X3177,X3178) != esk314_3(X3176,X3177,X3178)
| ~ relation(X3177)
| ~ relation(X3178)
| ~ function(X3178) )
& ( ~ in(X3192,cartesian_product2(X3176,X3176))
| X3192 != X3191
| X3191 != ordered_pair(X3193,X3194)
| ~ in(ordered_pair(apply(X3178,X3193),apply(X3178,X3194)),X3177)
| in(X3191,esk319_3(X3176,X3177,X3178))
| esk313_3(X3176,X3177,X3178) != esk314_3(X3176,X3177,X3178)
| ~ relation(X3177)
| ~ relation(X3178)
| ~ function(X3178) ) ),
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)],[s1_tarski__e6_21__wellord2__1])])])])])]) ).
fof(i_0_685,plain,
! [X3116,X3117,X3123,X3126,X3127,X3129,X3133,X3134,X3135,X3136,X3137] :
( ( in(esk290_4(X3116,X3117,X3127,X3129),cartesian_product2(complements_of_subsets(the_carrier(X3116),X3117),X3127))
| ~ in(X3129,esk289_3(X3116,X3117,X3127))
| esk282_2(X3116,X3117) = esk283_2(X3116,X3117)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( esk290_4(X3116,X3117,X3127,X3129) = X3129
| ~ in(X3129,esk289_3(X3116,X3117,X3127))
| esk282_2(X3116,X3117) = esk283_2(X3116,X3117)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( ordered_pair(esk291_4(X3116,X3117,X3127,X3129),esk292_4(X3116,X3117,X3127,X3129)) = X3129
| ~ in(X3129,esk289_3(X3116,X3117,X3127))
| esk282_2(X3116,X3117) = esk283_2(X3116,X3117)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( in(esk291_4(X3116,X3117,X3127,X3129),complements_of_subsets(the_carrier(X3116),X3117))
| ~ in(X3129,esk289_3(X3116,X3117,X3127))
| esk282_2(X3116,X3117) = esk283_2(X3116,X3117)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( ~ element(X3133,powerset(the_carrier(X3116)))
| X3133 != esk291_4(X3116,X3117,X3127,X3129)
| esk292_4(X3116,X3117,X3127,X3129) = subset_complement(the_carrier(X3116),X3133)
| ~ in(X3129,esk289_3(X3116,X3117,X3127))
| esk282_2(X3116,X3117) = esk283_2(X3116,X3117)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( element(esk293_6(X3116,X3117,X3127,X3134,X3136,X3137),powerset(the_carrier(X3116)))
| ordered_pair(X3136,X3137) != X3134
| ~ in(X3136,complements_of_subsets(the_carrier(X3116),X3117))
| ~ in(X3135,cartesian_product2(complements_of_subsets(the_carrier(X3116),X3117),X3127))
| X3135 != X3134
| in(X3134,esk289_3(X3116,X3117,X3127))
| esk282_2(X3116,X3117) = esk283_2(X3116,X3117)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( esk293_6(X3116,X3117,X3127,X3134,X3136,X3137) = X3136
| ordered_pair(X3136,X3137) != X3134
| ~ in(X3136,complements_of_subsets(the_carrier(X3116),X3117))
| ~ in(X3135,cartesian_product2(complements_of_subsets(the_carrier(X3116),X3117),X3127))
| X3135 != X3134
| in(X3134,esk289_3(X3116,X3117,X3127))
| esk282_2(X3116,X3117) = esk283_2(X3116,X3117)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( X3137 != subset_complement(the_carrier(X3116),esk293_6(X3116,X3117,X3127,X3134,X3136,X3137))
| ordered_pair(X3136,X3137) != X3134
| ~ in(X3136,complements_of_subsets(the_carrier(X3116),X3117))
| ~ in(X3135,cartesian_product2(complements_of_subsets(the_carrier(X3116),X3117),X3127))
| X3135 != X3134
| in(X3134,esk289_3(X3116,X3117,X3127))
| esk282_2(X3116,X3117) = esk283_2(X3116,X3117)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( in(esk290_4(X3116,X3117,X3127,X3129),cartesian_product2(complements_of_subsets(the_carrier(X3116),X3117),X3127))
| ~ in(X3129,esk289_3(X3116,X3117,X3127))
| ordered_pair(esk285_2(X3116,X3117),esk286_2(X3116,X3117)) = esk283_2(X3116,X3117)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( esk290_4(X3116,X3117,X3127,X3129) = X3129
| ~ in(X3129,esk289_3(X3116,X3117,X3127))
| ordered_pair(esk285_2(X3116,X3117),esk286_2(X3116,X3117)) = esk283_2(X3116,X3117)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( ordered_pair(esk291_4(X3116,X3117,X3127,X3129),esk292_4(X3116,X3117,X3127,X3129)) = X3129
| ~ in(X3129,esk289_3(X3116,X3117,X3127))
| ordered_pair(esk285_2(X3116,X3117),esk286_2(X3116,X3117)) = esk283_2(X3116,X3117)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( in(esk291_4(X3116,X3117,X3127,X3129),complements_of_subsets(the_carrier(X3116),X3117))
| ~ in(X3129,esk289_3(X3116,X3117,X3127))
| ordered_pair(esk285_2(X3116,X3117),esk286_2(X3116,X3117)) = esk283_2(X3116,X3117)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( ~ element(X3133,powerset(the_carrier(X3116)))
| X3133 != esk291_4(X3116,X3117,X3127,X3129)
| esk292_4(X3116,X3117,X3127,X3129) = subset_complement(the_carrier(X3116),X3133)
| ~ in(X3129,esk289_3(X3116,X3117,X3127))
| ordered_pair(esk285_2(X3116,X3117),esk286_2(X3116,X3117)) = esk283_2(X3116,X3117)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( element(esk293_6(X3116,X3117,X3127,X3134,X3136,X3137),powerset(the_carrier(X3116)))
| ordered_pair(X3136,X3137) != X3134
| ~ in(X3136,complements_of_subsets(the_carrier(X3116),X3117))
| ~ in(X3135,cartesian_product2(complements_of_subsets(the_carrier(X3116),X3117),X3127))
| X3135 != X3134
| in(X3134,esk289_3(X3116,X3117,X3127))
| ordered_pair(esk285_2(X3116,X3117),esk286_2(X3116,X3117)) = esk283_2(X3116,X3117)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( esk293_6(X3116,X3117,X3127,X3134,X3136,X3137) = X3136
| ordered_pair(X3136,X3137) != X3134
| ~ in(X3136,complements_of_subsets(the_carrier(X3116),X3117))
| ~ in(X3135,cartesian_product2(complements_of_subsets(the_carrier(X3116),X3117),X3127))
| X3135 != X3134
| in(X3134,esk289_3(X3116,X3117,X3127))
| ordered_pair(esk285_2(X3116,X3117),esk286_2(X3116,X3117)) = esk283_2(X3116,X3117)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( X3137 != subset_complement(the_carrier(X3116),esk293_6(X3116,X3117,X3127,X3134,X3136,X3137))
| ordered_pair(X3136,X3137) != X3134
| ~ in(X3136,complements_of_subsets(the_carrier(X3116),X3117))
| ~ in(X3135,cartesian_product2(complements_of_subsets(the_carrier(X3116),X3117),X3127))
| X3135 != X3134
| in(X3134,esk289_3(X3116,X3117,X3127))
| ordered_pair(esk285_2(X3116,X3117),esk286_2(X3116,X3117)) = esk283_2(X3116,X3117)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( in(esk290_4(X3116,X3117,X3127,X3129),cartesian_product2(complements_of_subsets(the_carrier(X3116),X3117),X3127))
| ~ in(X3129,esk289_3(X3116,X3117,X3127))
| in(esk285_2(X3116,X3117),complements_of_subsets(the_carrier(X3116),X3117))
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( esk290_4(X3116,X3117,X3127,X3129) = X3129
| ~ in(X3129,esk289_3(X3116,X3117,X3127))
| in(esk285_2(X3116,X3117),complements_of_subsets(the_carrier(X3116),X3117))
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( ordered_pair(esk291_4(X3116,X3117,X3127,X3129),esk292_4(X3116,X3117,X3127,X3129)) = X3129
| ~ in(X3129,esk289_3(X3116,X3117,X3127))
| in(esk285_2(X3116,X3117),complements_of_subsets(the_carrier(X3116),X3117))
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( in(esk291_4(X3116,X3117,X3127,X3129),complements_of_subsets(the_carrier(X3116),X3117))
| ~ in(X3129,esk289_3(X3116,X3117,X3127))
| in(esk285_2(X3116,X3117),complements_of_subsets(the_carrier(X3116),X3117))
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( ~ element(X3133,powerset(the_carrier(X3116)))
| X3133 != esk291_4(X3116,X3117,X3127,X3129)
| esk292_4(X3116,X3117,X3127,X3129) = subset_complement(the_carrier(X3116),X3133)
| ~ in(X3129,esk289_3(X3116,X3117,X3127))
| in(esk285_2(X3116,X3117),complements_of_subsets(the_carrier(X3116),X3117))
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( element(esk293_6(X3116,X3117,X3127,X3134,X3136,X3137),powerset(the_carrier(X3116)))
| ordered_pair(X3136,X3137) != X3134
| ~ in(X3136,complements_of_subsets(the_carrier(X3116),X3117))
| ~ in(X3135,cartesian_product2(complements_of_subsets(the_carrier(X3116),X3117),X3127))
| X3135 != X3134
| in(X3134,esk289_3(X3116,X3117,X3127))
| in(esk285_2(X3116,X3117),complements_of_subsets(the_carrier(X3116),X3117))
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( esk293_6(X3116,X3117,X3127,X3134,X3136,X3137) = X3136
| ordered_pair(X3136,X3137) != X3134
| ~ in(X3136,complements_of_subsets(the_carrier(X3116),X3117))
| ~ in(X3135,cartesian_product2(complements_of_subsets(the_carrier(X3116),X3117),X3127))
| X3135 != X3134
| in(X3134,esk289_3(X3116,X3117,X3127))
| in(esk285_2(X3116,X3117),complements_of_subsets(the_carrier(X3116),X3117))
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( X3137 != subset_complement(the_carrier(X3116),esk293_6(X3116,X3117,X3127,X3134,X3136,X3137))
| ordered_pair(X3136,X3137) != X3134
| ~ in(X3136,complements_of_subsets(the_carrier(X3116),X3117))
| ~ in(X3135,cartesian_product2(complements_of_subsets(the_carrier(X3116),X3117),X3127))
| X3135 != X3134
| in(X3134,esk289_3(X3116,X3117,X3127))
| in(esk285_2(X3116,X3117),complements_of_subsets(the_carrier(X3116),X3117))
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( in(esk290_4(X3116,X3117,X3127,X3129),cartesian_product2(complements_of_subsets(the_carrier(X3116),X3117),X3127))
| ~ in(X3129,esk289_3(X3116,X3117,X3127))
| ~ element(X3123,powerset(the_carrier(X3116)))
| X3123 != esk285_2(X3116,X3117)
| esk286_2(X3116,X3117) = subset_complement(the_carrier(X3116),X3123)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( esk290_4(X3116,X3117,X3127,X3129) = X3129
| ~ in(X3129,esk289_3(X3116,X3117,X3127))
| ~ element(X3123,powerset(the_carrier(X3116)))
| X3123 != esk285_2(X3116,X3117)
| esk286_2(X3116,X3117) = subset_complement(the_carrier(X3116),X3123)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( ordered_pair(esk291_4(X3116,X3117,X3127,X3129),esk292_4(X3116,X3117,X3127,X3129)) = X3129
| ~ in(X3129,esk289_3(X3116,X3117,X3127))
| ~ element(X3123,powerset(the_carrier(X3116)))
| X3123 != esk285_2(X3116,X3117)
| esk286_2(X3116,X3117) = subset_complement(the_carrier(X3116),X3123)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( in(esk291_4(X3116,X3117,X3127,X3129),complements_of_subsets(the_carrier(X3116),X3117))
| ~ in(X3129,esk289_3(X3116,X3117,X3127))
| ~ element(X3123,powerset(the_carrier(X3116)))
| X3123 != esk285_2(X3116,X3117)
| esk286_2(X3116,X3117) = subset_complement(the_carrier(X3116),X3123)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( ~ element(X3133,powerset(the_carrier(X3116)))
| X3133 != esk291_4(X3116,X3117,X3127,X3129)
| esk292_4(X3116,X3117,X3127,X3129) = subset_complement(the_carrier(X3116),X3133)
| ~ in(X3129,esk289_3(X3116,X3117,X3127))
| ~ element(X3123,powerset(the_carrier(X3116)))
| X3123 != esk285_2(X3116,X3117)
| esk286_2(X3116,X3117) = subset_complement(the_carrier(X3116),X3123)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( element(esk293_6(X3116,X3117,X3127,X3134,X3136,X3137),powerset(the_carrier(X3116)))
| ordered_pair(X3136,X3137) != X3134
| ~ in(X3136,complements_of_subsets(the_carrier(X3116),X3117))
| ~ in(X3135,cartesian_product2(complements_of_subsets(the_carrier(X3116),X3117),X3127))
| X3135 != X3134
| in(X3134,esk289_3(X3116,X3117,X3127))
| ~ element(X3123,powerset(the_carrier(X3116)))
| X3123 != esk285_2(X3116,X3117)
| esk286_2(X3116,X3117) = subset_complement(the_carrier(X3116),X3123)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( esk293_6(X3116,X3117,X3127,X3134,X3136,X3137) = X3136
| ordered_pair(X3136,X3137) != X3134
| ~ in(X3136,complements_of_subsets(the_carrier(X3116),X3117))
| ~ in(X3135,cartesian_product2(complements_of_subsets(the_carrier(X3116),X3117),X3127))
| X3135 != X3134
| in(X3134,esk289_3(X3116,X3117,X3127))
| ~ element(X3123,powerset(the_carrier(X3116)))
| X3123 != esk285_2(X3116,X3117)
| esk286_2(X3116,X3117) = subset_complement(the_carrier(X3116),X3123)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( X3137 != subset_complement(the_carrier(X3116),esk293_6(X3116,X3117,X3127,X3134,X3136,X3137))
| ordered_pair(X3136,X3137) != X3134
| ~ in(X3136,complements_of_subsets(the_carrier(X3116),X3117))
| ~ in(X3135,cartesian_product2(complements_of_subsets(the_carrier(X3116),X3117),X3127))
| X3135 != X3134
| in(X3134,esk289_3(X3116,X3117,X3127))
| ~ element(X3123,powerset(the_carrier(X3116)))
| X3123 != esk285_2(X3116,X3117)
| esk286_2(X3116,X3117) = subset_complement(the_carrier(X3116),X3123)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( in(esk290_4(X3116,X3117,X3127,X3129),cartesian_product2(complements_of_subsets(the_carrier(X3116),X3117),X3127))
| ~ in(X3129,esk289_3(X3116,X3117,X3127))
| esk282_2(X3116,X3117) = esk284_2(X3116,X3117)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( esk290_4(X3116,X3117,X3127,X3129) = X3129
| ~ in(X3129,esk289_3(X3116,X3117,X3127))
| esk282_2(X3116,X3117) = esk284_2(X3116,X3117)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( ordered_pair(esk291_4(X3116,X3117,X3127,X3129),esk292_4(X3116,X3117,X3127,X3129)) = X3129
| ~ in(X3129,esk289_3(X3116,X3117,X3127))
| esk282_2(X3116,X3117) = esk284_2(X3116,X3117)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( in(esk291_4(X3116,X3117,X3127,X3129),complements_of_subsets(the_carrier(X3116),X3117))
| ~ in(X3129,esk289_3(X3116,X3117,X3127))
| esk282_2(X3116,X3117) = esk284_2(X3116,X3117)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( ~ element(X3133,powerset(the_carrier(X3116)))
| X3133 != esk291_4(X3116,X3117,X3127,X3129)
| esk292_4(X3116,X3117,X3127,X3129) = subset_complement(the_carrier(X3116),X3133)
| ~ in(X3129,esk289_3(X3116,X3117,X3127))
| esk282_2(X3116,X3117) = esk284_2(X3116,X3117)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( element(esk293_6(X3116,X3117,X3127,X3134,X3136,X3137),powerset(the_carrier(X3116)))
| ordered_pair(X3136,X3137) != X3134
| ~ in(X3136,complements_of_subsets(the_carrier(X3116),X3117))
| ~ in(X3135,cartesian_product2(complements_of_subsets(the_carrier(X3116),X3117),X3127))
| X3135 != X3134
| in(X3134,esk289_3(X3116,X3117,X3127))
| esk282_2(X3116,X3117) = esk284_2(X3116,X3117)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( esk293_6(X3116,X3117,X3127,X3134,X3136,X3137) = X3136
| ordered_pair(X3136,X3137) != X3134
| ~ in(X3136,complements_of_subsets(the_carrier(X3116),X3117))
| ~ in(X3135,cartesian_product2(complements_of_subsets(the_carrier(X3116),X3117),X3127))
| X3135 != X3134
| in(X3134,esk289_3(X3116,X3117,X3127))
| esk282_2(X3116,X3117) = esk284_2(X3116,X3117)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( X3137 != subset_complement(the_carrier(X3116),esk293_6(X3116,X3117,X3127,X3134,X3136,X3137))
| ordered_pair(X3136,X3137) != X3134
| ~ in(X3136,complements_of_subsets(the_carrier(X3116),X3117))
| ~ in(X3135,cartesian_product2(complements_of_subsets(the_carrier(X3116),X3117),X3127))
| X3135 != X3134
| in(X3134,esk289_3(X3116,X3117,X3127))
| esk282_2(X3116,X3117) = esk284_2(X3116,X3117)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( in(esk290_4(X3116,X3117,X3127,X3129),cartesian_product2(complements_of_subsets(the_carrier(X3116),X3117),X3127))
| ~ in(X3129,esk289_3(X3116,X3117,X3127))
| ordered_pair(esk287_2(X3116,X3117),esk288_2(X3116,X3117)) = esk284_2(X3116,X3117)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( esk290_4(X3116,X3117,X3127,X3129) = X3129
| ~ in(X3129,esk289_3(X3116,X3117,X3127))
| ordered_pair(esk287_2(X3116,X3117),esk288_2(X3116,X3117)) = esk284_2(X3116,X3117)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( ordered_pair(esk291_4(X3116,X3117,X3127,X3129),esk292_4(X3116,X3117,X3127,X3129)) = X3129
| ~ in(X3129,esk289_3(X3116,X3117,X3127))
| ordered_pair(esk287_2(X3116,X3117),esk288_2(X3116,X3117)) = esk284_2(X3116,X3117)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( in(esk291_4(X3116,X3117,X3127,X3129),complements_of_subsets(the_carrier(X3116),X3117))
| ~ in(X3129,esk289_3(X3116,X3117,X3127))
| ordered_pair(esk287_2(X3116,X3117),esk288_2(X3116,X3117)) = esk284_2(X3116,X3117)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( ~ element(X3133,powerset(the_carrier(X3116)))
| X3133 != esk291_4(X3116,X3117,X3127,X3129)
| esk292_4(X3116,X3117,X3127,X3129) = subset_complement(the_carrier(X3116),X3133)
| ~ in(X3129,esk289_3(X3116,X3117,X3127))
| ordered_pair(esk287_2(X3116,X3117),esk288_2(X3116,X3117)) = esk284_2(X3116,X3117)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( element(esk293_6(X3116,X3117,X3127,X3134,X3136,X3137),powerset(the_carrier(X3116)))
| ordered_pair(X3136,X3137) != X3134
| ~ in(X3136,complements_of_subsets(the_carrier(X3116),X3117))
| ~ in(X3135,cartesian_product2(complements_of_subsets(the_carrier(X3116),X3117),X3127))
| X3135 != X3134
| in(X3134,esk289_3(X3116,X3117,X3127))
| ordered_pair(esk287_2(X3116,X3117),esk288_2(X3116,X3117)) = esk284_2(X3116,X3117)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( esk293_6(X3116,X3117,X3127,X3134,X3136,X3137) = X3136
| ordered_pair(X3136,X3137) != X3134
| ~ in(X3136,complements_of_subsets(the_carrier(X3116),X3117))
| ~ in(X3135,cartesian_product2(complements_of_subsets(the_carrier(X3116),X3117),X3127))
| X3135 != X3134
| in(X3134,esk289_3(X3116,X3117,X3127))
| ordered_pair(esk287_2(X3116,X3117),esk288_2(X3116,X3117)) = esk284_2(X3116,X3117)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( X3137 != subset_complement(the_carrier(X3116),esk293_6(X3116,X3117,X3127,X3134,X3136,X3137))
| ordered_pair(X3136,X3137) != X3134
| ~ in(X3136,complements_of_subsets(the_carrier(X3116),X3117))
| ~ in(X3135,cartesian_product2(complements_of_subsets(the_carrier(X3116),X3117),X3127))
| X3135 != X3134
| in(X3134,esk289_3(X3116,X3117,X3127))
| ordered_pair(esk287_2(X3116,X3117),esk288_2(X3116,X3117)) = esk284_2(X3116,X3117)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( in(esk290_4(X3116,X3117,X3127,X3129),cartesian_product2(complements_of_subsets(the_carrier(X3116),X3117),X3127))
| ~ in(X3129,esk289_3(X3116,X3117,X3127))
| in(esk287_2(X3116,X3117),complements_of_subsets(the_carrier(X3116),X3117))
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( esk290_4(X3116,X3117,X3127,X3129) = X3129
| ~ in(X3129,esk289_3(X3116,X3117,X3127))
| in(esk287_2(X3116,X3117),complements_of_subsets(the_carrier(X3116),X3117))
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( ordered_pair(esk291_4(X3116,X3117,X3127,X3129),esk292_4(X3116,X3117,X3127,X3129)) = X3129
| ~ in(X3129,esk289_3(X3116,X3117,X3127))
| in(esk287_2(X3116,X3117),complements_of_subsets(the_carrier(X3116),X3117))
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( in(esk291_4(X3116,X3117,X3127,X3129),complements_of_subsets(the_carrier(X3116),X3117))
| ~ in(X3129,esk289_3(X3116,X3117,X3127))
| in(esk287_2(X3116,X3117),complements_of_subsets(the_carrier(X3116),X3117))
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( ~ element(X3133,powerset(the_carrier(X3116)))
| X3133 != esk291_4(X3116,X3117,X3127,X3129)
| esk292_4(X3116,X3117,X3127,X3129) = subset_complement(the_carrier(X3116),X3133)
| ~ in(X3129,esk289_3(X3116,X3117,X3127))
| in(esk287_2(X3116,X3117),complements_of_subsets(the_carrier(X3116),X3117))
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( element(esk293_6(X3116,X3117,X3127,X3134,X3136,X3137),powerset(the_carrier(X3116)))
| ordered_pair(X3136,X3137) != X3134
| ~ in(X3136,complements_of_subsets(the_carrier(X3116),X3117))
| ~ in(X3135,cartesian_product2(complements_of_subsets(the_carrier(X3116),X3117),X3127))
| X3135 != X3134
| in(X3134,esk289_3(X3116,X3117,X3127))
| in(esk287_2(X3116,X3117),complements_of_subsets(the_carrier(X3116),X3117))
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( esk293_6(X3116,X3117,X3127,X3134,X3136,X3137) = X3136
| ordered_pair(X3136,X3137) != X3134
| ~ in(X3136,complements_of_subsets(the_carrier(X3116),X3117))
| ~ in(X3135,cartesian_product2(complements_of_subsets(the_carrier(X3116),X3117),X3127))
| X3135 != X3134
| in(X3134,esk289_3(X3116,X3117,X3127))
| in(esk287_2(X3116,X3117),complements_of_subsets(the_carrier(X3116),X3117))
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( X3137 != subset_complement(the_carrier(X3116),esk293_6(X3116,X3117,X3127,X3134,X3136,X3137))
| ordered_pair(X3136,X3137) != X3134
| ~ in(X3136,complements_of_subsets(the_carrier(X3116),X3117))
| ~ in(X3135,cartesian_product2(complements_of_subsets(the_carrier(X3116),X3117),X3127))
| X3135 != X3134
| in(X3134,esk289_3(X3116,X3117,X3127))
| in(esk287_2(X3116,X3117),complements_of_subsets(the_carrier(X3116),X3117))
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( in(esk290_4(X3116,X3117,X3127,X3129),cartesian_product2(complements_of_subsets(the_carrier(X3116),X3117),X3127))
| ~ in(X3129,esk289_3(X3116,X3117,X3127))
| ~ element(X3126,powerset(the_carrier(X3116)))
| X3126 != esk287_2(X3116,X3117)
| esk288_2(X3116,X3117) = subset_complement(the_carrier(X3116),X3126)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( esk290_4(X3116,X3117,X3127,X3129) = X3129
| ~ in(X3129,esk289_3(X3116,X3117,X3127))
| ~ element(X3126,powerset(the_carrier(X3116)))
| X3126 != esk287_2(X3116,X3117)
| esk288_2(X3116,X3117) = subset_complement(the_carrier(X3116),X3126)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( ordered_pair(esk291_4(X3116,X3117,X3127,X3129),esk292_4(X3116,X3117,X3127,X3129)) = X3129
| ~ in(X3129,esk289_3(X3116,X3117,X3127))
| ~ element(X3126,powerset(the_carrier(X3116)))
| X3126 != esk287_2(X3116,X3117)
| esk288_2(X3116,X3117) = subset_complement(the_carrier(X3116),X3126)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( in(esk291_4(X3116,X3117,X3127,X3129),complements_of_subsets(the_carrier(X3116),X3117))
| ~ in(X3129,esk289_3(X3116,X3117,X3127))
| ~ element(X3126,powerset(the_carrier(X3116)))
| X3126 != esk287_2(X3116,X3117)
| esk288_2(X3116,X3117) = subset_complement(the_carrier(X3116),X3126)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( ~ element(X3133,powerset(the_carrier(X3116)))
| X3133 != esk291_4(X3116,X3117,X3127,X3129)
| esk292_4(X3116,X3117,X3127,X3129) = subset_complement(the_carrier(X3116),X3133)
| ~ in(X3129,esk289_3(X3116,X3117,X3127))
| ~ element(X3126,powerset(the_carrier(X3116)))
| X3126 != esk287_2(X3116,X3117)
| esk288_2(X3116,X3117) = subset_complement(the_carrier(X3116),X3126)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( element(esk293_6(X3116,X3117,X3127,X3134,X3136,X3137),powerset(the_carrier(X3116)))
| ordered_pair(X3136,X3137) != X3134
| ~ in(X3136,complements_of_subsets(the_carrier(X3116),X3117))
| ~ in(X3135,cartesian_product2(complements_of_subsets(the_carrier(X3116),X3117),X3127))
| X3135 != X3134
| in(X3134,esk289_3(X3116,X3117,X3127))
| ~ element(X3126,powerset(the_carrier(X3116)))
| X3126 != esk287_2(X3116,X3117)
| esk288_2(X3116,X3117) = subset_complement(the_carrier(X3116),X3126)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( esk293_6(X3116,X3117,X3127,X3134,X3136,X3137) = X3136
| ordered_pair(X3136,X3137) != X3134
| ~ in(X3136,complements_of_subsets(the_carrier(X3116),X3117))
| ~ in(X3135,cartesian_product2(complements_of_subsets(the_carrier(X3116),X3117),X3127))
| X3135 != X3134
| in(X3134,esk289_3(X3116,X3117,X3127))
| ~ element(X3126,powerset(the_carrier(X3116)))
| X3126 != esk287_2(X3116,X3117)
| esk288_2(X3116,X3117) = subset_complement(the_carrier(X3116),X3126)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( X3137 != subset_complement(the_carrier(X3116),esk293_6(X3116,X3117,X3127,X3134,X3136,X3137))
| ordered_pair(X3136,X3137) != X3134
| ~ in(X3136,complements_of_subsets(the_carrier(X3116),X3117))
| ~ in(X3135,cartesian_product2(complements_of_subsets(the_carrier(X3116),X3117),X3127))
| X3135 != X3134
| in(X3134,esk289_3(X3116,X3117,X3127))
| ~ element(X3126,powerset(the_carrier(X3116)))
| X3126 != esk287_2(X3116,X3117)
| esk288_2(X3116,X3117) = subset_complement(the_carrier(X3116),X3126)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( in(esk290_4(X3116,X3117,X3127,X3129),cartesian_product2(complements_of_subsets(the_carrier(X3116),X3117),X3127))
| ~ in(X3129,esk289_3(X3116,X3117,X3127))
| esk283_2(X3116,X3117) != esk284_2(X3116,X3117)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( esk290_4(X3116,X3117,X3127,X3129) = X3129
| ~ in(X3129,esk289_3(X3116,X3117,X3127))
| esk283_2(X3116,X3117) != esk284_2(X3116,X3117)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( ordered_pair(esk291_4(X3116,X3117,X3127,X3129),esk292_4(X3116,X3117,X3127,X3129)) = X3129
| ~ in(X3129,esk289_3(X3116,X3117,X3127))
| esk283_2(X3116,X3117) != esk284_2(X3116,X3117)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( in(esk291_4(X3116,X3117,X3127,X3129),complements_of_subsets(the_carrier(X3116),X3117))
| ~ in(X3129,esk289_3(X3116,X3117,X3127))
| esk283_2(X3116,X3117) != esk284_2(X3116,X3117)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( ~ element(X3133,powerset(the_carrier(X3116)))
| X3133 != esk291_4(X3116,X3117,X3127,X3129)
| esk292_4(X3116,X3117,X3127,X3129) = subset_complement(the_carrier(X3116),X3133)
| ~ in(X3129,esk289_3(X3116,X3117,X3127))
| esk283_2(X3116,X3117) != esk284_2(X3116,X3117)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( element(esk293_6(X3116,X3117,X3127,X3134,X3136,X3137),powerset(the_carrier(X3116)))
| ordered_pair(X3136,X3137) != X3134
| ~ in(X3136,complements_of_subsets(the_carrier(X3116),X3117))
| ~ in(X3135,cartesian_product2(complements_of_subsets(the_carrier(X3116),X3117),X3127))
| X3135 != X3134
| in(X3134,esk289_3(X3116,X3117,X3127))
| esk283_2(X3116,X3117) != esk284_2(X3116,X3117)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( esk293_6(X3116,X3117,X3127,X3134,X3136,X3137) = X3136
| ordered_pair(X3136,X3137) != X3134
| ~ in(X3136,complements_of_subsets(the_carrier(X3116),X3117))
| ~ in(X3135,cartesian_product2(complements_of_subsets(the_carrier(X3116),X3117),X3127))
| X3135 != X3134
| in(X3134,esk289_3(X3116,X3117,X3127))
| esk283_2(X3116,X3117) != esk284_2(X3116,X3117)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) )
& ( X3137 != subset_complement(the_carrier(X3116),esk293_6(X3116,X3117,X3127,X3134,X3136,X3137))
| ordered_pair(X3136,X3137) != X3134
| ~ in(X3136,complements_of_subsets(the_carrier(X3116),X3117))
| ~ in(X3135,cartesian_product2(complements_of_subsets(the_carrier(X3116),X3117),X3127))
| X3135 != X3134
| in(X3134,esk289_3(X3116,X3117,X3127))
| esk283_2(X3116,X3117) != esk284_2(X3116,X3117)
| ~ one_sorted_str(X3116)
| ~ element(X3117,powerset(powerset(the_carrier(X3116)))) ) ),
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)],[s1_tarski__e4_7_1__tops_2__2])])])])])]) ).
fof(i_0_686,plain,
! [X3153,X3154,X3160,X3163,X3164,X3166,X3170,X3171,X3172,X3173,X3174] :
( ( in(esk308_4(X3153,X3154,X3164,X3166),cartesian_product2(X3154,X3164))
| ~ in(X3166,esk307_3(X3153,X3154,X3164))
| esk300_2(X3153,X3154) = esk301_2(X3153,X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( esk308_4(X3153,X3154,X3164,X3166) = X3166
| ~ in(X3166,esk307_3(X3153,X3154,X3164))
| esk300_2(X3153,X3154) = esk301_2(X3153,X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( ordered_pair(esk309_4(X3153,X3154,X3164,X3166),esk310_4(X3153,X3154,X3164,X3166)) = X3166
| ~ in(X3166,esk307_3(X3153,X3154,X3164))
| esk300_2(X3153,X3154) = esk301_2(X3153,X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( in(esk309_4(X3153,X3154,X3164,X3166),X3154)
| ~ in(X3166,esk307_3(X3153,X3154,X3164))
| esk300_2(X3153,X3154) = esk301_2(X3153,X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( ~ element(X3170,powerset(the_carrier(X3153)))
| X3170 != esk309_4(X3153,X3154,X3164,X3166)
| esk310_4(X3153,X3154,X3164,X3166) = subset_complement(the_carrier(X3153),X3170)
| ~ in(X3166,esk307_3(X3153,X3154,X3164))
| esk300_2(X3153,X3154) = esk301_2(X3153,X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( element(esk311_6(X3153,X3154,X3164,X3171,X3173,X3174),powerset(the_carrier(X3153)))
| ordered_pair(X3173,X3174) != X3171
| ~ in(X3173,X3154)
| ~ in(X3172,cartesian_product2(X3154,X3164))
| X3172 != X3171
| in(X3171,esk307_3(X3153,X3154,X3164))
| esk300_2(X3153,X3154) = esk301_2(X3153,X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( esk311_6(X3153,X3154,X3164,X3171,X3173,X3174) = X3173
| ordered_pair(X3173,X3174) != X3171
| ~ in(X3173,X3154)
| ~ in(X3172,cartesian_product2(X3154,X3164))
| X3172 != X3171
| in(X3171,esk307_3(X3153,X3154,X3164))
| esk300_2(X3153,X3154) = esk301_2(X3153,X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( X3174 != subset_complement(the_carrier(X3153),esk311_6(X3153,X3154,X3164,X3171,X3173,X3174))
| ordered_pair(X3173,X3174) != X3171
| ~ in(X3173,X3154)
| ~ in(X3172,cartesian_product2(X3154,X3164))
| X3172 != X3171
| in(X3171,esk307_3(X3153,X3154,X3164))
| esk300_2(X3153,X3154) = esk301_2(X3153,X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( in(esk308_4(X3153,X3154,X3164,X3166),cartesian_product2(X3154,X3164))
| ~ in(X3166,esk307_3(X3153,X3154,X3164))
| ordered_pair(esk303_2(X3153,X3154),esk304_2(X3153,X3154)) = esk301_2(X3153,X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( esk308_4(X3153,X3154,X3164,X3166) = X3166
| ~ in(X3166,esk307_3(X3153,X3154,X3164))
| ordered_pair(esk303_2(X3153,X3154),esk304_2(X3153,X3154)) = esk301_2(X3153,X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( ordered_pair(esk309_4(X3153,X3154,X3164,X3166),esk310_4(X3153,X3154,X3164,X3166)) = X3166
| ~ in(X3166,esk307_3(X3153,X3154,X3164))
| ordered_pair(esk303_2(X3153,X3154),esk304_2(X3153,X3154)) = esk301_2(X3153,X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( in(esk309_4(X3153,X3154,X3164,X3166),X3154)
| ~ in(X3166,esk307_3(X3153,X3154,X3164))
| ordered_pair(esk303_2(X3153,X3154),esk304_2(X3153,X3154)) = esk301_2(X3153,X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( ~ element(X3170,powerset(the_carrier(X3153)))
| X3170 != esk309_4(X3153,X3154,X3164,X3166)
| esk310_4(X3153,X3154,X3164,X3166) = subset_complement(the_carrier(X3153),X3170)
| ~ in(X3166,esk307_3(X3153,X3154,X3164))
| ordered_pair(esk303_2(X3153,X3154),esk304_2(X3153,X3154)) = esk301_2(X3153,X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( element(esk311_6(X3153,X3154,X3164,X3171,X3173,X3174),powerset(the_carrier(X3153)))
| ordered_pair(X3173,X3174) != X3171
| ~ in(X3173,X3154)
| ~ in(X3172,cartesian_product2(X3154,X3164))
| X3172 != X3171
| in(X3171,esk307_3(X3153,X3154,X3164))
| ordered_pair(esk303_2(X3153,X3154),esk304_2(X3153,X3154)) = esk301_2(X3153,X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( esk311_6(X3153,X3154,X3164,X3171,X3173,X3174) = X3173
| ordered_pair(X3173,X3174) != X3171
| ~ in(X3173,X3154)
| ~ in(X3172,cartesian_product2(X3154,X3164))
| X3172 != X3171
| in(X3171,esk307_3(X3153,X3154,X3164))
| ordered_pair(esk303_2(X3153,X3154),esk304_2(X3153,X3154)) = esk301_2(X3153,X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( X3174 != subset_complement(the_carrier(X3153),esk311_6(X3153,X3154,X3164,X3171,X3173,X3174))
| ordered_pair(X3173,X3174) != X3171
| ~ in(X3173,X3154)
| ~ in(X3172,cartesian_product2(X3154,X3164))
| X3172 != X3171
| in(X3171,esk307_3(X3153,X3154,X3164))
| ordered_pair(esk303_2(X3153,X3154),esk304_2(X3153,X3154)) = esk301_2(X3153,X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( in(esk308_4(X3153,X3154,X3164,X3166),cartesian_product2(X3154,X3164))
| ~ in(X3166,esk307_3(X3153,X3154,X3164))
| in(esk303_2(X3153,X3154),X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( esk308_4(X3153,X3154,X3164,X3166) = X3166
| ~ in(X3166,esk307_3(X3153,X3154,X3164))
| in(esk303_2(X3153,X3154),X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( ordered_pair(esk309_4(X3153,X3154,X3164,X3166),esk310_4(X3153,X3154,X3164,X3166)) = X3166
| ~ in(X3166,esk307_3(X3153,X3154,X3164))
| in(esk303_2(X3153,X3154),X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( in(esk309_4(X3153,X3154,X3164,X3166),X3154)
| ~ in(X3166,esk307_3(X3153,X3154,X3164))
| in(esk303_2(X3153,X3154),X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( ~ element(X3170,powerset(the_carrier(X3153)))
| X3170 != esk309_4(X3153,X3154,X3164,X3166)
| esk310_4(X3153,X3154,X3164,X3166) = subset_complement(the_carrier(X3153),X3170)
| ~ in(X3166,esk307_3(X3153,X3154,X3164))
| in(esk303_2(X3153,X3154),X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( element(esk311_6(X3153,X3154,X3164,X3171,X3173,X3174),powerset(the_carrier(X3153)))
| ordered_pair(X3173,X3174) != X3171
| ~ in(X3173,X3154)
| ~ in(X3172,cartesian_product2(X3154,X3164))
| X3172 != X3171
| in(X3171,esk307_3(X3153,X3154,X3164))
| in(esk303_2(X3153,X3154),X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( esk311_6(X3153,X3154,X3164,X3171,X3173,X3174) = X3173
| ordered_pair(X3173,X3174) != X3171
| ~ in(X3173,X3154)
| ~ in(X3172,cartesian_product2(X3154,X3164))
| X3172 != X3171
| in(X3171,esk307_3(X3153,X3154,X3164))
| in(esk303_2(X3153,X3154),X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( X3174 != subset_complement(the_carrier(X3153),esk311_6(X3153,X3154,X3164,X3171,X3173,X3174))
| ordered_pair(X3173,X3174) != X3171
| ~ in(X3173,X3154)
| ~ in(X3172,cartesian_product2(X3154,X3164))
| X3172 != X3171
| in(X3171,esk307_3(X3153,X3154,X3164))
| in(esk303_2(X3153,X3154),X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( in(esk308_4(X3153,X3154,X3164,X3166),cartesian_product2(X3154,X3164))
| ~ in(X3166,esk307_3(X3153,X3154,X3164))
| ~ element(X3160,powerset(the_carrier(X3153)))
| X3160 != esk303_2(X3153,X3154)
| esk304_2(X3153,X3154) = subset_complement(the_carrier(X3153),X3160)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( esk308_4(X3153,X3154,X3164,X3166) = X3166
| ~ in(X3166,esk307_3(X3153,X3154,X3164))
| ~ element(X3160,powerset(the_carrier(X3153)))
| X3160 != esk303_2(X3153,X3154)
| esk304_2(X3153,X3154) = subset_complement(the_carrier(X3153),X3160)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( ordered_pair(esk309_4(X3153,X3154,X3164,X3166),esk310_4(X3153,X3154,X3164,X3166)) = X3166
| ~ in(X3166,esk307_3(X3153,X3154,X3164))
| ~ element(X3160,powerset(the_carrier(X3153)))
| X3160 != esk303_2(X3153,X3154)
| esk304_2(X3153,X3154) = subset_complement(the_carrier(X3153),X3160)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( in(esk309_4(X3153,X3154,X3164,X3166),X3154)
| ~ in(X3166,esk307_3(X3153,X3154,X3164))
| ~ element(X3160,powerset(the_carrier(X3153)))
| X3160 != esk303_2(X3153,X3154)
| esk304_2(X3153,X3154) = subset_complement(the_carrier(X3153),X3160)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( ~ element(X3170,powerset(the_carrier(X3153)))
| X3170 != esk309_4(X3153,X3154,X3164,X3166)
| esk310_4(X3153,X3154,X3164,X3166) = subset_complement(the_carrier(X3153),X3170)
| ~ in(X3166,esk307_3(X3153,X3154,X3164))
| ~ element(X3160,powerset(the_carrier(X3153)))
| X3160 != esk303_2(X3153,X3154)
| esk304_2(X3153,X3154) = subset_complement(the_carrier(X3153),X3160)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( element(esk311_6(X3153,X3154,X3164,X3171,X3173,X3174),powerset(the_carrier(X3153)))
| ordered_pair(X3173,X3174) != X3171
| ~ in(X3173,X3154)
| ~ in(X3172,cartesian_product2(X3154,X3164))
| X3172 != X3171
| in(X3171,esk307_3(X3153,X3154,X3164))
| ~ element(X3160,powerset(the_carrier(X3153)))
| X3160 != esk303_2(X3153,X3154)
| esk304_2(X3153,X3154) = subset_complement(the_carrier(X3153),X3160)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( esk311_6(X3153,X3154,X3164,X3171,X3173,X3174) = X3173
| ordered_pair(X3173,X3174) != X3171
| ~ in(X3173,X3154)
| ~ in(X3172,cartesian_product2(X3154,X3164))
| X3172 != X3171
| in(X3171,esk307_3(X3153,X3154,X3164))
| ~ element(X3160,powerset(the_carrier(X3153)))
| X3160 != esk303_2(X3153,X3154)
| esk304_2(X3153,X3154) = subset_complement(the_carrier(X3153),X3160)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( X3174 != subset_complement(the_carrier(X3153),esk311_6(X3153,X3154,X3164,X3171,X3173,X3174))
| ordered_pair(X3173,X3174) != X3171
| ~ in(X3173,X3154)
| ~ in(X3172,cartesian_product2(X3154,X3164))
| X3172 != X3171
| in(X3171,esk307_3(X3153,X3154,X3164))
| ~ element(X3160,powerset(the_carrier(X3153)))
| X3160 != esk303_2(X3153,X3154)
| esk304_2(X3153,X3154) = subset_complement(the_carrier(X3153),X3160)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( in(esk308_4(X3153,X3154,X3164,X3166),cartesian_product2(X3154,X3164))
| ~ in(X3166,esk307_3(X3153,X3154,X3164))
| esk300_2(X3153,X3154) = esk302_2(X3153,X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( esk308_4(X3153,X3154,X3164,X3166) = X3166
| ~ in(X3166,esk307_3(X3153,X3154,X3164))
| esk300_2(X3153,X3154) = esk302_2(X3153,X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( ordered_pair(esk309_4(X3153,X3154,X3164,X3166),esk310_4(X3153,X3154,X3164,X3166)) = X3166
| ~ in(X3166,esk307_3(X3153,X3154,X3164))
| esk300_2(X3153,X3154) = esk302_2(X3153,X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( in(esk309_4(X3153,X3154,X3164,X3166),X3154)
| ~ in(X3166,esk307_3(X3153,X3154,X3164))
| esk300_2(X3153,X3154) = esk302_2(X3153,X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( ~ element(X3170,powerset(the_carrier(X3153)))
| X3170 != esk309_4(X3153,X3154,X3164,X3166)
| esk310_4(X3153,X3154,X3164,X3166) = subset_complement(the_carrier(X3153),X3170)
| ~ in(X3166,esk307_3(X3153,X3154,X3164))
| esk300_2(X3153,X3154) = esk302_2(X3153,X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( element(esk311_6(X3153,X3154,X3164,X3171,X3173,X3174),powerset(the_carrier(X3153)))
| ordered_pair(X3173,X3174) != X3171
| ~ in(X3173,X3154)
| ~ in(X3172,cartesian_product2(X3154,X3164))
| X3172 != X3171
| in(X3171,esk307_3(X3153,X3154,X3164))
| esk300_2(X3153,X3154) = esk302_2(X3153,X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( esk311_6(X3153,X3154,X3164,X3171,X3173,X3174) = X3173
| ordered_pair(X3173,X3174) != X3171
| ~ in(X3173,X3154)
| ~ in(X3172,cartesian_product2(X3154,X3164))
| X3172 != X3171
| in(X3171,esk307_3(X3153,X3154,X3164))
| esk300_2(X3153,X3154) = esk302_2(X3153,X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( X3174 != subset_complement(the_carrier(X3153),esk311_6(X3153,X3154,X3164,X3171,X3173,X3174))
| ordered_pair(X3173,X3174) != X3171
| ~ in(X3173,X3154)
| ~ in(X3172,cartesian_product2(X3154,X3164))
| X3172 != X3171
| in(X3171,esk307_3(X3153,X3154,X3164))
| esk300_2(X3153,X3154) = esk302_2(X3153,X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( in(esk308_4(X3153,X3154,X3164,X3166),cartesian_product2(X3154,X3164))
| ~ in(X3166,esk307_3(X3153,X3154,X3164))
| ordered_pair(esk305_2(X3153,X3154),esk306_2(X3153,X3154)) = esk302_2(X3153,X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( esk308_4(X3153,X3154,X3164,X3166) = X3166
| ~ in(X3166,esk307_3(X3153,X3154,X3164))
| ordered_pair(esk305_2(X3153,X3154),esk306_2(X3153,X3154)) = esk302_2(X3153,X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( ordered_pair(esk309_4(X3153,X3154,X3164,X3166),esk310_4(X3153,X3154,X3164,X3166)) = X3166
| ~ in(X3166,esk307_3(X3153,X3154,X3164))
| ordered_pair(esk305_2(X3153,X3154),esk306_2(X3153,X3154)) = esk302_2(X3153,X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( in(esk309_4(X3153,X3154,X3164,X3166),X3154)
| ~ in(X3166,esk307_3(X3153,X3154,X3164))
| ordered_pair(esk305_2(X3153,X3154),esk306_2(X3153,X3154)) = esk302_2(X3153,X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( ~ element(X3170,powerset(the_carrier(X3153)))
| X3170 != esk309_4(X3153,X3154,X3164,X3166)
| esk310_4(X3153,X3154,X3164,X3166) = subset_complement(the_carrier(X3153),X3170)
| ~ in(X3166,esk307_3(X3153,X3154,X3164))
| ordered_pair(esk305_2(X3153,X3154),esk306_2(X3153,X3154)) = esk302_2(X3153,X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( element(esk311_6(X3153,X3154,X3164,X3171,X3173,X3174),powerset(the_carrier(X3153)))
| ordered_pair(X3173,X3174) != X3171
| ~ in(X3173,X3154)
| ~ in(X3172,cartesian_product2(X3154,X3164))
| X3172 != X3171
| in(X3171,esk307_3(X3153,X3154,X3164))
| ordered_pair(esk305_2(X3153,X3154),esk306_2(X3153,X3154)) = esk302_2(X3153,X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( esk311_6(X3153,X3154,X3164,X3171,X3173,X3174) = X3173
| ordered_pair(X3173,X3174) != X3171
| ~ in(X3173,X3154)
| ~ in(X3172,cartesian_product2(X3154,X3164))
| X3172 != X3171
| in(X3171,esk307_3(X3153,X3154,X3164))
| ordered_pair(esk305_2(X3153,X3154),esk306_2(X3153,X3154)) = esk302_2(X3153,X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( X3174 != subset_complement(the_carrier(X3153),esk311_6(X3153,X3154,X3164,X3171,X3173,X3174))
| ordered_pair(X3173,X3174) != X3171
| ~ in(X3173,X3154)
| ~ in(X3172,cartesian_product2(X3154,X3164))
| X3172 != X3171
| in(X3171,esk307_3(X3153,X3154,X3164))
| ordered_pair(esk305_2(X3153,X3154),esk306_2(X3153,X3154)) = esk302_2(X3153,X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( in(esk308_4(X3153,X3154,X3164,X3166),cartesian_product2(X3154,X3164))
| ~ in(X3166,esk307_3(X3153,X3154,X3164))
| in(esk305_2(X3153,X3154),X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( esk308_4(X3153,X3154,X3164,X3166) = X3166
| ~ in(X3166,esk307_3(X3153,X3154,X3164))
| in(esk305_2(X3153,X3154),X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( ordered_pair(esk309_4(X3153,X3154,X3164,X3166),esk310_4(X3153,X3154,X3164,X3166)) = X3166
| ~ in(X3166,esk307_3(X3153,X3154,X3164))
| in(esk305_2(X3153,X3154),X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( in(esk309_4(X3153,X3154,X3164,X3166),X3154)
| ~ in(X3166,esk307_3(X3153,X3154,X3164))
| in(esk305_2(X3153,X3154),X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( ~ element(X3170,powerset(the_carrier(X3153)))
| X3170 != esk309_4(X3153,X3154,X3164,X3166)
| esk310_4(X3153,X3154,X3164,X3166) = subset_complement(the_carrier(X3153),X3170)
| ~ in(X3166,esk307_3(X3153,X3154,X3164))
| in(esk305_2(X3153,X3154),X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( element(esk311_6(X3153,X3154,X3164,X3171,X3173,X3174),powerset(the_carrier(X3153)))
| ordered_pair(X3173,X3174) != X3171
| ~ in(X3173,X3154)
| ~ in(X3172,cartesian_product2(X3154,X3164))
| X3172 != X3171
| in(X3171,esk307_3(X3153,X3154,X3164))
| in(esk305_2(X3153,X3154),X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( esk311_6(X3153,X3154,X3164,X3171,X3173,X3174) = X3173
| ordered_pair(X3173,X3174) != X3171
| ~ in(X3173,X3154)
| ~ in(X3172,cartesian_product2(X3154,X3164))
| X3172 != X3171
| in(X3171,esk307_3(X3153,X3154,X3164))
| in(esk305_2(X3153,X3154),X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( X3174 != subset_complement(the_carrier(X3153),esk311_6(X3153,X3154,X3164,X3171,X3173,X3174))
| ordered_pair(X3173,X3174) != X3171
| ~ in(X3173,X3154)
| ~ in(X3172,cartesian_product2(X3154,X3164))
| X3172 != X3171
| in(X3171,esk307_3(X3153,X3154,X3164))
| in(esk305_2(X3153,X3154),X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( in(esk308_4(X3153,X3154,X3164,X3166),cartesian_product2(X3154,X3164))
| ~ in(X3166,esk307_3(X3153,X3154,X3164))
| ~ element(X3163,powerset(the_carrier(X3153)))
| X3163 != esk305_2(X3153,X3154)
| esk306_2(X3153,X3154) = subset_complement(the_carrier(X3153),X3163)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( esk308_4(X3153,X3154,X3164,X3166) = X3166
| ~ in(X3166,esk307_3(X3153,X3154,X3164))
| ~ element(X3163,powerset(the_carrier(X3153)))
| X3163 != esk305_2(X3153,X3154)
| esk306_2(X3153,X3154) = subset_complement(the_carrier(X3153),X3163)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( ordered_pair(esk309_4(X3153,X3154,X3164,X3166),esk310_4(X3153,X3154,X3164,X3166)) = X3166
| ~ in(X3166,esk307_3(X3153,X3154,X3164))
| ~ element(X3163,powerset(the_carrier(X3153)))
| X3163 != esk305_2(X3153,X3154)
| esk306_2(X3153,X3154) = subset_complement(the_carrier(X3153),X3163)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( in(esk309_4(X3153,X3154,X3164,X3166),X3154)
| ~ in(X3166,esk307_3(X3153,X3154,X3164))
| ~ element(X3163,powerset(the_carrier(X3153)))
| X3163 != esk305_2(X3153,X3154)
| esk306_2(X3153,X3154) = subset_complement(the_carrier(X3153),X3163)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( ~ element(X3170,powerset(the_carrier(X3153)))
| X3170 != esk309_4(X3153,X3154,X3164,X3166)
| esk310_4(X3153,X3154,X3164,X3166) = subset_complement(the_carrier(X3153),X3170)
| ~ in(X3166,esk307_3(X3153,X3154,X3164))
| ~ element(X3163,powerset(the_carrier(X3153)))
| X3163 != esk305_2(X3153,X3154)
| esk306_2(X3153,X3154) = subset_complement(the_carrier(X3153),X3163)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( element(esk311_6(X3153,X3154,X3164,X3171,X3173,X3174),powerset(the_carrier(X3153)))
| ordered_pair(X3173,X3174) != X3171
| ~ in(X3173,X3154)
| ~ in(X3172,cartesian_product2(X3154,X3164))
| X3172 != X3171
| in(X3171,esk307_3(X3153,X3154,X3164))
| ~ element(X3163,powerset(the_carrier(X3153)))
| X3163 != esk305_2(X3153,X3154)
| esk306_2(X3153,X3154) = subset_complement(the_carrier(X3153),X3163)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( esk311_6(X3153,X3154,X3164,X3171,X3173,X3174) = X3173
| ordered_pair(X3173,X3174) != X3171
| ~ in(X3173,X3154)
| ~ in(X3172,cartesian_product2(X3154,X3164))
| X3172 != X3171
| in(X3171,esk307_3(X3153,X3154,X3164))
| ~ element(X3163,powerset(the_carrier(X3153)))
| X3163 != esk305_2(X3153,X3154)
| esk306_2(X3153,X3154) = subset_complement(the_carrier(X3153),X3163)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( X3174 != subset_complement(the_carrier(X3153),esk311_6(X3153,X3154,X3164,X3171,X3173,X3174))
| ordered_pair(X3173,X3174) != X3171
| ~ in(X3173,X3154)
| ~ in(X3172,cartesian_product2(X3154,X3164))
| X3172 != X3171
| in(X3171,esk307_3(X3153,X3154,X3164))
| ~ element(X3163,powerset(the_carrier(X3153)))
| X3163 != esk305_2(X3153,X3154)
| esk306_2(X3153,X3154) = subset_complement(the_carrier(X3153),X3163)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( in(esk308_4(X3153,X3154,X3164,X3166),cartesian_product2(X3154,X3164))
| ~ in(X3166,esk307_3(X3153,X3154,X3164))
| esk301_2(X3153,X3154) != esk302_2(X3153,X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( esk308_4(X3153,X3154,X3164,X3166) = X3166
| ~ in(X3166,esk307_3(X3153,X3154,X3164))
| esk301_2(X3153,X3154) != esk302_2(X3153,X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( ordered_pair(esk309_4(X3153,X3154,X3164,X3166),esk310_4(X3153,X3154,X3164,X3166)) = X3166
| ~ in(X3166,esk307_3(X3153,X3154,X3164))
| esk301_2(X3153,X3154) != esk302_2(X3153,X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( in(esk309_4(X3153,X3154,X3164,X3166),X3154)
| ~ in(X3166,esk307_3(X3153,X3154,X3164))
| esk301_2(X3153,X3154) != esk302_2(X3153,X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( ~ element(X3170,powerset(the_carrier(X3153)))
| X3170 != esk309_4(X3153,X3154,X3164,X3166)
| esk310_4(X3153,X3154,X3164,X3166) = subset_complement(the_carrier(X3153),X3170)
| ~ in(X3166,esk307_3(X3153,X3154,X3164))
| esk301_2(X3153,X3154) != esk302_2(X3153,X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( element(esk311_6(X3153,X3154,X3164,X3171,X3173,X3174),powerset(the_carrier(X3153)))
| ordered_pair(X3173,X3174) != X3171
| ~ in(X3173,X3154)
| ~ in(X3172,cartesian_product2(X3154,X3164))
| X3172 != X3171
| in(X3171,esk307_3(X3153,X3154,X3164))
| esk301_2(X3153,X3154) != esk302_2(X3153,X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( esk311_6(X3153,X3154,X3164,X3171,X3173,X3174) = X3173
| ordered_pair(X3173,X3174) != X3171
| ~ in(X3173,X3154)
| ~ in(X3172,cartesian_product2(X3154,X3164))
| X3172 != X3171
| in(X3171,esk307_3(X3153,X3154,X3164))
| esk301_2(X3153,X3154) != esk302_2(X3153,X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) )
& ( X3174 != subset_complement(the_carrier(X3153),esk311_6(X3153,X3154,X3164,X3171,X3173,X3174))
| ordered_pair(X3173,X3174) != X3171
| ~ in(X3173,X3154)
| ~ in(X3172,cartesian_product2(X3154,X3164))
| X3172 != X3171
| in(X3171,esk307_3(X3153,X3154,X3164))
| esk301_2(X3153,X3154) != esk302_2(X3153,X3154)
| ~ one_sorted_str(X3153)
| ~ element(X3154,powerset(powerset(the_carrier(X3153)))) ) ),
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)],[s1_tarski__e4_7_2__tops_2__2])])])])])]) ).
fof(i_0_687,lemma,
! [X3283,X3284,X3285,X3287,X3290,X3291,X3292,X3293] :
( ( in(X3287,cartesian_product2(complements_of_subsets(the_carrier(X3283),X3284),X3285))
| ~ in(X3287,esk359_3(X3283,X3284,X3285))
| ~ one_sorted_str(X3283)
| ~ element(X3284,powerset(powerset(the_carrier(X3283)))) )
& ( ordered_pair(esk360_4(X3283,X3284,X3285,X3287),esk361_4(X3283,X3284,X3285,X3287)) = X3287
| ~ in(X3287,esk359_3(X3283,X3284,X3285))
| ~ one_sorted_str(X3283)
| ~ element(X3284,powerset(powerset(the_carrier(X3283)))) )
& ( in(esk360_4(X3283,X3284,X3285,X3287),complements_of_subsets(the_carrier(X3283),X3284))
| ~ in(X3287,esk359_3(X3283,X3284,X3285))
| ~ one_sorted_str(X3283)
| ~ element(X3284,powerset(powerset(the_carrier(X3283)))) )
& ( ~ element(X3290,powerset(the_carrier(X3283)))
| X3290 != esk360_4(X3283,X3284,X3285,X3287)
| esk361_4(X3283,X3284,X3285,X3287) = subset_complement(the_carrier(X3283),X3290)
| ~ in(X3287,esk359_3(X3283,X3284,X3285))
| ~ one_sorted_str(X3283)
| ~ element(X3284,powerset(powerset(the_carrier(X3283)))) )
& ( element(esk362_6(X3283,X3284,X3285,X3291,X3292,X3293),powerset(the_carrier(X3283)))
| ordered_pair(X3292,X3293) != X3291
| ~ in(X3292,complements_of_subsets(the_carrier(X3283),X3284))
| ~ in(X3291,cartesian_product2(complements_of_subsets(the_carrier(X3283),X3284),X3285))
| in(X3291,esk359_3(X3283,X3284,X3285))
| ~ one_sorted_str(X3283)
| ~ element(X3284,powerset(powerset(the_carrier(X3283)))) )
& ( esk362_6(X3283,X3284,X3285,X3291,X3292,X3293) = X3292
| ordered_pair(X3292,X3293) != X3291
| ~ in(X3292,complements_of_subsets(the_carrier(X3283),X3284))
| ~ in(X3291,cartesian_product2(complements_of_subsets(the_carrier(X3283),X3284),X3285))
| in(X3291,esk359_3(X3283,X3284,X3285))
| ~ one_sorted_str(X3283)
| ~ element(X3284,powerset(powerset(the_carrier(X3283)))) )
& ( X3293 != subset_complement(the_carrier(X3283),esk362_6(X3283,X3284,X3285,X3291,X3292,X3293))
| ordered_pair(X3292,X3293) != X3291
| ~ in(X3292,complements_of_subsets(the_carrier(X3283),X3284))
| ~ in(X3291,cartesian_product2(complements_of_subsets(the_carrier(X3283),X3284),X3285))
| in(X3291,esk359_3(X3283,X3284,X3285))
| ~ one_sorted_str(X3283)
| ~ element(X3284,powerset(powerset(the_carrier(X3283)))) ) ),
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)],[s1_xboole_0__e4_7_1__tops_2__1])])])])])]) ).
fof(i_0_688,lemma,
! [X3295,X3296,X3297,X3299,X3302,X3303,X3304,X3305] :
( ( in(X3299,cartesian_product2(X3296,X3297))
| ~ in(X3299,esk363_3(X3295,X3296,X3297))
| ~ one_sorted_str(X3295)
| ~ element(X3296,powerset(powerset(the_carrier(X3295)))) )
& ( ordered_pair(esk364_4(X3295,X3296,X3297,X3299),esk365_4(X3295,X3296,X3297,X3299)) = X3299
| ~ in(X3299,esk363_3(X3295,X3296,X3297))
| ~ one_sorted_str(X3295)
| ~ element(X3296,powerset(powerset(the_carrier(X3295)))) )
& ( in(esk364_4(X3295,X3296,X3297,X3299),X3296)
| ~ in(X3299,esk363_3(X3295,X3296,X3297))
| ~ one_sorted_str(X3295)
| ~ element(X3296,powerset(powerset(the_carrier(X3295)))) )
& ( ~ element(X3302,powerset(the_carrier(X3295)))
| X3302 != esk364_4(X3295,X3296,X3297,X3299)
| esk365_4(X3295,X3296,X3297,X3299) = subset_complement(the_carrier(X3295),X3302)
| ~ in(X3299,esk363_3(X3295,X3296,X3297))
| ~ one_sorted_str(X3295)
| ~ element(X3296,powerset(powerset(the_carrier(X3295)))) )
& ( element(esk366_6(X3295,X3296,X3297,X3303,X3304,X3305),powerset(the_carrier(X3295)))
| ordered_pair(X3304,X3305) != X3303
| ~ in(X3304,X3296)
| ~ in(X3303,cartesian_product2(X3296,X3297))
| in(X3303,esk363_3(X3295,X3296,X3297))
| ~ one_sorted_str(X3295)
| ~ element(X3296,powerset(powerset(the_carrier(X3295)))) )
& ( esk366_6(X3295,X3296,X3297,X3303,X3304,X3305) = X3304
| ordered_pair(X3304,X3305) != X3303
| ~ in(X3304,X3296)
| ~ in(X3303,cartesian_product2(X3296,X3297))
| in(X3303,esk363_3(X3295,X3296,X3297))
| ~ one_sorted_str(X3295)
| ~ element(X3296,powerset(powerset(the_carrier(X3295)))) )
& ( X3305 != subset_complement(the_carrier(X3295),esk366_6(X3295,X3296,X3297,X3303,X3304,X3305))
| ordered_pair(X3304,X3305) != X3303
| ~ in(X3304,X3296)
| ~ in(X3303,cartesian_product2(X3296,X3297))
| in(X3303,esk363_3(X3295,X3296,X3297))
| ~ one_sorted_str(X3295)
| ~ element(X3296,powerset(powerset(the_carrier(X3295)))) ) ),
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)],[s1_xboole_0__e4_7_2__tops_2__1])])])])])]) ).
fof(i_0_689,lemma,
! [X3307,X3308,X3309,X3311,X3314,X3315,X3316] :
( ( in(X3311,cartesian_product2(X3307,X3307))
| ~ in(X3311,esk367_3(X3307,X3308,X3309))
| ~ relation(X3308)
| ~ relation(X3309)
| ~ function(X3309) )
& ( X3311 = ordered_pair(esk368_4(X3307,X3308,X3309,X3311),esk369_4(X3307,X3308,X3309,X3311))
| ~ in(X3311,esk367_3(X3307,X3308,X3309))
| ~ relation(X3308)
| ~ relation(X3309)
| ~ function(X3309) )
& ( in(ordered_pair(apply(X3309,esk368_4(X3307,X3308,X3309,X3311)),apply(X3309,esk369_4(X3307,X3308,X3309,X3311))),X3308)
| ~ in(X3311,esk367_3(X3307,X3308,X3309))
| ~ relation(X3308)
| ~ relation(X3309)
| ~ function(X3309) )
& ( ~ in(X3314,cartesian_product2(X3307,X3307))
| X3314 != ordered_pair(X3315,X3316)
| ~ in(ordered_pair(apply(X3309,X3315),apply(X3309,X3316)),X3308)
| in(X3314,esk367_3(X3307,X3308,X3309))
| ~ relation(X3308)
| ~ relation(X3309)
| ~ function(X3309) ) ),
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)],[s1_xboole_0__e6_21__wellord2__1])])])])])]) ).
fof(i_0_690,lemma,
! [X2896,X2897,X2902,X2904,X2906,X2907,X2909,X2910,X2911,X2912] :
( ( relation(esk182_2(X2896,X2897))
| in(esk177_2(X2896,X2897),X2896)
| empty(X2896)
| ~ relation(X2897) )
& ( function(esk182_2(X2896,X2897))
| in(esk177_2(X2896,X2897),X2896)
| empty(X2896)
| ~ relation(X2897) )
& ( in(X2906,X2896)
| ~ in(ordered_pair(X2906,X2907),esk182_2(X2896,X2897))
| in(esk177_2(X2896,X2897),X2896)
| empty(X2896)
| ~ relation(X2897) )
& ( X2906 = esk183_4(X2896,X2897,X2906,X2907)
| ~ in(ordered_pair(X2906,X2907),esk182_2(X2896,X2897))
| in(esk177_2(X2896,X2897),X2896)
| empty(X2896)
| ~ relation(X2897) )
& ( in(X2907,esk183_4(X2896,X2897,X2906,X2907))
| ~ in(ordered_pair(X2906,X2907),esk182_2(X2896,X2897))
| in(esk177_2(X2896,X2897),X2896)
| empty(X2896)
| ~ relation(X2897) )
& ( ~ in(X2909,esk183_4(X2896,X2897,X2906,X2907))
| in(ordered_pair(X2907,X2909),X2897)
| ~ in(ordered_pair(X2906,X2907),esk182_2(X2896,X2897))
| in(esk177_2(X2896,X2897),X2896)
| empty(X2896)
| ~ relation(X2897) )
& ( in(esk184_5(X2896,X2897,X2910,X2911,X2912),X2912)
| X2910 != X2912
| ~ in(X2911,X2912)
| ~ in(X2910,X2896)
| in(ordered_pair(X2910,X2911),esk182_2(X2896,X2897))
| in(esk177_2(X2896,X2897),X2896)
| empty(X2896)
| ~ relation(X2897) )
& ( ~ in(ordered_pair(X2911,esk184_5(X2896,X2897,X2910,X2911,X2912)),X2897)
| X2910 != X2912
| ~ in(X2911,X2912)
| ~ in(X2910,X2896)
| in(ordered_pair(X2910,X2911),esk182_2(X2896,X2897))
| in(esk177_2(X2896,X2897),X2896)
| empty(X2896)
| ~ relation(X2897) )
& ( relation(esk182_2(X2896,X2897))
| esk177_2(X2896,X2897) = esk180_2(X2896,X2897)
| empty(X2896)
| ~ relation(X2897) )
& ( function(esk182_2(X2896,X2897))
| esk177_2(X2896,X2897) = esk180_2(X2896,X2897)
| empty(X2896)
| ~ relation(X2897) )
& ( in(X2906,X2896)
| ~ in(ordered_pair(X2906,X2907),esk182_2(X2896,X2897))
| esk177_2(X2896,X2897) = esk180_2(X2896,X2897)
| empty(X2896)
| ~ relation(X2897) )
& ( X2906 = esk183_4(X2896,X2897,X2906,X2907)
| ~ in(ordered_pair(X2906,X2907),esk182_2(X2896,X2897))
| esk177_2(X2896,X2897) = esk180_2(X2896,X2897)
| empty(X2896)
| ~ relation(X2897) )
& ( in(X2907,esk183_4(X2896,X2897,X2906,X2907))
| ~ in(ordered_pair(X2906,X2907),esk182_2(X2896,X2897))
| esk177_2(X2896,X2897) = esk180_2(X2896,X2897)
| empty(X2896)
| ~ relation(X2897) )
& ( ~ in(X2909,esk183_4(X2896,X2897,X2906,X2907))
| in(ordered_pair(X2907,X2909),X2897)
| ~ in(ordered_pair(X2906,X2907),esk182_2(X2896,X2897))
| esk177_2(X2896,X2897) = esk180_2(X2896,X2897)
| empty(X2896)
| ~ relation(X2897) )
& ( in(esk184_5(X2896,X2897,X2910,X2911,X2912),X2912)
| X2910 != X2912
| ~ in(X2911,X2912)
| ~ in(X2910,X2896)
| in(ordered_pair(X2910,X2911),esk182_2(X2896,X2897))
| esk177_2(X2896,X2897) = esk180_2(X2896,X2897)
| empty(X2896)
| ~ relation(X2897) )
& ( ~ in(ordered_pair(X2911,esk184_5(X2896,X2897,X2910,X2911,X2912)),X2897)
| X2910 != X2912
| ~ in(X2911,X2912)
| ~ in(X2910,X2896)
| in(ordered_pair(X2910,X2911),esk182_2(X2896,X2897))
| esk177_2(X2896,X2897) = esk180_2(X2896,X2897)
| empty(X2896)
| ~ relation(X2897) )
& ( relation(esk182_2(X2896,X2897))
| in(esk178_2(X2896,X2897),esk180_2(X2896,X2897))
| empty(X2896)
| ~ relation(X2897) )
& ( function(esk182_2(X2896,X2897))
| in(esk178_2(X2896,X2897),esk180_2(X2896,X2897))
| empty(X2896)
| ~ relation(X2897) )
& ( in(X2906,X2896)
| ~ in(ordered_pair(X2906,X2907),esk182_2(X2896,X2897))
| in(esk178_2(X2896,X2897),esk180_2(X2896,X2897))
| empty(X2896)
| ~ relation(X2897) )
& ( X2906 = esk183_4(X2896,X2897,X2906,X2907)
| ~ in(ordered_pair(X2906,X2907),esk182_2(X2896,X2897))
| in(esk178_2(X2896,X2897),esk180_2(X2896,X2897))
| empty(X2896)
| ~ relation(X2897) )
& ( in(X2907,esk183_4(X2896,X2897,X2906,X2907))
| ~ in(ordered_pair(X2906,X2907),esk182_2(X2896,X2897))
| in(esk178_2(X2896,X2897),esk180_2(X2896,X2897))
| empty(X2896)
| ~ relation(X2897) )
& ( ~ in(X2909,esk183_4(X2896,X2897,X2906,X2907))
| in(ordered_pair(X2907,X2909),X2897)
| ~ in(ordered_pair(X2906,X2907),esk182_2(X2896,X2897))
| in(esk178_2(X2896,X2897),esk180_2(X2896,X2897))
| empty(X2896)
| ~ relation(X2897) )
& ( in(esk184_5(X2896,X2897,X2910,X2911,X2912),X2912)
| X2910 != X2912
| ~ in(X2911,X2912)
| ~ in(X2910,X2896)
| in(ordered_pair(X2910,X2911),esk182_2(X2896,X2897))
| in(esk178_2(X2896,X2897),esk180_2(X2896,X2897))
| empty(X2896)
| ~ relation(X2897) )
& ( ~ in(ordered_pair(X2911,esk184_5(X2896,X2897,X2910,X2911,X2912)),X2897)
| X2910 != X2912
| ~ in(X2911,X2912)
| ~ in(X2910,X2896)
| in(ordered_pair(X2910,X2911),esk182_2(X2896,X2897))
| in(esk178_2(X2896,X2897),esk180_2(X2896,X2897))
| empty(X2896)
| ~ relation(X2897) )
& ( relation(esk182_2(X2896,X2897))
| ~ in(X2902,esk180_2(X2896,X2897))
| in(ordered_pair(esk178_2(X2896,X2897),X2902),X2897)
| empty(X2896)
| ~ relation(X2897) )
& ( function(esk182_2(X2896,X2897))
| ~ in(X2902,esk180_2(X2896,X2897))
| in(ordered_pair(esk178_2(X2896,X2897),X2902),X2897)
| empty(X2896)
| ~ relation(X2897) )
& ( in(X2906,X2896)
| ~ in(ordered_pair(X2906,X2907),esk182_2(X2896,X2897))
| ~ in(X2902,esk180_2(X2896,X2897))
| in(ordered_pair(esk178_2(X2896,X2897),X2902),X2897)
| empty(X2896)
| ~ relation(X2897) )
& ( X2906 = esk183_4(X2896,X2897,X2906,X2907)
| ~ in(ordered_pair(X2906,X2907),esk182_2(X2896,X2897))
| ~ in(X2902,esk180_2(X2896,X2897))
| in(ordered_pair(esk178_2(X2896,X2897),X2902),X2897)
| empty(X2896)
| ~ relation(X2897) )
& ( in(X2907,esk183_4(X2896,X2897,X2906,X2907))
| ~ in(ordered_pair(X2906,X2907),esk182_2(X2896,X2897))
| ~ in(X2902,esk180_2(X2896,X2897))
| in(ordered_pair(esk178_2(X2896,X2897),X2902),X2897)
| empty(X2896)
| ~ relation(X2897) )
& ( ~ in(X2909,esk183_4(X2896,X2897,X2906,X2907))
| in(ordered_pair(X2907,X2909),X2897)
| ~ in(ordered_pair(X2906,X2907),esk182_2(X2896,X2897))
| ~ in(X2902,esk180_2(X2896,X2897))
| in(ordered_pair(esk178_2(X2896,X2897),X2902),X2897)
| empty(X2896)
| ~ relation(X2897) )
& ( in(esk184_5(X2896,X2897,X2910,X2911,X2912),X2912)
| X2910 != X2912
| ~ in(X2911,X2912)
| ~ in(X2910,X2896)
| in(ordered_pair(X2910,X2911),esk182_2(X2896,X2897))
| ~ in(X2902,esk180_2(X2896,X2897))
| in(ordered_pair(esk178_2(X2896,X2897),X2902),X2897)
| empty(X2896)
| ~ relation(X2897) )
& ( ~ in(ordered_pair(X2911,esk184_5(X2896,X2897,X2910,X2911,X2912)),X2897)
| X2910 != X2912
| ~ in(X2911,X2912)
| ~ in(X2910,X2896)
| in(ordered_pair(X2910,X2911),esk182_2(X2896,X2897))
| ~ in(X2902,esk180_2(X2896,X2897))
| in(ordered_pair(esk178_2(X2896,X2897),X2902),X2897)
| empty(X2896)
| ~ relation(X2897) )
& ( relation(esk182_2(X2896,X2897))
| in(esk177_2(X2896,X2897),X2896)
| empty(X2896)
| ~ relation(X2897) )
& ( function(esk182_2(X2896,X2897))
| in(esk177_2(X2896,X2897),X2896)
| empty(X2896)
| ~ relation(X2897) )
& ( in(X2906,X2896)
| ~ in(ordered_pair(X2906,X2907),esk182_2(X2896,X2897))
| in(esk177_2(X2896,X2897),X2896)
| empty(X2896)
| ~ relation(X2897) )
& ( X2906 = esk183_4(X2896,X2897,X2906,X2907)
| ~ in(ordered_pair(X2906,X2907),esk182_2(X2896,X2897))
| in(esk177_2(X2896,X2897),X2896)
| empty(X2896)
| ~ relation(X2897) )
& ( in(X2907,esk183_4(X2896,X2897,X2906,X2907))
| ~ in(ordered_pair(X2906,X2907),esk182_2(X2896,X2897))
| in(esk177_2(X2896,X2897),X2896)
| empty(X2896)
| ~ relation(X2897) )
& ( ~ in(X2909,esk183_4(X2896,X2897,X2906,X2907))
| in(ordered_pair(X2907,X2909),X2897)
| ~ in(ordered_pair(X2906,X2907),esk182_2(X2896,X2897))
| in(esk177_2(X2896,X2897),X2896)
| empty(X2896)
| ~ relation(X2897) )
& ( in(esk184_5(X2896,X2897,X2910,X2911,X2912),X2912)
| X2910 != X2912
| ~ in(X2911,X2912)
| ~ in(X2910,X2896)
| in(ordered_pair(X2910,X2911),esk182_2(X2896,X2897))
| in(esk177_2(X2896,X2897),X2896)
| empty(X2896)
| ~ relation(X2897) )
& ( ~ in(ordered_pair(X2911,esk184_5(X2896,X2897,X2910,X2911,X2912)),X2897)
| X2910 != X2912
| ~ in(X2911,X2912)
| ~ in(X2910,X2896)
| in(ordered_pair(X2910,X2911),esk182_2(X2896,X2897))
| in(esk177_2(X2896,X2897),X2896)
| empty(X2896)
| ~ relation(X2897) )
& ( relation(esk182_2(X2896,X2897))
| esk177_2(X2896,X2897) = esk181_2(X2896,X2897)
| empty(X2896)
| ~ relation(X2897) )
& ( function(esk182_2(X2896,X2897))
| esk177_2(X2896,X2897) = esk181_2(X2896,X2897)
| empty(X2896)
| ~ relation(X2897) )
& ( in(X2906,X2896)
| ~ in(ordered_pair(X2906,X2907),esk182_2(X2896,X2897))
| esk177_2(X2896,X2897) = esk181_2(X2896,X2897)
| empty(X2896)
| ~ relation(X2897) )
& ( X2906 = esk183_4(X2896,X2897,X2906,X2907)
| ~ in(ordered_pair(X2906,X2907),esk182_2(X2896,X2897))
| esk177_2(X2896,X2897) = esk181_2(X2896,X2897)
| empty(X2896)
| ~ relation(X2897) )
& ( in(X2907,esk183_4(X2896,X2897,X2906,X2907))
| ~ in(ordered_pair(X2906,X2907),esk182_2(X2896,X2897))
| esk177_2(X2896,X2897) = esk181_2(X2896,X2897)
| empty(X2896)
| ~ relation(X2897) )
& ( ~ in(X2909,esk183_4(X2896,X2897,X2906,X2907))
| in(ordered_pair(X2907,X2909),X2897)
| ~ in(ordered_pair(X2906,X2907),esk182_2(X2896,X2897))
| esk177_2(X2896,X2897) = esk181_2(X2896,X2897)
| empty(X2896)
| ~ relation(X2897) )
& ( in(esk184_5(X2896,X2897,X2910,X2911,X2912),X2912)
| X2910 != X2912
| ~ in(X2911,X2912)
| ~ in(X2910,X2896)
| in(ordered_pair(X2910,X2911),esk182_2(X2896,X2897))
| esk177_2(X2896,X2897) = esk181_2(X2896,X2897)
| empty(X2896)
| ~ relation(X2897) )
& ( ~ in(ordered_pair(X2911,esk184_5(X2896,X2897,X2910,X2911,X2912)),X2897)
| X2910 != X2912
| ~ in(X2911,X2912)
| ~ in(X2910,X2896)
| in(ordered_pair(X2910,X2911),esk182_2(X2896,X2897))
| esk177_2(X2896,X2897) = esk181_2(X2896,X2897)
| empty(X2896)
| ~ relation(X2897) )
& ( relation(esk182_2(X2896,X2897))
| in(esk179_2(X2896,X2897),esk181_2(X2896,X2897))
| empty(X2896)
| ~ relation(X2897) )
& ( function(esk182_2(X2896,X2897))
| in(esk179_2(X2896,X2897),esk181_2(X2896,X2897))
| empty(X2896)
| ~ relation(X2897) )
& ( in(X2906,X2896)
| ~ in(ordered_pair(X2906,X2907),esk182_2(X2896,X2897))
| in(esk179_2(X2896,X2897),esk181_2(X2896,X2897))
| empty(X2896)
| ~ relation(X2897) )
& ( X2906 = esk183_4(X2896,X2897,X2906,X2907)
| ~ in(ordered_pair(X2906,X2907),esk182_2(X2896,X2897))
| in(esk179_2(X2896,X2897),esk181_2(X2896,X2897))
| empty(X2896)
| ~ relation(X2897) )
& ( in(X2907,esk183_4(X2896,X2897,X2906,X2907))
| ~ in(ordered_pair(X2906,X2907),esk182_2(X2896,X2897))
| in(esk179_2(X2896,X2897),esk181_2(X2896,X2897))
| empty(X2896)
| ~ relation(X2897) )
& ( ~ in(X2909,esk183_4(X2896,X2897,X2906,X2907))
| in(ordered_pair(X2907,X2909),X2897)
| ~ in(ordered_pair(X2906,X2907),esk182_2(X2896,X2897))
| in(esk179_2(X2896,X2897),esk181_2(X2896,X2897))
| empty(X2896)
| ~ relation(X2897) )
& ( in(esk184_5(X2896,X2897,X2910,X2911,X2912),X2912)
| X2910 != X2912
| ~ in(X2911,X2912)
| ~ in(X2910,X2896)
| in(ordered_pair(X2910,X2911),esk182_2(X2896,X2897))
| in(esk179_2(X2896,X2897),esk181_2(X2896,X2897))
| empty(X2896)
| ~ relation(X2897) )
& ( ~ in(ordered_pair(X2911,esk184_5(X2896,X2897,X2910,X2911,X2912)),X2897)
| X2910 != X2912
| ~ in(X2911,X2912)
| ~ in(X2910,X2896)
| in(ordered_pair(X2910,X2911),esk182_2(X2896,X2897))
| in(esk179_2(X2896,X2897),esk181_2(X2896,X2897))
| empty(X2896)
| ~ relation(X2897) )
& ( relation(esk182_2(X2896,X2897))
| ~ in(X2904,esk181_2(X2896,X2897))
| in(ordered_pair(esk179_2(X2896,X2897),X2904),X2897)
| empty(X2896)
| ~ relation(X2897) )
& ( function(esk182_2(X2896,X2897))
| ~ in(X2904,esk181_2(X2896,X2897))
| in(ordered_pair(esk179_2(X2896,X2897),X2904),X2897)
| empty(X2896)
| ~ relation(X2897) )
& ( in(X2906,X2896)
| ~ in(ordered_pair(X2906,X2907),esk182_2(X2896,X2897))
| ~ in(X2904,esk181_2(X2896,X2897))
| in(ordered_pair(esk179_2(X2896,X2897),X2904),X2897)
| empty(X2896)
| ~ relation(X2897) )
& ( X2906 = esk183_4(X2896,X2897,X2906,X2907)
| ~ in(ordered_pair(X2906,X2907),esk182_2(X2896,X2897))
| ~ in(X2904,esk181_2(X2896,X2897))
| in(ordered_pair(esk179_2(X2896,X2897),X2904),X2897)
| empty(X2896)
| ~ relation(X2897) )
& ( in(X2907,esk183_4(X2896,X2897,X2906,X2907))
| ~ in(ordered_pair(X2906,X2907),esk182_2(X2896,X2897))
| ~ in(X2904,esk181_2(X2896,X2897))
| in(ordered_pair(esk179_2(X2896,X2897),X2904),X2897)
| empty(X2896)
| ~ relation(X2897) )
& ( ~ in(X2909,esk183_4(X2896,X2897,X2906,X2907))
| in(ordered_pair(X2907,X2909),X2897)
| ~ in(ordered_pair(X2906,X2907),esk182_2(X2896,X2897))
| ~ in(X2904,esk181_2(X2896,X2897))
| in(ordered_pair(esk179_2(X2896,X2897),X2904),X2897)
| empty(X2896)
| ~ relation(X2897) )
& ( in(esk184_5(X2896,X2897,X2910,X2911,X2912),X2912)
| X2910 != X2912
| ~ in(X2911,X2912)
| ~ in(X2910,X2896)
| in(ordered_pair(X2910,X2911),esk182_2(X2896,X2897))
| ~ in(X2904,esk181_2(X2896,X2897))
| in(ordered_pair(esk179_2(X2896,X2897),X2904),X2897)
| empty(X2896)
| ~ relation(X2897) )
& ( ~ in(ordered_pair(X2911,esk184_5(X2896,X2897,X2910,X2911,X2912)),X2897)
| X2910 != X2912
| ~ in(X2911,X2912)
| ~ in(X2910,X2896)
| in(ordered_pair(X2910,X2911),esk182_2(X2896,X2897))
| ~ in(X2904,esk181_2(X2896,X2897))
| in(ordered_pair(esk179_2(X2896,X2897),X2904),X2897)
| empty(X2896)
| ~ relation(X2897) )
& ( relation(esk182_2(X2896,X2897))
| esk178_2(X2896,X2897) != esk179_2(X2896,X2897)
| empty(X2896)
| ~ relation(X2897) )
& ( function(esk182_2(X2896,X2897))
| esk178_2(X2896,X2897) != esk179_2(X2896,X2897)
| empty(X2896)
| ~ relation(X2897) )
& ( in(X2906,X2896)
| ~ in(ordered_pair(X2906,X2907),esk182_2(X2896,X2897))
| esk178_2(X2896,X2897) != esk179_2(X2896,X2897)
| empty(X2896)
| ~ relation(X2897) )
& ( X2906 = esk183_4(X2896,X2897,X2906,X2907)
| ~ in(ordered_pair(X2906,X2907),esk182_2(X2896,X2897))
| esk178_2(X2896,X2897) != esk179_2(X2896,X2897)
| empty(X2896)
| ~ relation(X2897) )
& ( in(X2907,esk183_4(X2896,X2897,X2906,X2907))
| ~ in(ordered_pair(X2906,X2907),esk182_2(X2896,X2897))
| esk178_2(X2896,X2897) != esk179_2(X2896,X2897)
| empty(X2896)
| ~ relation(X2897) )
& ( ~ in(X2909,esk183_4(X2896,X2897,X2906,X2907))
| in(ordered_pair(X2907,X2909),X2897)
| ~ in(ordered_pair(X2906,X2907),esk182_2(X2896,X2897))
| esk178_2(X2896,X2897) != esk179_2(X2896,X2897)
| empty(X2896)
| ~ relation(X2897) )
& ( in(esk184_5(X2896,X2897,X2910,X2911,X2912),X2912)
| X2910 != X2912
| ~ in(X2911,X2912)
| ~ in(X2910,X2896)
| in(ordered_pair(X2910,X2911),esk182_2(X2896,X2897))
| esk178_2(X2896,X2897) != esk179_2(X2896,X2897)
| empty(X2896)
| ~ relation(X2897) )
& ( ~ in(ordered_pair(X2911,esk184_5(X2896,X2897,X2910,X2911,X2912)),X2897)
| X2910 != X2912
| ~ in(X2911,X2912)
| ~ in(X2910,X2896)
| in(ordered_pair(X2910,X2911),esk182_2(X2896,X2897))
| esk178_2(X2896,X2897) != esk179_2(X2896,X2897)
| empty(X2896)
| ~ relation(X2897) ) ),
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)],[i_0_649])])])])])]) ).
fof(i_0_691,plain,
! [X2975,X2976,X2981,X2983,X2985,X2988,X2989,X2990,X2991] :
( ( in(esk212_3(X2975,X2976,X2985),X2975)
| ~ in(X2985,esk211_2(X2975,X2976))
| in(esk206_2(X2975,X2976),X2975)
| empty(X2975)
| ~ relation(X2976) )
& ( esk212_3(X2975,X2976,X2985) = esk213_3(X2975,X2976,X2985)
| ~ in(X2985,esk211_2(X2975,X2976))
| in(esk206_2(X2975,X2976),X2975)
| empty(X2975)
| ~ relation(X2976) )
& ( in(X2985,esk213_3(X2975,X2976,X2985))
| ~ in(X2985,esk211_2(X2975,X2976))
| in(esk206_2(X2975,X2976),X2975)
| empty(X2975)
| ~ relation(X2976) )
& ( ~ in(X2988,esk213_3(X2975,X2976,X2985))
| in(ordered_pair(X2985,X2988),X2976)
| ~ in(X2985,esk211_2(X2975,X2976))
| in(esk206_2(X2975,X2976),X2975)
| empty(X2975)
| ~ relation(X2976) )
& ( in(esk214_5(X2975,X2976,X2989,X2990,X2991),X2991)
| X2990 != X2991
| ~ in(X2989,X2991)
| ~ in(X2990,X2975)
| in(X2989,esk211_2(X2975,X2976))
| in(esk206_2(X2975,X2976),X2975)
| empty(X2975)
| ~ relation(X2976) )
& ( ~ in(ordered_pair(X2989,esk214_5(X2975,X2976,X2989,X2990,X2991)),X2976)
| X2990 != X2991
| ~ in(X2989,X2991)
| ~ in(X2990,X2975)
| in(X2989,esk211_2(X2975,X2976))
| in(esk206_2(X2975,X2976),X2975)
| empty(X2975)
| ~ relation(X2976) )
& ( in(esk212_3(X2975,X2976,X2985),X2975)
| ~ in(X2985,esk211_2(X2975,X2976))
| esk206_2(X2975,X2976) = esk209_2(X2975,X2976)
| empty(X2975)
| ~ relation(X2976) )
& ( esk212_3(X2975,X2976,X2985) = esk213_3(X2975,X2976,X2985)
| ~ in(X2985,esk211_2(X2975,X2976))
| esk206_2(X2975,X2976) = esk209_2(X2975,X2976)
| empty(X2975)
| ~ relation(X2976) )
& ( in(X2985,esk213_3(X2975,X2976,X2985))
| ~ in(X2985,esk211_2(X2975,X2976))
| esk206_2(X2975,X2976) = esk209_2(X2975,X2976)
| empty(X2975)
| ~ relation(X2976) )
& ( ~ in(X2988,esk213_3(X2975,X2976,X2985))
| in(ordered_pair(X2985,X2988),X2976)
| ~ in(X2985,esk211_2(X2975,X2976))
| esk206_2(X2975,X2976) = esk209_2(X2975,X2976)
| empty(X2975)
| ~ relation(X2976) )
& ( in(esk214_5(X2975,X2976,X2989,X2990,X2991),X2991)
| X2990 != X2991
| ~ in(X2989,X2991)
| ~ in(X2990,X2975)
| in(X2989,esk211_2(X2975,X2976))
| esk206_2(X2975,X2976) = esk209_2(X2975,X2976)
| empty(X2975)
| ~ relation(X2976) )
& ( ~ in(ordered_pair(X2989,esk214_5(X2975,X2976,X2989,X2990,X2991)),X2976)
| X2990 != X2991
| ~ in(X2989,X2991)
| ~ in(X2990,X2975)
| in(X2989,esk211_2(X2975,X2976))
| esk206_2(X2975,X2976) = esk209_2(X2975,X2976)
| empty(X2975)
| ~ relation(X2976) )
& ( in(esk212_3(X2975,X2976,X2985),X2975)
| ~ in(X2985,esk211_2(X2975,X2976))
| in(esk207_2(X2975,X2976),esk209_2(X2975,X2976))
| empty(X2975)
| ~ relation(X2976) )
& ( esk212_3(X2975,X2976,X2985) = esk213_3(X2975,X2976,X2985)
| ~ in(X2985,esk211_2(X2975,X2976))
| in(esk207_2(X2975,X2976),esk209_2(X2975,X2976))
| empty(X2975)
| ~ relation(X2976) )
& ( in(X2985,esk213_3(X2975,X2976,X2985))
| ~ in(X2985,esk211_2(X2975,X2976))
| in(esk207_2(X2975,X2976),esk209_2(X2975,X2976))
| empty(X2975)
| ~ relation(X2976) )
& ( ~ in(X2988,esk213_3(X2975,X2976,X2985))
| in(ordered_pair(X2985,X2988),X2976)
| ~ in(X2985,esk211_2(X2975,X2976))
| in(esk207_2(X2975,X2976),esk209_2(X2975,X2976))
| empty(X2975)
| ~ relation(X2976) )
& ( in(esk214_5(X2975,X2976,X2989,X2990,X2991),X2991)
| X2990 != X2991
| ~ in(X2989,X2991)
| ~ in(X2990,X2975)
| in(X2989,esk211_2(X2975,X2976))
| in(esk207_2(X2975,X2976),esk209_2(X2975,X2976))
| empty(X2975)
| ~ relation(X2976) )
& ( ~ in(ordered_pair(X2989,esk214_5(X2975,X2976,X2989,X2990,X2991)),X2976)
| X2990 != X2991
| ~ in(X2989,X2991)
| ~ in(X2990,X2975)
| in(X2989,esk211_2(X2975,X2976))
| in(esk207_2(X2975,X2976),esk209_2(X2975,X2976))
| empty(X2975)
| ~ relation(X2976) )
& ( in(esk212_3(X2975,X2976,X2985),X2975)
| ~ in(X2985,esk211_2(X2975,X2976))
| ~ in(X2981,esk209_2(X2975,X2976))
| in(ordered_pair(esk207_2(X2975,X2976),X2981),X2976)
| empty(X2975)
| ~ relation(X2976) )
& ( esk212_3(X2975,X2976,X2985) = esk213_3(X2975,X2976,X2985)
| ~ in(X2985,esk211_2(X2975,X2976))
| ~ in(X2981,esk209_2(X2975,X2976))
| in(ordered_pair(esk207_2(X2975,X2976),X2981),X2976)
| empty(X2975)
| ~ relation(X2976) )
& ( in(X2985,esk213_3(X2975,X2976,X2985))
| ~ in(X2985,esk211_2(X2975,X2976))
| ~ in(X2981,esk209_2(X2975,X2976))
| in(ordered_pair(esk207_2(X2975,X2976),X2981),X2976)
| empty(X2975)
| ~ relation(X2976) )
& ( ~ in(X2988,esk213_3(X2975,X2976,X2985))
| in(ordered_pair(X2985,X2988),X2976)
| ~ in(X2985,esk211_2(X2975,X2976))
| ~ in(X2981,esk209_2(X2975,X2976))
| in(ordered_pair(esk207_2(X2975,X2976),X2981),X2976)
| empty(X2975)
| ~ relation(X2976) )
& ( in(esk214_5(X2975,X2976,X2989,X2990,X2991),X2991)
| X2990 != X2991
| ~ in(X2989,X2991)
| ~ in(X2990,X2975)
| in(X2989,esk211_2(X2975,X2976))
| ~ in(X2981,esk209_2(X2975,X2976))
| in(ordered_pair(esk207_2(X2975,X2976),X2981),X2976)
| empty(X2975)
| ~ relation(X2976) )
& ( ~ in(ordered_pair(X2989,esk214_5(X2975,X2976,X2989,X2990,X2991)),X2976)
| X2990 != X2991
| ~ in(X2989,X2991)
| ~ in(X2990,X2975)
| in(X2989,esk211_2(X2975,X2976))
| ~ in(X2981,esk209_2(X2975,X2976))
| in(ordered_pair(esk207_2(X2975,X2976),X2981),X2976)
| empty(X2975)
| ~ relation(X2976) )
& ( in(esk212_3(X2975,X2976,X2985),X2975)
| ~ in(X2985,esk211_2(X2975,X2976))
| in(esk206_2(X2975,X2976),X2975)
| empty(X2975)
| ~ relation(X2976) )
& ( esk212_3(X2975,X2976,X2985) = esk213_3(X2975,X2976,X2985)
| ~ in(X2985,esk211_2(X2975,X2976))
| in(esk206_2(X2975,X2976),X2975)
| empty(X2975)
| ~ relation(X2976) )
& ( in(X2985,esk213_3(X2975,X2976,X2985))
| ~ in(X2985,esk211_2(X2975,X2976))
| in(esk206_2(X2975,X2976),X2975)
| empty(X2975)
| ~ relation(X2976) )
& ( ~ in(X2988,esk213_3(X2975,X2976,X2985))
| in(ordered_pair(X2985,X2988),X2976)
| ~ in(X2985,esk211_2(X2975,X2976))
| in(esk206_2(X2975,X2976),X2975)
| empty(X2975)
| ~ relation(X2976) )
& ( in(esk214_5(X2975,X2976,X2989,X2990,X2991),X2991)
| X2990 != X2991
| ~ in(X2989,X2991)
| ~ in(X2990,X2975)
| in(X2989,esk211_2(X2975,X2976))
| in(esk206_2(X2975,X2976),X2975)
| empty(X2975)
| ~ relation(X2976) )
& ( ~ in(ordered_pair(X2989,esk214_5(X2975,X2976,X2989,X2990,X2991)),X2976)
| X2990 != X2991
| ~ in(X2989,X2991)
| ~ in(X2990,X2975)
| in(X2989,esk211_2(X2975,X2976))
| in(esk206_2(X2975,X2976),X2975)
| empty(X2975)
| ~ relation(X2976) )
& ( in(esk212_3(X2975,X2976,X2985),X2975)
| ~ in(X2985,esk211_2(X2975,X2976))
| esk206_2(X2975,X2976) = esk210_2(X2975,X2976)
| empty(X2975)
| ~ relation(X2976) )
& ( esk212_3(X2975,X2976,X2985) = esk213_3(X2975,X2976,X2985)
| ~ in(X2985,esk211_2(X2975,X2976))
| esk206_2(X2975,X2976) = esk210_2(X2975,X2976)
| empty(X2975)
| ~ relation(X2976) )
& ( in(X2985,esk213_3(X2975,X2976,X2985))
| ~ in(X2985,esk211_2(X2975,X2976))
| esk206_2(X2975,X2976) = esk210_2(X2975,X2976)
| empty(X2975)
| ~ relation(X2976) )
& ( ~ in(X2988,esk213_3(X2975,X2976,X2985))
| in(ordered_pair(X2985,X2988),X2976)
| ~ in(X2985,esk211_2(X2975,X2976))
| esk206_2(X2975,X2976) = esk210_2(X2975,X2976)
| empty(X2975)
| ~ relation(X2976) )
& ( in(esk214_5(X2975,X2976,X2989,X2990,X2991),X2991)
| X2990 != X2991
| ~ in(X2989,X2991)
| ~ in(X2990,X2975)
| in(X2989,esk211_2(X2975,X2976))
| esk206_2(X2975,X2976) = esk210_2(X2975,X2976)
| empty(X2975)
| ~ relation(X2976) )
& ( ~ in(ordered_pair(X2989,esk214_5(X2975,X2976,X2989,X2990,X2991)),X2976)
| X2990 != X2991
| ~ in(X2989,X2991)
| ~ in(X2990,X2975)
| in(X2989,esk211_2(X2975,X2976))
| esk206_2(X2975,X2976) = esk210_2(X2975,X2976)
| empty(X2975)
| ~ relation(X2976) )
& ( in(esk212_3(X2975,X2976,X2985),X2975)
| ~ in(X2985,esk211_2(X2975,X2976))
| in(esk208_2(X2975,X2976),esk210_2(X2975,X2976))
| empty(X2975)
| ~ relation(X2976) )
& ( esk212_3(X2975,X2976,X2985) = esk213_3(X2975,X2976,X2985)
| ~ in(X2985,esk211_2(X2975,X2976))
| in(esk208_2(X2975,X2976),esk210_2(X2975,X2976))
| empty(X2975)
| ~ relation(X2976) )
& ( in(X2985,esk213_3(X2975,X2976,X2985))
| ~ in(X2985,esk211_2(X2975,X2976))
| in(esk208_2(X2975,X2976),esk210_2(X2975,X2976))
| empty(X2975)
| ~ relation(X2976) )
& ( ~ in(X2988,esk213_3(X2975,X2976,X2985))
| in(ordered_pair(X2985,X2988),X2976)
| ~ in(X2985,esk211_2(X2975,X2976))
| in(esk208_2(X2975,X2976),esk210_2(X2975,X2976))
| empty(X2975)
| ~ relation(X2976) )
& ( in(esk214_5(X2975,X2976,X2989,X2990,X2991),X2991)
| X2990 != X2991
| ~ in(X2989,X2991)
| ~ in(X2990,X2975)
| in(X2989,esk211_2(X2975,X2976))
| in(esk208_2(X2975,X2976),esk210_2(X2975,X2976))
| empty(X2975)
| ~ relation(X2976) )
& ( ~ in(ordered_pair(X2989,esk214_5(X2975,X2976,X2989,X2990,X2991)),X2976)
| X2990 != X2991
| ~ in(X2989,X2991)
| ~ in(X2990,X2975)
| in(X2989,esk211_2(X2975,X2976))
| in(esk208_2(X2975,X2976),esk210_2(X2975,X2976))
| empty(X2975)
| ~ relation(X2976) )
& ( in(esk212_3(X2975,X2976,X2985),X2975)
| ~ in(X2985,esk211_2(X2975,X2976))
| ~ in(X2983,esk210_2(X2975,X2976))
| in(ordered_pair(esk208_2(X2975,X2976),X2983),X2976)
| empty(X2975)
| ~ relation(X2976) )
& ( esk212_3(X2975,X2976,X2985) = esk213_3(X2975,X2976,X2985)
| ~ in(X2985,esk211_2(X2975,X2976))
| ~ in(X2983,esk210_2(X2975,X2976))
| in(ordered_pair(esk208_2(X2975,X2976),X2983),X2976)
| empty(X2975)
| ~ relation(X2976) )
& ( in(X2985,esk213_3(X2975,X2976,X2985))
| ~ in(X2985,esk211_2(X2975,X2976))
| ~ in(X2983,esk210_2(X2975,X2976))
| in(ordered_pair(esk208_2(X2975,X2976),X2983),X2976)
| empty(X2975)
| ~ relation(X2976) )
& ( ~ in(X2988,esk213_3(X2975,X2976,X2985))
| in(ordered_pair(X2985,X2988),X2976)
| ~ in(X2985,esk211_2(X2975,X2976))
| ~ in(X2983,esk210_2(X2975,X2976))
| in(ordered_pair(esk208_2(X2975,X2976),X2983),X2976)
| empty(X2975)
| ~ relation(X2976) )
& ( in(esk214_5(X2975,X2976,X2989,X2990,X2991),X2991)
| X2990 != X2991
| ~ in(X2989,X2991)
| ~ in(X2990,X2975)
| in(X2989,esk211_2(X2975,X2976))
| ~ in(X2983,esk210_2(X2975,X2976))
| in(ordered_pair(esk208_2(X2975,X2976),X2983),X2976)
| empty(X2975)
| ~ relation(X2976) )
& ( ~ in(ordered_pair(X2989,esk214_5(X2975,X2976,X2989,X2990,X2991)),X2976)
| X2990 != X2991
| ~ in(X2989,X2991)
| ~ in(X2990,X2975)
| in(X2989,esk211_2(X2975,X2976))
| ~ in(X2983,esk210_2(X2975,X2976))
| in(ordered_pair(esk208_2(X2975,X2976),X2983),X2976)
| empty(X2975)
| ~ relation(X2976) )
& ( in(esk212_3(X2975,X2976,X2985),X2975)
| ~ in(X2985,esk211_2(X2975,X2976))
| esk207_2(X2975,X2976) != esk208_2(X2975,X2976)
| empty(X2975)
| ~ relation(X2976) )
& ( esk212_3(X2975,X2976,X2985) = esk213_3(X2975,X2976,X2985)
| ~ in(X2985,esk211_2(X2975,X2976))
| esk207_2(X2975,X2976) != esk208_2(X2975,X2976)
| empty(X2975)
| ~ relation(X2976) )
& ( in(X2985,esk213_3(X2975,X2976,X2985))
| ~ in(X2985,esk211_2(X2975,X2976))
| esk207_2(X2975,X2976) != esk208_2(X2975,X2976)
| empty(X2975)
| ~ relation(X2976) )
& ( ~ in(X2988,esk213_3(X2975,X2976,X2985))
| in(ordered_pair(X2985,X2988),X2976)
| ~ in(X2985,esk211_2(X2975,X2976))
| esk207_2(X2975,X2976) != esk208_2(X2975,X2976)
| empty(X2975)
| ~ relation(X2976) )
& ( in(esk214_5(X2975,X2976,X2989,X2990,X2991),X2991)
| X2990 != X2991
| ~ in(X2989,X2991)
| ~ in(X2990,X2975)
| in(X2989,esk211_2(X2975,X2976))
| esk207_2(X2975,X2976) != esk208_2(X2975,X2976)
| empty(X2975)
| ~ relation(X2976) )
& ( ~ in(ordered_pair(X2989,esk214_5(X2975,X2976,X2989,X2990,X2991)),X2976)
| X2990 != X2991
| ~ in(X2989,X2991)
| ~ in(X2990,X2975)
| in(X2989,esk211_2(X2975,X2976))
| esk207_2(X2975,X2976) != esk208_2(X2975,X2976)
| empty(X2975)
| ~ relation(X2976) ) ),
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)],[i_0_650])])])])])]) ).
fof(i_0_692,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)],[dt_k2_binop_1]) ).
fof(i_0_693,plain,
! [X2365,X2366,X2367,X2368,X2369,X2370,X2371] :
( ( relation_dom(X2367) = relation_field(X2365)
| ~ relation_isomorphism(X2365,X2366,X2367)
| ~ relation(X2367)
| ~ function(X2367)
| ~ relation(X2366)
| ~ relation(X2365) )
& ( relation_rng(X2367) = relation_field(X2366)
| ~ relation_isomorphism(X2365,X2366,X2367)
| ~ relation(X2367)
| ~ function(X2367)
| ~ relation(X2366)
| ~ relation(X2365) )
& ( one_to_one(X2367)
| ~ relation_isomorphism(X2365,X2366,X2367)
| ~ relation(X2367)
| ~ function(X2367)
| ~ relation(X2366)
| ~ relation(X2365) )
& ( in(X2368,relation_field(X2365))
| ~ in(ordered_pair(X2368,X2369),X2365)
| ~ relation_isomorphism(X2365,X2366,X2367)
| ~ relation(X2367)
| ~ function(X2367)
| ~ relation(X2366)
| ~ relation(X2365) )
& ( in(X2369,relation_field(X2365))
| ~ in(ordered_pair(X2368,X2369),X2365)
| ~ relation_isomorphism(X2365,X2366,X2367)
| ~ relation(X2367)
| ~ function(X2367)
| ~ relation(X2366)
| ~ relation(X2365) )
& ( in(ordered_pair(apply(X2367,X2368),apply(X2367,X2369)),X2366)
| ~ in(ordered_pair(X2368,X2369),X2365)
| ~ relation_isomorphism(X2365,X2366,X2367)
| ~ relation(X2367)
| ~ function(X2367)
| ~ relation(X2366)
| ~ relation(X2365) )
& ( ~ in(X2370,relation_field(X2365))
| ~ in(X2371,relation_field(X2365))
| ~ in(ordered_pair(apply(X2367,X2370),apply(X2367,X2371)),X2366)
| in(ordered_pair(X2370,X2371),X2365)
| ~ relation_isomorphism(X2365,X2366,X2367)
| ~ relation(X2367)
| ~ function(X2367)
| ~ relation(X2366)
| ~ relation(X2365) )
& ( ~ in(ordered_pair(esk99_3(X2365,X2366,X2367),esk100_3(X2365,X2366,X2367)),X2365)
| ~ in(esk99_3(X2365,X2366,X2367),relation_field(X2365))
| ~ in(esk100_3(X2365,X2366,X2367),relation_field(X2365))
| ~ in(ordered_pair(apply(X2367,esk99_3(X2365,X2366,X2367)),apply(X2367,esk100_3(X2365,X2366,X2367))),X2366)
| relation_dom(X2367) != relation_field(X2365)
| relation_rng(X2367) != relation_field(X2366)
| ~ one_to_one(X2367)
| relation_isomorphism(X2365,X2366,X2367)
| ~ relation(X2367)
| ~ function(X2367)
| ~ relation(X2366)
| ~ relation(X2365) )
& ( in(esk99_3(X2365,X2366,X2367),relation_field(X2365))
| in(ordered_pair(esk99_3(X2365,X2366,X2367),esk100_3(X2365,X2366,X2367)),X2365)
| relation_dom(X2367) != relation_field(X2365)
| relation_rng(X2367) != relation_field(X2366)
| ~ one_to_one(X2367)
| relation_isomorphism(X2365,X2366,X2367)
| ~ relation(X2367)
| ~ function(X2367)
| ~ relation(X2366)
| ~ relation(X2365) )
& ( in(esk100_3(X2365,X2366,X2367),relation_field(X2365))
| in(ordered_pair(esk99_3(X2365,X2366,X2367),esk100_3(X2365,X2366,X2367)),X2365)
| relation_dom(X2367) != relation_field(X2365)
| relation_rng(X2367) != relation_field(X2366)
| ~ one_to_one(X2367)
| relation_isomorphism(X2365,X2366,X2367)
| ~ relation(X2367)
| ~ function(X2367)
| ~ relation(X2366)
| ~ relation(X2365) )
& ( in(ordered_pair(apply(X2367,esk99_3(X2365,X2366,X2367)),apply(X2367,esk100_3(X2365,X2366,X2367))),X2366)
| in(ordered_pair(esk99_3(X2365,X2366,X2367),esk100_3(X2365,X2366,X2367)),X2365)
| relation_dom(X2367) != relation_field(X2365)
| relation_rng(X2367) != relation_field(X2366)
| ~ one_to_one(X2367)
| relation_isomorphism(X2365,X2366,X2367)
| ~ relation(X2367)
| ~ function(X2367)
| ~ relation(X2366)
| ~ relation(X2365) ) ),
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)],[d7_wellord1])])])])])]) ).
fof(i_0_694,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)],[redefinition_k2_binop_1]) ).
fof(i_0_695,lemma,
! [X3588,X3589,X3590,X3592,X3593] :
( ( in(esk416_3(X3588,X3589,X3590),X3589)
| relation_rng_as_subset(X3588,X3589,X3590) = X3589
| ~ relation_of2_as_subset(X3590,X3588,X3589) )
& ( ~ in(ordered_pair(X3592,esk416_3(X3588,X3589,X3590)),X3590)
| relation_rng_as_subset(X3588,X3589,X3590) = X3589
| ~ relation_of2_as_subset(X3590,X3588,X3589) )
& ( relation_rng_as_subset(X3588,X3589,X3590) != X3589
| ~ in(X3593,X3589)
| in(ordered_pair(esk417_4(X3588,X3589,X3590,X3593),X3593),X3590)
| ~ relation_of2_as_subset(X3590,X3588,X3589) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_651])])])])]) ).
fof(i_0_696,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)],[d1_lattices]) ).
fof(i_0_697,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)],[d2_lattices]) ).
fof(i_0_698,plain,
! [X1961,X1962,X1963,X1964,X1966,X1967,X1968,X1969,X1971] :
( ( in(ordered_pair(esk16_4(X1961,X1962,X1963,X1964),X1964),X1961)
| ~ in(X1964,X1963)
| X1963 != relation_image(X1961,X1962)
| ~ relation(X1961) )
& ( in(esk16_4(X1961,X1962,X1963,X1964),X1962)
| ~ in(X1964,X1963)
| X1963 != relation_image(X1961,X1962)
| ~ relation(X1961) )
& ( ~ in(ordered_pair(X1967,X1966),X1961)
| ~ in(X1967,X1962)
| in(X1966,X1963)
| X1963 != relation_image(X1961,X1962)
| ~ relation(X1961) )
& ( ~ in(esk17_3(X1961,X1968,X1969),X1969)
| ~ in(ordered_pair(X1971,esk17_3(X1961,X1968,X1969)),X1961)
| ~ in(X1971,X1968)
| X1969 = relation_image(X1961,X1968)
| ~ relation(X1961) )
& ( in(ordered_pair(esk18_3(X1961,X1968,X1969),esk17_3(X1961,X1968,X1969)),X1961)
| in(esk17_3(X1961,X1968,X1969),X1969)
| X1969 = relation_image(X1961,X1968)
| ~ relation(X1961) )
& ( in(esk18_3(X1961,X1968,X1969),X1968)
| in(esk17_3(X1961,X1968,X1969),X1969)
| X1969 = relation_image(X1961,X1968)
| ~ relation(X1961) ) ),
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)],[d13_relat_1])])])])])]) ).
fof(i_0_699,plain,
! [X1929,X1930,X1931,X1932,X1933,X1934,X1935] :
( ( in(X1933,X1929)
| ~ in(ordered_pair(X1932,X1933),X1931)
| X1931 != relation_rng_restriction(X1929,X1930)
| ~ relation(X1931)
| ~ relation(X1930) )
& ( in(ordered_pair(X1932,X1933),X1930)
| ~ in(ordered_pair(X1932,X1933),X1931)
| X1931 != relation_rng_restriction(X1929,X1930)
| ~ relation(X1931)
| ~ relation(X1930) )
& ( ~ in(X1935,X1929)
| ~ in(ordered_pair(X1934,X1935),X1930)
| in(ordered_pair(X1934,X1935),X1931)
| X1931 != relation_rng_restriction(X1929,X1930)
| ~ relation(X1931)
| ~ relation(X1930) )
& ( ~ in(ordered_pair(esk8_3(X1929,X1930,X1931),esk9_3(X1929,X1930,X1931)),X1931)
| ~ in(esk9_3(X1929,X1930,X1931),X1929)
| ~ in(ordered_pair(esk8_3(X1929,X1930,X1931),esk9_3(X1929,X1930,X1931)),X1930)
| X1931 = relation_rng_restriction(X1929,X1930)
| ~ relation(X1931)
| ~ relation(X1930) )
& ( in(esk9_3(X1929,X1930,X1931),X1929)
| in(ordered_pair(esk8_3(X1929,X1930,X1931),esk9_3(X1929,X1930,X1931)),X1931)
| X1931 = relation_rng_restriction(X1929,X1930)
| ~ relation(X1931)
| ~ relation(X1930) )
& ( in(ordered_pair(esk8_3(X1929,X1930,X1931),esk9_3(X1929,X1930,X1931)),X1930)
| in(ordered_pair(esk8_3(X1929,X1930,X1931),esk9_3(X1929,X1930,X1931)),X1931)
| X1931 = relation_rng_restriction(X1929,X1930)
| ~ relation(X1931)
| ~ relation(X1930) ) ),
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)],[d12_relat_1])])])])])]) ).
fof(i_0_700,plain,
! [X1908,X1909,X1910,X1911,X1912,X1913,X1914] :
( ( in(X1911,X1909)
| ~ in(ordered_pair(X1911,X1912),X1910)
| X1910 != relation_dom_restriction(X1908,X1909)
| ~ relation(X1910)
| ~ relation(X1908) )
& ( in(ordered_pair(X1911,X1912),X1908)
| ~ in(ordered_pair(X1911,X1912),X1910)
| X1910 != relation_dom_restriction(X1908,X1909)
| ~ relation(X1910)
| ~ relation(X1908) )
& ( ~ in(X1913,X1909)
| ~ in(ordered_pair(X1913,X1914),X1908)
| in(ordered_pair(X1913,X1914),X1910)
| X1910 != relation_dom_restriction(X1908,X1909)
| ~ relation(X1910)
| ~ relation(X1908) )
& ( ~ in(ordered_pair(esk3_3(X1908,X1909,X1910),esk4_3(X1908,X1909,X1910)),X1910)
| ~ in(esk3_3(X1908,X1909,X1910),X1909)
| ~ in(ordered_pair(esk3_3(X1908,X1909,X1910),esk4_3(X1908,X1909,X1910)),X1908)
| X1910 = relation_dom_restriction(X1908,X1909)
| ~ relation(X1910)
| ~ relation(X1908) )
& ( in(esk3_3(X1908,X1909,X1910),X1909)
| in(ordered_pair(esk3_3(X1908,X1909,X1910),esk4_3(X1908,X1909,X1910)),X1910)
| X1910 = relation_dom_restriction(X1908,X1909)
| ~ relation(X1910)
| ~ relation(X1908) )
& ( in(ordered_pair(esk3_3(X1908,X1909,X1910),esk4_3(X1908,X1909,X1910)),X1908)
| in(ordered_pair(esk3_3(X1908,X1909,X1910),esk4_3(X1908,X1909,X1910)),X1910)
| X1910 = relation_dom_restriction(X1908,X1909)
| ~ relation(X1910)
| ~ relation(X1908) ) ),
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)],[d11_relat_1])])])])])]) ).
fof(i_0_701,lemma,
! [X3334,X3335,X3340,X3342,X3344,X3345,X3348,X3350] :
( ( relation(esk381_2(X3334,X3335))
| in(esk379_2(X3334,X3335),X3334)
| in(esk374_2(X3334,X3335),X3334)
| empty(X3334)
| ~ relation(X3335) )
& ( function(esk381_2(X3334,X3335))
| in(esk379_2(X3334,X3335),X3334)
| in(esk374_2(X3334,X3335),X3334)
| empty(X3334)
| ~ relation(X3335) )
& ( relation_dom(esk381_2(X3334,X3335)) = X3334
| in(esk379_2(X3334,X3335),X3334)
| in(esk374_2(X3334,X3335),X3334)
| empty(X3334)
| ~ relation(X3335) )
& ( X3348 = esk382_3(X3334,X3335,X3348)
| ~ in(X3348,X3334)
| in(esk379_2(X3334,X3335),X3334)
| in(esk374_2(X3334,X3335),X3334)
| empty(X3334)
| ~ relation(X3335) )
& ( in(apply(esk381_2(X3334,X3335),X3348),esk382_3(X3334,X3335,X3348))
| ~ in(X3348,X3334)
| in(esk379_2(X3334,X3335),X3334)
| in(esk374_2(X3334,X3335),X3334)
| empty(X3334)
| ~ relation(X3335) )
& ( ~ in(X3350,esk382_3(X3334,X3335,X3348))
| in(ordered_pair(apply(esk381_2(X3334,X3335),X3348),X3350),X3335)
| ~ in(X3348,X3334)
| in(esk379_2(X3334,X3335),X3334)
| in(esk374_2(X3334,X3335),X3334)
| empty(X3334)
| ~ relation(X3335) )
& ( relation(esk381_2(X3334,X3335))
| in(esk380_4(X3334,X3335,X3344,X3345),X3345)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| in(esk374_2(X3334,X3335),X3334)
| empty(X3334)
| ~ relation(X3335) )
& ( function(esk381_2(X3334,X3335))
| in(esk380_4(X3334,X3335,X3344,X3345),X3345)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| in(esk374_2(X3334,X3335),X3334)
| empty(X3334)
| ~ relation(X3335) )
& ( relation_dom(esk381_2(X3334,X3335)) = X3334
| in(esk380_4(X3334,X3335,X3344,X3345),X3345)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| in(esk374_2(X3334,X3335),X3334)
| empty(X3334)
| ~ relation(X3335) )
& ( X3348 = esk382_3(X3334,X3335,X3348)
| ~ in(X3348,X3334)
| in(esk380_4(X3334,X3335,X3344,X3345),X3345)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| in(esk374_2(X3334,X3335),X3334)
| empty(X3334)
| ~ relation(X3335) )
& ( in(apply(esk381_2(X3334,X3335),X3348),esk382_3(X3334,X3335,X3348))
| ~ in(X3348,X3334)
| in(esk380_4(X3334,X3335,X3344,X3345),X3345)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| in(esk374_2(X3334,X3335),X3334)
| empty(X3334)
| ~ relation(X3335) )
& ( ~ in(X3350,esk382_3(X3334,X3335,X3348))
| in(ordered_pair(apply(esk381_2(X3334,X3335),X3348),X3350),X3335)
| ~ in(X3348,X3334)
| in(esk380_4(X3334,X3335,X3344,X3345),X3345)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| in(esk374_2(X3334,X3335),X3334)
| empty(X3334)
| ~ relation(X3335) )
& ( relation(esk381_2(X3334,X3335))
| ~ in(ordered_pair(X3344,esk380_4(X3334,X3335,X3344,X3345)),X3335)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| in(esk374_2(X3334,X3335),X3334)
| empty(X3334)
| ~ relation(X3335) )
& ( function(esk381_2(X3334,X3335))
| ~ in(ordered_pair(X3344,esk380_4(X3334,X3335,X3344,X3345)),X3335)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| in(esk374_2(X3334,X3335),X3334)
| empty(X3334)
| ~ relation(X3335) )
& ( relation_dom(esk381_2(X3334,X3335)) = X3334
| ~ in(ordered_pair(X3344,esk380_4(X3334,X3335,X3344,X3345)),X3335)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| in(esk374_2(X3334,X3335),X3334)
| empty(X3334)
| ~ relation(X3335) )
& ( X3348 = esk382_3(X3334,X3335,X3348)
| ~ in(X3348,X3334)
| ~ in(ordered_pair(X3344,esk380_4(X3334,X3335,X3344,X3345)),X3335)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| in(esk374_2(X3334,X3335),X3334)
| empty(X3334)
| ~ relation(X3335) )
& ( in(apply(esk381_2(X3334,X3335),X3348),esk382_3(X3334,X3335,X3348))
| ~ in(X3348,X3334)
| ~ in(ordered_pair(X3344,esk380_4(X3334,X3335,X3344,X3345)),X3335)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| in(esk374_2(X3334,X3335),X3334)
| empty(X3334)
| ~ relation(X3335) )
& ( ~ in(X3350,esk382_3(X3334,X3335,X3348))
| in(ordered_pair(apply(esk381_2(X3334,X3335),X3348),X3350),X3335)
| ~ in(X3348,X3334)
| ~ in(ordered_pair(X3344,esk380_4(X3334,X3335,X3344,X3345)),X3335)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| in(esk374_2(X3334,X3335),X3334)
| empty(X3334)
| ~ relation(X3335) )
& ( relation(esk381_2(X3334,X3335))
| in(esk379_2(X3334,X3335),X3334)
| esk374_2(X3334,X3335) = esk377_2(X3334,X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( function(esk381_2(X3334,X3335))
| in(esk379_2(X3334,X3335),X3334)
| esk374_2(X3334,X3335) = esk377_2(X3334,X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( relation_dom(esk381_2(X3334,X3335)) = X3334
| in(esk379_2(X3334,X3335),X3334)
| esk374_2(X3334,X3335) = esk377_2(X3334,X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( X3348 = esk382_3(X3334,X3335,X3348)
| ~ in(X3348,X3334)
| in(esk379_2(X3334,X3335),X3334)
| esk374_2(X3334,X3335) = esk377_2(X3334,X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( in(apply(esk381_2(X3334,X3335),X3348),esk382_3(X3334,X3335,X3348))
| ~ in(X3348,X3334)
| in(esk379_2(X3334,X3335),X3334)
| esk374_2(X3334,X3335) = esk377_2(X3334,X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( ~ in(X3350,esk382_3(X3334,X3335,X3348))
| in(ordered_pair(apply(esk381_2(X3334,X3335),X3348),X3350),X3335)
| ~ in(X3348,X3334)
| in(esk379_2(X3334,X3335),X3334)
| esk374_2(X3334,X3335) = esk377_2(X3334,X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( relation(esk381_2(X3334,X3335))
| in(esk380_4(X3334,X3335,X3344,X3345),X3345)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| esk374_2(X3334,X3335) = esk377_2(X3334,X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( function(esk381_2(X3334,X3335))
| in(esk380_4(X3334,X3335,X3344,X3345),X3345)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| esk374_2(X3334,X3335) = esk377_2(X3334,X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( relation_dom(esk381_2(X3334,X3335)) = X3334
| in(esk380_4(X3334,X3335,X3344,X3345),X3345)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| esk374_2(X3334,X3335) = esk377_2(X3334,X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( X3348 = esk382_3(X3334,X3335,X3348)
| ~ in(X3348,X3334)
| in(esk380_4(X3334,X3335,X3344,X3345),X3345)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| esk374_2(X3334,X3335) = esk377_2(X3334,X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( in(apply(esk381_2(X3334,X3335),X3348),esk382_3(X3334,X3335,X3348))
| ~ in(X3348,X3334)
| in(esk380_4(X3334,X3335,X3344,X3345),X3345)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| esk374_2(X3334,X3335) = esk377_2(X3334,X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( ~ in(X3350,esk382_3(X3334,X3335,X3348))
| in(ordered_pair(apply(esk381_2(X3334,X3335),X3348),X3350),X3335)
| ~ in(X3348,X3334)
| in(esk380_4(X3334,X3335,X3344,X3345),X3345)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| esk374_2(X3334,X3335) = esk377_2(X3334,X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( relation(esk381_2(X3334,X3335))
| ~ in(ordered_pair(X3344,esk380_4(X3334,X3335,X3344,X3345)),X3335)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| esk374_2(X3334,X3335) = esk377_2(X3334,X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( function(esk381_2(X3334,X3335))
| ~ in(ordered_pair(X3344,esk380_4(X3334,X3335,X3344,X3345)),X3335)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| esk374_2(X3334,X3335) = esk377_2(X3334,X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( relation_dom(esk381_2(X3334,X3335)) = X3334
| ~ in(ordered_pair(X3344,esk380_4(X3334,X3335,X3344,X3345)),X3335)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| esk374_2(X3334,X3335) = esk377_2(X3334,X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( X3348 = esk382_3(X3334,X3335,X3348)
| ~ in(X3348,X3334)
| ~ in(ordered_pair(X3344,esk380_4(X3334,X3335,X3344,X3345)),X3335)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| esk374_2(X3334,X3335) = esk377_2(X3334,X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( in(apply(esk381_2(X3334,X3335),X3348),esk382_3(X3334,X3335,X3348))
| ~ in(X3348,X3334)
| ~ in(ordered_pair(X3344,esk380_4(X3334,X3335,X3344,X3345)),X3335)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| esk374_2(X3334,X3335) = esk377_2(X3334,X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( ~ in(X3350,esk382_3(X3334,X3335,X3348))
| in(ordered_pair(apply(esk381_2(X3334,X3335),X3348),X3350),X3335)
| ~ in(X3348,X3334)
| ~ in(ordered_pair(X3344,esk380_4(X3334,X3335,X3344,X3345)),X3335)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| esk374_2(X3334,X3335) = esk377_2(X3334,X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( relation(esk381_2(X3334,X3335))
| in(esk379_2(X3334,X3335),X3334)
| in(esk375_2(X3334,X3335),esk377_2(X3334,X3335))
| empty(X3334)
| ~ relation(X3335) )
& ( function(esk381_2(X3334,X3335))
| in(esk379_2(X3334,X3335),X3334)
| in(esk375_2(X3334,X3335),esk377_2(X3334,X3335))
| empty(X3334)
| ~ relation(X3335) )
& ( relation_dom(esk381_2(X3334,X3335)) = X3334
| in(esk379_2(X3334,X3335),X3334)
| in(esk375_2(X3334,X3335),esk377_2(X3334,X3335))
| empty(X3334)
| ~ relation(X3335) )
& ( X3348 = esk382_3(X3334,X3335,X3348)
| ~ in(X3348,X3334)
| in(esk379_2(X3334,X3335),X3334)
| in(esk375_2(X3334,X3335),esk377_2(X3334,X3335))
| empty(X3334)
| ~ relation(X3335) )
& ( in(apply(esk381_2(X3334,X3335),X3348),esk382_3(X3334,X3335,X3348))
| ~ in(X3348,X3334)
| in(esk379_2(X3334,X3335),X3334)
| in(esk375_2(X3334,X3335),esk377_2(X3334,X3335))
| empty(X3334)
| ~ relation(X3335) )
& ( ~ in(X3350,esk382_3(X3334,X3335,X3348))
| in(ordered_pair(apply(esk381_2(X3334,X3335),X3348),X3350),X3335)
| ~ in(X3348,X3334)
| in(esk379_2(X3334,X3335),X3334)
| in(esk375_2(X3334,X3335),esk377_2(X3334,X3335))
| empty(X3334)
| ~ relation(X3335) )
& ( relation(esk381_2(X3334,X3335))
| in(esk380_4(X3334,X3335,X3344,X3345),X3345)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| in(esk375_2(X3334,X3335),esk377_2(X3334,X3335))
| empty(X3334)
| ~ relation(X3335) )
& ( function(esk381_2(X3334,X3335))
| in(esk380_4(X3334,X3335,X3344,X3345),X3345)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| in(esk375_2(X3334,X3335),esk377_2(X3334,X3335))
| empty(X3334)
| ~ relation(X3335) )
& ( relation_dom(esk381_2(X3334,X3335)) = X3334
| in(esk380_4(X3334,X3335,X3344,X3345),X3345)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| in(esk375_2(X3334,X3335),esk377_2(X3334,X3335))
| empty(X3334)
| ~ relation(X3335) )
& ( X3348 = esk382_3(X3334,X3335,X3348)
| ~ in(X3348,X3334)
| in(esk380_4(X3334,X3335,X3344,X3345),X3345)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| in(esk375_2(X3334,X3335),esk377_2(X3334,X3335))
| empty(X3334)
| ~ relation(X3335) )
& ( in(apply(esk381_2(X3334,X3335),X3348),esk382_3(X3334,X3335,X3348))
| ~ in(X3348,X3334)
| in(esk380_4(X3334,X3335,X3344,X3345),X3345)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| in(esk375_2(X3334,X3335),esk377_2(X3334,X3335))
| empty(X3334)
| ~ relation(X3335) )
& ( ~ in(X3350,esk382_3(X3334,X3335,X3348))
| in(ordered_pair(apply(esk381_2(X3334,X3335),X3348),X3350),X3335)
| ~ in(X3348,X3334)
| in(esk380_4(X3334,X3335,X3344,X3345),X3345)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| in(esk375_2(X3334,X3335),esk377_2(X3334,X3335))
| empty(X3334)
| ~ relation(X3335) )
& ( relation(esk381_2(X3334,X3335))
| ~ in(ordered_pair(X3344,esk380_4(X3334,X3335,X3344,X3345)),X3335)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| in(esk375_2(X3334,X3335),esk377_2(X3334,X3335))
| empty(X3334)
| ~ relation(X3335) )
& ( function(esk381_2(X3334,X3335))
| ~ in(ordered_pair(X3344,esk380_4(X3334,X3335,X3344,X3345)),X3335)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| in(esk375_2(X3334,X3335),esk377_2(X3334,X3335))
| empty(X3334)
| ~ relation(X3335) )
& ( relation_dom(esk381_2(X3334,X3335)) = X3334
| ~ in(ordered_pair(X3344,esk380_4(X3334,X3335,X3344,X3345)),X3335)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| in(esk375_2(X3334,X3335),esk377_2(X3334,X3335))
| empty(X3334)
| ~ relation(X3335) )
& ( X3348 = esk382_3(X3334,X3335,X3348)
| ~ in(X3348,X3334)
| ~ in(ordered_pair(X3344,esk380_4(X3334,X3335,X3344,X3345)),X3335)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| in(esk375_2(X3334,X3335),esk377_2(X3334,X3335))
| empty(X3334)
| ~ relation(X3335) )
& ( in(apply(esk381_2(X3334,X3335),X3348),esk382_3(X3334,X3335,X3348))
| ~ in(X3348,X3334)
| ~ in(ordered_pair(X3344,esk380_4(X3334,X3335,X3344,X3345)),X3335)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| in(esk375_2(X3334,X3335),esk377_2(X3334,X3335))
| empty(X3334)
| ~ relation(X3335) )
& ( ~ in(X3350,esk382_3(X3334,X3335,X3348))
| in(ordered_pair(apply(esk381_2(X3334,X3335),X3348),X3350),X3335)
| ~ in(X3348,X3334)
| ~ in(ordered_pair(X3344,esk380_4(X3334,X3335,X3344,X3345)),X3335)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| in(esk375_2(X3334,X3335),esk377_2(X3334,X3335))
| empty(X3334)
| ~ relation(X3335) )
& ( relation(esk381_2(X3334,X3335))
| in(esk379_2(X3334,X3335),X3334)
| ~ in(X3340,esk377_2(X3334,X3335))
| in(ordered_pair(esk375_2(X3334,X3335),X3340),X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( function(esk381_2(X3334,X3335))
| in(esk379_2(X3334,X3335),X3334)
| ~ in(X3340,esk377_2(X3334,X3335))
| in(ordered_pair(esk375_2(X3334,X3335),X3340),X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( relation_dom(esk381_2(X3334,X3335)) = X3334
| in(esk379_2(X3334,X3335),X3334)
| ~ in(X3340,esk377_2(X3334,X3335))
| in(ordered_pair(esk375_2(X3334,X3335),X3340),X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( X3348 = esk382_3(X3334,X3335,X3348)
| ~ in(X3348,X3334)
| in(esk379_2(X3334,X3335),X3334)
| ~ in(X3340,esk377_2(X3334,X3335))
| in(ordered_pair(esk375_2(X3334,X3335),X3340),X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( in(apply(esk381_2(X3334,X3335),X3348),esk382_3(X3334,X3335,X3348))
| ~ in(X3348,X3334)
| in(esk379_2(X3334,X3335),X3334)
| ~ in(X3340,esk377_2(X3334,X3335))
| in(ordered_pair(esk375_2(X3334,X3335),X3340),X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( ~ in(X3350,esk382_3(X3334,X3335,X3348))
| in(ordered_pair(apply(esk381_2(X3334,X3335),X3348),X3350),X3335)
| ~ in(X3348,X3334)
| in(esk379_2(X3334,X3335),X3334)
| ~ in(X3340,esk377_2(X3334,X3335))
| in(ordered_pair(esk375_2(X3334,X3335),X3340),X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( relation(esk381_2(X3334,X3335))
| in(esk380_4(X3334,X3335,X3344,X3345),X3345)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| ~ in(X3340,esk377_2(X3334,X3335))
| in(ordered_pair(esk375_2(X3334,X3335),X3340),X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( function(esk381_2(X3334,X3335))
| in(esk380_4(X3334,X3335,X3344,X3345),X3345)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| ~ in(X3340,esk377_2(X3334,X3335))
| in(ordered_pair(esk375_2(X3334,X3335),X3340),X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( relation_dom(esk381_2(X3334,X3335)) = X3334
| in(esk380_4(X3334,X3335,X3344,X3345),X3345)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| ~ in(X3340,esk377_2(X3334,X3335))
| in(ordered_pair(esk375_2(X3334,X3335),X3340),X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( X3348 = esk382_3(X3334,X3335,X3348)
| ~ in(X3348,X3334)
| in(esk380_4(X3334,X3335,X3344,X3345),X3345)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| ~ in(X3340,esk377_2(X3334,X3335))
| in(ordered_pair(esk375_2(X3334,X3335),X3340),X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( in(apply(esk381_2(X3334,X3335),X3348),esk382_3(X3334,X3335,X3348))
| ~ in(X3348,X3334)
| in(esk380_4(X3334,X3335,X3344,X3345),X3345)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| ~ in(X3340,esk377_2(X3334,X3335))
| in(ordered_pair(esk375_2(X3334,X3335),X3340),X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( ~ in(X3350,esk382_3(X3334,X3335,X3348))
| in(ordered_pair(apply(esk381_2(X3334,X3335),X3348),X3350),X3335)
| ~ in(X3348,X3334)
| in(esk380_4(X3334,X3335,X3344,X3345),X3345)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| ~ in(X3340,esk377_2(X3334,X3335))
| in(ordered_pair(esk375_2(X3334,X3335),X3340),X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( relation(esk381_2(X3334,X3335))
| ~ in(ordered_pair(X3344,esk380_4(X3334,X3335,X3344,X3345)),X3335)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| ~ in(X3340,esk377_2(X3334,X3335))
| in(ordered_pair(esk375_2(X3334,X3335),X3340),X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( function(esk381_2(X3334,X3335))
| ~ in(ordered_pair(X3344,esk380_4(X3334,X3335,X3344,X3345)),X3335)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| ~ in(X3340,esk377_2(X3334,X3335))
| in(ordered_pair(esk375_2(X3334,X3335),X3340),X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( relation_dom(esk381_2(X3334,X3335)) = X3334
| ~ in(ordered_pair(X3344,esk380_4(X3334,X3335,X3344,X3345)),X3335)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| ~ in(X3340,esk377_2(X3334,X3335))
| in(ordered_pair(esk375_2(X3334,X3335),X3340),X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( X3348 = esk382_3(X3334,X3335,X3348)
| ~ in(X3348,X3334)
| ~ in(ordered_pair(X3344,esk380_4(X3334,X3335,X3344,X3345)),X3335)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| ~ in(X3340,esk377_2(X3334,X3335))
| in(ordered_pair(esk375_2(X3334,X3335),X3340),X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( in(apply(esk381_2(X3334,X3335),X3348),esk382_3(X3334,X3335,X3348))
| ~ in(X3348,X3334)
| ~ in(ordered_pair(X3344,esk380_4(X3334,X3335,X3344,X3345)),X3335)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| ~ in(X3340,esk377_2(X3334,X3335))
| in(ordered_pair(esk375_2(X3334,X3335),X3340),X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( ~ in(X3350,esk382_3(X3334,X3335,X3348))
| in(ordered_pair(apply(esk381_2(X3334,X3335),X3348),X3350),X3335)
| ~ in(X3348,X3334)
| ~ in(ordered_pair(X3344,esk380_4(X3334,X3335,X3344,X3345)),X3335)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| ~ in(X3340,esk377_2(X3334,X3335))
| in(ordered_pair(esk375_2(X3334,X3335),X3340),X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( relation(esk381_2(X3334,X3335))
| in(esk379_2(X3334,X3335),X3334)
| esk374_2(X3334,X3335) = esk378_2(X3334,X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( function(esk381_2(X3334,X3335))
| in(esk379_2(X3334,X3335),X3334)
| esk374_2(X3334,X3335) = esk378_2(X3334,X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( relation_dom(esk381_2(X3334,X3335)) = X3334
| in(esk379_2(X3334,X3335),X3334)
| esk374_2(X3334,X3335) = esk378_2(X3334,X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( X3348 = esk382_3(X3334,X3335,X3348)
| ~ in(X3348,X3334)
| in(esk379_2(X3334,X3335),X3334)
| esk374_2(X3334,X3335) = esk378_2(X3334,X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( in(apply(esk381_2(X3334,X3335),X3348),esk382_3(X3334,X3335,X3348))
| ~ in(X3348,X3334)
| in(esk379_2(X3334,X3335),X3334)
| esk374_2(X3334,X3335) = esk378_2(X3334,X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( ~ in(X3350,esk382_3(X3334,X3335,X3348))
| in(ordered_pair(apply(esk381_2(X3334,X3335),X3348),X3350),X3335)
| ~ in(X3348,X3334)
| in(esk379_2(X3334,X3335),X3334)
| esk374_2(X3334,X3335) = esk378_2(X3334,X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( relation(esk381_2(X3334,X3335))
| in(esk380_4(X3334,X3335,X3344,X3345),X3345)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| esk374_2(X3334,X3335) = esk378_2(X3334,X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( function(esk381_2(X3334,X3335))
| in(esk380_4(X3334,X3335,X3344,X3345),X3345)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| esk374_2(X3334,X3335) = esk378_2(X3334,X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( relation_dom(esk381_2(X3334,X3335)) = X3334
| in(esk380_4(X3334,X3335,X3344,X3345),X3345)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| esk374_2(X3334,X3335) = esk378_2(X3334,X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( X3348 = esk382_3(X3334,X3335,X3348)
| ~ in(X3348,X3334)
| in(esk380_4(X3334,X3335,X3344,X3345),X3345)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| esk374_2(X3334,X3335) = esk378_2(X3334,X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( in(apply(esk381_2(X3334,X3335),X3348),esk382_3(X3334,X3335,X3348))
| ~ in(X3348,X3334)
| in(esk380_4(X3334,X3335,X3344,X3345),X3345)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| esk374_2(X3334,X3335) = esk378_2(X3334,X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( ~ in(X3350,esk382_3(X3334,X3335,X3348))
| in(ordered_pair(apply(esk381_2(X3334,X3335),X3348),X3350),X3335)
| ~ in(X3348,X3334)
| in(esk380_4(X3334,X3335,X3344,X3345),X3345)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| esk374_2(X3334,X3335) = esk378_2(X3334,X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( relation(esk381_2(X3334,X3335))
| ~ in(ordered_pair(X3344,esk380_4(X3334,X3335,X3344,X3345)),X3335)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| esk374_2(X3334,X3335) = esk378_2(X3334,X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( function(esk381_2(X3334,X3335))
| ~ in(ordered_pair(X3344,esk380_4(X3334,X3335,X3344,X3345)),X3335)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| esk374_2(X3334,X3335) = esk378_2(X3334,X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( relation_dom(esk381_2(X3334,X3335)) = X3334
| ~ in(ordered_pair(X3344,esk380_4(X3334,X3335,X3344,X3345)),X3335)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| esk374_2(X3334,X3335) = esk378_2(X3334,X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( X3348 = esk382_3(X3334,X3335,X3348)
| ~ in(X3348,X3334)
| ~ in(ordered_pair(X3344,esk380_4(X3334,X3335,X3344,X3345)),X3335)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| esk374_2(X3334,X3335) = esk378_2(X3334,X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( in(apply(esk381_2(X3334,X3335),X3348),esk382_3(X3334,X3335,X3348))
| ~ in(X3348,X3334)
| ~ in(ordered_pair(X3344,esk380_4(X3334,X3335,X3344,X3345)),X3335)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| esk374_2(X3334,X3335) = esk378_2(X3334,X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( ~ in(X3350,esk382_3(X3334,X3335,X3348))
| in(ordered_pair(apply(esk381_2(X3334,X3335),X3348),X3350),X3335)
| ~ in(X3348,X3334)
| ~ in(ordered_pair(X3344,esk380_4(X3334,X3335,X3344,X3345)),X3335)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| esk374_2(X3334,X3335) = esk378_2(X3334,X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( relation(esk381_2(X3334,X3335))
| in(esk379_2(X3334,X3335),X3334)
| in(esk376_2(X3334,X3335),esk378_2(X3334,X3335))
| empty(X3334)
| ~ relation(X3335) )
& ( function(esk381_2(X3334,X3335))
| in(esk379_2(X3334,X3335),X3334)
| in(esk376_2(X3334,X3335),esk378_2(X3334,X3335))
| empty(X3334)
| ~ relation(X3335) )
& ( relation_dom(esk381_2(X3334,X3335)) = X3334
| in(esk379_2(X3334,X3335),X3334)
| in(esk376_2(X3334,X3335),esk378_2(X3334,X3335))
| empty(X3334)
| ~ relation(X3335) )
& ( X3348 = esk382_3(X3334,X3335,X3348)
| ~ in(X3348,X3334)
| in(esk379_2(X3334,X3335),X3334)
| in(esk376_2(X3334,X3335),esk378_2(X3334,X3335))
| empty(X3334)
| ~ relation(X3335) )
& ( in(apply(esk381_2(X3334,X3335),X3348),esk382_3(X3334,X3335,X3348))
| ~ in(X3348,X3334)
| in(esk379_2(X3334,X3335),X3334)
| in(esk376_2(X3334,X3335),esk378_2(X3334,X3335))
| empty(X3334)
| ~ relation(X3335) )
& ( ~ in(X3350,esk382_3(X3334,X3335,X3348))
| in(ordered_pair(apply(esk381_2(X3334,X3335),X3348),X3350),X3335)
| ~ in(X3348,X3334)
| in(esk379_2(X3334,X3335),X3334)
| in(esk376_2(X3334,X3335),esk378_2(X3334,X3335))
| empty(X3334)
| ~ relation(X3335) )
& ( relation(esk381_2(X3334,X3335))
| in(esk380_4(X3334,X3335,X3344,X3345),X3345)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| in(esk376_2(X3334,X3335),esk378_2(X3334,X3335))
| empty(X3334)
| ~ relation(X3335) )
& ( function(esk381_2(X3334,X3335))
| in(esk380_4(X3334,X3335,X3344,X3345),X3345)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| in(esk376_2(X3334,X3335),esk378_2(X3334,X3335))
| empty(X3334)
| ~ relation(X3335) )
& ( relation_dom(esk381_2(X3334,X3335)) = X3334
| in(esk380_4(X3334,X3335,X3344,X3345),X3345)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| in(esk376_2(X3334,X3335),esk378_2(X3334,X3335))
| empty(X3334)
| ~ relation(X3335) )
& ( X3348 = esk382_3(X3334,X3335,X3348)
| ~ in(X3348,X3334)
| in(esk380_4(X3334,X3335,X3344,X3345),X3345)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| in(esk376_2(X3334,X3335),esk378_2(X3334,X3335))
| empty(X3334)
| ~ relation(X3335) )
& ( in(apply(esk381_2(X3334,X3335),X3348),esk382_3(X3334,X3335,X3348))
| ~ in(X3348,X3334)
| in(esk380_4(X3334,X3335,X3344,X3345),X3345)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| in(esk376_2(X3334,X3335),esk378_2(X3334,X3335))
| empty(X3334)
| ~ relation(X3335) )
& ( ~ in(X3350,esk382_3(X3334,X3335,X3348))
| in(ordered_pair(apply(esk381_2(X3334,X3335),X3348),X3350),X3335)
| ~ in(X3348,X3334)
| in(esk380_4(X3334,X3335,X3344,X3345),X3345)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| in(esk376_2(X3334,X3335),esk378_2(X3334,X3335))
| empty(X3334)
| ~ relation(X3335) )
& ( relation(esk381_2(X3334,X3335))
| ~ in(ordered_pair(X3344,esk380_4(X3334,X3335,X3344,X3345)),X3335)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| in(esk376_2(X3334,X3335),esk378_2(X3334,X3335))
| empty(X3334)
| ~ relation(X3335) )
& ( function(esk381_2(X3334,X3335))
| ~ in(ordered_pair(X3344,esk380_4(X3334,X3335,X3344,X3345)),X3335)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| in(esk376_2(X3334,X3335),esk378_2(X3334,X3335))
| empty(X3334)
| ~ relation(X3335) )
& ( relation_dom(esk381_2(X3334,X3335)) = X3334
| ~ in(ordered_pair(X3344,esk380_4(X3334,X3335,X3344,X3345)),X3335)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| in(esk376_2(X3334,X3335),esk378_2(X3334,X3335))
| empty(X3334)
| ~ relation(X3335) )
& ( X3348 = esk382_3(X3334,X3335,X3348)
| ~ in(X3348,X3334)
| ~ in(ordered_pair(X3344,esk380_4(X3334,X3335,X3344,X3345)),X3335)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| in(esk376_2(X3334,X3335),esk378_2(X3334,X3335))
| empty(X3334)
| ~ relation(X3335) )
& ( in(apply(esk381_2(X3334,X3335),X3348),esk382_3(X3334,X3335,X3348))
| ~ in(X3348,X3334)
| ~ in(ordered_pair(X3344,esk380_4(X3334,X3335,X3344,X3345)),X3335)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| in(esk376_2(X3334,X3335),esk378_2(X3334,X3335))
| empty(X3334)
| ~ relation(X3335) )
& ( ~ in(X3350,esk382_3(X3334,X3335,X3348))
| in(ordered_pair(apply(esk381_2(X3334,X3335),X3348),X3350),X3335)
| ~ in(X3348,X3334)
| ~ in(ordered_pair(X3344,esk380_4(X3334,X3335,X3344,X3345)),X3335)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| in(esk376_2(X3334,X3335),esk378_2(X3334,X3335))
| empty(X3334)
| ~ relation(X3335) )
& ( relation(esk381_2(X3334,X3335))
| in(esk379_2(X3334,X3335),X3334)
| ~ in(X3342,esk378_2(X3334,X3335))
| in(ordered_pair(esk376_2(X3334,X3335),X3342),X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( function(esk381_2(X3334,X3335))
| in(esk379_2(X3334,X3335),X3334)
| ~ in(X3342,esk378_2(X3334,X3335))
| in(ordered_pair(esk376_2(X3334,X3335),X3342),X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( relation_dom(esk381_2(X3334,X3335)) = X3334
| in(esk379_2(X3334,X3335),X3334)
| ~ in(X3342,esk378_2(X3334,X3335))
| in(ordered_pair(esk376_2(X3334,X3335),X3342),X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( X3348 = esk382_3(X3334,X3335,X3348)
| ~ in(X3348,X3334)
| in(esk379_2(X3334,X3335),X3334)
| ~ in(X3342,esk378_2(X3334,X3335))
| in(ordered_pair(esk376_2(X3334,X3335),X3342),X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( in(apply(esk381_2(X3334,X3335),X3348),esk382_3(X3334,X3335,X3348))
| ~ in(X3348,X3334)
| in(esk379_2(X3334,X3335),X3334)
| ~ in(X3342,esk378_2(X3334,X3335))
| in(ordered_pair(esk376_2(X3334,X3335),X3342),X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( ~ in(X3350,esk382_3(X3334,X3335,X3348))
| in(ordered_pair(apply(esk381_2(X3334,X3335),X3348),X3350),X3335)
| ~ in(X3348,X3334)
| in(esk379_2(X3334,X3335),X3334)
| ~ in(X3342,esk378_2(X3334,X3335))
| in(ordered_pair(esk376_2(X3334,X3335),X3342),X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( relation(esk381_2(X3334,X3335))
| in(esk380_4(X3334,X3335,X3344,X3345),X3345)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| ~ in(X3342,esk378_2(X3334,X3335))
| in(ordered_pair(esk376_2(X3334,X3335),X3342),X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( function(esk381_2(X3334,X3335))
| in(esk380_4(X3334,X3335,X3344,X3345),X3345)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| ~ in(X3342,esk378_2(X3334,X3335))
| in(ordered_pair(esk376_2(X3334,X3335),X3342),X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( relation_dom(esk381_2(X3334,X3335)) = X3334
| in(esk380_4(X3334,X3335,X3344,X3345),X3345)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| ~ in(X3342,esk378_2(X3334,X3335))
| in(ordered_pair(esk376_2(X3334,X3335),X3342),X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( X3348 = esk382_3(X3334,X3335,X3348)
| ~ in(X3348,X3334)
| in(esk380_4(X3334,X3335,X3344,X3345),X3345)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| ~ in(X3342,esk378_2(X3334,X3335))
| in(ordered_pair(esk376_2(X3334,X3335),X3342),X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( in(apply(esk381_2(X3334,X3335),X3348),esk382_3(X3334,X3335,X3348))
| ~ in(X3348,X3334)
| in(esk380_4(X3334,X3335,X3344,X3345),X3345)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| ~ in(X3342,esk378_2(X3334,X3335))
| in(ordered_pair(esk376_2(X3334,X3335),X3342),X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( ~ in(X3350,esk382_3(X3334,X3335,X3348))
| in(ordered_pair(apply(esk381_2(X3334,X3335),X3348),X3350),X3335)
| ~ in(X3348,X3334)
| in(esk380_4(X3334,X3335,X3344,X3345),X3345)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| ~ in(X3342,esk378_2(X3334,X3335))
| in(ordered_pair(esk376_2(X3334,X3335),X3342),X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( relation(esk381_2(X3334,X3335))
| ~ in(ordered_pair(X3344,esk380_4(X3334,X3335,X3344,X3345)),X3335)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| ~ in(X3342,esk378_2(X3334,X3335))
| in(ordered_pair(esk376_2(X3334,X3335),X3342),X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( function(esk381_2(X3334,X3335))
| ~ in(ordered_pair(X3344,esk380_4(X3334,X3335,X3344,X3345)),X3335)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| ~ in(X3342,esk378_2(X3334,X3335))
| in(ordered_pair(esk376_2(X3334,X3335),X3342),X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( relation_dom(esk381_2(X3334,X3335)) = X3334
| ~ in(ordered_pair(X3344,esk380_4(X3334,X3335,X3344,X3345)),X3335)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| ~ in(X3342,esk378_2(X3334,X3335))
| in(ordered_pair(esk376_2(X3334,X3335),X3342),X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( X3348 = esk382_3(X3334,X3335,X3348)
| ~ in(X3348,X3334)
| ~ in(ordered_pair(X3344,esk380_4(X3334,X3335,X3344,X3345)),X3335)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| ~ in(X3342,esk378_2(X3334,X3335))
| in(ordered_pair(esk376_2(X3334,X3335),X3342),X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( in(apply(esk381_2(X3334,X3335),X3348),esk382_3(X3334,X3335,X3348))
| ~ in(X3348,X3334)
| ~ in(ordered_pair(X3344,esk380_4(X3334,X3335,X3344,X3345)),X3335)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| ~ in(X3342,esk378_2(X3334,X3335))
| in(ordered_pair(esk376_2(X3334,X3335),X3342),X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( ~ in(X3350,esk382_3(X3334,X3335,X3348))
| in(ordered_pair(apply(esk381_2(X3334,X3335),X3348),X3350),X3335)
| ~ in(X3348,X3334)
| ~ in(ordered_pair(X3344,esk380_4(X3334,X3335,X3344,X3345)),X3335)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| ~ in(X3342,esk378_2(X3334,X3335))
| in(ordered_pair(esk376_2(X3334,X3335),X3342),X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( relation(esk381_2(X3334,X3335))
| in(esk379_2(X3334,X3335),X3334)
| esk375_2(X3334,X3335) != esk376_2(X3334,X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( function(esk381_2(X3334,X3335))
| in(esk379_2(X3334,X3335),X3334)
| esk375_2(X3334,X3335) != esk376_2(X3334,X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( relation_dom(esk381_2(X3334,X3335)) = X3334
| in(esk379_2(X3334,X3335),X3334)
| esk375_2(X3334,X3335) != esk376_2(X3334,X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( X3348 = esk382_3(X3334,X3335,X3348)
| ~ in(X3348,X3334)
| in(esk379_2(X3334,X3335),X3334)
| esk375_2(X3334,X3335) != esk376_2(X3334,X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( in(apply(esk381_2(X3334,X3335),X3348),esk382_3(X3334,X3335,X3348))
| ~ in(X3348,X3334)
| in(esk379_2(X3334,X3335),X3334)
| esk375_2(X3334,X3335) != esk376_2(X3334,X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( ~ in(X3350,esk382_3(X3334,X3335,X3348))
| in(ordered_pair(apply(esk381_2(X3334,X3335),X3348),X3350),X3335)
| ~ in(X3348,X3334)
| in(esk379_2(X3334,X3335),X3334)
| esk375_2(X3334,X3335) != esk376_2(X3334,X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( relation(esk381_2(X3334,X3335))
| in(esk380_4(X3334,X3335,X3344,X3345),X3345)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| esk375_2(X3334,X3335) != esk376_2(X3334,X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( function(esk381_2(X3334,X3335))
| in(esk380_4(X3334,X3335,X3344,X3345),X3345)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| esk375_2(X3334,X3335) != esk376_2(X3334,X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( relation_dom(esk381_2(X3334,X3335)) = X3334
| in(esk380_4(X3334,X3335,X3344,X3345),X3345)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| esk375_2(X3334,X3335) != esk376_2(X3334,X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( X3348 = esk382_3(X3334,X3335,X3348)
| ~ in(X3348,X3334)
| in(esk380_4(X3334,X3335,X3344,X3345),X3345)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| esk375_2(X3334,X3335) != esk376_2(X3334,X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( in(apply(esk381_2(X3334,X3335),X3348),esk382_3(X3334,X3335,X3348))
| ~ in(X3348,X3334)
| in(esk380_4(X3334,X3335,X3344,X3345),X3345)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| esk375_2(X3334,X3335) != esk376_2(X3334,X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( ~ in(X3350,esk382_3(X3334,X3335,X3348))
| in(ordered_pair(apply(esk381_2(X3334,X3335),X3348),X3350),X3335)
| ~ in(X3348,X3334)
| in(esk380_4(X3334,X3335,X3344,X3345),X3345)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| esk375_2(X3334,X3335) != esk376_2(X3334,X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( relation(esk381_2(X3334,X3335))
| ~ in(ordered_pair(X3344,esk380_4(X3334,X3335,X3344,X3345)),X3335)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| esk375_2(X3334,X3335) != esk376_2(X3334,X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( function(esk381_2(X3334,X3335))
| ~ in(ordered_pair(X3344,esk380_4(X3334,X3335,X3344,X3345)),X3335)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| esk375_2(X3334,X3335) != esk376_2(X3334,X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( relation_dom(esk381_2(X3334,X3335)) = X3334
| ~ in(ordered_pair(X3344,esk380_4(X3334,X3335,X3344,X3345)),X3335)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| esk375_2(X3334,X3335) != esk376_2(X3334,X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( X3348 = esk382_3(X3334,X3335,X3348)
| ~ in(X3348,X3334)
| ~ in(ordered_pair(X3344,esk380_4(X3334,X3335,X3344,X3345)),X3335)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| esk375_2(X3334,X3335) != esk376_2(X3334,X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( in(apply(esk381_2(X3334,X3335),X3348),esk382_3(X3334,X3335,X3348))
| ~ in(X3348,X3334)
| ~ in(ordered_pair(X3344,esk380_4(X3334,X3335,X3344,X3345)),X3335)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| esk375_2(X3334,X3335) != esk376_2(X3334,X3335)
| empty(X3334)
| ~ relation(X3335) )
& ( ~ in(X3350,esk382_3(X3334,X3335,X3348))
| in(ordered_pair(apply(esk381_2(X3334,X3335),X3348),X3350),X3335)
| ~ in(X3348,X3334)
| ~ in(ordered_pair(X3344,esk380_4(X3334,X3335,X3344,X3345)),X3335)
| esk379_2(X3334,X3335) != X3345
| ~ in(X3344,X3345)
| esk375_2(X3334,X3335) != esk376_2(X3334,X3335)
| empty(X3334)
| ~ relation(X3335) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_652])])])])]) ).
fof(i_0_702,plain,
! [X2197,X2198,X2199,X2200,X2203,X2204,X2205,X2206,X2207,X2208,X2210,X2211] :
( ( in(esk63_4(X2197,X2198,X2199,X2200),X2197)
| ~ in(X2200,X2199)
| X2199 != cartesian_product2(X2197,X2198) )
& ( in(esk64_4(X2197,X2198,X2199,X2200),X2198)
| ~ in(X2200,X2199)
| X2199 != cartesian_product2(X2197,X2198) )
& ( X2200 = ordered_pair(esk63_4(X2197,X2198,X2199,X2200),esk64_4(X2197,X2198,X2199,X2200))
| ~ in(X2200,X2199)
| X2199 != cartesian_product2(X2197,X2198) )
& ( ~ in(X2204,X2197)
| ~ in(X2205,X2198)
| X2203 != ordered_pair(X2204,X2205)
| in(X2203,X2199)
| X2199 != cartesian_product2(X2197,X2198) )
& ( ~ in(esk65_3(X2206,X2207,X2208),X2208)
| ~ in(X2210,X2206)
| ~ in(X2211,X2207)
| esk65_3(X2206,X2207,X2208) != ordered_pair(X2210,X2211)
| X2208 = cartesian_product2(X2206,X2207) )
& ( in(esk66_3(X2206,X2207,X2208),X2206)
| in(esk65_3(X2206,X2207,X2208),X2208)
| X2208 = cartesian_product2(X2206,X2207) )
& ( in(esk67_3(X2206,X2207,X2208),X2207)
| in(esk65_3(X2206,X2207,X2208),X2208)
| X2208 = cartesian_product2(X2206,X2207) )
& ( esk65_3(X2206,X2207,X2208) = ordered_pair(esk66_3(X2206,X2207,X2208),esk67_3(X2206,X2207,X2208))
| in(esk65_3(X2206,X2207,X2208),X2208)
| X2208 = cartesian_product2(X2206,X2207) ) ),
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)],[d2_zfmisc_1])])])])])]) ).
fof(i_0_703,plain,
! [X2104,X2105,X2106,X2107,X2108,X2109,X2110] :
( ( X2107 != X2105
| ~ in(X2107,X2106)
| X2106 != fiber(X2104,X2105)
| ~ relation(X2104) )
& ( in(ordered_pair(X2107,X2105),X2104)
| ~ in(X2107,X2106)
| X2106 != fiber(X2104,X2105)
| ~ relation(X2104) )
& ( X2108 = X2105
| ~ in(ordered_pair(X2108,X2105),X2104)
| in(X2108,X2106)
| X2106 != fiber(X2104,X2105)
| ~ relation(X2104) )
& ( ~ in(esk46_3(X2104,X2109,X2110),X2110)
| esk46_3(X2104,X2109,X2110) = X2109
| ~ in(ordered_pair(esk46_3(X2104,X2109,X2110),X2109),X2104)
| X2110 = fiber(X2104,X2109)
| ~ relation(X2104) )
& ( esk46_3(X2104,X2109,X2110) != X2109
| in(esk46_3(X2104,X2109,X2110),X2110)
| X2110 = fiber(X2104,X2109)
| ~ relation(X2104) )
& ( in(ordered_pair(esk46_3(X2104,X2109,X2110),X2109),X2104)
| in(esk46_3(X2104,X2109,X2110),X2110)
| X2110 = fiber(X2104,X2109)
| ~ relation(X2104) ) ),
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)],[d1_wellord1])])])])])]) ).
fof(i_0_704,plain,
! [X1973,X1974,X1975,X1976,X1978,X1979,X1980,X1981,X1983] :
( ( in(ordered_pair(X1976,esk19_4(X1973,X1974,X1975,X1976)),X1973)
| ~ in(X1976,X1975)
| X1975 != relation_inverse_image(X1973,X1974)
| ~ relation(X1973) )
& ( in(esk19_4(X1973,X1974,X1975,X1976),X1974)
| ~ in(X1976,X1975)
| X1975 != relation_inverse_image(X1973,X1974)
| ~ relation(X1973) )
& ( ~ in(ordered_pair(X1978,X1979),X1973)
| ~ in(X1979,X1974)
| in(X1978,X1975)
| X1975 != relation_inverse_image(X1973,X1974)
| ~ relation(X1973) )
& ( ~ in(esk20_3(X1973,X1980,X1981),X1981)
| ~ in(ordered_pair(esk20_3(X1973,X1980,X1981),X1983),X1973)
| ~ in(X1983,X1980)
| X1981 = relation_inverse_image(X1973,X1980)
| ~ relation(X1973) )
& ( in(ordered_pair(esk20_3(X1973,X1980,X1981),esk21_3(X1973,X1980,X1981)),X1973)
| in(esk20_3(X1973,X1980,X1981),X1981)
| X1981 = relation_inverse_image(X1973,X1980)
| ~ relation(X1973) )
& ( in(esk21_3(X1973,X1980,X1981),X1980)
| in(esk20_3(X1973,X1980,X1981),X1981)
| X1981 = relation_inverse_image(X1973,X1980)
| ~ relation(X1973) ) ),
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)],[d14_relat_1])])])])])]) ).
fof(i_0_705,lemma,
! [X3571,X3572,X3573,X3575,X3576] :
( ( in(esk414_3(X3571,X3572,X3573),X3572)
| relation_dom_as_subset(X3572,X3571,X3573) = X3572
| ~ relation_of2_as_subset(X3573,X3572,X3571) )
& ( ~ in(ordered_pair(esk414_3(X3571,X3572,X3573),X3575),X3573)
| relation_dom_as_subset(X3572,X3571,X3573) = X3572
| ~ relation_of2_as_subset(X3573,X3572,X3571) )
& ( relation_dom_as_subset(X3572,X3571,X3573) != X3572
| ~ in(X3576,X3572)
| in(ordered_pair(X3576,esk415_4(X3571,X3572,X3573,X3576)),X3573)
| ~ relation_of2_as_subset(X3573,X3572,X3571) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_653])])])])]) ).
fof(i_0_706,plain,
! [X2,X3,X4] :
( epred2_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)],[i_0_643]) ).
fof(i_0_707,plain,
! [X2357,X2358,X2359,X2360,X2361,X2362] :
( ( ~ in(ordered_pair(X2359,X2360),X2358)
| in(ordered_pair(X2360,X2359),X2357)
| X2358 != relation_inverse(X2357)
| ~ relation(X2358)
| ~ relation(X2357) )
& ( ~ in(ordered_pair(X2362,X2361),X2357)
| in(ordered_pair(X2361,X2362),X2358)
| X2358 != relation_inverse(X2357)
| ~ relation(X2358)
| ~ relation(X2357) )
& ( ~ in(ordered_pair(esk97_2(X2357,X2358),esk98_2(X2357,X2358)),X2358)
| ~ in(ordered_pair(esk98_2(X2357,X2358),esk97_2(X2357,X2358)),X2357)
| X2358 = relation_inverse(X2357)
| ~ relation(X2358)
| ~ relation(X2357) )
& ( in(ordered_pair(esk97_2(X2357,X2358),esk98_2(X2357,X2358)),X2358)
| in(ordered_pair(esk98_2(X2357,X2358),esk97_2(X2357,X2358)),X2357)
| X2358 = relation_inverse(X2357)
| ~ relation(X2358)
| ~ relation(X2357) ) ),
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)],[d7_relat_1])])])])])]) ).
fof(i_0_708,plain,
! [X2158,X2159,X2160,X2161,X2162,X2163] :
( ( ~ in(ordered_pair(X2160,X2161),X2158)
| in(ordered_pair(X2160,X2161),X2159)
| X2158 != X2159
| ~ relation(X2159)
| ~ relation(X2158) )
& ( ~ in(ordered_pair(X2162,X2163),X2159)
| in(ordered_pair(X2162,X2163),X2158)
| X2158 != X2159
| ~ relation(X2159)
| ~ relation(X2158) )
& ( ~ in(ordered_pair(esk56_2(X2158,X2159),esk57_2(X2158,X2159)),X2158)
| ~ in(ordered_pair(esk56_2(X2158,X2159),esk57_2(X2158,X2159)),X2159)
| X2158 = X2159
| ~ relation(X2159)
| ~ relation(X2158) )
& ( in(ordered_pair(esk56_2(X2158,X2159),esk57_2(X2158,X2159)),X2158)
| in(ordered_pair(esk56_2(X2158,X2159),esk57_2(X2158,X2159)),X2159)
| X2158 = X2159
| ~ relation(X2159)
| ~ relation(X2158) ) ),
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)],[d2_relat_1])])])])])]) ).
fof(i_0_709,lemma,
! [X3469,X3470,X3471,X3473] :
( ( in(esk411_3(X3469,X3470,X3471),relation_dom(X3471))
| ~ in(X3469,relation_image(X3471,X3470))
| ~ relation(X3471) )
& ( in(ordered_pair(esk411_3(X3469,X3470,X3471),X3469),X3471)
| ~ in(X3469,relation_image(X3471,X3470))
| ~ relation(X3471) )
& ( in(esk411_3(X3469,X3470,X3471),X3470)
| ~ in(X3469,relation_image(X3471,X3470))
| ~ relation(X3471) )
& ( ~ in(X3473,relation_dom(X3471))
| ~ in(ordered_pair(X3473,X3469),X3471)
| ~ in(X3473,X3470)
| in(X3469,relation_image(X3471,X3470))
| ~ relation(X3471) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t143_relat_1])])])])]) ).
fof(i_0_710,plain,
! [X2327,X2328,X2329,X2331,X2332,X2333,X2335] :
( ( ~ in(X2329,X2328)
| in(ordered_pair(esk92_3(X2327,X2328,X2329),X2329),X2327)
| X2328 != relation_rng(X2327)
| ~ relation(X2327) )
& ( ~ in(ordered_pair(X2332,X2331),X2327)
| in(X2331,X2328)
| X2328 != relation_rng(X2327)
| ~ relation(X2327) )
& ( ~ in(esk93_2(X2327,X2333),X2333)
| ~ in(ordered_pair(X2335,esk93_2(X2327,X2333)),X2327)
| X2333 = relation_rng(X2327)
| ~ relation(X2327) )
& ( in(esk93_2(X2327,X2333),X2333)
| in(ordered_pair(esk94_2(X2327,X2333),esk93_2(X2327,X2333)),X2327)
| X2333 = relation_rng(X2327)
| ~ relation(X2327) ) ),
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)],[d5_relat_1])])])])])]) ).
fof(i_0_711,lemma,
! [X2923,X2924,X2928,X2929,X2931,X2932,X2933,X2934,X2935] :
( ( relation(esk192_2(X2923,X2924))
| in(esk189_2(X2923,X2924),complements_of_subsets(the_carrier(X2923),X2924))
| ~ one_sorted_str(X2923)
| ~ element(X2924,powerset(powerset(the_carrier(X2923)))) )
& ( function(esk192_2(X2923,X2924))
| in(esk189_2(X2923,X2924),complements_of_subsets(the_carrier(X2923),X2924))
| ~ one_sorted_str(X2923)
| ~ element(X2924,powerset(powerset(the_carrier(X2923)))) )
& ( in(X2931,complements_of_subsets(the_carrier(X2923),X2924))
| ~ in(ordered_pair(X2931,X2932),esk192_2(X2923,X2924))
| in(esk189_2(X2923,X2924),complements_of_subsets(the_carrier(X2923),X2924))
| ~ one_sorted_str(X2923)
| ~ element(X2924,powerset(powerset(the_carrier(X2923)))) )
& ( ~ element(X2933,powerset(the_carrier(X2923)))
| X2933 != X2931
| X2932 = subset_complement(the_carrier(X2923),X2933)
| ~ in(ordered_pair(X2931,X2932),esk192_2(X2923,X2924))
| in(esk189_2(X2923,X2924),complements_of_subsets(the_carrier(X2923),X2924))
| ~ one_sorted_str(X2923)
| ~ element(X2924,powerset(powerset(the_carrier(X2923)))) )
& ( element(esk193_4(X2923,X2924,X2934,X2935),powerset(the_carrier(X2923)))
| ~ in(X2934,complements_of_subsets(the_carrier(X2923),X2924))
| in(ordered_pair(X2934,X2935),esk192_2(X2923,X2924))
| in(esk189_2(X2923,X2924),complements_of_subsets(the_carrier(X2923),X2924))
| ~ one_sorted_str(X2923)
| ~ element(X2924,powerset(powerset(the_carrier(X2923)))) )
& ( esk193_4(X2923,X2924,X2934,X2935) = X2934
| ~ in(X2934,complements_of_subsets(the_carrier(X2923),X2924))
| in(ordered_pair(X2934,X2935),esk192_2(X2923,X2924))
| in(esk189_2(X2923,X2924),complements_of_subsets(the_carrier(X2923),X2924))
| ~ one_sorted_str(X2923)
| ~ element(X2924,powerset(powerset(the_carrier(X2923)))) )
& ( X2935 != subset_complement(the_carrier(X2923),esk193_4(X2923,X2924,X2934,X2935))
| ~ in(X2934,complements_of_subsets(the_carrier(X2923),X2924))
| in(ordered_pair(X2934,X2935),esk192_2(X2923,X2924))
| in(esk189_2(X2923,X2924),complements_of_subsets(the_carrier(X2923),X2924))
| ~ one_sorted_str(X2923)
| ~ element(X2924,powerset(powerset(the_carrier(X2923)))) )
& ( relation(esk192_2(X2923,X2924))
| ~ element(X2928,powerset(the_carrier(X2923)))
| X2928 != esk189_2(X2923,X2924)
| esk190_2(X2923,X2924) = subset_complement(the_carrier(X2923),X2928)
| ~ one_sorted_str(X2923)
| ~ element(X2924,powerset(powerset(the_carrier(X2923)))) )
& ( function(esk192_2(X2923,X2924))
| ~ element(X2928,powerset(the_carrier(X2923)))
| X2928 != esk189_2(X2923,X2924)
| esk190_2(X2923,X2924) = subset_complement(the_carrier(X2923),X2928)
| ~ one_sorted_str(X2923)
| ~ element(X2924,powerset(powerset(the_carrier(X2923)))) )
& ( in(X2931,complements_of_subsets(the_carrier(X2923),X2924))
| ~ in(ordered_pair(X2931,X2932),esk192_2(X2923,X2924))
| ~ element(X2928,powerset(the_carrier(X2923)))
| X2928 != esk189_2(X2923,X2924)
| esk190_2(X2923,X2924) = subset_complement(the_carrier(X2923),X2928)
| ~ one_sorted_str(X2923)
| ~ element(X2924,powerset(powerset(the_carrier(X2923)))) )
& ( ~ element(X2933,powerset(the_carrier(X2923)))
| X2933 != X2931
| X2932 = subset_complement(the_carrier(X2923),X2933)
| ~ in(ordered_pair(X2931,X2932),esk192_2(X2923,X2924))
| ~ element(X2928,powerset(the_carrier(X2923)))
| X2928 != esk189_2(X2923,X2924)
| esk190_2(X2923,X2924) = subset_complement(the_carrier(X2923),X2928)
| ~ one_sorted_str(X2923)
| ~ element(X2924,powerset(powerset(the_carrier(X2923)))) )
& ( element(esk193_4(X2923,X2924,X2934,X2935),powerset(the_carrier(X2923)))
| ~ in(X2934,complements_of_subsets(the_carrier(X2923),X2924))
| in(ordered_pair(X2934,X2935),esk192_2(X2923,X2924))
| ~ element(X2928,powerset(the_carrier(X2923)))
| X2928 != esk189_2(X2923,X2924)
| esk190_2(X2923,X2924) = subset_complement(the_carrier(X2923),X2928)
| ~ one_sorted_str(X2923)
| ~ element(X2924,powerset(powerset(the_carrier(X2923)))) )
& ( esk193_4(X2923,X2924,X2934,X2935) = X2934
| ~ in(X2934,complements_of_subsets(the_carrier(X2923),X2924))
| in(ordered_pair(X2934,X2935),esk192_2(X2923,X2924))
| ~ element(X2928,powerset(the_carrier(X2923)))
| X2928 != esk189_2(X2923,X2924)
| esk190_2(X2923,X2924) = subset_complement(the_carrier(X2923),X2928)
| ~ one_sorted_str(X2923)
| ~ element(X2924,powerset(powerset(the_carrier(X2923)))) )
& ( X2935 != subset_complement(the_carrier(X2923),esk193_4(X2923,X2924,X2934,X2935))
| ~ in(X2934,complements_of_subsets(the_carrier(X2923),X2924))
| in(ordered_pair(X2934,X2935),esk192_2(X2923,X2924))
| ~ element(X2928,powerset(the_carrier(X2923)))
| X2928 != esk189_2(X2923,X2924)
| esk190_2(X2923,X2924) = subset_complement(the_carrier(X2923),X2928)
| ~ one_sorted_str(X2923)
| ~ element(X2924,powerset(powerset(the_carrier(X2923)))) )
& ( relation(esk192_2(X2923,X2924))
| in(esk189_2(X2923,X2924),complements_of_subsets(the_carrier(X2923),X2924))
| ~ one_sorted_str(X2923)
| ~ element(X2924,powerset(powerset(the_carrier(X2923)))) )
& ( function(esk192_2(X2923,X2924))
| in(esk189_2(X2923,X2924),complements_of_subsets(the_carrier(X2923),X2924))
| ~ one_sorted_str(X2923)
| ~ element(X2924,powerset(powerset(the_carrier(X2923)))) )
& ( in(X2931,complements_of_subsets(the_carrier(X2923),X2924))
| ~ in(ordered_pair(X2931,X2932),esk192_2(X2923,X2924))
| in(esk189_2(X2923,X2924),complements_of_subsets(the_carrier(X2923),X2924))
| ~ one_sorted_str(X2923)
| ~ element(X2924,powerset(powerset(the_carrier(X2923)))) )
& ( ~ element(X2933,powerset(the_carrier(X2923)))
| X2933 != X2931
| X2932 = subset_complement(the_carrier(X2923),X2933)
| ~ in(ordered_pair(X2931,X2932),esk192_2(X2923,X2924))
| in(esk189_2(X2923,X2924),complements_of_subsets(the_carrier(X2923),X2924))
| ~ one_sorted_str(X2923)
| ~ element(X2924,powerset(powerset(the_carrier(X2923)))) )
& ( element(esk193_4(X2923,X2924,X2934,X2935),powerset(the_carrier(X2923)))
| ~ in(X2934,complements_of_subsets(the_carrier(X2923),X2924))
| in(ordered_pair(X2934,X2935),esk192_2(X2923,X2924))
| in(esk189_2(X2923,X2924),complements_of_subsets(the_carrier(X2923),X2924))
| ~ one_sorted_str(X2923)
| ~ element(X2924,powerset(powerset(the_carrier(X2923)))) )
& ( esk193_4(X2923,X2924,X2934,X2935) = X2934
| ~ in(X2934,complements_of_subsets(the_carrier(X2923),X2924))
| in(ordered_pair(X2934,X2935),esk192_2(X2923,X2924))
| in(esk189_2(X2923,X2924),complements_of_subsets(the_carrier(X2923),X2924))
| ~ one_sorted_str(X2923)
| ~ element(X2924,powerset(powerset(the_carrier(X2923)))) )
& ( X2935 != subset_complement(the_carrier(X2923),esk193_4(X2923,X2924,X2934,X2935))
| ~ in(X2934,complements_of_subsets(the_carrier(X2923),X2924))
| in(ordered_pair(X2934,X2935),esk192_2(X2923,X2924))
| in(esk189_2(X2923,X2924),complements_of_subsets(the_carrier(X2923),X2924))
| ~ one_sorted_str(X2923)
| ~ element(X2924,powerset(powerset(the_carrier(X2923)))) )
& ( relation(esk192_2(X2923,X2924))
| ~ element(X2929,powerset(the_carrier(X2923)))
| X2929 != esk189_2(X2923,X2924)
| esk191_2(X2923,X2924) = subset_complement(the_carrier(X2923),X2929)
| ~ one_sorted_str(X2923)
| ~ element(X2924,powerset(powerset(the_carrier(X2923)))) )
& ( function(esk192_2(X2923,X2924))
| ~ element(X2929,powerset(the_carrier(X2923)))
| X2929 != esk189_2(X2923,X2924)
| esk191_2(X2923,X2924) = subset_complement(the_carrier(X2923),X2929)
| ~ one_sorted_str(X2923)
| ~ element(X2924,powerset(powerset(the_carrier(X2923)))) )
& ( in(X2931,complements_of_subsets(the_carrier(X2923),X2924))
| ~ in(ordered_pair(X2931,X2932),esk192_2(X2923,X2924))
| ~ element(X2929,powerset(the_carrier(X2923)))
| X2929 != esk189_2(X2923,X2924)
| esk191_2(X2923,X2924) = subset_complement(the_carrier(X2923),X2929)
| ~ one_sorted_str(X2923)
| ~ element(X2924,powerset(powerset(the_carrier(X2923)))) )
& ( ~ element(X2933,powerset(the_carrier(X2923)))
| X2933 != X2931
| X2932 = subset_complement(the_carrier(X2923),X2933)
| ~ in(ordered_pair(X2931,X2932),esk192_2(X2923,X2924))
| ~ element(X2929,powerset(the_carrier(X2923)))
| X2929 != esk189_2(X2923,X2924)
| esk191_2(X2923,X2924) = subset_complement(the_carrier(X2923),X2929)
| ~ one_sorted_str(X2923)
| ~ element(X2924,powerset(powerset(the_carrier(X2923)))) )
& ( element(esk193_4(X2923,X2924,X2934,X2935),powerset(the_carrier(X2923)))
| ~ in(X2934,complements_of_subsets(the_carrier(X2923),X2924))
| in(ordered_pair(X2934,X2935),esk192_2(X2923,X2924))
| ~ element(X2929,powerset(the_carrier(X2923)))
| X2929 != esk189_2(X2923,X2924)
| esk191_2(X2923,X2924) = subset_complement(the_carrier(X2923),X2929)
| ~ one_sorted_str(X2923)
| ~ element(X2924,powerset(powerset(the_carrier(X2923)))) )
& ( esk193_4(X2923,X2924,X2934,X2935) = X2934
| ~ in(X2934,complements_of_subsets(the_carrier(X2923),X2924))
| in(ordered_pair(X2934,X2935),esk192_2(X2923,X2924))
| ~ element(X2929,powerset(the_carrier(X2923)))
| X2929 != esk189_2(X2923,X2924)
| esk191_2(X2923,X2924) = subset_complement(the_carrier(X2923),X2929)
| ~ one_sorted_str(X2923)
| ~ element(X2924,powerset(powerset(the_carrier(X2923)))) )
& ( X2935 != subset_complement(the_carrier(X2923),esk193_4(X2923,X2924,X2934,X2935))
| ~ in(X2934,complements_of_subsets(the_carrier(X2923),X2924))
| in(ordered_pair(X2934,X2935),esk192_2(X2923,X2924))
| ~ element(X2929,powerset(the_carrier(X2923)))
| X2929 != esk189_2(X2923,X2924)
| esk191_2(X2923,X2924) = subset_complement(the_carrier(X2923),X2929)
| ~ one_sorted_str(X2923)
| ~ element(X2924,powerset(powerset(the_carrier(X2923)))) )
& ( relation(esk192_2(X2923,X2924))
| esk190_2(X2923,X2924) != esk191_2(X2923,X2924)
| ~ one_sorted_str(X2923)
| ~ element(X2924,powerset(powerset(the_carrier(X2923)))) )
& ( function(esk192_2(X2923,X2924))
| esk190_2(X2923,X2924) != esk191_2(X2923,X2924)
| ~ one_sorted_str(X2923)
| ~ element(X2924,powerset(powerset(the_carrier(X2923)))) )
& ( in(X2931,complements_of_subsets(the_carrier(X2923),X2924))
| ~ in(ordered_pair(X2931,X2932),esk192_2(X2923,X2924))
| esk190_2(X2923,X2924) != esk191_2(X2923,X2924)
| ~ one_sorted_str(X2923)
| ~ element(X2924,powerset(powerset(the_carrier(X2923)))) )
& ( ~ element(X2933,powerset(the_carrier(X2923)))
| X2933 != X2931
| X2932 = subset_complement(the_carrier(X2923),X2933)
| ~ in(ordered_pair(X2931,X2932),esk192_2(X2923,X2924))
| esk190_2(X2923,X2924) != esk191_2(X2923,X2924)
| ~ one_sorted_str(X2923)
| ~ element(X2924,powerset(powerset(the_carrier(X2923)))) )
& ( element(esk193_4(X2923,X2924,X2934,X2935),powerset(the_carrier(X2923)))
| ~ in(X2934,complements_of_subsets(the_carrier(X2923),X2924))
| in(ordered_pair(X2934,X2935),esk192_2(X2923,X2924))
| esk190_2(X2923,X2924) != esk191_2(X2923,X2924)
| ~ one_sorted_str(X2923)
| ~ element(X2924,powerset(powerset(the_carrier(X2923)))) )
& ( esk193_4(X2923,X2924,X2934,X2935) = X2934
| ~ in(X2934,complements_of_subsets(the_carrier(X2923),X2924))
| in(ordered_pair(X2934,X2935),esk192_2(X2923,X2924))
| esk190_2(X2923,X2924) != esk191_2(X2923,X2924)
| ~ one_sorted_str(X2923)
| ~ element(X2924,powerset(powerset(the_carrier(X2923)))) )
& ( X2935 != subset_complement(the_carrier(X2923),esk193_4(X2923,X2924,X2934,X2935))
| ~ in(X2934,complements_of_subsets(the_carrier(X2923),X2924))
| in(ordered_pair(X2934,X2935),esk192_2(X2923,X2924))
| esk190_2(X2923,X2924) != esk191_2(X2923,X2924)
| ~ one_sorted_str(X2923)
| ~ element(X2924,powerset(powerset(the_carrier(X2923)))) ) ),
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)],[i_0_654])])])])])]) ).
fof(i_0_712,lemma,
! [X2937,X2938,X2942,X2943,X2945,X2946,X2947,X2948,X2949] :
( ( relation(esk197_2(X2937,X2938))
| in(esk194_2(X2937,X2938),X2938)
| ~ one_sorted_str(X2937)
| ~ element(X2938,powerset(powerset(the_carrier(X2937)))) )
& ( function(esk197_2(X2937,X2938))
| in(esk194_2(X2937,X2938),X2938)
| ~ one_sorted_str(X2937)
| ~ element(X2938,powerset(powerset(the_carrier(X2937)))) )
& ( in(X2945,X2938)
| ~ in(ordered_pair(X2945,X2946),esk197_2(X2937,X2938))
| in(esk194_2(X2937,X2938),X2938)
| ~ one_sorted_str(X2937)
| ~ element(X2938,powerset(powerset(the_carrier(X2937)))) )
& ( ~ element(X2947,powerset(the_carrier(X2937)))
| X2947 != X2945
| X2946 = subset_complement(the_carrier(X2937),X2947)
| ~ in(ordered_pair(X2945,X2946),esk197_2(X2937,X2938))
| in(esk194_2(X2937,X2938),X2938)
| ~ one_sorted_str(X2937)
| ~ element(X2938,powerset(powerset(the_carrier(X2937)))) )
& ( element(esk198_4(X2937,X2938,X2948,X2949),powerset(the_carrier(X2937)))
| ~ in(X2948,X2938)
| in(ordered_pair(X2948,X2949),esk197_2(X2937,X2938))
| in(esk194_2(X2937,X2938),X2938)
| ~ one_sorted_str(X2937)
| ~ element(X2938,powerset(powerset(the_carrier(X2937)))) )
& ( esk198_4(X2937,X2938,X2948,X2949) = X2948
| ~ in(X2948,X2938)
| in(ordered_pair(X2948,X2949),esk197_2(X2937,X2938))
| in(esk194_2(X2937,X2938),X2938)
| ~ one_sorted_str(X2937)
| ~ element(X2938,powerset(powerset(the_carrier(X2937)))) )
& ( X2949 != subset_complement(the_carrier(X2937),esk198_4(X2937,X2938,X2948,X2949))
| ~ in(X2948,X2938)
| in(ordered_pair(X2948,X2949),esk197_2(X2937,X2938))
| in(esk194_2(X2937,X2938),X2938)
| ~ one_sorted_str(X2937)
| ~ element(X2938,powerset(powerset(the_carrier(X2937)))) )
& ( relation(esk197_2(X2937,X2938))
| ~ element(X2942,powerset(the_carrier(X2937)))
| X2942 != esk194_2(X2937,X2938)
| esk195_2(X2937,X2938) = subset_complement(the_carrier(X2937),X2942)
| ~ one_sorted_str(X2937)
| ~ element(X2938,powerset(powerset(the_carrier(X2937)))) )
& ( function(esk197_2(X2937,X2938))
| ~ element(X2942,powerset(the_carrier(X2937)))
| X2942 != esk194_2(X2937,X2938)
| esk195_2(X2937,X2938) = subset_complement(the_carrier(X2937),X2942)
| ~ one_sorted_str(X2937)
| ~ element(X2938,powerset(powerset(the_carrier(X2937)))) )
& ( in(X2945,X2938)
| ~ in(ordered_pair(X2945,X2946),esk197_2(X2937,X2938))
| ~ element(X2942,powerset(the_carrier(X2937)))
| X2942 != esk194_2(X2937,X2938)
| esk195_2(X2937,X2938) = subset_complement(the_carrier(X2937),X2942)
| ~ one_sorted_str(X2937)
| ~ element(X2938,powerset(powerset(the_carrier(X2937)))) )
& ( ~ element(X2947,powerset(the_carrier(X2937)))
| X2947 != X2945
| X2946 = subset_complement(the_carrier(X2937),X2947)
| ~ in(ordered_pair(X2945,X2946),esk197_2(X2937,X2938))
| ~ element(X2942,powerset(the_carrier(X2937)))
| X2942 != esk194_2(X2937,X2938)
| esk195_2(X2937,X2938) = subset_complement(the_carrier(X2937),X2942)
| ~ one_sorted_str(X2937)
| ~ element(X2938,powerset(powerset(the_carrier(X2937)))) )
& ( element(esk198_4(X2937,X2938,X2948,X2949),powerset(the_carrier(X2937)))
| ~ in(X2948,X2938)
| in(ordered_pair(X2948,X2949),esk197_2(X2937,X2938))
| ~ element(X2942,powerset(the_carrier(X2937)))
| X2942 != esk194_2(X2937,X2938)
| esk195_2(X2937,X2938) = subset_complement(the_carrier(X2937),X2942)
| ~ one_sorted_str(X2937)
| ~ element(X2938,powerset(powerset(the_carrier(X2937)))) )
& ( esk198_4(X2937,X2938,X2948,X2949) = X2948
| ~ in(X2948,X2938)
| in(ordered_pair(X2948,X2949),esk197_2(X2937,X2938))
| ~ element(X2942,powerset(the_carrier(X2937)))
| X2942 != esk194_2(X2937,X2938)
| esk195_2(X2937,X2938) = subset_complement(the_carrier(X2937),X2942)
| ~ one_sorted_str(X2937)
| ~ element(X2938,powerset(powerset(the_carrier(X2937)))) )
& ( X2949 != subset_complement(the_carrier(X2937),esk198_4(X2937,X2938,X2948,X2949))
| ~ in(X2948,X2938)
| in(ordered_pair(X2948,X2949),esk197_2(X2937,X2938))
| ~ element(X2942,powerset(the_carrier(X2937)))
| X2942 != esk194_2(X2937,X2938)
| esk195_2(X2937,X2938) = subset_complement(the_carrier(X2937),X2942)
| ~ one_sorted_str(X2937)
| ~ element(X2938,powerset(powerset(the_carrier(X2937)))) )
& ( relation(esk197_2(X2937,X2938))
| in(esk194_2(X2937,X2938),X2938)
| ~ one_sorted_str(X2937)
| ~ element(X2938,powerset(powerset(the_carrier(X2937)))) )
& ( function(esk197_2(X2937,X2938))
| in(esk194_2(X2937,X2938),X2938)
| ~ one_sorted_str(X2937)
| ~ element(X2938,powerset(powerset(the_carrier(X2937)))) )
& ( in(X2945,X2938)
| ~ in(ordered_pair(X2945,X2946),esk197_2(X2937,X2938))
| in(esk194_2(X2937,X2938),X2938)
| ~ one_sorted_str(X2937)
| ~ element(X2938,powerset(powerset(the_carrier(X2937)))) )
& ( ~ element(X2947,powerset(the_carrier(X2937)))
| X2947 != X2945
| X2946 = subset_complement(the_carrier(X2937),X2947)
| ~ in(ordered_pair(X2945,X2946),esk197_2(X2937,X2938))
| in(esk194_2(X2937,X2938),X2938)
| ~ one_sorted_str(X2937)
| ~ element(X2938,powerset(powerset(the_carrier(X2937)))) )
& ( element(esk198_4(X2937,X2938,X2948,X2949),powerset(the_carrier(X2937)))
| ~ in(X2948,X2938)
| in(ordered_pair(X2948,X2949),esk197_2(X2937,X2938))
| in(esk194_2(X2937,X2938),X2938)
| ~ one_sorted_str(X2937)
| ~ element(X2938,powerset(powerset(the_carrier(X2937)))) )
& ( esk198_4(X2937,X2938,X2948,X2949) = X2948
| ~ in(X2948,X2938)
| in(ordered_pair(X2948,X2949),esk197_2(X2937,X2938))
| in(esk194_2(X2937,X2938),X2938)
| ~ one_sorted_str(X2937)
| ~ element(X2938,powerset(powerset(the_carrier(X2937)))) )
& ( X2949 != subset_complement(the_carrier(X2937),esk198_4(X2937,X2938,X2948,X2949))
| ~ in(X2948,X2938)
| in(ordered_pair(X2948,X2949),esk197_2(X2937,X2938))
| in(esk194_2(X2937,X2938),X2938)
| ~ one_sorted_str(X2937)
| ~ element(X2938,powerset(powerset(the_carrier(X2937)))) )
& ( relation(esk197_2(X2937,X2938))
| ~ element(X2943,powerset(the_carrier(X2937)))
| X2943 != esk194_2(X2937,X2938)
| esk196_2(X2937,X2938) = subset_complement(the_carrier(X2937),X2943)
| ~ one_sorted_str(X2937)
| ~ element(X2938,powerset(powerset(the_carrier(X2937)))) )
& ( function(esk197_2(X2937,X2938))
| ~ element(X2943,powerset(the_carrier(X2937)))
| X2943 != esk194_2(X2937,X2938)
| esk196_2(X2937,X2938) = subset_complement(the_carrier(X2937),X2943)
| ~ one_sorted_str(X2937)
| ~ element(X2938,powerset(powerset(the_carrier(X2937)))) )
& ( in(X2945,X2938)
| ~ in(ordered_pair(X2945,X2946),esk197_2(X2937,X2938))
| ~ element(X2943,powerset(the_carrier(X2937)))
| X2943 != esk194_2(X2937,X2938)
| esk196_2(X2937,X2938) = subset_complement(the_carrier(X2937),X2943)
| ~ one_sorted_str(X2937)
| ~ element(X2938,powerset(powerset(the_carrier(X2937)))) )
& ( ~ element(X2947,powerset(the_carrier(X2937)))
| X2947 != X2945
| X2946 = subset_complement(the_carrier(X2937),X2947)
| ~ in(ordered_pair(X2945,X2946),esk197_2(X2937,X2938))
| ~ element(X2943,powerset(the_carrier(X2937)))
| X2943 != esk194_2(X2937,X2938)
| esk196_2(X2937,X2938) = subset_complement(the_carrier(X2937),X2943)
| ~ one_sorted_str(X2937)
| ~ element(X2938,powerset(powerset(the_carrier(X2937)))) )
& ( element(esk198_4(X2937,X2938,X2948,X2949),powerset(the_carrier(X2937)))
| ~ in(X2948,X2938)
| in(ordered_pair(X2948,X2949),esk197_2(X2937,X2938))
| ~ element(X2943,powerset(the_carrier(X2937)))
| X2943 != esk194_2(X2937,X2938)
| esk196_2(X2937,X2938) = subset_complement(the_carrier(X2937),X2943)
| ~ one_sorted_str(X2937)
| ~ element(X2938,powerset(powerset(the_carrier(X2937)))) )
& ( esk198_4(X2937,X2938,X2948,X2949) = X2948
| ~ in(X2948,X2938)
| in(ordered_pair(X2948,X2949),esk197_2(X2937,X2938))
| ~ element(X2943,powerset(the_carrier(X2937)))
| X2943 != esk194_2(X2937,X2938)
| esk196_2(X2937,X2938) = subset_complement(the_carrier(X2937),X2943)
| ~ one_sorted_str(X2937)
| ~ element(X2938,powerset(powerset(the_carrier(X2937)))) )
& ( X2949 != subset_complement(the_carrier(X2937),esk198_4(X2937,X2938,X2948,X2949))
| ~ in(X2948,X2938)
| in(ordered_pair(X2948,X2949),esk197_2(X2937,X2938))
| ~ element(X2943,powerset(the_carrier(X2937)))
| X2943 != esk194_2(X2937,X2938)
| esk196_2(X2937,X2938) = subset_complement(the_carrier(X2937),X2943)
| ~ one_sorted_str(X2937)
| ~ element(X2938,powerset(powerset(the_carrier(X2937)))) )
& ( relation(esk197_2(X2937,X2938))
| esk195_2(X2937,X2938) != esk196_2(X2937,X2938)
| ~ one_sorted_str(X2937)
| ~ element(X2938,powerset(powerset(the_carrier(X2937)))) )
& ( function(esk197_2(X2937,X2938))
| esk195_2(X2937,X2938) != esk196_2(X2937,X2938)
| ~ one_sorted_str(X2937)
| ~ element(X2938,powerset(powerset(the_carrier(X2937)))) )
& ( in(X2945,X2938)
| ~ in(ordered_pair(X2945,X2946),esk197_2(X2937,X2938))
| esk195_2(X2937,X2938) != esk196_2(X2937,X2938)
| ~ one_sorted_str(X2937)
| ~ element(X2938,powerset(powerset(the_carrier(X2937)))) )
& ( ~ element(X2947,powerset(the_carrier(X2937)))
| X2947 != X2945
| X2946 = subset_complement(the_carrier(X2937),X2947)
| ~ in(ordered_pair(X2945,X2946),esk197_2(X2937,X2938))
| esk195_2(X2937,X2938) != esk196_2(X2937,X2938)
| ~ one_sorted_str(X2937)
| ~ element(X2938,powerset(powerset(the_carrier(X2937)))) )
& ( element(esk198_4(X2937,X2938,X2948,X2949),powerset(the_carrier(X2937)))
| ~ in(X2948,X2938)
| in(ordered_pair(X2948,X2949),esk197_2(X2937,X2938))
| esk195_2(X2937,X2938) != esk196_2(X2937,X2938)
| ~ one_sorted_str(X2937)
| ~ element(X2938,powerset(powerset(the_carrier(X2937)))) )
& ( esk198_4(X2937,X2938,X2948,X2949) = X2948
| ~ in(X2948,X2938)
| in(ordered_pair(X2948,X2949),esk197_2(X2937,X2938))
| esk195_2(X2937,X2938) != esk196_2(X2937,X2938)
| ~ one_sorted_str(X2937)
| ~ element(X2938,powerset(powerset(the_carrier(X2937)))) )
& ( X2949 != subset_complement(the_carrier(X2937),esk198_4(X2937,X2938,X2948,X2949))
| ~ in(X2948,X2938)
| in(ordered_pair(X2948,X2949),esk197_2(X2937,X2938))
| esk195_2(X2937,X2938) != esk196_2(X2937,X2938)
| ~ one_sorted_str(X2937)
| ~ element(X2938,powerset(powerset(the_carrier(X2937)))) ) ),
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)],[i_0_655])])])])])]) ).
fof(i_0_713,lemma,
! [X2967,X2968,X2969,X2971,X2972,X2973,X2974] :
( ( relation(esk205_3(X2967,X2968,X2969))
| ~ relation(X2968)
| ~ relation(X2969)
| ~ function(X2969) )
& ( in(X2971,X2967)
| ~ in(ordered_pair(X2971,X2972),esk205_3(X2967,X2968,X2969))
| ~ relation(X2968)
| ~ relation(X2969)
| ~ function(X2969) )
& ( in(X2972,X2967)
| ~ in(ordered_pair(X2971,X2972),esk205_3(X2967,X2968,X2969))
| ~ relation(X2968)
| ~ relation(X2969)
| ~ function(X2969) )
& ( in(ordered_pair(apply(X2969,X2971),apply(X2969,X2972)),X2968)
| ~ in(ordered_pair(X2971,X2972),esk205_3(X2967,X2968,X2969))
| ~ relation(X2968)
| ~ relation(X2969)
| ~ function(X2969) )
& ( ~ in(X2973,X2967)
| ~ in(X2974,X2967)
| ~ in(ordered_pair(apply(X2969,X2973),apply(X2969,X2974)),X2968)
| in(ordered_pair(X2973,X2974),esk205_3(X2967,X2968,X2969))
| ~ relation(X2968)
| ~ relation(X2969)
| ~ function(X2969) ) ),
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)],[s1_relat_1__e6_21__wellord2])])])])])]) ).
fof(i_0_714,plain,
! [X1,X2] :
( ( one_sorted_str(X1)
& element(X2,powerset(powerset(the_carrier(X1)))) )
=> ( ! [X3,X4,X5] :
( ( in(X3,complements_of_subsets(the_carrier(X1),X2))
& ! [X6] :
( element(X6,powerset(the_carrier(X1)))
=> ( X6 = X3
=> X4 = subset_complement(the_carrier(X1),X6) ) )
& in(X3,complements_of_subsets(the_carrier(X1),X2))
& ! [X7] :
( element(X7,powerset(the_carrier(X1)))
=> ( X7 = X3
=> X5 = subset_complement(the_carrier(X1),X7) ) ) )
=> X4 = X5 )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(X5,complements_of_subsets(the_carrier(X1),X2))
& ! [X8] :
( element(X8,powerset(the_carrier(X1)))
=> ( X8 = X5
=> X4 = subset_complement(the_carrier(X1),X8) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[s1_tarski__e4_7_1__tops_2__1]) ).
fof(i_0_715,plain,
! [X3029,X3037,X3039,X3043,X3044,X3045,X3046] :
( ( in(esk243_3(X3029,X3037,X3039),cartesian_product2(X3029,X3037))
| ~ in(X3039,esk242_2(X3029,X3037))
| esk235_1(X3029) = esk236_1(X3029) )
& ( esk243_3(X3029,X3037,X3039) = X3039
| ~ in(X3039,esk242_2(X3029,X3037))
| esk235_1(X3029) = esk236_1(X3029) )
& ( ordered_pair(esk244_3(X3029,X3037,X3039),esk245_3(X3029,X3037,X3039)) = X3039
| ~ in(X3039,esk242_2(X3029,X3037))
| esk235_1(X3029) = esk236_1(X3029) )
& ( in(esk244_3(X3029,X3037,X3039),X3029)
| ~ in(X3039,esk242_2(X3029,X3037))
| esk235_1(X3029) = esk236_1(X3029) )
& ( esk245_3(X3029,X3037,X3039) = singleton(esk244_3(X3029,X3037,X3039))
| ~ in(X3039,esk242_2(X3029,X3037))
| esk235_1(X3029) = esk236_1(X3029) )
& ( ~ in(X3044,cartesian_product2(X3029,X3037))
| X3044 != X3043
| ordered_pair(X3045,X3046) != X3043
| ~ in(X3045,X3029)
| X3046 != singleton(X3045)
| in(X3043,esk242_2(X3029,X3037))
| esk235_1(X3029) = esk236_1(X3029) )
& ( in(esk243_3(X3029,X3037,X3039),cartesian_product2(X3029,X3037))
| ~ in(X3039,esk242_2(X3029,X3037))
| ordered_pair(esk238_1(X3029),esk239_1(X3029)) = esk236_1(X3029) )
& ( esk243_3(X3029,X3037,X3039) = X3039
| ~ in(X3039,esk242_2(X3029,X3037))
| ordered_pair(esk238_1(X3029),esk239_1(X3029)) = esk236_1(X3029) )
& ( ordered_pair(esk244_3(X3029,X3037,X3039),esk245_3(X3029,X3037,X3039)) = X3039
| ~ in(X3039,esk242_2(X3029,X3037))
| ordered_pair(esk238_1(X3029),esk239_1(X3029)) = esk236_1(X3029) )
& ( in(esk244_3(X3029,X3037,X3039),X3029)
| ~ in(X3039,esk242_2(X3029,X3037))
| ordered_pair(esk238_1(X3029),esk239_1(X3029)) = esk236_1(X3029) )
& ( esk245_3(X3029,X3037,X3039) = singleton(esk244_3(X3029,X3037,X3039))
| ~ in(X3039,esk242_2(X3029,X3037))
| ordered_pair(esk238_1(X3029),esk239_1(X3029)) = esk236_1(X3029) )
& ( ~ in(X3044,cartesian_product2(X3029,X3037))
| X3044 != X3043
| ordered_pair(X3045,X3046) != X3043
| ~ in(X3045,X3029)
| X3046 != singleton(X3045)
| in(X3043,esk242_2(X3029,X3037))
| ordered_pair(esk238_1(X3029),esk239_1(X3029)) = esk236_1(X3029) )
& ( in(esk243_3(X3029,X3037,X3039),cartesian_product2(X3029,X3037))
| ~ in(X3039,esk242_2(X3029,X3037))
| in(esk238_1(X3029),X3029) )
& ( esk243_3(X3029,X3037,X3039) = X3039
| ~ in(X3039,esk242_2(X3029,X3037))
| in(esk238_1(X3029),X3029) )
& ( ordered_pair(esk244_3(X3029,X3037,X3039),esk245_3(X3029,X3037,X3039)) = X3039
| ~ in(X3039,esk242_2(X3029,X3037))
| in(esk238_1(X3029),X3029) )
& ( in(esk244_3(X3029,X3037,X3039),X3029)
| ~ in(X3039,esk242_2(X3029,X3037))
| in(esk238_1(X3029),X3029) )
& ( esk245_3(X3029,X3037,X3039) = singleton(esk244_3(X3029,X3037,X3039))
| ~ in(X3039,esk242_2(X3029,X3037))
| in(esk238_1(X3029),X3029) )
& ( ~ in(X3044,cartesian_product2(X3029,X3037))
| X3044 != X3043
| ordered_pair(X3045,X3046) != X3043
| ~ in(X3045,X3029)
| X3046 != singleton(X3045)
| in(X3043,esk242_2(X3029,X3037))
| in(esk238_1(X3029),X3029) )
& ( in(esk243_3(X3029,X3037,X3039),cartesian_product2(X3029,X3037))
| ~ in(X3039,esk242_2(X3029,X3037))
| esk239_1(X3029) = singleton(esk238_1(X3029)) )
& ( esk243_3(X3029,X3037,X3039) = X3039
| ~ in(X3039,esk242_2(X3029,X3037))
| esk239_1(X3029) = singleton(esk238_1(X3029)) )
& ( ordered_pair(esk244_3(X3029,X3037,X3039),esk245_3(X3029,X3037,X3039)) = X3039
| ~ in(X3039,esk242_2(X3029,X3037))
| esk239_1(X3029) = singleton(esk238_1(X3029)) )
& ( in(esk244_3(X3029,X3037,X3039),X3029)
| ~ in(X3039,esk242_2(X3029,X3037))
| esk239_1(X3029) = singleton(esk238_1(X3029)) )
& ( esk245_3(X3029,X3037,X3039) = singleton(esk244_3(X3029,X3037,X3039))
| ~ in(X3039,esk242_2(X3029,X3037))
| esk239_1(X3029) = singleton(esk238_1(X3029)) )
& ( ~ in(X3044,cartesian_product2(X3029,X3037))
| X3044 != X3043
| ordered_pair(X3045,X3046) != X3043
| ~ in(X3045,X3029)
| X3046 != singleton(X3045)
| in(X3043,esk242_2(X3029,X3037))
| esk239_1(X3029) = singleton(esk238_1(X3029)) )
& ( in(esk243_3(X3029,X3037,X3039),cartesian_product2(X3029,X3037))
| ~ in(X3039,esk242_2(X3029,X3037))
| esk235_1(X3029) = esk237_1(X3029) )
& ( esk243_3(X3029,X3037,X3039) = X3039
| ~ in(X3039,esk242_2(X3029,X3037))
| esk235_1(X3029) = esk237_1(X3029) )
& ( ordered_pair(esk244_3(X3029,X3037,X3039),esk245_3(X3029,X3037,X3039)) = X3039
| ~ in(X3039,esk242_2(X3029,X3037))
| esk235_1(X3029) = esk237_1(X3029) )
& ( in(esk244_3(X3029,X3037,X3039),X3029)
| ~ in(X3039,esk242_2(X3029,X3037))
| esk235_1(X3029) = esk237_1(X3029) )
& ( esk245_3(X3029,X3037,X3039) = singleton(esk244_3(X3029,X3037,X3039))
| ~ in(X3039,esk242_2(X3029,X3037))
| esk235_1(X3029) = esk237_1(X3029) )
& ( ~ in(X3044,cartesian_product2(X3029,X3037))
| X3044 != X3043
| ordered_pair(X3045,X3046) != X3043
| ~ in(X3045,X3029)
| X3046 != singleton(X3045)
| in(X3043,esk242_2(X3029,X3037))
| esk235_1(X3029) = esk237_1(X3029) )
& ( in(esk243_3(X3029,X3037,X3039),cartesian_product2(X3029,X3037))
| ~ in(X3039,esk242_2(X3029,X3037))
| ordered_pair(esk240_1(X3029),esk241_1(X3029)) = esk237_1(X3029) )
& ( esk243_3(X3029,X3037,X3039) = X3039
| ~ in(X3039,esk242_2(X3029,X3037))
| ordered_pair(esk240_1(X3029),esk241_1(X3029)) = esk237_1(X3029) )
& ( ordered_pair(esk244_3(X3029,X3037,X3039),esk245_3(X3029,X3037,X3039)) = X3039
| ~ in(X3039,esk242_2(X3029,X3037))
| ordered_pair(esk240_1(X3029),esk241_1(X3029)) = esk237_1(X3029) )
& ( in(esk244_3(X3029,X3037,X3039),X3029)
| ~ in(X3039,esk242_2(X3029,X3037))
| ordered_pair(esk240_1(X3029),esk241_1(X3029)) = esk237_1(X3029) )
& ( esk245_3(X3029,X3037,X3039) = singleton(esk244_3(X3029,X3037,X3039))
| ~ in(X3039,esk242_2(X3029,X3037))
| ordered_pair(esk240_1(X3029),esk241_1(X3029)) = esk237_1(X3029) )
& ( ~ in(X3044,cartesian_product2(X3029,X3037))
| X3044 != X3043
| ordered_pair(X3045,X3046) != X3043
| ~ in(X3045,X3029)
| X3046 != singleton(X3045)
| in(X3043,esk242_2(X3029,X3037))
| ordered_pair(esk240_1(X3029),esk241_1(X3029)) = esk237_1(X3029) )
& ( in(esk243_3(X3029,X3037,X3039),cartesian_product2(X3029,X3037))
| ~ in(X3039,esk242_2(X3029,X3037))
| in(esk240_1(X3029),X3029) )
& ( esk243_3(X3029,X3037,X3039) = X3039
| ~ in(X3039,esk242_2(X3029,X3037))
| in(esk240_1(X3029),X3029) )
& ( ordered_pair(esk244_3(X3029,X3037,X3039),esk245_3(X3029,X3037,X3039)) = X3039
| ~ in(X3039,esk242_2(X3029,X3037))
| in(esk240_1(X3029),X3029) )
& ( in(esk244_3(X3029,X3037,X3039),X3029)
| ~ in(X3039,esk242_2(X3029,X3037))
| in(esk240_1(X3029),X3029) )
& ( esk245_3(X3029,X3037,X3039) = singleton(esk244_3(X3029,X3037,X3039))
| ~ in(X3039,esk242_2(X3029,X3037))
| in(esk240_1(X3029),X3029) )
& ( ~ in(X3044,cartesian_product2(X3029,X3037))
| X3044 != X3043
| ordered_pair(X3045,X3046) != X3043
| ~ in(X3045,X3029)
| X3046 != singleton(X3045)
| in(X3043,esk242_2(X3029,X3037))
| in(esk240_1(X3029),X3029) )
& ( in(esk243_3(X3029,X3037,X3039),cartesian_product2(X3029,X3037))
| ~ in(X3039,esk242_2(X3029,X3037))
| esk241_1(X3029) = singleton(esk240_1(X3029)) )
& ( esk243_3(X3029,X3037,X3039) = X3039
| ~ in(X3039,esk242_2(X3029,X3037))
| esk241_1(X3029) = singleton(esk240_1(X3029)) )
& ( ordered_pair(esk244_3(X3029,X3037,X3039),esk245_3(X3029,X3037,X3039)) = X3039
| ~ in(X3039,esk242_2(X3029,X3037))
| esk241_1(X3029) = singleton(esk240_1(X3029)) )
& ( in(esk244_3(X3029,X3037,X3039),X3029)
| ~ in(X3039,esk242_2(X3029,X3037))
| esk241_1(X3029) = singleton(esk240_1(X3029)) )
& ( esk245_3(X3029,X3037,X3039) = singleton(esk244_3(X3029,X3037,X3039))
| ~ in(X3039,esk242_2(X3029,X3037))
| esk241_1(X3029) = singleton(esk240_1(X3029)) )
& ( ~ in(X3044,cartesian_product2(X3029,X3037))
| X3044 != X3043
| ordered_pair(X3045,X3046) != X3043
| ~ in(X3045,X3029)
| X3046 != singleton(X3045)
| in(X3043,esk242_2(X3029,X3037))
| esk241_1(X3029) = singleton(esk240_1(X3029)) )
& ( in(esk243_3(X3029,X3037,X3039),cartesian_product2(X3029,X3037))
| ~ in(X3039,esk242_2(X3029,X3037))
| esk236_1(X3029) != esk237_1(X3029) )
& ( esk243_3(X3029,X3037,X3039) = X3039
| ~ in(X3039,esk242_2(X3029,X3037))
| esk236_1(X3029) != esk237_1(X3029) )
& ( ordered_pair(esk244_3(X3029,X3037,X3039),esk245_3(X3029,X3037,X3039)) = X3039
| ~ in(X3039,esk242_2(X3029,X3037))
| esk236_1(X3029) != esk237_1(X3029) )
& ( in(esk244_3(X3029,X3037,X3039),X3029)
| ~ in(X3039,esk242_2(X3029,X3037))
| esk236_1(X3029) != esk237_1(X3029) )
& ( esk245_3(X3029,X3037,X3039) = singleton(esk244_3(X3029,X3037,X3039))
| ~ in(X3039,esk242_2(X3029,X3037))
| esk236_1(X3029) != esk237_1(X3029) )
& ( ~ in(X3044,cartesian_product2(X3029,X3037))
| X3044 != X3043
| ordered_pair(X3045,X3046) != X3043
| ~ in(X3045,X3029)
| X3046 != singleton(X3045)
| in(X3043,esk242_2(X3029,X3037))
| esk236_1(X3029) != esk237_1(X3029) ) ),
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)],[s1_tarski__e16_22__wellord2__2])])])])])]) ).
fof(i_0_716,plain,
! [X1,X2] :
( ( one_sorted_str(X1)
& element(X2,powerset(powerset(the_carrier(X1)))) )
=> ( ! [X3,X4,X5] :
( ( in(X3,X2)
& ! [X6] :
( element(X6,powerset(the_carrier(X1)))
=> ( X6 = X3
=> X4 = subset_complement(the_carrier(X1),X6) ) )
& in(X3,X2)
& ! [X7] :
( element(X7,powerset(the_carrier(X1)))
=> ( X7 = X3
=> X5 = subset_complement(the_carrier(X1),X7) ) ) )
=> X4 = X5 )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(X5,X2)
& ! [X8] :
( element(X8,powerset(the_carrier(X1)))
=> ( X8 = X5
=> X4 = subset_complement(the_carrier(X1),X8) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[s1_tarski__e4_7_2__tops_2__1]) ).
fof(i_0_717,plain,
! [X3047,X3052,X3055,X3057,X3058,X3059,X3060,X3062] :
( ( in(esk250_2(X3047,X3052),succ(X3047))
| ~ in(X3052,esk249_1(X3047))
| epred2_3(esk248_1(X3047),esk247_1(X3047),esk246_1(X3047))
| ~ ordinal(X3047) )
& ( esk250_2(X3047,X3052) = X3052
| ~ in(X3052,esk249_1(X3047))
| epred2_3(esk248_1(X3047),esk247_1(X3047),esk246_1(X3047))
| ~ ordinal(X3047) )
& ( ordinal(esk251_2(X3047,X3052))
| ~ in(X3052,esk249_1(X3047))
| epred2_3(esk248_1(X3047),esk247_1(X3047),esk246_1(X3047))
| ~ ordinal(X3047) )
& ( X3052 = esk251_2(X3047,X3052)
| ~ in(X3052,esk249_1(X3047))
| epred2_3(esk248_1(X3047),esk247_1(X3047),esk246_1(X3047))
| ~ ordinal(X3047) )
& ( in(esk252_3(X3047,X3052,X3055),X3055)
| X3055 = empty_set
| ~ element(X3055,powerset(powerset(esk251_2(X3047,X3052))))
| ~ in(esk251_2(X3047,X3052),omega)
| ~ in(X3052,esk249_1(X3047))
| epred2_3(esk248_1(X3047),esk247_1(X3047),esk246_1(X3047))
| ~ ordinal(X3047) )
& ( ~ in(X3057,X3055)
| ~ subset(esk252_3(X3047,X3052,X3055),X3057)
| X3057 = esk252_3(X3047,X3052,X3055)
| X3055 = empty_set
| ~ element(X3055,powerset(powerset(esk251_2(X3047,X3052))))
| ~ in(esk251_2(X3047,X3052),omega)
| ~ in(X3052,esk249_1(X3047))
| epred2_3(esk248_1(X3047),esk247_1(X3047),esk246_1(X3047))
| ~ ordinal(X3047) )
& ( in(X3060,omega)
| ~ ordinal(X3060)
| X3058 != X3060
| ~ in(X3059,succ(X3047))
| X3059 != X3058
| in(X3058,esk249_1(X3047))
| epred2_3(esk248_1(X3047),esk247_1(X3047),esk246_1(X3047))
| ~ ordinal(X3047) )
& ( element(esk253_3(X3047,X3058,X3060),powerset(powerset(X3060)))
| ~ ordinal(X3060)
| X3058 != X3060
| ~ in(X3059,succ(X3047))
| X3059 != X3058
| in(X3058,esk249_1(X3047))
| epred2_3(esk248_1(X3047),esk247_1(X3047),esk246_1(X3047))
| ~ ordinal(X3047) )
& ( esk253_3(X3047,X3058,X3060) != empty_set
| ~ ordinal(X3060)
| X3058 != X3060
| ~ in(X3059,succ(X3047))
| X3059 != X3058
| in(X3058,esk249_1(X3047))
| epred2_3(esk248_1(X3047),esk247_1(X3047),esk246_1(X3047))
| ~ ordinal(X3047) )
& ( in(esk254_4(X3047,X3058,X3060,X3062),esk253_3(X3047,X3058,X3060))
| ~ in(X3062,esk253_3(X3047,X3058,X3060))
| ~ ordinal(X3060)
| X3058 != X3060
| ~ in(X3059,succ(X3047))
| X3059 != X3058
| in(X3058,esk249_1(X3047))
| epred2_3(esk248_1(X3047),esk247_1(X3047),esk246_1(X3047))
| ~ ordinal(X3047) )
& ( subset(X3062,esk254_4(X3047,X3058,X3060,X3062))
| ~ in(X3062,esk253_3(X3047,X3058,X3060))
| ~ ordinal(X3060)
| X3058 != X3060
| ~ in(X3059,succ(X3047))
| X3059 != X3058
| in(X3058,esk249_1(X3047))
| epred2_3(esk248_1(X3047),esk247_1(X3047),esk246_1(X3047))
| ~ ordinal(X3047) )
& ( esk254_4(X3047,X3058,X3060,X3062) != X3062
| ~ in(X3062,esk253_3(X3047,X3058,X3060))
| ~ ordinal(X3060)
| X3058 != X3060
| ~ in(X3059,succ(X3047))
| X3059 != X3058
| in(X3058,esk249_1(X3047))
| epred2_3(esk248_1(X3047),esk247_1(X3047),esk246_1(X3047))
| ~ ordinal(X3047) )
& ( in(esk250_2(X3047,X3052),succ(X3047))
| ~ in(X3052,esk249_1(X3047))
| esk247_1(X3047) != esk248_1(X3047)
| ~ ordinal(X3047) )
& ( esk250_2(X3047,X3052) = X3052
| ~ in(X3052,esk249_1(X3047))
| esk247_1(X3047) != esk248_1(X3047)
| ~ ordinal(X3047) )
& ( ordinal(esk251_2(X3047,X3052))
| ~ in(X3052,esk249_1(X3047))
| esk247_1(X3047) != esk248_1(X3047)
| ~ ordinal(X3047) )
& ( X3052 = esk251_2(X3047,X3052)
| ~ in(X3052,esk249_1(X3047))
| esk247_1(X3047) != esk248_1(X3047)
| ~ ordinal(X3047) )
& ( in(esk252_3(X3047,X3052,X3055),X3055)
| X3055 = empty_set
| ~ element(X3055,powerset(powerset(esk251_2(X3047,X3052))))
| ~ in(esk251_2(X3047,X3052),omega)
| ~ in(X3052,esk249_1(X3047))
| esk247_1(X3047) != esk248_1(X3047)
| ~ ordinal(X3047) )
& ( ~ in(X3057,X3055)
| ~ subset(esk252_3(X3047,X3052,X3055),X3057)
| X3057 = esk252_3(X3047,X3052,X3055)
| X3055 = empty_set
| ~ element(X3055,powerset(powerset(esk251_2(X3047,X3052))))
| ~ in(esk251_2(X3047,X3052),omega)
| ~ in(X3052,esk249_1(X3047))
| esk247_1(X3047) != esk248_1(X3047)
| ~ ordinal(X3047) )
& ( in(X3060,omega)
| ~ ordinal(X3060)
| X3058 != X3060
| ~ in(X3059,succ(X3047))
| X3059 != X3058
| in(X3058,esk249_1(X3047))
| esk247_1(X3047) != esk248_1(X3047)
| ~ ordinal(X3047) )
& ( element(esk253_3(X3047,X3058,X3060),powerset(powerset(X3060)))
| ~ ordinal(X3060)
| X3058 != X3060
| ~ in(X3059,succ(X3047))
| X3059 != X3058
| in(X3058,esk249_1(X3047))
| esk247_1(X3047) != esk248_1(X3047)
| ~ ordinal(X3047) )
& ( esk253_3(X3047,X3058,X3060) != empty_set
| ~ ordinal(X3060)
| X3058 != X3060
| ~ in(X3059,succ(X3047))
| X3059 != X3058
| in(X3058,esk249_1(X3047))
| esk247_1(X3047) != esk248_1(X3047)
| ~ ordinal(X3047) )
& ( in(esk254_4(X3047,X3058,X3060,X3062),esk253_3(X3047,X3058,X3060))
| ~ in(X3062,esk253_3(X3047,X3058,X3060))
| ~ ordinal(X3060)
| X3058 != X3060
| ~ in(X3059,succ(X3047))
| X3059 != X3058
| in(X3058,esk249_1(X3047))
| esk247_1(X3047) != esk248_1(X3047)
| ~ ordinal(X3047) )
& ( subset(X3062,esk254_4(X3047,X3058,X3060,X3062))
| ~ in(X3062,esk253_3(X3047,X3058,X3060))
| ~ ordinal(X3060)
| X3058 != X3060
| ~ in(X3059,succ(X3047))
| X3059 != X3058
| in(X3058,esk249_1(X3047))
| esk247_1(X3047) != esk248_1(X3047)
| ~ ordinal(X3047) )
& ( esk254_4(X3047,X3058,X3060,X3062) != X3062
| ~ in(X3062,esk253_3(X3047,X3058,X3060))
| ~ ordinal(X3060)
| X3058 != X3060
| ~ in(X3059,succ(X3047))
| X3059 != X3058
| in(X3058,esk249_1(X3047))
| esk247_1(X3047) != esk248_1(X3047)
| ~ ordinal(X3047) ) ),
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)],[i_0_656])])])])])]) ).
cnf(i_0_718,plain,
succ(X1) = set_union2(X1,singleton(X1)),
inference(split_conjunct,[status(thm)],[i_0_657]) ).
fof(i_0_719,plain,
! [X2112,X2113,X2114,X2115] :
( ( relation_field(X2113) = X2112
| X2113 != inclusion_relation(X2112)
| ~ relation(X2113) )
& ( ~ in(ordered_pair(X2114,X2115),X2113)
| subset(X2114,X2115)
| ~ in(X2114,X2112)
| ~ in(X2115,X2112)
| X2113 != inclusion_relation(X2112)
| ~ relation(X2113) )
& ( ~ subset(X2114,X2115)
| in(ordered_pair(X2114,X2115),X2113)
| ~ in(X2114,X2112)
| ~ in(X2115,X2112)
| X2113 != inclusion_relation(X2112)
| ~ relation(X2113) )
& ( in(esk47_2(X2112,X2113),X2112)
| relation_field(X2113) != X2112
| X2113 = inclusion_relation(X2112)
| ~ relation(X2113) )
& ( in(esk48_2(X2112,X2113),X2112)
| relation_field(X2113) != X2112
| X2113 = inclusion_relation(X2112)
| ~ relation(X2113) )
& ( ~ in(ordered_pair(esk47_2(X2112,X2113),esk48_2(X2112,X2113)),X2113)
| ~ subset(esk47_2(X2112,X2113),esk48_2(X2112,X2113))
| relation_field(X2113) != X2112
| X2113 = inclusion_relation(X2112)
| ~ relation(X2113) )
& ( in(ordered_pair(esk47_2(X2112,X2113),esk48_2(X2112,X2113)),X2113)
| subset(esk47_2(X2112,X2113),esk48_2(X2112,X2113))
| relation_field(X2113) != X2112
| X2113 = inclusion_relation(X2112)
| ~ relation(X2113) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_wellord2])])])])]) ).
fof(i_0_720,plain,
! [X1897,X1898,X1899,X1900,X1901,X1902] :
( ( in(X1899,X1897)
| ~ in(ordered_pair(X1899,X1900),X1898)
| X1898 != identity_relation(X1897)
| ~ relation(X1898) )
& ( X1899 = X1900
| ~ in(ordered_pair(X1899,X1900),X1898)
| X1898 != identity_relation(X1897)
| ~ relation(X1898) )
& ( ~ in(X1901,X1897)
| X1901 != X1902
| in(ordered_pair(X1901,X1902),X1898)
| X1898 != identity_relation(X1897)
| ~ relation(X1898) )
& ( ~ in(ordered_pair(esk1_2(X1897,X1898),esk2_2(X1897,X1898)),X1898)
| ~ in(esk1_2(X1897,X1898),X1897)
| esk1_2(X1897,X1898) != esk2_2(X1897,X1898)
| X1898 = identity_relation(X1897)
| ~ relation(X1898) )
& ( in(esk1_2(X1897,X1898),X1897)
| in(ordered_pair(esk1_2(X1897,X1898),esk2_2(X1897,X1898)),X1898)
| X1898 = identity_relation(X1897)
| ~ relation(X1898) )
& ( esk1_2(X1897,X1898) = esk2_2(X1897,X1898)
| in(ordered_pair(esk1_2(X1897,X1898),esk2_2(X1897,X1898)),X1898)
| X1898 = identity_relation(X1897)
| ~ relation(X1898) ) ),
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)],[d10_relat_1])])])])])]) ).
fof(i_0_721,lemma,
! [X3252,X3254,X3256,X3258,X3259,X3260,X3262] :
( ( in(X3254,succ(X3252))
| ~ in(X3254,esk349_1(X3252))
| ~ ordinal(X3252) )
& ( ordinal(esk350_2(X3252,X3254))
| ~ in(X3254,esk349_1(X3252))
| ~ ordinal(X3252) )
& ( X3254 = esk350_2(X3252,X3254)
| ~ in(X3254,esk349_1(X3252))
| ~ ordinal(X3252) )
& ( in(esk351_3(X3252,X3254,X3256),X3256)
| X3256 = empty_set
| ~ element(X3256,powerset(powerset(esk350_2(X3252,X3254))))
| ~ in(esk350_2(X3252,X3254),omega)
| ~ in(X3254,esk349_1(X3252))
| ~ ordinal(X3252) )
& ( ~ in(X3258,X3256)
| ~ subset(esk351_3(X3252,X3254,X3256),X3258)
| X3258 = esk351_3(X3252,X3254,X3256)
| X3256 = empty_set
| ~ element(X3256,powerset(powerset(esk350_2(X3252,X3254))))
| ~ in(esk350_2(X3252,X3254),omega)
| ~ in(X3254,esk349_1(X3252))
| ~ ordinal(X3252) )
& ( in(X3260,omega)
| ~ ordinal(X3260)
| X3259 != X3260
| ~ in(X3259,succ(X3252))
| in(X3259,esk349_1(X3252))
| ~ ordinal(X3252) )
& ( element(esk352_3(X3252,X3259,X3260),powerset(powerset(X3260)))
| ~ ordinal(X3260)
| X3259 != X3260
| ~ in(X3259,succ(X3252))
| in(X3259,esk349_1(X3252))
| ~ ordinal(X3252) )
& ( esk352_3(X3252,X3259,X3260) != empty_set
| ~ ordinal(X3260)
| X3259 != X3260
| ~ in(X3259,succ(X3252))
| in(X3259,esk349_1(X3252))
| ~ ordinal(X3252) )
& ( in(esk353_4(X3252,X3259,X3260,X3262),esk352_3(X3252,X3259,X3260))
| ~ in(X3262,esk352_3(X3252,X3259,X3260))
| ~ ordinal(X3260)
| X3259 != X3260
| ~ in(X3259,succ(X3252))
| in(X3259,esk349_1(X3252))
| ~ ordinal(X3252) )
& ( subset(X3262,esk353_4(X3252,X3259,X3260,X3262))
| ~ in(X3262,esk352_3(X3252,X3259,X3260))
| ~ ordinal(X3260)
| X3259 != X3260
| ~ in(X3259,succ(X3252))
| in(X3259,esk349_1(X3252))
| ~ ordinal(X3252) )
& ( esk353_4(X3252,X3259,X3260,X3262) != X3262
| ~ in(X3262,esk352_3(X3252,X3259,X3260))
| ~ ordinal(X3260)
| X3259 != X3260
| ~ in(X3259,succ(X3252))
| in(X3259,esk349_1(X3252))
| ~ ordinal(X3252) ) ),
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)],[s1_xboole_0__e18_27__finset_1__1])])])])])]) ).
fof(i_0_722,lemma,
! [X3243,X3244,X3246,X3249,X3250,X3251] :
( ( in(X3246,cartesian_product2(X3243,X3244))
| ~ in(X3246,esk346_2(X3243,X3244)) )
& ( ordered_pair(esk347_3(X3243,X3244,X3246),esk348_3(X3243,X3244,X3246)) = X3246
| ~ in(X3246,esk346_2(X3243,X3244)) )
& ( in(esk347_3(X3243,X3244,X3246),X3243)
| ~ in(X3246,esk346_2(X3243,X3244)) )
& ( esk348_3(X3243,X3244,X3246) = singleton(esk347_3(X3243,X3244,X3246))
| ~ in(X3246,esk346_2(X3243,X3244)) )
& ( ~ in(X3249,cartesian_product2(X3243,X3244))
| ordered_pair(X3250,X3251) != X3249
| ~ in(X3250,X3243)
| X3251 != singleton(X3250)
| in(X3249,esk346_2(X3243,X3244)) ) ),
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)],[s1_xboole_0__e16_22__wellord2__1])])])])])]) ).
fof(i_0_723,lemma,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( in(ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3),relation_of_lattice(X1))
<=> below_refl(X1,X2,X3) ) ) ) ),
inference(fof_simplification,[status(thm)],[t32_filter_1]) ).
fof(i_0_724,plain,
! [X2231,X2232,X2233,X2234] :
( ( ~ subset(X2231,X2232)
| ~ in(ordered_pair(X2233,X2234),X2231)
| in(ordered_pair(X2233,X2234),X2232)
| ~ relation(X2232)
| ~ relation(X2231) )
& ( in(ordered_pair(esk72_2(X2231,X2232),esk73_2(X2231,X2232)),X2231)
| subset(X2231,X2232)
| ~ relation(X2232)
| ~ relation(X2231) )
& ( ~ in(ordered_pair(esk72_2(X2231,X2232),esk73_2(X2231,X2232)),X2232)
| subset(X2231,X2232)
| ~ relation(X2232)
| ~ relation(X2231) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_relat_1])])])])]) ).
fof(i_0_725,plain,
! [X2069,X2070,X2071,X2072] :
( ( ~ is_reflexive_in(X2069,X2070)
| ~ in(X2071,X2070)
| in(ordered_pair(X2071,X2071),X2069)
| ~ relation(X2069) )
& ( in(esk40_2(X2069,X2072),X2072)
| is_reflexive_in(X2069,X2072)
| ~ relation(X2069) )
& ( ~ in(ordered_pair(esk40_2(X2069,X2072),esk40_2(X2069,X2072)),X2069)
| is_reflexive_in(X2069,X2072)
| ~ relation(X2069) ) ),
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)],[d1_relat_2])])])])])]) ).
fof(i_0_726,plain,
! [X2407,X2408,X2409,X2410,X2411,X2412] :
( ( ~ is_transitive_in(X2407,X2408)
| ~ in(X2409,X2408)
| ~ in(X2410,X2408)
| ~ in(X2411,X2408)
| ~ in(ordered_pair(X2409,X2410),X2407)
| ~ in(ordered_pair(X2410,X2411),X2407)
| in(ordered_pair(X2409,X2411),X2407)
| ~ relation(X2407) )
& ( in(esk110_2(X2407,X2412),X2412)
| is_transitive_in(X2407,X2412)
| ~ relation(X2407) )
& ( in(esk111_2(X2407,X2412),X2412)
| is_transitive_in(X2407,X2412)
| ~ relation(X2407) )
& ( in(esk112_2(X2407,X2412),X2412)
| is_transitive_in(X2407,X2412)
| ~ relation(X2407) )
& ( in(ordered_pair(esk110_2(X2407,X2412),esk111_2(X2407,X2412)),X2407)
| is_transitive_in(X2407,X2412)
| ~ relation(X2407) )
& ( in(ordered_pair(esk111_2(X2407,X2412),esk112_2(X2407,X2412)),X2407)
| is_transitive_in(X2407,X2412)
| ~ relation(X2407) )
& ( ~ in(ordered_pair(esk110_2(X2407,X2412),esk112_2(X2407,X2412)),X2407)
| is_transitive_in(X2407,X2412)
| ~ relation(X2407) ) ),
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)],[d8_relat_2])])])])])]) ).
fof(i_0_727,plain,
! [X2348,X2349,X2350,X2351,X2352] :
( ( ~ is_connected_in(X2348,X2349)
| ~ in(X2350,X2349)
| ~ in(X2351,X2349)
| X2350 = X2351
| in(ordered_pair(X2350,X2351),X2348)
| in(ordered_pair(X2351,X2350),X2348)
| ~ relation(X2348) )
& ( in(esk95_2(X2348,X2352),X2352)
| is_connected_in(X2348,X2352)
| ~ relation(X2348) )
& ( in(esk96_2(X2348,X2352),X2352)
| is_connected_in(X2348,X2352)
| ~ relation(X2348) )
& ( esk95_2(X2348,X2352) != esk96_2(X2348,X2352)
| is_connected_in(X2348,X2352)
| ~ relation(X2348) )
& ( ~ in(ordered_pair(esk95_2(X2348,X2352),esk96_2(X2348,X2352)),X2348)
| is_connected_in(X2348,X2352)
| ~ relation(X2348) )
& ( ~ in(ordered_pair(esk96_2(X2348,X2352),esk95_2(X2348,X2352)),X2348)
| is_connected_in(X2348,X2352)
| ~ relation(X2348) ) ),
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)],[i_0_658])])])])])]) ).
fof(i_0_728,plain,
! [X3088,X3089,X3096,X3099,X3100,X3101] :
( ( in(esk274_3(X3088,X3089,X3096),powerset(X3088))
| ~ in(X3096,esk273_2(X3088,X3089))
| esk268_2(X3088,X3089) = esk269_2(X3088,X3089)
| ~ ordinal(X3088)
| ~ element(X3089,powerset(powerset(succ(X3088)))) )
& ( esk274_3(X3088,X3089,X3096) = X3096
| ~ in(X3096,esk273_2(X3088,X3089))
| esk268_2(X3088,X3089) = esk269_2(X3088,X3089)
| ~ ordinal(X3088)
| ~ element(X3089,powerset(powerset(succ(X3088)))) )
& ( in(esk275_3(X3088,X3089,X3096),X3089)
| ~ in(X3096,esk273_2(X3088,X3089))
| esk268_2(X3088,X3089) = esk269_2(X3088,X3089)
| ~ ordinal(X3088)
| ~ element(X3089,powerset(powerset(succ(X3088)))) )
& ( X3096 = set_difference(esk275_3(X3088,X3089,X3096),singleton(X3088))
| ~ in(X3096,esk273_2(X3088,X3089))
| esk268_2(X3088,X3089) = esk269_2(X3088,X3089)
| ~ ordinal(X3088)
| ~ element(X3089,powerset(powerset(succ(X3088)))) )
& ( ~ in(X3100,powerset(X3088))
| X3100 != X3099
| ~ in(X3101,X3089)
| X3099 != set_difference(X3101,singleton(X3088))
| in(X3099,esk273_2(X3088,X3089))
| esk268_2(X3088,X3089) = esk269_2(X3088,X3089)
| ~ ordinal(X3088)
| ~ element(X3089,powerset(powerset(succ(X3088)))) )
& ( in(esk274_3(X3088,X3089,X3096),powerset(X3088))
| ~ in(X3096,esk273_2(X3088,X3089))
| in(esk271_2(X3088,X3089),X3089)
| ~ ordinal(X3088)
| ~ element(X3089,powerset(powerset(succ(X3088)))) )
& ( esk274_3(X3088,X3089,X3096) = X3096
| ~ in(X3096,esk273_2(X3088,X3089))
| in(esk271_2(X3088,X3089),X3089)
| ~ ordinal(X3088)
| ~ element(X3089,powerset(powerset(succ(X3088)))) )
& ( in(esk275_3(X3088,X3089,X3096),X3089)
| ~ in(X3096,esk273_2(X3088,X3089))
| in(esk271_2(X3088,X3089),X3089)
| ~ ordinal(X3088)
| ~ element(X3089,powerset(powerset(succ(X3088)))) )
& ( X3096 = set_difference(esk275_3(X3088,X3089,X3096),singleton(X3088))
| ~ in(X3096,esk273_2(X3088,X3089))
| in(esk271_2(X3088,X3089),X3089)
| ~ ordinal(X3088)
| ~ element(X3089,powerset(powerset(succ(X3088)))) )
& ( ~ in(X3100,powerset(X3088))
| X3100 != X3099
| ~ in(X3101,X3089)
| X3099 != set_difference(X3101,singleton(X3088))
| in(X3099,esk273_2(X3088,X3089))
| in(esk271_2(X3088,X3089),X3089)
| ~ ordinal(X3088)
| ~ element(X3089,powerset(powerset(succ(X3088)))) )
& ( in(esk274_3(X3088,X3089,X3096),powerset(X3088))
| ~ in(X3096,esk273_2(X3088,X3089))
| esk269_2(X3088,X3089) = set_difference(esk271_2(X3088,X3089),singleton(X3088))
| ~ ordinal(X3088)
| ~ element(X3089,powerset(powerset(succ(X3088)))) )
& ( esk274_3(X3088,X3089,X3096) = X3096
| ~ in(X3096,esk273_2(X3088,X3089))
| esk269_2(X3088,X3089) = set_difference(esk271_2(X3088,X3089),singleton(X3088))
| ~ ordinal(X3088)
| ~ element(X3089,powerset(powerset(succ(X3088)))) )
& ( in(esk275_3(X3088,X3089,X3096),X3089)
| ~ in(X3096,esk273_2(X3088,X3089))
| esk269_2(X3088,X3089) = set_difference(esk271_2(X3088,X3089),singleton(X3088))
| ~ ordinal(X3088)
| ~ element(X3089,powerset(powerset(succ(X3088)))) )
& ( X3096 = set_difference(esk275_3(X3088,X3089,X3096),singleton(X3088))
| ~ in(X3096,esk273_2(X3088,X3089))
| esk269_2(X3088,X3089) = set_difference(esk271_2(X3088,X3089),singleton(X3088))
| ~ ordinal(X3088)
| ~ element(X3089,powerset(powerset(succ(X3088)))) )
& ( ~ in(X3100,powerset(X3088))
| X3100 != X3099
| ~ in(X3101,X3089)
| X3099 != set_difference(X3101,singleton(X3088))
| in(X3099,esk273_2(X3088,X3089))
| esk269_2(X3088,X3089) = set_difference(esk271_2(X3088,X3089),singleton(X3088))
| ~ ordinal(X3088)
| ~ element(X3089,powerset(powerset(succ(X3088)))) )
& ( in(esk274_3(X3088,X3089,X3096),powerset(X3088))
| ~ in(X3096,esk273_2(X3088,X3089))
| esk268_2(X3088,X3089) = esk270_2(X3088,X3089)
| ~ ordinal(X3088)
| ~ element(X3089,powerset(powerset(succ(X3088)))) )
& ( esk274_3(X3088,X3089,X3096) = X3096
| ~ in(X3096,esk273_2(X3088,X3089))
| esk268_2(X3088,X3089) = esk270_2(X3088,X3089)
| ~ ordinal(X3088)
| ~ element(X3089,powerset(powerset(succ(X3088)))) )
& ( in(esk275_3(X3088,X3089,X3096),X3089)
| ~ in(X3096,esk273_2(X3088,X3089))
| esk268_2(X3088,X3089) = esk270_2(X3088,X3089)
| ~ ordinal(X3088)
| ~ element(X3089,powerset(powerset(succ(X3088)))) )
& ( X3096 = set_difference(esk275_3(X3088,X3089,X3096),singleton(X3088))
| ~ in(X3096,esk273_2(X3088,X3089))
| esk268_2(X3088,X3089) = esk270_2(X3088,X3089)
| ~ ordinal(X3088)
| ~ element(X3089,powerset(powerset(succ(X3088)))) )
& ( ~ in(X3100,powerset(X3088))
| X3100 != X3099
| ~ in(X3101,X3089)
| X3099 != set_difference(X3101,singleton(X3088))
| in(X3099,esk273_2(X3088,X3089))
| esk268_2(X3088,X3089) = esk270_2(X3088,X3089)
| ~ ordinal(X3088)
| ~ element(X3089,powerset(powerset(succ(X3088)))) )
& ( in(esk274_3(X3088,X3089,X3096),powerset(X3088))
| ~ in(X3096,esk273_2(X3088,X3089))
| in(esk272_2(X3088,X3089),X3089)
| ~ ordinal(X3088)
| ~ element(X3089,powerset(powerset(succ(X3088)))) )
& ( esk274_3(X3088,X3089,X3096) = X3096
| ~ in(X3096,esk273_2(X3088,X3089))
| in(esk272_2(X3088,X3089),X3089)
| ~ ordinal(X3088)
| ~ element(X3089,powerset(powerset(succ(X3088)))) )
& ( in(esk275_3(X3088,X3089,X3096),X3089)
| ~ in(X3096,esk273_2(X3088,X3089))
| in(esk272_2(X3088,X3089),X3089)
| ~ ordinal(X3088)
| ~ element(X3089,powerset(powerset(succ(X3088)))) )
& ( X3096 = set_difference(esk275_3(X3088,X3089,X3096),singleton(X3088))
| ~ in(X3096,esk273_2(X3088,X3089))
| in(esk272_2(X3088,X3089),X3089)
| ~ ordinal(X3088)
| ~ element(X3089,powerset(powerset(succ(X3088)))) )
& ( ~ in(X3100,powerset(X3088))
| X3100 != X3099
| ~ in(X3101,X3089)
| X3099 != set_difference(X3101,singleton(X3088))
| in(X3099,esk273_2(X3088,X3089))
| in(esk272_2(X3088,X3089),X3089)
| ~ ordinal(X3088)
| ~ element(X3089,powerset(powerset(succ(X3088)))) )
& ( in(esk274_3(X3088,X3089,X3096),powerset(X3088))
| ~ in(X3096,esk273_2(X3088,X3089))
| esk270_2(X3088,X3089) = set_difference(esk272_2(X3088,X3089),singleton(X3088))
| ~ ordinal(X3088)
| ~ element(X3089,powerset(powerset(succ(X3088)))) )
& ( esk274_3(X3088,X3089,X3096) = X3096
| ~ in(X3096,esk273_2(X3088,X3089))
| esk270_2(X3088,X3089) = set_difference(esk272_2(X3088,X3089),singleton(X3088))
| ~ ordinal(X3088)
| ~ element(X3089,powerset(powerset(succ(X3088)))) )
& ( in(esk275_3(X3088,X3089,X3096),X3089)
| ~ in(X3096,esk273_2(X3088,X3089))
| esk270_2(X3088,X3089) = set_difference(esk272_2(X3088,X3089),singleton(X3088))
| ~ ordinal(X3088)
| ~ element(X3089,powerset(powerset(succ(X3088)))) )
& ( X3096 = set_difference(esk275_3(X3088,X3089,X3096),singleton(X3088))
| ~ in(X3096,esk273_2(X3088,X3089))
| esk270_2(X3088,X3089) = set_difference(esk272_2(X3088,X3089),singleton(X3088))
| ~ ordinal(X3088)
| ~ element(X3089,powerset(powerset(succ(X3088)))) )
& ( ~ in(X3100,powerset(X3088))
| X3100 != X3099
| ~ in(X3101,X3089)
| X3099 != set_difference(X3101,singleton(X3088))
| in(X3099,esk273_2(X3088,X3089))
| esk270_2(X3088,X3089) = set_difference(esk272_2(X3088,X3089),singleton(X3088))
| ~ ordinal(X3088)
| ~ element(X3089,powerset(powerset(succ(X3088)))) )
& ( in(esk274_3(X3088,X3089,X3096),powerset(X3088))
| ~ in(X3096,esk273_2(X3088,X3089))
| esk269_2(X3088,X3089) != esk270_2(X3088,X3089)
| ~ ordinal(X3088)
| ~ element(X3089,powerset(powerset(succ(X3088)))) )
& ( esk274_3(X3088,X3089,X3096) = X3096
| ~ in(X3096,esk273_2(X3088,X3089))
| esk269_2(X3088,X3089) != esk270_2(X3088,X3089)
| ~ ordinal(X3088)
| ~ element(X3089,powerset(powerset(succ(X3088)))) )
& ( in(esk275_3(X3088,X3089,X3096),X3089)
| ~ in(X3096,esk273_2(X3088,X3089))
| esk269_2(X3088,X3089) != esk270_2(X3088,X3089)
| ~ ordinal(X3088)
| ~ element(X3089,powerset(powerset(succ(X3088)))) )
& ( X3096 = set_difference(esk275_3(X3088,X3089,X3096),singleton(X3088))
| ~ in(X3096,esk273_2(X3088,X3089))
| esk269_2(X3088,X3089) != esk270_2(X3088,X3089)
| ~ ordinal(X3088)
| ~ element(X3089,powerset(powerset(succ(X3088)))) )
& ( ~ in(X3100,powerset(X3088))
| X3100 != X3099
| ~ in(X3101,X3089)
| X3099 != set_difference(X3101,singleton(X3088))
| in(X3099,esk273_2(X3088,X3089))
| esk269_2(X3088,X3089) != esk270_2(X3088,X3089)
| ~ ordinal(X3088)
| ~ element(X3089,powerset(powerset(succ(X3088)))) ) ),
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)],[s1_tarski__e4_27_3_1__finset_1__1])])])])])]) ).
fof(i_0_729,plain,
! [X2265,X2266,X2267,X2269,X2270,X2271,X2273] :
( ( ~ in(X2267,X2266)
| in(ordered_pair(X2267,esk78_3(X2265,X2266,X2267)),X2265)
| X2266 != relation_dom(X2265)
| ~ relation(X2265) )
& ( ~ in(ordered_pair(X2269,X2270),X2265)
| in(X2269,X2266)
| X2266 != relation_dom(X2265)
| ~ relation(X2265) )
& ( ~ in(esk79_2(X2265,X2271),X2271)
| ~ in(ordered_pair(esk79_2(X2265,X2271),X2273),X2265)
| X2271 = relation_dom(X2265)
| ~ relation(X2265) )
& ( in(esk79_2(X2265,X2271),X2271)
| in(ordered_pair(esk79_2(X2265,X2271),esk80_2(X2265,X2271)),X2265)
| X2271 = relation_dom(X2265)
| ~ relation(X2265) ) ),
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)],[d4_relat_1])])])])])]) ).
fof(i_0_730,lemma,
! [X3276,X3277,X3279,X3281,X3282] :
( ( in(X3279,powerset(X3276))
| ~ in(X3279,esk357_2(X3276,X3277))
| ~ ordinal(X3276)
| ~ element(X3277,powerset(powerset(succ(X3276)))) )
& ( in(esk358_3(X3276,X3277,X3279),X3277)
| ~ in(X3279,esk357_2(X3276,X3277))
| ~ ordinal(X3276)
| ~ element(X3277,powerset(powerset(succ(X3276)))) )
& ( X3279 = set_difference(esk358_3(X3276,X3277,X3279),singleton(X3276))
| ~ in(X3279,esk357_2(X3276,X3277))
| ~ ordinal(X3276)
| ~ element(X3277,powerset(powerset(succ(X3276)))) )
& ( ~ in(X3281,powerset(X3276))
| ~ in(X3282,X3277)
| X3281 != set_difference(X3282,singleton(X3276))
| in(X3281,esk357_2(X3276,X3277))
| ~ ordinal(X3276)
| ~ element(X3277,powerset(powerset(succ(X3276)))) ) ),
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)],[s1_xboole_0__e4_27_3_1__finset_1])])])])])]) ).
fof(i_0_731,plain,
! [X1,X2,X3,X4] :
( ( ~ empty(X1)
& function(X3)
& quasi_total(X3,X1,X2)
& relation_of2(X3,X1,X2)
& element(X4,X1) )
=> element(apply_as_element(X1,X2,X3,X4),X2) ),
inference(fof_simplification,[status(thm)],[dt_k8_funct_2]) ).
fof(i_0_732,plain,
! [X1,X2,X3] :
( ( ~ empty(X1)
& function(X2)
& quasi_total(X2,cartesian_product2(X1,X1),X1)
& relation_of2(X2,cartesian_product2(X1,X1),X1)
& function(X3)
& quasi_total(X3,cartesian_product2(X1,X1),X1)
& relation_of2(X3,cartesian_product2(X1,X1),X1) )
=> ( ~ empty_carrier(latt_str_of(X1,X2,X3))
& strict_latt_str(latt_str_of(X1,X2,X3)) ) ),
inference(fof_simplification,[status(thm)],[fc3_lattices]) ).
fof(i_0_733,plain,
! [X1,X2,X3,X4] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1)
& ~ empty_carrier(X2)
& lattice(X2)
& latt_str(X2)
& element(X3,the_carrier(X1))
& element(X4,the_carrier(X2)) )
=> element(k10_filter_1(X1,X2,X3,X4),the_carrier(k8_filter_1(X1,X2))) ),
inference(fof_simplification,[status(thm)],[dt_k10_filter_1]) ).
fof(i_0_734,lemma,
! [X3495,X3496,X3497,X3499] :
( ( in(esk412_3(X3495,X3496,X3497),relation_rng(X3497))
| ~ in(X3495,relation_inverse_image(X3497,X3496))
| ~ relation(X3497) )
& ( in(ordered_pair(X3495,esk412_3(X3495,X3496,X3497)),X3497)
| ~ in(X3495,relation_inverse_image(X3497,X3496))
| ~ relation(X3497) )
& ( in(esk412_3(X3495,X3496,X3497),X3496)
| ~ in(X3495,relation_inverse_image(X3497,X3496))
| ~ relation(X3497) )
& ( ~ in(X3499,relation_rng(X3497))
| ~ in(ordered_pair(X3495,X3499),X3497)
| ~ in(X3499,X3496)
| in(X3495,relation_inverse_image(X3497,X3496))
| ~ relation(X3497) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t166_relat_1])])])])]) ).
fof(i_0_735,plain,
! [X2250,X2251,X2252,X2253,X2254,X2255,X2256,X2257] :
( ( in(X2253,X2250)
| ~ in(X2253,X2252)
| X2252 != set_intersection2(X2250,X2251) )
& ( in(X2253,X2251)
| ~ in(X2253,X2252)
| X2252 != set_intersection2(X2250,X2251) )
& ( ~ in(X2254,X2250)
| ~ in(X2254,X2251)
| in(X2254,X2252)
| X2252 != set_intersection2(X2250,X2251) )
& ( ~ in(esk77_3(X2255,X2256,X2257),X2257)
| ~ in(esk77_3(X2255,X2256,X2257),X2255)
| ~ in(esk77_3(X2255,X2256,X2257),X2256)
| X2257 = set_intersection2(X2255,X2256) )
& ( in(esk77_3(X2255,X2256,X2257),X2255)
| in(esk77_3(X2255,X2256,X2257),X2257)
| X2257 = set_intersection2(X2255,X2256) )
& ( in(esk77_3(X2255,X2256,X2257),X2256)
| in(esk77_3(X2255,X2256,X2257),X2257)
| X2257 = set_intersection2(X2255,X2256) ) ),
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)],[d3_xboole_0])])])])])]) ).
fof(i_0_736,lemma,
! [X3774,X3775] : set_difference(X3774,set_difference(X3774,X3775)) = set_intersection2(X3774,X3775),
inference(variable_rename,[status(thm)],[t48_xboole_1]) ).
fof(i_0_737,lemma,
! [X2725,X2726,X2727,X2728] :
( ( ~ transitive(X2725)
| ~ in(ordered_pair(X2726,X2727),X2725)
| ~ in(ordered_pair(X2727,X2728),X2725)
| in(ordered_pair(X2726,X2728),X2725)
| ~ relation(X2725) )
& ( in(ordered_pair(esk130_1(X2725),esk131_1(X2725)),X2725)
| transitive(X2725)
| ~ relation(X2725) )
& ( in(ordered_pair(esk131_1(X2725),esk132_1(X2725)),X2725)
| transitive(X2725)
| ~ relation(X2725) )
& ( ~ in(ordered_pair(esk130_1(X2725),esk132_1(X2725)),X2725)
| transitive(X2725)
| ~ relation(X2725) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l2_wellord1])])])])]) ).
fof(i_0_738,plain,
! [X1,X2] :
( ( ~ empty_carrier(X2)
& lattice(X2)
& latt_str(X2) )
=> ( in(X1,a_1_0_filter_1(X2))
<=> ? [X3,X4] :
( element(X3,the_carrier(X2))
& element(X4,the_carrier(X2))
& X1 = ordered_pair_as_product_element(the_carrier(X2),the_carrier(X2),X3,X4)
& below_refl(X2,X3,X4) ) ) ),
inference(fof_simplification,[status(thm)],[fraenkel_a_1_0_filter_1]) ).
fof(i_0_739,plain,
! [X1,X2,X3,X4] :
( ( ~ empty(X1)
& ~ empty(X2)
& element(X3,X1)
& element(X4,X2) )
=> element(ordered_pair_as_product_element(X1,X2,X3,X4),cartesian_product2(X1,X2)) ),
inference(fof_simplification,[status(thm)],[dt_k1_domain_1]) ).
fof(i_0_740,plain,
! [X2275,X2276,X2277,X2278,X2279] :
( ( ~ is_antisymmetric_in(X2275,X2276)
| ~ in(X2277,X2276)
| ~ in(X2278,X2276)
| ~ in(ordered_pair(X2277,X2278),X2275)
| ~ in(ordered_pair(X2278,X2277),X2275)
| X2277 = X2278
| ~ relation(X2275) )
& ( in(esk81_2(X2275,X2279),X2279)
| is_antisymmetric_in(X2275,X2279)
| ~ relation(X2275) )
& ( in(esk82_2(X2275,X2279),X2279)
| is_antisymmetric_in(X2275,X2279)
| ~ relation(X2275) )
& ( in(ordered_pair(esk81_2(X2275,X2279),esk82_2(X2275,X2279)),X2275)
| is_antisymmetric_in(X2275,X2279)
| ~ relation(X2275) )
& ( in(ordered_pair(esk82_2(X2275,X2279),esk81_2(X2275,X2279)),X2275)
| is_antisymmetric_in(X2275,X2279)
| ~ relation(X2275) )
& ( esk81_2(X2275,X2279) != esk82_2(X2275,X2279)
| is_antisymmetric_in(X2275,X2279)
| ~ relation(X2275) ) ),
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)],[d4_relat_2])])])])])]) ).
fof(i_0_741,lemma,
! [X3849,X3850,X3851,X3852] :
( ( relation_dom(X3850) = set_intersection2(relation_dom(X3851),X3849)
| X3850 != relation_dom_restriction(X3851,X3849)
| ~ relation(X3851)
| ~ function(X3851)
| ~ relation(X3850)
| ~ function(X3850) )
& ( ~ in(X3852,relation_dom(X3850))
| apply(X3850,X3852) = apply(X3851,X3852)
| X3850 != relation_dom_restriction(X3851,X3849)
| ~ relation(X3851)
| ~ function(X3851)
| ~ relation(X3850)
| ~ function(X3850) )
& ( in(esk439_3(X3849,X3850,X3851),relation_dom(X3850))
| relation_dom(X3850) != set_intersection2(relation_dom(X3851),X3849)
| X3850 = relation_dom_restriction(X3851,X3849)
| ~ relation(X3851)
| ~ function(X3851)
| ~ relation(X3850)
| ~ function(X3850) )
& ( apply(X3850,esk439_3(X3849,X3850,X3851)) != apply(X3851,esk439_3(X3849,X3850,X3851))
| relation_dom(X3850) != set_intersection2(relation_dom(X3851),X3849)
| X3850 = relation_dom_restriction(X3851,X3849)
| ~ relation(X3851)
| ~ function(X3851)
| ~ relation(X3850)
| ~ function(X3850) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t68_funct_1])])])])]) ).
fof(i_0_742,plain,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
inference(fof_simplification,[status(thm)],[d4_xboole_0]) ).
fof(i_0_743,lemma,
! [X2742,X2743,X2744] :
( ( ~ antisymmetric(X2742)
| ~ in(ordered_pair(X2743,X2744),X2742)
| ~ in(ordered_pair(X2744,X2743),X2742)
| X2743 = X2744
| ~ relation(X2742) )
& ( in(ordered_pair(esk134_1(X2742),esk135_1(X2742)),X2742)
| antisymmetric(X2742)
| ~ relation(X2742) )
& ( in(ordered_pair(esk135_1(X2742),esk134_1(X2742)),X2742)
| antisymmetric(X2742)
| ~ relation(X2742) )
& ( esk134_1(X2742) != esk135_1(X2742)
| antisymmetric(X2742)
| ~ relation(X2742) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l3_wellord1])])])])]) ).
fof(i_0_744,plain,
! [X1,X2,X3,X4] :
( ( ~ empty(X1)
& function(X3)
& quasi_total(X3,X1,X2)
& relation_of2(X3,X1,X2)
& element(X4,X1) )
=> apply_as_element(X1,X2,X3,X4) = apply(X3,X4) ),
inference(fof_simplification,[status(thm)],[redefinition_k8_funct_2]) ).
fof(i_0_745,plain,
! [X2024,X2025,X2026,X2027,X2028] :
( ( ~ function(X2024)
| ~ in(ordered_pair(X2025,X2026),X2024)
| ~ in(ordered_pair(X2025,X2027),X2024)
| X2026 = X2027 )
& ( in(ordered_pair(esk27_1(X2028),esk28_1(X2028)),X2028)
| function(X2028) )
& ( in(ordered_pair(esk27_1(X2028),esk29_1(X2028)),X2028)
| function(X2028) )
& ( esk28_1(X2028) != esk29_1(X2028)
| function(X2028) ) ),
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)],[d1_funct_1])])])])])]) ).
fof(i_0_746,lemma,
! [X3872,X3873,X3874,X3875] :
( ( in(X3872,X3874)
| ~ in(ordered_pair(X3872,X3873),relation_composition(identity_relation(X3874),X3875))
| ~ relation(X3875) )
& ( in(ordered_pair(X3872,X3873),X3875)
| ~ in(ordered_pair(X3872,X3873),relation_composition(identity_relation(X3874),X3875))
| ~ relation(X3875) )
& ( ~ in(X3872,X3874)
| ~ in(ordered_pair(X3872,X3873),X3875)
| in(ordered_pair(X3872,X3873),relation_composition(identity_relation(X3874),X3875))
| ~ relation(X3875) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t74_relat_1])])]) ).
fof(i_0_747,plain,
! [X2827,X2828,X2829,X2830] :
( empty_carrier(X2827)
| ~ lattice(X2827)
| ~ latt_str(X2827)
| empty_carrier(X2828)
| ~ lattice(X2828)
| ~ latt_str(X2828)
| ~ element(X2829,the_carrier(X2827))
| ~ element(X2830,the_carrier(X2828))
| k10_filter_1(X2827,X2828,X2829,X2830) = ordered_pair(X2829,X2830) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_659])]) ).
fof(i_0_748,lemma,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& complete_latt_str(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( X2 = meet_of_latt_set(X1,X3)
<=> ( latt_set_smaller(X1,X2,X3)
& ! [X4] :
( element(X4,the_carrier(X1))
=> ( latt_set_smaller(X1,X4,X3)
=> below_refl(X1,X4,X2) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[t34_lattice3]) ).
fof(i_0_749,plain,
! [X2129,X2130,X2131,X2132] :
( ( latt_element_smaller(X2129,X2131,X2130)
| X2131 != join_of_latt_set(X2129,X2130)
| ~ element(X2131,the_carrier(X2129))
| empty_carrier(X2129)
| ~ lattice(X2129)
| ~ complete_latt_str(X2129)
| ~ latt_str(X2129)
| empty_carrier(X2129)
| ~ latt_str(X2129) )
& ( ~ element(X2132,the_carrier(X2129))
| ~ latt_element_smaller(X2129,X2132,X2130)
| below(X2129,X2131,X2132)
| X2131 != join_of_latt_set(X2129,X2130)
| ~ element(X2131,the_carrier(X2129))
| empty_carrier(X2129)
| ~ lattice(X2129)
| ~ complete_latt_str(X2129)
| ~ latt_str(X2129)
| empty_carrier(X2129)
| ~ latt_str(X2129) )
& ( element(esk51_3(X2129,X2130,X2131),the_carrier(X2129))
| ~ latt_element_smaller(X2129,X2131,X2130)
| X2131 = join_of_latt_set(X2129,X2130)
| ~ element(X2131,the_carrier(X2129))
| empty_carrier(X2129)
| ~ lattice(X2129)
| ~ complete_latt_str(X2129)
| ~ latt_str(X2129)
| empty_carrier(X2129)
| ~ latt_str(X2129) )
& ( latt_element_smaller(X2129,esk51_3(X2129,X2130,X2131),X2130)
| ~ latt_element_smaller(X2129,X2131,X2130)
| X2131 = join_of_latt_set(X2129,X2130)
| ~ element(X2131,the_carrier(X2129))
| empty_carrier(X2129)
| ~ lattice(X2129)
| ~ complete_latt_str(X2129)
| ~ latt_str(X2129)
| empty_carrier(X2129)
| ~ latt_str(X2129) )
& ( ~ below(X2129,X2131,esk51_3(X2129,X2130,X2131))
| ~ latt_element_smaller(X2129,X2131,X2130)
| X2131 = join_of_latt_set(X2129,X2130)
| ~ element(X2131,the_carrier(X2129))
| empty_carrier(X2129)
| ~ lattice(X2129)
| ~ complete_latt_str(X2129)
| ~ latt_str(X2129)
| empty_carrier(X2129)
| ~ latt_str(X2129) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_660])])])])]) ).
fof(i_0_750,lemma,
! [X2753,X2754,X2755] :
( ( ~ connected(X2753)
| ~ in(X2754,relation_field(X2753))
| ~ in(X2755,relation_field(X2753))
| X2754 = X2755
| in(ordered_pair(X2754,X2755),X2753)
| in(ordered_pair(X2755,X2754),X2753)
| ~ relation(X2753) )
& ( in(esk136_1(X2753),relation_field(X2753))
| connected(X2753)
| ~ relation(X2753) )
& ( in(esk137_1(X2753),relation_field(X2753))
| connected(X2753)
| ~ relation(X2753) )
& ( esk136_1(X2753) != esk137_1(X2753)
| connected(X2753)
| ~ relation(X2753) )
& ( ~ in(ordered_pair(esk136_1(X2753),esk137_1(X2753)),X2753)
| connected(X2753)
| ~ relation(X2753) )
& ( ~ in(ordered_pair(esk137_1(X2753),esk136_1(X2753)),X2753)
| connected(X2753)
| ~ relation(X2753) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_661])])])])]) ).
fof(i_0_751,lemma,
! [X2713,X2714] :
( ( ~ reflexive(X2713)
| ~ in(X2714,relation_field(X2713))
| in(ordered_pair(X2714,X2714),X2713)
| ~ relation(X2713) )
& ( in(esk129_1(X2713),relation_field(X2713))
| reflexive(X2713)
| ~ relation(X2713) )
& ( ~ in(ordered_pair(esk129_1(X2713),esk129_1(X2713)),X2713)
| reflexive(X2713)
| ~ relation(X2713) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l1_wellord1])])])])]) ).
fof(i_0_752,lemma,
( ( epred1_0
& ! [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 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[s1_ordinal2__e18_27__finset_1,c_0_644]) ).
fof(i_0_753,plain,
! [X2144,X2145,X2146,X2147,X2148,X2149,X2150] :
( ( X2147 != pair_second(X2144)
| X2144 != ordered_pair(X2148,X2149)
| X2147 = X2149
| X2144 != ordered_pair(X2145,X2146) )
& ( X2144 = ordered_pair(esk53_2(X2144,X2150),esk54_2(X2144,X2150))
| X2150 = pair_second(X2144)
| X2144 != ordered_pair(X2145,X2146) )
& ( X2150 != esk54_2(X2144,X2150)
| X2150 = pair_second(X2144)
| X2144 != ordered_pair(X2145,X2146) ) ),
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)],[d2_mcart_1])])])])])]) ).
fof(i_0_754,plain,
! [X2044,X2045,X2046,X2047,X2048,X2049,X2050] :
( ( X2047 != pair_first(X2044)
| X2044 != ordered_pair(X2048,X2049)
| X2047 = X2048
| X2044 != ordered_pair(X2045,X2046) )
& ( X2044 = ordered_pair(esk32_2(X2044,X2050),esk33_2(X2044,X2050))
| X2050 = pair_first(X2044)
| X2044 != ordered_pair(X2045,X2046) )
& ( X2050 != esk32_2(X2044,X2050)
| X2050 = pair_first(X2044)
| X2044 != ordered_pair(X2045,X2046) ) ),
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)],[d1_mcart_1])])])])])]) ).
fof(i_0_755,plain,
! [X2831,X2832,X2833,X2834] :
( empty(X2831)
| empty(X2832)
| ~ element(X2833,X2831)
| ~ element(X2834,X2832)
| ordered_pair_as_product_element(X2831,X2832,X2833,X2834) = ordered_pair(X2833,X2834) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_662])]) ).
fof(i_0_756,plain,
! [X2429,X2430,X2431] :
( ( ~ related(X2429,X2430,X2431)
| in(ordered_pair(X2430,X2431),the_InternalRel(X2429))
| ~ element(X2431,the_carrier(X2429))
| ~ element(X2430,the_carrier(X2429))
| ~ rel_str(X2429) )
& ( ~ in(ordered_pair(X2430,X2431),the_InternalRel(X2429))
| related(X2429,X2430,X2431)
| ~ element(X2431,the_carrier(X2429))
| ~ element(X2430,the_carrier(X2429))
| ~ rel_str(X2429) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d9_orders_2])])])]) ).
fof(i_0_757,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( latt_element_smaller(X1,X2,X3)
<=> ! [X4] :
( element(X4,the_carrier(X1))
=> ( in(X4,X3)
=> below(X1,X4,X2) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[d17_lattice3]) ).
fof(i_0_758,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( latt_set_smaller(X1,X2,X3)
<=> ! [X4] :
( element(X4,the_carrier(X1))
=> ( in(X4,X3)
=> below(X1,X2,X4) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[d16_lattice3]) ).
fof(i_0_759,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)],[d8_lattices]) ).
fof(i_0_760,plain,
! [X3936,X3939,X3941,X3943] :
( ( ordinal(esk447_0)
| in(empty_set,omega)
| epred1_0 )
& ( in(esk448_1(X3939),X3939)
| X3939 = empty_set
| ~ element(X3939,powerset(powerset(esk447_0)))
| ~ in(esk447_0,omega)
| in(empty_set,omega)
| epred1_0 )
& ( ~ in(X3941,X3939)
| ~ subset(esk448_1(X3939),X3941)
| X3941 = esk448_1(X3939)
| X3939 = empty_set
| ~ element(X3939,powerset(powerset(esk447_0)))
| ~ in(esk447_0,omega)
| in(empty_set,omega)
| epred1_0 )
& ( in(succ(esk447_0),omega)
| in(empty_set,omega)
| epred1_0 )
& ( element(esk449_0,powerset(powerset(succ(esk447_0))))
| in(empty_set,omega)
| epred1_0 )
& ( esk449_0 != empty_set
| in(empty_set,omega)
| epred1_0 )
& ( in(esk450_1(X3943),esk449_0)
| ~ in(X3943,esk449_0)
| in(empty_set,omega)
| epred1_0 )
& ( subset(X3943,esk450_1(X3943))
| ~ in(X3943,esk449_0)
| in(empty_set,omega)
| epred1_0 )
& ( esk450_1(X3943) != X3943
| ~ in(X3943,esk449_0)
| in(empty_set,omega)
| epred1_0 )
& ( ordinal(esk447_0)
| element(esk445_0,powerset(powerset(empty_set)))
| epred1_0 )
& ( in(esk448_1(X3939),X3939)
| X3939 = empty_set
| ~ element(X3939,powerset(powerset(esk447_0)))
| ~ in(esk447_0,omega)
| element(esk445_0,powerset(powerset(empty_set)))
| epred1_0 )
& ( ~ in(X3941,X3939)
| ~ subset(esk448_1(X3939),X3941)
| X3941 = esk448_1(X3939)
| X3939 = empty_set
| ~ element(X3939,powerset(powerset(esk447_0)))
| ~ in(esk447_0,omega)
| element(esk445_0,powerset(powerset(empty_set)))
| epred1_0 )
& ( in(succ(esk447_0),omega)
| element(esk445_0,powerset(powerset(empty_set)))
| epred1_0 )
& ( element(esk449_0,powerset(powerset(succ(esk447_0))))
| element(esk445_0,powerset(powerset(empty_set)))
| epred1_0 )
& ( esk449_0 != empty_set
| element(esk445_0,powerset(powerset(empty_set)))
| epred1_0 )
& ( in(esk450_1(X3943),esk449_0)
| ~ in(X3943,esk449_0)
| element(esk445_0,powerset(powerset(empty_set)))
| epred1_0 )
& ( subset(X3943,esk450_1(X3943))
| ~ in(X3943,esk449_0)
| element(esk445_0,powerset(powerset(empty_set)))
| epred1_0 )
& ( esk450_1(X3943) != X3943
| ~ in(X3943,esk449_0)
| element(esk445_0,powerset(powerset(empty_set)))
| epred1_0 )
& ( ordinal(esk447_0)
| esk445_0 != empty_set
| epred1_0 )
& ( in(esk448_1(X3939),X3939)
| X3939 = empty_set
| ~ element(X3939,powerset(powerset(esk447_0)))
| ~ in(esk447_0,omega)
| esk445_0 != empty_set
| epred1_0 )
& ( ~ in(X3941,X3939)
| ~ subset(esk448_1(X3939),X3941)
| X3941 = esk448_1(X3939)
| X3939 = empty_set
| ~ element(X3939,powerset(powerset(esk447_0)))
| ~ in(esk447_0,omega)
| esk445_0 != empty_set
| epred1_0 )
& ( in(succ(esk447_0),omega)
| esk445_0 != empty_set
| epred1_0 )
& ( element(esk449_0,powerset(powerset(succ(esk447_0))))
| esk445_0 != empty_set
| epred1_0 )
& ( esk449_0 != empty_set
| esk445_0 != empty_set
| epred1_0 )
& ( in(esk450_1(X3943),esk449_0)
| ~ in(X3943,esk449_0)
| esk445_0 != empty_set
| epred1_0 )
& ( subset(X3943,esk450_1(X3943))
| ~ in(X3943,esk449_0)
| esk445_0 != empty_set
| epred1_0 )
& ( esk450_1(X3943) != X3943
| ~ in(X3943,esk449_0)
| esk445_0 != empty_set
| epred1_0 )
& ( ordinal(esk447_0)
| in(esk446_1(X3936),esk445_0)
| ~ in(X3936,esk445_0)
| epred1_0 )
& ( in(esk448_1(X3939),X3939)
| X3939 = empty_set
| ~ element(X3939,powerset(powerset(esk447_0)))
| ~ in(esk447_0,omega)
| in(esk446_1(X3936),esk445_0)
| ~ in(X3936,esk445_0)
| epred1_0 )
& ( ~ in(X3941,X3939)
| ~ subset(esk448_1(X3939),X3941)
| X3941 = esk448_1(X3939)
| X3939 = empty_set
| ~ element(X3939,powerset(powerset(esk447_0)))
| ~ in(esk447_0,omega)
| in(esk446_1(X3936),esk445_0)
| ~ in(X3936,esk445_0)
| epred1_0 )
& ( in(succ(esk447_0),omega)
| in(esk446_1(X3936),esk445_0)
| ~ in(X3936,esk445_0)
| epred1_0 )
& ( element(esk449_0,powerset(powerset(succ(esk447_0))))
| in(esk446_1(X3936),esk445_0)
| ~ in(X3936,esk445_0)
| epred1_0 )
& ( esk449_0 != empty_set
| in(esk446_1(X3936),esk445_0)
| ~ in(X3936,esk445_0)
| epred1_0 )
& ( in(esk450_1(X3943),esk449_0)
| ~ in(X3943,esk449_0)
| in(esk446_1(X3936),esk445_0)
| ~ in(X3936,esk445_0)
| epred1_0 )
& ( subset(X3943,esk450_1(X3943))
| ~ in(X3943,esk449_0)
| in(esk446_1(X3936),esk445_0)
| ~ in(X3936,esk445_0)
| epred1_0 )
& ( esk450_1(X3943) != X3943
| ~ in(X3943,esk449_0)
| in(esk446_1(X3936),esk445_0)
| ~ in(X3936,esk445_0)
| epred1_0 )
& ( ordinal(esk447_0)
| subset(X3936,esk446_1(X3936))
| ~ in(X3936,esk445_0)
| epred1_0 )
& ( in(esk448_1(X3939),X3939)
| X3939 = empty_set
| ~ element(X3939,powerset(powerset(esk447_0)))
| ~ in(esk447_0,omega)
| subset(X3936,esk446_1(X3936))
| ~ in(X3936,esk445_0)
| epred1_0 )
& ( ~ in(X3941,X3939)
| ~ subset(esk448_1(X3939),X3941)
| X3941 = esk448_1(X3939)
| X3939 = empty_set
| ~ element(X3939,powerset(powerset(esk447_0)))
| ~ in(esk447_0,omega)
| subset(X3936,esk446_1(X3936))
| ~ in(X3936,esk445_0)
| epred1_0 )
& ( in(succ(esk447_0),omega)
| subset(X3936,esk446_1(X3936))
| ~ in(X3936,esk445_0)
| epred1_0 )
& ( element(esk449_0,powerset(powerset(succ(esk447_0))))
| subset(X3936,esk446_1(X3936))
| ~ in(X3936,esk445_0)
| epred1_0 )
& ( esk449_0 != empty_set
| subset(X3936,esk446_1(X3936))
| ~ in(X3936,esk445_0)
| epred1_0 )
& ( in(esk450_1(X3943),esk449_0)
| ~ in(X3943,esk449_0)
| subset(X3936,esk446_1(X3936))
| ~ in(X3936,esk445_0)
| epred1_0 )
& ( subset(X3943,esk450_1(X3943))
| ~ in(X3943,esk449_0)
| subset(X3936,esk446_1(X3936))
| ~ in(X3936,esk445_0)
| epred1_0 )
& ( esk450_1(X3943) != X3943
| ~ in(X3943,esk449_0)
| subset(X3936,esk446_1(X3936))
| ~ in(X3936,esk445_0)
| epred1_0 )
& ( ordinal(esk447_0)
| esk446_1(X3936) != X3936
| ~ in(X3936,esk445_0)
| epred1_0 )
& ( in(esk448_1(X3939),X3939)
| X3939 = empty_set
| ~ element(X3939,powerset(powerset(esk447_0)))
| ~ in(esk447_0,omega)
| esk446_1(X3936) != X3936
| ~ in(X3936,esk445_0)
| epred1_0 )
& ( ~ in(X3941,X3939)
| ~ subset(esk448_1(X3939),X3941)
| X3941 = esk448_1(X3939)
| X3939 = empty_set
| ~ element(X3939,powerset(powerset(esk447_0)))
| ~ in(esk447_0,omega)
| esk446_1(X3936) != X3936
| ~ in(X3936,esk445_0)
| epred1_0 )
& ( in(succ(esk447_0),omega)
| esk446_1(X3936) != X3936
| ~ in(X3936,esk445_0)
| epred1_0 )
& ( element(esk449_0,powerset(powerset(succ(esk447_0))))
| esk446_1(X3936) != X3936
| ~ in(X3936,esk445_0)
| epred1_0 )
& ( esk449_0 != empty_set
| esk446_1(X3936) != X3936
| ~ in(X3936,esk445_0)
| epred1_0 )
& ( in(esk450_1(X3943),esk449_0)
| ~ in(X3943,esk449_0)
| esk446_1(X3936) != X3936
| ~ in(X3936,esk445_0)
| epred1_0 )
& ( subset(X3943,esk450_1(X3943))
| ~ in(X3943,esk449_0)
| esk446_1(X3936) != X3936
| ~ in(X3936,esk445_0)
| epred1_0 )
& ( esk450_1(X3943) != X3943
| ~ in(X3943,esk449_0)
| esk446_1(X3936) != X3936
| ~ in(X3936,esk445_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)],[i_0_663])])])])]) ).
fof(i_0_761,lemma,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( below_refl(X1,X2,X3)
<=> related_reflexive(poset_of_lattice(X1),cast_to_el_of_LattPOSet(X1,X2),cast_to_el_of_LattPOSet(X1,X3)) ) ) ) ),
inference(fof_simplification,[status(thm)],[t7_lattice3]) ).
fof(i_0_762,plain,
! [X3215,X3216,X3223,X3226,X3227,X3228] :
( ( in(esk339_3(X3215,X3216,X3223),succ(X3216))
| ~ in(X3223,esk338_2(X3215,X3216))
| esk333_2(X3215,X3216) = esk334_2(X3215,X3216)
| ~ ordinal(X3216) )
& ( esk339_3(X3215,X3216,X3223) = X3223
| ~ in(X3223,esk338_2(X3215,X3216))
| esk333_2(X3215,X3216) = esk334_2(X3215,X3216)
| ~ ordinal(X3216) )
& ( ordinal(esk340_3(X3215,X3216,X3223))
| ~ in(X3223,esk338_2(X3215,X3216))
| esk333_2(X3215,X3216) = esk334_2(X3215,X3216)
| ~ ordinal(X3216) )
& ( X3223 = esk340_3(X3215,X3216,X3223)
| ~ in(X3223,esk338_2(X3215,X3216))
| esk333_2(X3215,X3216) = esk334_2(X3215,X3216)
| ~ ordinal(X3216) )
& ( in(esk340_3(X3215,X3216,X3223),X3215)
| ~ in(X3223,esk338_2(X3215,X3216))
| esk333_2(X3215,X3216) = esk334_2(X3215,X3216)
| ~ ordinal(X3216) )
& ( ~ in(X3227,succ(X3216))
| X3227 != X3226
| ~ ordinal(X3228)
| X3226 != X3228
| ~ in(X3228,X3215)
| in(X3226,esk338_2(X3215,X3216))
| esk333_2(X3215,X3216) = esk334_2(X3215,X3216)
| ~ ordinal(X3216) )
& ( in(esk339_3(X3215,X3216,X3223),succ(X3216))
| ~ in(X3223,esk338_2(X3215,X3216))
| ordinal(esk336_2(X3215,X3216))
| ~ ordinal(X3216) )
& ( esk339_3(X3215,X3216,X3223) = X3223
| ~ in(X3223,esk338_2(X3215,X3216))
| ordinal(esk336_2(X3215,X3216))
| ~ ordinal(X3216) )
& ( ordinal(esk340_3(X3215,X3216,X3223))
| ~ in(X3223,esk338_2(X3215,X3216))
| ordinal(esk336_2(X3215,X3216))
| ~ ordinal(X3216) )
& ( X3223 = esk340_3(X3215,X3216,X3223)
| ~ in(X3223,esk338_2(X3215,X3216))
| ordinal(esk336_2(X3215,X3216))
| ~ ordinal(X3216) )
& ( in(esk340_3(X3215,X3216,X3223),X3215)
| ~ in(X3223,esk338_2(X3215,X3216))
| ordinal(esk336_2(X3215,X3216))
| ~ ordinal(X3216) )
& ( ~ in(X3227,succ(X3216))
| X3227 != X3226
| ~ ordinal(X3228)
| X3226 != X3228
| ~ in(X3228,X3215)
| in(X3226,esk338_2(X3215,X3216))
| ordinal(esk336_2(X3215,X3216))
| ~ ordinal(X3216) )
& ( in(esk339_3(X3215,X3216,X3223),succ(X3216))
| ~ in(X3223,esk338_2(X3215,X3216))
| esk334_2(X3215,X3216) = esk336_2(X3215,X3216)
| ~ ordinal(X3216) )
& ( esk339_3(X3215,X3216,X3223) = X3223
| ~ in(X3223,esk338_2(X3215,X3216))
| esk334_2(X3215,X3216) = esk336_2(X3215,X3216)
| ~ ordinal(X3216) )
& ( ordinal(esk340_3(X3215,X3216,X3223))
| ~ in(X3223,esk338_2(X3215,X3216))
| esk334_2(X3215,X3216) = esk336_2(X3215,X3216)
| ~ ordinal(X3216) )
& ( X3223 = esk340_3(X3215,X3216,X3223)
| ~ in(X3223,esk338_2(X3215,X3216))
| esk334_2(X3215,X3216) = esk336_2(X3215,X3216)
| ~ ordinal(X3216) )
& ( in(esk340_3(X3215,X3216,X3223),X3215)
| ~ in(X3223,esk338_2(X3215,X3216))
| esk334_2(X3215,X3216) = esk336_2(X3215,X3216)
| ~ ordinal(X3216) )
& ( ~ in(X3227,succ(X3216))
| X3227 != X3226
| ~ ordinal(X3228)
| X3226 != X3228
| ~ in(X3228,X3215)
| in(X3226,esk338_2(X3215,X3216))
| esk334_2(X3215,X3216) = esk336_2(X3215,X3216)
| ~ ordinal(X3216) )
& ( in(esk339_3(X3215,X3216,X3223),succ(X3216))
| ~ in(X3223,esk338_2(X3215,X3216))
| in(esk336_2(X3215,X3216),X3215)
| ~ ordinal(X3216) )
& ( esk339_3(X3215,X3216,X3223) = X3223
| ~ in(X3223,esk338_2(X3215,X3216))
| in(esk336_2(X3215,X3216),X3215)
| ~ ordinal(X3216) )
& ( ordinal(esk340_3(X3215,X3216,X3223))
| ~ in(X3223,esk338_2(X3215,X3216))
| in(esk336_2(X3215,X3216),X3215)
| ~ ordinal(X3216) )
& ( X3223 = esk340_3(X3215,X3216,X3223)
| ~ in(X3223,esk338_2(X3215,X3216))
| in(esk336_2(X3215,X3216),X3215)
| ~ ordinal(X3216) )
& ( in(esk340_3(X3215,X3216,X3223),X3215)
| ~ in(X3223,esk338_2(X3215,X3216))
| in(esk336_2(X3215,X3216),X3215)
| ~ ordinal(X3216) )
& ( ~ in(X3227,succ(X3216))
| X3227 != X3226
| ~ ordinal(X3228)
| X3226 != X3228
| ~ in(X3228,X3215)
| in(X3226,esk338_2(X3215,X3216))
| in(esk336_2(X3215,X3216),X3215)
| ~ ordinal(X3216) )
& ( in(esk339_3(X3215,X3216,X3223),succ(X3216))
| ~ in(X3223,esk338_2(X3215,X3216))
| esk333_2(X3215,X3216) = esk335_2(X3215,X3216)
| ~ ordinal(X3216) )
& ( esk339_3(X3215,X3216,X3223) = X3223
| ~ in(X3223,esk338_2(X3215,X3216))
| esk333_2(X3215,X3216) = esk335_2(X3215,X3216)
| ~ ordinal(X3216) )
& ( ordinal(esk340_3(X3215,X3216,X3223))
| ~ in(X3223,esk338_2(X3215,X3216))
| esk333_2(X3215,X3216) = esk335_2(X3215,X3216)
| ~ ordinal(X3216) )
& ( X3223 = esk340_3(X3215,X3216,X3223)
| ~ in(X3223,esk338_2(X3215,X3216))
| esk333_2(X3215,X3216) = esk335_2(X3215,X3216)
| ~ ordinal(X3216) )
& ( in(esk340_3(X3215,X3216,X3223),X3215)
| ~ in(X3223,esk338_2(X3215,X3216))
| esk333_2(X3215,X3216) = esk335_2(X3215,X3216)
| ~ ordinal(X3216) )
& ( ~ in(X3227,succ(X3216))
| X3227 != X3226
| ~ ordinal(X3228)
| X3226 != X3228
| ~ in(X3228,X3215)
| in(X3226,esk338_2(X3215,X3216))
| esk333_2(X3215,X3216) = esk335_2(X3215,X3216)
| ~ ordinal(X3216) )
& ( in(esk339_3(X3215,X3216,X3223),succ(X3216))
| ~ in(X3223,esk338_2(X3215,X3216))
| ordinal(esk337_2(X3215,X3216))
| ~ ordinal(X3216) )
& ( esk339_3(X3215,X3216,X3223) = X3223
| ~ in(X3223,esk338_2(X3215,X3216))
| ordinal(esk337_2(X3215,X3216))
| ~ ordinal(X3216) )
& ( ordinal(esk340_3(X3215,X3216,X3223))
| ~ in(X3223,esk338_2(X3215,X3216))
| ordinal(esk337_2(X3215,X3216))
| ~ ordinal(X3216) )
& ( X3223 = esk340_3(X3215,X3216,X3223)
| ~ in(X3223,esk338_2(X3215,X3216))
| ordinal(esk337_2(X3215,X3216))
| ~ ordinal(X3216) )
& ( in(esk340_3(X3215,X3216,X3223),X3215)
| ~ in(X3223,esk338_2(X3215,X3216))
| ordinal(esk337_2(X3215,X3216))
| ~ ordinal(X3216) )
& ( ~ in(X3227,succ(X3216))
| X3227 != X3226
| ~ ordinal(X3228)
| X3226 != X3228
| ~ in(X3228,X3215)
| in(X3226,esk338_2(X3215,X3216))
| ordinal(esk337_2(X3215,X3216))
| ~ ordinal(X3216) )
& ( in(esk339_3(X3215,X3216,X3223),succ(X3216))
| ~ in(X3223,esk338_2(X3215,X3216))
| esk335_2(X3215,X3216) = esk337_2(X3215,X3216)
| ~ ordinal(X3216) )
& ( esk339_3(X3215,X3216,X3223) = X3223
| ~ in(X3223,esk338_2(X3215,X3216))
| esk335_2(X3215,X3216) = esk337_2(X3215,X3216)
| ~ ordinal(X3216) )
& ( ordinal(esk340_3(X3215,X3216,X3223))
| ~ in(X3223,esk338_2(X3215,X3216))
| esk335_2(X3215,X3216) = esk337_2(X3215,X3216)
| ~ ordinal(X3216) )
& ( X3223 = esk340_3(X3215,X3216,X3223)
| ~ in(X3223,esk338_2(X3215,X3216))
| esk335_2(X3215,X3216) = esk337_2(X3215,X3216)
| ~ ordinal(X3216) )
& ( in(esk340_3(X3215,X3216,X3223),X3215)
| ~ in(X3223,esk338_2(X3215,X3216))
| esk335_2(X3215,X3216) = esk337_2(X3215,X3216)
| ~ ordinal(X3216) )
& ( ~ in(X3227,succ(X3216))
| X3227 != X3226
| ~ ordinal(X3228)
| X3226 != X3228
| ~ in(X3228,X3215)
| in(X3226,esk338_2(X3215,X3216))
| esk335_2(X3215,X3216) = esk337_2(X3215,X3216)
| ~ ordinal(X3216) )
& ( in(esk339_3(X3215,X3216,X3223),succ(X3216))
| ~ in(X3223,esk338_2(X3215,X3216))
| in(esk337_2(X3215,X3216),X3215)
| ~ ordinal(X3216) )
& ( esk339_3(X3215,X3216,X3223) = X3223
| ~ in(X3223,esk338_2(X3215,X3216))
| in(esk337_2(X3215,X3216),X3215)
| ~ ordinal(X3216) )
& ( ordinal(esk340_3(X3215,X3216,X3223))
| ~ in(X3223,esk338_2(X3215,X3216))
| in(esk337_2(X3215,X3216),X3215)
| ~ ordinal(X3216) )
& ( X3223 = esk340_3(X3215,X3216,X3223)
| ~ in(X3223,esk338_2(X3215,X3216))
| in(esk337_2(X3215,X3216),X3215)
| ~ ordinal(X3216) )
& ( in(esk340_3(X3215,X3216,X3223),X3215)
| ~ in(X3223,esk338_2(X3215,X3216))
| in(esk337_2(X3215,X3216),X3215)
| ~ ordinal(X3216) )
& ( ~ in(X3227,succ(X3216))
| X3227 != X3226
| ~ ordinal(X3228)
| X3226 != X3228
| ~ in(X3228,X3215)
| in(X3226,esk338_2(X3215,X3216))
| in(esk337_2(X3215,X3216),X3215)
| ~ ordinal(X3216) )
& ( in(esk339_3(X3215,X3216,X3223),succ(X3216))
| ~ in(X3223,esk338_2(X3215,X3216))
| esk334_2(X3215,X3216) != esk335_2(X3215,X3216)
| ~ ordinal(X3216) )
& ( esk339_3(X3215,X3216,X3223) = X3223
| ~ in(X3223,esk338_2(X3215,X3216))
| esk334_2(X3215,X3216) != esk335_2(X3215,X3216)
| ~ ordinal(X3216) )
& ( ordinal(esk340_3(X3215,X3216,X3223))
| ~ in(X3223,esk338_2(X3215,X3216))
| esk334_2(X3215,X3216) != esk335_2(X3215,X3216)
| ~ ordinal(X3216) )
& ( X3223 = esk340_3(X3215,X3216,X3223)
| ~ in(X3223,esk338_2(X3215,X3216))
| esk334_2(X3215,X3216) != esk335_2(X3215,X3216)
| ~ ordinal(X3216) )
& ( in(esk340_3(X3215,X3216,X3223),X3215)
| ~ in(X3223,esk338_2(X3215,X3216))
| esk334_2(X3215,X3216) != esk335_2(X3215,X3216)
| ~ ordinal(X3216) )
& ( ~ in(X3227,succ(X3216))
| X3227 != X3226
| ~ ordinal(X3228)
| X3226 != X3228
| ~ in(X3228,X3215)
| in(X3226,esk338_2(X3215,X3216))
| esk334_2(X3215,X3216) != esk335_2(X3215,X3216)
| ~ ordinal(X3216) ) ),
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)],[s1_tarski__e8_6__wellord2__1])])])])])]) ).
fof(i_0_763,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& meet_semilatt_str(X1) )
=> ( lower_bounded_semilattstr(X1)
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ( X2 = bottom_of_semilattstr(X1)
<=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( meet(X1,X2,X3) = X2
& meet(X1,X3,X2) = X2 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[d16_lattices]) ).
fof(i_0_764,lemma,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> apply_as_element(the_carrier(X1),the_carrier(X1),identity_on_carrier(X1),X2) = X2 ) ),
inference(fof_simplification,[status(thm)],[t91_tmap_1]) ).
fof(i_0_765,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& meet_semilatt_str(X1) )
=> ( lower_bounded_semilattstr(X1)
<=> ? [X2] :
( element(X2,the_carrier(X1))
& ! [X3] :
( element(X3,the_carrier(X1))
=> ( meet(X1,X2,X3) = X2
& meet(X1,X3,X2) = X2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[d13_lattices]) ).
fof(i_0_766,plain,
! [X2061,X2062,X2065,X2067,X2068] :
( ( ~ relation(X2061)
| ~ in(X2062,X2061)
| X2062 = ordered_pair(esk37_2(X2061,X2062),esk38_2(X2061,X2062)) )
& ( in(esk39_1(X2065),X2065)
| relation(X2065) )
& ( esk39_1(X2065) != ordered_pair(X2067,X2068)
| relation(X2065) ) ),
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)],[d1_relat_1])])])])])]) ).
fof(i_0_767,plain,
! [X2259,X2260,X2261] :
( ( X2261 != apply(X2259,X2260)
| in(ordered_pair(X2260,X2261),X2259)
| ~ in(X2260,relation_dom(X2259))
| ~ relation(X2259)
| ~ function(X2259) )
& ( ~ in(ordered_pair(X2260,X2261),X2259)
| X2261 = apply(X2259,X2260)
| ~ in(X2260,relation_dom(X2259))
| ~ relation(X2259)
| ~ function(X2259) )
& ( X2261 != apply(X2259,X2260)
| X2261 = empty_set
| in(X2260,relation_dom(X2259))
| ~ relation(X2259)
| ~ function(X2259) )
& ( X2261 != empty_set
| X2261 = apply(X2259,X2260)
| in(X2260,relation_dom(X2259))
| ~ relation(X2259)
| ~ function(X2259) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_664])])])]) ).
fof(i_0_768,lemma,
! [X2914,X2919,X2920,X2921,X2922] :
( ( relation(esk188_1(X2914))
| in(esk185_1(X2914),X2914) )
& ( function(esk188_1(X2914))
| in(esk185_1(X2914),X2914) )
& ( in(X2919,X2914)
| ~ in(ordered_pair(X2919,X2920),esk188_1(X2914))
| in(esk185_1(X2914),X2914) )
& ( X2920 = singleton(X2919)
| ~ in(ordered_pair(X2919,X2920),esk188_1(X2914))
| in(esk185_1(X2914),X2914) )
& ( ~ in(X2921,X2914)
| X2922 != singleton(X2921)
| in(ordered_pair(X2921,X2922),esk188_1(X2914))
| in(esk185_1(X2914),X2914) )
& ( relation(esk188_1(X2914))
| esk186_1(X2914) = singleton(esk185_1(X2914)) )
& ( function(esk188_1(X2914))
| esk186_1(X2914) = singleton(esk185_1(X2914)) )
& ( in(X2919,X2914)
| ~ in(ordered_pair(X2919,X2920),esk188_1(X2914))
| esk186_1(X2914) = singleton(esk185_1(X2914)) )
& ( X2920 = singleton(X2919)
| ~ in(ordered_pair(X2919,X2920),esk188_1(X2914))
| esk186_1(X2914) = singleton(esk185_1(X2914)) )
& ( ~ in(X2921,X2914)
| X2922 != singleton(X2921)
| in(ordered_pair(X2921,X2922),esk188_1(X2914))
| esk186_1(X2914) = singleton(esk185_1(X2914)) )
& ( relation(esk188_1(X2914))
| in(esk185_1(X2914),X2914) )
& ( function(esk188_1(X2914))
| in(esk185_1(X2914),X2914) )
& ( in(X2919,X2914)
| ~ in(ordered_pair(X2919,X2920),esk188_1(X2914))
| in(esk185_1(X2914),X2914) )
& ( X2920 = singleton(X2919)
| ~ in(ordered_pair(X2919,X2920),esk188_1(X2914))
| in(esk185_1(X2914),X2914) )
& ( ~ in(X2921,X2914)
| X2922 != singleton(X2921)
| in(ordered_pair(X2921,X2922),esk188_1(X2914))
| in(esk185_1(X2914),X2914) )
& ( relation(esk188_1(X2914))
| esk187_1(X2914) = singleton(esk185_1(X2914)) )
& ( function(esk188_1(X2914))
| esk187_1(X2914) = singleton(esk185_1(X2914)) )
& ( in(X2919,X2914)
| ~ in(ordered_pair(X2919,X2920),esk188_1(X2914))
| esk187_1(X2914) = singleton(esk185_1(X2914)) )
& ( X2920 = singleton(X2919)
| ~ in(ordered_pair(X2919,X2920),esk188_1(X2914))
| esk187_1(X2914) = singleton(esk185_1(X2914)) )
& ( ~ in(X2921,X2914)
| X2922 != singleton(X2921)
| in(ordered_pair(X2921,X2922),esk188_1(X2914))
| esk187_1(X2914) = singleton(esk185_1(X2914)) )
& ( relation(esk188_1(X2914))
| esk186_1(X2914) != esk187_1(X2914) )
& ( function(esk188_1(X2914))
| esk186_1(X2914) != esk187_1(X2914) )
& ( in(X2919,X2914)
| ~ in(ordered_pair(X2919,X2920),esk188_1(X2914))
| esk186_1(X2914) != esk187_1(X2914) )
& ( X2920 = singleton(X2919)
| ~ in(ordered_pair(X2919,X2920),esk188_1(X2914))
| esk186_1(X2914) != esk187_1(X2914) )
& ( ~ in(X2921,X2914)
| X2922 != singleton(X2921)
| in(ordered_pair(X2921,X2922),esk188_1(X2914))
| esk186_1(X2914) != esk187_1(X2914) ) ),
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)],[i_0_665])])])])])]) ).
fof(i_0_769,lemma,
! [X3414,X3415,X3416,X3417] :
( ( in(X3414,X3416)
| ~ in(ordered_pair(X3414,X3415),cartesian_product2(X3416,X3417)) )
& ( in(X3415,X3417)
| ~ in(ordered_pair(X3414,X3415),cartesian_product2(X3416,X3417)) )
& ( ~ in(X3414,X3416)
| ~ in(X3415,X3417)
| in(ordered_pair(X3414,X3415),cartesian_product2(X3416,X3417)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t106_zfmisc_1])])]) ).
fof(i_0_770,lemma,
! [X2762,X2763,X2764,X2765] :
( ( in(X2762,X2764)
| ~ in(ordered_pair(X2762,X2763),cartesian_product2(X2764,X2765)) )
& ( in(X2763,X2765)
| ~ in(ordered_pair(X2762,X2763),cartesian_product2(X2764,X2765)) )
& ( ~ in(X2762,X2764)
| ~ in(X2763,X2765)
| in(ordered_pair(X2762,X2763),cartesian_product2(X2764,X2765)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l55_zfmisc_1])])]) ).
fof(i_0_771,lemma,
! [X3899,X3900,X3901] :
( ( in(X3899,relation_dom(X3901))
| ~ in(ordered_pair(X3899,X3900),X3901)
| ~ relation(X3901)
| ~ function(X3901) )
& ( X3900 = apply(X3901,X3899)
| ~ in(ordered_pair(X3899,X3900),X3901)
| ~ relation(X3901)
| ~ function(X3901) )
& ( ~ in(X3899,relation_dom(X3901))
| X3900 != apply(X3901,X3899)
| in(ordered_pair(X3899,X3900),X3901)
| ~ relation(X3901)
| ~ function(X3901) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_funct_1])])]) ).
fof(i_0_772,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)],[t26_lattices]) ).
fof(i_0_773,lemma,
! [X1,X2] :
( ( ~ empty_carrier(X2)
& lattice(X2)
& latt_str(X2) )
=> ! [X3] :
( element(X3,the_carrier(poset_of_lattice(X2)))
=> ( relstr_set_smaller(poset_of_lattice(X2),X1,X3)
<=> latt_element_smaller(X2,cast_to_el_of_lattice(X2,X3),X1) ) ) ),
inference(fof_simplification,[status(thm)],[t31_lattice3]) ).
fof(i_0_774,lemma,
! [X1,X2] :
( ( ~ empty_carrier(X2)
& lattice(X2)
& latt_str(X2) )
=> ! [X3] :
( element(X3,the_carrier(poset_of_lattice(X2)))
=> ( relstr_element_smaller(poset_of_lattice(X2),X1,X3)
<=> latt_set_smaller(X2,cast_to_el_of_lattice(X2,X3),X1) ) ) ),
inference(fof_simplification,[status(thm)],[t29_lattice3]) ).
fof(i_0_775,lemma,
! [X3547,X3548,X3549] :
( ( in(X3547,relation_dom(X3549))
| ~ in(ordered_pair(X3547,X3548),X3549)
| ~ relation(X3549) )
& ( in(X3548,relation_rng(X3549))
| ~ in(ordered_pair(X3547,X3548),X3549)
| ~ relation(X3549) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t20_relat_1])])]) ).
fof(i_0_776,lemma,
! [X3651,X3652,X3653] :
( ( in(X3651,relation_field(X3653))
| ~ in(ordered_pair(X3651,X3652),X3653)
| ~ relation(X3653) )
& ( in(X3652,relation_field(X3653))
| ~ in(ordered_pair(X3651,X3652),X3653)
| ~ relation(X3653) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t30_relat_1])])]) ).
fof(i_0_777,lemma,
! [X3726,X3727] :
( ( ~ being_limit_ordinal(X3726)
| ~ ordinal(X3727)
| ~ in(X3727,X3726)
| in(succ(X3727),X3726)
| ~ ordinal(X3726) )
& ( ordinal(esk427_1(X3726))
| being_limit_ordinal(X3726)
| ~ ordinal(X3726) )
& ( in(esk427_1(X3726),X3726)
| being_limit_ordinal(X3726)
| ~ ordinal(X3726) )
& ( ~ in(succ(esk427_1(X3726)),X3726)
| being_limit_ordinal(X3726)
| ~ ordinal(X3726) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t41_ordinal1])])])])]) ).
fof(i_0_778,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)],[t23_lattices]) ).
fof(i_0_779,plain,
! [X1,X2,X3] :
( ( ~ empty_carrier(X2)
& lattice(X2)
& complete_latt_str(X2)
& latt_str(X2) )
=> ( in(X1,a_2_3_lattice3(X2,X3))
<=> ? [X4] :
( element(X4,the_carrier(X2))
& X1 = X4
& latt_set_smaller(X2,X4,X3) ) ) ),
inference(fof_simplification,[status(thm)],[fraenkel_a_2_3_lattice3]) ).
fof(i_0_780,lemma,
! [X3822] :
( ~ relation(X3822)
| in(ordered_pair(esk437_1(X3822),esk438_1(X3822)),X3822)
| X3822 = empty_set ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_666])])]) ).
fof(i_0_781,plain,
! [X1,X2] :
( ( ~ empty(X1)
& ~ empty(X2) )
=> ! [X3] :
( relation_of2(X3,X1,X2)
=> ( ( function(X3)
& quasi_total(X3,X1,X2) )
=> ( function(X3)
& ~ empty(X3)
& v1_partfun1(X3,X1,X2)
& quasi_total(X3,X1,X2) ) ) ) ),
inference(fof_simplification,[status(thm)],[cc6_funct_2]) ).
fof(i_0_782,lemma,
! [X1,X2] :
( ( ~ empty_carrier(X2)
& lattice(X2)
& latt_str(X2) )
=> ! [X3] :
( element(X3,the_carrier(X2))
=> ( latt_element_smaller(X2,X3,X1)
<=> relstr_set_smaller(poset_of_lattice(X2),X1,cast_to_el_of_LattPOSet(X2,X3)) ) ) ),
inference(fof_simplification,[status(thm)],[t30_lattice3]) ).
fof(i_0_783,lemma,
! [X1,X2] :
( ( ~ empty_carrier(X2)
& lattice(X2)
& latt_str(X2) )
=> ! [X3] :
( element(X3,the_carrier(X2))
=> ( latt_set_smaller(X2,X3,X1)
<=> relstr_element_smaller(poset_of_lattice(X2),X1,cast_to_el_of_LattPOSet(X2,X3)) ) ) ),
inference(fof_simplification,[status(thm)],[t28_lattice3]) ).
fof(i_0_784,plain,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& meet_commutative(X1)
& meet_absorbing(X1)
& join_absorbing(X1)
& latt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> ( below_refl(X1,X2,X3)
<=> below(X1,X2,X3) ) ),
inference(fof_simplification,[status(thm)],[redefinition_r3_lattices]) ).
fof(i_0_785,plain,
! [X1,X2] :
( ~ empty(X2)
=> ! [X3] :
( relation_of2(X3,X1,X2)
=> ( ( function(X3)
& quasi_total(X3,X1,X2) )
=> ( function(X3)
& v1_partfun1(X3,X1,X2)
& quasi_total(X3,X1,X2) ) ) ) ),
inference(fof_simplification,[status(thm)],[cc5_funct_2]) ).
fof(i_0_786,plain,
! [X1,X2,X3] :
( ( ~ empty_carrier(X2)
& latt_str(X2) )
=> ( in(X1,a_2_2_lattice3(X2,X3))
<=> ? [X4] :
( element(X4,the_carrier(X2))
& X1 = X4
& latt_set_smaller(X2,X4,X3) ) ) ),
inference(fof_simplification,[status(thm)],[fraenkel_a_2_2_lattice3]) ).
fof(i_0_787,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,powerset(the_carrier(X1)))
=> ( point_neighbourhood(X3,X1,X2)
<=> in(X2,interior(X1,X3)) ) ) ) ),
inference(fof_simplification,[status(thm)],[d1_connsp_2]) ).
fof(i_0_788,lemma,
! [X3327,X3328,X3330,X3332,X3333] :
( ( in(X3330,succ(X3328))
| ~ in(X3330,esk372_2(X3327,X3328))
| ~ ordinal(X3328) )
& ( ordinal(esk373_3(X3327,X3328,X3330))
| ~ in(X3330,esk372_2(X3327,X3328))
| ~ ordinal(X3328) )
& ( X3330 = esk373_3(X3327,X3328,X3330)
| ~ in(X3330,esk372_2(X3327,X3328))
| ~ ordinal(X3328) )
& ( in(esk373_3(X3327,X3328,X3330),X3327)
| ~ in(X3330,esk372_2(X3327,X3328))
| ~ ordinal(X3328) )
& ( ~ in(X3332,succ(X3328))
| ~ ordinal(X3333)
| X3332 != X3333
| ~ in(X3333,X3327)
| in(X3332,esk372_2(X3327,X3328))
| ~ ordinal(X3328) ) ),
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)],[s1_xboole_0__e8_6__wellord2__1])])])])])]) ).
fof(i_0_789,plain,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& reflexive_relstr(X1)
& rel_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> ( related_reflexive(X1,X2,X3)
<=> related(X1,X2,X3) ) ),
inference(fof_simplification,[status(thm)],[redefinition_r3_orders_2]) ).
fof(i_0_790,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)],[d3_lattices]) ).
fof(i_0_791,plain,
! [X2003,X2004,X2005] :
( ~ relation(X2003)
| ~ function(X2003)
| apply_binary(X2003,X2004,X2005) = apply(X2003,ordered_pair(X2004,X2005)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_binop_1])])]) ).
fof(i_0_792,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)],[dt_k4_lattices]) ).
fof(i_0_793,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)],[dt_k3_lattices]) ).
fof(i_0_794,plain,
! [X2586,X2587] : ~ empty(ordered_pair(X2586,X2587)),
inference(variable_rename,[status(thm)],[i_0_667]) ).
fof(i_0_795,lemma,
! [X3677,X3678,X3679,X3680] :
( ( X3677 = X3679
| ordered_pair(X3677,X3678) != ordered_pair(X3679,X3680) )
& ( X3678 = X3680
| ordered_pair(X3677,X3678) != ordered_pair(X3679,X3680) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t33_zfmisc_1])])]) ).
fof(i_0_796,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)],[dt_k1_lattices]) ).
fof(i_0_797,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)],[dt_k2_lattices]) ).
fof(i_0_798,lemma,
! [X3539,X3540,X3541] :
( ( join(boole_lattice(X3539),X3540,X3541) = set_union2(X3540,X3541)
| ~ element(X3541,the_carrier(boole_lattice(X3539)))
| ~ element(X3540,the_carrier(boole_lattice(X3539))) )
& ( meet(boole_lattice(X3539),X3540,X3541) = set_intersection2(X3540,X3541)
| ~ element(X3541,the_carrier(boole_lattice(X3539)))
| ~ element(X3540,the_carrier(boole_lattice(X3539))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_lattice3])])])]) ).
fof(i_0_799,lemma,
! [X1] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( ( open_subset(X2,X1)
& in(X3,X2) )
=> point_neighbourhood(X2,X1,X3) ) ) ) ),
inference(fof_simplification,[status(thm)],[t5_connsp_2]) ).
fof(i_0_800,lemma,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( in(X3,subset_complement(the_carrier(X1),X2))
<=> ~ in(X3,X2) ) ) ) ),
inference(fof_simplification,[status(thm)],[l40_tops_1]) ).
fof(i_0_801,lemma,
! [X3620,X3621,X3622] :
( ~ subset(X3620,X3621)
| subset(set_intersection2(X3620,X3622),set_intersection2(X3621,X3622)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t26_xboole_1])]) ).
fof(i_0_802,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)],[redefinition_k3_lattices]) ).
fof(i_0_803,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)],[redefinition_k4_lattices]) ).
fof(i_0_804,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)],[commutativity_k4_lattices]) ).
fof(i_0_805,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)],[commutativity_k3_lattices]) ).
fof(i_0_806,lemma,
! [X1] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1) )
=> ( compact_top_space(X1)
<=> ! [X2] :
( element(X2,powerset(powerset(the_carrier(X1))))
=> ~ ( centered(X2)
& closed_subsets(X2,X1)
& meet_of_subsets(the_carrier(X1),X2) = empty_set ) ) ) ),
inference(fof_simplification,[status(thm)],[t13_compts_1]) ).
fof(i_0_807,lemma,
! [X3672,X3673] :
( ( ~ in(X3672,X3673)
| ordinal_subset(succ(X3672),X3673)
| ~ ordinal(X3673)
| ~ ordinal(X3672) )
& ( ~ ordinal_subset(succ(X3672),X3673)
| in(X3672,X3673)
| ~ ordinal(X3673)
| ~ ordinal(X3672) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t33_ordinal1])])])]) ).
fof(i_0_808,lemma,
! [X3768,X3769] :
( ~ element(X3769,powerset(powerset(X3768)))
| X3769 = empty_set
| subset_difference(X3768,cast_to_subset(X3768),union_of_subsets(X3768,X3769)) = meet_of_subsets(X3768,complements_of_subsets(X3768,X3769)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t47_setfam_1])]) ).
fof(i_0_809,plain,
! [X2282] : cast_to_subset(X2282) = X2282,
inference(variable_rename,[status(thm)],[d4_subset_1]) ).
fof(i_0_810,lemma,
! [X3772,X3773] :
( ~ element(X3773,powerset(powerset(X3772)))
| X3773 = empty_set
| union_of_subsets(X3772,complements_of_subsets(X3772,X3773)) = subset_difference(X3772,cast_to_subset(X3772),meet_of_subsets(X3772,X3773)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t48_setfam_1])]) ).
fof(i_0_811,plain,
! [X1,X2] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1)
& element(X2,the_carrier(X1)) )
=> ! [X3] :
( point_neighbourhood(X3,X1,X2)
=> element(X3,powerset(the_carrier(X1))) ) ),
inference(fof_simplification,[status(thm)],[dt_m1_connsp_2]) ).
fof(i_0_812,lemma,
! [X3784,X3785,X3787,X3788,X3789] :
( ( disjoint(X3784,X3785)
| in(esk432_2(X3784,X3785),set_intersection2(X3784,X3785)) )
& ( ~ in(X3789,set_intersection2(X3787,X3788))
| ~ disjoint(X3787,X3788) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_668])])])])]) ).
fof(i_0_813,plain,
! [X2860,X2861,X2862] :
( ~ element(X2861,powerset(X2860))
| ~ element(X2862,powerset(X2860))
| subset_intersection2(X2860,X2861,X2862) = set_intersection2(X2861,X2862) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k5_subset_1])]) ).
fof(i_0_814,negated_conjecture,
~ ! [X1] :
( rel_str(X1)
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ( relstr_set_smaller(X1,empty_set,X2)
& relstr_element_smaller(X1,empty_set,X2) ) ) ),
inference(assume_negation,[status(cth)],[t6_yellow_0]) ).
fof(i_0_815,plain,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& meet_commutative(X1)
& meet_absorbing(X1)
& join_absorbing(X1)
& latt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> below_refl(X1,X2,X2) ),
inference(fof_simplification,[status(thm)],[reflexivity_r3_lattices]) ).
fof(i_0_816,lemma,
! [X3478,X3479] :
( ~ relation(X3479)
| relation_image(X3479,X3478) = relation_image(X3479,set_intersection2(relation_dom(X3479),X3478)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t145_relat_1])]) ).
fof(i_0_817,plain,
! [X2594] :
( ( ~ empty(succ(X2594))
| ~ ordinal(X2594)
| ~ natural(X2594) )
& ( epsilon_transitive(succ(X2594))
| ~ ordinal(X2594)
| ~ natural(X2594) )
& ( epsilon_connected(succ(X2594))
| ~ ordinal(X2594)
| ~ natural(X2594) )
& ( ordinal(succ(X2594))
| ~ ordinal(X2594)
| ~ natural(X2594) )
& ( natural(succ(X2594))
| ~ ordinal(X2594)
| ~ natural(X2594) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_669])])]) ).
fof(i_0_818,plain,
! [X1,X2] :
( ( ~ empty(X1)
& relation_of2(X2,X1,X1) )
=> ( ~ empty_carrier(rel_str_of(X1,X2))
& strict_rel_str(rel_str_of(X1,X2)) ) ),
inference(fof_simplification,[status(thm)],[fc1_orders_2]) ).
fof(i_0_819,plain,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& reflexive_relstr(X1)
& rel_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> related_reflexive(X1,X2,X2) ),
inference(fof_simplification,[status(thm)],[reflexivity_r3_orders_2]) ).
fof(i_0_820,lemma,
! [X3535,X3536,X3537] :
( ~ subset(X3535,X3536)
| ~ subset(X3535,X3537)
| subset(X3535,set_intersection2(X3536,X3537)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t19_xboole_1])]) ).
fof(i_0_821,plain,
! [X2635] :
( ( ~ empty(succ(X2635))
| ~ ordinal(X2635) )
& ( epsilon_transitive(succ(X2635))
| ~ ordinal(X2635) )
& ( epsilon_connected(succ(X2635))
| ~ ordinal(X2635) )
& ( ordinal(succ(X2635))
| ~ ordinal(X2635) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_670])])]) ).
fof(i_0_822,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& meet_associative(X1)
& meet_semilatt_str(X1) )
=> ( relation(the_L_meet(X1))
& function(the_L_meet(X1))
& quasi_total(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
& v2_binop_1(the_L_meet(X1),the_carrier(X1))
& v1_partfun1(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1)) ) ),
inference(fof_simplification,[status(thm)],[fc5_lattice2]) ).
fof(i_0_823,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& meet_commutative(X1)
& meet_semilatt_str(X1) )
=> ( relation(the_L_meet(X1))
& function(the_L_meet(X1))
& quasi_total(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
& v1_binop_1(the_L_meet(X1),the_carrier(X1))
& v1_partfun1(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1)) ) ),
inference(fof_simplification,[status(thm)],[fc4_lattice2]) ).
fof(i_0_824,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& join_associative(X1)
& join_semilatt_str(X1) )
=> ( relation(the_L_join(X1))
& function(the_L_join(X1))
& quasi_total(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
& v2_binop_1(the_L_join(X1),the_carrier(X1))
& v1_partfun1(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1)) ) ),
inference(fof_simplification,[status(thm)],[fc3_lattice2]) ).
fof(i_0_825,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& join_commutative(X1)
& join_semilatt_str(X1) )
=> ( relation(the_L_join(X1))
& function(the_L_join(X1))
& quasi_total(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
& v1_binop_1(the_L_join(X1),the_carrier(X1))
& v1_partfun1(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1)) ) ),
inference(fof_simplification,[status(thm)],[fc2_lattice2]) ).
fof(i_0_826,lemma,
! [X3881,X3882] :
( pair_first(ordered_pair(X3881,X3882)) = X3881
& pair_second(ordered_pair(X3881,X3882)) = X3882 ),
inference(variable_rename,[status(thm)],[t7_mcart_1]) ).
fof(i_0_827,plain,
! [X1,X2] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1)
& element(X2,the_carrier(X1)) )
=> ? [X3] : point_neighbourhood(X3,X1,X2) ),
inference(fof_simplification,[status(thm)],[existence_m1_connsp_2]) ).
fof(i_0_828,lemma,
! [X3351,X3356,X3358] :
( ( relation(esk387_1(X3351))
| in(esk386_1(X3351),X3351)
| in(esk383_1(X3351),X3351) )
& ( function(esk387_1(X3351))
| in(esk386_1(X3351),X3351)
| in(esk383_1(X3351),X3351) )
& ( relation_dom(esk387_1(X3351)) = X3351
| in(esk386_1(X3351),X3351)
| in(esk383_1(X3351),X3351) )
& ( ~ in(X3358,X3351)
| apply(esk387_1(X3351),X3358) = singleton(X3358)
| in(esk386_1(X3351),X3351)
| in(esk383_1(X3351),X3351) )
& ( relation(esk387_1(X3351))
| X3356 != singleton(esk386_1(X3351))
| in(esk383_1(X3351),X3351) )
& ( function(esk387_1(X3351))
| X3356 != singleton(esk386_1(X3351))
| in(esk383_1(X3351),X3351) )
& ( relation_dom(esk387_1(X3351)) = X3351
| X3356 != singleton(esk386_1(X3351))
| in(esk383_1(X3351),X3351) )
& ( ~ in(X3358,X3351)
| apply(esk387_1(X3351),X3358) = singleton(X3358)
| X3356 != singleton(esk386_1(X3351))
| in(esk383_1(X3351),X3351) )
& ( relation(esk387_1(X3351))
| in(esk386_1(X3351),X3351)
| esk384_1(X3351) = singleton(esk383_1(X3351)) )
& ( function(esk387_1(X3351))
| in(esk386_1(X3351),X3351)
| esk384_1(X3351) = singleton(esk383_1(X3351)) )
& ( relation_dom(esk387_1(X3351)) = X3351
| in(esk386_1(X3351),X3351)
| esk384_1(X3351) = singleton(esk383_1(X3351)) )
& ( ~ in(X3358,X3351)
| apply(esk387_1(X3351),X3358) = singleton(X3358)
| in(esk386_1(X3351),X3351)
| esk384_1(X3351) = singleton(esk383_1(X3351)) )
& ( relation(esk387_1(X3351))
| X3356 != singleton(esk386_1(X3351))
| esk384_1(X3351) = singleton(esk383_1(X3351)) )
& ( function(esk387_1(X3351))
| X3356 != singleton(esk386_1(X3351))
| esk384_1(X3351) = singleton(esk383_1(X3351)) )
& ( relation_dom(esk387_1(X3351)) = X3351
| X3356 != singleton(esk386_1(X3351))
| esk384_1(X3351) = singleton(esk383_1(X3351)) )
& ( ~ in(X3358,X3351)
| apply(esk387_1(X3351),X3358) = singleton(X3358)
| X3356 != singleton(esk386_1(X3351))
| esk384_1(X3351) = singleton(esk383_1(X3351)) )
& ( relation(esk387_1(X3351))
| in(esk386_1(X3351),X3351)
| esk385_1(X3351) = singleton(esk383_1(X3351)) )
& ( function(esk387_1(X3351))
| in(esk386_1(X3351),X3351)
| esk385_1(X3351) = singleton(esk383_1(X3351)) )
& ( relation_dom(esk387_1(X3351)) = X3351
| in(esk386_1(X3351),X3351)
| esk385_1(X3351) = singleton(esk383_1(X3351)) )
& ( ~ in(X3358,X3351)
| apply(esk387_1(X3351),X3358) = singleton(X3358)
| in(esk386_1(X3351),X3351)
| esk385_1(X3351) = singleton(esk383_1(X3351)) )
& ( relation(esk387_1(X3351))
| X3356 != singleton(esk386_1(X3351))
| esk385_1(X3351) = singleton(esk383_1(X3351)) )
& ( function(esk387_1(X3351))
| X3356 != singleton(esk386_1(X3351))
| esk385_1(X3351) = singleton(esk383_1(X3351)) )
& ( relation_dom(esk387_1(X3351)) = X3351
| X3356 != singleton(esk386_1(X3351))
| esk385_1(X3351) = singleton(esk383_1(X3351)) )
& ( ~ in(X3358,X3351)
| apply(esk387_1(X3351),X3358) = singleton(X3358)
| X3356 != singleton(esk386_1(X3351))
| esk385_1(X3351) = singleton(esk383_1(X3351)) )
& ( relation(esk387_1(X3351))
| in(esk386_1(X3351),X3351)
| esk384_1(X3351) != esk385_1(X3351) )
& ( function(esk387_1(X3351))
| in(esk386_1(X3351),X3351)
| esk384_1(X3351) != esk385_1(X3351) )
& ( relation_dom(esk387_1(X3351)) = X3351
| in(esk386_1(X3351),X3351)
| esk384_1(X3351) != esk385_1(X3351) )
& ( ~ in(X3358,X3351)
| apply(esk387_1(X3351),X3358) = singleton(X3358)
| in(esk386_1(X3351),X3351)
| esk384_1(X3351) != esk385_1(X3351) )
& ( relation(esk387_1(X3351))
| X3356 != singleton(esk386_1(X3351))
| esk384_1(X3351) != esk385_1(X3351) )
& ( function(esk387_1(X3351))
| X3356 != singleton(esk386_1(X3351))
| esk384_1(X3351) != esk385_1(X3351) )
& ( relation_dom(esk387_1(X3351)) = X3351
| X3356 != singleton(esk386_1(X3351))
| esk384_1(X3351) != esk385_1(X3351) )
& ( ~ in(X3358,X3351)
| apply(esk387_1(X3351),X3358) = singleton(X3358)
| X3356 != singleton(esk386_1(X3351))
| esk384_1(X3351) != esk385_1(X3351) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[s2_funct_1__e16_22__wellord2__1])])])])]) ).
fof(i_0_829,plain,
! [X3020,X3025,X3027,X3028] :
( ( in(esk234_2(X3020,X3025),X3020)
| ~ in(X3025,esk233_1(X3020))
| in(esk230_1(X3020),X3020) )
& ( X3025 = singleton(esk234_2(X3020,X3025))
| ~ in(X3025,esk233_1(X3020))
| in(esk230_1(X3020),X3020) )
& ( ~ in(X3028,X3020)
| X3027 != singleton(X3028)
| in(X3027,esk233_1(X3020))
| in(esk230_1(X3020),X3020) )
& ( in(esk234_2(X3020,X3025),X3020)
| ~ in(X3025,esk233_1(X3020))
| esk231_1(X3020) = singleton(esk230_1(X3020)) )
& ( X3025 = singleton(esk234_2(X3020,X3025))
| ~ in(X3025,esk233_1(X3020))
| esk231_1(X3020) = singleton(esk230_1(X3020)) )
& ( ~ in(X3028,X3020)
| X3027 != singleton(X3028)
| in(X3027,esk233_1(X3020))
| esk231_1(X3020) = singleton(esk230_1(X3020)) )
& ( in(esk234_2(X3020,X3025),X3020)
| ~ in(X3025,esk233_1(X3020))
| in(esk230_1(X3020),X3020) )
& ( X3025 = singleton(esk234_2(X3020,X3025))
| ~ in(X3025,esk233_1(X3020))
| in(esk230_1(X3020),X3020) )
& ( ~ in(X3028,X3020)
| X3027 != singleton(X3028)
| in(X3027,esk233_1(X3020))
| in(esk230_1(X3020),X3020) )
& ( in(esk234_2(X3020,X3025),X3020)
| ~ in(X3025,esk233_1(X3020))
| esk232_1(X3020) = singleton(esk230_1(X3020)) )
& ( X3025 = singleton(esk234_2(X3020,X3025))
| ~ in(X3025,esk233_1(X3020))
| esk232_1(X3020) = singleton(esk230_1(X3020)) )
& ( ~ in(X3028,X3020)
| X3027 != singleton(X3028)
| in(X3027,esk233_1(X3020))
| esk232_1(X3020) = singleton(esk230_1(X3020)) )
& ( in(esk234_2(X3020,X3025),X3020)
| ~ in(X3025,esk233_1(X3020))
| esk231_1(X3020) != esk232_1(X3020) )
& ( X3025 = singleton(esk234_2(X3020,X3025))
| ~ in(X3025,esk233_1(X3020))
| esk231_1(X3020) != esk232_1(X3020) )
& ( ~ in(X3028,X3020)
| X3027 != singleton(X3028)
| in(X3027,esk233_1(X3020))
| esk231_1(X3020) != esk232_1(X3020) ) ),
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)],[i_0_671])])])])])]) ).
fof(i_0_830,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( relation_isomorphism(X1,X2,X3)
=> epred3_2(X2,X1) ) ) ) ),
inference(apply_def,[status(thm)],[t53_wellord1,c_0_672]) ).
fof(i_0_831,lemma,
! [X2747,X2748,X2749] :
( ~ subset(X2747,X2748)
| in(X2749,X2747)
| subset(X2747,set_difference(X2748,singleton(X2749))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l3_zfmisc_1])]) ).
fof(i_0_832,plain,
! [X2580] : ~ empty(succ(X2580)),
inference(variable_rename,[status(thm)],[i_0_673]) ).
fof(i_0_833,lemma,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( element(X2,powerset(powerset(the_carrier(X1))))
=> ~ ( is_a_cover_of_carrier(X1,X2)
& X2 = empty_set ) ) ),
inference(fof_simplification,[status(thm)],[t5_tops_2]) ).
fof(i_0_834,plain,
! [X1,X2] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1)
& element(X2,the_carrier(poset_of_lattice(X1))) )
=> element(cast_to_el_of_lattice(X1,X2),the_carrier(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k5_lattice3]) ).
fof(i_0_835,plain,
! [X2355,X2356] :
( ~ relation(X2355)
| relation_restriction(X2355,X2356) = set_intersection2(X2355,cartesian_product2(X2356,X2356)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d6_wellord1])])]) ).
fof(i_0_836,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)],[t50_subset_1]) ).
fof(i_0_837,plain,
! [X1,X2] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1)
& element(X2,the_carrier(X1)) )
=> element(cast_to_el_of_LattPOSet(X1,X2),the_carrier(poset_of_lattice(X1))) ),
inference(fof_simplification,[status(thm)],[dt_k4_lattice3]) ).
fof(i_0_838,lemma,
! [X3863,X3864] :
( ~ subset(singleton(X3863),singleton(X3864))
| X3863 = X3864 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_zfmisc_1])]) ).
fof(i_0_839,plain,
! [X2091,X2092,X2093,X2094,X2095,X2096] :
( ( ~ in(X2093,X2092)
| X2093 = X2091
| X2092 != singleton(X2091) )
& ( X2094 != X2091
| in(X2094,X2092)
| X2092 != singleton(X2091) )
& ( ~ in(esk44_2(X2095,X2096),X2096)
| esk44_2(X2095,X2096) != X2095
| X2096 = singleton(X2095) )
& ( in(esk44_2(X2095,X2096),X2096)
| esk44_2(X2095,X2096) = X2095
| X2096 = singleton(X2095) ) ),
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)],[d1_tarski])])])])])]) ).
fof(i_0_840,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)],[t28_wellord2]) ).
fof(i_0_841,plain,
! [X2582,X2583] :
( ~ relation(X2582)
| ~ relation(X2583)
| relation(set_intersection2(X2582,X2583)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc1_relat_1])]) ).
fof(i_0_842,lemma,
! [X3437,X3438] :
( ~ relation(X3438)
| relation_rng(relation_rng_restriction(X3437,X3438)) = set_intersection2(relation_rng(X3438),X3437) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t119_relat_1])]) ).
fof(i_0_843,lemma,
! [X3909,X3910] :
( ~ relation(X3910)
| relation_dom(relation_dom_restriction(X3910,X3909)) = set_intersection2(relation_dom(X3910),X3909) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t90_relat_1])]) ).
fof(i_0_844,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)],[t9_tarski]) ).
fof(i_0_845,lemma,
! [X3524,X3525] : subset(set_intersection2(X3524,X3525),X3524),
inference(variable_rename,[status(thm)],[t17_xboole_1]) ).
fof(i_0_846,lemma,
! [X3418] : in(X3418,succ(X3418)),
inference(variable_rename,[status(thm)],[t10_ordinal1]) ).
fof(i_0_847,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ( reflexive(k2_lattice3(X1))
& antisymmetric(k2_lattice3(X1))
& transitive(k2_lattice3(X1))
& v1_partfun1(k2_lattice3(X1),the_carrier(X1),the_carrier(X1))
& relation_of2_as_subset(k2_lattice3(X1),the_carrier(X1),the_carrier(X1)) ) ),
inference(fof_simplification,[status(thm)],[dt_k2_lattice3]) ).
fof(i_0_848,lemma,
! [X3489,X3490] :
( ~ finite(X3489)
| finite(set_intersection2(X3489,X3490)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t15_finset_1])]) ).
fof(i_0_849,plain,
! [X2564,X2565] :
( ~ finite(X2564)
| finite(set_intersection2(X2564,X2565)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc11_finset_1])]) ).
fof(i_0_850,plain,
! [X2560,X2561] :
( ~ finite(X2561)
| finite(set_intersection2(X2560,X2561)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc10_finset_1])]) ).
fof(i_0_851,plain,
! [X2618,X2619] :
( ( v1_membered(set_intersection2(X2618,X2619))
| ~ v5_membered(X2618) )
& ( v2_membered(set_intersection2(X2618,X2619))
| ~ v5_membered(X2618) )
& ( v3_membered(set_intersection2(X2618,X2619))
| ~ v5_membered(X2618) )
& ( v4_membered(set_intersection2(X2618,X2619))
| ~ v5_membered(X2618) )
& ( v5_membered(set_intersection2(X2618,X2619))
| ~ v5_membered(X2618) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc35_membered])])]) ).
fof(i_0_852,plain,
! [X2620,X2621] :
( ( v1_membered(set_intersection2(X2621,X2620))
| ~ v5_membered(X2620) )
& ( v2_membered(set_intersection2(X2621,X2620))
| ~ v5_membered(X2620) )
& ( v3_membered(set_intersection2(X2621,X2620))
| ~ v5_membered(X2620) )
& ( v4_membered(set_intersection2(X2621,X2620))
| ~ v5_membered(X2620) )
& ( v5_membered(set_intersection2(X2621,X2620))
| ~ v5_membered(X2620) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc36_membered])])]) ).
fof(i_0_853,plain,
! [X2614,X2615] :
( ( v1_membered(set_intersection2(X2614,X2615))
| ~ v4_membered(X2614) )
& ( v2_membered(set_intersection2(X2614,X2615))
| ~ v4_membered(X2614) )
& ( v3_membered(set_intersection2(X2614,X2615))
| ~ v4_membered(X2614) )
& ( v4_membered(set_intersection2(X2614,X2615))
| ~ v4_membered(X2614) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc33_membered])])]) ).
fof(i_0_854,plain,
! [X2616,X2617] :
( ( v1_membered(set_intersection2(X2617,X2616))
| ~ v4_membered(X2616) )
& ( v2_membered(set_intersection2(X2617,X2616))
| ~ v4_membered(X2616) )
& ( v3_membered(set_intersection2(X2617,X2616))
| ~ v4_membered(X2616) )
& ( v4_membered(set_intersection2(X2617,X2616))
| ~ v4_membered(X2616) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc34_membered])])]) ).
fof(i_0_855,plain,
! [X2610,X2611] :
( ( v1_membered(set_intersection2(X2610,X2611))
| ~ v3_membered(X2610) )
& ( v2_membered(set_intersection2(X2610,X2611))
| ~ v3_membered(X2610) )
& ( v3_membered(set_intersection2(X2610,X2611))
| ~ v3_membered(X2610) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc31_membered])])]) ).
fof(i_0_856,plain,
! [X2612,X2613] :
( ( v1_membered(set_intersection2(X2613,X2612))
| ~ v3_membered(X2612) )
& ( v2_membered(set_intersection2(X2613,X2612))
| ~ v3_membered(X2612) )
& ( v3_membered(set_intersection2(X2613,X2612))
| ~ v3_membered(X2612) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc32_membered])])]) ).
fof(i_0_857,plain,
! [X2592,X2593] :
( ( v1_membered(set_intersection2(X2592,X2593))
| ~ v2_membered(X2592) )
& ( v2_membered(set_intersection2(X2592,X2593))
| ~ v2_membered(X2592) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc29_membered])])]) ).
fof(i_0_858,plain,
! [X2608,X2609] :
( ( v1_membered(set_intersection2(X2609,X2608))
| ~ v2_membered(X2608) )
& ( v2_membered(set_intersection2(X2609,X2608))
| ~ v2_membered(X2608) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc30_membered])])]) ).
fof(i_0_859,plain,
! [X2588,X2589] :
( ~ v1_membered(X2588)
| v1_membered(set_intersection2(X2588,X2589)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc27_membered])]) ).
fof(i_0_860,plain,
! [X2590,X2591] :
( ~ v1_membered(X2590)
| v1_membered(set_intersection2(X2591,X2590)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc28_membered])]) ).
fof(i_0_861,lemma,
! [X3847,X3848] :
( ( set_difference(X3847,singleton(X3848)) != X3847
| ~ in(X3848,X3847) )
& ( in(X3848,X3847)
| set_difference(X3847,singleton(X3848)) = X3847 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_674])]) ).
fof(i_0_862,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)],[l30_wellord2]) ).
fof(i_0_863,lemma,
! [X3729,X3731] :
( ( ordinal(esk428_1(X3729))
| being_limit_ordinal(X3729)
| ~ ordinal(X3729) )
& ( X3729 = succ(esk428_1(X3729))
| being_limit_ordinal(X3729)
| ~ ordinal(X3729) )
& ( ~ ordinal(X3731)
| X3729 != succ(X3731)
| ~ being_limit_ordinal(X3729)
| ~ ordinal(X3729) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_675])])])])]) ).
fof(i_0_864,lemma,
! [X2719,X2720] :
( ~ disjoint(singleton(X2719),X2720)
| ~ in(X2719,X2720) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l25_zfmisc_1])]) ).
fof(i_0_865,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(poset_of_lattice(X1)))
=> cast_to_el_of_lattice(X1,X2) = X2 ) ),
inference(fof_simplification,[status(thm)],[d4_lattice3]) ).
fof(i_0_866,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)],[d3_ordinal1]) ).
fof(i_0_867,lemma,
! [X3707,X3708] :
( ( ~ subset(X3707,singleton(X3708))
| X3707 = empty_set
| X3707 = singleton(X3708) )
& ( X3707 != empty_set
| subset(X3707,singleton(X3708)) )
& ( X3707 != singleton(X3708)
| subset(X3707,singleton(X3708)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t39_zfmisc_1])])]) ).
fof(i_0_868,lemma,
! [X2758,X2759] :
( ( ~ subset(X2758,singleton(X2759))
| X2758 = empty_set
| X2758 = singleton(X2759) )
& ( X2758 != empty_set
| subset(X2758,singleton(X2759)) )
& ( X2758 != singleton(X2759)
| subset(X2758,singleton(X2759)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l4_zfmisc_1])])]) ).
fof(i_0_869,plain,
! [X1884,X1885] : set_intersection2(X1884,X1885) = set_intersection2(X1885,X1884),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(i_0_870,lemma,
! [X3698,X3699] :
( ( ~ subset(singleton(X3698),X3699)
| in(X3698,X3699) )
& ( ~ in(X3698,X3699)
| subset(singleton(X3698),X3699) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t37_zfmisc_1])]) ).
fof(i_0_871,lemma,
! [X2732,X2733] :
( ( ~ subset(singleton(X2732),X2733)
| in(X2732,X2733) )
& ( ~ in(X2732,X2733)
| subset(singleton(X2732),X2733) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l2_zfmisc_1])]) ).
fof(i_0_872,plain,
! [X2374,X2375] :
( ( ~ disjoint(X2374,X2375)
| set_intersection2(X2374,X2375) = empty_set )
& ( set_intersection2(X2374,X2375) != empty_set
| disjoint(X2374,X2375) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_xboole_0])]) ).
fof(i_0_873,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)],[t136_zfmisc_1]) ).
fof(i_0_874,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)],[t3_xboole_0]) ).
fof(i_0_875,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> cast_to_el_of_LattPOSet(X1,X2) = X2 ) ),
inference(fof_simplification,[status(thm)],[d3_lattice3]) ).
fof(i_0_876,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& latt_str(X1) )
=> ! [X2] : meet_of_latt_set(X1,X2) = join_of_latt_set(X1,a_2_2_lattice3(X1,X2)) ),
inference(fof_simplification,[status(thm)],[d22_lattice3]) ).
fof(i_0_877,lemma,
! [X3764,X3765] :
( ~ in(X3764,X3765)
| set_union2(singleton(X3764),X3765) = X3765 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t46_zfmisc_1])]) ).
fof(i_0_878,lemma,
! [X2717,X2718] :
( ~ in(X2717,X2718)
| set_union2(singleton(X2717),X2718) = X2718 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l23_zfmisc_1])]) ).
fof(i_0_879,lemma,
! [X3630,X3631] :
( ~ subset(X3630,X3631)
| set_intersection2(X3630,X3631) = X3630 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t28_xboole_1])]) ).
fof(i_0_880,plain,
! [X2505] :
( v1_partfun1(identity_as_relation_of(X2505),X2505,X2505)
& relation_of2_as_subset(identity_as_relation_of(X2505),X2505,X2505) ),
inference(variable_rename,[status(thm)],[dt_k6_partfun1]) ).
fof(i_0_881,plain,
! [X2863] : identity_as_relation_of(X2863) = identity_relation(X2863),
inference(variable_rename,[status(thm)],[redefinition_k6_partfun1]) ).
fof(i_0_882,plain,
! [X1] :
( latt_str(X1)
=> ( ( ~ empty_carrier(X1)
& join_commutative(X1)
& join_associative(X1)
& meet_commutative(X1)
& meet_associative(X1)
& meet_absorbing(X1)
& join_absorbing(X1) )
=> ( ~ empty_carrier(X1)
& lattice(X1) ) ) ),
inference(fof_simplification,[status(thm)],[cc2_lattices]) ).
fof(i_0_883,plain,
! [X1,X2] :
( ( ~ empty_carrier(X1)
& latt_str(X1) )
=> element(meet_of_latt_set(X1,X2),the_carrier(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k16_lattice3]) ).
fof(i_0_884,plain,
! [X1,X2] :
( ( ~ empty_carrier(X1)
& latt_str(X1) )
=> element(join_of_latt_set(X1,X2),the_carrier(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k15_lattice3]) ).
fof(i_0_885,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1) )
=> ? [X2] :
( element(X2,powerset(the_carrier(X1)))
& ~ empty(X2)
& closed_subset(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[rc7_pre_topc]) ).
fof(i_0_886,plain,
! [X1,X2] :
( ( ~ empty(X1)
& ~ empty(X2) )
=> ~ empty(cartesian_product2(X1,X2)) ),
inference(fof_simplification,[status(thm)],[fc4_subset_1]) ).
fof(i_0_887,lemma,
! [X3397,X3399] :
( relation(esk405_1(X3397))
& function(esk405_1(X3397))
& relation_dom(esk405_1(X3397)) = X3397
& ( ~ in(X3399,X3397)
| apply(esk405_1(X3397),X3399) = singleton(X3399) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[s3_funct_1__e16_22__wellord2])])])]) ).
fof(i_0_888,lemma,
! [X2721,X2722] :
( in(X2721,X2722)
| disjoint(singleton(X2721),X2722) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_676])]) ).
fof(i_0_889,plain,
! [X1,X2] :
( ( ~ empty_carrier(X1)
& latt_str(X1)
& ~ empty_carrier(X2)
& latt_str(X2) )
=> ( strict_latt_str(k8_filter_1(X1,X2))
& latt_str(k8_filter_1(X1,X2)) ) ),
inference(fof_simplification,[status(thm)],[dt_k8_filter_1]) ).
fof(i_0_890,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X1,X2)) ),
inference(fof_simplification,[status(thm)],[fc2_xboole_0]) ).
fof(i_0_891,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X2,X1)) ),
inference(fof_simplification,[status(thm)],[fc3_xboole_0]) ).
fof(i_0_892,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ? [X2] :
( element(X2,powerset(the_carrier(X1)))
& ~ empty(X2) ) ),
inference(fof_simplification,[status(thm)],[rc5_struct_0]) ).
fof(i_0_893,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> poset_of_lattice(X1) = rel_str_of(the_carrier(X1),k2_lattice3(X1)) ),
inference(fof_simplification,[status(thm)],[d2_lattice3]) ).
fof(i_0_894,plain,
! [X2603] : ~ empty(singleton(X2603)),
inference(variable_rename,[status(thm)],[i_0_677]) ).
fof(i_0_895,plain,
! [X2573] :
( ~ empty(singleton(X2573))
& finite(singleton(X2573)) ),
inference(variable_rename,[status(thm)],[i_0_678]) ).
fof(i_0_896,plain,
! [X1,X2] : ~ empty(unordered_pair(X1,X2)),
inference(fof_simplification,[status(thm)],[fc3_subset_1]) ).
fof(i_0_897,lemma,
! [X3906,X3907,X3908] :
( singleton(X3906) != unordered_pair(X3907,X3908)
| X3906 = X3907 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_zfmisc_1])]) ).
fof(i_0_898,lemma,
! [X3932,X3933,X3934] :
( singleton(X3932) != unordered_pair(X3933,X3934)
| X3933 = X3934 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t9_zfmisc_1])]) ).
fof(i_0_899,lemma,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ~ ( ~ in(X1,X2)
& X1 != X2
& ~ in(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[t24_ordinal1]) ).
fof(i_0_900,plain,
! [X1,X2] :
( proper_subset(X1,X2)
=> ~ proper_subset(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_xboole_0]) ).
fof(i_0_901,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(i_0_902,lemma,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& complete_latt_str(X1)
& latt_str(X1) )
=> ( ~ empty_carrier(X1)
& lattice(X1)
& lower_bounded_semilattstr(X1)
& latt_str(X1)
& bottom_of_semilattstr(X1) = join_of_latt_set(X1,empty_set) ) ),
inference(fof_simplification,[status(thm)],[t50_lattice3]) ).
fof(i_0_903,plain,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& ~ proper_element(X2,powerset(X1)) ),
inference(fof_simplification,[status(thm)],[rc2_tex_2]) ).
fof(i_0_904,plain,
! [X1,X2] :
( ( ~ empty(X1)
=> ( element(X2,X1)
<=> in(X2,X1) ) )
& ( empty(X1)
=> ( element(X2,X1)
<=> empty(X2) ) ) ),
inference(fof_simplification,[status(thm)],[d2_subset_1]) ).
fof(i_0_905,plain,
! [X2700] : set_intersection2(X2700,X2700) = X2700,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k3_xboole_0])]) ).
fof(i_0_906,plain,
! [X2454] : element(k1_pcomps_1(X2454),powerset(powerset(X2454))),
inference(variable_rename,[status(thm)],[dt_k1_pcomps_1]) ).
fof(i_0_907,plain,
! [X2835] : k1_pcomps_1(X2835) = powerset(X2835),
inference(variable_rename,[status(thm)],[redefinition_k1_pcomps_1]) ).
fof(i_0_908,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& meet_semilatt_str(X1) )
=> element(bottom_of_semilattstr(X1),the_carrier(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k5_lattices]) ).
fof(i_0_909,plain,
! [X3637] : set_intersection2(X3637,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[t2_boole]) ).
fof(i_0_910,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ( ~ empty_carrier(poset_of_lattice(X1))
& strict_rel_str(poset_of_lattice(X1))
& reflexive_relstr(poset_of_lattice(X1))
& transitive_relstr(poset_of_lattice(X1))
& antisymmetric_relstr(poset_of_lattice(X1)) ) ),
inference(fof_simplification,[status(thm)],[fc4_lattice3]) ).
fof(i_0_911,plain,
! [X1,X2] :
( epred3_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)],[i_0_672]) ).
fof(i_0_912,plain,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2)
& finite(X2) ) ),
inference(fof_simplification,[status(thm)],[rc4_finset_1]) ).
fof(i_0_913,plain,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2)
& finite(X2) ) ),
inference(fof_simplification,[status(thm)],[rc3_finset_1]) ).
fof(i_0_914,plain,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
inference(fof_simplification,[status(thm)],[rc1_subset_1]) ).
fof(i_0_915,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ( strict_rel_str(poset_of_lattice(X1))
& reflexive_relstr(poset_of_lattice(X1))
& transitive_relstr(poset_of_lattice(X1))
& antisymmetric_relstr(poset_of_lattice(X1))
& rel_str(poset_of_lattice(X1)) ) ),
inference(fof_simplification,[status(thm)],[dt_k3_lattice3]) ).
fof(i_0_916,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> relation(relation_of_lattice(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k9_filter_1]) ).
fof(i_0_917,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ~ empty(cast_as_carrier_subset(X1)) ),
inference(fof_simplification,[status(thm)],[fc2_pre_topc]) ).
fof(i_0_918,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ~ empty(the_carrier(X1)) ),
inference(fof_simplification,[status(thm)],[fc1_struct_0]) ).
fof(i_0_919,plain,
! [X1] :
( ( ~ empty(X1)
& relation(X1) )
=> ~ empty(relation_rng(X1)) ),
inference(fof_simplification,[status(thm)],[fc6_relat_1]) ).
fof(i_0_920,plain,
! [X1] :
( ( ~ empty(X1)
& relation(X1) )
=> ~ empty(relation_dom(X1)) ),
inference(fof_simplification,[status(thm)],[fc5_relat_1]) ).
fof(i_0_921,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> relation_of_lattice(X1) = a_1_0_filter_1(X1) ),
inference(fof_simplification,[status(thm)],[d8_filter_1]) ).
fof(i_0_922,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> k2_lattice3(X1) = relation_of_lattice(X1) ),
inference(fof_simplification,[status(thm)],[redefinition_k2_lattice3]) ).
fof(i_0_923,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
fof(i_0_924,plain,
! [X1] :
( latt_str(X1)
=> ( ( ~ empty_carrier(X1)
& lattice(X1) )
=> ( ~ empty_carrier(X1)
& join_commutative(X1)
& join_associative(X1)
& meet_commutative(X1)
& meet_associative(X1)
& meet_absorbing(X1)
& join_absorbing(X1) ) ) ),
inference(fof_simplification,[status(thm)],[cc1_lattices]) ).
fof(i_0_925,plain,
! [X1,X2] : ~ proper_subset(X1,X1),
inference(fof_simplification,[status(thm)],[irreflexivity_r2_xboole_0]) ).
fof(i_0_926,lemma,
! [X2716] : singleton(X2716) != empty_set,
inference(variable_rename,[status(thm)],[l1_zfmisc_1]) ).
fof(i_0_927,plain,
! [X1907] :
( ~ one_sorted_str(X1907)
| identity_on_carrier(X1907) = identity_as_relation_of(the_carrier(X1907)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d11_grcat_1])]) ).
fof(i_0_928,plain,
! [X2471] : element(cast_to_subset(X2471),powerset(X2471)),
inference(variable_rename,[status(thm)],[dt_k2_subset_1]) ).
fof(i_0_929,plain,
! [X1] :
( ~ empty_carrier(boole_lattice(X1))
& strict_latt_str(boole_lattice(X1))
& join_commutative(boole_lattice(X1))
& join_associative(boole_lattice(X1))
& meet_commutative(boole_lattice(X1))
& meet_associative(boole_lattice(X1))
& meet_absorbing(boole_lattice(X1))
& join_absorbing(boole_lattice(X1))
& lattice(boole_lattice(X1)) ),
inference(fof_simplification,[status(thm)],[fc2_lattice3]) ).
fof(i_0_930,plain,
! [X1] :
( ~ empty_carrier(boole_lattice(X1))
& strict_latt_str(boole_lattice(X1)) ),
inference(fof_simplification,[status(thm)],[fc1_lattice3]) ).
fof(i_0_931,plain,
! [X1] : ~ empty(powerset(X1)),
inference(fof_simplification,[status(thm)],[fc1_subset_1]) ).
fof(i_0_932,plain,
! [X1] :
( ~ empty(powerset(X1))
& cup_closed(powerset(X1))
& diff_closed(powerset(X1))
& preboolean(powerset(X1)) ),
inference(fof_simplification,[status(thm)],[fc1_finsub_1]) ).
fof(i_0_933,plain,
? [X1] :
( latt_str(X1)
& ~ empty_carrier(X1)
& strict_latt_str(X1)
& join_commutative(X1)
& join_associative(X1)
& meet_commutative(X1)
& meet_associative(X1)
& meet_absorbing(X1)
& join_absorbing(X1)
& lattice(X1) ),
inference(fof_simplification,[status(thm)],[rc9_lattices]) ).
fof(i_0_934,plain,
? [X1] :
( latt_str(X1)
& ~ empty_carrier(X1)
& strict_latt_str(X1) ),
inference(fof_simplification,[status(thm)],[rc6_lattices]) ).
fof(i_0_935,plain,
? [X1] :
( one_sorted_str(X1)
& ~ empty_carrier(X1) ),
inference(fof_simplification,[status(thm)],[rc3_struct_0]) ).
fof(i_0_936,plain,
? [X1] :
( rel_str(X1)
& ~ empty_carrier(X1)
& strict_rel_str(X1)
& reflexive_relstr(X1)
& transitive_relstr(X1)
& antisymmetric_relstr(X1) ),
inference(fof_simplification,[status(thm)],[rc2_orders_2]) ).
fof(i_0_937,plain,
? [X1] :
( ~ empty(X1)
& epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
inference(fof_simplification,[status(thm)],[rc3_ordinal1]) ).
fof(i_0_938,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).
fof(i_0_939,plain,
? [X1] :
( ~ empty(X1)
& relation(X1) ),
inference(fof_simplification,[status(thm)],[rc2_relat_1]) ).
fof(i_0_940,plain,
? [X1] :
( ~ empty(X1)
& v1_membered(X1)
& v2_membered(X1)
& v3_membered(X1)
& v4_membered(X1)
& v5_membered(X1) ),
inference(fof_simplification,[status(thm)],[rc1_membered]) ).
fof(i_0_941,plain,
? [X1] :
( ~ empty(X1)
& finite(X1) ),
inference(fof_simplification,[status(thm)],[rc1_finset_1]) ).
fof(i_0_942,plain,
? [X1] :
( ~ empty(X1)
& epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1)
& natural(X1) ),
inference(fof_simplification,[status(thm)],[rc1_arytm_3]) ).
cnf(i_0_943,plain,
( in(X5,esk224_3(X2,X3,X4))
| in(ordered_pair(esk222_2(X2,X3),X9),X3)
| empty(X2)
| ~ in(ordered_pair(X1,esk229_7(X2,X3,X4,X5,X6,X1,X7)),X3)
| X6 != X7
| ~ in(X1,X7)
| ordered_pair(X6,X1) != X5
| ~ in(X6,X2)
| ~ in(X8,cartesian_product2(X2,X4))
| X8 != X5
| ~ in(X9,esk223_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_944,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),
inference(rw,[status(thm)],[i_0_680,c_0_681]) ).
cnf(i_0_945,plain,
( in(X5,esk224_3(X2,X3,X4))
| in(ordered_pair(esk219_2(X2,X3),X9),X3)
| empty(X2)
| ~ in(ordered_pair(X1,esk229_7(X2,X3,X4,X5,X6,X1,X7)),X3)
| X6 != X7
| ~ in(X1,X7)
| ordered_pair(X6,X1) != X5
| ~ in(X6,X2)
| ~ in(X8,cartesian_product2(X2,X4))
| X8 != X5
| ~ in(X9,esk220_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_946,plain,
( in(X5,esk224_3(X2,X3,X4))
| ordered_pair(esk221_2(X2,X3),esk222_2(X2,X3)) = esk217_2(X2,X3)
| empty(X2)
| ~ in(ordered_pair(X1,esk229_7(X2,X3,X4,X5,X6,X1,X7)),X3)
| X6 != X7
| ~ in(X1,X7)
| ordered_pair(X6,X1) != X5
| ~ in(X6,X2)
| ~ in(X8,cartesian_product2(X2,X4))
| X8 != X5
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_947,plain,
( in(X5,esk224_3(X2,X3,X4))
| ordered_pair(esk218_2(X2,X3),esk219_2(X2,X3)) = esk216_2(X2,X3)
| empty(X2)
| ~ in(ordered_pair(X1,esk229_7(X2,X3,X4,X5,X6,X1,X7)),X3)
| X6 != X7
| ~ in(X1,X7)
| ordered_pair(X6,X1) != X5
| ~ in(X6,X2)
| ~ in(X8,cartesian_product2(X2,X4))
| X8 != X5
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_948,plain,
( in(X5,esk224_3(X2,X3,X4))
| in(esk222_2(X2,X3),esk223_2(X2,X3))
| empty(X2)
| ~ in(ordered_pair(X1,esk229_7(X2,X3,X4,X5,X6,X1,X7)),X3)
| X6 != X7
| ~ in(X1,X7)
| ordered_pair(X6,X1) != X5
| ~ in(X6,X2)
| ~ in(X8,cartesian_product2(X2,X4))
| X8 != X5
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_949,plain,
( in(X5,esk224_3(X2,X3,X4))
| in(esk219_2(X2,X3),esk220_2(X2,X3))
| empty(X2)
| ~ in(ordered_pair(X1,esk229_7(X2,X3,X4,X5,X6,X1,X7)),X3)
| X6 != X7
| ~ in(X1,X7)
| ordered_pair(X6,X1) != X5
| ~ in(X6,X2)
| ~ in(X8,cartesian_product2(X2,X4))
| X8 != X5
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_950,plain,
( in(X5,esk224_3(X2,X3,X4))
| empty(X2)
| ~ in(ordered_pair(X1,esk229_7(X2,X3,X4,X5,X6,X1,X7)),X3)
| X6 != X7
| ~ in(X1,X7)
| ordered_pair(X6,X1) != X5
| ~ in(X6,X2)
| ~ in(X8,cartesian_product2(X2,X4))
| X8 != X5
| esk216_2(X2,X3) != esk217_2(X2,X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_951,plain,
( in(X5,esk224_3(X2,X3,X4))
| in(esk221_2(X2,X3),X2)
| empty(X2)
| ~ in(ordered_pair(X1,esk229_7(X2,X3,X4,X5,X6,X1,X7)),X3)
| X6 != X7
| ~ in(X1,X7)
| ordered_pair(X6,X1) != X5
| ~ in(X6,X2)
| ~ in(X8,cartesian_product2(X2,X4))
| X8 != X5
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_952,plain,
( in(X5,esk224_3(X2,X3,X4))
| in(esk218_2(X2,X3),X2)
| empty(X2)
| ~ in(ordered_pair(X1,esk229_7(X2,X3,X4,X5,X6,X1,X7)),X3)
| X6 != X7
| ~ in(X1,X7)
| ordered_pair(X6,X1) != X5
| ~ in(X6,X2)
| ~ in(X8,cartesian_product2(X2,X4))
| X8 != X5
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_953,plain,
( in(X5,esk224_3(X2,X3,X4))
| esk221_2(X2,X3) = esk223_2(X2,X3)
| empty(X2)
| ~ in(ordered_pair(X1,esk229_7(X2,X3,X4,X5,X6,X1,X7)),X3)
| X6 != X7
| ~ in(X1,X7)
| ordered_pair(X6,X1) != X5
| ~ in(X6,X2)
| ~ in(X8,cartesian_product2(X2,X4))
| X8 != X5
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_954,plain,
( in(X5,esk224_3(X2,X3,X4))
| esk218_2(X2,X3) = esk220_2(X2,X3)
| empty(X2)
| ~ in(ordered_pair(X1,esk229_7(X2,X3,X4,X5,X6,X1,X7)),X3)
| X6 != X7
| ~ in(X1,X7)
| ordered_pair(X6,X1) != X5
| ~ in(X6,X2)
| ~ in(X8,cartesian_product2(X2,X4))
| X8 != X5
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_955,plain,
( in(X5,esk224_3(X2,X3,X4))
| esk215_2(X2,X3) = esk217_2(X2,X3)
| empty(X2)
| ~ in(ordered_pair(X1,esk229_7(X2,X3,X4,X5,X6,X1,X7)),X3)
| X6 != X7
| ~ in(X1,X7)
| ordered_pair(X6,X1) != X5
| ~ in(X6,X2)
| ~ in(X8,cartesian_product2(X2,X4))
| X8 != X5
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_956,plain,
( in(X5,esk224_3(X2,X3,X4))
| esk215_2(X2,X3) = esk216_2(X2,X3)
| empty(X2)
| ~ in(ordered_pair(X1,esk229_7(X2,X3,X4,X5,X6,X1,X7)),X3)
| X6 != X7
| ~ in(X1,X7)
| ordered_pair(X6,X1) != X5
| ~ in(X6,X2)
| ~ in(X8,cartesian_product2(X2,X4))
| X8 != X5
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_957,lemma,
( in(X5,esk341_3(X2,X3,X4))
| empty(X2)
| ~ in(ordered_pair(X1,esk345_7(X2,X3,X4,X5,X6,X1,X7)),X3)
| X6 != X7
| ~ in(X1,X7)
| ordered_pair(X6,X1) != X5
| ~ in(X6,X2)
| ~ in(X5,cartesian_product2(X2,X4))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_682]) ).
cnf(i_0_958,plain,
( in(esk229_7(X1,X2,X3,X4,X5,X6,X7),X7)
| in(X4,esk224_3(X1,X2,X3))
| in(ordered_pair(esk222_2(X1,X2),X9),X2)
| empty(X1)
| X5 != X7
| ~ in(X6,X7)
| ordered_pair(X5,X6) != X4
| ~ in(X5,X1)
| ~ in(X8,cartesian_product2(X1,X3))
| X8 != X4
| ~ in(X9,esk223_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_959,plain,
( in(esk229_7(X1,X2,X3,X4,X5,X6,X7),X7)
| in(X4,esk224_3(X1,X2,X3))
| in(ordered_pair(esk219_2(X1,X2),X9),X2)
| empty(X1)
| X5 != X7
| ~ in(X6,X7)
| ordered_pair(X5,X6) != X4
| ~ in(X5,X1)
| ~ in(X8,cartesian_product2(X1,X3))
| X8 != X4
| ~ in(X9,esk220_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_960,plain,
( in(esk229_7(X1,X2,X3,X4,X5,X6,X7),X7)
| in(X4,esk224_3(X1,X2,X3))
| ordered_pair(esk221_2(X1,X2),esk222_2(X1,X2)) = esk217_2(X1,X2)
| empty(X1)
| X5 != X7
| ~ in(X6,X7)
| ordered_pair(X5,X6) != X4
| ~ in(X5,X1)
| ~ in(X8,cartesian_product2(X1,X3))
| X8 != X4
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_961,plain,
( in(esk229_7(X1,X2,X3,X4,X5,X6,X7),X7)
| in(X4,esk224_3(X1,X2,X3))
| ordered_pair(esk218_2(X1,X2),esk219_2(X1,X2)) = esk216_2(X1,X2)
| empty(X1)
| X5 != X7
| ~ in(X6,X7)
| ordered_pair(X5,X6) != X4
| ~ in(X5,X1)
| ~ in(X8,cartesian_product2(X1,X3))
| X8 != X4
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_962,plain,
( in(esk229_7(X1,X2,X3,X4,X5,X6,X7),X7)
| in(X4,esk224_3(X1,X2,X3))
| in(esk222_2(X1,X2),esk223_2(X1,X2))
| empty(X1)
| X5 != X7
| ~ in(X6,X7)
| ordered_pair(X5,X6) != X4
| ~ in(X5,X1)
| ~ in(X8,cartesian_product2(X1,X3))
| X8 != X4
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_963,plain,
( in(esk229_7(X1,X2,X3,X4,X5,X6,X7),X7)
| in(X4,esk224_3(X1,X2,X3))
| in(esk219_2(X1,X2),esk220_2(X1,X2))
| empty(X1)
| X5 != X7
| ~ in(X6,X7)
| ordered_pair(X5,X6) != X4
| ~ in(X5,X1)
| ~ in(X8,cartesian_product2(X1,X3))
| X8 != X4
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_964,plain,
( in(esk229_7(X1,X2,X3,X4,X5,X6,X7),X7)
| in(X4,esk224_3(X1,X2,X3))
| empty(X1)
| X5 != X7
| ~ in(X6,X7)
| ordered_pair(X5,X6) != X4
| ~ in(X5,X1)
| ~ in(X8,cartesian_product2(X1,X3))
| X8 != X4
| esk216_2(X1,X2) != esk217_2(X1,X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_965,plain,
( in(esk229_7(X1,X2,X3,X4,X5,X6,X7),X7)
| in(X4,esk224_3(X1,X2,X3))
| in(esk221_2(X1,X2),X1)
| empty(X1)
| X5 != X7
| ~ in(X6,X7)
| ordered_pair(X5,X6) != X4
| ~ in(X5,X1)
| ~ in(X8,cartesian_product2(X1,X3))
| X8 != X4
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_966,plain,
( in(esk229_7(X1,X2,X3,X4,X5,X6,X7),X7)
| in(X4,esk224_3(X1,X2,X3))
| in(esk218_2(X1,X2),X1)
| empty(X1)
| X5 != X7
| ~ in(X6,X7)
| ordered_pair(X5,X6) != X4
| ~ in(X5,X1)
| ~ in(X8,cartesian_product2(X1,X3))
| X8 != X4
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_967,plain,
( in(esk229_7(X1,X2,X3,X4,X5,X6,X7),X7)
| in(X4,esk224_3(X1,X2,X3))
| esk221_2(X1,X2) = esk223_2(X1,X2)
| empty(X1)
| X5 != X7
| ~ in(X6,X7)
| ordered_pair(X5,X6) != X4
| ~ in(X5,X1)
| ~ in(X8,cartesian_product2(X1,X3))
| X8 != X4
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_968,plain,
( in(esk229_7(X1,X2,X3,X4,X5,X6,X7),X7)
| in(X4,esk224_3(X1,X2,X3))
| esk218_2(X1,X2) = esk220_2(X1,X2)
| empty(X1)
| X5 != X7
| ~ in(X6,X7)
| ordered_pair(X5,X6) != X4
| ~ in(X5,X1)
| ~ in(X8,cartesian_product2(X1,X3))
| X8 != X4
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_969,plain,
( in(esk229_7(X1,X2,X3,X4,X5,X6,X7),X7)
| in(X4,esk224_3(X1,X2,X3))
| esk215_2(X1,X2) = esk217_2(X1,X2)
| empty(X1)
| X5 != X7
| ~ in(X6,X7)
| ordered_pair(X5,X6) != X4
| ~ in(X5,X1)
| ~ in(X8,cartesian_product2(X1,X3))
| X8 != X4
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_970,plain,
( in(esk229_7(X1,X2,X3,X4,X5,X6,X7),X7)
| in(X4,esk224_3(X1,X2,X3))
| esk215_2(X1,X2) = esk216_2(X1,X2)
| empty(X1)
| X5 != X7
| ~ in(X6,X7)
| ordered_pair(X5,X6) != X4
| ~ in(X5,X1)
| ~ in(X8,cartesian_product2(X1,X3))
| X8 != X4
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_971,lemma,
( in(esk345_7(X1,X2,X3,X4,X5,X6,X7),X7)
| in(X4,esk341_3(X1,X2,X3))
| empty(X1)
| X5 != X7
| ~ in(X6,X7)
| ordered_pair(X5,X6) != X4
| ~ in(X5,X1)
| ~ in(X4,cartesian_product2(X1,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_682]) ).
cnf(i_0_972,plain,
( in(ordered_pair(esk106_5(X1,X2,X3,X4,X5),X5),X2)
| ~ in(ordered_pair(X4,X5),X3)
| X3 != relation_composition(X1,X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_683]) ).
cnf(i_0_973,plain,
( in(ordered_pair(apply(X1,esk321_4(X2,X3,X1,X4)),apply(X1,esk322_4(X2,X3,X1,X4))),X3)
| in(ordered_pair(apply(X1,esk317_3(X2,X3,X1)),apply(X1,esk318_3(X2,X3,X1))),X3)
| ~ in(X4,esk319_3(X2,X3,X1))
| ~ relation(X3)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_684]) ).
cnf(i_0_974,plain,
( in(ordered_pair(apply(X1,esk321_4(X2,X3,X1,X4)),apply(X1,esk322_4(X2,X3,X1,X4))),X3)
| in(ordered_pair(apply(X1,esk315_3(X2,X3,X1)),apply(X1,esk316_3(X2,X3,X1))),X3)
| ~ in(X4,esk319_3(X2,X3,X1))
| ~ relation(X3)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_684]) ).
cnf(i_0_975,plain,
( in(X5,esk289_3(X2,X3,X4))
| ordered_pair(esk287_2(X2,X3),esk288_2(X2,X3)) = esk284_2(X2,X3)
| X1 != subset_complement(the_carrier(X2),esk293_6(X2,X3,X4,X5,X6,X1))
| ordered_pair(X6,X1) != X5
| ~ in(X6,complements_of_subsets(the_carrier(X2),X3))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X2),X3),X4))
| X7 != X5
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]) ).
cnf(i_0_976,plain,
( in(X5,esk289_3(X2,X3,X4))
| ordered_pair(esk285_2(X2,X3),esk286_2(X2,X3)) = esk283_2(X2,X3)
| X1 != subset_complement(the_carrier(X2),esk293_6(X2,X3,X4,X5,X6,X1))
| ordered_pair(X6,X1) != X5
| ~ in(X6,complements_of_subsets(the_carrier(X2),X3))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X2),X3),X4))
| X7 != X5
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]) ).
cnf(i_0_977,plain,
( in(X5,esk289_3(X2,X3,X4))
| esk288_2(X2,X3) = subset_complement(the_carrier(X2),X8)
| X1 != subset_complement(the_carrier(X2),esk293_6(X2,X3,X4,X5,X6,X1))
| ordered_pair(X6,X1) != X5
| ~ in(X6,complements_of_subsets(the_carrier(X2),X3))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X2),X3),X4))
| X7 != X5
| ~ element(X8,powerset(the_carrier(X2)))
| X8 != esk287_2(X2,X3)
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]) ).
cnf(i_0_978,plain,
( in(X5,esk289_3(X2,X3,X4))
| esk286_2(X2,X3) = subset_complement(the_carrier(X2),X8)
| X1 != subset_complement(the_carrier(X2),esk293_6(X2,X3,X4,X5,X6,X1))
| ordered_pair(X6,X1) != X5
| ~ in(X6,complements_of_subsets(the_carrier(X2),X3))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X2),X3),X4))
| X7 != X5
| ~ element(X8,powerset(the_carrier(X2)))
| X8 != esk285_2(X2,X3)
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]) ).
cnf(i_0_979,plain,
( in(X5,esk307_3(X2,X3,X4))
| ordered_pair(esk305_2(X2,X3),esk306_2(X2,X3)) = esk302_2(X2,X3)
| X1 != subset_complement(the_carrier(X2),esk311_6(X2,X3,X4,X5,X6,X1))
| ordered_pair(X6,X1) != X5
| ~ in(X6,X3)
| ~ in(X7,cartesian_product2(X3,X4))
| X7 != X5
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]) ).
cnf(i_0_980,plain,
( in(X5,esk307_3(X2,X3,X4))
| ordered_pair(esk303_2(X2,X3),esk304_2(X2,X3)) = esk301_2(X2,X3)
| X1 != subset_complement(the_carrier(X2),esk311_6(X2,X3,X4,X5,X6,X1))
| ordered_pair(X6,X1) != X5
| ~ in(X6,X3)
| ~ in(X7,cartesian_product2(X3,X4))
| X7 != X5
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]) ).
cnf(i_0_981,plain,
( in(X5,esk289_3(X2,X3,X4))
| in(esk287_2(X2,X3),complements_of_subsets(the_carrier(X2),X3))
| X1 != subset_complement(the_carrier(X2),esk293_6(X2,X3,X4,X5,X6,X1))
| ordered_pair(X6,X1) != X5
| ~ in(X6,complements_of_subsets(the_carrier(X2),X3))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X2),X3),X4))
| X7 != X5
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]) ).
cnf(i_0_982,plain,
( in(X5,esk289_3(X2,X3,X4))
| in(esk285_2(X2,X3),complements_of_subsets(the_carrier(X2),X3))
| X1 != subset_complement(the_carrier(X2),esk293_6(X2,X3,X4,X5,X6,X1))
| ordered_pair(X6,X1) != X5
| ~ in(X6,complements_of_subsets(the_carrier(X2),X3))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X2),X3),X4))
| X7 != X5
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]) ).
cnf(i_0_983,plain,
( in(X5,esk289_3(X2,X3,X4))
| X1 != subset_complement(the_carrier(X2),esk293_6(X2,X3,X4,X5,X6,X1))
| ordered_pair(X6,X1) != X5
| ~ in(X6,complements_of_subsets(the_carrier(X2),X3))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X2),X3),X4))
| X7 != X5
| esk283_2(X2,X3) != esk284_2(X2,X3)
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]) ).
cnf(i_0_984,plain,
( in(X5,esk289_3(X2,X3,X4))
| esk282_2(X2,X3) = esk284_2(X2,X3)
| X1 != subset_complement(the_carrier(X2),esk293_6(X2,X3,X4,X5,X6,X1))
| ordered_pair(X6,X1) != X5
| ~ in(X6,complements_of_subsets(the_carrier(X2),X3))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X2),X3),X4))
| X7 != X5
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]) ).
cnf(i_0_985,plain,
( in(X5,esk289_3(X2,X3,X4))
| esk282_2(X2,X3) = esk283_2(X2,X3)
| X1 != subset_complement(the_carrier(X2),esk293_6(X2,X3,X4,X5,X6,X1))
| ordered_pair(X6,X1) != X5
| ~ in(X6,complements_of_subsets(the_carrier(X2),X3))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X2),X3),X4))
| X7 != X5
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]) ).
cnf(i_0_986,lemma,
( in(X5,esk359_3(X2,X3,X4))
| X1 != subset_complement(the_carrier(X2),esk362_6(X2,X3,X4,X5,X6,X1))
| ordered_pair(X6,X1) != X5
| ~ in(X6,complements_of_subsets(the_carrier(X2),X3))
| ~ in(X5,cartesian_product2(complements_of_subsets(the_carrier(X2),X3),X4))
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_687]) ).
cnf(i_0_987,plain,
( in(X5,esk307_3(X2,X3,X4))
| esk306_2(X2,X3) = subset_complement(the_carrier(X2),X8)
| X1 != subset_complement(the_carrier(X2),esk311_6(X2,X3,X4,X5,X6,X1))
| ordered_pair(X6,X1) != X5
| ~ in(X6,X3)
| ~ in(X7,cartesian_product2(X3,X4))
| X7 != X5
| ~ element(X8,powerset(the_carrier(X2)))
| X8 != esk305_2(X2,X3)
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]) ).
cnf(i_0_988,plain,
( in(X5,esk307_3(X2,X3,X4))
| esk304_2(X2,X3) = subset_complement(the_carrier(X2),X8)
| X1 != subset_complement(the_carrier(X2),esk311_6(X2,X3,X4,X5,X6,X1))
| ordered_pair(X6,X1) != X5
| ~ in(X6,X3)
| ~ in(X7,cartesian_product2(X3,X4))
| X7 != X5
| ~ element(X8,powerset(the_carrier(X2)))
| X8 != esk303_2(X2,X3)
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]) ).
cnf(i_0_989,plain,
( in(X5,esk307_3(X2,X3,X4))
| X1 != subset_complement(the_carrier(X2),esk311_6(X2,X3,X4,X5,X6,X1))
| ordered_pair(X6,X1) != X5
| ~ in(X6,X3)
| ~ in(X7,cartesian_product2(X3,X4))
| X7 != X5
| esk301_2(X2,X3) != esk302_2(X2,X3)
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]) ).
cnf(i_0_990,plain,
( in(X5,esk307_3(X2,X3,X4))
| in(esk305_2(X2,X3),X3)
| X1 != subset_complement(the_carrier(X2),esk311_6(X2,X3,X4,X5,X6,X1))
| ordered_pair(X6,X1) != X5
| ~ in(X6,X3)
| ~ in(X7,cartesian_product2(X3,X4))
| X7 != X5
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]) ).
cnf(i_0_991,plain,
( in(X5,esk307_3(X2,X3,X4))
| in(esk303_2(X2,X3),X3)
| X1 != subset_complement(the_carrier(X2),esk311_6(X2,X3,X4,X5,X6,X1))
| ordered_pair(X6,X1) != X5
| ~ in(X6,X3)
| ~ in(X7,cartesian_product2(X3,X4))
| X7 != X5
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]) ).
cnf(i_0_992,plain,
( in(X5,esk307_3(X2,X3,X4))
| esk300_2(X2,X3) = esk302_2(X2,X3)
| X1 != subset_complement(the_carrier(X2),esk311_6(X2,X3,X4,X5,X6,X1))
| ordered_pair(X6,X1) != X5
| ~ in(X6,X3)
| ~ in(X7,cartesian_product2(X3,X4))
| X7 != X5
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]) ).
cnf(i_0_993,plain,
( in(X5,esk307_3(X2,X3,X4))
| esk300_2(X2,X3) = esk301_2(X2,X3)
| X1 != subset_complement(the_carrier(X2),esk311_6(X2,X3,X4,X5,X6,X1))
| ordered_pair(X6,X1) != X5
| ~ in(X6,X3)
| ~ in(X7,cartesian_product2(X3,X4))
| X7 != X5
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]) ).
cnf(i_0_994,lemma,
( in(X5,esk363_3(X2,X3,X4))
| X1 != subset_complement(the_carrier(X2),esk366_6(X2,X3,X4,X5,X6,X1))
| ordered_pair(X6,X1) != X5
| ~ in(X6,X3)
| ~ in(X5,cartesian_product2(X3,X4))
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_688]) ).
cnf(i_0_995,plain,
( in(ordered_pair(apply(X1,esk321_4(X2,X3,X1,X4)),apply(X1,esk322_4(X2,X3,X1,X4))),X3)
| esk314_3(X2,X3,X1) = ordered_pair(esk317_3(X2,X3,X1),esk318_3(X2,X3,X1))
| ~ in(X4,esk319_3(X2,X3,X1))
| ~ relation(X3)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_684]) ).
cnf(i_0_996,plain,
( in(ordered_pair(apply(X1,esk321_4(X2,X3,X1,X4)),apply(X1,esk322_4(X2,X3,X1,X4))),X3)
| esk313_3(X2,X3,X1) = ordered_pair(esk315_3(X2,X3,X1),esk316_3(X2,X3,X1))
| ~ in(X4,esk319_3(X2,X3,X1))
| ~ relation(X3)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_684]) ).
cnf(i_0_997,plain,
( in(ordered_pair(apply(X1,esk321_4(X2,X3,X1,X4)),apply(X1,esk322_4(X2,X3,X1,X4))),X3)
| ~ in(X4,esk319_3(X2,X3,X1))
| esk313_3(X2,X3,X1) != esk314_3(X2,X3,X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_684]) ).
cnf(i_0_998,plain,
( in(ordered_pair(apply(X1,esk321_4(X2,X3,X1,X4)),apply(X1,esk322_4(X2,X3,X1,X4))),X3)
| esk312_3(X2,X3,X1) = esk314_3(X2,X3,X1)
| ~ in(X4,esk319_3(X2,X3,X1))
| ~ relation(X3)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_684]) ).
cnf(i_0_999,plain,
( in(ordered_pair(apply(X1,esk321_4(X2,X3,X1,X4)),apply(X1,esk322_4(X2,X3,X1,X4))),X3)
| esk312_3(X2,X3,X1) = esk313_3(X2,X3,X1)
| ~ in(X4,esk319_3(X2,X3,X1))
| ~ relation(X3)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_684]) ).
cnf(i_0_1000,lemma,
( in(ordered_pair(apply(X1,esk368_4(X2,X3,X1,X4)),apply(X1,esk369_4(X2,X3,X1,X4))),X3)
| ~ in(X4,esk367_3(X2,X3,X1))
| ~ relation(X3)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_689]) ).
cnf(i_0_1001,lemma,
( in(ordered_pair(X4,X1),esk182_2(X2,X3))
| in(ordered_pair(esk179_2(X2,X3),X6),X3)
| empty(X2)
| ~ in(ordered_pair(X1,esk184_5(X2,X3,X4,X1,X5)),X3)
| X4 != X5
| ~ in(X1,X5)
| ~ in(X4,X2)
| ~ in(X6,esk181_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1002,lemma,
( in(ordered_pair(X4,X1),esk182_2(X2,X3))
| in(ordered_pair(esk178_2(X2,X3),X6),X3)
| empty(X2)
| ~ in(ordered_pair(X1,esk184_5(X2,X3,X4,X1,X5)),X3)
| X4 != X5
| ~ in(X1,X5)
| ~ in(X4,X2)
| ~ in(X6,esk180_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1003,plain,
( in(X1,esk211_2(X2,X3))
| in(ordered_pair(esk208_2(X2,X3),X6),X3)
| empty(X2)
| ~ in(ordered_pair(X1,esk214_5(X2,X3,X1,X4,X5)),X3)
| X4 != X5
| ~ in(X1,X5)
| ~ in(X4,X2)
| ~ in(X6,esk210_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_691]) ).
cnf(i_0_1004,plain,
( in(X1,esk211_2(X2,X3))
| in(ordered_pair(esk207_2(X2,X3),X6),X3)
| empty(X2)
| ~ in(ordered_pair(X1,esk214_5(X2,X3,X1,X4,X5)),X3)
| X4 != X5
| ~ in(X1,X5)
| ~ in(X4,X2)
| ~ in(X6,esk209_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_691]) ).
cnf(i_0_1005,lemma,
( in(ordered_pair(X4,X1),esk182_2(X2,X3))
| in(esk179_2(X2,X3),esk181_2(X2,X3))
| empty(X2)
| ~ in(ordered_pair(X1,esk184_5(X2,X3,X4,X1,X5)),X3)
| X4 != X5
| ~ in(X1,X5)
| ~ in(X4,X2)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1006,lemma,
( in(ordered_pair(X4,X1),esk182_2(X2,X3))
| in(esk178_2(X2,X3),esk180_2(X2,X3))
| empty(X2)
| ~ in(ordered_pair(X1,esk184_5(X2,X3,X4,X1,X5)),X3)
| X4 != X5
| ~ in(X1,X5)
| ~ in(X4,X2)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1007,lemma,
( in(ordered_pair(X4,X1),esk182_2(X2,X3))
| empty(X2)
| ~ in(ordered_pair(X1,esk184_5(X2,X3,X4,X1,X5)),X3)
| X4 != X5
| ~ in(X1,X5)
| ~ in(X4,X2)
| esk178_2(X2,X3) != esk179_2(X2,X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1008,lemma,
( in(ordered_pair(X4,X1),esk182_2(X2,X3))
| in(esk177_2(X2,X3),X2)
| empty(X2)
| ~ in(ordered_pair(X1,esk184_5(X2,X3,X4,X1,X5)),X3)
| X4 != X5
| ~ in(X1,X5)
| ~ in(X4,X2)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1009,lemma,
( in(ordered_pair(X4,X1),esk182_2(X2,X3))
| in(esk177_2(X2,X3),X2)
| empty(X2)
| ~ in(ordered_pair(X1,esk184_5(X2,X3,X4,X1,X5)),X3)
| X4 != X5
| ~ in(X1,X5)
| ~ in(X4,X2)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1010,lemma,
( in(ordered_pair(X4,X1),esk182_2(X2,X3))
| esk177_2(X2,X3) = esk181_2(X2,X3)
| empty(X2)
| ~ in(ordered_pair(X1,esk184_5(X2,X3,X4,X1,X5)),X3)
| X4 != X5
| ~ in(X1,X5)
| ~ in(X4,X2)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1011,lemma,
( in(ordered_pair(X4,X1),esk182_2(X2,X3))
| esk177_2(X2,X3) = esk180_2(X2,X3)
| empty(X2)
| ~ in(ordered_pair(X1,esk184_5(X2,X3,X4,X1,X5)),X3)
| X4 != X5
| ~ in(X1,X5)
| ~ in(X4,X2)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1012,plain,
( in(X1,esk211_2(X2,X3))
| in(esk208_2(X2,X3),esk210_2(X2,X3))
| empty(X2)
| ~ in(ordered_pair(X1,esk214_5(X2,X3,X1,X4,X5)),X3)
| X4 != X5
| ~ in(X1,X5)
| ~ in(X4,X2)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_691]) ).
cnf(i_0_1013,plain,
( in(X1,esk211_2(X2,X3))
| in(esk207_2(X2,X3),esk209_2(X2,X3))
| empty(X2)
| ~ in(ordered_pair(X1,esk214_5(X2,X3,X1,X4,X5)),X3)
| X4 != X5
| ~ in(X1,X5)
| ~ in(X4,X2)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_691]) ).
cnf(i_0_1014,plain,
( in(X1,esk211_2(X2,X3))
| empty(X2)
| ~ in(ordered_pair(X1,esk214_5(X2,X3,X1,X4,X5)),X3)
| X4 != X5
| ~ in(X1,X5)
| ~ in(X4,X2)
| esk207_2(X2,X3) != esk208_2(X2,X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_691]) ).
cnf(i_0_1015,plain,
( in(X1,esk211_2(X2,X3))
| in(esk206_2(X2,X3),X2)
| empty(X2)
| ~ in(ordered_pair(X1,esk214_5(X2,X3,X1,X4,X5)),X3)
| X4 != X5
| ~ in(X1,X5)
| ~ in(X4,X2)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_691]) ).
cnf(i_0_1016,plain,
( in(X1,esk211_2(X2,X3))
| in(esk206_2(X2,X3),X2)
| empty(X2)
| ~ in(ordered_pair(X1,esk214_5(X2,X3,X1,X4,X5)),X3)
| X4 != X5
| ~ in(X1,X5)
| ~ in(X4,X2)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_691]) ).
cnf(i_0_1017,plain,
( in(X1,esk211_2(X2,X3))
| esk206_2(X2,X3) = esk210_2(X2,X3)
| empty(X2)
| ~ in(ordered_pair(X1,esk214_5(X2,X3,X1,X4,X5)),X3)
| X4 != X5
| ~ in(X1,X5)
| ~ in(X4,X2)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_691]) ).
cnf(i_0_1018,plain,
( in(X1,esk211_2(X2,X3))
| esk206_2(X2,X3) = esk209_2(X2,X3)
| empty(X2)
| ~ in(ordered_pair(X1,esk214_5(X2,X3,X1,X4,X5)),X3)
| X4 != X5
| ~ in(X1,X5)
| ~ in(X4,X2)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_691]) ).
cnf(i_0_1019,plain,
( element(esk293_6(X1,X2,X3,X4,X5,X6),powerset(the_carrier(X1)))
| in(X4,esk289_3(X1,X2,X3))
| ordered_pair(esk287_2(X1,X2),esk288_2(X1,X2)) = esk284_2(X1,X2)
| ordered_pair(X5,X6) != X4
| ~ in(X5,complements_of_subsets(the_carrier(X1),X2))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| X7 != X4
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]) ).
cnf(i_0_1020,plain,
( element(esk293_6(X1,X2,X3,X4,X5,X6),powerset(the_carrier(X1)))
| in(X4,esk289_3(X1,X2,X3))
| ordered_pair(esk285_2(X1,X2),esk286_2(X1,X2)) = esk283_2(X1,X2)
| ordered_pair(X5,X6) != X4
| ~ in(X5,complements_of_subsets(the_carrier(X1),X2))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| X7 != X4
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]) ).
cnf(i_0_1021,plain,
( element(esk293_6(X1,X2,X3,X4,X5,X6),powerset(the_carrier(X1)))
| in(X4,esk289_3(X1,X2,X3))
| esk288_2(X1,X2) = subset_complement(the_carrier(X1),X8)
| ordered_pair(X5,X6) != X4
| ~ in(X5,complements_of_subsets(the_carrier(X1),X2))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| X7 != X4
| ~ element(X8,powerset(the_carrier(X1)))
| X8 != esk287_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]) ).
cnf(i_0_1022,plain,
( element(esk293_6(X1,X2,X3,X4,X5,X6),powerset(the_carrier(X1)))
| in(X4,esk289_3(X1,X2,X3))
| esk286_2(X1,X2) = subset_complement(the_carrier(X1),X8)
| ordered_pair(X5,X6) != X4
| ~ in(X5,complements_of_subsets(the_carrier(X1),X2))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| X7 != X4
| ~ element(X8,powerset(the_carrier(X1)))
| X8 != esk285_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]) ).
cnf(i_0_1023,plain,
( element(esk311_6(X1,X2,X3,X4,X5,X6),powerset(the_carrier(X1)))
| in(X4,esk307_3(X1,X2,X3))
| ordered_pair(esk305_2(X1,X2),esk306_2(X1,X2)) = esk302_2(X1,X2)
| ordered_pair(X5,X6) != X4
| ~ in(X5,X2)
| ~ in(X7,cartesian_product2(X2,X3))
| X7 != X4
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]) ).
cnf(i_0_1024,plain,
( element(esk311_6(X1,X2,X3,X4,X5,X6),powerset(the_carrier(X1)))
| in(X4,esk307_3(X1,X2,X3))
| ordered_pair(esk303_2(X1,X2),esk304_2(X1,X2)) = esk301_2(X1,X2)
| ordered_pair(X5,X6) != X4
| ~ in(X5,X2)
| ~ in(X7,cartesian_product2(X2,X3))
| X7 != X4
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]) ).
cnf(i_0_1025,plain,
( element(esk293_6(X1,X2,X3,X4,X5,X6),powerset(the_carrier(X1)))
| in(X4,esk289_3(X1,X2,X3))
| in(esk287_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| ordered_pair(X5,X6) != X4
| ~ in(X5,complements_of_subsets(the_carrier(X1),X2))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| X7 != X4
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]) ).
cnf(i_0_1026,plain,
( element(esk293_6(X1,X2,X3,X4,X5,X6),powerset(the_carrier(X1)))
| in(X4,esk289_3(X1,X2,X3))
| in(esk285_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| ordered_pair(X5,X6) != X4
| ~ in(X5,complements_of_subsets(the_carrier(X1),X2))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| X7 != X4
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]) ).
cnf(i_0_1027,plain,
( element(esk293_6(X1,X2,X3,X4,X5,X6),powerset(the_carrier(X1)))
| in(X4,esk289_3(X1,X2,X3))
| ordered_pair(X5,X6) != X4
| ~ in(X5,complements_of_subsets(the_carrier(X1),X2))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| X7 != X4
| esk283_2(X1,X2) != esk284_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]) ).
cnf(i_0_1028,plain,
( element(esk293_6(X1,X2,X3,X4,X5,X6),powerset(the_carrier(X1)))
| in(X4,esk289_3(X1,X2,X3))
| esk282_2(X1,X2) = esk284_2(X1,X2)
| ordered_pair(X5,X6) != X4
| ~ in(X5,complements_of_subsets(the_carrier(X1),X2))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| X7 != X4
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]) ).
cnf(i_0_1029,plain,
( element(esk293_6(X1,X2,X3,X4,X5,X6),powerset(the_carrier(X1)))
| in(X4,esk289_3(X1,X2,X3))
| esk282_2(X1,X2) = esk283_2(X1,X2)
| ordered_pair(X5,X6) != X4
| ~ in(X5,complements_of_subsets(the_carrier(X1),X2))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| X7 != X4
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]) ).
cnf(i_0_1030,lemma,
( element(esk362_6(X1,X2,X3,X4,X5,X6),powerset(the_carrier(X1)))
| in(X4,esk359_3(X1,X2,X3))
| ordered_pair(X5,X6) != X4
| ~ in(X5,complements_of_subsets(the_carrier(X1),X2))
| ~ in(X4,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_687]) ).
cnf(i_0_1031,plain,
( element(esk311_6(X1,X2,X3,X4,X5,X6),powerset(the_carrier(X1)))
| in(X4,esk307_3(X1,X2,X3))
| esk306_2(X1,X2) = subset_complement(the_carrier(X1),X8)
| ordered_pair(X5,X6) != X4
| ~ in(X5,X2)
| ~ in(X7,cartesian_product2(X2,X3))
| X7 != X4
| ~ element(X8,powerset(the_carrier(X1)))
| X8 != esk305_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]) ).
cnf(i_0_1032,plain,
( element(esk311_6(X1,X2,X3,X4,X5,X6),powerset(the_carrier(X1)))
| in(X4,esk307_3(X1,X2,X3))
| esk304_2(X1,X2) = subset_complement(the_carrier(X1),X8)
| ordered_pair(X5,X6) != X4
| ~ in(X5,X2)
| ~ in(X7,cartesian_product2(X2,X3))
| X7 != X4
| ~ element(X8,powerset(the_carrier(X1)))
| X8 != esk303_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]) ).
cnf(i_0_1033,plain,
( element(esk311_6(X1,X2,X3,X4,X5,X6),powerset(the_carrier(X1)))
| in(X4,esk307_3(X1,X2,X3))
| ordered_pair(X5,X6) != X4
| ~ in(X5,X2)
| ~ in(X7,cartesian_product2(X2,X3))
| X7 != X4
| esk301_2(X1,X2) != esk302_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]) ).
cnf(i_0_1034,plain,
( element(esk311_6(X1,X2,X3,X4,X5,X6),powerset(the_carrier(X1)))
| in(X4,esk307_3(X1,X2,X3))
| in(esk305_2(X1,X2),X2)
| ordered_pair(X5,X6) != X4
| ~ in(X5,X2)
| ~ in(X7,cartesian_product2(X2,X3))
| X7 != X4
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]) ).
cnf(i_0_1035,plain,
( element(esk311_6(X1,X2,X3,X4,X5,X6),powerset(the_carrier(X1)))
| in(X4,esk307_3(X1,X2,X3))
| in(esk303_2(X1,X2),X2)
| ordered_pair(X5,X6) != X4
| ~ in(X5,X2)
| ~ in(X7,cartesian_product2(X2,X3))
| X7 != X4
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]) ).
cnf(i_0_1036,plain,
( element(esk311_6(X1,X2,X3,X4,X5,X6),powerset(the_carrier(X1)))
| in(X4,esk307_3(X1,X2,X3))
| esk300_2(X1,X2) = esk302_2(X1,X2)
| ordered_pair(X5,X6) != X4
| ~ in(X5,X2)
| ~ in(X7,cartesian_product2(X2,X3))
| X7 != X4
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]) ).
cnf(i_0_1037,plain,
( element(esk311_6(X1,X2,X3,X4,X5,X6),powerset(the_carrier(X1)))
| in(X4,esk307_3(X1,X2,X3))
| esk300_2(X1,X2) = esk301_2(X1,X2)
| ordered_pair(X5,X6) != X4
| ~ in(X5,X2)
| ~ in(X7,cartesian_product2(X2,X3))
| X7 != X4
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]) ).
cnf(i_0_1038,lemma,
( element(esk366_6(X1,X2,X3,X4,X5,X6),powerset(the_carrier(X1)))
| in(X4,esk363_3(X1,X2,X3))
| ordered_pair(X5,X6) != X4
| ~ in(X5,X2)
| ~ in(X4,cartesian_product2(X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_688]) ).
fof(i_0_1039,plain,
! [X2459,X2460,X2461,X2462,X2463,X2464] :
( empty(X2459)
| empty(X2460)
| ~ function(X2462)
| ~ quasi_total(X2462,cartesian_product2(X2459,X2460),X2461)
| ~ relation_of2(X2462,cartesian_product2(X2459,X2460),X2461)
| ~ element(X2463,X2459)
| ~ element(X2464,X2460)
| element(apply_binary_as_element(X2459,X2460,X2461,X2462,X2463,X2464),X2461) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_692])]) ).
cnf(i_0_1040,plain,
( in(ordered_pair(X1,esk106_5(X2,X3,X4,X1,X5)),X2)
| ~ in(ordered_pair(X1,X5),X4)
| X4 != relation_composition(X2,X3)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_683]) ).
cnf(i_0_1041,plain,
( relation_isomorphism(X1,X2,X3)
| ~ in(ordered_pair(esk99_3(X1,X2,X3),esk100_3(X1,X2,X3)),X1)
| ~ in(esk99_3(X1,X2,X3),relation_field(X1))
| ~ in(esk100_3(X1,X2,X3),relation_field(X1))
| ~ in(ordered_pair(apply(X3,esk99_3(X1,X2,X3)),apply(X3,esk100_3(X1,X2,X3))),X2)
| relation_dom(X3) != relation_field(X1)
| relation_rng(X3) != relation_field(X2)
| ~ one_to_one(X3)
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_693]) ).
cnf(i_0_1042,plain,
( X1 = ordered_pair(esk321_4(X2,X3,X4,X1),esk322_4(X2,X3,X4,X1))
| in(ordered_pair(apply(X4,esk317_3(X2,X3,X4)),apply(X4,esk318_3(X2,X3,X4))),X3)
| ~ in(X1,esk319_3(X2,X3,X4))
| ~ relation(X3)
| ~ relation(X4)
| ~ function(X4) ),
inference(split_conjunct,[status(thm)],[i_0_684]) ).
cnf(i_0_1043,plain,
( X1 = ordered_pair(esk321_4(X2,X3,X4,X1),esk322_4(X2,X3,X4,X1))
| in(ordered_pair(apply(X4,esk315_3(X2,X3,X4)),apply(X4,esk316_3(X2,X3,X4))),X3)
| ~ in(X1,esk319_3(X2,X3,X4))
| ~ relation(X3)
| ~ relation(X4)
| ~ function(X4) ),
inference(split_conjunct,[status(thm)],[i_0_684]) ).
cnf(i_0_1044,plain,
( in(ordered_pair(esk227_4(X2,X3,X4,X5),X1),X3)
| in(ordered_pair(esk222_2(X2,X3),X6),X3)
| empty(X2)
| ~ in(X1,esk228_4(X2,X3,X4,X5))
| ~ in(X5,esk224_3(X2,X3,X4))
| ~ in(X6,esk223_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_1045,plain,
( in(ordered_pair(esk227_4(X2,X3,X4,X5),X1),X3)
| in(ordered_pair(esk219_2(X2,X3),X6),X3)
| empty(X2)
| ~ in(X1,esk228_4(X2,X3,X4,X5))
| ~ in(X5,esk224_3(X2,X3,X4))
| ~ in(X6,esk220_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_1046,plain,
( in(ordered_pair(esk227_4(X2,X3,X4,X5),X1),X3)
| ordered_pair(esk221_2(X2,X3),esk222_2(X2,X3)) = esk217_2(X2,X3)
| empty(X2)
| ~ in(X1,esk228_4(X2,X3,X4,X5))
| ~ in(X5,esk224_3(X2,X3,X4))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_1047,plain,
( in(ordered_pair(esk227_4(X2,X3,X4,X5),X1),X3)
| ordered_pair(esk218_2(X2,X3),esk219_2(X2,X3)) = esk216_2(X2,X3)
| empty(X2)
| ~ in(X1,esk228_4(X2,X3,X4,X5))
| ~ in(X5,esk224_3(X2,X3,X4))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_1048,plain,
( in(ordered_pair(esk227_4(X2,X3,X4,X5),X1),X3)
| in(esk222_2(X2,X3),esk223_2(X2,X3))
| empty(X2)
| ~ in(X1,esk228_4(X2,X3,X4,X5))
| ~ in(X5,esk224_3(X2,X3,X4))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_1049,plain,
( in(ordered_pair(esk227_4(X2,X3,X4,X5),X1),X3)
| in(esk219_2(X2,X3),esk220_2(X2,X3))
| empty(X2)
| ~ in(X1,esk228_4(X2,X3,X4,X5))
| ~ in(X5,esk224_3(X2,X3,X4))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_1050,plain,
( in(ordered_pair(esk227_4(X2,X3,X4,X5),X1),X3)
| empty(X2)
| ~ in(X1,esk228_4(X2,X3,X4,X5))
| ~ in(X5,esk224_3(X2,X3,X4))
| esk216_2(X2,X3) != esk217_2(X2,X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_1051,plain,
( in(ordered_pair(esk227_4(X2,X3,X4,X5),X1),X3)
| in(esk221_2(X2,X3),X2)
| empty(X2)
| ~ in(X1,esk228_4(X2,X3,X4,X5))
| ~ in(X5,esk224_3(X2,X3,X4))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_1052,plain,
( in(ordered_pair(esk227_4(X2,X3,X4,X5),X1),X3)
| in(esk218_2(X2,X3),X2)
| empty(X2)
| ~ in(X1,esk228_4(X2,X3,X4,X5))
| ~ in(X5,esk224_3(X2,X3,X4))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_1053,plain,
( in(ordered_pair(esk227_4(X2,X3,X4,X5),X1),X3)
| esk221_2(X2,X3) = esk223_2(X2,X3)
| empty(X2)
| ~ in(X1,esk228_4(X2,X3,X4,X5))
| ~ in(X5,esk224_3(X2,X3,X4))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_1054,plain,
( in(ordered_pair(esk227_4(X2,X3,X4,X5),X1),X3)
| esk218_2(X2,X3) = esk220_2(X2,X3)
| empty(X2)
| ~ in(X1,esk228_4(X2,X3,X4,X5))
| ~ in(X5,esk224_3(X2,X3,X4))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_1055,plain,
( in(ordered_pair(esk227_4(X2,X3,X4,X5),X1),X3)
| esk215_2(X2,X3) = esk217_2(X2,X3)
| empty(X2)
| ~ in(X1,esk228_4(X2,X3,X4,X5))
| ~ in(X5,esk224_3(X2,X3,X4))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_1056,plain,
( in(ordered_pair(esk227_4(X2,X3,X4,X5),X1),X3)
| esk215_2(X2,X3) = esk216_2(X2,X3)
| empty(X2)
| ~ in(X1,esk228_4(X2,X3,X4,X5))
| ~ in(X5,esk224_3(X2,X3,X4))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_1057,lemma,
( in(ordered_pair(esk343_4(X2,X3,X4,X5),X1),X3)
| empty(X2)
| ~ in(X1,esk344_4(X2,X3,X4,X5))
| ~ in(X5,esk341_3(X2,X3,X4))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_682]) ).
cnf(i_0_1058,plain,
( esk293_6(X1,X2,X3,X4,X5,X6) = X5
| in(X4,esk289_3(X1,X2,X3))
| ordered_pair(esk287_2(X1,X2),esk288_2(X1,X2)) = esk284_2(X1,X2)
| ordered_pair(X5,X6) != X4
| ~ in(X5,complements_of_subsets(the_carrier(X1),X2))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| X7 != X4
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]) ).
cnf(i_0_1059,plain,
( esk293_6(X1,X2,X3,X4,X5,X6) = X5
| in(X4,esk289_3(X1,X2,X3))
| ordered_pair(esk285_2(X1,X2),esk286_2(X1,X2)) = esk283_2(X1,X2)
| ordered_pair(X5,X6) != X4
| ~ in(X5,complements_of_subsets(the_carrier(X1),X2))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| X7 != X4
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]) ).
cnf(i_0_1060,plain,
( esk293_6(X1,X2,X3,X4,X5,X6) = X5
| in(X4,esk289_3(X1,X2,X3))
| esk288_2(X1,X2) = subset_complement(the_carrier(X1),X8)
| ordered_pair(X5,X6) != X4
| ~ in(X5,complements_of_subsets(the_carrier(X1),X2))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| X7 != X4
| ~ element(X8,powerset(the_carrier(X1)))
| X8 != esk287_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]) ).
cnf(i_0_1061,plain,
( esk293_6(X1,X2,X3,X4,X5,X6) = X5
| in(X4,esk289_3(X1,X2,X3))
| esk286_2(X1,X2) = subset_complement(the_carrier(X1),X8)
| ordered_pair(X5,X6) != X4
| ~ in(X5,complements_of_subsets(the_carrier(X1),X2))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| X7 != X4
| ~ element(X8,powerset(the_carrier(X1)))
| X8 != esk285_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]) ).
cnf(i_0_1062,plain,
( esk311_6(X1,X2,X3,X4,X5,X6) = X5
| in(X4,esk307_3(X1,X2,X3))
| ordered_pair(esk305_2(X1,X2),esk306_2(X1,X2)) = esk302_2(X1,X2)
| ordered_pair(X5,X6) != X4
| ~ in(X5,X2)
| ~ in(X7,cartesian_product2(X2,X3))
| X7 != X4
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]) ).
cnf(i_0_1063,plain,
( esk311_6(X1,X2,X3,X4,X5,X6) = X5
| in(X4,esk307_3(X1,X2,X3))
| ordered_pair(esk303_2(X1,X2),esk304_2(X1,X2)) = esk301_2(X1,X2)
| ordered_pair(X5,X6) != X4
| ~ in(X5,X2)
| ~ in(X7,cartesian_product2(X2,X3))
| X7 != X4
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]) ).
cnf(i_0_1064,plain,
( esk293_6(X1,X2,X3,X4,X5,X6) = X5
| in(X4,esk289_3(X1,X2,X3))
| in(esk287_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| ordered_pair(X5,X6) != X4
| ~ in(X5,complements_of_subsets(the_carrier(X1),X2))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| X7 != X4
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]) ).
cnf(i_0_1065,plain,
( esk293_6(X1,X2,X3,X4,X5,X6) = X5
| in(X4,esk289_3(X1,X2,X3))
| in(esk285_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| ordered_pair(X5,X6) != X4
| ~ in(X5,complements_of_subsets(the_carrier(X1),X2))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| X7 != X4
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]) ).
cnf(i_0_1066,plain,
( esk293_6(X1,X2,X3,X4,X5,X6) = X5
| in(X4,esk289_3(X1,X2,X3))
| ordered_pair(X5,X6) != X4
| ~ in(X5,complements_of_subsets(the_carrier(X1),X2))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| X7 != X4
| esk283_2(X1,X2) != esk284_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]) ).
cnf(i_0_1067,plain,
( esk293_6(X1,X2,X3,X4,X5,X6) = X5
| in(X4,esk289_3(X1,X2,X3))
| esk282_2(X1,X2) = esk284_2(X1,X2)
| ordered_pair(X5,X6) != X4
| ~ in(X5,complements_of_subsets(the_carrier(X1),X2))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| X7 != X4
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]) ).
cnf(i_0_1068,plain,
( esk293_6(X1,X2,X3,X4,X5,X6) = X5
| in(X4,esk289_3(X1,X2,X3))
| esk282_2(X1,X2) = esk283_2(X1,X2)
| ordered_pair(X5,X6) != X4
| ~ in(X5,complements_of_subsets(the_carrier(X1),X2))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| X7 != X4
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]) ).
cnf(i_0_1069,lemma,
( esk362_6(X1,X2,X3,X4,X5,X6) = X5
| in(X4,esk359_3(X1,X2,X3))
| ordered_pair(X5,X6) != X4
| ~ in(X5,complements_of_subsets(the_carrier(X1),X2))
| ~ in(X4,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_687]) ).
cnf(i_0_1070,plain,
( esk311_6(X1,X2,X3,X4,X5,X6) = X5
| in(X4,esk307_3(X1,X2,X3))
| esk306_2(X1,X2) = subset_complement(the_carrier(X1),X8)
| ordered_pair(X5,X6) != X4
| ~ in(X5,X2)
| ~ in(X7,cartesian_product2(X2,X3))
| X7 != X4
| ~ element(X8,powerset(the_carrier(X1)))
| X8 != esk305_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]) ).
cnf(i_0_1071,plain,
( esk311_6(X1,X2,X3,X4,X5,X6) = X5
| in(X4,esk307_3(X1,X2,X3))
| esk304_2(X1,X2) = subset_complement(the_carrier(X1),X8)
| ordered_pair(X5,X6) != X4
| ~ in(X5,X2)
| ~ in(X7,cartesian_product2(X2,X3))
| X7 != X4
| ~ element(X8,powerset(the_carrier(X1)))
| X8 != esk303_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]) ).
cnf(i_0_1072,plain,
( esk311_6(X1,X2,X3,X4,X5,X6) = X5
| in(X4,esk307_3(X1,X2,X3))
| ordered_pair(X5,X6) != X4
| ~ in(X5,X2)
| ~ in(X7,cartesian_product2(X2,X3))
| X7 != X4
| esk301_2(X1,X2) != esk302_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]) ).
cnf(i_0_1073,plain,
( esk311_6(X1,X2,X3,X4,X5,X6) = X5
| in(X4,esk307_3(X1,X2,X3))
| in(esk305_2(X1,X2),X2)
| ordered_pair(X5,X6) != X4
| ~ in(X5,X2)
| ~ in(X7,cartesian_product2(X2,X3))
| X7 != X4
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]) ).
cnf(i_0_1074,plain,
( esk311_6(X1,X2,X3,X4,X5,X6) = X5
| in(X4,esk307_3(X1,X2,X3))
| in(esk303_2(X1,X2),X2)
| ordered_pair(X5,X6) != X4
| ~ in(X5,X2)
| ~ in(X7,cartesian_product2(X2,X3))
| X7 != X4
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]) ).
cnf(i_0_1075,plain,
( esk311_6(X1,X2,X3,X4,X5,X6) = X5
| in(X4,esk307_3(X1,X2,X3))
| esk300_2(X1,X2) = esk302_2(X1,X2)
| ordered_pair(X5,X6) != X4
| ~ in(X5,X2)
| ~ in(X7,cartesian_product2(X2,X3))
| X7 != X4
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]) ).
cnf(i_0_1076,plain,
( esk311_6(X1,X2,X3,X4,X5,X6) = X5
| in(X4,esk307_3(X1,X2,X3))
| esk300_2(X1,X2) = esk301_2(X1,X2)
| ordered_pair(X5,X6) != X4
| ~ in(X5,X2)
| ~ in(X7,cartesian_product2(X2,X3))
| X7 != X4
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]) ).
cnf(i_0_1077,lemma,
( esk366_6(X1,X2,X3,X4,X5,X6) = X5
| in(X4,esk363_3(X1,X2,X3))
| ordered_pair(X5,X6) != X4
| ~ in(X5,X2)
| ~ in(X4,cartesian_product2(X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_688]) ).
fof(i_0_1078,plain,
! [X2836,X2837,X2838,X2839,X2840,X2841] :
( empty(X2836)
| empty(X2837)
| ~ function(X2839)
| ~ quasi_total(X2839,cartesian_product2(X2836,X2837),X2838)
| ~ relation_of2(X2839,cartesian_product2(X2836,X2837),X2838)
| ~ element(X2840,X2836)
| ~ element(X2841,X2837)
| apply_binary_as_element(X2836,X2837,X2838,X2839,X2840,X2841) = apply_binary(X2839,X2840,X2841) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_694])]) ).
cnf(i_0_1079,lemma,
( in(ordered_pair(esk417_4(X1,X2,X3,X4),X4),X3)
| relation_rng_as_subset(X1,X2,X3) != X2
| ~ in(X4,X2)
| ~ relation_of2_as_subset(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_695]) ).
fof(i_0_1080,plain,
! [X2041,X2042,X2043] :
( empty_carrier(X2041)
| ~ join_semilatt_str(X2041)
| ~ element(X2042,the_carrier(X2041))
| ~ element(X2043,the_carrier(X2041))
| join(X2041,X2042,X2043) = apply_binary_as_element(the_carrier(X2041),the_carrier(X2041),the_carrier(X2041),the_L_join(X2041),X2042,X2043) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_696])])]) ).
fof(i_0_1081,plain,
! [X2141,X2142,X2143] :
( empty_carrier(X2141)
| ~ meet_semilatt_str(X2141)
| ~ element(X2142,the_carrier(X2141))
| ~ element(X2143,the_carrier(X2141))
| meet(X2141,X2142,X2143) = apply_binary_as_element(the_carrier(X2141),the_carrier(X2141),the_carrier(X2141),the_L_meet(X2141),X2142,X2143) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_697])])]) ).
cnf(i_0_1082,plain,
( in(ordered_pair(esk16_4(X1,X2,X3,X4),X4),X1)
| ~ in(X4,X3)
| X3 != relation_image(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_698]) ).
cnf(i_0_1083,plain,
( X3 = relation_composition(X1,X2)
| ~ in(ordered_pair(esk107_3(X1,X2,X3),esk108_3(X1,X2,X3)),X3)
| ~ in(ordered_pair(esk107_3(X1,X2,X3),X4),X1)
| ~ in(ordered_pair(X4,esk108_3(X1,X2,X3)),X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_683]) ).
cnf(i_0_1084,plain,
( X3 = relation_rng_restriction(X1,X2)
| ~ in(ordered_pair(esk8_3(X1,X2,X3),esk9_3(X1,X2,X3)),X3)
| ~ in(esk9_3(X1,X2,X3),X1)
| ~ in(ordered_pair(esk8_3(X1,X2,X3),esk9_3(X1,X2,X3)),X2)
| ~ relation(X3)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_699]) ).
cnf(i_0_1085,plain,
( X3 = relation_dom_restriction(X1,X2)
| ~ in(ordered_pair(esk3_3(X1,X2,X3),esk4_3(X1,X2,X3)),X3)
| ~ in(esk3_3(X1,X2,X3),X2)
| ~ in(ordered_pair(esk3_3(X1,X2,X3),esk4_3(X1,X2,X3)),X1)
| ~ relation(X3)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_700]) ).
cnf(i_0_1086,plain,
( in(ordered_pair(apply(X1,esk99_3(X2,X3,X1)),apply(X1,esk100_3(X2,X3,X1))),X3)
| in(ordered_pair(esk99_3(X2,X3,X1),esk100_3(X2,X3,X1)),X2)
| relation_isomorphism(X2,X3,X1)
| relation_dom(X1) != relation_field(X2)
| relation_rng(X1) != relation_field(X3)
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_693]) ).
cnf(i_0_1087,plain,
( X1 = ordered_pair(esk321_4(X2,X3,X4,X1),esk322_4(X2,X3,X4,X1))
| esk314_3(X2,X3,X4) = ordered_pair(esk317_3(X2,X3,X4),esk318_3(X2,X3,X4))
| ~ in(X1,esk319_3(X2,X3,X4))
| ~ relation(X3)
| ~ relation(X4)
| ~ function(X4) ),
inference(split_conjunct,[status(thm)],[i_0_684]) ).
cnf(i_0_1088,plain,
( X1 = ordered_pair(esk321_4(X2,X3,X4,X1),esk322_4(X2,X3,X4,X1))
| esk313_3(X2,X3,X4) = ordered_pair(esk315_3(X2,X3,X4),esk316_3(X2,X3,X4))
| ~ in(X1,esk319_3(X2,X3,X4))
| ~ relation(X3)
| ~ relation(X4)
| ~ function(X4) ),
inference(split_conjunct,[status(thm)],[i_0_684]) ).
cnf(i_0_1089,lemma,
( in(ordered_pair(apply(esk381_2(X2,X3),X4),X1),X3)
| in(ordered_pair(esk376_2(X2,X3),X7),X3)
| empty(X2)
| ~ in(X1,esk382_3(X2,X3,X4))
| ~ in(X4,X2)
| ~ in(ordered_pair(X5,esk380_4(X2,X3,X5,X6)),X3)
| esk379_2(X2,X3) != X6
| ~ in(X5,X6)
| ~ in(X7,esk378_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1090,lemma,
( in(ordered_pair(apply(esk381_2(X2,X3),X4),X1),X3)
| in(ordered_pair(esk375_2(X2,X3),X7),X3)
| empty(X2)
| ~ in(X1,esk382_3(X2,X3,X4))
| ~ in(X4,X2)
| ~ in(ordered_pair(X5,esk380_4(X2,X3,X5,X6)),X3)
| esk379_2(X2,X3) != X6
| ~ in(X5,X6)
| ~ in(X7,esk377_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1091,plain,
( in(X3,esk319_3(X2,X7,X6))
| in(ordered_pair(apply(X6,esk317_3(X2,X7,X6)),apply(X6,esk318_3(X2,X7,X6))),X7)
| ~ in(X1,cartesian_product2(X2,X2))
| X1 != X3
| X3 != ordered_pair(X4,X5)
| ~ in(ordered_pair(apply(X6,X4),apply(X6,X5)),X7)
| ~ relation(X7)
| ~ relation(X6)
| ~ function(X6) ),
inference(split_conjunct,[status(thm)],[i_0_684]) ).
cnf(i_0_1092,plain,
( in(X3,esk319_3(X2,X7,X6))
| in(ordered_pair(apply(X6,esk315_3(X2,X7,X6)),apply(X6,esk316_3(X2,X7,X6))),X7)
| ~ in(X1,cartesian_product2(X2,X2))
| X1 != X3
| X3 != ordered_pair(X4,X5)
| ~ in(ordered_pair(apply(X6,X4),apply(X6,X5)),X7)
| ~ relation(X7)
| ~ relation(X6)
| ~ function(X6) ),
inference(split_conjunct,[status(thm)],[i_0_684]) ).
cnf(i_0_1093,lemma,
( in(ordered_pair(apply(esk381_2(X2,X3),X4),X1),X3)
| in(esk376_2(X2,X3),esk378_2(X2,X3))
| empty(X2)
| ~ in(X1,esk382_3(X2,X3,X4))
| ~ in(X4,X2)
| ~ in(ordered_pair(X5,esk380_4(X2,X3,X5,X6)),X3)
| esk379_2(X2,X3) != X6
| ~ in(X5,X6)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1094,lemma,
( in(ordered_pair(apply(esk381_2(X2,X3),X4),X1),X3)
| in(esk375_2(X2,X3),esk377_2(X2,X3))
| empty(X2)
| ~ in(X1,esk382_3(X2,X3,X4))
| ~ in(X4,X2)
| ~ in(ordered_pair(X5,esk380_4(X2,X3,X5,X6)),X3)
| esk379_2(X2,X3) != X6
| ~ in(X5,X6)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1095,plain,
( ordered_pair(esk226_4(X1,X2,X3,X4),esk227_4(X1,X2,X3,X4)) = X4
| in(ordered_pair(esk222_2(X1,X2),X5),X2)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ in(X5,esk223_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_1096,plain,
( ordered_pair(esk226_4(X1,X2,X3,X4),esk227_4(X1,X2,X3,X4)) = X4
| in(ordered_pair(esk219_2(X1,X2),X5),X2)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ in(X5,esk220_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_1097,plain,
( in(esk320_4(X1,X2,X3,X4),cartesian_product2(X1,X1))
| in(ordered_pair(apply(X3,esk317_3(X1,X2,X3)),apply(X3,esk318_3(X1,X2,X3))),X2)
| ~ in(X4,esk319_3(X1,X2,X3))
| ~ relation(X2)
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[i_0_684]) ).
cnf(i_0_1098,plain,
( in(esk320_4(X1,X2,X3,X4),cartesian_product2(X1,X1))
| in(ordered_pair(apply(X3,esk315_3(X1,X2,X3)),apply(X3,esk316_3(X1,X2,X3))),X2)
| ~ in(X4,esk319_3(X1,X2,X3))
| ~ relation(X2)
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[i_0_684]) ).
cnf(i_0_1099,lemma,
( in(ordered_pair(apply(esk381_2(X2,X3),X4),X1),X3)
| empty(X2)
| ~ in(X1,esk382_3(X2,X3,X4))
| ~ in(X4,X2)
| ~ in(ordered_pair(X5,esk380_4(X2,X3,X5,X6)),X3)
| esk379_2(X2,X3) != X6
| ~ in(X5,X6)
| esk375_2(X2,X3) != esk376_2(X2,X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1100,lemma,
( in(ordered_pair(apply(esk381_2(X2,X3),X4),X1),X3)
| in(esk374_2(X2,X3),X2)
| empty(X2)
| ~ in(X1,esk382_3(X2,X3,X4))
| ~ in(X4,X2)
| ~ in(ordered_pair(X5,esk380_4(X2,X3,X5,X6)),X3)
| esk379_2(X2,X3) != X6
| ~ in(X5,X6)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1101,lemma,
( in(ordered_pair(apply(esk381_2(X2,X3),X4),X1),X3)
| esk374_2(X2,X3) = esk378_2(X2,X3)
| empty(X2)
| ~ in(X1,esk382_3(X2,X3,X4))
| ~ in(X4,X2)
| ~ in(ordered_pair(X5,esk380_4(X2,X3,X5,X6)),X3)
| esk379_2(X2,X3) != X6
| ~ in(X5,X6)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1102,lemma,
( in(ordered_pair(apply(esk381_2(X2,X3),X4),X1),X3)
| esk374_2(X2,X3) = esk377_2(X2,X3)
| empty(X2)
| ~ in(X1,esk382_3(X2,X3,X4))
| ~ in(X4,X2)
| ~ in(ordered_pair(X5,esk380_4(X2,X3,X5,X6)),X3)
| esk379_2(X2,X3) != X6
| ~ in(X5,X6)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1103,plain,
( ordered_pair(esk309_4(X1,X2,X3,X4),esk310_4(X1,X2,X3,X4)) = X4
| ordered_pair(esk305_2(X1,X2),esk306_2(X1,X2)) = esk302_2(X1,X2)
| ~ in(X4,esk307_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]) ).
cnf(i_0_1104,plain,
( ordered_pair(esk309_4(X1,X2,X3,X4),esk310_4(X1,X2,X3,X4)) = X4
| ordered_pair(esk303_2(X1,X2),esk304_2(X1,X2)) = esk301_2(X1,X2)
| ~ in(X4,esk307_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]) ).
cnf(i_0_1105,plain,
( ordered_pair(esk291_4(X1,X2,X3,X4),esk292_4(X1,X2,X3,X4)) = X4
| ordered_pair(esk287_2(X1,X2),esk288_2(X1,X2)) = esk284_2(X1,X2)
| ~ in(X4,esk289_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]) ).
cnf(i_0_1106,plain,
( ordered_pair(esk291_4(X1,X2,X3,X4),esk292_4(X1,X2,X3,X4)) = X4
| ordered_pair(esk285_2(X1,X2),esk286_2(X1,X2)) = esk283_2(X1,X2)
| ~ in(X4,esk289_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]) ).
cnf(i_0_1107,plain,
( ordered_pair(esk226_4(X1,X2,X3,X4),esk227_4(X1,X2,X3,X4)) = X4
| ordered_pair(esk221_2(X1,X2),esk222_2(X1,X2)) = esk217_2(X1,X2)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_1108,plain,
( ordered_pair(esk226_4(X1,X2,X3,X4),esk227_4(X1,X2,X3,X4)) = X4
| ordered_pair(esk218_2(X1,X2),esk219_2(X1,X2)) = esk216_2(X1,X2)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_1109,plain,
( esk320_4(X1,X2,X3,X4) = X4
| in(ordered_pair(apply(X3,esk317_3(X1,X2,X3)),apply(X3,esk318_3(X1,X2,X3))),X2)
| ~ in(X4,esk319_3(X1,X2,X3))
| ~ relation(X2)
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[i_0_684]) ).
cnf(i_0_1110,plain,
( esk320_4(X1,X2,X3,X4) = X4
| in(ordered_pair(apply(X3,esk315_3(X1,X2,X3)),apply(X3,esk316_3(X1,X2,X3))),X2)
| ~ in(X4,esk319_3(X1,X2,X3))
| ~ relation(X2)
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[i_0_684]) ).
cnf(i_0_1111,plain,
( ordered_pair(esk309_4(X1,X2,X3,X4),esk310_4(X1,X2,X3,X4)) = X4
| esk306_2(X1,X2) = subset_complement(the_carrier(X1),X5)
| ~ in(X4,esk307_3(X1,X2,X3))
| ~ element(X5,powerset(the_carrier(X1)))
| X5 != esk305_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]) ).
cnf(i_0_1112,plain,
( ordered_pair(esk309_4(X1,X2,X3,X4),esk310_4(X1,X2,X3,X4)) = X4
| esk304_2(X1,X2) = subset_complement(the_carrier(X1),X5)
| ~ in(X4,esk307_3(X1,X2,X3))
| ~ element(X5,powerset(the_carrier(X1)))
| X5 != esk303_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]) ).
cnf(i_0_1113,plain,
( ordered_pair(esk291_4(X1,X2,X3,X4),esk292_4(X1,X2,X3,X4)) = X4
| esk288_2(X1,X2) = subset_complement(the_carrier(X1),X5)
| ~ in(X4,esk289_3(X1,X2,X3))
| ~ element(X5,powerset(the_carrier(X1)))
| X5 != esk287_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]) ).
cnf(i_0_1114,plain,
( ordered_pair(esk291_4(X1,X2,X3,X4),esk292_4(X1,X2,X3,X4)) = X4
| esk286_2(X1,X2) = subset_complement(the_carrier(X1),X5)
| ~ in(X4,esk289_3(X1,X2,X3))
| ~ element(X5,powerset(the_carrier(X1)))
| X5 != esk285_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]) ).
cnf(i_0_1115,plain,
( X1 = ordered_pair(esk321_4(X2,X3,X4,X1),esk322_4(X2,X3,X4,X1))
| ~ in(X1,esk319_3(X2,X3,X4))
| esk313_3(X2,X3,X4) != esk314_3(X2,X3,X4)
| ~ relation(X3)
| ~ relation(X4)
| ~ function(X4) ),
inference(split_conjunct,[status(thm)],[i_0_684]) ).
cnf(i_0_1116,plain,
( ordered_pair(esk291_4(X1,X2,X3,X4),esk292_4(X1,X2,X3,X4)) = X4
| in(esk287_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| ~ in(X4,esk289_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]) ).
cnf(i_0_1117,plain,
( ordered_pair(esk291_4(X1,X2,X3,X4),esk292_4(X1,X2,X3,X4)) = X4
| in(esk285_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| ~ in(X4,esk289_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]) ).
cnf(i_0_1118,plain,
( ordered_pair(esk309_4(X1,X2,X3,X4),esk310_4(X1,X2,X3,X4)) = X4
| ~ in(X4,esk307_3(X1,X2,X3))
| esk301_2(X1,X2) != esk302_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]) ).
cnf(i_0_1119,plain,
( ordered_pair(esk291_4(X1,X2,X3,X4),esk292_4(X1,X2,X3,X4)) = X4
| ~ in(X4,esk289_3(X1,X2,X3))
| esk283_2(X1,X2) != esk284_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]) ).
cnf(i_0_1120,plain,
( ordered_pair(esk309_4(X1,X2,X3,X4),esk310_4(X1,X2,X3,X4)) = X4
| in(esk305_2(X1,X2),X2)
| ~ in(X4,esk307_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]) ).
cnf(i_0_1121,plain,
( ordered_pair(esk309_4(X1,X2,X3,X4),esk310_4(X1,X2,X3,X4)) = X4
| in(esk303_2(X1,X2),X2)
| ~ in(X4,esk307_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]) ).
cnf(i_0_1122,plain,
( X1 = ordered_pair(esk321_4(X2,X3,X4,X1),esk322_4(X2,X3,X4,X1))
| esk312_3(X2,X3,X4) = esk314_3(X2,X3,X4)
| ~ in(X1,esk319_3(X2,X3,X4))
| ~ relation(X3)
| ~ relation(X4)
| ~ function(X4) ),
inference(split_conjunct,[status(thm)],[i_0_684]) ).
cnf(i_0_1123,plain,
( X1 = ordered_pair(esk321_4(X2,X3,X4,X1),esk322_4(X2,X3,X4,X1))
| esk312_3(X2,X3,X4) = esk313_3(X2,X3,X4)
| ~ in(X1,esk319_3(X2,X3,X4))
| ~ relation(X3)
| ~ relation(X4)
| ~ function(X4) ),
inference(split_conjunct,[status(thm)],[i_0_684]) ).
cnf(i_0_1124,plain,
( ordered_pair(esk309_4(X1,X2,X3,X4),esk310_4(X1,X2,X3,X4)) = X4
| esk300_2(X1,X2) = esk302_2(X1,X2)
| ~ in(X4,esk307_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]) ).
cnf(i_0_1125,plain,
( ordered_pair(esk309_4(X1,X2,X3,X4),esk310_4(X1,X2,X3,X4)) = X4
| esk300_2(X1,X2) = esk301_2(X1,X2)
| ~ in(X4,esk307_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]) ).
cnf(i_0_1126,plain,
( ordered_pair(esk291_4(X1,X2,X3,X4),esk292_4(X1,X2,X3,X4)) = X4
| esk282_2(X1,X2) = esk284_2(X1,X2)
| ~ in(X4,esk289_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]) ).
cnf(i_0_1127,plain,
( ordered_pair(esk291_4(X1,X2,X3,X4),esk292_4(X1,X2,X3,X4)) = X4
| esk282_2(X1,X2) = esk283_2(X1,X2)
| ~ in(X4,esk289_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]) ).
cnf(i_0_1128,lemma,
( ordered_pair(esk364_4(X1,X2,X3,X4),esk365_4(X1,X2,X3,X4)) = X4
| ~ in(X4,esk363_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_688]) ).
cnf(i_0_1129,lemma,
( ordered_pair(esk360_4(X1,X2,X3,X4),esk361_4(X1,X2,X3,X4)) = X4
| ~ in(X4,esk359_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_687]) ).
cnf(i_0_1130,plain,
( ordered_pair(esk226_4(X1,X2,X3,X4),esk227_4(X1,X2,X3,X4)) = X4
| in(esk222_2(X1,X2),esk223_2(X1,X2))
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_1131,plain,
( ordered_pair(esk226_4(X1,X2,X3,X4),esk227_4(X1,X2,X3,X4)) = X4
| in(esk219_2(X1,X2),esk220_2(X1,X2))
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_1132,plain,
( ordered_pair(esk226_4(X1,X2,X3,X4),esk227_4(X1,X2,X3,X4)) = X4
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| esk216_2(X1,X2) != esk217_2(X1,X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_1133,plain,
( ordered_pair(esk226_4(X1,X2,X3,X4),esk227_4(X1,X2,X3,X4)) = X4
| in(esk221_2(X1,X2),X1)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_1134,plain,
( ordered_pair(esk226_4(X1,X2,X3,X4),esk227_4(X1,X2,X3,X4)) = X4
| in(esk218_2(X1,X2),X1)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_1135,plain,
( ordered_pair(esk226_4(X1,X2,X3,X4),esk227_4(X1,X2,X3,X4)) = X4
| esk221_2(X1,X2) = esk223_2(X1,X2)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_1136,plain,
( ordered_pair(esk226_4(X1,X2,X3,X4),esk227_4(X1,X2,X3,X4)) = X4
| esk218_2(X1,X2) = esk220_2(X1,X2)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_1137,plain,
( ordered_pair(esk226_4(X1,X2,X3,X4),esk227_4(X1,X2,X3,X4)) = X4
| esk215_2(X1,X2) = esk217_2(X1,X2)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_1138,plain,
( ordered_pair(esk226_4(X1,X2,X3,X4),esk227_4(X1,X2,X3,X4)) = X4
| esk215_2(X1,X2) = esk216_2(X1,X2)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_1139,lemma,
( X1 = ordered_pair(esk368_4(X2,X3,X4,X1),esk369_4(X2,X3,X4,X1))
| ~ in(X1,esk367_3(X2,X3,X4))
| ~ relation(X3)
| ~ relation(X4)
| ~ function(X4) ),
inference(split_conjunct,[status(thm)],[i_0_689]) ).
cnf(i_0_1140,lemma,
( ordered_pair(esk342_4(X1,X2,X3,X4),esk343_4(X1,X2,X3,X4)) = X4
| empty(X1)
| ~ in(X4,esk341_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_682]) ).
cnf(i_0_1141,lemma,
( in(apply(esk381_2(X1,X2),X3),esk382_3(X1,X2,X3))
| in(ordered_pair(esk376_2(X1,X2),X6),X2)
| empty(X1)
| ~ in(X3,X1)
| ~ in(ordered_pair(X4,esk380_4(X1,X2,X4,X5)),X2)
| esk379_2(X1,X2) != X5
| ~ in(X4,X5)
| ~ in(X6,esk378_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1142,lemma,
( in(apply(esk381_2(X1,X2),X3),esk382_3(X1,X2,X3))
| in(ordered_pair(esk375_2(X1,X2),X6),X2)
| empty(X1)
| ~ in(X3,X1)
| ~ in(ordered_pair(X4,esk380_4(X1,X2,X4,X5)),X2)
| esk379_2(X1,X2) != X5
| ~ in(X4,X5)
| ~ in(X6,esk377_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1143,plain,
( X1 = ordered_pair(esk63_4(X2,X3,X4,X1),esk64_4(X2,X3,X4,X1))
| ~ in(X1,X4)
| X4 != cartesian_product2(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_702]) ).
cnf(i_0_1144,lemma,
( X1 = esk382_3(X2,X3,X1)
| in(ordered_pair(esk376_2(X2,X3),X6),X3)
| empty(X2)
| ~ in(X1,X2)
| ~ in(ordered_pair(X4,esk380_4(X2,X3,X4,X5)),X3)
| esk379_2(X2,X3) != X5
| ~ in(X4,X5)
| ~ in(X6,esk378_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1145,lemma,
( X1 = esk382_3(X2,X3,X1)
| in(ordered_pair(esk375_2(X2,X3),X6),X3)
| empty(X2)
| ~ in(X1,X2)
| ~ in(ordered_pair(X4,esk380_4(X2,X3,X4,X5)),X3)
| esk379_2(X2,X3) != X5
| ~ in(X4,X5)
| ~ in(X6,esk377_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1146,lemma,
( relation_dom(esk381_2(X1,X2)) = X1
| in(ordered_pair(esk376_2(X1,X2),X5),X2)
| empty(X1)
| ~ in(ordered_pair(X3,esk380_4(X1,X2,X3,X4)),X2)
| esk379_2(X1,X2) != X4
| ~ in(X3,X4)
| ~ in(X5,esk378_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1147,lemma,
( relation_dom(esk381_2(X1,X2)) = X1
| in(ordered_pair(esk375_2(X1,X2),X5),X2)
| empty(X1)
| ~ in(ordered_pair(X3,esk380_4(X1,X2,X3,X4)),X2)
| esk379_2(X1,X2) != X4
| ~ in(X3,X4)
| ~ in(X5,esk377_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1148,lemma,
( relation(esk381_2(X1,X2))
| in(ordered_pair(esk376_2(X1,X2),X5),X2)
| empty(X1)
| ~ in(ordered_pair(X3,esk380_4(X1,X2,X3,X4)),X2)
| esk379_2(X1,X2) != X4
| ~ in(X3,X4)
| ~ in(X5,esk378_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1149,lemma,
( relation(esk381_2(X1,X2))
| in(ordered_pair(esk375_2(X1,X2),X5),X2)
| empty(X1)
| ~ in(ordered_pair(X3,esk380_4(X1,X2,X3,X4)),X2)
| esk379_2(X1,X2) != X4
| ~ in(X3,X4)
| ~ in(X5,esk377_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1150,lemma,
( function(esk381_2(X1,X2))
| in(ordered_pair(esk376_2(X1,X2),X5),X2)
| empty(X1)
| ~ in(ordered_pair(X3,esk380_4(X1,X2,X3,X4)),X2)
| esk379_2(X1,X2) != X4
| ~ in(X3,X4)
| ~ in(X5,esk378_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1151,lemma,
( function(esk381_2(X1,X2))
| in(ordered_pair(esk375_2(X1,X2),X5),X2)
| empty(X1)
| ~ in(ordered_pair(X3,esk380_4(X1,X2,X3,X4)),X2)
| esk379_2(X1,X2) != X4
| ~ in(X3,X4)
| ~ in(X5,esk377_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1152,plain,
( in(ordered_pair(esk109_3(X1,X2,X3),esk108_3(X1,X2,X3)),X2)
| in(ordered_pair(esk107_3(X1,X2,X3),esk108_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_683]) ).
cnf(i_0_1153,plain,
( in(ordered_pair(esk107_3(X1,X2,X3),esk109_3(X1,X2,X3)),X1)
| in(ordered_pair(esk107_3(X1,X2,X3),esk108_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_683]) ).
cnf(i_0_1154,plain,
( in(ordered_pair(esk8_3(X1,X2,X3),esk9_3(X1,X2,X3)),X2)
| in(ordered_pair(esk8_3(X1,X2,X3),esk9_3(X1,X2,X3)),X3)
| X3 = relation_rng_restriction(X1,X2)
| ~ relation(X3)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_699]) ).
cnf(i_0_1155,plain,
( in(ordered_pair(esk3_3(X1,X2,X3),esk4_3(X1,X2,X3)),X1)
| in(ordered_pair(esk3_3(X1,X2,X3),esk4_3(X1,X2,X3)),X3)
| X3 = relation_dom_restriction(X1,X2)
| ~ relation(X3)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_700]) ).
cnf(i_0_1156,lemma,
( in(apply(esk381_2(X1,X2),X3),esk382_3(X1,X2,X3))
| in(esk376_2(X1,X2),esk378_2(X1,X2))
| empty(X1)
| ~ in(X3,X1)
| ~ in(ordered_pair(X4,esk380_4(X1,X2,X4,X5)),X2)
| esk379_2(X1,X2) != X5
| ~ in(X4,X5)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1157,lemma,
( in(apply(esk381_2(X1,X2),X3),esk382_3(X1,X2,X3))
| in(esk375_2(X1,X2),esk377_2(X1,X2))
| empty(X1)
| ~ in(X3,X1)
| ~ in(ordered_pair(X4,esk380_4(X1,X2,X4,X5)),X2)
| esk379_2(X1,X2) != X5
| ~ in(X4,X5)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1158,lemma,
( in(apply(esk381_2(X1,X2),X3),esk382_3(X1,X2,X3))
| empty(X1)
| ~ in(X3,X1)
| ~ in(ordered_pair(X4,esk380_4(X1,X2,X4,X5)),X2)
| esk379_2(X1,X2) != X5
| ~ in(X4,X5)
| esk375_2(X1,X2) != esk376_2(X1,X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1159,lemma,
( in(apply(esk381_2(X1,X2),X3),esk382_3(X1,X2,X3))
| in(esk374_2(X1,X2),X1)
| empty(X1)
| ~ in(X3,X1)
| ~ in(ordered_pair(X4,esk380_4(X1,X2,X4,X5)),X2)
| esk379_2(X1,X2) != X5
| ~ in(X4,X5)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1160,lemma,
( in(apply(esk381_2(X1,X2),X3),esk382_3(X1,X2,X3))
| esk374_2(X1,X2) = esk378_2(X1,X2)
| empty(X1)
| ~ in(X3,X1)
| ~ in(ordered_pair(X4,esk380_4(X1,X2,X4,X5)),X2)
| esk379_2(X1,X2) != X5
| ~ in(X4,X5)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1161,lemma,
( in(apply(esk381_2(X1,X2),X3),esk382_3(X1,X2,X3))
| esk374_2(X1,X2) = esk377_2(X1,X2)
| empty(X1)
| ~ in(X3,X1)
| ~ in(ordered_pair(X4,esk380_4(X1,X2,X4,X5)),X2)
| esk379_2(X1,X2) != X5
| ~ in(X4,X5)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1162,lemma,
( X1 = esk382_3(X2,X3,X1)
| in(esk376_2(X2,X3),esk378_2(X2,X3))
| empty(X2)
| ~ in(X1,X2)
| ~ in(ordered_pair(X4,esk380_4(X2,X3,X4,X5)),X3)
| esk379_2(X2,X3) != X5
| ~ in(X4,X5)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1163,lemma,
( X1 = esk382_3(X2,X3,X1)
| in(esk375_2(X2,X3),esk377_2(X2,X3))
| empty(X2)
| ~ in(X1,X2)
| ~ in(ordered_pair(X4,esk380_4(X2,X3,X4,X5)),X3)
| esk379_2(X2,X3) != X5
| ~ in(X4,X5)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1164,lemma,
( X1 = esk382_3(X2,X3,X1)
| empty(X2)
| ~ in(X1,X2)
| ~ in(ordered_pair(X4,esk380_4(X2,X3,X4,X5)),X3)
| esk379_2(X2,X3) != X5
| ~ in(X4,X5)
| esk375_2(X2,X3) != esk376_2(X2,X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1165,lemma,
( X1 = esk382_3(X2,X3,X1)
| in(esk374_2(X2,X3),X2)
| empty(X2)
| ~ in(X1,X2)
| ~ in(ordered_pair(X4,esk380_4(X2,X3,X4,X5)),X3)
| esk379_2(X2,X3) != X5
| ~ in(X4,X5)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1166,lemma,
( X1 = esk382_3(X2,X3,X1)
| esk374_2(X2,X3) = esk378_2(X2,X3)
| empty(X2)
| ~ in(X1,X2)
| ~ in(ordered_pair(X4,esk380_4(X2,X3,X4,X5)),X3)
| esk379_2(X2,X3) != X5
| ~ in(X4,X5)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1167,lemma,
( X1 = esk382_3(X2,X3,X1)
| esk374_2(X2,X3) = esk377_2(X2,X3)
| empty(X2)
| ~ in(X1,X2)
| ~ in(ordered_pair(X4,esk380_4(X2,X3,X4,X5)),X3)
| esk379_2(X2,X3) != X5
| ~ in(X4,X5)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1168,lemma,
( relation_dom(esk381_2(X1,X2)) = X1
| in(esk376_2(X1,X2),esk378_2(X1,X2))
| empty(X1)
| ~ in(ordered_pair(X3,esk380_4(X1,X2,X3,X4)),X2)
| esk379_2(X1,X2) != X4
| ~ in(X3,X4)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1169,lemma,
( relation_dom(esk381_2(X1,X2)) = X1
| in(esk375_2(X1,X2),esk377_2(X1,X2))
| empty(X1)
| ~ in(ordered_pair(X3,esk380_4(X1,X2,X3,X4)),X2)
| esk379_2(X1,X2) != X4
| ~ in(X3,X4)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1170,lemma,
( relation(esk381_2(X1,X2))
| in(esk376_2(X1,X2),esk378_2(X1,X2))
| empty(X1)
| ~ in(ordered_pair(X3,esk380_4(X1,X2,X3,X4)),X2)
| esk379_2(X1,X2) != X4
| ~ in(X3,X4)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1171,lemma,
( relation(esk381_2(X1,X2))
| in(esk375_2(X1,X2),esk377_2(X1,X2))
| empty(X1)
| ~ in(ordered_pair(X3,esk380_4(X1,X2,X3,X4)),X2)
| esk379_2(X1,X2) != X4
| ~ in(X3,X4)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1172,lemma,
( function(esk381_2(X1,X2))
| in(esk376_2(X1,X2),esk378_2(X1,X2))
| empty(X1)
| ~ in(ordered_pair(X3,esk380_4(X1,X2,X3,X4)),X2)
| esk379_2(X1,X2) != X4
| ~ in(X3,X4)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1173,lemma,
( function(esk381_2(X1,X2))
| in(esk375_2(X1,X2),esk377_2(X1,X2))
| empty(X1)
| ~ in(ordered_pair(X3,esk380_4(X1,X2,X3,X4)),X2)
| esk379_2(X1,X2) != X4
| ~ in(X3,X4)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1174,lemma,
( relation_dom(esk381_2(X1,X2)) = X1
| empty(X1)
| ~ in(ordered_pair(X3,esk380_4(X1,X2,X3,X4)),X2)
| esk379_2(X1,X2) != X4
| ~ in(X3,X4)
| esk375_2(X1,X2) != esk376_2(X1,X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1175,lemma,
( relation(esk381_2(X1,X2))
| empty(X1)
| ~ in(ordered_pair(X3,esk380_4(X1,X2,X3,X4)),X2)
| esk379_2(X1,X2) != X4
| ~ in(X3,X4)
| esk375_2(X1,X2) != esk376_2(X1,X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1176,lemma,
( function(esk381_2(X1,X2))
| empty(X1)
| ~ in(ordered_pair(X3,esk380_4(X1,X2,X3,X4)),X2)
| esk379_2(X1,X2) != X4
| ~ in(X3,X4)
| esk375_2(X1,X2) != esk376_2(X1,X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1177,lemma,
( relation_dom(esk381_2(X1,X2)) = X1
| in(esk374_2(X1,X2),X1)
| empty(X1)
| ~ in(ordered_pair(X3,esk380_4(X1,X2,X3,X4)),X2)
| esk379_2(X1,X2) != X4
| ~ in(X3,X4)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1178,lemma,
( relation(esk381_2(X1,X2))
| in(esk374_2(X1,X2),X1)
| empty(X1)
| ~ in(ordered_pair(X3,esk380_4(X1,X2,X3,X4)),X2)
| esk379_2(X1,X2) != X4
| ~ in(X3,X4)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1179,lemma,
( function(esk381_2(X1,X2))
| in(esk374_2(X1,X2),X1)
| empty(X1)
| ~ in(ordered_pair(X3,esk380_4(X1,X2,X3,X4)),X2)
| esk379_2(X1,X2) != X4
| ~ in(X3,X4)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1180,lemma,
( relation_dom(esk381_2(X1,X2)) = X1
| esk374_2(X1,X2) = esk378_2(X1,X2)
| empty(X1)
| ~ in(ordered_pair(X3,esk380_4(X1,X2,X3,X4)),X2)
| esk379_2(X1,X2) != X4
| ~ in(X3,X4)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1181,lemma,
( relation_dom(esk381_2(X1,X2)) = X1
| esk374_2(X1,X2) = esk377_2(X1,X2)
| empty(X1)
| ~ in(ordered_pair(X3,esk380_4(X1,X2,X3,X4)),X2)
| esk379_2(X1,X2) != X4
| ~ in(X3,X4)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1182,lemma,
( relation(esk381_2(X1,X2))
| esk374_2(X1,X2) = esk378_2(X1,X2)
| empty(X1)
| ~ in(ordered_pair(X3,esk380_4(X1,X2,X3,X4)),X2)
| esk379_2(X1,X2) != X4
| ~ in(X3,X4)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1183,lemma,
( function(esk381_2(X1,X2))
| esk374_2(X1,X2) = esk378_2(X1,X2)
| empty(X1)
| ~ in(ordered_pair(X3,esk380_4(X1,X2,X3,X4)),X2)
| esk379_2(X1,X2) != X4
| ~ in(X3,X4)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1184,lemma,
( relation(esk381_2(X1,X2))
| esk374_2(X1,X2) = esk377_2(X1,X2)
| empty(X1)
| ~ in(ordered_pair(X3,esk380_4(X1,X2,X3,X4)),X2)
| esk379_2(X1,X2) != X4
| ~ in(X3,X4)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1185,lemma,
( function(esk381_2(X1,X2))
| esk374_2(X1,X2) = esk377_2(X1,X2)
| empty(X1)
| ~ in(ordered_pair(X3,esk380_4(X1,X2,X3,X4)),X2)
| esk379_2(X1,X2) != X4
| ~ in(X3,X4)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1186,lemma,
( in(esk184_5(X1,X2,X3,X4,X5),X5)
| in(ordered_pair(X3,X4),esk182_2(X1,X2))
| in(ordered_pair(esk179_2(X1,X2),X6),X2)
| empty(X1)
| X3 != X5
| ~ in(X4,X5)
| ~ in(X3,X1)
| ~ in(X6,esk181_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1187,lemma,
( in(esk184_5(X1,X2,X3,X4,X5),X5)
| in(ordered_pair(X3,X4),esk182_2(X1,X2))
| in(ordered_pair(esk178_2(X1,X2),X6),X2)
| empty(X1)
| X3 != X5
| ~ in(X4,X5)
| ~ in(X3,X1)
| ~ in(X6,esk180_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1188,plain,
( in(esk214_5(X1,X2,X3,X4,X5),X5)
| in(X3,esk211_2(X1,X2))
| in(ordered_pair(esk208_2(X1,X2),X6),X2)
| empty(X1)
| X4 != X5
| ~ in(X3,X5)
| ~ in(X4,X1)
| ~ in(X6,esk210_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_691]) ).
cnf(i_0_1189,plain,
( in(esk214_5(X1,X2,X3,X4,X5),X5)
| in(X3,esk211_2(X1,X2))
| in(ordered_pair(esk207_2(X1,X2),X6),X2)
| empty(X1)
| X4 != X5
| ~ in(X3,X5)
| ~ in(X4,X1)
| ~ in(X6,esk209_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_691]) ).
cnf(i_0_1190,lemma,
( in(esk184_5(X1,X2,X3,X4,X5),X5)
| in(ordered_pair(X3,X4),esk182_2(X1,X2))
| in(esk179_2(X1,X2),esk181_2(X1,X2))
| empty(X1)
| X3 != X5
| ~ in(X4,X5)
| ~ in(X3,X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1191,lemma,
( in(esk184_5(X1,X2,X3,X4,X5),X5)
| in(ordered_pair(X3,X4),esk182_2(X1,X2))
| in(esk178_2(X1,X2),esk180_2(X1,X2))
| empty(X1)
| X3 != X5
| ~ in(X4,X5)
| ~ in(X3,X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1192,lemma,
( in(esk184_5(X1,X2,X3,X4,X5),X5)
| in(ordered_pair(X3,X4),esk182_2(X1,X2))
| empty(X1)
| X3 != X5
| ~ in(X4,X5)
| ~ in(X3,X1)
| esk178_2(X1,X2) != esk179_2(X1,X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1193,lemma,
( in(esk184_5(X1,X2,X3,X4,X5),X5)
| in(ordered_pair(X3,X4),esk182_2(X1,X2))
| in(esk177_2(X1,X2),X1)
| empty(X1)
| X3 != X5
| ~ in(X4,X5)
| ~ in(X3,X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1194,lemma,
( in(esk184_5(X1,X2,X3,X4,X5),X5)
| in(ordered_pair(X3,X4),esk182_2(X1,X2))
| in(esk177_2(X1,X2),X1)
| empty(X1)
| X3 != X5
| ~ in(X4,X5)
| ~ in(X3,X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1195,lemma,
( in(esk184_5(X1,X2,X3,X4,X5),X5)
| in(ordered_pair(X3,X4),esk182_2(X1,X2))
| esk177_2(X1,X2) = esk181_2(X1,X2)
| empty(X1)
| X3 != X5
| ~ in(X4,X5)
| ~ in(X3,X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1196,lemma,
( in(esk184_5(X1,X2,X3,X4,X5),X5)
| in(ordered_pair(X3,X4),esk182_2(X1,X2))
| esk177_2(X1,X2) = esk180_2(X1,X2)
| empty(X1)
| X3 != X5
| ~ in(X4,X5)
| ~ in(X3,X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1197,plain,
( esk46_3(X1,X2,X3) = X2
| X3 = fiber(X1,X2)
| ~ in(esk46_3(X1,X2,X3),X3)
| ~ in(ordered_pair(esk46_3(X1,X2,X3),X2),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_703]) ).
cnf(i_0_1198,plain,
( X3 = relation_inverse_image(X1,X2)
| ~ in(esk20_3(X1,X2,X3),X3)
| ~ in(ordered_pair(esk20_3(X1,X2,X3),X4),X1)
| ~ in(X4,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_704]) ).
cnf(i_0_1199,lemma,
( relation_dom_as_subset(X2,X1,X3) = X2
| ~ in(ordered_pair(esk414_3(X1,X2,X3),X4),X3)
| ~ relation_of2_as_subset(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_705]) ).
cnf(i_0_1200,lemma,
( in(ordered_pair(apply(esk381_2(X2,X3),X4),X1),X3)
| in(esk380_4(X2,X3,X5,X6),X6)
| in(ordered_pair(esk376_2(X2,X3),X7),X3)
| empty(X2)
| ~ in(X1,esk382_3(X2,X3,X4))
| ~ in(X4,X2)
| esk379_2(X2,X3) != X6
| ~ in(X5,X6)
| ~ in(X7,esk378_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1201,lemma,
( in(ordered_pair(apply(esk381_2(X2,X3),X4),X1),X3)
| in(esk380_4(X2,X3,X5,X6),X6)
| in(ordered_pair(esk375_2(X2,X3),X7),X3)
| empty(X2)
| ~ in(X1,esk382_3(X2,X3,X4))
| ~ in(X4,X2)
| esk379_2(X2,X3) != X6
| ~ in(X5,X6)
| ~ in(X7,esk377_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1202,lemma,
( in(ordered_pair(X4,esk415_4(X2,X1,X3,X4)),X3)
| relation_dom_as_subset(X1,X2,X3) != X1
| ~ in(X4,X1)
| ~ relation_of2_as_subset(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_705]) ).
cnf(i_0_1203,plain,
( in(ordered_pair(X1,esk19_4(X2,X3,X4,X1)),X2)
| ~ in(X1,X4)
| X4 != relation_inverse_image(X2,X3)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_704]) ).
cnf(i_0_1204,plain,
( in(X3,esk319_3(X2,X7,X6))
| esk314_3(X2,X7,X6) = ordered_pair(esk317_3(X2,X7,X6),esk318_3(X2,X7,X6))
| ~ in(X1,cartesian_product2(X2,X2))
| X1 != X3
| X3 != ordered_pair(X4,X5)
| ~ in(ordered_pair(apply(X6,X4),apply(X6,X5)),X7)
| ~ relation(X7)
| ~ relation(X6)
| ~ function(X6) ),
inference(split_conjunct,[status(thm)],[i_0_684]) ).
cnf(i_0_1205,plain,
( in(X3,esk319_3(X2,X7,X6))
| esk313_3(X2,X7,X6) = ordered_pair(esk315_3(X2,X7,X6),esk316_3(X2,X7,X6))
| ~ in(X1,cartesian_product2(X2,X2))
| X1 != X3
| X3 != ordered_pair(X4,X5)
| ~ in(ordered_pair(apply(X6,X4),apply(X6,X5)),X7)
| ~ relation(X7)
| ~ relation(X6)
| ~ function(X6) ),
inference(split_conjunct,[status(thm)],[i_0_684]) ).
cnf(i_0_1206,plain,
( in(esk100_3(X1,X2,X3),relation_field(X1))
| in(ordered_pair(esk99_3(X1,X2,X3),esk100_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)
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_693]) ).
cnf(i_0_1207,plain,
( in(esk99_3(X1,X2,X3),relation_field(X1))
| in(ordered_pair(esk99_3(X1,X2,X3),esk100_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)
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_693]) ).
fof(i_0_1208,plain,
! [X3945,X3946,X3947,X3949,X3951,X3953,X3955] :
( ( X3945 = X3946
| ~ epred2_3(X3947,X3946,X3945) )
& ( ordinal(esk451_3(X3945,X3946,X3947))
| ~ epred2_3(X3947,X3946,X3945) )
& ( X3946 = esk451_3(X3945,X3946,X3947)
| ~ epred2_3(X3947,X3946,X3945) )
& ( in(esk452_4(X3945,X3946,X3947,X3949),X3949)
| X3949 = empty_set
| ~ element(X3949,powerset(powerset(esk451_3(X3945,X3946,X3947))))
| ~ in(esk451_3(X3945,X3946,X3947),omega)
| ~ epred2_3(X3947,X3946,X3945) )
& ( ~ in(X3951,X3949)
| ~ subset(esk452_4(X3945,X3946,X3947,X3949),X3951)
| X3951 = esk452_4(X3945,X3946,X3947,X3949)
| X3949 = empty_set
| ~ element(X3949,powerset(powerset(esk451_3(X3945,X3946,X3947))))
| ~ in(esk451_3(X3945,X3946,X3947),omega)
| ~ epred2_3(X3947,X3946,X3945) )
& ( X3945 = X3947
| ~ epred2_3(X3947,X3946,X3945) )
& ( ordinal(esk453_3(X3945,X3946,X3947))
| ~ epred2_3(X3947,X3946,X3945) )
& ( X3947 = esk453_3(X3945,X3946,X3947)
| ~ epred2_3(X3947,X3946,X3945) )
& ( in(esk454_4(X3945,X3946,X3947,X3953),X3953)
| X3953 = empty_set
| ~ element(X3953,powerset(powerset(esk453_3(X3945,X3946,X3947))))
| ~ in(esk453_3(X3945,X3946,X3947),omega)
| ~ epred2_3(X3947,X3946,X3945) )
& ( ~ in(X3955,X3953)
| ~ subset(esk454_4(X3945,X3946,X3947,X3953),X3955)
| X3955 = esk454_4(X3945,X3946,X3947,X3953)
| X3953 = empty_set
| ~ element(X3953,powerset(powerset(esk453_3(X3945,X3946,X3947))))
| ~ in(esk453_3(X3945,X3946,X3947),omega)
| ~ epred2_3(X3947,X3946,X3945) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_706])])])])]) ).
cnf(i_0_1209,plain,
( in(esk9_3(X1,X2,X3),X1)
| in(ordered_pair(esk8_3(X1,X2,X3),esk9_3(X1,X2,X3)),X3)
| X3 = relation_rng_restriction(X1,X2)
| ~ relation(X3)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_699]) ).
cnf(i_0_1210,plain,
( in(esk3_3(X1,X2,X3),X2)
| in(ordered_pair(esk3_3(X1,X2,X3),esk4_3(X1,X2,X3)),X3)
| X3 = relation_dom_restriction(X1,X2)
| ~ relation(X3)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_700]) ).
cnf(i_0_1211,plain,
( in(ordered_pair(esk20_3(X1,X2,X3),esk21_3(X1,X2,X3)),X1)
| in(esk20_3(X1,X2,X3),X3)
| X3 = relation_inverse_image(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_704]) ).
cnf(i_0_1212,plain,
( in(ordered_pair(esk18_3(X1,X2,X3),esk17_3(X1,X2,X3)),X1)
| in(esk17_3(X1,X2,X3),X3)
| X3 = relation_image(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_698]) ).
cnf(i_0_1213,lemma,
( in(ordered_pair(apply(esk381_2(X2,X3),X4),X1),X3)
| in(esk380_4(X2,X3,X5,X6),X6)
| in(esk376_2(X2,X3),esk378_2(X2,X3))
| empty(X2)
| ~ in(X1,esk382_3(X2,X3,X4))
| ~ in(X4,X2)
| esk379_2(X2,X3) != X6
| ~ in(X5,X6)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1214,lemma,
( in(ordered_pair(apply(esk381_2(X2,X3),X4),X1),X3)
| in(esk380_4(X2,X3,X5,X6),X6)
| in(esk375_2(X2,X3),esk377_2(X2,X3))
| empty(X2)
| ~ in(X1,esk382_3(X2,X3,X4))
| ~ in(X4,X2)
| esk379_2(X2,X3) != X6
| ~ in(X5,X6)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1215,lemma,
( in(ordered_pair(apply(esk381_2(X2,X3),X4),X1),X3)
| in(esk380_4(X2,X3,X5,X6),X6)
| empty(X2)
| ~ in(X1,esk382_3(X2,X3,X4))
| ~ in(X4,X2)
| esk379_2(X2,X3) != X6
| ~ in(X5,X6)
| esk375_2(X2,X3) != esk376_2(X2,X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1216,lemma,
( in(ordered_pair(apply(esk381_2(X2,X3),X4),X1),X3)
| in(esk380_4(X2,X3,X5,X6),X6)
| in(esk374_2(X2,X3),X2)
| empty(X2)
| ~ in(X1,esk382_3(X2,X3,X4))
| ~ in(X4,X2)
| esk379_2(X2,X3) != X6
| ~ in(X5,X6)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1217,lemma,
( in(ordered_pair(apply(esk381_2(X2,X3),X4),X1),X3)
| in(esk380_4(X2,X3,X5,X6),X6)
| esk374_2(X2,X3) = esk378_2(X2,X3)
| empty(X2)
| ~ in(X1,esk382_3(X2,X3,X4))
| ~ in(X4,X2)
| esk379_2(X2,X3) != X6
| ~ in(X5,X6)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1218,lemma,
( in(ordered_pair(apply(esk381_2(X2,X3),X4),X1),X3)
| in(esk380_4(X2,X3,X5,X6),X6)
| esk374_2(X2,X3) = esk377_2(X2,X3)
| empty(X2)
| ~ in(X1,esk382_3(X2,X3,X4))
| ~ in(X4,X2)
| esk379_2(X2,X3) != X6
| ~ in(X5,X6)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1219,lemma,
( in(ordered_pair(apply(esk381_2(X2,X3),X4),X1),X3)
| in(esk379_2(X2,X3),X2)
| in(ordered_pair(esk376_2(X2,X3),X5),X3)
| empty(X2)
| ~ in(X1,esk382_3(X2,X3,X4))
| ~ in(X4,X2)
| ~ in(X5,esk378_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1220,lemma,
( in(ordered_pair(apply(esk381_2(X2,X3),X4),X1),X3)
| in(esk379_2(X2,X3),X2)
| in(ordered_pair(esk375_2(X2,X3),X5),X3)
| empty(X2)
| ~ in(X1,esk382_3(X2,X3,X4))
| ~ in(X4,X2)
| ~ in(X5,esk377_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1221,plain,
( X2 = relation_inverse(X1)
| ~ in(ordered_pair(esk97_2(X1,X2),esk98_2(X1,X2)),X2)
| ~ in(ordered_pair(esk98_2(X1,X2),esk97_2(X1,X2)),X1)
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_707]) ).
cnf(i_0_1222,plain,
( X1 = X2
| ~ in(ordered_pair(esk56_2(X1,X2),esk57_2(X1,X2)),X1)
| ~ in(ordered_pair(esk56_2(X1,X2),esk57_2(X1,X2)),X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_708]) ).
cnf(i_0_1223,lemma,
( in(ordered_pair(X5,X1),X3)
| in(ordered_pair(esk179_2(X2,X3),X6),X3)
| empty(X2)
| ~ in(X1,esk183_4(X2,X3,X4,X5))
| ~ in(ordered_pair(X4,X5),esk182_2(X2,X3))
| ~ in(X6,esk181_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1224,lemma,
( in(ordered_pair(X5,X1),X3)
| in(ordered_pair(esk178_2(X2,X3),X6),X3)
| empty(X2)
| ~ in(X1,esk183_4(X2,X3,X4,X5))
| ~ in(ordered_pair(X4,X5),esk182_2(X2,X3))
| ~ in(X6,esk180_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1225,plain,
( in(esk227_4(X1,X2,X3,X4),esk228_4(X1,X2,X3,X4))
| in(ordered_pair(esk222_2(X1,X2),X5),X2)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ in(X5,esk223_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_1226,plain,
( in(esk227_4(X1,X2,X3,X4),esk228_4(X1,X2,X3,X4))
| in(ordered_pair(esk219_2(X1,X2),X5),X2)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ in(X5,esk220_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_1227,plain,
( in(esk320_4(X1,X2,X3,X4),cartesian_product2(X1,X1))
| esk314_3(X1,X2,X3) = ordered_pair(esk317_3(X1,X2,X3),esk318_3(X1,X2,X3))
| ~ in(X4,esk319_3(X1,X2,X3))
| ~ relation(X2)
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[i_0_684]) ).
cnf(i_0_1228,plain,
( in(esk320_4(X1,X2,X3,X4),cartesian_product2(X1,X1))
| esk313_3(X1,X2,X3) = ordered_pair(esk315_3(X1,X2,X3),esk316_3(X1,X2,X3))
| ~ in(X4,esk319_3(X1,X2,X3))
| ~ relation(X2)
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[i_0_684]) ).
cnf(i_0_1229,plain,
( in(ordered_pair(esk46_3(X1,X2,X3),X2),X1)
| in(esk46_3(X1,X2,X3),X3)
| X3 = fiber(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_703]) ).
cnf(i_0_1230,lemma,
( in(ordered_pair(esk411_3(X1,X2,X3),X1),X3)
| ~ in(X1,relation_image(X3,X2))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_709]) ).
cnf(i_0_1231,plain,
( in(esk227_4(X1,X2,X3,X4),esk228_4(X1,X2,X3,X4))
| ordered_pair(esk221_2(X1,X2),esk222_2(X1,X2)) = esk217_2(X1,X2)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_1232,plain,
( in(esk227_4(X1,X2,X3,X4),esk228_4(X1,X2,X3,X4))
| ordered_pair(esk218_2(X1,X2),esk219_2(X1,X2)) = esk216_2(X1,X2)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_1233,plain,
( in(ordered_pair(esk92_3(X3,X2,X1),X1),X3)
| ~ in(X1,X2)
| X2 != relation_rng(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_710]) ).
cnf(i_0_1234,plain,
( esk320_4(X1,X2,X3,X4) = X4
| esk314_3(X1,X2,X3) = ordered_pair(esk317_3(X1,X2,X3),esk318_3(X1,X2,X3))
| ~ in(X4,esk319_3(X1,X2,X3))
| ~ relation(X2)
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[i_0_684]) ).
cnf(i_0_1235,plain,
( esk320_4(X1,X2,X3,X4) = X4
| esk313_3(X1,X2,X3) = ordered_pair(esk315_3(X1,X2,X3),esk316_3(X1,X2,X3))
| ~ in(X4,esk319_3(X1,X2,X3))
| ~ relation(X2)
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[i_0_684]) ).
cnf(i_0_1236,lemma,
( in(ordered_pair(apply(esk381_2(X2,X3),X4),X1),X3)
| in(esk379_2(X2,X3),X2)
| in(esk376_2(X2,X3),esk378_2(X2,X3))
| empty(X2)
| ~ in(X1,esk382_3(X2,X3,X4))
| ~ in(X4,X2)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1237,lemma,
( in(ordered_pair(apply(esk381_2(X2,X3),X4),X1),X3)
| in(esk379_2(X2,X3),X2)
| in(esk375_2(X2,X3),esk377_2(X2,X3))
| empty(X2)
| ~ in(X1,esk382_3(X2,X3,X4))
| ~ in(X4,X2)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1238,lemma,
( in(ordered_pair(apply(esk381_2(X2,X3),X4),X1),X3)
| in(esk379_2(X2,X3),X2)
| empty(X2)
| ~ in(X1,esk382_3(X2,X3,X4))
| ~ in(X4,X2)
| esk375_2(X2,X3) != esk376_2(X2,X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1239,lemma,
( in(ordered_pair(apply(esk381_2(X2,X3),X4),X1),X3)
| in(esk379_2(X2,X3),X2)
| in(esk374_2(X2,X3),X2)
| empty(X2)
| ~ in(X1,esk382_3(X2,X3,X4))
| ~ in(X4,X2)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1240,lemma,
( in(ordered_pair(apply(esk381_2(X2,X3),X4),X1),X3)
| in(esk379_2(X2,X3),X2)
| esk374_2(X2,X3) = esk378_2(X2,X3)
| empty(X2)
| ~ in(X1,esk382_3(X2,X3,X4))
| ~ in(X4,X2)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1241,lemma,
( in(ordered_pair(apply(esk381_2(X2,X3),X4),X1),X3)
| in(esk379_2(X2,X3),X2)
| esk374_2(X2,X3) = esk377_2(X2,X3)
| empty(X2)
| ~ in(X1,esk382_3(X2,X3,X4))
| ~ in(X4,X2)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1242,plain,
( in(X3,esk319_3(X2,X7,X6))
| ~ in(X1,cartesian_product2(X2,X2))
| X1 != X3
| X3 != ordered_pair(X4,X5)
| ~ in(ordered_pair(apply(X6,X4),apply(X6,X5)),X7)
| esk313_3(X2,X7,X6) != esk314_3(X2,X7,X6)
| ~ relation(X7)
| ~ relation(X6)
| ~ function(X6) ),
inference(split_conjunct,[status(thm)],[i_0_684]) ).
fof(i_0_1243,plain,
! [X2009,X2010,X2011,X2012,X2013,X2014,X2015,X2016,X2017,X2018] :
( ( ~ in(X2013,X2012)
| X2013 = X2009
| X2013 = X2010
| X2013 = X2011
| X2012 != unordered_triple(X2009,X2010,X2011) )
& ( X2014 != X2009
| in(X2014,X2012)
| X2012 != unordered_triple(X2009,X2010,X2011) )
& ( X2014 != X2010
| in(X2014,X2012)
| X2012 != unordered_triple(X2009,X2010,X2011) )
& ( X2014 != X2011
| in(X2014,X2012)
| X2012 != unordered_triple(X2009,X2010,X2011) )
& ( esk25_4(X2015,X2016,X2017,X2018) != X2015
| ~ in(esk25_4(X2015,X2016,X2017,X2018),X2018)
| X2018 = unordered_triple(X2015,X2016,X2017) )
& ( esk25_4(X2015,X2016,X2017,X2018) != X2016
| ~ in(esk25_4(X2015,X2016,X2017,X2018),X2018)
| X2018 = unordered_triple(X2015,X2016,X2017) )
& ( esk25_4(X2015,X2016,X2017,X2018) != X2017
| ~ in(esk25_4(X2015,X2016,X2017,X2018),X2018)
| X2018 = unordered_triple(X2015,X2016,X2017) )
& ( in(esk25_4(X2015,X2016,X2017,X2018),X2018)
| esk25_4(X2015,X2016,X2017,X2018) = X2015
| esk25_4(X2015,X2016,X2017,X2018) = X2016
| esk25_4(X2015,X2016,X2017,X2018) = X2017
| X2018 = unordered_triple(X2015,X2016,X2017) ) ),
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)],[d1_enumset1])])])])])]) ).
cnf(i_0_1244,lemma,
( in(apply(esk381_2(X1,X2),X3),esk382_3(X1,X2,X3))
| in(esk380_4(X1,X2,X4,X5),X5)
| in(ordered_pair(esk376_2(X1,X2),X6),X2)
| empty(X1)
| ~ in(X3,X1)
| esk379_2(X1,X2) != X5
| ~ in(X4,X5)
| ~ in(X6,esk378_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1245,lemma,
( in(apply(esk381_2(X1,X2),X3),esk382_3(X1,X2,X3))
| in(esk380_4(X1,X2,X4,X5),X5)
| in(ordered_pair(esk375_2(X1,X2),X6),X2)
| empty(X1)
| ~ in(X3,X1)
| esk379_2(X1,X2) != X5
| ~ in(X4,X5)
| ~ in(X6,esk377_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1246,lemma,
( in(X1,esk183_4(X2,X3,X4,X1))
| in(ordered_pair(esk179_2(X2,X3),X5),X3)
| empty(X2)
| ~ in(ordered_pair(X4,X1),esk182_2(X2,X3))
| ~ in(X5,esk181_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1247,lemma,
( in(X1,esk183_4(X2,X3,X4,X1))
| in(ordered_pair(esk178_2(X2,X3),X5),X3)
| empty(X2)
| ~ in(ordered_pair(X4,X1),esk182_2(X2,X3))
| ~ in(X5,esk180_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1248,plain,
( in(X3,esk319_3(X2,X7,X6))
| esk312_3(X2,X7,X6) = esk314_3(X2,X7,X6)
| ~ in(X1,cartesian_product2(X2,X2))
| X1 != X3
| X3 != ordered_pair(X4,X5)
| ~ in(ordered_pair(apply(X6,X4),apply(X6,X5)),X7)
| ~ relation(X7)
| ~ relation(X6)
| ~ function(X6) ),
inference(split_conjunct,[status(thm)],[i_0_684]) ).
cnf(i_0_1249,plain,
( in(X3,esk319_3(X2,X7,X6))
| esk312_3(X2,X7,X6) = esk313_3(X2,X7,X6)
| ~ in(X1,cartesian_product2(X2,X2))
| X1 != X3
| X3 != ordered_pair(X4,X5)
| ~ in(ordered_pair(apply(X6,X4),apply(X6,X5)),X7)
| ~ relation(X7)
| ~ relation(X6)
| ~ function(X6) ),
inference(split_conjunct,[status(thm)],[i_0_684]) ).
cnf(i_0_1250,lemma,
( in(ordered_pair(X5,X1),X3)
| in(esk179_2(X2,X3),esk181_2(X2,X3))
| empty(X2)
| ~ in(X1,esk183_4(X2,X3,X4,X5))
| ~ in(ordered_pair(X4,X5),esk182_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1251,lemma,
( in(ordered_pair(X5,X1),X3)
| in(esk178_2(X2,X3),esk180_2(X2,X3))
| empty(X2)
| ~ in(X1,esk183_4(X2,X3,X4,X5))
| ~ in(ordered_pair(X4,X5),esk182_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1252,plain,
( esk310_4(X2,X3,X4,X5) = subset_complement(the_carrier(X2),X1)
| ordered_pair(esk305_2(X2,X3),esk306_2(X2,X3)) = esk302_2(X2,X3)
| ~ element(X1,powerset(the_carrier(X2)))
| X1 != esk309_4(X2,X3,X4,X5)
| ~ in(X5,esk307_3(X2,X3,X4))
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]) ).
cnf(i_0_1253,plain,
( esk310_4(X2,X3,X4,X5) = subset_complement(the_carrier(X2),X1)
| ordered_pair(esk303_2(X2,X3),esk304_2(X2,X3)) = esk301_2(X2,X3)
| ~ element(X1,powerset(the_carrier(X2)))
| X1 != esk309_4(X2,X3,X4,X5)
| ~ in(X5,esk307_3(X2,X3,X4))
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]) ).
cnf(i_0_1254,plain,
( esk292_4(X2,X3,X4,X5) = subset_complement(the_carrier(X2),X1)
| ordered_pair(esk287_2(X2,X3),esk288_2(X2,X3)) = esk284_2(X2,X3)
| ~ element(X1,powerset(the_carrier(X2)))
| X1 != esk291_4(X2,X3,X4,X5)
| ~ in(X5,esk289_3(X2,X3,X4))
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]) ).
cnf(i_0_1255,plain,
( esk292_4(X2,X3,X4,X5) = subset_complement(the_carrier(X2),X1)
| ordered_pair(esk285_2(X2,X3),esk286_2(X2,X3)) = esk283_2(X2,X3)
| ~ element(X1,powerset(the_carrier(X2)))
| X1 != esk291_4(X2,X3,X4,X5)
| ~ in(X5,esk289_3(X2,X3,X4))
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]) ).
cnf(i_0_1256,lemma,
( in(ordered_pair(X4,X1),esk192_2(X2,X3))
| esk191_2(X2,X3) = subset_complement(the_carrier(X2),X5)
| X1 != subset_complement(the_carrier(X2),esk193_4(X2,X3,X4,X1))
| ~ in(X4,complements_of_subsets(the_carrier(X2),X3))
| ~ element(X5,powerset(the_carrier(X2)))
| X5 != esk189_2(X2,X3)
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_711]) ).
cnf(i_0_1257,lemma,
( in(ordered_pair(X4,X1),esk192_2(X2,X3))
| esk190_2(X2,X3) = subset_complement(the_carrier(X2),X5)
| X1 != subset_complement(the_carrier(X2),esk193_4(X2,X3,X4,X1))
| ~ in(X4,complements_of_subsets(the_carrier(X2),X3))
| ~ element(X5,powerset(the_carrier(X2)))
| X5 != esk189_2(X2,X3)
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_711]) ).
cnf(i_0_1258,lemma,
( in(ordered_pair(X5,X1),X3)
| empty(X2)
| ~ in(X1,esk183_4(X2,X3,X4,X5))
| ~ in(ordered_pair(X4,X5),esk182_2(X2,X3))
| esk178_2(X2,X3) != esk179_2(X2,X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1259,lemma,
( in(ordered_pair(X5,X1),X3)
| in(esk177_2(X2,X3),X2)
| empty(X2)
| ~ in(X1,esk183_4(X2,X3,X4,X5))
| ~ in(ordered_pair(X4,X5),esk182_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1260,lemma,
( in(ordered_pair(X5,X1),X3)
| in(esk177_2(X2,X3),X2)
| empty(X2)
| ~ in(X1,esk183_4(X2,X3,X4,X5))
| ~ in(ordered_pair(X4,X5),esk182_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1261,plain,
( in(esk225_4(X1,X2,X3,X4),cartesian_product2(X1,X3))
| in(ordered_pair(esk222_2(X1,X2),X5),X2)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ in(X5,esk223_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_1262,plain,
( in(esk225_4(X1,X2,X3,X4),cartesian_product2(X1,X3))
| in(ordered_pair(esk219_2(X1,X2),X5),X2)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ in(X5,esk220_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_1263,lemma,
( in(ordered_pair(X5,X1),X3)
| esk177_2(X2,X3) = esk181_2(X2,X3)
| empty(X2)
| ~ in(X1,esk183_4(X2,X3,X4,X5))
| ~ in(ordered_pair(X4,X5),esk182_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1264,lemma,
( in(ordered_pair(X5,X1),X3)
| esk177_2(X2,X3) = esk180_2(X2,X3)
| empty(X2)
| ~ in(X1,esk183_4(X2,X3,X4,X5))
| ~ in(ordered_pair(X4,X5),esk182_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1265,lemma,
( in(ordered_pair(X4,X1),esk192_2(X2,X3))
| in(esk189_2(X2,X3),complements_of_subsets(the_carrier(X2),X3))
| X1 != subset_complement(the_carrier(X2),esk193_4(X2,X3,X4,X1))
| ~ in(X4,complements_of_subsets(the_carrier(X2),X3))
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_711]) ).
cnf(i_0_1266,lemma,
( in(ordered_pair(X4,X1),esk192_2(X2,X3))
| in(esk189_2(X2,X3),complements_of_subsets(the_carrier(X2),X3))
| X1 != subset_complement(the_carrier(X2),esk193_4(X2,X3,X4,X1))
| ~ in(X4,complements_of_subsets(the_carrier(X2),X3))
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_711]) ).
cnf(i_0_1267,plain,
( in(esk226_4(X1,X2,X3,X4),X1)
| in(ordered_pair(esk222_2(X1,X2),X5),X2)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ in(X5,esk223_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_1268,plain,
( in(esk226_4(X1,X2,X3,X4),X1)
| in(ordered_pair(esk219_2(X1,X2),X5),X2)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ in(X5,esk220_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_1269,plain,
( esk226_4(X1,X2,X3,X4) = esk228_4(X1,X2,X3,X4)
| in(ordered_pair(esk222_2(X1,X2),X5),X2)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ in(X5,esk223_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_1270,plain,
( esk226_4(X1,X2,X3,X4) = esk228_4(X1,X2,X3,X4)
| in(ordered_pair(esk219_2(X1,X2),X5),X2)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ in(X5,esk220_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_1271,lemma,
( in(ordered_pair(X4,X1),esk197_2(X2,X3))
| esk196_2(X2,X3) = subset_complement(the_carrier(X2),X5)
| X1 != subset_complement(the_carrier(X2),esk198_4(X2,X3,X4,X1))
| ~ in(X4,X3)
| ~ element(X5,powerset(the_carrier(X2)))
| X5 != esk194_2(X2,X3)
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_712]) ).
cnf(i_0_1272,lemma,
( in(ordered_pair(X4,X1),esk197_2(X2,X3))
| esk195_2(X2,X3) = subset_complement(the_carrier(X2),X5)
| X1 != subset_complement(the_carrier(X2),esk198_4(X2,X3,X4,X1))
| ~ in(X4,X3)
| ~ element(X5,powerset(the_carrier(X2)))
| X5 != esk194_2(X2,X3)
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_712]) ).
cnf(i_0_1273,plain,
( in(ordered_pair(X1,X3),X2)
| ~ in(X1,relation_field(X2))
| ~ in(X3,relation_field(X2))
| ~ in(ordered_pair(apply(X4,X1),apply(X4,X3)),X5)
| ~ relation_isomorphism(X2,X5,X4)
| ~ relation(X4)
| ~ function(X4)
| ~ relation(X5)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_693]) ).
cnf(i_0_1274,lemma,
( in(ordered_pair(X4,X1),esk192_2(X2,X3))
| X1 != subset_complement(the_carrier(X2),esk193_4(X2,X3,X4,X1))
| ~ in(X4,complements_of_subsets(the_carrier(X2),X3))
| esk190_2(X2,X3) != esk191_2(X2,X3)
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_711]) ).
cnf(i_0_1275,lemma,
( in(ordered_pair(X1,X3),esk205_3(X2,X5,X4))
| ~ in(X1,X2)
| ~ in(X3,X2)
| ~ in(ordered_pair(apply(X4,X1),apply(X4,X3)),X5)
| ~ relation(X5)
| ~ relation(X4)
| ~ function(X4) ),
inference(split_conjunct,[status(thm)],[i_0_713]) ).
cnf(i_0_1276,lemma,
( in(X1,esk367_3(X2,X6,X5))
| ~ in(X1,cartesian_product2(X2,X2))
| X1 != ordered_pair(X3,X4)
| ~ in(ordered_pair(apply(X5,X3),apply(X5,X4)),X6)
| ~ relation(X6)
| ~ relation(X5)
| ~ function(X5) ),
inference(split_conjunct,[status(thm)],[i_0_689]) ).
cnf(i_0_1277,plain,
( in(esk290_4(X1,X2,X3,X4),cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| ordered_pair(esk287_2(X1,X2),esk288_2(X1,X2)) = esk284_2(X1,X2)
| ~ in(X4,esk289_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]) ).
cnf(i_0_1278,plain,
( in(esk290_4(X1,X2,X3,X4),cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| ordered_pair(esk285_2(X1,X2),esk286_2(X1,X2)) = esk283_2(X1,X2)
| ~ in(X4,esk289_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]) ).
cnf(i_0_1279,lemma,
( X1 = esk382_3(X2,X3,X1)
| in(esk380_4(X2,X3,X4,X5),X5)
| in(ordered_pair(esk376_2(X2,X3),X6),X3)
| empty(X2)
| ~ in(X1,X2)
| esk379_2(X2,X3) != X5
| ~ in(X4,X5)
| ~ in(X6,esk378_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1280,lemma,
( X1 = esk382_3(X2,X3,X1)
| in(esk380_4(X2,X3,X4,X5),X5)
| in(ordered_pair(esk375_2(X2,X3),X6),X3)
| empty(X2)
| ~ in(X1,X2)
| esk379_2(X2,X3) != X5
| ~ in(X4,X5)
| ~ in(X6,esk377_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1281,lemma,
( in(ordered_pair(X4,X1),esk197_2(X2,X3))
| X1 != subset_complement(the_carrier(X2),esk198_4(X2,X3,X4,X1))
| ~ in(X4,X3)
| esk195_2(X2,X3) != esk196_2(X2,X3)
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_712]) ).
cnf(i_0_1282,lemma,
( in(ordered_pair(X4,X1),esk197_2(X2,X3))
| in(esk194_2(X2,X3),X3)
| X1 != subset_complement(the_carrier(X2),esk198_4(X2,X3,X4,X1))
| ~ in(X4,X3)
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_712]) ).
cnf(i_0_1283,lemma,
( in(ordered_pair(X4,X1),esk197_2(X2,X3))
| in(esk194_2(X2,X3),X3)
| X1 != subset_complement(the_carrier(X2),esk198_4(X2,X3,X4,X1))
| ~ in(X4,X3)
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_712]) ).
fof(i_0_1284,plain,
! [X3102,X3103,X3107,X3108,X3110,X3112,X3113,X3114] :
( ( in(esk280_3(X3102,X3103,X3110),complements_of_subsets(the_carrier(X3102),X3103))
| ~ in(X3110,esk279_2(X3102,X3103))
| in(esk276_2(X3102,X3103),complements_of_subsets(the_carrier(X3102),X3103))
| ~ one_sorted_str(X3102)
| ~ element(X3103,powerset(powerset(the_carrier(X3102)))) )
& ( ~ element(X3112,powerset(the_carrier(X3102)))
| X3112 != esk280_3(X3102,X3103,X3110)
| X3110 = subset_complement(the_carrier(X3102),X3112)
| ~ in(X3110,esk279_2(X3102,X3103))
| in(esk276_2(X3102,X3103),complements_of_subsets(the_carrier(X3102),X3103))
| ~ one_sorted_str(X3102)
| ~ element(X3103,powerset(powerset(the_carrier(X3102)))) )
& ( element(esk281_4(X3102,X3103,X3113,X3114),powerset(the_carrier(X3102)))
| ~ in(X3114,complements_of_subsets(the_carrier(X3102),X3103))
| in(X3113,esk279_2(X3102,X3103))
| in(esk276_2(X3102,X3103),complements_of_subsets(the_carrier(X3102),X3103))
| ~ one_sorted_str(X3102)
| ~ element(X3103,powerset(powerset(the_carrier(X3102)))) )
& ( esk281_4(X3102,X3103,X3113,X3114) = X3114
| ~ in(X3114,complements_of_subsets(the_carrier(X3102),X3103))
| in(X3113,esk279_2(X3102,X3103))
| in(esk276_2(X3102,X3103),complements_of_subsets(the_carrier(X3102),X3103))
| ~ one_sorted_str(X3102)
| ~ element(X3103,powerset(powerset(the_carrier(X3102)))) )
& ( X3113 != subset_complement(the_carrier(X3102),esk281_4(X3102,X3103,X3113,X3114))
| ~ in(X3114,complements_of_subsets(the_carrier(X3102),X3103))
| in(X3113,esk279_2(X3102,X3103))
| in(esk276_2(X3102,X3103),complements_of_subsets(the_carrier(X3102),X3103))
| ~ one_sorted_str(X3102)
| ~ element(X3103,powerset(powerset(the_carrier(X3102)))) )
& ( in(esk280_3(X3102,X3103,X3110),complements_of_subsets(the_carrier(X3102),X3103))
| ~ in(X3110,esk279_2(X3102,X3103))
| ~ element(X3107,powerset(the_carrier(X3102)))
| X3107 != esk276_2(X3102,X3103)
| esk277_2(X3102,X3103) = subset_complement(the_carrier(X3102),X3107)
| ~ one_sorted_str(X3102)
| ~ element(X3103,powerset(powerset(the_carrier(X3102)))) )
& ( ~ element(X3112,powerset(the_carrier(X3102)))
| X3112 != esk280_3(X3102,X3103,X3110)
| X3110 = subset_complement(the_carrier(X3102),X3112)
| ~ in(X3110,esk279_2(X3102,X3103))
| ~ element(X3107,powerset(the_carrier(X3102)))
| X3107 != esk276_2(X3102,X3103)
| esk277_2(X3102,X3103) = subset_complement(the_carrier(X3102),X3107)
| ~ one_sorted_str(X3102)
| ~ element(X3103,powerset(powerset(the_carrier(X3102)))) )
& ( element(esk281_4(X3102,X3103,X3113,X3114),powerset(the_carrier(X3102)))
| ~ in(X3114,complements_of_subsets(the_carrier(X3102),X3103))
| in(X3113,esk279_2(X3102,X3103))
| ~ element(X3107,powerset(the_carrier(X3102)))
| X3107 != esk276_2(X3102,X3103)
| esk277_2(X3102,X3103) = subset_complement(the_carrier(X3102),X3107)
| ~ one_sorted_str(X3102)
| ~ element(X3103,powerset(powerset(the_carrier(X3102)))) )
& ( esk281_4(X3102,X3103,X3113,X3114) = X3114
| ~ in(X3114,complements_of_subsets(the_carrier(X3102),X3103))
| in(X3113,esk279_2(X3102,X3103))
| ~ element(X3107,powerset(the_carrier(X3102)))
| X3107 != esk276_2(X3102,X3103)
| esk277_2(X3102,X3103) = subset_complement(the_carrier(X3102),X3107)
| ~ one_sorted_str(X3102)
| ~ element(X3103,powerset(powerset(the_carrier(X3102)))) )
& ( X3113 != subset_complement(the_carrier(X3102),esk281_4(X3102,X3103,X3113,X3114))
| ~ in(X3114,complements_of_subsets(the_carrier(X3102),X3103))
| in(X3113,esk279_2(X3102,X3103))
| ~ element(X3107,powerset(the_carrier(X3102)))
| X3107 != esk276_2(X3102,X3103)
| esk277_2(X3102,X3103) = subset_complement(the_carrier(X3102),X3107)
| ~ one_sorted_str(X3102)
| ~ element(X3103,powerset(powerset(the_carrier(X3102)))) )
& ( in(esk280_3(X3102,X3103,X3110),complements_of_subsets(the_carrier(X3102),X3103))
| ~ in(X3110,esk279_2(X3102,X3103))
| in(esk276_2(X3102,X3103),complements_of_subsets(the_carrier(X3102),X3103))
| ~ one_sorted_str(X3102)
| ~ element(X3103,powerset(powerset(the_carrier(X3102)))) )
& ( ~ element(X3112,powerset(the_carrier(X3102)))
| X3112 != esk280_3(X3102,X3103,X3110)
| X3110 = subset_complement(the_carrier(X3102),X3112)
| ~ in(X3110,esk279_2(X3102,X3103))
| in(esk276_2(X3102,X3103),complements_of_subsets(the_carrier(X3102),X3103))
| ~ one_sorted_str(X3102)
| ~ element(X3103,powerset(powerset(the_carrier(X3102)))) )
& ( element(esk281_4(X3102,X3103,X3113,X3114),powerset(the_carrier(X3102)))
| ~ in(X3114,complements_of_subsets(the_carrier(X3102),X3103))
| in(X3113,esk279_2(X3102,X3103))
| in(esk276_2(X3102,X3103),complements_of_subsets(the_carrier(X3102),X3103))
| ~ one_sorted_str(X3102)
| ~ element(X3103,powerset(powerset(the_carrier(X3102)))) )
& ( esk281_4(X3102,X3103,X3113,X3114) = X3114
| ~ in(X3114,complements_of_subsets(the_carrier(X3102),X3103))
| in(X3113,esk279_2(X3102,X3103))
| in(esk276_2(X3102,X3103),complements_of_subsets(the_carrier(X3102),X3103))
| ~ one_sorted_str(X3102)
| ~ element(X3103,powerset(powerset(the_carrier(X3102)))) )
& ( X3113 != subset_complement(the_carrier(X3102),esk281_4(X3102,X3103,X3113,X3114))
| ~ in(X3114,complements_of_subsets(the_carrier(X3102),X3103))
| in(X3113,esk279_2(X3102,X3103))
| in(esk276_2(X3102,X3103),complements_of_subsets(the_carrier(X3102),X3103))
| ~ one_sorted_str(X3102)
| ~ element(X3103,powerset(powerset(the_carrier(X3102)))) )
& ( in(esk280_3(X3102,X3103,X3110),complements_of_subsets(the_carrier(X3102),X3103))
| ~ in(X3110,esk279_2(X3102,X3103))
| ~ element(X3108,powerset(the_carrier(X3102)))
| X3108 != esk276_2(X3102,X3103)
| esk278_2(X3102,X3103) = subset_complement(the_carrier(X3102),X3108)
| ~ one_sorted_str(X3102)
| ~ element(X3103,powerset(powerset(the_carrier(X3102)))) )
& ( ~ element(X3112,powerset(the_carrier(X3102)))
| X3112 != esk280_3(X3102,X3103,X3110)
| X3110 = subset_complement(the_carrier(X3102),X3112)
| ~ in(X3110,esk279_2(X3102,X3103))
| ~ element(X3108,powerset(the_carrier(X3102)))
| X3108 != esk276_2(X3102,X3103)
| esk278_2(X3102,X3103) = subset_complement(the_carrier(X3102),X3108)
| ~ one_sorted_str(X3102)
| ~ element(X3103,powerset(powerset(the_carrier(X3102)))) )
& ( element(esk281_4(X3102,X3103,X3113,X3114),powerset(the_carrier(X3102)))
| ~ in(X3114,complements_of_subsets(the_carrier(X3102),X3103))
| in(X3113,esk279_2(X3102,X3103))
| ~ element(X3108,powerset(the_carrier(X3102)))
| X3108 != esk276_2(X3102,X3103)
| esk278_2(X3102,X3103) = subset_complement(the_carrier(X3102),X3108)
| ~ one_sorted_str(X3102)
| ~ element(X3103,powerset(powerset(the_carrier(X3102)))) )
& ( esk281_4(X3102,X3103,X3113,X3114) = X3114
| ~ in(X3114,complements_of_subsets(the_carrier(X3102),X3103))
| in(X3113,esk279_2(X3102,X3103))
| ~ element(X3108,powerset(the_carrier(X3102)))
| X3108 != esk276_2(X3102,X3103)
| esk278_2(X3102,X3103) = subset_complement(the_carrier(X3102),X3108)
| ~ one_sorted_str(X3102)
| ~ element(X3103,powerset(powerset(the_carrier(X3102)))) )
& ( X3113 != subset_complement(the_carrier(X3102),esk281_4(X3102,X3103,X3113,X3114))
| ~ in(X3114,complements_of_subsets(the_carrier(X3102),X3103))
| in(X3113,esk279_2(X3102,X3103))
| ~ element(X3108,powerset(the_carrier(X3102)))
| X3108 != esk276_2(X3102,X3103)
| esk278_2(X3102,X3103) = subset_complement(the_carrier(X3102),X3108)
| ~ one_sorted_str(X3102)
| ~ element(X3103,powerset(powerset(the_carrier(X3102)))) )
& ( in(esk280_3(X3102,X3103,X3110),complements_of_subsets(the_carrier(X3102),X3103))
| ~ in(X3110,esk279_2(X3102,X3103))
| esk277_2(X3102,X3103) != esk278_2(X3102,X3103)
| ~ one_sorted_str(X3102)
| ~ element(X3103,powerset(powerset(the_carrier(X3102)))) )
& ( ~ element(X3112,powerset(the_carrier(X3102)))
| X3112 != esk280_3(X3102,X3103,X3110)
| X3110 = subset_complement(the_carrier(X3102),X3112)
| ~ in(X3110,esk279_2(X3102,X3103))
| esk277_2(X3102,X3103) != esk278_2(X3102,X3103)
| ~ one_sorted_str(X3102)
| ~ element(X3103,powerset(powerset(the_carrier(X3102)))) )
& ( element(esk281_4(X3102,X3103,X3113,X3114),powerset(the_carrier(X3102)))
| ~ in(X3114,complements_of_subsets(the_carrier(X3102),X3103))
| in(X3113,esk279_2(X3102,X3103))
| esk277_2(X3102,X3103) != esk278_2(X3102,X3103)
| ~ one_sorted_str(X3102)
| ~ element(X3103,powerset(powerset(the_carrier(X3102)))) )
& ( esk281_4(X3102,X3103,X3113,X3114) = X3114
| ~ in(X3114,complements_of_subsets(the_carrier(X3102),X3103))
| in(X3113,esk279_2(X3102,X3103))
| esk277_2(X3102,X3103) != esk278_2(X3102,X3103)
| ~ one_sorted_str(X3102)
| ~ element(X3103,powerset(powerset(the_carrier(X3102)))) )
& ( X3113 != subset_complement(the_carrier(X3102),esk281_4(X3102,X3103,X3113,X3114))
| ~ in(X3114,complements_of_subsets(the_carrier(X3102),X3103))
| in(X3113,esk279_2(X3102,X3103))
| esk277_2(X3102,X3103) != esk278_2(X3102,X3103)
| ~ one_sorted_str(X3102)
| ~ element(X3103,powerset(powerset(the_carrier(X3102)))) ) ),
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)],[i_0_714])])])])])]) ).
cnf(i_0_1285,plain,
( in(ordered_pair(esk97_2(X1,X2),esk98_2(X1,X2)),X2)
| in(ordered_pair(esk98_2(X1,X2),esk97_2(X1,X2)),X1)
| X2 = relation_inverse(X1)
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_707]) ).
cnf(i_0_1286,plain,
( in(ordered_pair(esk56_2(X1,X2),esk57_2(X1,X2)),X1)
| in(ordered_pair(esk56_2(X1,X2),esk57_2(X1,X2)),X2)
| X1 = X2
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_708]) ).
cnf(i_0_1287,plain,
( X3 = relation_image(X1,X2)
| ~ in(esk17_3(X1,X2,X3),X3)
| ~ in(ordered_pair(X4,esk17_3(X1,X2,X3)),X1)
| ~ in(X4,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_698]) ).
cnf(i_0_1288,plain,
( in(esk291_4(X1,X2,X3,X4),complements_of_subsets(the_carrier(X1),X2))
| ordered_pair(esk287_2(X1,X2),esk288_2(X1,X2)) = esk284_2(X1,X2)
| ~ in(X4,esk289_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]) ).
cnf(i_0_1289,plain,
( in(esk291_4(X1,X2,X3,X4),complements_of_subsets(the_carrier(X1),X2))
| ordered_pair(esk285_2(X1,X2),esk286_2(X1,X2)) = esk283_2(X1,X2)
| ~ in(X4,esk289_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]) ).
cnf(i_0_1290,lemma,
( relation_dom(esk381_2(X1,X2)) = X1
| in(esk380_4(X1,X2,X3,X4),X4)
| in(ordered_pair(esk376_2(X1,X2),X5),X2)
| empty(X1)
| esk379_2(X1,X2) != X4
| ~ in(X3,X4)
| ~ in(X5,esk378_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1291,lemma,
( relation_dom(esk381_2(X1,X2)) = X1
| in(esk380_4(X1,X2,X3,X4),X4)
| in(ordered_pair(esk375_2(X1,X2),X5),X2)
| empty(X1)
| esk379_2(X1,X2) != X4
| ~ in(X3,X4)
| ~ in(X5,esk377_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1292,lemma,
( relation(esk381_2(X1,X2))
| in(esk380_4(X1,X2,X3,X4),X4)
| in(ordered_pair(esk376_2(X1,X2),X5),X2)
| empty(X1)
| esk379_2(X1,X2) != X4
| ~ in(X3,X4)
| ~ in(X5,esk378_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1293,lemma,
( relation(esk381_2(X1,X2))
| in(esk380_4(X1,X2,X3,X4),X4)
| in(ordered_pair(esk375_2(X1,X2),X5),X2)
| empty(X1)
| esk379_2(X1,X2) != X4
| ~ in(X3,X4)
| ~ in(X5,esk377_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1294,lemma,
( function(esk381_2(X1,X2))
| in(esk380_4(X1,X2,X3,X4),X4)
| in(ordered_pair(esk376_2(X1,X2),X5),X2)
| empty(X1)
| esk379_2(X1,X2) != X4
| ~ in(X3,X4)
| ~ in(X5,esk378_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1295,lemma,
( function(esk381_2(X1,X2))
| in(esk380_4(X1,X2,X3,X4),X4)
| in(ordered_pair(esk375_2(X1,X2),X5),X2)
| empty(X1)
| esk379_2(X1,X2) != X4
| ~ in(X3,X4)
| ~ in(X5,esk377_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1296,plain,
( esk65_3(X1,X2,X3) = ordered_pair(esk66_3(X1,X2,X3),esk67_3(X1,X2,X3))
| in(esk65_3(X1,X2,X3),X3)
| X3 = cartesian_product2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_702]) ).
cnf(i_0_1297,plain,
( in(esk308_4(X1,X2,X3,X4),cartesian_product2(X2,X3))
| ordered_pair(esk305_2(X1,X2),esk306_2(X1,X2)) = esk302_2(X1,X2)
| ~ in(X4,esk307_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]) ).
cnf(i_0_1298,plain,
( in(esk308_4(X1,X2,X3,X4),cartesian_product2(X2,X3))
| ordered_pair(esk303_2(X1,X2),esk304_2(X1,X2)) = esk301_2(X1,X2)
| ~ in(X4,esk307_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]) ).
cnf(i_0_1299,plain,
( ordered_pair(esk244_3(X1,X2,X3),esk245_3(X1,X2,X3)) = X3
| ordered_pair(esk240_1(X1),esk241_1(X1)) = esk237_1(X1)
| ~ in(X3,esk242_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_715]) ).
cnf(i_0_1300,plain,
( ordered_pair(esk244_3(X1,X2,X3),esk245_3(X1,X2,X3)) = X3
| ordered_pair(esk238_1(X1),esk239_1(X1)) = esk236_1(X1)
| ~ in(X3,esk242_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_715]) ).
cnf(i_0_1301,plain,
( in(esk309_4(X1,X2,X3,X4),X2)
| ordered_pair(esk305_2(X1,X2),esk306_2(X1,X2)) = esk302_2(X1,X2)
| ~ in(X4,esk307_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]) ).
cnf(i_0_1302,plain,
( in(esk309_4(X1,X2,X3,X4),X2)
| ordered_pair(esk303_2(X1,X2),esk304_2(X1,X2)) = esk301_2(X1,X2)
| ~ in(X4,esk307_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]) ).
fof(i_0_1303,plain,
! [X3139,X3140,X3144,X3145,X3147,X3149,X3150,X3151] :
( ( in(esk298_3(X3139,X3140,X3147),X3140)
| ~ in(X3147,esk297_2(X3139,X3140))
| in(esk294_2(X3139,X3140),X3140)
| ~ one_sorted_str(X3139)
| ~ element(X3140,powerset(powerset(the_carrier(X3139)))) )
& ( ~ element(X3149,powerset(the_carrier(X3139)))
| X3149 != esk298_3(X3139,X3140,X3147)
| X3147 = subset_complement(the_carrier(X3139),X3149)
| ~ in(X3147,esk297_2(X3139,X3140))
| in(esk294_2(X3139,X3140),X3140)
| ~ one_sorted_str(X3139)
| ~ element(X3140,powerset(powerset(the_carrier(X3139)))) )
& ( element(esk299_4(X3139,X3140,X3150,X3151),powerset(the_carrier(X3139)))
| ~ in(X3151,X3140)
| in(X3150,esk297_2(X3139,X3140))
| in(esk294_2(X3139,X3140),X3140)
| ~ one_sorted_str(X3139)
| ~ element(X3140,powerset(powerset(the_carrier(X3139)))) )
& ( esk299_4(X3139,X3140,X3150,X3151) = X3151
| ~ in(X3151,X3140)
| in(X3150,esk297_2(X3139,X3140))
| in(esk294_2(X3139,X3140),X3140)
| ~ one_sorted_str(X3139)
| ~ element(X3140,powerset(powerset(the_carrier(X3139)))) )
& ( X3150 != subset_complement(the_carrier(X3139),esk299_4(X3139,X3140,X3150,X3151))
| ~ in(X3151,X3140)
| in(X3150,esk297_2(X3139,X3140))
| in(esk294_2(X3139,X3140),X3140)
| ~ one_sorted_str(X3139)
| ~ element(X3140,powerset(powerset(the_carrier(X3139)))) )
& ( in(esk298_3(X3139,X3140,X3147),X3140)
| ~ in(X3147,esk297_2(X3139,X3140))
| ~ element(X3144,powerset(the_carrier(X3139)))
| X3144 != esk294_2(X3139,X3140)
| esk295_2(X3139,X3140) = subset_complement(the_carrier(X3139),X3144)
| ~ one_sorted_str(X3139)
| ~ element(X3140,powerset(powerset(the_carrier(X3139)))) )
& ( ~ element(X3149,powerset(the_carrier(X3139)))
| X3149 != esk298_3(X3139,X3140,X3147)
| X3147 = subset_complement(the_carrier(X3139),X3149)
| ~ in(X3147,esk297_2(X3139,X3140))
| ~ element(X3144,powerset(the_carrier(X3139)))
| X3144 != esk294_2(X3139,X3140)
| esk295_2(X3139,X3140) = subset_complement(the_carrier(X3139),X3144)
| ~ one_sorted_str(X3139)
| ~ element(X3140,powerset(powerset(the_carrier(X3139)))) )
& ( element(esk299_4(X3139,X3140,X3150,X3151),powerset(the_carrier(X3139)))
| ~ in(X3151,X3140)
| in(X3150,esk297_2(X3139,X3140))
| ~ element(X3144,powerset(the_carrier(X3139)))
| X3144 != esk294_2(X3139,X3140)
| esk295_2(X3139,X3140) = subset_complement(the_carrier(X3139),X3144)
| ~ one_sorted_str(X3139)
| ~ element(X3140,powerset(powerset(the_carrier(X3139)))) )
& ( esk299_4(X3139,X3140,X3150,X3151) = X3151
| ~ in(X3151,X3140)
| in(X3150,esk297_2(X3139,X3140))
| ~ element(X3144,powerset(the_carrier(X3139)))
| X3144 != esk294_2(X3139,X3140)
| esk295_2(X3139,X3140) = subset_complement(the_carrier(X3139),X3144)
| ~ one_sorted_str(X3139)
| ~ element(X3140,powerset(powerset(the_carrier(X3139)))) )
& ( X3150 != subset_complement(the_carrier(X3139),esk299_4(X3139,X3140,X3150,X3151))
| ~ in(X3151,X3140)
| in(X3150,esk297_2(X3139,X3140))
| ~ element(X3144,powerset(the_carrier(X3139)))
| X3144 != esk294_2(X3139,X3140)
| esk295_2(X3139,X3140) = subset_complement(the_carrier(X3139),X3144)
| ~ one_sorted_str(X3139)
| ~ element(X3140,powerset(powerset(the_carrier(X3139)))) )
& ( in(esk298_3(X3139,X3140,X3147),X3140)
| ~ in(X3147,esk297_2(X3139,X3140))
| in(esk294_2(X3139,X3140),X3140)
| ~ one_sorted_str(X3139)
| ~ element(X3140,powerset(powerset(the_carrier(X3139)))) )
& ( ~ element(X3149,powerset(the_carrier(X3139)))
| X3149 != esk298_3(X3139,X3140,X3147)
| X3147 = subset_complement(the_carrier(X3139),X3149)
| ~ in(X3147,esk297_2(X3139,X3140))
| in(esk294_2(X3139,X3140),X3140)
| ~ one_sorted_str(X3139)
| ~ element(X3140,powerset(powerset(the_carrier(X3139)))) )
& ( element(esk299_4(X3139,X3140,X3150,X3151),powerset(the_carrier(X3139)))
| ~ in(X3151,X3140)
| in(X3150,esk297_2(X3139,X3140))
| in(esk294_2(X3139,X3140),X3140)
| ~ one_sorted_str(X3139)
| ~ element(X3140,powerset(powerset(the_carrier(X3139)))) )
& ( esk299_4(X3139,X3140,X3150,X3151) = X3151
| ~ in(X3151,X3140)
| in(X3150,esk297_2(X3139,X3140))
| in(esk294_2(X3139,X3140),X3140)
| ~ one_sorted_str(X3139)
| ~ element(X3140,powerset(powerset(the_carrier(X3139)))) )
& ( X3150 != subset_complement(the_carrier(X3139),esk299_4(X3139,X3140,X3150,X3151))
| ~ in(X3151,X3140)
| in(X3150,esk297_2(X3139,X3140))
| in(esk294_2(X3139,X3140),X3140)
| ~ one_sorted_str(X3139)
| ~ element(X3140,powerset(powerset(the_carrier(X3139)))) )
& ( in(esk298_3(X3139,X3140,X3147),X3140)
| ~ in(X3147,esk297_2(X3139,X3140))
| ~ element(X3145,powerset(the_carrier(X3139)))
| X3145 != esk294_2(X3139,X3140)
| esk296_2(X3139,X3140) = subset_complement(the_carrier(X3139),X3145)
| ~ one_sorted_str(X3139)
| ~ element(X3140,powerset(powerset(the_carrier(X3139)))) )
& ( ~ element(X3149,powerset(the_carrier(X3139)))
| X3149 != esk298_3(X3139,X3140,X3147)
| X3147 = subset_complement(the_carrier(X3139),X3149)
| ~ in(X3147,esk297_2(X3139,X3140))
| ~ element(X3145,powerset(the_carrier(X3139)))
| X3145 != esk294_2(X3139,X3140)
| esk296_2(X3139,X3140) = subset_complement(the_carrier(X3139),X3145)
| ~ one_sorted_str(X3139)
| ~ element(X3140,powerset(powerset(the_carrier(X3139)))) )
& ( element(esk299_4(X3139,X3140,X3150,X3151),powerset(the_carrier(X3139)))
| ~ in(X3151,X3140)
| in(X3150,esk297_2(X3139,X3140))
| ~ element(X3145,powerset(the_carrier(X3139)))
| X3145 != esk294_2(X3139,X3140)
| esk296_2(X3139,X3140) = subset_complement(the_carrier(X3139),X3145)
| ~ one_sorted_str(X3139)
| ~ element(X3140,powerset(powerset(the_carrier(X3139)))) )
& ( esk299_4(X3139,X3140,X3150,X3151) = X3151
| ~ in(X3151,X3140)
| in(X3150,esk297_2(X3139,X3140))
| ~ element(X3145,powerset(the_carrier(X3139)))
| X3145 != esk294_2(X3139,X3140)
| esk296_2(X3139,X3140) = subset_complement(the_carrier(X3139),X3145)
| ~ one_sorted_str(X3139)
| ~ element(X3140,powerset(powerset(the_carrier(X3139)))) )
& ( X3150 != subset_complement(the_carrier(X3139),esk299_4(X3139,X3140,X3150,X3151))
| ~ in(X3151,X3140)
| in(X3150,esk297_2(X3139,X3140))
| ~ element(X3145,powerset(the_carrier(X3139)))
| X3145 != esk294_2(X3139,X3140)
| esk296_2(X3139,X3140) = subset_complement(the_carrier(X3139),X3145)
| ~ one_sorted_str(X3139)
| ~ element(X3140,powerset(powerset(the_carrier(X3139)))) )
& ( in(esk298_3(X3139,X3140,X3147),X3140)
| ~ in(X3147,esk297_2(X3139,X3140))
| esk295_2(X3139,X3140) != esk296_2(X3139,X3140)
| ~ one_sorted_str(X3139)
| ~ element(X3140,powerset(powerset(the_carrier(X3139)))) )
& ( ~ element(X3149,powerset(the_carrier(X3139)))
| X3149 != esk298_3(X3139,X3140,X3147)
| X3147 = subset_complement(the_carrier(X3139),X3149)
| ~ in(X3147,esk297_2(X3139,X3140))
| esk295_2(X3139,X3140) != esk296_2(X3139,X3140)
| ~ one_sorted_str(X3139)
| ~ element(X3140,powerset(powerset(the_carrier(X3139)))) )
& ( element(esk299_4(X3139,X3140,X3150,X3151),powerset(the_carrier(X3139)))
| ~ in(X3151,X3140)
| in(X3150,esk297_2(X3139,X3140))
| esk295_2(X3139,X3140) != esk296_2(X3139,X3140)
| ~ one_sorted_str(X3139)
| ~ element(X3140,powerset(powerset(the_carrier(X3139)))) )
& ( esk299_4(X3139,X3140,X3150,X3151) = X3151
| ~ in(X3151,X3140)
| in(X3150,esk297_2(X3139,X3140))
| esk295_2(X3139,X3140) != esk296_2(X3139,X3140)
| ~ one_sorted_str(X3139)
| ~ element(X3140,powerset(powerset(the_carrier(X3139)))) )
& ( X3150 != subset_complement(the_carrier(X3139),esk299_4(X3139,X3140,X3150,X3151))
| ~ in(X3151,X3140)
| in(X3150,esk297_2(X3139,X3140))
| esk295_2(X3139,X3140) != esk296_2(X3139,X3140)
| ~ one_sorted_str(X3139)
| ~ element(X3140,powerset(powerset(the_carrier(X3139)))) ) ),
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)],[i_0_716])])])])])]) ).
cnf(i_0_1304,plain,
( in(esk254_4(X1,X2,X3,X4),esk253_3(X1,X2,X3))
| in(X2,esk249_1(X1))
| epred2_3(esk248_1(X1),esk247_1(X1),esk246_1(X1))
| ~ in(X4,esk253_3(X1,X2,X3))
| ~ ordinal(X3)
| X2 != X3
| ~ in(X5,succ(X1))
| X5 != X2
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_717]) ).
cnf(i_0_1305,plain,
succ(X1) = set_union2(X1,unordered_pair(X1,X1)),
inference(rw,[status(thm)],[i_0_718,c_0_681]) ).
cnf(i_0_1306,lemma,
( X1 = esk183_4(X2,X3,X1,X4)
| in(ordered_pair(esk179_2(X2,X3),X5),X3)
| empty(X2)
| ~ in(ordered_pair(X1,X4),esk182_2(X2,X3))
| ~ in(X5,esk181_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1307,lemma,
( X1 = esk183_4(X2,X3,X1,X4)
| in(ordered_pair(esk178_2(X2,X3),X5),X3)
| empty(X2)
| ~ in(ordered_pair(X1,X4),esk182_2(X2,X3))
| ~ in(X5,esk180_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1308,lemma,
( relation_rng_as_subset(X2,X3,X4) = X3
| ~ in(ordered_pair(X1,esk416_3(X2,X3,X4)),X4)
| ~ relation_of2_as_subset(X4,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_695]) ).
fof(i_0_1309,plain,
! [X3204,X3205,X3206,X3211,X3213,X3214] :
( ( in(esk332_4(X3204,X3205,X3206,X3211),powerset(relation_dom(X3206)))
| ~ in(X3211,esk331_3(X3204,X3205,X3206))
| esk328_3(X3204,X3205,X3206) = esk329_3(X3204,X3205,X3206)
| ~ element(X3205,powerset(powerset(X3204)))
| ~ relation(X3206)
| ~ function(X3206) )
& ( esk332_4(X3204,X3205,X3206,X3211) = X3211
| ~ in(X3211,esk331_3(X3204,X3205,X3206))
| esk328_3(X3204,X3205,X3206) = esk329_3(X3204,X3205,X3206)
| ~ element(X3205,powerset(powerset(X3204)))
| ~ relation(X3206)
| ~ function(X3206) )
& ( in(relation_image(X3206,X3211),X3205)
| ~ in(X3211,esk331_3(X3204,X3205,X3206))
| esk328_3(X3204,X3205,X3206) = esk329_3(X3204,X3205,X3206)
| ~ element(X3205,powerset(powerset(X3204)))
| ~ relation(X3206)
| ~ function(X3206) )
& ( ~ in(X3214,powerset(relation_dom(X3206)))
| X3214 != X3213
| ~ in(relation_image(X3206,X3213),X3205)
| in(X3213,esk331_3(X3204,X3205,X3206))
| esk328_3(X3204,X3205,X3206) = esk329_3(X3204,X3205,X3206)
| ~ element(X3205,powerset(powerset(X3204)))
| ~ relation(X3206)
| ~ function(X3206) )
& ( in(esk332_4(X3204,X3205,X3206,X3211),powerset(relation_dom(X3206)))
| ~ in(X3211,esk331_3(X3204,X3205,X3206))
| in(relation_image(X3206,esk329_3(X3204,X3205,X3206)),X3205)
| ~ element(X3205,powerset(powerset(X3204)))
| ~ relation(X3206)
| ~ function(X3206) )
& ( esk332_4(X3204,X3205,X3206,X3211) = X3211
| ~ in(X3211,esk331_3(X3204,X3205,X3206))
| in(relation_image(X3206,esk329_3(X3204,X3205,X3206)),X3205)
| ~ element(X3205,powerset(powerset(X3204)))
| ~ relation(X3206)
| ~ function(X3206) )
& ( in(relation_image(X3206,X3211),X3205)
| ~ in(X3211,esk331_3(X3204,X3205,X3206))
| in(relation_image(X3206,esk329_3(X3204,X3205,X3206)),X3205)
| ~ element(X3205,powerset(powerset(X3204)))
| ~ relation(X3206)
| ~ function(X3206) )
& ( ~ in(X3214,powerset(relation_dom(X3206)))
| X3214 != X3213
| ~ in(relation_image(X3206,X3213),X3205)
| in(X3213,esk331_3(X3204,X3205,X3206))
| in(relation_image(X3206,esk329_3(X3204,X3205,X3206)),X3205)
| ~ element(X3205,powerset(powerset(X3204)))
| ~ relation(X3206)
| ~ function(X3206) )
& ( in(esk332_4(X3204,X3205,X3206,X3211),powerset(relation_dom(X3206)))
| ~ in(X3211,esk331_3(X3204,X3205,X3206))
| esk328_3(X3204,X3205,X3206) = esk330_3(X3204,X3205,X3206)
| ~ element(X3205,powerset(powerset(X3204)))
| ~ relation(X3206)
| ~ function(X3206) )
& ( esk332_4(X3204,X3205,X3206,X3211) = X3211
| ~ in(X3211,esk331_3(X3204,X3205,X3206))
| esk328_3(X3204,X3205,X3206) = esk330_3(X3204,X3205,X3206)
| ~ element(X3205,powerset(powerset(X3204)))
| ~ relation(X3206)
| ~ function(X3206) )
& ( in(relation_image(X3206,X3211),X3205)
| ~ in(X3211,esk331_3(X3204,X3205,X3206))
| esk328_3(X3204,X3205,X3206) = esk330_3(X3204,X3205,X3206)
| ~ element(X3205,powerset(powerset(X3204)))
| ~ relation(X3206)
| ~ function(X3206) )
& ( ~ in(X3214,powerset(relation_dom(X3206)))
| X3214 != X3213
| ~ in(relation_image(X3206,X3213),X3205)
| in(X3213,esk331_3(X3204,X3205,X3206))
| esk328_3(X3204,X3205,X3206) = esk330_3(X3204,X3205,X3206)
| ~ element(X3205,powerset(powerset(X3204)))
| ~ relation(X3206)
| ~ function(X3206) )
& ( in(esk332_4(X3204,X3205,X3206,X3211),powerset(relation_dom(X3206)))
| ~ in(X3211,esk331_3(X3204,X3205,X3206))
| in(relation_image(X3206,esk330_3(X3204,X3205,X3206)),X3205)
| ~ element(X3205,powerset(powerset(X3204)))
| ~ relation(X3206)
| ~ function(X3206) )
& ( esk332_4(X3204,X3205,X3206,X3211) = X3211
| ~ in(X3211,esk331_3(X3204,X3205,X3206))
| in(relation_image(X3206,esk330_3(X3204,X3205,X3206)),X3205)
| ~ element(X3205,powerset(powerset(X3204)))
| ~ relation(X3206)
| ~ function(X3206) )
& ( in(relation_image(X3206,X3211),X3205)
| ~ in(X3211,esk331_3(X3204,X3205,X3206))
| in(relation_image(X3206,esk330_3(X3204,X3205,X3206)),X3205)
| ~ element(X3205,powerset(powerset(X3204)))
| ~ relation(X3206)
| ~ function(X3206) )
& ( ~ in(X3214,powerset(relation_dom(X3206)))
| X3214 != X3213
| ~ in(relation_image(X3206,X3213),X3205)
| in(X3213,esk331_3(X3204,X3205,X3206))
| in(relation_image(X3206,esk330_3(X3204,X3205,X3206)),X3205)
| ~ element(X3205,powerset(powerset(X3204)))
| ~ relation(X3206)
| ~ function(X3206) )
& ( in(esk332_4(X3204,X3205,X3206,X3211),powerset(relation_dom(X3206)))
| ~ in(X3211,esk331_3(X3204,X3205,X3206))
| esk329_3(X3204,X3205,X3206) != esk330_3(X3204,X3205,X3206)
| ~ element(X3205,powerset(powerset(X3204)))
| ~ relation(X3206)
| ~ function(X3206) )
& ( esk332_4(X3204,X3205,X3206,X3211) = X3211
| ~ in(X3211,esk331_3(X3204,X3205,X3206))
| esk329_3(X3204,X3205,X3206) != esk330_3(X3204,X3205,X3206)
| ~ element(X3205,powerset(powerset(X3204)))
| ~ relation(X3206)
| ~ function(X3206) )
& ( in(relation_image(X3206,X3211),X3205)
| ~ in(X3211,esk331_3(X3204,X3205,X3206))
| esk329_3(X3204,X3205,X3206) != esk330_3(X3204,X3205,X3206)
| ~ element(X3205,powerset(powerset(X3204)))
| ~ relation(X3206)
| ~ function(X3206) )
& ( ~ in(X3214,powerset(relation_dom(X3206)))
| X3214 != X3213
| ~ in(relation_image(X3206,X3213),X3205)
| in(X3213,esk331_3(X3204,X3205,X3206))
| esk329_3(X3204,X3205,X3206) != esk330_3(X3204,X3205,X3206)
| ~ element(X3205,powerset(powerset(X3204)))
| ~ relation(X3206)
| ~ function(X3206) ) ),
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)],[s1_tarski__e6_27__finset_1__1])])])])])]) ).
cnf(i_0_1310,plain,
( in(esk225_4(X1,X2,X3,X4),cartesian_product2(X1,X3))
| ordered_pair(esk221_2(X1,X2),esk222_2(X1,X2)) = esk217_2(X1,X2)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_1311,plain,
( in(esk225_4(X1,X2,X3,X4),cartesian_product2(X1,X3))
| ordered_pair(esk218_2(X1,X2),esk219_2(X1,X2)) = esk216_2(X1,X2)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_1312,plain,
( ordered_pair(esk244_3(X1,X2,X3),esk245_3(X1,X2,X3)) = X3
| esk241_1(X1) = singleton(esk240_1(X1))
| ~ in(X3,esk242_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_715]) ).
cnf(i_0_1313,plain,
( ordered_pair(esk244_3(X1,X2,X3),esk245_3(X1,X2,X3)) = X3
| esk239_1(X1) = singleton(esk238_1(X1))
| ~ in(X3,esk242_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_715]) ).
cnf(i_0_1314,plain,
( ordered_pair(esk244_3(X1,X2,X3),esk245_3(X1,X2,X3)) = X3
| in(esk240_1(X1),X1)
| ~ in(X3,esk242_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_715]) ).
cnf(i_0_1315,plain,
( ordered_pair(esk244_3(X1,X2,X3),esk245_3(X1,X2,X3)) = X3
| in(esk238_1(X1),X1)
| ~ in(X3,esk242_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_715]) ).
cnf(i_0_1316,plain,
( in(esk254_4(X1,X2,X3,X4),esk253_3(X1,X2,X3))
| in(X2,esk249_1(X1))
| ~ in(X4,esk253_3(X1,X2,X3))
| ~ ordinal(X3)
| X2 != X3
| ~ in(X5,succ(X1))
| X5 != X2
| esk247_1(X1) != esk248_1(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_717]) ).
cnf(i_0_1317,plain,
( X2 = inclusion_relation(X1)
| ~ in(ordered_pair(esk47_2(X1,X2),esk48_2(X1,X2)),X2)
| ~ subset(esk47_2(X1,X2),esk48_2(X1,X2))
| relation_field(X2) != X1
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_719]) ).
cnf(i_0_1318,plain,
( X2 = identity_relation(X1)
| ~ in(ordered_pair(esk1_2(X1,X2),esk2_2(X1,X2)),X2)
| ~ in(esk1_2(X1,X2),X1)
| esk1_2(X1,X2) != esk2_2(X1,X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_720]) ).
cnf(i_0_1319,plain,
( ordered_pair(esk244_3(X1,X2,X3),esk245_3(X1,X2,X3)) = X3
| ~ in(X3,esk242_2(X1,X2))
| esk236_1(X1) != esk237_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_715]) ).
cnf(i_0_1320,plain,
( in(esk226_4(X1,X2,X3,X4),X1)
| ordered_pair(esk221_2(X1,X2),esk222_2(X1,X2)) = esk217_2(X1,X2)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_1321,plain,
( in(esk226_4(X1,X2,X3,X4),X1)
| ordered_pair(esk218_2(X1,X2),esk219_2(X1,X2)) = esk216_2(X1,X2)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_1322,plain,
( ordered_pair(esk244_3(X1,X2,X3),esk245_3(X1,X2,X3)) = X3
| esk235_1(X1) = esk237_1(X1)
| ~ in(X3,esk242_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_715]) ).
cnf(i_0_1323,plain,
( ordered_pair(esk244_3(X1,X2,X3),esk245_3(X1,X2,X3)) = X3
| esk235_1(X1) = esk236_1(X1)
| ~ in(X3,esk242_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_715]) ).
cnf(i_0_1324,lemma,
( in(esk353_4(X1,X2,X3,X4),esk352_3(X1,X2,X3))
| in(X2,esk349_1(X1))
| ~ in(X4,esk352_3(X1,X2,X3))
| ~ ordinal(X3)
| X2 != X3
| ~ in(X2,succ(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_721]) ).
cnf(i_0_1325,lemma,
( element(esk193_4(X1,X2,X3,X4),powerset(the_carrier(X1)))
| in(ordered_pair(X3,X4),esk192_2(X1,X2))
| esk191_2(X1,X2) = subset_complement(the_carrier(X1),X5)
| ~ in(X3,complements_of_subsets(the_carrier(X1),X2))
| ~ element(X5,powerset(the_carrier(X1)))
| X5 != esk189_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_711]) ).
cnf(i_0_1326,lemma,
( element(esk193_4(X1,X2,X3,X4),powerset(the_carrier(X1)))
| in(ordered_pair(X3,X4),esk192_2(X1,X2))
| esk190_2(X1,X2) = subset_complement(the_carrier(X1),X5)
| ~ in(X3,complements_of_subsets(the_carrier(X1),X2))
| ~ element(X5,powerset(the_carrier(X1)))
| X5 != esk189_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_711]) ).
cnf(i_0_1327,plain,
( esk226_4(X1,X2,X3,X4) = esk228_4(X1,X2,X3,X4)
| ordered_pair(esk221_2(X1,X2),esk222_2(X1,X2)) = esk217_2(X1,X2)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_1328,plain,
( esk226_4(X1,X2,X3,X4) = esk228_4(X1,X2,X3,X4)
| ordered_pair(esk218_2(X1,X2),esk219_2(X1,X2)) = esk216_2(X1,X2)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_1329,lemma,
( ordered_pair(esk347_3(X1,X2,X3),esk348_3(X1,X2,X3)) = X3
| ~ in(X3,esk346_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_722]) ).
fof(i_0_1330,lemma,
! [X3663,X3664,X3665] :
( ( ~ in(ordered_pair_as_product_element(the_carrier(X3663),the_carrier(X3663),X3664,X3665),relation_of_lattice(X3663))
| below_refl(X3663,X3664,X3665)
| ~ element(X3665,the_carrier(X3663))
| ~ element(X3664,the_carrier(X3663))
| empty_carrier(X3663)
| ~ lattice(X3663)
| ~ latt_str(X3663) )
& ( ~ below_refl(X3663,X3664,X3665)
| in(ordered_pair_as_product_element(the_carrier(X3663),the_carrier(X3663),X3664,X3665),relation_of_lattice(X3663))
| ~ element(X3665,the_carrier(X3663))
| ~ element(X3664,the_carrier(X3663))
| empty_carrier(X3663)
| ~ lattice(X3663)
| ~ latt_str(X3663) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_723])])])]) ).
cnf(i_0_1331,lemma,
( in(ordered_pair(apply(X1,X2),apply(X1,X3)),X4)
| ~ in(ordered_pair(X2,X3),esk205_3(X5,X4,X1))
| ~ relation(X4)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_713]) ).
cnf(i_0_1332,plain,
( esk225_4(X1,X2,X3,X4) = X4
| in(ordered_pair(esk222_2(X1,X2),X5),X2)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ in(X5,esk223_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_1333,plain,
( esk225_4(X1,X2,X3,X4) = X4
| in(ordered_pair(esk219_2(X1,X2),X5),X2)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ in(X5,esk220_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_1334,plain,
( subset(X1,esk254_4(X2,X3,X4,X1))
| in(X3,esk249_1(X2))
| epred2_3(esk248_1(X2),esk247_1(X2),esk246_1(X2))
| ~ in(X1,esk253_3(X2,X3,X4))
| ~ ordinal(X4)
| X3 != X4
| ~ in(X5,succ(X2))
| X5 != X3
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_717]) ).
cnf(i_0_1335,lemma,
( element(esk193_4(X1,X2,X3,X4),powerset(the_carrier(X1)))
| in(ordered_pair(X3,X4),esk192_2(X1,X2))
| in(esk189_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| ~ in(X3,complements_of_subsets(the_carrier(X1),X2))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_711]) ).
cnf(i_0_1336,lemma,
( element(esk193_4(X1,X2,X3,X4),powerset(the_carrier(X1)))
| in(ordered_pair(X3,X4),esk192_2(X1,X2))
| in(esk189_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| ~ in(X3,complements_of_subsets(the_carrier(X1),X2))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_711]) ).
cnf(i_0_1337,plain,
( in(ordered_pair(X4,X1),X3)
| in(ordered_pair(esk208_2(X2,X3),X5),X3)
| empty(X2)
| ~ in(X1,esk213_3(X2,X3,X4))
| ~ in(X4,esk211_2(X2,X3))
| ~ in(X5,esk210_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_691]) ).
cnf(i_0_1338,plain,
( in(ordered_pair(X4,X1),X3)
| in(ordered_pair(esk207_2(X2,X3),X5),X3)
| empty(X2)
| ~ in(X1,esk213_3(X2,X3,X4))
| ~ in(X4,esk211_2(X2,X3))
| ~ in(X5,esk209_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_691]) ).
cnf(i_0_1339,lemma,
( element(esk198_4(X1,X2,X3,X4),powerset(the_carrier(X1)))
| in(ordered_pair(X3,X4),esk197_2(X1,X2))
| esk196_2(X1,X2) = subset_complement(the_carrier(X1),X5)
| ~ in(X3,X2)
| ~ element(X5,powerset(the_carrier(X1)))
| X5 != esk194_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_712]) ).
cnf(i_0_1340,lemma,
( element(esk198_4(X1,X2,X3,X4),powerset(the_carrier(X1)))
| in(ordered_pair(X3,X4),esk197_2(X1,X2))
| esk195_2(X1,X2) = subset_complement(the_carrier(X1),X5)
| ~ in(X3,X2)
| ~ element(X5,powerset(the_carrier(X1)))
| X5 != esk194_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_712]) ).
cnf(i_0_1341,lemma,
( element(esk193_4(X1,X2,X3,X4),powerset(the_carrier(X1)))
| in(ordered_pair(X3,X4),esk192_2(X1,X2))
| ~ in(X3,complements_of_subsets(the_carrier(X1),X2))
| esk190_2(X1,X2) != esk191_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_711]) ).
cnf(i_0_1342,plain,
( subset(X1,X2)
| ~ in(ordered_pair(esk72_2(X1,X2),esk73_2(X1,X2)),X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_724]) ).
cnf(i_0_1343,plain,
( in(ordered_pair(apply(X1,X2),apply(X1,X3)),X4)
| ~ in(ordered_pair(X2,X3),X5)
| ~ relation_isomorphism(X5,X4,X1)
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X4)
| ~ relation(X5) ),
inference(split_conjunct,[status(thm)],[i_0_693]) ).
cnf(i_0_1344,plain,
( is_reflexive_in(X1,X2)
| ~ in(ordered_pair(esk40_2(X1,X2),esk40_2(X1,X2)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_725]) ).
cnf(i_0_1345,plain,
( is_transitive_in(X1,X2)
| ~ in(ordered_pair(esk110_2(X1,X2),esk112_2(X1,X2)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_726]) ).
cnf(i_0_1346,plain,
( is_connected_in(X1,X2)
| ~ in(ordered_pair(esk96_2(X1,X2),esk95_2(X1,X2)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_727]) ).
cnf(i_0_1347,plain,
( is_connected_in(X1,X2)
| ~ in(ordered_pair(esk95_2(X1,X2),esk96_2(X1,X2)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_727]) ).
cnf(i_0_1348,plain,
( subset(X1,esk254_4(X2,X3,X4,X1))
| in(X3,esk249_1(X2))
| ~ in(X1,esk253_3(X2,X3,X4))
| ~ ordinal(X4)
| X3 != X4
| ~ in(X5,succ(X2))
| X5 != X3
| esk247_1(X2) != esk248_1(X2)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_717]) ).
cnf(i_0_1349,lemma,
( subset(X1,esk353_4(X2,X3,X4,X1))
| in(X3,esk349_1(X2))
| ~ in(X1,esk352_3(X2,X3,X4))
| ~ ordinal(X4)
| X3 != X4
| ~ in(X3,succ(X2))
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_721]) ).
cnf(i_0_1350,lemma,
( element(esk198_4(X1,X2,X3,X4),powerset(the_carrier(X1)))
| in(ordered_pair(X3,X4),esk197_2(X1,X2))
| ~ in(X3,X2)
| esk195_2(X1,X2) != esk196_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_712]) ).
cnf(i_0_1351,lemma,
( element(esk198_4(X1,X2,X3,X4),powerset(the_carrier(X1)))
| in(ordered_pair(X3,X4),esk197_2(X1,X2))
| in(esk194_2(X1,X2),X2)
| ~ in(X3,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_712]) ).
cnf(i_0_1352,lemma,
( element(esk198_4(X1,X2,X3,X4),powerset(the_carrier(X1)))
| in(ordered_pair(X3,X4),esk197_2(X1,X2))
| in(esk194_2(X1,X2),X2)
| ~ in(X3,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_712]) ).
cnf(i_0_1353,lemma,
( in(X1,esk183_4(X2,X3,X4,X1))
| in(esk179_2(X2,X3),esk181_2(X2,X3))
| empty(X2)
| ~ in(ordered_pair(X4,X1),esk182_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1354,lemma,
( in(X1,esk183_4(X2,X3,X4,X1))
| in(esk178_2(X2,X3),esk180_2(X2,X3))
| empty(X2)
| ~ in(ordered_pair(X4,X1),esk182_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1355,plain,
( in(X2,esk249_1(X1))
| epred2_3(esk248_1(X1),esk247_1(X1),esk246_1(X1))
| esk254_4(X1,X2,X3,X4) != X4
| ~ in(X4,esk253_3(X1,X2,X3))
| ~ ordinal(X3)
| X2 != X3
| ~ in(X5,succ(X1))
| X5 != X2
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_717]) ).
cnf(i_0_1356,plain,
( X1 = set_difference(esk275_3(X2,X3,X1),singleton(X2))
| esk270_2(X2,X3) = set_difference(esk272_2(X2,X3),singleton(X2))
| ~ in(X1,esk273_2(X2,X3))
| ~ ordinal(X2)
| ~ element(X3,powerset(powerset(succ(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_728]) ).
cnf(i_0_1357,plain,
( X1 = set_difference(esk275_3(X2,X3,X1),singleton(X2))
| esk269_2(X2,X3) = set_difference(esk271_2(X2,X3),singleton(X2))
| ~ in(X1,esk273_2(X2,X3))
| ~ ordinal(X2)
| ~ element(X3,powerset(powerset(succ(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_728]) ).
cnf(i_0_1358,lemma,
( in(X1,esk183_4(X2,X3,X4,X1))
| empty(X2)
| ~ in(ordered_pair(X4,X1),esk182_2(X2,X3))
| esk178_2(X2,X3) != esk179_2(X2,X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1359,lemma,
( in(X1,esk183_4(X2,X3,X4,X1))
| in(esk177_2(X2,X3),X2)
| empty(X2)
| ~ in(ordered_pair(X4,X1),esk182_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1360,lemma,
( in(X1,esk183_4(X2,X3,X4,X1))
| in(esk177_2(X2,X3),X2)
| empty(X2)
| ~ in(ordered_pair(X4,X1),esk182_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1361,plain,
( esk308_4(X1,X2,X3,X4) = X4
| ordered_pair(esk305_2(X1,X2),esk306_2(X1,X2)) = esk302_2(X1,X2)
| ~ in(X4,esk307_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]) ).
cnf(i_0_1362,plain,
( esk308_4(X1,X2,X3,X4) = X4
| ordered_pair(esk303_2(X1,X2),esk304_2(X1,X2)) = esk301_2(X1,X2)
| ~ in(X4,esk307_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]) ).
cnf(i_0_1363,plain,
( esk290_4(X1,X2,X3,X4) = X4
| ordered_pair(esk287_2(X1,X2),esk288_2(X1,X2)) = esk284_2(X1,X2)
| ~ in(X4,esk289_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]) ).
cnf(i_0_1364,plain,
( esk290_4(X1,X2,X3,X4) = X4
| ordered_pair(esk285_2(X1,X2),esk286_2(X1,X2)) = esk283_2(X1,X2)
| ~ in(X4,esk289_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]) ).
fof(i_0_1365,plain,
! [X1939,X1940,X1941,X1942,X1943,X1944,X1945] :
( ( in(X1942,relation_dom(X1939))
| ~ in(X1942,X1941)
| X1941 != relation_inverse_image(X1939,X1940)
| ~ relation(X1939)
| ~ function(X1939) )
& ( in(apply(X1939,X1942),X1940)
| ~ in(X1942,X1941)
| X1941 != relation_inverse_image(X1939,X1940)
| ~ relation(X1939)
| ~ function(X1939) )
& ( ~ in(X1943,relation_dom(X1939))
| ~ in(apply(X1939,X1943),X1940)
| in(X1943,X1941)
| X1941 != relation_inverse_image(X1939,X1940)
| ~ relation(X1939)
| ~ function(X1939) )
& ( ~ in(esk10_3(X1939,X1944,X1945),X1945)
| ~ in(esk10_3(X1939,X1944,X1945),relation_dom(X1939))
| ~ in(apply(X1939,esk10_3(X1939,X1944,X1945)),X1944)
| X1945 = relation_inverse_image(X1939,X1944)
| ~ relation(X1939)
| ~ function(X1939) )
& ( in(esk10_3(X1939,X1944,X1945),relation_dom(X1939))
| in(esk10_3(X1939,X1944,X1945),X1945)
| X1945 = relation_inverse_image(X1939,X1944)
| ~ relation(X1939)
| ~ function(X1939) )
& ( in(apply(X1939,esk10_3(X1939,X1944,X1945)),X1944)
| in(esk10_3(X1939,X1944,X1945),X1945)
| X1945 = relation_inverse_image(X1939,X1944)
| ~ relation(X1939)
| ~ function(X1939) ) ),
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)],[d13_funct_1])])])])])]) ).
cnf(i_0_1366,plain,
( in(esk274_3(X1,X2,X3),powerset(X1))
| esk270_2(X1,X2) = set_difference(esk272_2(X1,X2),singleton(X1))
| ~ in(X3,esk273_2(X1,X2))
| ~ ordinal(X1)
| ~ element(X2,powerset(powerset(succ(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_728]) ).
cnf(i_0_1367,plain,
( in(esk274_3(X1,X2,X3),powerset(X1))
| esk269_2(X1,X2) = set_difference(esk271_2(X1,X2),singleton(X1))
| ~ in(X3,esk273_2(X1,X2))
| ~ ordinal(X1)
| ~ element(X2,powerset(powerset(succ(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_728]) ).
cnf(i_0_1368,lemma,
( in(X1,esk183_4(X2,X3,X4,X1))
| esk177_2(X2,X3) = esk181_2(X2,X3)
| empty(X2)
| ~ in(ordered_pair(X4,X1),esk182_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1369,lemma,
( in(X1,esk183_4(X2,X3,X4,X1))
| esk177_2(X2,X3) = esk180_2(X2,X3)
| empty(X2)
| ~ in(ordered_pair(X4,X1),esk182_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1370,plain,
( in(esk275_3(X1,X2,X3),X2)
| esk270_2(X1,X2) = set_difference(esk272_2(X1,X2),singleton(X1))
| ~ in(X3,esk273_2(X1,X2))
| ~ ordinal(X1)
| ~ element(X2,powerset(powerset(succ(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_728]) ).
cnf(i_0_1371,plain,
( in(esk275_3(X1,X2,X3),X2)
| esk269_2(X1,X2) = set_difference(esk271_2(X1,X2),singleton(X1))
| ~ in(X3,esk273_2(X1,X2))
| ~ ordinal(X1)
| ~ element(X2,powerset(powerset(succ(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_728]) ).
cnf(i_0_1372,lemma,
( in(X1,X2)
| in(ordered_pair(esk179_2(X2,X4),X5),X4)
| empty(X2)
| ~ in(ordered_pair(X1,X3),esk182_2(X2,X4))
| ~ in(X5,esk181_2(X2,X4))
| ~ relation(X4) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1373,lemma,
( in(X1,X2)
| in(ordered_pair(esk178_2(X2,X4),X5),X4)
| empty(X2)
| ~ in(ordered_pair(X1,X3),esk182_2(X2,X4))
| ~ in(X5,esk180_2(X2,X4))
| ~ relation(X4) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1374,plain,
( X1 = set_difference(esk275_3(X2,X3,X1),singleton(X2))
| ~ in(X1,esk273_2(X2,X3))
| esk269_2(X2,X3) != esk270_2(X2,X3)
| ~ ordinal(X2)
| ~ element(X3,powerset(powerset(succ(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_728]) ).
cnf(i_0_1375,plain,
( X1 = set_difference(esk275_3(X2,X3,X1),singleton(X2))
| in(esk272_2(X2,X3),X3)
| ~ in(X1,esk273_2(X2,X3))
| ~ ordinal(X2)
| ~ element(X3,powerset(powerset(succ(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_728]) ).
cnf(i_0_1376,plain,
( X1 = set_difference(esk275_3(X2,X3,X1),singleton(X2))
| in(esk271_2(X2,X3),X3)
| ~ in(X1,esk273_2(X2,X3))
| ~ ordinal(X2)
| ~ element(X3,powerset(powerset(succ(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_728]) ).
cnf(i_0_1377,lemma,
( in(apply(esk381_2(X1,X2),X3),esk382_3(X1,X2,X3))
| in(esk379_2(X1,X2),X1)
| in(ordered_pair(esk376_2(X1,X2),X4),X2)
| empty(X1)
| ~ in(X3,X1)
| ~ in(X4,esk378_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1378,lemma,
( in(apply(esk381_2(X1,X2),X3),esk382_3(X1,X2,X3))
| in(esk379_2(X1,X2),X1)
| in(ordered_pair(esk375_2(X1,X2),X4),X2)
| empty(X1)
| ~ in(X3,X1)
| ~ in(X4,esk377_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1379,plain,
( in(X3,esk273_2(X2,X5))
| esk270_2(X2,X5) = set_difference(esk272_2(X2,X5),singleton(X2))
| ~ in(X1,powerset(X2))
| X1 != X3
| ~ in(X4,X5)
| X3 != set_difference(X4,singleton(X2))
| ~ ordinal(X2)
| ~ element(X5,powerset(powerset(succ(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_728]) ).
cnf(i_0_1380,plain,
( in(X3,esk273_2(X2,X5))
| esk269_2(X2,X5) = set_difference(esk271_2(X2,X5),singleton(X2))
| ~ in(X1,powerset(X2))
| X1 != X3
| ~ in(X4,X5)
| X3 != set_difference(X4,singleton(X2))
| ~ ordinal(X2)
| ~ element(X5,powerset(powerset(succ(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_728]) ).
cnf(i_0_1381,plain,
( X2 = relation_dom(X1)
| ~ in(esk79_2(X1,X2),X2)
| ~ in(ordered_pair(esk79_2(X1,X2),X3),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_729]) ).
cnf(i_0_1382,plain,
( X1 = set_difference(esk275_3(X2,X3,X1),singleton(X2))
| esk268_2(X2,X3) = esk270_2(X2,X3)
| ~ in(X1,esk273_2(X2,X3))
| ~ ordinal(X2)
| ~ element(X3,powerset(powerset(succ(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_728]) ).
cnf(i_0_1383,plain,
( X1 = set_difference(esk275_3(X2,X3,X1),singleton(X2))
| esk268_2(X2,X3) = esk269_2(X2,X3)
| ~ in(X1,esk273_2(X2,X3))
| ~ ordinal(X2)
| ~ element(X3,powerset(powerset(succ(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_728]) ).
cnf(i_0_1384,plain,
( in(esk274_3(X1,X2,X3),powerset(X1))
| ~ in(X3,esk273_2(X1,X2))
| esk269_2(X1,X2) != esk270_2(X1,X2)
| ~ ordinal(X1)
| ~ element(X2,powerset(powerset(succ(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_728]) ).
cnf(i_0_1385,plain,
( in(X2,esk249_1(X1))
| esk254_4(X1,X2,X3,X4) != X4
| ~ in(X4,esk253_3(X1,X2,X3))
| ~ ordinal(X3)
| X2 != X3
| ~ in(X5,succ(X1))
| X5 != X2
| esk247_1(X1) != esk248_1(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_717]) ).
cnf(i_0_1386,plain,
( in(esk274_3(X1,X2,X3),powerset(X1))
| in(esk272_2(X1,X2),X2)
| ~ in(X3,esk273_2(X1,X2))
| ~ ordinal(X1)
| ~ element(X2,powerset(powerset(succ(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_728]) ).
cnf(i_0_1387,plain,
( in(esk274_3(X1,X2,X3),powerset(X1))
| in(esk271_2(X1,X2),X2)
| ~ in(X3,esk273_2(X1,X2))
| ~ ordinal(X1)
| ~ element(X2,powerset(powerset(succ(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_728]) ).
cnf(i_0_1388,plain,
( in(esk275_3(X1,X2,X3),X2)
| ~ in(X3,esk273_2(X1,X2))
| esk269_2(X1,X2) != esk270_2(X1,X2)
| ~ ordinal(X1)
| ~ element(X2,powerset(powerset(succ(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_728]) ).
cnf(i_0_1389,plain,
( in(esk275_3(X1,X2,X3),X2)
| in(esk272_2(X1,X2),X2)
| ~ in(X3,esk273_2(X1,X2))
| ~ ordinal(X1)
| ~ element(X2,powerset(powerset(succ(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_728]) ).
cnf(i_0_1390,plain,
( in(esk275_3(X1,X2,X3),X2)
| in(esk271_2(X1,X2),X2)
| ~ in(X3,esk273_2(X1,X2))
| ~ ordinal(X1)
| ~ element(X2,powerset(powerset(succ(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_728]) ).
cnf(i_0_1391,plain,
( in(esk274_3(X1,X2,X3),powerset(X1))
| esk268_2(X1,X2) = esk270_2(X1,X2)
| ~ in(X3,esk273_2(X1,X2))
| ~ ordinal(X1)
| ~ element(X2,powerset(powerset(succ(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_728]) ).
cnf(i_0_1392,plain,
( in(esk274_3(X1,X2,X3),powerset(X1))
| esk268_2(X1,X2) = esk269_2(X1,X2)
| ~ in(X3,esk273_2(X1,X2))
| ~ ordinal(X1)
| ~ element(X2,powerset(powerset(succ(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_728]) ).
cnf(i_0_1393,lemma,
( in(X2,esk349_1(X1))
| esk353_4(X1,X2,X3,X4) != X4
| ~ in(X4,esk352_3(X1,X2,X3))
| ~ ordinal(X3)
| X2 != X3
| ~ in(X2,succ(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_721]) ).
cnf(i_0_1394,plain,
( in(esk275_3(X1,X2,X3),X2)
| esk268_2(X1,X2) = esk270_2(X1,X2)
| ~ in(X3,esk273_2(X1,X2))
| ~ ordinal(X1)
| ~ element(X2,powerset(powerset(succ(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_728]) ).
cnf(i_0_1395,plain,
( in(esk275_3(X1,X2,X3),X2)
| esk268_2(X1,X2) = esk269_2(X1,X2)
| ~ in(X3,esk273_2(X1,X2))
| ~ ordinal(X1)
| ~ element(X2,powerset(powerset(succ(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_728]) ).
cnf(i_0_1396,lemma,
( X1 = set_difference(esk358_3(X2,X3,X1),singleton(X2))
| ~ in(X1,esk357_2(X2,X3))
| ~ ordinal(X2)
| ~ element(X3,powerset(powerset(succ(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_730]) ).
cnf(i_0_1397,plain,
( in(X3,esk273_2(X2,X5))
| ~ in(X1,powerset(X2))
| X1 != X3
| ~ in(X4,X5)
| X3 != set_difference(X4,singleton(X2))
| esk269_2(X2,X5) != esk270_2(X2,X5)
| ~ ordinal(X2)
| ~ element(X5,powerset(powerset(succ(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_728]) ).
cnf(i_0_1398,plain,
( in(X3,esk273_2(X2,X5))
| in(esk272_2(X2,X5),X5)
| ~ in(X1,powerset(X2))
| X1 != X3
| ~ in(X4,X5)
| X3 != set_difference(X4,singleton(X2))
| ~ ordinal(X2)
| ~ element(X5,powerset(powerset(succ(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_728]) ).
cnf(i_0_1399,plain,
( in(X3,esk273_2(X2,X5))
| in(esk271_2(X2,X5),X5)
| ~ in(X1,powerset(X2))
| X1 != X3
| ~ in(X4,X5)
| X3 != set_difference(X4,singleton(X2))
| ~ ordinal(X2)
| ~ element(X5,powerset(powerset(succ(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_728]) ).
cnf(i_0_1400,plain,
( esk274_3(X1,X2,X3) = X3
| esk270_2(X1,X2) = set_difference(esk272_2(X1,X2),singleton(X1))
| ~ in(X3,esk273_2(X1,X2))
| ~ ordinal(X1)
| ~ element(X2,powerset(powerset(succ(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_728]) ).
cnf(i_0_1401,plain,
( esk274_3(X1,X2,X3) = X3
| esk269_2(X1,X2) = set_difference(esk271_2(X1,X2),singleton(X1))
| ~ in(X3,esk273_2(X1,X2))
| ~ ordinal(X1)
| ~ element(X2,powerset(powerset(succ(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_728]) ).
cnf(i_0_1402,plain,
( in(X3,esk273_2(X2,X5))
| esk268_2(X2,X5) = esk270_2(X2,X5)
| ~ in(X1,powerset(X2))
| X1 != X3
| ~ in(X4,X5)
| X3 != set_difference(X4,singleton(X2))
| ~ ordinal(X2)
| ~ element(X5,powerset(powerset(succ(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_728]) ).
cnf(i_0_1403,plain,
( in(X3,esk273_2(X2,X5))
| esk268_2(X2,X5) = esk269_2(X2,X5)
| ~ in(X1,powerset(X2))
| X1 != X3
| ~ in(X4,X5)
| X3 != set_difference(X4,singleton(X2))
| ~ ordinal(X2)
| ~ element(X5,powerset(powerset(succ(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_728]) ).
cnf(i_0_1404,plain,
( esk225_4(X1,X2,X3,X4) = X4
| ordered_pair(esk221_2(X1,X2),esk222_2(X1,X2)) = esk217_2(X1,X2)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_1405,plain,
( esk225_4(X1,X2,X3,X4) = X4
| ordered_pair(esk218_2(X1,X2),esk219_2(X1,X2)) = esk216_2(X1,X2)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]) ).
cnf(i_0_1406,lemma,
( in(esk358_3(X1,X2,X3),X2)
| ~ in(X3,esk357_2(X1,X2))
| ~ ordinal(X1)
| ~ element(X2,powerset(powerset(succ(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_730]) ).
fof(i_0_1407,plain,
! [X2035,X2036,X2037,X2038] :
( ( the_carrier(X2036) = powerset(X2035)
| X2036 != boole_lattice(X2035)
| ~ strict_latt_str(X2036)
| ~ latt_str(X2036) )
& ( apply_binary(the_L_join(X2036),X2037,X2038) = subset_union2(X2035,X2037,X2038)
| ~ element(X2038,powerset(X2035))
| ~ element(X2037,powerset(X2035))
| X2036 != boole_lattice(X2035)
| ~ strict_latt_str(X2036)
| ~ latt_str(X2036) )
& ( apply_binary(the_L_meet(X2036),X2037,X2038) = subset_intersection2(X2035,X2037,X2038)
| ~ element(X2038,powerset(X2035))
| ~ element(X2037,powerset(X2035))
| X2036 != boole_lattice(X2035)
| ~ strict_latt_str(X2036)
| ~ latt_str(X2036) )
& ( element(esk30_2(X2035,X2036),powerset(X2035))
| the_carrier(X2036) != powerset(X2035)
| X2036 = boole_lattice(X2035)
| ~ strict_latt_str(X2036)
| ~ latt_str(X2036) )
& ( element(esk31_2(X2035,X2036),powerset(X2035))
| the_carrier(X2036) != powerset(X2035)
| X2036 = boole_lattice(X2035)
| ~ strict_latt_str(X2036)
| ~ latt_str(X2036) )
& ( apply_binary(the_L_join(X2036),esk30_2(X2035,X2036),esk31_2(X2035,X2036)) != subset_union2(X2035,esk30_2(X2035,X2036),esk31_2(X2035,X2036))
| apply_binary(the_L_meet(X2036),esk30_2(X2035,X2036),esk31_2(X2035,X2036)) != subset_intersection2(X2035,esk30_2(X2035,X2036),esk31_2(X2035,X2036))
| the_carrier(X2036) != powerset(X2035)
| X2036 = boole_lattice(X2035)
| ~ strict_latt_str(X2036)
| ~ latt_str(X2036) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_lattice3])])])])]) ).
cnf(i_0_1408,plain,
( in(esk212_3(X1,X2,X3),X1)
| in(ordered_pair(esk208_2(X1,X2),X4),X2)
| empty(X1)
| ~ in(X3,esk211_2(X1,X2))
| ~ in(X4,esk210_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_691]) ).
cnf(i_0_1409,plain,
( in(esk212_3(X1,X2,X3),X1)
| in(ordered_pair(esk207_2(X1,X2),X4),X2)
| empty(X1)
| ~ in(X3,esk211_2(X1,X2))
| ~ in(X4,esk209_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_691]) ).
cnf(i_0_1410,plain,
( in(X1,esk213_3(X2,X3,X1))
| in(ordered_pair(esk208_2(X2,X3),X4),X3)
| empty(X2)
| ~ in(X1,esk211_2(X2,X3))
| ~ in(X4,esk210_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_691]) ).
cnf(i_0_1411,plain,
( in(X1,esk213_3(X2,X3,X1))
| in(ordered_pair(esk207_2(X2,X3),X4),X3)
| empty(X2)
| ~ in(X1,esk211_2(X2,X3))
| ~ in(X4,esk209_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_691]) ).
fof(i_0_1412,plain,
! [X2521,X2522,X2523,X2524] :
( empty(X2521)
| ~ function(X2523)
| ~ quasi_total(X2523,X2521,X2522)
| ~ relation_of2(X2523,X2521,X2522)
| ~ element(X2524,X2521)
| element(apply_as_element(X2521,X2522,X2523,X2524),X2522) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_731])]) ).
cnf(i_0_1413,plain,
( esk274_3(X1,X2,X3) = X3
| ~ in(X3,esk273_2(X1,X2))
| esk269_2(X1,X2) != esk270_2(X1,X2)
| ~ ordinal(X1)
| ~ element(X2,powerset(powerset(succ(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_728]) ).
cnf(i_0_1414,lemma,
( esk193_4(X1,X2,X3,X4) = X3
| in(ordered_pair(X3,X4),esk192_2(X1,X2))
| esk191_2(X1,X2) = subset_complement(the_carrier(X1),X5)
| ~ in(X3,complements_of_subsets(the_carrier(X1),X2))
| ~ element(X5,powerset(the_carrier(X1)))
| X5 != esk189_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_711]) ).
cnf(i_0_1415,lemma,
( esk193_4(X1,X2,X3,X4) = X3
| in(ordered_pair(X3,X4),esk192_2(X1,X2))
| esk190_2(X1,X2) = subset_complement(the_carrier(X1),X5)
| ~ in(X3,complements_of_subsets(the_carrier(X1),X2))
| ~ element(X5,powerset(the_carrier(X1)))
| X5 != esk189_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_711]) ).
cnf(i_0_1416,lemma,
( in(X1,esk357_2(X2,X4))
| ~ in(X1,powerset(X2))
| ~ in(X3,X4)
| X1 != set_difference(X3,singleton(X2))
| ~ ordinal(X2)
| ~ element(X4,powerset(powerset(succ(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_730]) ).
fof(i_0_1417,plain,
! [X2416,X2417,X2418,X2419] :
( ( ~ in(X2419,X2418)
| in(subset_complement(X2416,X2419),X2417)
| ~ element(X2419,powerset(X2416))
| X2418 != complements_of_subsets(X2416,X2417)
| ~ element(X2418,powerset(powerset(X2416)))
| ~ element(X2417,powerset(powerset(X2416))) )
& ( ~ in(subset_complement(X2416,X2419),X2417)
| in(X2419,X2418)
| ~ element(X2419,powerset(X2416))
| X2418 != complements_of_subsets(X2416,X2417)
| ~ element(X2418,powerset(powerset(X2416)))
| ~ element(X2417,powerset(powerset(X2416))) )
& ( element(esk113_3(X2416,X2417,X2418),powerset(X2416))
| X2418 = complements_of_subsets(X2416,X2417)
| ~ element(X2418,powerset(powerset(X2416)))
| ~ element(X2417,powerset(powerset(X2416))) )
& ( ~ in(esk113_3(X2416,X2417,X2418),X2418)
| ~ in(subset_complement(X2416,esk113_3(X2416,X2417,X2418)),X2417)
| X2418 = complements_of_subsets(X2416,X2417)
| ~ element(X2418,powerset(powerset(X2416)))
| ~ element(X2417,powerset(powerset(X2416))) )
& ( in(esk113_3(X2416,X2417,X2418),X2418)
| in(subset_complement(X2416,esk113_3(X2416,X2417,X2418)),X2417)
| X2418 = complements_of_subsets(X2416,X2417)
| ~ element(X2418,powerset(powerset(X2416)))
| ~ element(X2417,powerset(powerset(X2416))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_setfam_1])])])])]) ).
cnf(i_0_1418,plain,
( esk274_3(X1,X2,X3) = X3
| in(esk272_2(X1,X2),X2)
| ~ in(X3,esk273_2(X1,X2))
| ~ ordinal(X1)
| ~ element(X2,powerset(powerset(succ(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_728]) ).
cnf(i_0_1419,plain,
( esk274_3(X1,X2,X3) = X3
| in(esk271_2(X1,X2),X2)
| ~ in(X3,esk273_2(X1,X2))
| ~ ordinal(X1)
| ~ element(X2,powerset(powerset(succ(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_728]) ).
fof(i_0_1420,plain,
! [X1952,X1953,X1954,X1955,X1956,X1960] :
( ( ~ in(X1955,X1954)
| ~ element(X1956,powerset(the_carrier(X1952)))
| ~ open_subset(X1956,X1952)
| ~ in(X1955,X1956)
| ~ disjoint(X1953,X1956)
| ~ in(X1955,the_carrier(X1952))
| X1954 != topstr_closure(X1952,X1953)
| ~ element(X1954,powerset(the_carrier(X1952)))
| ~ element(X1953,powerset(the_carrier(X1952)))
| ~ top_str(X1952) )
& ( element(esk13_4(X1952,X1953,X1954,X1955),powerset(the_carrier(X1952)))
| in(X1955,X1954)
| ~ in(X1955,the_carrier(X1952))
| X1954 != topstr_closure(X1952,X1953)
| ~ element(X1954,powerset(the_carrier(X1952)))
| ~ element(X1953,powerset(the_carrier(X1952)))
| ~ top_str(X1952) )
& ( open_subset(esk13_4(X1952,X1953,X1954,X1955),X1952)
| in(X1955,X1954)
| ~ in(X1955,the_carrier(X1952))
| X1954 != topstr_closure(X1952,X1953)
| ~ element(X1954,powerset(the_carrier(X1952)))
| ~ element(X1953,powerset(the_carrier(X1952)))
| ~ top_str(X1952) )
& ( in(X1955,esk13_4(X1952,X1953,X1954,X1955))
| in(X1955,X1954)
| ~ in(X1955,the_carrier(X1952))
| X1954 != topstr_closure(X1952,X1953)
| ~ element(X1954,powerset(the_carrier(X1952)))
| ~ element(X1953,powerset(the_carrier(X1952)))
| ~ top_str(X1952) )
& ( disjoint(X1953,esk13_4(X1952,X1953,X1954,X1955))
| in(X1955,X1954)
| ~ in(X1955,the_carrier(X1952))
| X1954 != topstr_closure(X1952,X1953)
| ~ element(X1954,powerset(the_carrier(X1952)))
| ~ element(X1953,powerset(the_carrier(X1952)))
| ~ top_str(X1952) )
& ( in(esk14_3(X1952,X1953,X1954),the_carrier(X1952))
| X1954 = topstr_closure(X1952,X1953)
| ~ element(X1954,powerset(the_carrier(X1952)))
| ~ element(X1953,powerset(the_carrier(X1952)))
| ~ top_str(X1952) )
& ( element(esk15_3(X1952,X1953,X1954),powerset(the_carrier(X1952)))
| ~ in(esk14_3(X1952,X1953,X1954),X1954)
| X1954 = topstr_closure(X1952,X1953)
| ~ element(X1954,powerset(the_carrier(X1952)))
| ~ element(X1953,powerset(the_carrier(X1952)))
| ~ top_str(X1952) )
& ( open_subset(esk15_3(X1952,X1953,X1954),X1952)
| ~ in(esk14_3(X1952,X1953,X1954),X1954)
| X1954 = topstr_closure(X1952,X1953)
| ~ element(X1954,powerset(the_carrier(X1952)))
| ~ element(X1953,powerset(the_carrier(X1952)))
| ~ top_str(X1952) )
& ( in(esk14_3(X1952,X1953,X1954),esk15_3(X1952,X1953,X1954))
| ~ in(esk14_3(X1952,X1953,X1954),X1954)
| X1954 = topstr_closure(X1952,X1953)
| ~ element(X1954,powerset(the_carrier(X1952)))
| ~ element(X1953,powerset(the_carrier(X1952)))
| ~ top_str(X1952) )
& ( disjoint(X1953,esk15_3(X1952,X1953,X1954))
| ~ in(esk14_3(X1952,X1953,X1954),X1954)
| X1954 = topstr_closure(X1952,X1953)
| ~ element(X1954,powerset(the_carrier(X1952)))
| ~ element(X1953,powerset(the_carrier(X1952)))
| ~ top_str(X1952) )
& ( in(esk14_3(X1952,X1953,X1954),X1954)
| ~ element(X1960,powerset(the_carrier(X1952)))
| ~ open_subset(X1960,X1952)
| ~ in(esk14_3(X1952,X1953,X1954),X1960)
| ~ disjoint(X1953,X1960)
| X1954 = topstr_closure(X1952,X1953)
| ~ element(X1954,powerset(the_carrier(X1952)))
| ~ element(X1953,powerset(the_carrier(X1952)))
| ~ top_str(X1952) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d13_pre_topc])])])])]) ).
cnf(i_0_1421,plain,
( esk212_3(X1,X2,X3) = esk213_3(X1,X2,X3)
| in(ordered_pair(esk208_2(X1,X2),X4),X2)
| empty(X1)
| ~ in(X3,esk211_2(X1,X2))
| ~ in(X4,esk210_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_691]) ).
cnf(i_0_1422,plain,
( esk212_3(X1,X2,X3) = esk213_3(X1,X2,X3)
| in(ordered_pair(esk207_2(X1,X2),X4),X2)
| empty(X1)
| ~ in(X3,esk211_2(X1,X2))
| ~ in(X4,esk209_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_691]) ).
fof(i_0_1423,plain,
! [X2630,X2631,X2632] :
( ( ~ empty_carrier(latt_str_of(X2630,X2631,X2632))
| empty(X2630)
| ~ function(X2631)
| ~ quasi_total(X2631,cartesian_product2(X2630,X2630),X2630)
| ~ relation_of2(X2631,cartesian_product2(X2630,X2630),X2630)
| ~ function(X2632)
| ~ quasi_total(X2632,cartesian_product2(X2630,X2630),X2630)
| ~ relation_of2(X2632,cartesian_product2(X2630,X2630),X2630) )
& ( strict_latt_str(latt_str_of(X2630,X2631,X2632))
| empty(X2630)
| ~ function(X2631)
| ~ quasi_total(X2631,cartesian_product2(X2630,X2630),X2630)
| ~ relation_of2(X2631,cartesian_product2(X2630,X2630),X2630)
| ~ function(X2632)
| ~ quasi_total(X2632,cartesian_product2(X2630,X2630),X2630)
| ~ relation_of2(X2632,cartesian_product2(X2630,X2630),X2630) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_732])])]) ).
fof(i_0_1424,plain,
! [X2693,X2694,X2695,X2696,X2697,X2698] :
( ( X2693 = X2696
| latt_str_of(X2693,X2694,X2695) != latt_str_of(X2696,X2697,X2698)
| ~ function(X2694)
| ~ quasi_total(X2694,cartesian_product2(X2693,X2693),X2693)
| ~ relation_of2(X2694,cartesian_product2(X2693,X2693),X2693)
| ~ function(X2695)
| ~ quasi_total(X2695,cartesian_product2(X2693,X2693),X2693)
| ~ relation_of2(X2695,cartesian_product2(X2693,X2693),X2693) )
& ( X2694 = X2697
| latt_str_of(X2693,X2694,X2695) != latt_str_of(X2696,X2697,X2698)
| ~ function(X2694)
| ~ quasi_total(X2694,cartesian_product2(X2693,X2693),X2693)
| ~ relation_of2(X2694,cartesian_product2(X2693,X2693),X2693)
| ~ function(X2695)
| ~ quasi_total(X2695,cartesian_product2(X2693,X2693),X2693)
| ~ relation_of2(X2695,cartesian_product2(X2693,X2693),X2693) )
& ( X2695 = X2698
| latt_str_of(X2693,X2694,X2695) != latt_str_of(X2696,X2697,X2698)
| ~ function(X2694)
| ~ quasi_total(X2694,cartesian_product2(X2693,X2693),X2693)
| ~ relation_of2(X2694,cartesian_product2(X2693,X2693),X2693)
| ~ function(X2695)
| ~ quasi_total(X2695,cartesian_product2(X2693,X2693),X2693)
| ~ relation_of2(X2695,cartesian_product2(X2693,X2693),X2693) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[free_g3_lattices])])])]) ).
cnf(i_0_1425,plain,
( in(ordered_pair(X3,X5),X1)
| ~ is_transitive_in(X1,X2)
| ~ in(X3,X2)
| ~ in(X4,X2)
| ~ in(X5,X2)
| ~ in(ordered_pair(X3,X4),X1)
| ~ in(ordered_pair(X4,X5),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_726]) ).
cnf(i_0_1426,plain,
( esk274_3(X1,X2,X3) = X3
| esk268_2(X1,X2) = esk270_2(X1,X2)
| ~ in(X3,esk273_2(X1,X2))
| ~ ordinal(X1)
| ~ element(X2,powerset(powerset(succ(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_728]) ).
cnf(i_0_1427,plain,
( esk274_3(X1,X2,X3) = X3
| esk268_2(X1,X2) = esk269_2(X1,X2)
| ~ in(X3,esk273_2(X1,X2))
| ~ ordinal(X1)
| ~ element(X2,powerset(powerset(succ(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_728]) ).
cnf(i_0_1428,lemma,
( esk193_4(X1,X2,X3,X4) = X3
| in(ordered_pair(X3,X4),esk192_2(X1,X2))
| in(esk189_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| ~ in(X3,complements_of_subsets(the_carrier(X1),X2))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_711]) ).
cnf(i_0_1429,lemma,
( esk193_4(X1,X2,X3,X4) = X3
| in(ordered_pair(X3,X4),esk192_2(X1,X2))
| in(esk189_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| ~ in(X3,complements_of_subsets(the_carrier(X1),X2))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_711]) ).
fof(i_0_1430,plain,
! [X2438,X2439,X2440,X2441] :
( empty_carrier(X2438)
| ~ lattice(X2438)
| ~ latt_str(X2438)
| empty_carrier(X2439)
| ~ lattice(X2439)
| ~ latt_str(X2439)
| ~ element(X2440,the_carrier(X2438))
| ~ element(X2441,the_carrier(X2439))
| element(k10_filter_1(X2438,X2439,X2440,X2441),the_carrier(k8_filter_1(X2438,X2439))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_733])]) ).
cnf(i_0_1431,lemma,
( X1 = esk382_3(X2,X3,X1)
| in(esk379_2(X2,X3),X2)
| in(ordered_pair(esk376_2(X2,X3),X4),X3)
| empty(X2)
| ~ in(X1,X2)
| ~ in(X4,esk378_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1432,lemma,
( X1 = esk382_3(X2,X3,X1)
| in(esk379_2(X2,X3),X2)
| in(ordered_pair(esk375_2(X2,X3),X4),X3)
| empty(X2)
| ~ in(X1,X2)
| ~ in(X4,esk377_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1433,lemma,
( esk198_4(X1,X2,X3,X4) = X3
| in(ordered_pair(X3,X4),esk197_2(X1,X2))
| esk196_2(X1,X2) = subset_complement(the_carrier(X1),X5)
| ~ in(X3,X2)
| ~ element(X5,powerset(the_carrier(X1)))
| X5 != esk194_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_712]) ).
cnf(i_0_1434,lemma,
( esk198_4(X1,X2,X3,X4) = X3
| in(ordered_pair(X3,X4),esk197_2(X1,X2))
| esk195_2(X1,X2) = subset_complement(the_carrier(X1),X5)
| ~ in(X3,X2)
| ~ element(X5,powerset(the_carrier(X1)))
| X5 != esk194_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_712]) ).
cnf(i_0_1435,plain,
( in(ordered_pair(esk47_2(X1,X2),esk48_2(X1,X2)),X2)
| subset(esk47_2(X1,X2),esk48_2(X1,X2))
| X2 = inclusion_relation(X1)
| relation_field(X2) != X1
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_719]) ).
cnf(i_0_1436,lemma,
( esk193_4(X1,X2,X3,X4) = X3
| in(ordered_pair(X3,X4),esk192_2(X1,X2))
| ~ in(X3,complements_of_subsets(the_carrier(X1),X2))
| esk190_2(X1,X2) != esk191_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_711]) ).
cnf(i_0_1437,plain,
( in(ordered_pair(X1,X4),X6)
| ~ in(ordered_pair(X1,X2),X3)
| ~ in(ordered_pair(X2,X4),X5)
| X6 != relation_composition(X3,X5)
| ~ relation(X6)
| ~ relation(X5)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_683]) ).
cnf(i_0_1438,lemma,
( in(ordered_pair(X1,esk412_3(X1,X2,X3)),X3)
| ~ in(X1,relation_inverse_image(X3,X2))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_734]) ).
fof(i_0_1439,plain,
! [X2435,X2436,X2437] :
( ( strict_latt_str(latt_str_of(X2435,X2436,X2437))
| ~ function(X2436)
| ~ quasi_total(X2436,cartesian_product2(X2435,X2435),X2435)
| ~ relation_of2(X2436,cartesian_product2(X2435,X2435),X2435)
| ~ function(X2437)
| ~ quasi_total(X2437,cartesian_product2(X2435,X2435),X2435)
| ~ relation_of2(X2437,cartesian_product2(X2435,X2435),X2435) )
& ( latt_str(latt_str_of(X2435,X2436,X2437))
| ~ function(X2436)
| ~ quasi_total(X2436,cartesian_product2(X2435,X2435),X2435)
| ~ relation_of2(X2436,cartesian_product2(X2435,X2435),X2435)
| ~ function(X2437)
| ~ quasi_total(X2437,cartesian_product2(X2435,X2435),X2435)
| ~ relation_of2(X2437,cartesian_product2(X2435,X2435),X2435) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_g3_lattices])])]) ).
cnf(i_0_1440,lemma,
( in(X1,powerset(X2))
| ~ in(X1,esk357_2(X2,X3))
| ~ ordinal(X2)
| ~ element(X3,powerset(powerset(succ(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_730]) ).
cnf(i_0_1441,plain,
( X3 = set_intersection2(X1,X2)
| ~ in(esk77_3(X1,X2,X3),X3)
| ~ in(esk77_3(X1,X2,X3),X1)
| ~ in(esk77_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_735]) ).
cnf(i_0_1442,lemma,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_736]) ).
cnf(i_0_1443,plain,
( in(esk93_2(X1,X2),X2)
| in(ordered_pair(esk94_2(X1,X2),esk93_2(X1,X2)),X1)
| X2 = relation_rng(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_710]) ).
cnf(i_0_1444,plain,
( in(esk79_2(X1,X2),X2)
| in(ordered_pair(esk79_2(X1,X2),esk80_2(X1,X2)),X1)
| X2 = relation_dom(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_729]) ).
cnf(i_0_1445,plain,
( in(esk1_2(X1,X2),X1)
| in(ordered_pair(esk1_2(X1,X2),esk2_2(X1,X2)),X2)
| X2 = identity_relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_720]) ).
cnf(i_0_1446,lemma,
( in(ordered_pair(X2,X4),X1)
| ~ transitive(X1)
| ~ in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X3,X4),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_737]) ).
cnf(i_0_1447,plain,
( in(ordered_pair(X1,esk78_3(X3,X2,X1)),X3)
| ~ in(X1,X2)
| X2 != relation_dom(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_729]) ).
fof(i_0_1448,lemma,
! [X3359,X3360,X3364,X3365,X3367,X3370,X3371] :
( ( relation(esk393_2(X3359,X3360))
| in(esk391_2(X3359,X3360),complements_of_subsets(the_carrier(X3359),X3360))
| in(esk388_2(X3359,X3360),complements_of_subsets(the_carrier(X3359),X3360))
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( function(esk393_2(X3359,X3360))
| in(esk391_2(X3359,X3360),complements_of_subsets(the_carrier(X3359),X3360))
| in(esk388_2(X3359,X3360),complements_of_subsets(the_carrier(X3359),X3360))
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( relation_dom(esk393_2(X3359,X3360)) = complements_of_subsets(the_carrier(X3359),X3360)
| in(esk391_2(X3359,X3360),complements_of_subsets(the_carrier(X3359),X3360))
| in(esk388_2(X3359,X3360),complements_of_subsets(the_carrier(X3359),X3360))
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( ~ in(X3370,complements_of_subsets(the_carrier(X3359),X3360))
| ~ element(X3371,powerset(the_carrier(X3359)))
| X3371 != X3370
| apply(esk393_2(X3359,X3360),X3370) = subset_complement(the_carrier(X3359),X3371)
| in(esk391_2(X3359,X3360),complements_of_subsets(the_carrier(X3359),X3360))
| in(esk388_2(X3359,X3360),complements_of_subsets(the_carrier(X3359),X3360))
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( relation(esk393_2(X3359,X3360))
| element(esk392_3(X3359,X3360,X3367),powerset(the_carrier(X3359)))
| in(esk388_2(X3359,X3360),complements_of_subsets(the_carrier(X3359),X3360))
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( function(esk393_2(X3359,X3360))
| element(esk392_3(X3359,X3360,X3367),powerset(the_carrier(X3359)))
| in(esk388_2(X3359,X3360),complements_of_subsets(the_carrier(X3359),X3360))
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( relation_dom(esk393_2(X3359,X3360)) = complements_of_subsets(the_carrier(X3359),X3360)
| element(esk392_3(X3359,X3360,X3367),powerset(the_carrier(X3359)))
| in(esk388_2(X3359,X3360),complements_of_subsets(the_carrier(X3359),X3360))
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( ~ in(X3370,complements_of_subsets(the_carrier(X3359),X3360))
| ~ element(X3371,powerset(the_carrier(X3359)))
| X3371 != X3370
| apply(esk393_2(X3359,X3360),X3370) = subset_complement(the_carrier(X3359),X3371)
| element(esk392_3(X3359,X3360,X3367),powerset(the_carrier(X3359)))
| in(esk388_2(X3359,X3360),complements_of_subsets(the_carrier(X3359),X3360))
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( relation(esk393_2(X3359,X3360))
| esk392_3(X3359,X3360,X3367) = esk391_2(X3359,X3360)
| in(esk388_2(X3359,X3360),complements_of_subsets(the_carrier(X3359),X3360))
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( function(esk393_2(X3359,X3360))
| esk392_3(X3359,X3360,X3367) = esk391_2(X3359,X3360)
| in(esk388_2(X3359,X3360),complements_of_subsets(the_carrier(X3359),X3360))
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( relation_dom(esk393_2(X3359,X3360)) = complements_of_subsets(the_carrier(X3359),X3360)
| esk392_3(X3359,X3360,X3367) = esk391_2(X3359,X3360)
| in(esk388_2(X3359,X3360),complements_of_subsets(the_carrier(X3359),X3360))
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( ~ in(X3370,complements_of_subsets(the_carrier(X3359),X3360))
| ~ element(X3371,powerset(the_carrier(X3359)))
| X3371 != X3370
| apply(esk393_2(X3359,X3360),X3370) = subset_complement(the_carrier(X3359),X3371)
| esk392_3(X3359,X3360,X3367) = esk391_2(X3359,X3360)
| in(esk388_2(X3359,X3360),complements_of_subsets(the_carrier(X3359),X3360))
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( relation(esk393_2(X3359,X3360))
| X3367 != subset_complement(the_carrier(X3359),esk392_3(X3359,X3360,X3367))
| in(esk388_2(X3359,X3360),complements_of_subsets(the_carrier(X3359),X3360))
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( function(esk393_2(X3359,X3360))
| X3367 != subset_complement(the_carrier(X3359),esk392_3(X3359,X3360,X3367))
| in(esk388_2(X3359,X3360),complements_of_subsets(the_carrier(X3359),X3360))
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( relation_dom(esk393_2(X3359,X3360)) = complements_of_subsets(the_carrier(X3359),X3360)
| X3367 != subset_complement(the_carrier(X3359),esk392_3(X3359,X3360,X3367))
| in(esk388_2(X3359,X3360),complements_of_subsets(the_carrier(X3359),X3360))
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( ~ in(X3370,complements_of_subsets(the_carrier(X3359),X3360))
| ~ element(X3371,powerset(the_carrier(X3359)))
| X3371 != X3370
| apply(esk393_2(X3359,X3360),X3370) = subset_complement(the_carrier(X3359),X3371)
| X3367 != subset_complement(the_carrier(X3359),esk392_3(X3359,X3360,X3367))
| in(esk388_2(X3359,X3360),complements_of_subsets(the_carrier(X3359),X3360))
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( relation(esk393_2(X3359,X3360))
| in(esk391_2(X3359,X3360),complements_of_subsets(the_carrier(X3359),X3360))
| ~ element(X3364,powerset(the_carrier(X3359)))
| X3364 != esk388_2(X3359,X3360)
| esk389_2(X3359,X3360) = subset_complement(the_carrier(X3359),X3364)
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( function(esk393_2(X3359,X3360))
| in(esk391_2(X3359,X3360),complements_of_subsets(the_carrier(X3359),X3360))
| ~ element(X3364,powerset(the_carrier(X3359)))
| X3364 != esk388_2(X3359,X3360)
| esk389_2(X3359,X3360) = subset_complement(the_carrier(X3359),X3364)
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( relation_dom(esk393_2(X3359,X3360)) = complements_of_subsets(the_carrier(X3359),X3360)
| in(esk391_2(X3359,X3360),complements_of_subsets(the_carrier(X3359),X3360))
| ~ element(X3364,powerset(the_carrier(X3359)))
| X3364 != esk388_2(X3359,X3360)
| esk389_2(X3359,X3360) = subset_complement(the_carrier(X3359),X3364)
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( ~ in(X3370,complements_of_subsets(the_carrier(X3359),X3360))
| ~ element(X3371,powerset(the_carrier(X3359)))
| X3371 != X3370
| apply(esk393_2(X3359,X3360),X3370) = subset_complement(the_carrier(X3359),X3371)
| in(esk391_2(X3359,X3360),complements_of_subsets(the_carrier(X3359),X3360))
| ~ element(X3364,powerset(the_carrier(X3359)))
| X3364 != esk388_2(X3359,X3360)
| esk389_2(X3359,X3360) = subset_complement(the_carrier(X3359),X3364)
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( relation(esk393_2(X3359,X3360))
| element(esk392_3(X3359,X3360,X3367),powerset(the_carrier(X3359)))
| ~ element(X3364,powerset(the_carrier(X3359)))
| X3364 != esk388_2(X3359,X3360)
| esk389_2(X3359,X3360) = subset_complement(the_carrier(X3359),X3364)
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( function(esk393_2(X3359,X3360))
| element(esk392_3(X3359,X3360,X3367),powerset(the_carrier(X3359)))
| ~ element(X3364,powerset(the_carrier(X3359)))
| X3364 != esk388_2(X3359,X3360)
| esk389_2(X3359,X3360) = subset_complement(the_carrier(X3359),X3364)
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( relation_dom(esk393_2(X3359,X3360)) = complements_of_subsets(the_carrier(X3359),X3360)
| element(esk392_3(X3359,X3360,X3367),powerset(the_carrier(X3359)))
| ~ element(X3364,powerset(the_carrier(X3359)))
| X3364 != esk388_2(X3359,X3360)
| esk389_2(X3359,X3360) = subset_complement(the_carrier(X3359),X3364)
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( ~ in(X3370,complements_of_subsets(the_carrier(X3359),X3360))
| ~ element(X3371,powerset(the_carrier(X3359)))
| X3371 != X3370
| apply(esk393_2(X3359,X3360),X3370) = subset_complement(the_carrier(X3359),X3371)
| element(esk392_3(X3359,X3360,X3367),powerset(the_carrier(X3359)))
| ~ element(X3364,powerset(the_carrier(X3359)))
| X3364 != esk388_2(X3359,X3360)
| esk389_2(X3359,X3360) = subset_complement(the_carrier(X3359),X3364)
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( relation(esk393_2(X3359,X3360))
| esk392_3(X3359,X3360,X3367) = esk391_2(X3359,X3360)
| ~ element(X3364,powerset(the_carrier(X3359)))
| X3364 != esk388_2(X3359,X3360)
| esk389_2(X3359,X3360) = subset_complement(the_carrier(X3359),X3364)
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( function(esk393_2(X3359,X3360))
| esk392_3(X3359,X3360,X3367) = esk391_2(X3359,X3360)
| ~ element(X3364,powerset(the_carrier(X3359)))
| X3364 != esk388_2(X3359,X3360)
| esk389_2(X3359,X3360) = subset_complement(the_carrier(X3359),X3364)
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( relation_dom(esk393_2(X3359,X3360)) = complements_of_subsets(the_carrier(X3359),X3360)
| esk392_3(X3359,X3360,X3367) = esk391_2(X3359,X3360)
| ~ element(X3364,powerset(the_carrier(X3359)))
| X3364 != esk388_2(X3359,X3360)
| esk389_2(X3359,X3360) = subset_complement(the_carrier(X3359),X3364)
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( ~ in(X3370,complements_of_subsets(the_carrier(X3359),X3360))
| ~ element(X3371,powerset(the_carrier(X3359)))
| X3371 != X3370
| apply(esk393_2(X3359,X3360),X3370) = subset_complement(the_carrier(X3359),X3371)
| esk392_3(X3359,X3360,X3367) = esk391_2(X3359,X3360)
| ~ element(X3364,powerset(the_carrier(X3359)))
| X3364 != esk388_2(X3359,X3360)
| esk389_2(X3359,X3360) = subset_complement(the_carrier(X3359),X3364)
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( relation(esk393_2(X3359,X3360))
| X3367 != subset_complement(the_carrier(X3359),esk392_3(X3359,X3360,X3367))
| ~ element(X3364,powerset(the_carrier(X3359)))
| X3364 != esk388_2(X3359,X3360)
| esk389_2(X3359,X3360) = subset_complement(the_carrier(X3359),X3364)
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( function(esk393_2(X3359,X3360))
| X3367 != subset_complement(the_carrier(X3359),esk392_3(X3359,X3360,X3367))
| ~ element(X3364,powerset(the_carrier(X3359)))
| X3364 != esk388_2(X3359,X3360)
| esk389_2(X3359,X3360) = subset_complement(the_carrier(X3359),X3364)
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( relation_dom(esk393_2(X3359,X3360)) = complements_of_subsets(the_carrier(X3359),X3360)
| X3367 != subset_complement(the_carrier(X3359),esk392_3(X3359,X3360,X3367))
| ~ element(X3364,powerset(the_carrier(X3359)))
| X3364 != esk388_2(X3359,X3360)
| esk389_2(X3359,X3360) = subset_complement(the_carrier(X3359),X3364)
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( ~ in(X3370,complements_of_subsets(the_carrier(X3359),X3360))
| ~ element(X3371,powerset(the_carrier(X3359)))
| X3371 != X3370
| apply(esk393_2(X3359,X3360),X3370) = subset_complement(the_carrier(X3359),X3371)
| X3367 != subset_complement(the_carrier(X3359),esk392_3(X3359,X3360,X3367))
| ~ element(X3364,powerset(the_carrier(X3359)))
| X3364 != esk388_2(X3359,X3360)
| esk389_2(X3359,X3360) = subset_complement(the_carrier(X3359),X3364)
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( relation(esk393_2(X3359,X3360))
| in(esk391_2(X3359,X3360),complements_of_subsets(the_carrier(X3359),X3360))
| ~ element(X3365,powerset(the_carrier(X3359)))
| X3365 != esk388_2(X3359,X3360)
| esk390_2(X3359,X3360) = subset_complement(the_carrier(X3359),X3365)
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( function(esk393_2(X3359,X3360))
| in(esk391_2(X3359,X3360),complements_of_subsets(the_carrier(X3359),X3360))
| ~ element(X3365,powerset(the_carrier(X3359)))
| X3365 != esk388_2(X3359,X3360)
| esk390_2(X3359,X3360) = subset_complement(the_carrier(X3359),X3365)
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( relation_dom(esk393_2(X3359,X3360)) = complements_of_subsets(the_carrier(X3359),X3360)
| in(esk391_2(X3359,X3360),complements_of_subsets(the_carrier(X3359),X3360))
| ~ element(X3365,powerset(the_carrier(X3359)))
| X3365 != esk388_2(X3359,X3360)
| esk390_2(X3359,X3360) = subset_complement(the_carrier(X3359),X3365)
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( ~ in(X3370,complements_of_subsets(the_carrier(X3359),X3360))
| ~ element(X3371,powerset(the_carrier(X3359)))
| X3371 != X3370
| apply(esk393_2(X3359,X3360),X3370) = subset_complement(the_carrier(X3359),X3371)
| in(esk391_2(X3359,X3360),complements_of_subsets(the_carrier(X3359),X3360))
| ~ element(X3365,powerset(the_carrier(X3359)))
| X3365 != esk388_2(X3359,X3360)
| esk390_2(X3359,X3360) = subset_complement(the_carrier(X3359),X3365)
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( relation(esk393_2(X3359,X3360))
| element(esk392_3(X3359,X3360,X3367),powerset(the_carrier(X3359)))
| ~ element(X3365,powerset(the_carrier(X3359)))
| X3365 != esk388_2(X3359,X3360)
| esk390_2(X3359,X3360) = subset_complement(the_carrier(X3359),X3365)
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( function(esk393_2(X3359,X3360))
| element(esk392_3(X3359,X3360,X3367),powerset(the_carrier(X3359)))
| ~ element(X3365,powerset(the_carrier(X3359)))
| X3365 != esk388_2(X3359,X3360)
| esk390_2(X3359,X3360) = subset_complement(the_carrier(X3359),X3365)
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( relation_dom(esk393_2(X3359,X3360)) = complements_of_subsets(the_carrier(X3359),X3360)
| element(esk392_3(X3359,X3360,X3367),powerset(the_carrier(X3359)))
| ~ element(X3365,powerset(the_carrier(X3359)))
| X3365 != esk388_2(X3359,X3360)
| esk390_2(X3359,X3360) = subset_complement(the_carrier(X3359),X3365)
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( ~ in(X3370,complements_of_subsets(the_carrier(X3359),X3360))
| ~ element(X3371,powerset(the_carrier(X3359)))
| X3371 != X3370
| apply(esk393_2(X3359,X3360),X3370) = subset_complement(the_carrier(X3359),X3371)
| element(esk392_3(X3359,X3360,X3367),powerset(the_carrier(X3359)))
| ~ element(X3365,powerset(the_carrier(X3359)))
| X3365 != esk388_2(X3359,X3360)
| esk390_2(X3359,X3360) = subset_complement(the_carrier(X3359),X3365)
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( relation(esk393_2(X3359,X3360))
| esk392_3(X3359,X3360,X3367) = esk391_2(X3359,X3360)
| ~ element(X3365,powerset(the_carrier(X3359)))
| X3365 != esk388_2(X3359,X3360)
| esk390_2(X3359,X3360) = subset_complement(the_carrier(X3359),X3365)
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( function(esk393_2(X3359,X3360))
| esk392_3(X3359,X3360,X3367) = esk391_2(X3359,X3360)
| ~ element(X3365,powerset(the_carrier(X3359)))
| X3365 != esk388_2(X3359,X3360)
| esk390_2(X3359,X3360) = subset_complement(the_carrier(X3359),X3365)
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( relation_dom(esk393_2(X3359,X3360)) = complements_of_subsets(the_carrier(X3359),X3360)
| esk392_3(X3359,X3360,X3367) = esk391_2(X3359,X3360)
| ~ element(X3365,powerset(the_carrier(X3359)))
| X3365 != esk388_2(X3359,X3360)
| esk390_2(X3359,X3360) = subset_complement(the_carrier(X3359),X3365)
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( ~ in(X3370,complements_of_subsets(the_carrier(X3359),X3360))
| ~ element(X3371,powerset(the_carrier(X3359)))
| X3371 != X3370
| apply(esk393_2(X3359,X3360),X3370) = subset_complement(the_carrier(X3359),X3371)
| esk392_3(X3359,X3360,X3367) = esk391_2(X3359,X3360)
| ~ element(X3365,powerset(the_carrier(X3359)))
| X3365 != esk388_2(X3359,X3360)
| esk390_2(X3359,X3360) = subset_complement(the_carrier(X3359),X3365)
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( relation(esk393_2(X3359,X3360))
| X3367 != subset_complement(the_carrier(X3359),esk392_3(X3359,X3360,X3367))
| ~ element(X3365,powerset(the_carrier(X3359)))
| X3365 != esk388_2(X3359,X3360)
| esk390_2(X3359,X3360) = subset_complement(the_carrier(X3359),X3365)
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( function(esk393_2(X3359,X3360))
| X3367 != subset_complement(the_carrier(X3359),esk392_3(X3359,X3360,X3367))
| ~ element(X3365,powerset(the_carrier(X3359)))
| X3365 != esk388_2(X3359,X3360)
| esk390_2(X3359,X3360) = subset_complement(the_carrier(X3359),X3365)
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( relation_dom(esk393_2(X3359,X3360)) = complements_of_subsets(the_carrier(X3359),X3360)
| X3367 != subset_complement(the_carrier(X3359),esk392_3(X3359,X3360,X3367))
| ~ element(X3365,powerset(the_carrier(X3359)))
| X3365 != esk388_2(X3359,X3360)
| esk390_2(X3359,X3360) = subset_complement(the_carrier(X3359),X3365)
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( ~ in(X3370,complements_of_subsets(the_carrier(X3359),X3360))
| ~ element(X3371,powerset(the_carrier(X3359)))
| X3371 != X3370
| apply(esk393_2(X3359,X3360),X3370) = subset_complement(the_carrier(X3359),X3371)
| X3367 != subset_complement(the_carrier(X3359),esk392_3(X3359,X3360,X3367))
| ~ element(X3365,powerset(the_carrier(X3359)))
| X3365 != esk388_2(X3359,X3360)
| esk390_2(X3359,X3360) = subset_complement(the_carrier(X3359),X3365)
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( relation(esk393_2(X3359,X3360))
| in(esk391_2(X3359,X3360),complements_of_subsets(the_carrier(X3359),X3360))
| esk389_2(X3359,X3360) != esk390_2(X3359,X3360)
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( function(esk393_2(X3359,X3360))
| in(esk391_2(X3359,X3360),complements_of_subsets(the_carrier(X3359),X3360))
| esk389_2(X3359,X3360) != esk390_2(X3359,X3360)
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( relation_dom(esk393_2(X3359,X3360)) = complements_of_subsets(the_carrier(X3359),X3360)
| in(esk391_2(X3359,X3360),complements_of_subsets(the_carrier(X3359),X3360))
| esk389_2(X3359,X3360) != esk390_2(X3359,X3360)
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( ~ in(X3370,complements_of_subsets(the_carrier(X3359),X3360))
| ~ element(X3371,powerset(the_carrier(X3359)))
| X3371 != X3370
| apply(esk393_2(X3359,X3360),X3370) = subset_complement(the_carrier(X3359),X3371)
| in(esk391_2(X3359,X3360),complements_of_subsets(the_carrier(X3359),X3360))
| esk389_2(X3359,X3360) != esk390_2(X3359,X3360)
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( relation(esk393_2(X3359,X3360))
| element(esk392_3(X3359,X3360,X3367),powerset(the_carrier(X3359)))
| esk389_2(X3359,X3360) != esk390_2(X3359,X3360)
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( function(esk393_2(X3359,X3360))
| element(esk392_3(X3359,X3360,X3367),powerset(the_carrier(X3359)))
| esk389_2(X3359,X3360) != esk390_2(X3359,X3360)
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( relation_dom(esk393_2(X3359,X3360)) = complements_of_subsets(the_carrier(X3359),X3360)
| element(esk392_3(X3359,X3360,X3367),powerset(the_carrier(X3359)))
| esk389_2(X3359,X3360) != esk390_2(X3359,X3360)
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( ~ in(X3370,complements_of_subsets(the_carrier(X3359),X3360))
| ~ element(X3371,powerset(the_carrier(X3359)))
| X3371 != X3370
| apply(esk393_2(X3359,X3360),X3370) = subset_complement(the_carrier(X3359),X3371)
| element(esk392_3(X3359,X3360,X3367),powerset(the_carrier(X3359)))
| esk389_2(X3359,X3360) != esk390_2(X3359,X3360)
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( relation(esk393_2(X3359,X3360))
| esk392_3(X3359,X3360,X3367) = esk391_2(X3359,X3360)
| esk389_2(X3359,X3360) != esk390_2(X3359,X3360)
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( function(esk393_2(X3359,X3360))
| esk392_3(X3359,X3360,X3367) = esk391_2(X3359,X3360)
| esk389_2(X3359,X3360) != esk390_2(X3359,X3360)
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( relation_dom(esk393_2(X3359,X3360)) = complements_of_subsets(the_carrier(X3359),X3360)
| esk392_3(X3359,X3360,X3367) = esk391_2(X3359,X3360)
| esk389_2(X3359,X3360) != esk390_2(X3359,X3360)
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( ~ in(X3370,complements_of_subsets(the_carrier(X3359),X3360))
| ~ element(X3371,powerset(the_carrier(X3359)))
| X3371 != X3370
| apply(esk393_2(X3359,X3360),X3370) = subset_complement(the_carrier(X3359),X3371)
| esk392_3(X3359,X3360,X3367) = esk391_2(X3359,X3360)
| esk389_2(X3359,X3360) != esk390_2(X3359,X3360)
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( relation(esk393_2(X3359,X3360))
| X3367 != subset_complement(the_carrier(X3359),esk392_3(X3359,X3360,X3367))
| esk389_2(X3359,X3360) != esk390_2(X3359,X3360)
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( function(esk393_2(X3359,X3360))
| X3367 != subset_complement(the_carrier(X3359),esk392_3(X3359,X3360,X3367))
| esk389_2(X3359,X3360) != esk390_2(X3359,X3360)
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( relation_dom(esk393_2(X3359,X3360)) = complements_of_subsets(the_carrier(X3359),X3360)
| X3367 != subset_complement(the_carrier(X3359),esk392_3(X3359,X3360,X3367))
| esk389_2(X3359,X3360) != esk390_2(X3359,X3360)
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) )
& ( ~ in(X3370,complements_of_subsets(the_carrier(X3359),X3360))
| ~ element(X3371,powerset(the_carrier(X3359)))
| X3371 != X3370
| apply(esk393_2(X3359,X3360),X3370) = subset_complement(the_carrier(X3359),X3371)
| X3367 != subset_complement(the_carrier(X3359),esk392_3(X3359,X3360,X3367))
| esk389_2(X3359,X3360) != esk390_2(X3359,X3360)
| ~ one_sorted_str(X3359)
| ~ element(X3360,powerset(powerset(the_carrier(X3359)))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[s2_funct_1__e4_7_1__tops_2])])])])]) ).
cnf(i_0_1449,lemma,
( relation_dom(esk381_2(X1,X2)) = X1
| in(esk379_2(X1,X2),X1)
| in(ordered_pair(esk376_2(X1,X2),X3),X2)
| empty(X1)
| ~ in(X3,esk378_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1450,lemma,
( relation_dom(esk381_2(X1,X2)) = X1
| in(esk379_2(X1,X2),X1)
| in(ordered_pair(esk375_2(X1,X2),X3),X2)
| empty(X1)
| ~ in(X3,esk377_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1451,lemma,
( relation(esk381_2(X1,X2))
| in(esk379_2(X1,X2),X1)
| in(ordered_pair(esk376_2(X1,X2),X3),X2)
| empty(X1)
| ~ in(X3,esk378_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1452,lemma,
( relation(esk381_2(X1,X2))
| in(esk379_2(X1,X2),X1)
| in(ordered_pair(esk375_2(X1,X2),X3),X2)
| empty(X1)
| ~ in(X3,esk377_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1453,lemma,
( function(esk381_2(X1,X2))
| in(esk379_2(X1,X2),X1)
| in(ordered_pair(esk376_2(X1,X2),X3),X2)
| empty(X1)
| ~ in(X3,esk378_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
cnf(i_0_1454,lemma,
( function(esk381_2(X1,X2))
| in(esk379_2(X1,X2),X1)
| in(ordered_pair(esk375_2(X1,X2),X3),X2)
| empty(X1)
| ~ in(X3,esk377_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]) ).
fof(i_0_1455,plain,
! [X2671,X2672,X2675,X2676] :
( ( element(esk125_2(X2671,X2672),the_carrier(X2672))
| ~ in(X2671,a_1_0_filter_1(X2672))
| empty_carrier(X2672)
| ~ lattice(X2672)
| ~ latt_str(X2672) )
& ( element(esk126_2(X2671,X2672),the_carrier(X2672))
| ~ in(X2671,a_1_0_filter_1(X2672))
| empty_carrier(X2672)
| ~ lattice(X2672)
| ~ latt_str(X2672) )
& ( X2671 = ordered_pair_as_product_element(the_carrier(X2672),the_carrier(X2672),esk125_2(X2671,X2672),esk126_2(X2671,X2672))
| ~ in(X2671,a_1_0_filter_1(X2672))
| empty_carrier(X2672)
| ~ lattice(X2672)
| ~ latt_str(X2672) )
& ( below_refl(X2672,esk125_2(X2671,X2672),esk126_2(X2671,X2672))
| ~ in(X2671,a_1_0_filter_1(X2672))
| empty_carrier(X2672)
| ~ lattice(X2672)
| ~ latt_str(X2672) )
& ( ~ element(X2675,the_carrier(X2672))
| ~ element(X2676,the_carrier(X2672))
| X2671 != ordered_pair_as_product_element(the_carrier(X2672),the_carrier(X2672),X2675,X2676)
| ~ below_refl(X2672,X2675,X2676)
| in(X2671,a_1_0_filter_1(X2672))
| empty_carrier(X2672)
| ~ lattice(X2672)
| ~ latt_str(X2672) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_738])])])])]) ).
cnf(i_0_1456,plain,
( esk1_2(X1,X2) = esk2_2(X1,X2)
| in(ordered_pair(esk1_2(X1,X2),esk2_2(X1,X2)),X2)
| X2 = identity_relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_720]) ).
cnf(i_0_1457,lemma,
( X1 = esk183_4(X2,X3,X1,X4)
| in(esk179_2(X2,X3),esk181_2(X2,X3))
| empty(X2)
| ~ in(ordered_pair(X1,X4),esk182_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1458,lemma,
( X1 = esk183_4(X2,X3,X1,X4)
| in(esk178_2(X2,X3),esk180_2(X2,X3))
| empty(X2)
| ~ in(ordered_pair(X1,X4),esk182_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1459,plain,
( in(ordered_pair(esk72_2(X1,X2),esk73_2(X1,X2)),X1)
| subset(X1,X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_724]) ).
fof(i_0_1460,plain,
! [X2446,X2447,X2448,X2449] :
( empty(X2446)
| empty(X2447)
| ~ element(X2448,X2446)
| ~ element(X2449,X2447)
| element(ordered_pair_as_product_element(X2446,X2447,X2448,X2449),cartesian_product2(X2446,X2447)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_739])]) ).
cnf(i_0_1461,lemma,
( esk198_4(X1,X2,X3,X4) = X3
| in(ordered_pair(X3,X4),esk197_2(X1,X2))
| ~ in(X3,X2)
| esk195_2(X1,X2) != esk196_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_712]) ).
cnf(i_0_1462,plain,
( in(ordered_pair(esk111_2(X1,X2),esk112_2(X1,X2)),X1)
| is_transitive_in(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_726]) ).
cnf(i_0_1463,plain,
( in(ordered_pair(esk110_2(X1,X2),esk111_2(X1,X2)),X1)
| is_transitive_in(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_726]) ).
cnf(i_0_1464,plain,
( in(ordered_pair(esk82_2(X1,X2),esk81_2(X1,X2)),X1)
| is_antisymmetric_in(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_740]) ).
cnf(i_0_1465,plain,
( in(ordered_pair(esk81_2(X1,X2),esk82_2(X1,X2)),X1)
| is_antisymmetric_in(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_740]) ).
cnf(i_0_1466,lemma,
( esk198_4(X1,X2,X3,X4) = X3
| in(ordered_pair(X3,X4),esk197_2(X1,X2))
| in(esk194_2(X1,X2),X2)
| ~ in(X3,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_712]) ).
cnf(i_0_1467,lemma,
( esk198_4(X1,X2,X3,X4) = X3
| in(ordered_pair(X3,X4),esk197_2(X1,X2))
| in(esk194_2(X1,X2),X2)
| ~ in(X3,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_712]) ).
fof(i_0_1468,plain,
! [X1917,X1918,X1919,X1920,X1922,X1923,X1924,X1925,X1927] :
( ( in(esk5_4(X1917,X1918,X1919,X1920),relation_dom(X1917))
| ~ in(X1920,X1919)
| X1919 != relation_image(X1917,X1918)
| ~ relation(X1917)
| ~ function(X1917) )
& ( in(esk5_4(X1917,X1918,X1919,X1920),X1918)
| ~ in(X1920,X1919)
| X1919 != relation_image(X1917,X1918)
| ~ relation(X1917)
| ~ function(X1917) )
& ( X1920 = apply(X1917,esk5_4(X1917,X1918,X1919,X1920))
| ~ in(X1920,X1919)
| X1919 != relation_image(X1917,X1918)
| ~ relation(X1917)
| ~ function(X1917) )
& ( ~ in(X1923,relation_dom(X1917))
| ~ in(X1923,X1918)
| X1922 != apply(X1917,X1923)
| in(X1922,X1919)
| X1919 != relation_image(X1917,X1918)
| ~ relation(X1917)
| ~ function(X1917) )
& ( ~ in(esk6_3(X1917,X1924,X1925),X1925)
| ~ in(X1927,relation_dom(X1917))
| ~ in(X1927,X1924)
| esk6_3(X1917,X1924,X1925) != apply(X1917,X1927)
| X1925 = relation_image(X1917,X1924)
| ~ relation(X1917)
| ~ function(X1917) )
& ( in(esk7_3(X1917,X1924,X1925),relation_dom(X1917))
| in(esk6_3(X1917,X1924,X1925),X1925)
| X1925 = relation_image(X1917,X1924)
| ~ relation(X1917)
| ~ function(X1917) )
& ( in(esk7_3(X1917,X1924,X1925),X1924)
| in(esk6_3(X1917,X1924,X1925),X1925)
| X1925 = relation_image(X1917,X1924)
| ~ relation(X1917)
| ~ function(X1917) )
& ( esk6_3(X1917,X1924,X1925) = apply(X1917,esk7_3(X1917,X1924,X1925))
| in(esk6_3(X1917,X1924,X1925),X1925)
| X1925 = relation_image(X1917,X1924)
| ~ relation(X1917)
| ~ function(X1917) ) ),
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)],[d12_funct_1])])])])])]) ).
cnf(i_0_1469,lemma,
( X1 = esk183_4(X2,X3,X1,X4)
| empty(X2)
| ~ in(ordered_pair(X1,X4),esk182_2(X2,X3))
| esk178_2(X2,X3) != esk179_2(X2,X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1470,lemma,
( X1 = esk183_4(X2,X3,X1,X4)
| in(esk177_2(X2,X3),X2)
| empty(X2)
| ~ in(ordered_pair(X1,X4),esk182_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1471,lemma,
( X1 = esk183_4(X2,X3,X1,X4)
| in(esk177_2(X2,X3),X2)
| empty(X2)
| ~ in(ordered_pair(X1,X4),esk182_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1472,lemma,
( relation(esk182_2(X1,X2))
| in(ordered_pair(esk179_2(X1,X2),X3),X2)
| empty(X1)
| ~ in(X3,esk181_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1473,lemma,
( relation(esk182_2(X1,X2))
| in(ordered_pair(esk178_2(X1,X2),X3),X2)
| empty(X1)
| ~ in(X3,esk180_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1474,lemma,
( function(esk182_2(X1,X2))
| in(ordered_pair(esk179_2(X1,X2),X3),X2)
| empty(X1)
| ~ in(X3,esk181_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1475,lemma,
( function(esk182_2(X1,X2))
| in(ordered_pair(esk178_2(X1,X2),X3),X2)
| empty(X1)
| ~ in(X3,esk180_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1476,lemma,
( X1 = esk183_4(X2,X3,X1,X4)
| esk177_2(X2,X3) = esk181_2(X2,X3)
| empty(X2)
| ~ in(ordered_pair(X1,X4),esk182_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1477,lemma,
( X1 = esk183_4(X2,X3,X1,X4)
| esk177_2(X2,X3) = esk180_2(X2,X3)
| empty(X2)
| ~ in(ordered_pair(X1,X4),esk182_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1478,lemma,
( X4 = subset_complement(the_carrier(X2),X1)
| esk196_2(X2,X5) = subset_complement(the_carrier(X2),X6)
| ~ element(X1,powerset(the_carrier(X2)))
| X1 != X3
| ~ in(ordered_pair(X3,X4),esk197_2(X2,X5))
| ~ element(X6,powerset(the_carrier(X2)))
| X6 != esk194_2(X2,X5)
| ~ one_sorted_str(X2)
| ~ element(X5,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_712]) ).
cnf(i_0_1479,lemma,
( X4 = subset_complement(the_carrier(X2),X1)
| esk195_2(X2,X5) = subset_complement(the_carrier(X2),X6)
| ~ element(X1,powerset(the_carrier(X2)))
| X1 != X3
| ~ in(ordered_pair(X3,X4),esk197_2(X2,X5))
| ~ element(X6,powerset(the_carrier(X2)))
| X6 != esk194_2(X2,X5)
| ~ one_sorted_str(X2)
| ~ element(X5,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_712]) ).
cnf(i_0_1480,lemma,
( X4 = subset_complement(the_carrier(X2),X1)
| esk191_2(X2,X5) = subset_complement(the_carrier(X2),X6)
| ~ element(X1,powerset(the_carrier(X2)))
| X1 != X3
| ~ in(ordered_pair(X3,X4),esk192_2(X2,X5))
| ~ element(X6,powerset(the_carrier(X2)))
| X6 != esk189_2(X2,X5)
| ~ one_sorted_str(X2)
| ~ element(X5,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_711]) ).
cnf(i_0_1481,lemma,
( X4 = subset_complement(the_carrier(X2),X1)
| esk190_2(X2,X5) = subset_complement(the_carrier(X2),X6)
| ~ element(X1,powerset(the_carrier(X2)))
| X1 != X3
| ~ in(ordered_pair(X3,X4),esk192_2(X2,X5))
| ~ element(X6,powerset(the_carrier(X2)))
| X6 != esk189_2(X2,X5)
| ~ one_sorted_str(X2)
| ~ element(X5,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_711]) ).
fof(i_0_1482,lemma,
! [X3372,X3373,X3377,X3378,X3380,X3383,X3384] :
( ( relation(esk399_2(X3372,X3373))
| in(esk397_2(X3372,X3373),X3373)
| in(esk394_2(X3372,X3373),X3373)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( function(esk399_2(X3372,X3373))
| in(esk397_2(X3372,X3373),X3373)
| in(esk394_2(X3372,X3373),X3373)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( relation_dom(esk399_2(X3372,X3373)) = X3373
| in(esk397_2(X3372,X3373),X3373)
| in(esk394_2(X3372,X3373),X3373)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( ~ in(X3383,X3373)
| ~ element(X3384,powerset(the_carrier(X3372)))
| X3384 != X3383
| apply(esk399_2(X3372,X3373),X3383) = subset_complement(the_carrier(X3372),X3384)
| in(esk397_2(X3372,X3373),X3373)
| in(esk394_2(X3372,X3373),X3373)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( relation(esk399_2(X3372,X3373))
| element(esk398_3(X3372,X3373,X3380),powerset(the_carrier(X3372)))
| in(esk394_2(X3372,X3373),X3373)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( function(esk399_2(X3372,X3373))
| element(esk398_3(X3372,X3373,X3380),powerset(the_carrier(X3372)))
| in(esk394_2(X3372,X3373),X3373)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( relation_dom(esk399_2(X3372,X3373)) = X3373
| element(esk398_3(X3372,X3373,X3380),powerset(the_carrier(X3372)))
| in(esk394_2(X3372,X3373),X3373)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( ~ in(X3383,X3373)
| ~ element(X3384,powerset(the_carrier(X3372)))
| X3384 != X3383
| apply(esk399_2(X3372,X3373),X3383) = subset_complement(the_carrier(X3372),X3384)
| element(esk398_3(X3372,X3373,X3380),powerset(the_carrier(X3372)))
| in(esk394_2(X3372,X3373),X3373)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( relation(esk399_2(X3372,X3373))
| esk398_3(X3372,X3373,X3380) = esk397_2(X3372,X3373)
| in(esk394_2(X3372,X3373),X3373)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( function(esk399_2(X3372,X3373))
| esk398_3(X3372,X3373,X3380) = esk397_2(X3372,X3373)
| in(esk394_2(X3372,X3373),X3373)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( relation_dom(esk399_2(X3372,X3373)) = X3373
| esk398_3(X3372,X3373,X3380) = esk397_2(X3372,X3373)
| in(esk394_2(X3372,X3373),X3373)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( ~ in(X3383,X3373)
| ~ element(X3384,powerset(the_carrier(X3372)))
| X3384 != X3383
| apply(esk399_2(X3372,X3373),X3383) = subset_complement(the_carrier(X3372),X3384)
| esk398_3(X3372,X3373,X3380) = esk397_2(X3372,X3373)
| in(esk394_2(X3372,X3373),X3373)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( relation(esk399_2(X3372,X3373))
| X3380 != subset_complement(the_carrier(X3372),esk398_3(X3372,X3373,X3380))
| in(esk394_2(X3372,X3373),X3373)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( function(esk399_2(X3372,X3373))
| X3380 != subset_complement(the_carrier(X3372),esk398_3(X3372,X3373,X3380))
| in(esk394_2(X3372,X3373),X3373)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( relation_dom(esk399_2(X3372,X3373)) = X3373
| X3380 != subset_complement(the_carrier(X3372),esk398_3(X3372,X3373,X3380))
| in(esk394_2(X3372,X3373),X3373)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( ~ in(X3383,X3373)
| ~ element(X3384,powerset(the_carrier(X3372)))
| X3384 != X3383
| apply(esk399_2(X3372,X3373),X3383) = subset_complement(the_carrier(X3372),X3384)
| X3380 != subset_complement(the_carrier(X3372),esk398_3(X3372,X3373,X3380))
| in(esk394_2(X3372,X3373),X3373)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( relation(esk399_2(X3372,X3373))
| in(esk397_2(X3372,X3373),X3373)
| ~ element(X3377,powerset(the_carrier(X3372)))
| X3377 != esk394_2(X3372,X3373)
| esk395_2(X3372,X3373) = subset_complement(the_carrier(X3372),X3377)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( function(esk399_2(X3372,X3373))
| in(esk397_2(X3372,X3373),X3373)
| ~ element(X3377,powerset(the_carrier(X3372)))
| X3377 != esk394_2(X3372,X3373)
| esk395_2(X3372,X3373) = subset_complement(the_carrier(X3372),X3377)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( relation_dom(esk399_2(X3372,X3373)) = X3373
| in(esk397_2(X3372,X3373),X3373)
| ~ element(X3377,powerset(the_carrier(X3372)))
| X3377 != esk394_2(X3372,X3373)
| esk395_2(X3372,X3373) = subset_complement(the_carrier(X3372),X3377)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( ~ in(X3383,X3373)
| ~ element(X3384,powerset(the_carrier(X3372)))
| X3384 != X3383
| apply(esk399_2(X3372,X3373),X3383) = subset_complement(the_carrier(X3372),X3384)
| in(esk397_2(X3372,X3373),X3373)
| ~ element(X3377,powerset(the_carrier(X3372)))
| X3377 != esk394_2(X3372,X3373)
| esk395_2(X3372,X3373) = subset_complement(the_carrier(X3372),X3377)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( relation(esk399_2(X3372,X3373))
| element(esk398_3(X3372,X3373,X3380),powerset(the_carrier(X3372)))
| ~ element(X3377,powerset(the_carrier(X3372)))
| X3377 != esk394_2(X3372,X3373)
| esk395_2(X3372,X3373) = subset_complement(the_carrier(X3372),X3377)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( function(esk399_2(X3372,X3373))
| element(esk398_3(X3372,X3373,X3380),powerset(the_carrier(X3372)))
| ~ element(X3377,powerset(the_carrier(X3372)))
| X3377 != esk394_2(X3372,X3373)
| esk395_2(X3372,X3373) = subset_complement(the_carrier(X3372),X3377)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( relation_dom(esk399_2(X3372,X3373)) = X3373
| element(esk398_3(X3372,X3373,X3380),powerset(the_carrier(X3372)))
| ~ element(X3377,powerset(the_carrier(X3372)))
| X3377 != esk394_2(X3372,X3373)
| esk395_2(X3372,X3373) = subset_complement(the_carrier(X3372),X3377)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( ~ in(X3383,X3373)
| ~ element(X3384,powerset(the_carrier(X3372)))
| X3384 != X3383
| apply(esk399_2(X3372,X3373),X3383) = subset_complement(the_carrier(X3372),X3384)
| element(esk398_3(X3372,X3373,X3380),powerset(the_carrier(X3372)))
| ~ element(X3377,powerset(the_carrier(X3372)))
| X3377 != esk394_2(X3372,X3373)
| esk395_2(X3372,X3373) = subset_complement(the_carrier(X3372),X3377)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( relation(esk399_2(X3372,X3373))
| esk398_3(X3372,X3373,X3380) = esk397_2(X3372,X3373)
| ~ element(X3377,powerset(the_carrier(X3372)))
| X3377 != esk394_2(X3372,X3373)
| esk395_2(X3372,X3373) = subset_complement(the_carrier(X3372),X3377)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( function(esk399_2(X3372,X3373))
| esk398_3(X3372,X3373,X3380) = esk397_2(X3372,X3373)
| ~ element(X3377,powerset(the_carrier(X3372)))
| X3377 != esk394_2(X3372,X3373)
| esk395_2(X3372,X3373) = subset_complement(the_carrier(X3372),X3377)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( relation_dom(esk399_2(X3372,X3373)) = X3373
| esk398_3(X3372,X3373,X3380) = esk397_2(X3372,X3373)
| ~ element(X3377,powerset(the_carrier(X3372)))
| X3377 != esk394_2(X3372,X3373)
| esk395_2(X3372,X3373) = subset_complement(the_carrier(X3372),X3377)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( ~ in(X3383,X3373)
| ~ element(X3384,powerset(the_carrier(X3372)))
| X3384 != X3383
| apply(esk399_2(X3372,X3373),X3383) = subset_complement(the_carrier(X3372),X3384)
| esk398_3(X3372,X3373,X3380) = esk397_2(X3372,X3373)
| ~ element(X3377,powerset(the_carrier(X3372)))
| X3377 != esk394_2(X3372,X3373)
| esk395_2(X3372,X3373) = subset_complement(the_carrier(X3372),X3377)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( relation(esk399_2(X3372,X3373))
| X3380 != subset_complement(the_carrier(X3372),esk398_3(X3372,X3373,X3380))
| ~ element(X3377,powerset(the_carrier(X3372)))
| X3377 != esk394_2(X3372,X3373)
| esk395_2(X3372,X3373) = subset_complement(the_carrier(X3372),X3377)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( function(esk399_2(X3372,X3373))
| X3380 != subset_complement(the_carrier(X3372),esk398_3(X3372,X3373,X3380))
| ~ element(X3377,powerset(the_carrier(X3372)))
| X3377 != esk394_2(X3372,X3373)
| esk395_2(X3372,X3373) = subset_complement(the_carrier(X3372),X3377)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( relation_dom(esk399_2(X3372,X3373)) = X3373
| X3380 != subset_complement(the_carrier(X3372),esk398_3(X3372,X3373,X3380))
| ~ element(X3377,powerset(the_carrier(X3372)))
| X3377 != esk394_2(X3372,X3373)
| esk395_2(X3372,X3373) = subset_complement(the_carrier(X3372),X3377)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( ~ in(X3383,X3373)
| ~ element(X3384,powerset(the_carrier(X3372)))
| X3384 != X3383
| apply(esk399_2(X3372,X3373),X3383) = subset_complement(the_carrier(X3372),X3384)
| X3380 != subset_complement(the_carrier(X3372),esk398_3(X3372,X3373,X3380))
| ~ element(X3377,powerset(the_carrier(X3372)))
| X3377 != esk394_2(X3372,X3373)
| esk395_2(X3372,X3373) = subset_complement(the_carrier(X3372),X3377)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( relation(esk399_2(X3372,X3373))
| in(esk397_2(X3372,X3373),X3373)
| ~ element(X3378,powerset(the_carrier(X3372)))
| X3378 != esk394_2(X3372,X3373)
| esk396_2(X3372,X3373) = subset_complement(the_carrier(X3372),X3378)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( function(esk399_2(X3372,X3373))
| in(esk397_2(X3372,X3373),X3373)
| ~ element(X3378,powerset(the_carrier(X3372)))
| X3378 != esk394_2(X3372,X3373)
| esk396_2(X3372,X3373) = subset_complement(the_carrier(X3372),X3378)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( relation_dom(esk399_2(X3372,X3373)) = X3373
| in(esk397_2(X3372,X3373),X3373)
| ~ element(X3378,powerset(the_carrier(X3372)))
| X3378 != esk394_2(X3372,X3373)
| esk396_2(X3372,X3373) = subset_complement(the_carrier(X3372),X3378)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( ~ in(X3383,X3373)
| ~ element(X3384,powerset(the_carrier(X3372)))
| X3384 != X3383
| apply(esk399_2(X3372,X3373),X3383) = subset_complement(the_carrier(X3372),X3384)
| in(esk397_2(X3372,X3373),X3373)
| ~ element(X3378,powerset(the_carrier(X3372)))
| X3378 != esk394_2(X3372,X3373)
| esk396_2(X3372,X3373) = subset_complement(the_carrier(X3372),X3378)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( relation(esk399_2(X3372,X3373))
| element(esk398_3(X3372,X3373,X3380),powerset(the_carrier(X3372)))
| ~ element(X3378,powerset(the_carrier(X3372)))
| X3378 != esk394_2(X3372,X3373)
| esk396_2(X3372,X3373) = subset_complement(the_carrier(X3372),X3378)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( function(esk399_2(X3372,X3373))
| element(esk398_3(X3372,X3373,X3380),powerset(the_carrier(X3372)))
| ~ element(X3378,powerset(the_carrier(X3372)))
| X3378 != esk394_2(X3372,X3373)
| esk396_2(X3372,X3373) = subset_complement(the_carrier(X3372),X3378)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( relation_dom(esk399_2(X3372,X3373)) = X3373
| element(esk398_3(X3372,X3373,X3380),powerset(the_carrier(X3372)))
| ~ element(X3378,powerset(the_carrier(X3372)))
| X3378 != esk394_2(X3372,X3373)
| esk396_2(X3372,X3373) = subset_complement(the_carrier(X3372),X3378)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( ~ in(X3383,X3373)
| ~ element(X3384,powerset(the_carrier(X3372)))
| X3384 != X3383
| apply(esk399_2(X3372,X3373),X3383) = subset_complement(the_carrier(X3372),X3384)
| element(esk398_3(X3372,X3373,X3380),powerset(the_carrier(X3372)))
| ~ element(X3378,powerset(the_carrier(X3372)))
| X3378 != esk394_2(X3372,X3373)
| esk396_2(X3372,X3373) = subset_complement(the_carrier(X3372),X3378)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( relation(esk399_2(X3372,X3373))
| esk398_3(X3372,X3373,X3380) = esk397_2(X3372,X3373)
| ~ element(X3378,powerset(the_carrier(X3372)))
| X3378 != esk394_2(X3372,X3373)
| esk396_2(X3372,X3373) = subset_complement(the_carrier(X3372),X3378)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( function(esk399_2(X3372,X3373))
| esk398_3(X3372,X3373,X3380) = esk397_2(X3372,X3373)
| ~ element(X3378,powerset(the_carrier(X3372)))
| X3378 != esk394_2(X3372,X3373)
| esk396_2(X3372,X3373) = subset_complement(the_carrier(X3372),X3378)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( relation_dom(esk399_2(X3372,X3373)) = X3373
| esk398_3(X3372,X3373,X3380) = esk397_2(X3372,X3373)
| ~ element(X3378,powerset(the_carrier(X3372)))
| X3378 != esk394_2(X3372,X3373)
| esk396_2(X3372,X3373) = subset_complement(the_carrier(X3372),X3378)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( ~ in(X3383,X3373)
| ~ element(X3384,powerset(the_carrier(X3372)))
| X3384 != X3383
| apply(esk399_2(X3372,X3373),X3383) = subset_complement(the_carrier(X3372),X3384)
| esk398_3(X3372,X3373,X3380) = esk397_2(X3372,X3373)
| ~ element(X3378,powerset(the_carrier(X3372)))
| X3378 != esk394_2(X3372,X3373)
| esk396_2(X3372,X3373) = subset_complement(the_carrier(X3372),X3378)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( relation(esk399_2(X3372,X3373))
| X3380 != subset_complement(the_carrier(X3372),esk398_3(X3372,X3373,X3380))
| ~ element(X3378,powerset(the_carrier(X3372)))
| X3378 != esk394_2(X3372,X3373)
| esk396_2(X3372,X3373) = subset_complement(the_carrier(X3372),X3378)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( function(esk399_2(X3372,X3373))
| X3380 != subset_complement(the_carrier(X3372),esk398_3(X3372,X3373,X3380))
| ~ element(X3378,powerset(the_carrier(X3372)))
| X3378 != esk394_2(X3372,X3373)
| esk396_2(X3372,X3373) = subset_complement(the_carrier(X3372),X3378)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( relation_dom(esk399_2(X3372,X3373)) = X3373
| X3380 != subset_complement(the_carrier(X3372),esk398_3(X3372,X3373,X3380))
| ~ element(X3378,powerset(the_carrier(X3372)))
| X3378 != esk394_2(X3372,X3373)
| esk396_2(X3372,X3373) = subset_complement(the_carrier(X3372),X3378)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( ~ in(X3383,X3373)
| ~ element(X3384,powerset(the_carrier(X3372)))
| X3384 != X3383
| apply(esk399_2(X3372,X3373),X3383) = subset_complement(the_carrier(X3372),X3384)
| X3380 != subset_complement(the_carrier(X3372),esk398_3(X3372,X3373,X3380))
| ~ element(X3378,powerset(the_carrier(X3372)))
| X3378 != esk394_2(X3372,X3373)
| esk396_2(X3372,X3373) = subset_complement(the_carrier(X3372),X3378)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( relation(esk399_2(X3372,X3373))
| in(esk397_2(X3372,X3373),X3373)
| esk395_2(X3372,X3373) != esk396_2(X3372,X3373)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( function(esk399_2(X3372,X3373))
| in(esk397_2(X3372,X3373),X3373)
| esk395_2(X3372,X3373) != esk396_2(X3372,X3373)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( relation_dom(esk399_2(X3372,X3373)) = X3373
| in(esk397_2(X3372,X3373),X3373)
| esk395_2(X3372,X3373) != esk396_2(X3372,X3373)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( ~ in(X3383,X3373)
| ~ element(X3384,powerset(the_carrier(X3372)))
| X3384 != X3383
| apply(esk399_2(X3372,X3373),X3383) = subset_complement(the_carrier(X3372),X3384)
| in(esk397_2(X3372,X3373),X3373)
| esk395_2(X3372,X3373) != esk396_2(X3372,X3373)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( relation(esk399_2(X3372,X3373))
| element(esk398_3(X3372,X3373,X3380),powerset(the_carrier(X3372)))
| esk395_2(X3372,X3373) != esk396_2(X3372,X3373)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( function(esk399_2(X3372,X3373))
| element(esk398_3(X3372,X3373,X3380),powerset(the_carrier(X3372)))
| esk395_2(X3372,X3373) != esk396_2(X3372,X3373)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( relation_dom(esk399_2(X3372,X3373)) = X3373
| element(esk398_3(X3372,X3373,X3380),powerset(the_carrier(X3372)))
| esk395_2(X3372,X3373) != esk396_2(X3372,X3373)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( ~ in(X3383,X3373)
| ~ element(X3384,powerset(the_carrier(X3372)))
| X3384 != X3383
| apply(esk399_2(X3372,X3373),X3383) = subset_complement(the_carrier(X3372),X3384)
| element(esk398_3(X3372,X3373,X3380),powerset(the_carrier(X3372)))
| esk395_2(X3372,X3373) != esk396_2(X3372,X3373)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( relation(esk399_2(X3372,X3373))
| esk398_3(X3372,X3373,X3380) = esk397_2(X3372,X3373)
| esk395_2(X3372,X3373) != esk396_2(X3372,X3373)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( function(esk399_2(X3372,X3373))
| esk398_3(X3372,X3373,X3380) = esk397_2(X3372,X3373)
| esk395_2(X3372,X3373) != esk396_2(X3372,X3373)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( relation_dom(esk399_2(X3372,X3373)) = X3373
| esk398_3(X3372,X3373,X3380) = esk397_2(X3372,X3373)
| esk395_2(X3372,X3373) != esk396_2(X3372,X3373)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( ~ in(X3383,X3373)
| ~ element(X3384,powerset(the_carrier(X3372)))
| X3384 != X3383
| apply(esk399_2(X3372,X3373),X3383) = subset_complement(the_carrier(X3372),X3384)
| esk398_3(X3372,X3373,X3380) = esk397_2(X3372,X3373)
| esk395_2(X3372,X3373) != esk396_2(X3372,X3373)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( relation(esk399_2(X3372,X3373))
| X3380 != subset_complement(the_carrier(X3372),esk398_3(X3372,X3373,X3380))
| esk395_2(X3372,X3373) != esk396_2(X3372,X3373)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( function(esk399_2(X3372,X3373))
| X3380 != subset_complement(the_carrier(X3372),esk398_3(X3372,X3373,X3380))
| esk395_2(X3372,X3373) != esk396_2(X3372,X3373)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( relation_dom(esk399_2(X3372,X3373)) = X3373
| X3380 != subset_complement(the_carrier(X3372),esk398_3(X3372,X3373,X3380))
| esk395_2(X3372,X3373) != esk396_2(X3372,X3373)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) )
& ( ~ in(X3383,X3373)
| ~ element(X3384,powerset(the_carrier(X3372)))
| X3384 != X3383
| apply(esk399_2(X3372,X3373),X3383) = subset_complement(the_carrier(X3372),X3384)
| X3380 != subset_complement(the_carrier(X3372),esk398_3(X3372,X3373,X3380))
| esk395_2(X3372,X3373) != esk396_2(X3372,X3373)
| ~ one_sorted_str(X3372)
| ~ element(X3373,powerset(powerset(the_carrier(X3372)))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[s2_funct_1__e4_7_2__tops_2])])])])]) ).
cnf(i_0_1483,plain,
( X3 = X4
| ~ is_antisymmetric_in(X1,X2)
| ~ in(X3,X2)
| ~ in(X4,X2)
| ~ in(ordered_pair(X3,X4),X1)
| ~ in(ordered_pair(X4,X3),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_740]) ).
cnf(i_0_1484,lemma,
( in(X1,complements_of_subsets(the_carrier(X2),X3))
| esk191_2(X2,X3) = subset_complement(the_carrier(X2),X5)
| ~ in(ordered_pair(X1,X4),esk192_2(X2,X3))
| ~ element(X5,powerset(the_carrier(X2)))
| X5 != esk189_2(X2,X3)
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_711]) ).
cnf(i_0_1485,lemma,
( in(X1,complements_of_subsets(the_carrier(X2),X3))
| esk190_2(X2,X3) = subset_complement(the_carrier(X2),X5)
| ~ in(ordered_pair(X1,X4),esk192_2(X2,X3))
| ~ element(X5,powerset(the_carrier(X2)))
| X5 != esk189_2(X2,X3)
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_711]) ).
cnf(i_0_1486,lemma,
( X1 = relation_dom_restriction(X3,X2)
| apply(X1,esk439_3(X2,X1,X3)) != apply(X3,esk439_3(X2,X1,X3))
| relation_dom(X1) != set_intersection2(relation_dom(X3),X2)
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_741]) ).
cnf(i_0_1487,lemma,
( X4 = subset_complement(the_carrier(X2),X1)
| in(esk189_2(X2,X5),complements_of_subsets(the_carrier(X2),X5))
| ~ element(X1,powerset(the_carrier(X2)))
| X1 != X3
| ~ in(ordered_pair(X3,X4),esk192_2(X2,X5))
| ~ one_sorted_str(X2)
| ~ element(X5,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_711]) ).
cnf(i_0_1488,lemma,
( X4 = subset_complement(the_carrier(X2),X1)
| in(esk189_2(X2,X5),complements_of_subsets(the_carrier(X2),X5))
| ~ element(X1,powerset(the_carrier(X2)))
| X1 != X3
| ~ in(ordered_pair(X3,X4),esk192_2(X2,X5))
| ~ one_sorted_str(X2)
| ~ element(X5,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_711]) ).
fof(i_0_1489,plain,
! [X2301,X2302,X2303,X2304,X2305,X2306,X2307,X2308] :
( ( in(X2304,X2301)
| ~ in(X2304,X2303)
| X2303 != set_difference(X2301,X2302) )
& ( ~ in(X2304,X2302)
| ~ in(X2304,X2303)
| X2303 != set_difference(X2301,X2302) )
& ( ~ in(X2305,X2301)
| in(X2305,X2302)
| in(X2305,X2303)
| X2303 != set_difference(X2301,X2302) )
& ( ~ in(esk87_3(X2306,X2307,X2308),X2308)
| ~ in(esk87_3(X2306,X2307,X2308),X2306)
| in(esk87_3(X2306,X2307,X2308),X2307)
| X2308 = set_difference(X2306,X2307) )
& ( in(esk87_3(X2306,X2307,X2308),X2306)
| in(esk87_3(X2306,X2307,X2308),X2308)
| X2308 = set_difference(X2306,X2307) )
& ( ~ in(esk87_3(X2306,X2307,X2308),X2307)
| in(esk87_3(X2306,X2307,X2308),X2308)
| X2308 = set_difference(X2306,X2307) ) ),
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)],[i_0_742])])])])])]) ).
cnf(i_0_1490,lemma,
( in(X1,complements_of_subsets(the_carrier(X2),X3))
| in(esk189_2(X2,X3),complements_of_subsets(the_carrier(X2),X3))
| ~ in(ordered_pair(X1,X4),esk192_2(X2,X3))
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_711]) ).
cnf(i_0_1491,lemma,
( in(X1,complements_of_subsets(the_carrier(X2),X3))
| in(esk189_2(X2,X3),complements_of_subsets(the_carrier(X2),X3))
| ~ in(ordered_pair(X1,X4),esk192_2(X2,X3))
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_711]) ).
cnf(i_0_1492,lemma,
( in(X1,X2)
| esk196_2(X4,X2) = subset_complement(the_carrier(X4),X5)
| ~ in(ordered_pair(X1,X3),esk197_2(X4,X2))
| ~ element(X5,powerset(the_carrier(X4)))
| X5 != esk194_2(X4,X2)
| ~ one_sorted_str(X4)
| ~ element(X2,powerset(powerset(the_carrier(X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_712]) ).
cnf(i_0_1493,lemma,
( in(X1,X2)
| esk195_2(X4,X2) = subset_complement(the_carrier(X4),X5)
| ~ in(ordered_pair(X1,X3),esk197_2(X4,X2))
| ~ element(X5,powerset(the_carrier(X4)))
| X5 != esk194_2(X4,X2)
| ~ one_sorted_str(X4)
| ~ element(X2,powerset(powerset(the_carrier(X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_712]) ).
cnf(i_0_1494,lemma,
( X4 = subset_complement(the_carrier(X2),X1)
| ~ element(X1,powerset(the_carrier(X2)))
| X1 != X3
| ~ in(ordered_pair(X3,X4),esk197_2(X2,X5))
| esk195_2(X2,X5) != esk196_2(X2,X5)
| ~ one_sorted_str(X2)
| ~ element(X5,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_712]) ).
cnf(i_0_1495,lemma,
( X4 = subset_complement(the_carrier(X2),X1)
| ~ element(X1,powerset(the_carrier(X2)))
| X1 != X3
| ~ in(ordered_pair(X3,X4),esk192_2(X2,X5))
| esk190_2(X2,X5) != esk191_2(X2,X5)
| ~ one_sorted_str(X2)
| ~ element(X5,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_711]) ).
cnf(i_0_1496,lemma,
( X4 = subset_complement(the_carrier(X2),X1)
| in(esk194_2(X2,X5),X5)
| ~ element(X1,powerset(the_carrier(X2)))
| X1 != X3
| ~ in(ordered_pair(X3,X4),esk197_2(X2,X5))
| ~ one_sorted_str(X2)
| ~ element(X5,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_712]) ).
cnf(i_0_1497,lemma,
( X4 = subset_complement(the_carrier(X2),X1)
| in(esk194_2(X2,X5),X5)
| ~ element(X1,powerset(the_carrier(X2)))
| X1 != X3
| ~ in(ordered_pair(X3,X4),esk197_2(X2,X5))
| ~ one_sorted_str(X2)
| ~ element(X5,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_712]) ).
cnf(i_0_1498,plain,
( in(ordered_pair(X4,X1),X3)
| in(esk208_2(X2,X3),esk210_2(X2,X3))
| empty(X2)
| ~ in(X1,esk213_3(X2,X3,X4))
| ~ in(X4,esk211_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_691]) ).
cnf(i_0_1499,plain,
( in(ordered_pair(X4,X1),X3)
| in(esk207_2(X2,X3),esk209_2(X2,X3))
| empty(X2)
| ~ in(X1,esk213_3(X2,X3,X4))
| ~ in(X4,esk211_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_691]) ).
cnf(i_0_1500,lemma,
( X2 = X3
| ~ antisymmetric(X1)
| ~ in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X3,X2),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_743]) ).
fof(i_0_1501,plain,
! [X2869,X2870,X2871,X2872] :
( empty(X2869)
| ~ function(X2871)
| ~ quasi_total(X2871,X2869,X2870)
| ~ relation_of2(X2871,X2869,X2870)
| ~ element(X2872,X2869)
| apply_as_element(X2869,X2870,X2871,X2872) = apply(X2871,X2872) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_744])]) ).
cnf(i_0_1502,plain,
( X2 = relation_rng(X1)
| ~ in(esk93_2(X1,X2),X2)
| ~ in(ordered_pair(X3,esk93_2(X1,X2)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_710]) ).
cnf(i_0_1503,plain,
( esk245_3(X1,X2,X3) = singleton(esk244_3(X1,X2,X3))
| ordered_pair(esk240_1(X1),esk241_1(X1)) = esk237_1(X1)
| ~ in(X3,esk242_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_715]) ).
cnf(i_0_1504,plain,
( esk245_3(X1,X2,X3) = singleton(esk244_3(X1,X2,X3))
| ordered_pair(esk238_1(X1),esk239_1(X1)) = esk236_1(X1)
| ~ in(X3,esk242_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_715]) ).
cnf(i_0_1505,plain,
( X3 = X4
| ~ function(X1)
| ~ in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X2,X4),X1) ),
inference(split_conjunct,[status(thm)],[i_0_745]) ).
cnf(i_0_1506,lemma,
( in(X1,complements_of_subsets(the_carrier(X2),X3))
| ~ in(ordered_pair(X1,X4),esk192_2(X2,X3))
| esk190_2(X2,X3) != esk191_2(X2,X3)
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_711]) ).
cnf(i_0_1507,plain,
( in(ordered_pair(X4,X1),X3)
| empty(X2)
| ~ in(X1,esk213_3(X2,X3,X4))
| ~ in(X4,esk211_2(X2,X3))
| esk207_2(X2,X3) != esk208_2(X2,X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_691]) ).
cnf(i_0_1508,plain,
( in(ordered_pair(X4,X1),X3)
| in(esk206_2(X2,X3),X2)
| empty(X2)
| ~ in(X1,esk213_3(X2,X3,X4))
| ~ in(X4,esk211_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_691]) ).
cnf(i_0_1509,plain,
( in(ordered_pair(X4,X1),X3)
| in(esk206_2(X2,X3),X2)
| empty(X2)
| ~ in(X1,esk213_3(X2,X3,X4))
| ~ in(X4,esk211_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_691]) ).
cnf(i_0_1510,plain,
( X3 = cartesian_product2(X1,X2)
| ~ in(esk65_3(X1,X2,X3),X3)
| ~ in(X4,X1)
| ~ in(X5,X2)
| esk65_3(X1,X2,X3) != ordered_pair(X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_702]) ).
cnf(i_0_1511,lemma,
( in(ordered_pair(X1,X3),relation_composition(identity_relation(X2),X4))
| ~ in(X1,X2)
| ~ in(ordered_pair(X1,X3),X4)
| ~ relation(X4) ),
inference(split_conjunct,[status(thm)],[i_0_746]) ).
cnf(i_0_1512,plain,
( in(ordered_pair(X4,X1),X3)
| esk206_2(X2,X3) = esk210_2(X2,X3)
| empty(X2)
| ~ in(X1,esk213_3(X2,X3,X4))
| ~ in(X4,esk211_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_691]) ).
cnf(i_0_1513,plain,
( in(ordered_pair(X4,X1),X3)
| esk206_2(X2,X3) = esk209_2(X2,X3)
| empty(X2)
| ~ in(X1,esk213_3(X2,X3,X4))
| ~ in(X4,esk211_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_691]) ).
cnf(i_0_1514,lemma,
( in(ordered_pair(X1,X2),X3)
| ~ in(ordered_pair(X1,X2),relation_composition(identity_relation(X4),X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_746]) ).
cnf(i_0_1515,plain,
( in(ordered_pair(X1,X3),X5)
| ~ in(X1,X2)
| ~ in(ordered_pair(X1,X3),X4)
| X5 != relation_dom_restriction(X4,X2)
| ~ relation(X5)
| ~ relation(X4) ),
inference(split_conjunct,[status(thm)],[i_0_700]) ).
cnf(i_0_1516,plain,
( in(ordered_pair(X3,X1),X5)
| ~ in(X1,X2)
| ~ in(ordered_pair(X3,X1),X4)
| X5 != relation_rng_restriction(X2,X4)
| ~ relation(X5)
| ~ relation(X4) ),
inference(split_conjunct,[status(thm)],[i_0_699]) ).
cnf(i_0_1517,lemma,
( in(X1,X2)
| ~ in(ordered_pair(X1,X3),esk205_3(X2,X4,X5))
| ~ relation(X4)
| ~ relation(X5)
| ~ function(X5) ),
inference(split_conjunct,[status(thm)],[i_0_713]) ).
cnf(i_0_1518,lemma,
( in(X1,X2)
| ~ in(ordered_pair(X3,X1),esk205_3(X2,X4,X5))
| ~ relation(X4)
| ~ relation(X5)
| ~ function(X5) ),
inference(split_conjunct,[status(thm)],[i_0_713]) ).
cnf(i_0_1519,lemma,
( in(X1,X2)
| ~ in(ordered_pair(X1,X3),esk197_2(X4,X2))
| esk195_2(X4,X2) != esk196_2(X4,X2)
| ~ one_sorted_str(X4)
| ~ element(X2,powerset(powerset(the_carrier(X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_712]) ).
fof(i_0_1520,plain,
! [X2054,X2055,X2056,X2057] :
( ( in(the_carrier(X2054),the_topology(X2054))
| ~ topological_space(X2054)
| ~ top_str(X2054) )
& ( ~ element(X2055,powerset(powerset(the_carrier(X2054))))
| ~ subset(X2055,the_topology(X2054))
| in(union_of_subsets(the_carrier(X2054),X2055),the_topology(X2054))
| ~ topological_space(X2054)
| ~ top_str(X2054) )
& ( ~ element(X2056,powerset(the_carrier(X2054)))
| ~ element(X2057,powerset(the_carrier(X2054)))
| ~ in(X2056,the_topology(X2054))
| ~ in(X2057,the_topology(X2054))
| in(subset_intersection2(the_carrier(X2054),X2056,X2057),the_topology(X2054))
| ~ topological_space(X2054)
| ~ top_str(X2054) )
& ( element(esk35_1(X2054),powerset(the_carrier(X2054)))
| element(esk34_1(X2054),powerset(powerset(the_carrier(X2054))))
| ~ in(the_carrier(X2054),the_topology(X2054))
| topological_space(X2054)
| ~ top_str(X2054) )
& ( element(esk36_1(X2054),powerset(the_carrier(X2054)))
| element(esk34_1(X2054),powerset(powerset(the_carrier(X2054))))
| ~ in(the_carrier(X2054),the_topology(X2054))
| topological_space(X2054)
| ~ top_str(X2054) )
& ( in(esk35_1(X2054),the_topology(X2054))
| element(esk34_1(X2054),powerset(powerset(the_carrier(X2054))))
| ~ in(the_carrier(X2054),the_topology(X2054))
| topological_space(X2054)
| ~ top_str(X2054) )
& ( in(esk36_1(X2054),the_topology(X2054))
| element(esk34_1(X2054),powerset(powerset(the_carrier(X2054))))
| ~ in(the_carrier(X2054),the_topology(X2054))
| topological_space(X2054)
| ~ top_str(X2054) )
& ( ~ in(subset_intersection2(the_carrier(X2054),esk35_1(X2054),esk36_1(X2054)),the_topology(X2054))
| element(esk34_1(X2054),powerset(powerset(the_carrier(X2054))))
| ~ in(the_carrier(X2054),the_topology(X2054))
| topological_space(X2054)
| ~ top_str(X2054) )
& ( element(esk35_1(X2054),powerset(the_carrier(X2054)))
| subset(esk34_1(X2054),the_topology(X2054))
| ~ in(the_carrier(X2054),the_topology(X2054))
| topological_space(X2054)
| ~ top_str(X2054) )
& ( element(esk36_1(X2054),powerset(the_carrier(X2054)))
| subset(esk34_1(X2054),the_topology(X2054))
| ~ in(the_carrier(X2054),the_topology(X2054))
| topological_space(X2054)
| ~ top_str(X2054) )
& ( in(esk35_1(X2054),the_topology(X2054))
| subset(esk34_1(X2054),the_topology(X2054))
| ~ in(the_carrier(X2054),the_topology(X2054))
| topological_space(X2054)
| ~ top_str(X2054) )
& ( in(esk36_1(X2054),the_topology(X2054))
| subset(esk34_1(X2054),the_topology(X2054))
| ~ in(the_carrier(X2054),the_topology(X2054))
| topological_space(X2054)
| ~ top_str(X2054) )
& ( ~ in(subset_intersection2(the_carrier(X2054),esk35_1(X2054),esk36_1(X2054)),the_topology(X2054))
| subset(esk34_1(X2054),the_topology(X2054))
| ~ in(the_carrier(X2054),the_topology(X2054))
| topological_space(X2054)
| ~ top_str(X2054) )
& ( element(esk35_1(X2054),powerset(the_carrier(X2054)))
| ~ in(union_of_subsets(the_carrier(X2054),esk34_1(X2054)),the_topology(X2054))
| ~ in(the_carrier(X2054),the_topology(X2054))
| topological_space(X2054)
| ~ top_str(X2054) )
& ( element(esk36_1(X2054),powerset(the_carrier(X2054)))
| ~ in(union_of_subsets(the_carrier(X2054),esk34_1(X2054)),the_topology(X2054))
| ~ in(the_carrier(X2054),the_topology(X2054))
| topological_space(X2054)
| ~ top_str(X2054) )
& ( in(esk35_1(X2054),the_topology(X2054))
| ~ in(union_of_subsets(the_carrier(X2054),esk34_1(X2054)),the_topology(X2054))
| ~ in(the_carrier(X2054),the_topology(X2054))
| topological_space(X2054)
| ~ top_str(X2054) )
& ( in(esk36_1(X2054),the_topology(X2054))
| ~ in(union_of_subsets(the_carrier(X2054),esk34_1(X2054)),the_topology(X2054))
| ~ in(the_carrier(X2054),the_topology(X2054))
| topological_space(X2054)
| ~ top_str(X2054) )
& ( ~ in(subset_intersection2(the_carrier(X2054),esk35_1(X2054),esk36_1(X2054)),the_topology(X2054))
| ~ in(union_of_subsets(the_carrier(X2054),esk34_1(X2054)),the_topology(X2054))
| ~ in(the_carrier(X2054),the_topology(X2054))
| topological_space(X2054)
| ~ top_str(X2054) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_pre_topc])])])])]) ).
cnf(i_0_1521,lemma,
( in(X1,X2)
| in(esk194_2(X4,X2),X2)
| ~ in(ordered_pair(X1,X3),esk197_2(X4,X2))
| ~ one_sorted_str(X4)
| ~ element(X2,powerset(powerset(the_carrier(X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_712]) ).
cnf(i_0_1522,lemma,
( in(X1,X2)
| in(esk194_2(X4,X2),X2)
| ~ in(ordered_pair(X1,X3),esk197_2(X4,X2))
| ~ one_sorted_str(X4)
| ~ element(X2,powerset(powerset(the_carrier(X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_712]) ).
cnf(i_0_1523,plain,
( empty_carrier(X1)
| empty_carrier(X2)
| k10_filter_1(X1,X2,X3,X4) = ordered_pair(X3,X4)
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ lattice(X2)
| ~ latt_str(X2)
| ~ element(X3,the_carrier(X1))
| ~ element(X4,the_carrier(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_747]) ).
fof(i_0_1524,lemma,
! [X3685,X3686,X3687,X3688,X3689] :
( ( latt_set_smaller(X3685,X3686,X3687)
| X3686 != meet_of_latt_set(X3685,X3687)
| ~ element(X3686,the_carrier(X3685))
| empty_carrier(X3685)
| ~ lattice(X3685)
| ~ complete_latt_str(X3685)
| ~ latt_str(X3685) )
& ( ~ element(X3688,the_carrier(X3685))
| ~ latt_set_smaller(X3685,X3688,X3687)
| below_refl(X3685,X3688,X3686)
| X3686 != meet_of_latt_set(X3685,X3687)
| ~ element(X3686,the_carrier(X3685))
| empty_carrier(X3685)
| ~ lattice(X3685)
| ~ complete_latt_str(X3685)
| ~ latt_str(X3685) )
& ( element(esk425_3(X3685,X3686,X3689),the_carrier(X3685))
| ~ latt_set_smaller(X3685,X3686,X3689)
| X3686 = meet_of_latt_set(X3685,X3689)
| ~ element(X3686,the_carrier(X3685))
| empty_carrier(X3685)
| ~ lattice(X3685)
| ~ complete_latt_str(X3685)
| ~ latt_str(X3685) )
& ( latt_set_smaller(X3685,esk425_3(X3685,X3686,X3689),X3689)
| ~ latt_set_smaller(X3685,X3686,X3689)
| X3686 = meet_of_latt_set(X3685,X3689)
| ~ element(X3686,the_carrier(X3685))
| empty_carrier(X3685)
| ~ lattice(X3685)
| ~ complete_latt_str(X3685)
| ~ latt_str(X3685) )
& ( ~ below_refl(X3685,esk425_3(X3685,X3686,X3689),X3686)
| ~ latt_set_smaller(X3685,X3686,X3689)
| X3686 = meet_of_latt_set(X3685,X3689)
| ~ element(X3686,the_carrier(X3685))
| empty_carrier(X3685)
| ~ lattice(X3685)
| ~ complete_latt_str(X3685)
| ~ latt_str(X3685) ) ),
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)],[i_0_748])])])])])]) ).
cnf(i_0_1525,plain,
( X2 = join_of_latt_set(X1,X3)
| empty_carrier(X1)
| empty_carrier(X1)
| ~ below(X1,X2,esk51_3(X1,X3,X2))
| ~ latt_element_smaller(X1,X2,X3)
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ complete_latt_str(X1)
| ~ latt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_749]) ).
fof(i_0_1526,plain,
! [X3078,X3079,X3084,X3086,X3087] :
( ( in(esk267_3(X3078,X3079,X3084),powerset(the_carrier(X3078)))
| ~ in(X3084,esk266_2(X3078,X3079))
| esk263_2(X3078,X3079) = esk264_2(X3078,X3079)
| ~ topological_space(X3078)
| ~ top_str(X3078)
| ~ element(X3079,powerset(powerset(the_carrier(X3078)))) )
& ( esk267_3(X3078,X3079,X3084) = X3084
| ~ in(X3084,esk266_2(X3078,X3079))
| esk263_2(X3078,X3079) = esk264_2(X3078,X3079)
| ~ topological_space(X3078)
| ~ top_str(X3078)
| ~ element(X3079,powerset(powerset(the_carrier(X3078)))) )
& ( in(set_difference(cast_as_carrier_subset(X3078),X3084),X3079)
| ~ in(X3084,esk266_2(X3078,X3079))
| esk263_2(X3078,X3079) = esk264_2(X3078,X3079)
| ~ topological_space(X3078)
| ~ top_str(X3078)
| ~ element(X3079,powerset(powerset(the_carrier(X3078)))) )
& ( ~ in(X3087,powerset(the_carrier(X3078)))
| X3087 != X3086
| ~ in(set_difference(cast_as_carrier_subset(X3078),X3086),X3079)
| in(X3086,esk266_2(X3078,X3079))
| esk263_2(X3078,X3079) = esk264_2(X3078,X3079)
| ~ topological_space(X3078)
| ~ top_str(X3078)
| ~ element(X3079,powerset(powerset(the_carrier(X3078)))) )
& ( in(esk267_3(X3078,X3079,X3084),powerset(the_carrier(X3078)))
| ~ in(X3084,esk266_2(X3078,X3079))
| in(set_difference(cast_as_carrier_subset(X3078),esk264_2(X3078,X3079)),X3079)
| ~ topological_space(X3078)
| ~ top_str(X3078)
| ~ element(X3079,powerset(powerset(the_carrier(X3078)))) )
& ( esk267_3(X3078,X3079,X3084) = X3084
| ~ in(X3084,esk266_2(X3078,X3079))
| in(set_difference(cast_as_carrier_subset(X3078),esk264_2(X3078,X3079)),X3079)
| ~ topological_space(X3078)
| ~ top_str(X3078)
| ~ element(X3079,powerset(powerset(the_carrier(X3078)))) )
& ( in(set_difference(cast_as_carrier_subset(X3078),X3084),X3079)
| ~ in(X3084,esk266_2(X3078,X3079))
| in(set_difference(cast_as_carrier_subset(X3078),esk264_2(X3078,X3079)),X3079)
| ~ topological_space(X3078)
| ~ top_str(X3078)
| ~ element(X3079,powerset(powerset(the_carrier(X3078)))) )
& ( ~ in(X3087,powerset(the_carrier(X3078)))
| X3087 != X3086
| ~ in(set_difference(cast_as_carrier_subset(X3078),X3086),X3079)
| in(X3086,esk266_2(X3078,X3079))
| in(set_difference(cast_as_carrier_subset(X3078),esk264_2(X3078,X3079)),X3079)
| ~ topological_space(X3078)
| ~ top_str(X3078)
| ~ element(X3079,powerset(powerset(the_carrier(X3078)))) )
& ( in(esk267_3(X3078,X3079,X3084),powerset(the_carrier(X3078)))
| ~ in(X3084,esk266_2(X3078,X3079))
| esk263_2(X3078,X3079) = esk265_2(X3078,X3079)
| ~ topological_space(X3078)
| ~ top_str(X3078)
| ~ element(X3079,powerset(powerset(the_carrier(X3078)))) )
& ( esk267_3(X3078,X3079,X3084) = X3084
| ~ in(X3084,esk266_2(X3078,X3079))
| esk263_2(X3078,X3079) = esk265_2(X3078,X3079)
| ~ topological_space(X3078)
| ~ top_str(X3078)
| ~ element(X3079,powerset(powerset(the_carrier(X3078)))) )
& ( in(set_difference(cast_as_carrier_subset(X3078),X3084),X3079)
| ~ in(X3084,esk266_2(X3078,X3079))
| esk263_2(X3078,X3079) = esk265_2(X3078,X3079)
| ~ topological_space(X3078)
| ~ top_str(X3078)
| ~ element(X3079,powerset(powerset(the_carrier(X3078)))) )
& ( ~ in(X3087,powerset(the_carrier(X3078)))
| X3087 != X3086
| ~ in(set_difference(cast_as_carrier_subset(X3078),X3086),X3079)
| in(X3086,esk266_2(X3078,X3079))
| esk263_2(X3078,X3079) = esk265_2(X3078,X3079)
| ~ topological_space(X3078)
| ~ top_str(X3078)
| ~ element(X3079,powerset(powerset(the_carrier(X3078)))) )
& ( in(esk267_3(X3078,X3079,X3084),powerset(the_carrier(X3078)))
| ~ in(X3084,esk266_2(X3078,X3079))
| in(set_difference(cast_as_carrier_subset(X3078),esk265_2(X3078,X3079)),X3079)
| ~ topological_space(X3078)
| ~ top_str(X3078)
| ~ element(X3079,powerset(powerset(the_carrier(X3078)))) )
& ( esk267_3(X3078,X3079,X3084) = X3084
| ~ in(X3084,esk266_2(X3078,X3079))
| in(set_difference(cast_as_carrier_subset(X3078),esk265_2(X3078,X3079)),X3079)
| ~ topological_space(X3078)
| ~ top_str(X3078)
| ~ element(X3079,powerset(powerset(the_carrier(X3078)))) )
& ( in(set_difference(cast_as_carrier_subset(X3078),X3084),X3079)
| ~ in(X3084,esk266_2(X3078,X3079))
| in(set_difference(cast_as_carrier_subset(X3078),esk265_2(X3078,X3079)),X3079)
| ~ topological_space(X3078)
| ~ top_str(X3078)
| ~ element(X3079,powerset(powerset(the_carrier(X3078)))) )
& ( ~ in(X3087,powerset(the_carrier(X3078)))
| X3087 != X3086
| ~ in(set_difference(cast_as_carrier_subset(X3078),X3086),X3079)
| in(X3086,esk266_2(X3078,X3079))
| in(set_difference(cast_as_carrier_subset(X3078),esk265_2(X3078,X3079)),X3079)
| ~ topological_space(X3078)
| ~ top_str(X3078)
| ~ element(X3079,powerset(powerset(the_carrier(X3078)))) )
& ( in(esk267_3(X3078,X3079,X3084),powerset(the_carrier(X3078)))
| ~ in(X3084,esk266_2(X3078,X3079))
| esk264_2(X3078,X3079) != esk265_2(X3078,X3079)
| ~ topological_space(X3078)
| ~ top_str(X3078)
| ~ element(X3079,powerset(powerset(the_carrier(X3078)))) )
& ( esk267_3(X3078,X3079,X3084) = X3084
| ~ in(X3084,esk266_2(X3078,X3079))
| esk264_2(X3078,X3079) != esk265_2(X3078,X3079)
| ~ topological_space(X3078)
| ~ top_str(X3078)
| ~ element(X3079,powerset(powerset(the_carrier(X3078)))) )
& ( in(set_difference(cast_as_carrier_subset(X3078),X3084),X3079)
| ~ in(X3084,esk266_2(X3078,X3079))
| esk264_2(X3078,X3079) != esk265_2(X3078,X3079)
| ~ topological_space(X3078)
| ~ top_str(X3078)
| ~ element(X3079,powerset(powerset(the_carrier(X3078)))) )
& ( ~ in(X3087,powerset(the_carrier(X3078)))
| X3087 != X3086
| ~ in(set_difference(cast_as_carrier_subset(X3078),X3086),X3079)
| in(X3086,esk266_2(X3078,X3079))
| esk264_2(X3078,X3079) != esk265_2(X3078,X3079)
| ~ topological_space(X3078)
| ~ top_str(X3078)
| ~ element(X3079,powerset(powerset(the_carrier(X3078)))) ) ),
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)],[s1_tarski__e2_37_1_1__pre_topc__1])])])])])]) ).
cnf(i_0_1527,plain,
( in(ordered_pair(X1,X2),X3)
| ~ in(ordered_pair(X1,X2),X4)
| X4 != relation_rng_restriction(X5,X3)
| ~ relation(X4)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_699]) ).
cnf(i_0_1528,plain,
( in(ordered_pair(X1,X2),X3)
| ~ in(ordered_pair(X1,X2),X4)
| X4 != relation_dom_restriction(X3,X5)
| ~ relation(X4)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_700]) ).
cnf(i_0_1529,plain,
( in(ordered_pair(X3,X4),X2)
| ~ subset(X1,X2)
| ~ in(ordered_pair(X3,X4),X1)
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_724]) ).
cnf(i_0_1530,plain,
( element(esk253_3(X1,X2,X3),powerset(powerset(X3)))
| in(X2,esk249_1(X1))
| epred2_3(esk248_1(X1),esk247_1(X1),esk246_1(X1))
| ~ ordinal(X3)
| X2 != X3
| ~ in(X4,succ(X1))
| X4 != X2
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_717]) ).
fof(i_0_1531,plain,
! [X2188,X2189,X2190,X2191,X2192,X2193,X2194,X2195] :
( ( ~ in(X2191,X2190)
| in(X2191,X2188)
| in(X2191,X2189)
| X2190 != set_union2(X2188,X2189) )
& ( ~ in(X2192,X2188)
| in(X2192,X2190)
| X2190 != set_union2(X2188,X2189) )
& ( ~ in(X2192,X2189)
| in(X2192,X2190)
| X2190 != set_union2(X2188,X2189) )
& ( ~ in(esk62_3(X2193,X2194,X2195),X2193)
| ~ in(esk62_3(X2193,X2194,X2195),X2195)
| X2195 = set_union2(X2193,X2194) )
& ( ~ in(esk62_3(X2193,X2194,X2195),X2194)
| ~ in(esk62_3(X2193,X2194,X2195),X2195)
| X2195 = set_union2(X2193,X2194) )
& ( in(esk62_3(X2193,X2194,X2195),X2195)
| in(esk62_3(X2193,X2194,X2195),X2193)
| in(esk62_3(X2193,X2194,X2195),X2194)
| X2195 = set_union2(X2193,X2194) ) ),
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)],[d2_xboole_0])])])])])]) ).
cnf(i_0_1532,plain,
( in(ordered_pair(X2,X1),X4)
| ~ in(ordered_pair(X1,X2),X3)
| X3 != relation_inverse(X4)
| ~ relation(X3)
| ~ relation(X4) ),
inference(split_conjunct,[status(thm)],[i_0_707]) ).
cnf(i_0_1533,plain,
( in(ordered_pair(X2,X1),X4)
| ~ in(ordered_pair(X1,X2),X3)
| X4 != relation_inverse(X3)
| ~ relation(X4)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_707]) ).
cnf(i_0_1534,lemma,
( connected(X1)
| ~ in(ordered_pair(esk137_1(X1),esk136_1(X1)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_750]) ).
cnf(i_0_1535,lemma,
( connected(X1)
| ~ in(ordered_pair(esk136_1(X1),esk137_1(X1)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_750]) ).
cnf(i_0_1536,lemma,
( reflexive(X1)
| ~ in(ordered_pair(esk129_1(X1),esk129_1(X1)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_751]) ).
cnf(i_0_1537,lemma,
( transitive(X1)
| ~ in(ordered_pair(esk130_1(X1),esk132_1(X1)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_737]) ).
fof(i_0_1538,lemma,
! [X2956,X2957,X2959,X2961,X2963,X2964,X2966] :
( ( in(esk204_2(X2963,X2964),X2964)
| X2964 = empty_set
| ~ element(X2964,powerset(powerset(X2963)))
| ~ in(X2963,omega)
| ~ ordinal(X2963)
| ordinal(esk200_0)
| ~ epred1_0 )
& ( ~ in(X2966,X2964)
| ~ subset(esk204_2(X2963,X2964),X2966)
| X2966 = esk204_2(X2963,X2964)
| X2964 = empty_set
| ~ element(X2964,powerset(powerset(X2963)))
| ~ in(X2963,omega)
| ~ ordinal(X2963)
| ordinal(esk200_0)
| ~ epred1_0 )
& ( in(esk204_2(X2963,X2964),X2964)
| X2964 = empty_set
| ~ element(X2964,powerset(powerset(X2963)))
| ~ in(X2963,omega)
| ~ ordinal(X2963)
| being_limit_ordinal(esk200_0)
| ~ epred1_0 )
& ( ~ in(X2966,X2964)
| ~ subset(esk204_2(X2963,X2964),X2966)
| X2966 = esk204_2(X2963,X2964)
| X2964 = empty_set
| ~ element(X2964,powerset(powerset(X2963)))
| ~ in(X2963,omega)
| ~ ordinal(X2963)
| being_limit_ordinal(esk200_0)
| ~ epred1_0 )
& ( in(esk204_2(X2963,X2964),X2964)
| X2964 = empty_set
| ~ element(X2964,powerset(powerset(X2963)))
| ~ in(X2963,omega)
| ~ ordinal(X2963)
| in(esk201_2(X2956,X2957),X2957)
| X2957 = empty_set
| ~ element(X2957,powerset(powerset(X2956)))
| ~ in(X2956,omega)
| ~ in(X2956,esk200_0)
| ~ ordinal(X2956)
| ~ epred1_0 )
& ( ~ in(X2966,X2964)
| ~ subset(esk204_2(X2963,X2964),X2966)
| X2966 = esk204_2(X2963,X2964)
| X2964 = empty_set
| ~ element(X2964,powerset(powerset(X2963)))
| ~ in(X2963,omega)
| ~ ordinal(X2963)
| in(esk201_2(X2956,X2957),X2957)
| X2957 = empty_set
| ~ element(X2957,powerset(powerset(X2956)))
| ~ in(X2956,omega)
| ~ in(X2956,esk200_0)
| ~ ordinal(X2956)
| ~ epred1_0 )
& ( in(esk204_2(X2963,X2964),X2964)
| X2964 = empty_set
| ~ element(X2964,powerset(powerset(X2963)))
| ~ in(X2963,omega)
| ~ ordinal(X2963)
| ~ in(X2959,X2957)
| ~ subset(esk201_2(X2956,X2957),X2959)
| X2959 = esk201_2(X2956,X2957)
| X2957 = empty_set
| ~ element(X2957,powerset(powerset(X2956)))
| ~ in(X2956,omega)
| ~ in(X2956,esk200_0)
| ~ ordinal(X2956)
| ~ epred1_0 )
& ( ~ in(X2966,X2964)
| ~ subset(esk204_2(X2963,X2964),X2966)
| X2966 = esk204_2(X2963,X2964)
| X2964 = empty_set
| ~ element(X2964,powerset(powerset(X2963)))
| ~ in(X2963,omega)
| ~ ordinal(X2963)
| ~ in(X2959,X2957)
| ~ subset(esk201_2(X2956,X2957),X2959)
| X2959 = esk201_2(X2956,X2957)
| X2957 = empty_set
| ~ element(X2957,powerset(powerset(X2956)))
| ~ in(X2956,omega)
| ~ in(X2956,esk200_0)
| ~ ordinal(X2956)
| ~ epred1_0 )
& ( in(esk204_2(X2963,X2964),X2964)
| X2964 = empty_set
| ~ element(X2964,powerset(powerset(X2963)))
| ~ in(X2963,omega)
| ~ ordinal(X2963)
| esk200_0 != empty_set
| ~ epred1_0 )
& ( ~ in(X2966,X2964)
| ~ subset(esk204_2(X2963,X2964),X2966)
| X2966 = esk204_2(X2963,X2964)
| X2964 = empty_set
| ~ element(X2964,powerset(powerset(X2963)))
| ~ in(X2963,omega)
| ~ ordinal(X2963)
| esk200_0 != empty_set
| ~ epred1_0 )
& ( in(esk204_2(X2963,X2964),X2964)
| X2964 = empty_set
| ~ element(X2964,powerset(powerset(X2963)))
| ~ in(X2963,omega)
| ~ ordinal(X2963)
| in(esk200_0,omega)
| ~ epred1_0 )
& ( ~ in(X2966,X2964)
| ~ subset(esk204_2(X2963,X2964),X2966)
| X2966 = esk204_2(X2963,X2964)
| X2964 = empty_set
| ~ element(X2964,powerset(powerset(X2963)))
| ~ in(X2963,omega)
| ~ ordinal(X2963)
| in(esk200_0,omega)
| ~ epred1_0 )
& ( in(esk204_2(X2963,X2964),X2964)
| X2964 = empty_set
| ~ element(X2964,powerset(powerset(X2963)))
| ~ in(X2963,omega)
| ~ ordinal(X2963)
| element(esk202_0,powerset(powerset(esk200_0)))
| ~ epred1_0 )
& ( ~ in(X2966,X2964)
| ~ subset(esk204_2(X2963,X2964),X2966)
| X2966 = esk204_2(X2963,X2964)
| X2964 = empty_set
| ~ element(X2964,powerset(powerset(X2963)))
| ~ in(X2963,omega)
| ~ ordinal(X2963)
| element(esk202_0,powerset(powerset(esk200_0)))
| ~ epred1_0 )
& ( in(esk204_2(X2963,X2964),X2964)
| X2964 = empty_set
| ~ element(X2964,powerset(powerset(X2963)))
| ~ in(X2963,omega)
| ~ ordinal(X2963)
| esk202_0 != empty_set
| ~ epred1_0 )
& ( ~ in(X2966,X2964)
| ~ subset(esk204_2(X2963,X2964),X2966)
| X2966 = esk204_2(X2963,X2964)
| X2964 = empty_set
| ~ element(X2964,powerset(powerset(X2963)))
| ~ in(X2963,omega)
| ~ ordinal(X2963)
| esk202_0 != empty_set
| ~ epred1_0 )
& ( in(esk204_2(X2963,X2964),X2964)
| X2964 = empty_set
| ~ element(X2964,powerset(powerset(X2963)))
| ~ in(X2963,omega)
| ~ ordinal(X2963)
| in(esk203_1(X2961),esk202_0)
| ~ in(X2961,esk202_0)
| ~ epred1_0 )
& ( ~ in(X2966,X2964)
| ~ subset(esk204_2(X2963,X2964),X2966)
| X2966 = esk204_2(X2963,X2964)
| X2964 = empty_set
| ~ element(X2964,powerset(powerset(X2963)))
| ~ in(X2963,omega)
| ~ ordinal(X2963)
| in(esk203_1(X2961),esk202_0)
| ~ in(X2961,esk202_0)
| ~ epred1_0 )
& ( in(esk204_2(X2963,X2964),X2964)
| X2964 = empty_set
| ~ element(X2964,powerset(powerset(X2963)))
| ~ in(X2963,omega)
| ~ ordinal(X2963)
| subset(X2961,esk203_1(X2961))
| ~ in(X2961,esk202_0)
| ~ epred1_0 )
& ( ~ in(X2966,X2964)
| ~ subset(esk204_2(X2963,X2964),X2966)
| X2966 = esk204_2(X2963,X2964)
| X2964 = empty_set
| ~ element(X2964,powerset(powerset(X2963)))
| ~ in(X2963,omega)
| ~ ordinal(X2963)
| subset(X2961,esk203_1(X2961))
| ~ in(X2961,esk202_0)
| ~ epred1_0 )
& ( in(esk204_2(X2963,X2964),X2964)
| X2964 = empty_set
| ~ element(X2964,powerset(powerset(X2963)))
| ~ in(X2963,omega)
| ~ ordinal(X2963)
| esk203_1(X2961) != X2961
| ~ in(X2961,esk202_0)
| ~ epred1_0 )
& ( ~ in(X2966,X2964)
| ~ subset(esk204_2(X2963,X2964),X2966)
| X2966 = esk204_2(X2963,X2964)
| X2964 = empty_set
| ~ element(X2964,powerset(powerset(X2963)))
| ~ in(X2963,omega)
| ~ ordinal(X2963)
| esk203_1(X2961) != X2961
| ~ in(X2961,esk202_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)],[i_0_752])])])])]) ).
cnf(i_0_1539,plain,
( X1 = ordered_pair(esk53_2(X1,X2),esk54_2(X1,X2))
| X2 = pair_second(X1)
| X1 != ordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_753]) ).
cnf(i_0_1540,plain,
( X1 = ordered_pair(esk32_2(X1,X2),esk33_2(X1,X2))
| X2 = pair_first(X1)
| X1 != ordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_754]) ).
fof(i_0_1541,lemma,
! [X3386,X3387,X3389,X3391,X3393,X3394,X3396] :
( ( in(esk404_2(X3393,X3394),X3394)
| X3394 = empty_set
| ~ element(X3394,powerset(powerset(X3393)))
| ~ in(X3393,omega)
| ~ ordinal(X3393)
| ordinal(esk400_0) )
& ( ~ in(X3396,X3394)
| ~ subset(esk404_2(X3393,X3394),X3396)
| X3396 = esk404_2(X3393,X3394)
| X3394 = empty_set
| ~ element(X3394,powerset(powerset(X3393)))
| ~ in(X3393,omega)
| ~ ordinal(X3393)
| ordinal(esk400_0) )
& ( in(esk404_2(X3393,X3394),X3394)
| X3394 = empty_set
| ~ element(X3394,powerset(powerset(X3393)))
| ~ in(X3393,omega)
| ~ ordinal(X3393)
| in(esk401_2(X3386,X3387),X3387)
| X3387 = empty_set
| ~ element(X3387,powerset(powerset(X3386)))
| ~ in(X3386,omega)
| ~ in(X3386,esk400_0)
| ~ ordinal(X3386) )
& ( ~ in(X3396,X3394)
| ~ subset(esk404_2(X3393,X3394),X3396)
| X3396 = esk404_2(X3393,X3394)
| X3394 = empty_set
| ~ element(X3394,powerset(powerset(X3393)))
| ~ in(X3393,omega)
| ~ ordinal(X3393)
| in(esk401_2(X3386,X3387),X3387)
| X3387 = empty_set
| ~ element(X3387,powerset(powerset(X3386)))
| ~ in(X3386,omega)
| ~ in(X3386,esk400_0)
| ~ ordinal(X3386) )
& ( in(esk404_2(X3393,X3394),X3394)
| X3394 = empty_set
| ~ element(X3394,powerset(powerset(X3393)))
| ~ in(X3393,omega)
| ~ ordinal(X3393)
| ~ in(X3389,X3387)
| ~ subset(esk401_2(X3386,X3387),X3389)
| X3389 = esk401_2(X3386,X3387)
| X3387 = empty_set
| ~ element(X3387,powerset(powerset(X3386)))
| ~ in(X3386,omega)
| ~ in(X3386,esk400_0)
| ~ ordinal(X3386) )
& ( ~ in(X3396,X3394)
| ~ subset(esk404_2(X3393,X3394),X3396)
| X3396 = esk404_2(X3393,X3394)
| X3394 = empty_set
| ~ element(X3394,powerset(powerset(X3393)))
| ~ in(X3393,omega)
| ~ ordinal(X3393)
| ~ in(X3389,X3387)
| ~ subset(esk401_2(X3386,X3387),X3389)
| X3389 = esk401_2(X3386,X3387)
| X3387 = empty_set
| ~ element(X3387,powerset(powerset(X3386)))
| ~ in(X3386,omega)
| ~ in(X3386,esk400_0)
| ~ ordinal(X3386) )
& ( in(esk404_2(X3393,X3394),X3394)
| X3394 = empty_set
| ~ element(X3394,powerset(powerset(X3393)))
| ~ in(X3393,omega)
| ~ ordinal(X3393)
| in(esk400_0,omega) )
& ( ~ in(X3396,X3394)
| ~ subset(esk404_2(X3393,X3394),X3396)
| X3396 = esk404_2(X3393,X3394)
| X3394 = empty_set
| ~ element(X3394,powerset(powerset(X3393)))
| ~ in(X3393,omega)
| ~ ordinal(X3393)
| in(esk400_0,omega) )
& ( in(esk404_2(X3393,X3394),X3394)
| X3394 = empty_set
| ~ element(X3394,powerset(powerset(X3393)))
| ~ in(X3393,omega)
| ~ ordinal(X3393)
| element(esk402_0,powerset(powerset(esk400_0))) )
& ( ~ in(X3396,X3394)
| ~ subset(esk404_2(X3393,X3394),X3396)
| X3396 = esk404_2(X3393,X3394)
| X3394 = empty_set
| ~ element(X3394,powerset(powerset(X3393)))
| ~ in(X3393,omega)
| ~ ordinal(X3393)
| element(esk402_0,powerset(powerset(esk400_0))) )
& ( in(esk404_2(X3393,X3394),X3394)
| X3394 = empty_set
| ~ element(X3394,powerset(powerset(X3393)))
| ~ in(X3393,omega)
| ~ ordinal(X3393)
| esk402_0 != empty_set )
& ( ~ in(X3396,X3394)
| ~ subset(esk404_2(X3393,X3394),X3396)
| X3396 = esk404_2(X3393,X3394)
| X3394 = empty_set
| ~ element(X3394,powerset(powerset(X3393)))
| ~ in(X3393,omega)
| ~ ordinal(X3393)
| esk402_0 != empty_set )
& ( in(esk404_2(X3393,X3394),X3394)
| X3394 = empty_set
| ~ element(X3394,powerset(powerset(X3393)))
| ~ in(X3393,omega)
| ~ ordinal(X3393)
| in(esk403_1(X3391),esk402_0)
| ~ in(X3391,esk402_0) )
& ( ~ in(X3396,X3394)
| ~ subset(esk404_2(X3393,X3394),X3396)
| X3396 = esk404_2(X3393,X3394)
| X3394 = empty_set
| ~ element(X3394,powerset(powerset(X3393)))
| ~ in(X3393,omega)
| ~ ordinal(X3393)
| in(esk403_1(X3391),esk402_0)
| ~ in(X3391,esk402_0) )
& ( in(esk404_2(X3393,X3394),X3394)
| X3394 = empty_set
| ~ element(X3394,powerset(powerset(X3393)))
| ~ in(X3393,omega)
| ~ ordinal(X3393)
| subset(X3391,esk403_1(X3391))
| ~ in(X3391,esk402_0) )
& ( ~ in(X3396,X3394)
| ~ subset(esk404_2(X3393,X3394),X3396)
| X3396 = esk404_2(X3393,X3394)
| X3394 = empty_set
| ~ element(X3394,powerset(powerset(X3393)))
| ~ in(X3393,omega)
| ~ ordinal(X3393)
| subset(X3391,esk403_1(X3391))
| ~ in(X3391,esk402_0) )
& ( in(esk404_2(X3393,X3394),X3394)
| X3394 = empty_set
| ~ element(X3394,powerset(powerset(X3393)))
| ~ in(X3393,omega)
| ~ ordinal(X3393)
| esk403_1(X3391) != X3391
| ~ in(X3391,esk402_0) )
& ( ~ in(X3396,X3394)
| ~ subset(esk404_2(X3393,X3394),X3396)
| X3396 = esk404_2(X3393,X3394)
| X3394 = empty_set
| ~ element(X3394,powerset(powerset(X3393)))
| ~ in(X3393,omega)
| ~ ordinal(X3393)
| esk403_1(X3391) != X3391
| ~ in(X3391,esk402_0) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[s2_ordinal1__e18_27__finset_1__1])])])])]) ).
cnf(i_0_1542,plain,
( in(X4,esk242_2(X2,X3))
| ordered_pair(esk240_1(X2),esk241_1(X2)) = esk237_1(X2)
| ~ in(X1,cartesian_product2(X2,X3))
| X1 != X4
| ordered_pair(X5,X6) != X4
| ~ in(X5,X2)
| X6 != singleton(X5) ),
inference(split_conjunct,[status(thm)],[i_0_715]) ).
cnf(i_0_1543,plain,
( in(X4,esk242_2(X2,X3))
| ordered_pair(esk238_1(X2),esk239_1(X2)) = esk236_1(X2)
| ~ in(X1,cartesian_product2(X2,X3))
| X1 != X4
| ordered_pair(X5,X6) != X4
| ~ in(X5,X2)
| X6 != singleton(X5) ),
inference(split_conjunct,[status(thm)],[i_0_715]) ).
cnf(i_0_1544,plain,
( esk245_3(X1,X2,X3) = singleton(esk244_3(X1,X2,X3))
| esk241_1(X1) = singleton(esk240_1(X1))
| ~ in(X3,esk242_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_715]) ).
cnf(i_0_1545,plain,
( esk245_3(X1,X2,X3) = singleton(esk244_3(X1,X2,X3))
| esk239_1(X1) = singleton(esk238_1(X1))
| ~ in(X3,esk242_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_715]) ).
fof(i_0_1546,lemma,
! [X3801,X3802,X3803,X3804,X3805,X3806] :
( ( relation_dom(X3802) = relation_rng(X3801)
| X3802 != function_inverse(X3801)
| ~ relation(X3802)
| ~ function(X3802)
| ~ one_to_one(X3801)
| ~ relation(X3801)
| ~ function(X3801) )
& ( in(X3804,relation_dom(X3801))
| ~ in(X3803,relation_rng(X3801))
| X3804 != apply(X3802,X3803)
| X3802 != function_inverse(X3801)
| ~ relation(X3802)
| ~ function(X3802)
| ~ one_to_one(X3801)
| ~ relation(X3801)
| ~ function(X3801) )
& ( X3803 = apply(X3801,X3804)
| ~ in(X3803,relation_rng(X3801))
| X3804 != apply(X3802,X3803)
| X3802 != function_inverse(X3801)
| ~ relation(X3802)
| ~ function(X3802)
| ~ one_to_one(X3801)
| ~ relation(X3801)
| ~ function(X3801) )
& ( in(X3805,relation_rng(X3801))
| ~ in(X3806,relation_dom(X3801))
| X3805 != apply(X3801,X3806)
| X3802 != function_inverse(X3801)
| ~ relation(X3802)
| ~ function(X3802)
| ~ one_to_one(X3801)
| ~ relation(X3801)
| ~ function(X3801) )
& ( X3806 = apply(X3802,X3805)
| ~ in(X3806,relation_dom(X3801))
| X3805 != apply(X3801,X3806)
| X3802 != function_inverse(X3801)
| ~ relation(X3802)
| ~ function(X3802)
| ~ one_to_one(X3801)
| ~ relation(X3801)
| ~ function(X3801) )
& ( in(esk436_2(X3801,X3802),relation_dom(X3801))
| in(esk433_2(X3801,X3802),relation_rng(X3801))
| relation_dom(X3802) != relation_rng(X3801)
| X3802 = function_inverse(X3801)
| ~ relation(X3802)
| ~ function(X3802)
| ~ one_to_one(X3801)
| ~ relation(X3801)
| ~ function(X3801) )
& ( esk435_2(X3801,X3802) = apply(X3801,esk436_2(X3801,X3802))
| in(esk433_2(X3801,X3802),relation_rng(X3801))
| relation_dom(X3802) != relation_rng(X3801)
| X3802 = function_inverse(X3801)
| ~ relation(X3802)
| ~ function(X3802)
| ~ one_to_one(X3801)
| ~ relation(X3801)
| ~ function(X3801) )
& ( ~ in(esk435_2(X3801,X3802),relation_rng(X3801))
| esk436_2(X3801,X3802) != apply(X3802,esk435_2(X3801,X3802))
| in(esk433_2(X3801,X3802),relation_rng(X3801))
| relation_dom(X3802) != relation_rng(X3801)
| X3802 = function_inverse(X3801)
| ~ relation(X3802)
| ~ function(X3802)
| ~ one_to_one(X3801)
| ~ relation(X3801)
| ~ function(X3801) )
& ( in(esk436_2(X3801,X3802),relation_dom(X3801))
| esk434_2(X3801,X3802) = apply(X3802,esk433_2(X3801,X3802))
| relation_dom(X3802) != relation_rng(X3801)
| X3802 = function_inverse(X3801)
| ~ relation(X3802)
| ~ function(X3802)
| ~ one_to_one(X3801)
| ~ relation(X3801)
| ~ function(X3801) )
& ( esk435_2(X3801,X3802) = apply(X3801,esk436_2(X3801,X3802))
| esk434_2(X3801,X3802) = apply(X3802,esk433_2(X3801,X3802))
| relation_dom(X3802) != relation_rng(X3801)
| X3802 = function_inverse(X3801)
| ~ relation(X3802)
| ~ function(X3802)
| ~ one_to_one(X3801)
| ~ relation(X3801)
| ~ function(X3801) )
& ( ~ in(esk435_2(X3801,X3802),relation_rng(X3801))
| esk436_2(X3801,X3802) != apply(X3802,esk435_2(X3801,X3802))
| esk434_2(X3801,X3802) = apply(X3802,esk433_2(X3801,X3802))
| relation_dom(X3802) != relation_rng(X3801)
| X3802 = function_inverse(X3801)
| ~ relation(X3802)
| ~ function(X3802)
| ~ one_to_one(X3801)
| ~ relation(X3801)
| ~ function(X3801) )
& ( in(esk436_2(X3801,X3802),relation_dom(X3801))
| ~ in(esk434_2(X3801,X3802),relation_dom(X3801))
| esk433_2(X3801,X3802) != apply(X3801,esk434_2(X3801,X3802))
| relation_dom(X3802) != relation_rng(X3801)
| X3802 = function_inverse(X3801)
| ~ relation(X3802)
| ~ function(X3802)
| ~ one_to_one(X3801)
| ~ relation(X3801)
| ~ function(X3801) )
& ( esk435_2(X3801,X3802) = apply(X3801,esk436_2(X3801,X3802))
| ~ in(esk434_2(X3801,X3802),relation_dom(X3801))
| esk433_2(X3801,X3802) != apply(X3801,esk434_2(X3801,X3802))
| relation_dom(X3802) != relation_rng(X3801)
| X3802 = function_inverse(X3801)
| ~ relation(X3802)
| ~ function(X3802)
| ~ one_to_one(X3801)
| ~ relation(X3801)
| ~ function(X3801) )
& ( ~ in(esk435_2(X3801,X3802),relation_rng(X3801))
| esk436_2(X3801,X3802) != apply(X3802,esk435_2(X3801,X3802))
| ~ in(esk434_2(X3801,X3802),relation_dom(X3801))
| esk433_2(X3801,X3802) != apply(X3801,esk434_2(X3801,X3802))
| relation_dom(X3802) != relation_rng(X3801)
| X3802 = function_inverse(X3801)
| ~ relation(X3802)
| ~ function(X3802)
| ~ one_to_one(X3801)
| ~ relation(X3801)
| ~ function(X3801) ) ),
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)],[t54_funct_1])])])])])]) ).
cnf(i_0_1547,lemma,
( X2 = X3
| in(ordered_pair(X2,X3),X1)
| in(ordered_pair(X3,X2),X1)
| ~ connected(X1)
| ~ in(X2,relation_field(X1))
| ~ in(X3,relation_field(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_750]) ).
cnf(i_0_1548,plain,
( empty(X1)
| empty(X2)
| ordered_pair_as_product_element(X1,X2,X3,X4) = ordered_pair(X3,X4)
| ~ element(X3,X1)
| ~ element(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_755]) ).
cnf(i_0_1549,plain,
( esk245_3(X1,X2,X3) = singleton(esk244_3(X1,X2,X3))
| in(esk240_1(X1),X1)
| ~ in(X3,esk242_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_715]) ).
cnf(i_0_1550,plain,
( esk245_3(X1,X2,X3) = singleton(esk244_3(X1,X2,X3))
| in(esk238_1(X1),X1)
| ~ in(X3,esk242_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_715]) ).
cnf(i_0_1551,plain,
( X3 = X4
| in(ordered_pair(X3,X4),X1)
| in(ordered_pair(X4,X3),X1)
| ~ is_connected_in(X1,X2)
| ~ in(X3,X2)
| ~ in(X4,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_727]) ).
cnf(i_0_1552,plain,
( related(X3,X1,X2)
| ~ in(ordered_pair(X1,X2),the_InternalRel(X3))
| ~ element(X2,the_carrier(X3))
| ~ element(X1,the_carrier(X3))
| ~ rel_str(X3) ),
inference(split_conjunct,[status(thm)],[i_0_756]) ).
cnf(i_0_1553,plain,
( in(X1,relation_field(X2))
| ~ in(ordered_pair(X1,X3),X2)
| ~ relation_isomorphism(X2,X4,X5)
| ~ relation(X5)
| ~ function(X5)
| ~ relation(X4)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_693]) ).
cnf(i_0_1554,plain,
( in(X1,relation_field(X2))
| ~ in(ordered_pair(X3,X1),X2)
| ~ relation_isomorphism(X2,X4,X5)
| ~ relation(X5)
| ~ function(X5)
| ~ relation(X4)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_693]) ).
cnf(i_0_1555,lemma,
( in(X1,X2)
| in(esk179_2(X2,X4),esk181_2(X2,X4))
| empty(X2)
| ~ in(ordered_pair(X1,X3),esk182_2(X2,X4))
| ~ relation(X4) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1556,lemma,
( in(X1,X2)
| in(esk178_2(X2,X4),esk180_2(X2,X4))
| empty(X2)
| ~ in(ordered_pair(X1,X3),esk182_2(X2,X4))
| ~ relation(X4) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1557,plain,
( esk245_3(X1,X2,X3) = singleton(esk244_3(X1,X2,X3))
| ~ in(X3,esk242_2(X1,X2))
| esk236_1(X1) != esk237_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_715]) ).
cnf(i_0_1558,plain,
( esk245_3(X1,X2,X3) = singleton(esk244_3(X1,X2,X3))
| esk235_1(X1) = esk237_1(X1)
| ~ in(X3,esk242_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_715]) ).
cnf(i_0_1559,plain,
( esk245_3(X1,X2,X3) = singleton(esk244_3(X1,X2,X3))
| esk235_1(X1) = esk236_1(X1)
| ~ in(X3,esk242_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_715]) ).
fof(i_0_1560,plain,
! [X1997,X1998,X1999,X2000,X2001] :
( ( ~ latt_element_smaller(X1997,X1998,X1999)
| ~ element(X2000,the_carrier(X1997))
| ~ in(X2000,X1999)
| below(X1997,X2000,X1998)
| ~ element(X1998,the_carrier(X1997))
| empty_carrier(X1997)
| ~ latt_str(X1997) )
& ( element(esk24_3(X1997,X1998,X2001),the_carrier(X1997))
| latt_element_smaller(X1997,X1998,X2001)
| ~ element(X1998,the_carrier(X1997))
| empty_carrier(X1997)
| ~ latt_str(X1997) )
& ( in(esk24_3(X1997,X1998,X2001),X2001)
| latt_element_smaller(X1997,X1998,X2001)
| ~ element(X1998,the_carrier(X1997))
| empty_carrier(X1997)
| ~ latt_str(X1997) )
& ( ~ below(X1997,esk24_3(X1997,X1998,X2001),X1998)
| latt_element_smaller(X1997,X1998,X2001)
| ~ element(X1998,the_carrier(X1997))
| empty_carrier(X1997)
| ~ latt_str(X1997) ) ),
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)],[i_0_757])])])])])]) ).
fof(i_0_1561,plain,
! [X1986,X1987,X1988,X1989,X1990] :
( ( ~ latt_set_smaller(X1986,X1987,X1988)
| ~ element(X1989,the_carrier(X1986))
| ~ in(X1989,X1988)
| below(X1986,X1987,X1989)
| ~ element(X1987,the_carrier(X1986))
| empty_carrier(X1986)
| ~ latt_str(X1986) )
& ( element(esk22_3(X1986,X1987,X1990),the_carrier(X1986))
| latt_set_smaller(X1986,X1987,X1990)
| ~ element(X1987,the_carrier(X1986))
| empty_carrier(X1986)
| ~ latt_str(X1986) )
& ( in(esk22_3(X1986,X1987,X1990),X1990)
| latt_set_smaller(X1986,X1987,X1990)
| ~ element(X1987,the_carrier(X1986))
| empty_carrier(X1986)
| ~ latt_str(X1986) )
& ( ~ below(X1986,X1987,esk22_3(X1986,X1987,X1990))
| latt_set_smaller(X1986,X1987,X1990)
| ~ element(X1987,the_carrier(X1986))
| empty_carrier(X1986)
| ~ latt_str(X1986) ) ),
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)],[i_0_758])])])])])]) ).
fof(i_0_1562,plain,
! [X2424,X2425,X2426,X2427] :
( ( ~ relstr_set_smaller(X2424,X2425,X2426)
| ~ element(X2427,the_carrier(X2424))
| ~ in(X2427,X2425)
| related(X2424,X2427,X2426)
| ~ element(X2426,the_carrier(X2424))
| ~ rel_str(X2424) )
& ( element(esk114_3(X2424,X2425,X2426),the_carrier(X2424))
| relstr_set_smaller(X2424,X2425,X2426)
| ~ element(X2426,the_carrier(X2424))
| ~ rel_str(X2424) )
& ( in(esk114_3(X2424,X2425,X2426),X2425)
| relstr_set_smaller(X2424,X2425,X2426)
| ~ element(X2426,the_carrier(X2424))
| ~ rel_str(X2424) )
& ( ~ related(X2424,esk114_3(X2424,X2425,X2426),X2426)
| relstr_set_smaller(X2424,X2425,X2426)
| ~ element(X2426,the_carrier(X2424))
| ~ rel_str(X2424) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d9_lattice3])])])])]) ).
fof(i_0_1563,plain,
! [X2382,X2383,X2384,X2385] :
( ( ~ relstr_element_smaller(X2382,X2383,X2384)
| ~ element(X2385,the_carrier(X2382))
| ~ in(X2385,X2383)
| related(X2382,X2384,X2385)
| ~ element(X2384,the_carrier(X2382))
| ~ rel_str(X2382) )
& ( element(esk103_3(X2382,X2383,X2384),the_carrier(X2382))
| relstr_element_smaller(X2382,X2383,X2384)
| ~ element(X2384,the_carrier(X2382))
| ~ rel_str(X2382) )
& ( in(esk103_3(X2382,X2383,X2384),X2383)
| relstr_element_smaller(X2382,X2383,X2384)
| ~ element(X2384,the_carrier(X2382))
| ~ rel_str(X2382) )
& ( ~ related(X2382,X2384,esk103_3(X2382,X2383,X2384))
| relstr_element_smaller(X2382,X2383,X2384)
| ~ element(X2384,the_carrier(X2382))
| ~ rel_str(X2382) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_lattice3])])])])]) ).
cnf(i_0_1564,plain,
( in(X2,esk249_1(X1))
| epred2_3(esk248_1(X1),esk247_1(X1),esk246_1(X1))
| esk253_3(X1,X2,X3) != empty_set
| ~ ordinal(X3)
| X2 != X3
| ~ in(X4,succ(X1))
| X4 != X2
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_717]) ).
cnf(i_0_1565,lemma,
( esk348_3(X1,X2,X3) = singleton(esk347_3(X1,X2,X3))
| ~ in(X3,esk346_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_722]) ).
cnf(i_0_1566,plain,
( element(esk253_3(X1,X2,X3),powerset(powerset(X3)))
| in(X2,esk249_1(X1))
| ~ ordinal(X3)
| X2 != X3
| ~ in(X4,succ(X1))
| X4 != X2
| esk247_1(X1) != esk248_1(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_717]) ).
fof(i_0_1567,lemma,
! [X3614,X3615,X3616,X3617] :
( ~ transitive_relstr(X3614)
| ~ rel_str(X3614)
| ~ element(X3615,the_carrier(X3614))
| ~ element(X3616,the_carrier(X3614))
| ~ element(X3617,the_carrier(X3614))
| ~ related(X3614,X3615,X3616)
| ~ related(X3614,X3616,X3617)
| related(X3614,X3615,X3617) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t26_orders_2])])]) ).
cnf(i_0_1568,lemma,
( in(X1,X2)
| empty(X2)
| ~ in(ordered_pair(X1,X3),esk182_2(X2,X4))
| esk178_2(X2,X4) != esk179_2(X2,X4)
| ~ relation(X4) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1569,lemma,
( in(X1,X2)
| in(esk177_2(X2,X4),X2)
| empty(X2)
| ~ in(ordered_pair(X1,X3),esk182_2(X2,X4))
| ~ relation(X4) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1570,lemma,
( in(X1,X2)
| in(esk177_2(X2,X4),X2)
| empty(X2)
| ~ in(ordered_pair(X1,X3),esk182_2(X2,X4))
| ~ relation(X4) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1571,plain,
( in(esk243_3(X1,X2,X3),cartesian_product2(X1,X2))
| ordered_pair(esk240_1(X1),esk241_1(X1)) = esk237_1(X1)
| ~ in(X3,esk242_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_715]) ).
cnf(i_0_1572,plain,
( in(esk243_3(X1,X2,X3),cartesian_product2(X1,X2))
| ordered_pair(esk238_1(X1),esk239_1(X1)) = esk236_1(X1)
| ~ in(X3,esk242_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_715]) ).
cnf(i_0_1573,lemma,
( in(X3,relation_inverse_image(X2,X4))
| ~ in(X1,relation_rng(X2))
| ~ in(ordered_pair(X3,X1),X2)
| ~ in(X1,X4)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_734]) ).
cnf(i_0_1574,lemma,
( in(X3,relation_image(X2,X4))
| ~ in(X1,relation_dom(X2))
| ~ in(ordered_pair(X1,X3),X2)
| ~ in(X1,X4)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_709]) ).
fof(i_0_1575,plain,
! [X1868,X1869] :
( ( function(X1869)
| ~ function(X1869)
| ~ v1_partfun1(X1869,X1868,X1868)
| ~ reflexive(X1869)
| ~ quasi_total(X1869,X1868,X1868)
| ~ relation_of2(X1869,X1868,X1868) )
& ( one_to_one(X1869)
| ~ function(X1869)
| ~ v1_partfun1(X1869,X1868,X1868)
| ~ reflexive(X1869)
| ~ quasi_total(X1869,X1868,X1868)
| ~ relation_of2(X1869,X1868,X1868) )
& ( quasi_total(X1869,X1868,X1868)
| ~ function(X1869)
| ~ v1_partfun1(X1869,X1868,X1868)
| ~ reflexive(X1869)
| ~ quasi_total(X1869,X1868,X1868)
| ~ relation_of2(X1869,X1868,X1868) )
& ( onto(X1869,X1868,X1868)
| ~ function(X1869)
| ~ v1_partfun1(X1869,X1868,X1868)
| ~ reflexive(X1869)
| ~ quasi_total(X1869,X1868,X1868)
| ~ relation_of2(X1869,X1868,X1868) )
& ( bijective(X1869,X1868,X1868)
| ~ function(X1869)
| ~ v1_partfun1(X1869,X1868,X1868)
| ~ reflexive(X1869)
| ~ quasi_total(X1869,X1868,X1868)
| ~ relation_of2(X1869,X1868,X1868) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc4_funct_2])])]) ).
fof(i_0_1576,plain,
! [X1863,X1864,X1865] :
( ( function(X1865)
| ~ function(X1865)
| ~ one_to_one(X1865)
| ~ quasi_total(X1865,X1863,X1864)
| ~ onto(X1865,X1863,X1864)
| ~ relation_of2(X1865,X1863,X1864) )
& ( quasi_total(X1865,X1863,X1864)
| ~ function(X1865)
| ~ one_to_one(X1865)
| ~ quasi_total(X1865,X1863,X1864)
| ~ onto(X1865,X1863,X1864)
| ~ relation_of2(X1865,X1863,X1864) )
& ( bijective(X1865,X1863,X1864)
| ~ function(X1865)
| ~ one_to_one(X1865)
| ~ quasi_total(X1865,X1863,X1864)
| ~ onto(X1865,X1863,X1864)
| ~ relation_of2(X1865,X1863,X1864) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc3_funct_2])])]) ).
fof(i_0_1577,plain,
! [X3064,X3065,X3072,X3075,X3076,X3077] :
( ( in(esk261_3(X3064,X3065,X3072),powerset(the_carrier(X3064)))
| ~ in(X3072,esk260_2(X3064,X3065))
| esk255_2(X3064,X3065) = esk256_2(X3064,X3065)
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( esk261_3(X3064,X3065,X3072) = X3072
| ~ in(X3072,esk260_2(X3064,X3065))
| esk255_2(X3064,X3065) = esk256_2(X3064,X3065)
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( element(esk262_3(X3064,X3065,X3072),powerset(the_carrier(X3064)))
| ~ in(X3072,esk260_2(X3064,X3065))
| esk255_2(X3064,X3065) = esk256_2(X3064,X3065)
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( esk262_3(X3064,X3065,X3072) = X3072
| ~ in(X3072,esk260_2(X3064,X3065))
| esk255_2(X3064,X3065) = esk256_2(X3064,X3065)
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( closed_subset(esk262_3(X3064,X3065,X3072),X3064)
| ~ in(X3072,esk260_2(X3064,X3065))
| esk255_2(X3064,X3065) = esk256_2(X3064,X3065)
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( subset(X3065,X3072)
| ~ in(X3072,esk260_2(X3064,X3065))
| esk255_2(X3064,X3065) = esk256_2(X3064,X3065)
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( ~ in(X3076,powerset(the_carrier(X3064)))
| X3076 != X3075
| ~ element(X3077,powerset(the_carrier(X3064)))
| X3077 != X3075
| ~ closed_subset(X3077,X3064)
| ~ subset(X3065,X3075)
| in(X3075,esk260_2(X3064,X3065))
| esk255_2(X3064,X3065) = esk256_2(X3064,X3065)
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( in(esk261_3(X3064,X3065,X3072),powerset(the_carrier(X3064)))
| ~ in(X3072,esk260_2(X3064,X3065))
| element(esk258_2(X3064,X3065),powerset(the_carrier(X3064)))
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( esk261_3(X3064,X3065,X3072) = X3072
| ~ in(X3072,esk260_2(X3064,X3065))
| element(esk258_2(X3064,X3065),powerset(the_carrier(X3064)))
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( element(esk262_3(X3064,X3065,X3072),powerset(the_carrier(X3064)))
| ~ in(X3072,esk260_2(X3064,X3065))
| element(esk258_2(X3064,X3065),powerset(the_carrier(X3064)))
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( esk262_3(X3064,X3065,X3072) = X3072
| ~ in(X3072,esk260_2(X3064,X3065))
| element(esk258_2(X3064,X3065),powerset(the_carrier(X3064)))
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( closed_subset(esk262_3(X3064,X3065,X3072),X3064)
| ~ in(X3072,esk260_2(X3064,X3065))
| element(esk258_2(X3064,X3065),powerset(the_carrier(X3064)))
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( subset(X3065,X3072)
| ~ in(X3072,esk260_2(X3064,X3065))
| element(esk258_2(X3064,X3065),powerset(the_carrier(X3064)))
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( ~ in(X3076,powerset(the_carrier(X3064)))
| X3076 != X3075
| ~ element(X3077,powerset(the_carrier(X3064)))
| X3077 != X3075
| ~ closed_subset(X3077,X3064)
| ~ subset(X3065,X3075)
| in(X3075,esk260_2(X3064,X3065))
| element(esk258_2(X3064,X3065),powerset(the_carrier(X3064)))
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( in(esk261_3(X3064,X3065,X3072),powerset(the_carrier(X3064)))
| ~ in(X3072,esk260_2(X3064,X3065))
| esk258_2(X3064,X3065) = esk256_2(X3064,X3065)
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( esk261_3(X3064,X3065,X3072) = X3072
| ~ in(X3072,esk260_2(X3064,X3065))
| esk258_2(X3064,X3065) = esk256_2(X3064,X3065)
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( element(esk262_3(X3064,X3065,X3072),powerset(the_carrier(X3064)))
| ~ in(X3072,esk260_2(X3064,X3065))
| esk258_2(X3064,X3065) = esk256_2(X3064,X3065)
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( esk262_3(X3064,X3065,X3072) = X3072
| ~ in(X3072,esk260_2(X3064,X3065))
| esk258_2(X3064,X3065) = esk256_2(X3064,X3065)
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( closed_subset(esk262_3(X3064,X3065,X3072),X3064)
| ~ in(X3072,esk260_2(X3064,X3065))
| esk258_2(X3064,X3065) = esk256_2(X3064,X3065)
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( subset(X3065,X3072)
| ~ in(X3072,esk260_2(X3064,X3065))
| esk258_2(X3064,X3065) = esk256_2(X3064,X3065)
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( ~ in(X3076,powerset(the_carrier(X3064)))
| X3076 != X3075
| ~ element(X3077,powerset(the_carrier(X3064)))
| X3077 != X3075
| ~ closed_subset(X3077,X3064)
| ~ subset(X3065,X3075)
| in(X3075,esk260_2(X3064,X3065))
| esk258_2(X3064,X3065) = esk256_2(X3064,X3065)
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( in(esk261_3(X3064,X3065,X3072),powerset(the_carrier(X3064)))
| ~ in(X3072,esk260_2(X3064,X3065))
| closed_subset(esk258_2(X3064,X3065),X3064)
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( esk261_3(X3064,X3065,X3072) = X3072
| ~ in(X3072,esk260_2(X3064,X3065))
| closed_subset(esk258_2(X3064,X3065),X3064)
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( element(esk262_3(X3064,X3065,X3072),powerset(the_carrier(X3064)))
| ~ in(X3072,esk260_2(X3064,X3065))
| closed_subset(esk258_2(X3064,X3065),X3064)
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( esk262_3(X3064,X3065,X3072) = X3072
| ~ in(X3072,esk260_2(X3064,X3065))
| closed_subset(esk258_2(X3064,X3065),X3064)
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( closed_subset(esk262_3(X3064,X3065,X3072),X3064)
| ~ in(X3072,esk260_2(X3064,X3065))
| closed_subset(esk258_2(X3064,X3065),X3064)
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( subset(X3065,X3072)
| ~ in(X3072,esk260_2(X3064,X3065))
| closed_subset(esk258_2(X3064,X3065),X3064)
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( ~ in(X3076,powerset(the_carrier(X3064)))
| X3076 != X3075
| ~ element(X3077,powerset(the_carrier(X3064)))
| X3077 != X3075
| ~ closed_subset(X3077,X3064)
| ~ subset(X3065,X3075)
| in(X3075,esk260_2(X3064,X3065))
| closed_subset(esk258_2(X3064,X3065),X3064)
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( in(esk261_3(X3064,X3065,X3072),powerset(the_carrier(X3064)))
| ~ in(X3072,esk260_2(X3064,X3065))
| subset(X3065,esk256_2(X3064,X3065))
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( esk261_3(X3064,X3065,X3072) = X3072
| ~ in(X3072,esk260_2(X3064,X3065))
| subset(X3065,esk256_2(X3064,X3065))
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( element(esk262_3(X3064,X3065,X3072),powerset(the_carrier(X3064)))
| ~ in(X3072,esk260_2(X3064,X3065))
| subset(X3065,esk256_2(X3064,X3065))
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( esk262_3(X3064,X3065,X3072) = X3072
| ~ in(X3072,esk260_2(X3064,X3065))
| subset(X3065,esk256_2(X3064,X3065))
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( closed_subset(esk262_3(X3064,X3065,X3072),X3064)
| ~ in(X3072,esk260_2(X3064,X3065))
| subset(X3065,esk256_2(X3064,X3065))
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( subset(X3065,X3072)
| ~ in(X3072,esk260_2(X3064,X3065))
| subset(X3065,esk256_2(X3064,X3065))
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( ~ in(X3076,powerset(the_carrier(X3064)))
| X3076 != X3075
| ~ element(X3077,powerset(the_carrier(X3064)))
| X3077 != X3075
| ~ closed_subset(X3077,X3064)
| ~ subset(X3065,X3075)
| in(X3075,esk260_2(X3064,X3065))
| subset(X3065,esk256_2(X3064,X3065))
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( in(esk261_3(X3064,X3065,X3072),powerset(the_carrier(X3064)))
| ~ in(X3072,esk260_2(X3064,X3065))
| esk255_2(X3064,X3065) = esk257_2(X3064,X3065)
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( esk261_3(X3064,X3065,X3072) = X3072
| ~ in(X3072,esk260_2(X3064,X3065))
| esk255_2(X3064,X3065) = esk257_2(X3064,X3065)
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( element(esk262_3(X3064,X3065,X3072),powerset(the_carrier(X3064)))
| ~ in(X3072,esk260_2(X3064,X3065))
| esk255_2(X3064,X3065) = esk257_2(X3064,X3065)
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( esk262_3(X3064,X3065,X3072) = X3072
| ~ in(X3072,esk260_2(X3064,X3065))
| esk255_2(X3064,X3065) = esk257_2(X3064,X3065)
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( closed_subset(esk262_3(X3064,X3065,X3072),X3064)
| ~ in(X3072,esk260_2(X3064,X3065))
| esk255_2(X3064,X3065) = esk257_2(X3064,X3065)
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( subset(X3065,X3072)
| ~ in(X3072,esk260_2(X3064,X3065))
| esk255_2(X3064,X3065) = esk257_2(X3064,X3065)
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( ~ in(X3076,powerset(the_carrier(X3064)))
| X3076 != X3075
| ~ element(X3077,powerset(the_carrier(X3064)))
| X3077 != X3075
| ~ closed_subset(X3077,X3064)
| ~ subset(X3065,X3075)
| in(X3075,esk260_2(X3064,X3065))
| esk255_2(X3064,X3065) = esk257_2(X3064,X3065)
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( in(esk261_3(X3064,X3065,X3072),powerset(the_carrier(X3064)))
| ~ in(X3072,esk260_2(X3064,X3065))
| element(esk259_2(X3064,X3065),powerset(the_carrier(X3064)))
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( esk261_3(X3064,X3065,X3072) = X3072
| ~ in(X3072,esk260_2(X3064,X3065))
| element(esk259_2(X3064,X3065),powerset(the_carrier(X3064)))
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( element(esk262_3(X3064,X3065,X3072),powerset(the_carrier(X3064)))
| ~ in(X3072,esk260_2(X3064,X3065))
| element(esk259_2(X3064,X3065),powerset(the_carrier(X3064)))
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( esk262_3(X3064,X3065,X3072) = X3072
| ~ in(X3072,esk260_2(X3064,X3065))
| element(esk259_2(X3064,X3065),powerset(the_carrier(X3064)))
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( closed_subset(esk262_3(X3064,X3065,X3072),X3064)
| ~ in(X3072,esk260_2(X3064,X3065))
| element(esk259_2(X3064,X3065),powerset(the_carrier(X3064)))
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( subset(X3065,X3072)
| ~ in(X3072,esk260_2(X3064,X3065))
| element(esk259_2(X3064,X3065),powerset(the_carrier(X3064)))
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( ~ in(X3076,powerset(the_carrier(X3064)))
| X3076 != X3075
| ~ element(X3077,powerset(the_carrier(X3064)))
| X3077 != X3075
| ~ closed_subset(X3077,X3064)
| ~ subset(X3065,X3075)
| in(X3075,esk260_2(X3064,X3065))
| element(esk259_2(X3064,X3065),powerset(the_carrier(X3064)))
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( in(esk261_3(X3064,X3065,X3072),powerset(the_carrier(X3064)))
| ~ in(X3072,esk260_2(X3064,X3065))
| esk259_2(X3064,X3065) = esk257_2(X3064,X3065)
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( esk261_3(X3064,X3065,X3072) = X3072
| ~ in(X3072,esk260_2(X3064,X3065))
| esk259_2(X3064,X3065) = esk257_2(X3064,X3065)
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( element(esk262_3(X3064,X3065,X3072),powerset(the_carrier(X3064)))
| ~ in(X3072,esk260_2(X3064,X3065))
| esk259_2(X3064,X3065) = esk257_2(X3064,X3065)
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( esk262_3(X3064,X3065,X3072) = X3072
| ~ in(X3072,esk260_2(X3064,X3065))
| esk259_2(X3064,X3065) = esk257_2(X3064,X3065)
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( closed_subset(esk262_3(X3064,X3065,X3072),X3064)
| ~ in(X3072,esk260_2(X3064,X3065))
| esk259_2(X3064,X3065) = esk257_2(X3064,X3065)
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( subset(X3065,X3072)
| ~ in(X3072,esk260_2(X3064,X3065))
| esk259_2(X3064,X3065) = esk257_2(X3064,X3065)
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( ~ in(X3076,powerset(the_carrier(X3064)))
| X3076 != X3075
| ~ element(X3077,powerset(the_carrier(X3064)))
| X3077 != X3075
| ~ closed_subset(X3077,X3064)
| ~ subset(X3065,X3075)
| in(X3075,esk260_2(X3064,X3065))
| esk259_2(X3064,X3065) = esk257_2(X3064,X3065)
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( in(esk261_3(X3064,X3065,X3072),powerset(the_carrier(X3064)))
| ~ in(X3072,esk260_2(X3064,X3065))
| closed_subset(esk259_2(X3064,X3065),X3064)
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( esk261_3(X3064,X3065,X3072) = X3072
| ~ in(X3072,esk260_2(X3064,X3065))
| closed_subset(esk259_2(X3064,X3065),X3064)
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( element(esk262_3(X3064,X3065,X3072),powerset(the_carrier(X3064)))
| ~ in(X3072,esk260_2(X3064,X3065))
| closed_subset(esk259_2(X3064,X3065),X3064)
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( esk262_3(X3064,X3065,X3072) = X3072
| ~ in(X3072,esk260_2(X3064,X3065))
| closed_subset(esk259_2(X3064,X3065),X3064)
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( closed_subset(esk262_3(X3064,X3065,X3072),X3064)
| ~ in(X3072,esk260_2(X3064,X3065))
| closed_subset(esk259_2(X3064,X3065),X3064)
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( subset(X3065,X3072)
| ~ in(X3072,esk260_2(X3064,X3065))
| closed_subset(esk259_2(X3064,X3065),X3064)
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( ~ in(X3076,powerset(the_carrier(X3064)))
| X3076 != X3075
| ~ element(X3077,powerset(the_carrier(X3064)))
| X3077 != X3075
| ~ closed_subset(X3077,X3064)
| ~ subset(X3065,X3075)
| in(X3075,esk260_2(X3064,X3065))
| closed_subset(esk259_2(X3064,X3065),X3064)
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( in(esk261_3(X3064,X3065,X3072),powerset(the_carrier(X3064)))
| ~ in(X3072,esk260_2(X3064,X3065))
| subset(X3065,esk257_2(X3064,X3065))
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( esk261_3(X3064,X3065,X3072) = X3072
| ~ in(X3072,esk260_2(X3064,X3065))
| subset(X3065,esk257_2(X3064,X3065))
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( element(esk262_3(X3064,X3065,X3072),powerset(the_carrier(X3064)))
| ~ in(X3072,esk260_2(X3064,X3065))
| subset(X3065,esk257_2(X3064,X3065))
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( esk262_3(X3064,X3065,X3072) = X3072
| ~ in(X3072,esk260_2(X3064,X3065))
| subset(X3065,esk257_2(X3064,X3065))
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( closed_subset(esk262_3(X3064,X3065,X3072),X3064)
| ~ in(X3072,esk260_2(X3064,X3065))
| subset(X3065,esk257_2(X3064,X3065))
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( subset(X3065,X3072)
| ~ in(X3072,esk260_2(X3064,X3065))
| subset(X3065,esk257_2(X3064,X3065))
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( ~ in(X3076,powerset(the_carrier(X3064)))
| X3076 != X3075
| ~ element(X3077,powerset(the_carrier(X3064)))
| X3077 != X3075
| ~ closed_subset(X3077,X3064)
| ~ subset(X3065,X3075)
| in(X3075,esk260_2(X3064,X3065))
| subset(X3065,esk257_2(X3064,X3065))
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( in(esk261_3(X3064,X3065,X3072),powerset(the_carrier(X3064)))
| ~ in(X3072,esk260_2(X3064,X3065))
| esk256_2(X3064,X3065) != esk257_2(X3064,X3065)
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( esk261_3(X3064,X3065,X3072) = X3072
| ~ in(X3072,esk260_2(X3064,X3065))
| esk256_2(X3064,X3065) != esk257_2(X3064,X3065)
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( element(esk262_3(X3064,X3065,X3072),powerset(the_carrier(X3064)))
| ~ in(X3072,esk260_2(X3064,X3065))
| esk256_2(X3064,X3065) != esk257_2(X3064,X3065)
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( esk262_3(X3064,X3065,X3072) = X3072
| ~ in(X3072,esk260_2(X3064,X3065))
| esk256_2(X3064,X3065) != esk257_2(X3064,X3065)
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( closed_subset(esk262_3(X3064,X3065,X3072),X3064)
| ~ in(X3072,esk260_2(X3064,X3065))
| esk256_2(X3064,X3065) != esk257_2(X3064,X3065)
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( subset(X3065,X3072)
| ~ in(X3072,esk260_2(X3064,X3065))
| esk256_2(X3064,X3065) != esk257_2(X3064,X3065)
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) )
& ( ~ in(X3076,powerset(the_carrier(X3064)))
| X3076 != X3075
| ~ element(X3077,powerset(the_carrier(X3064)))
| X3077 != X3075
| ~ closed_subset(X3077,X3064)
| ~ subset(X3065,X3075)
| in(X3075,esk260_2(X3064,X3065))
| esk256_2(X3064,X3065) != esk257_2(X3064,X3065)
| ~ topological_space(X3064)
| ~ top_str(X3064)
| ~ element(X3065,powerset(the_carrier(X3064))) ) ),
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)],[s1_tarski__e1_40__pre_topc__1])])])])])]) ).
fof(i_0_1578,plain,
! [X2387,X2388,X2389] :
( ( ~ meet_absorbing(X2387)
| ~ element(X2388,the_carrier(X2387))
| ~ element(X2389,the_carrier(X2387))
| join(X2387,meet(X2387,X2388,X2389),X2389) = X2389
| empty_carrier(X2387)
| ~ latt_str(X2387) )
& ( element(esk104_1(X2387),the_carrier(X2387))
| meet_absorbing(X2387)
| empty_carrier(X2387)
| ~ latt_str(X2387) )
& ( element(esk105_1(X2387),the_carrier(X2387))
| meet_absorbing(X2387)
| empty_carrier(X2387)
| ~ latt_str(X2387) )
& ( join(X2387,meet(X2387,esk104_1(X2387),esk105_1(X2387)),esk105_1(X2387)) != esk105_1(X2387)
| meet_absorbing(X2387)
| empty_carrier(X2387)
| ~ latt_str(X2387) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_759])])])])]) ).
cnf(i_0_1579,lemma,
( element(esk352_3(X1,X2,X3),powerset(powerset(X3)))
| in(X2,esk349_1(X1))
| ~ ordinal(X3)
| X2 != X3
| ~ in(X2,succ(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_721]) ).
cnf(i_0_1580,plain,
( element(esk449_0,powerset(powerset(succ(esk447_0))))
| subset(X1,esk446_1(X1))
| epred1_0
| ~ in(X1,esk445_0) ),
inference(split_conjunct,[status(thm)],[i_0_760]) ).
fof(i_0_1581,lemma,
! [X3742,X3743,X3744,X3745] :
( ( ~ in(X3744,topstr_closure(X3742,X3743))
| ~ element(X3745,powerset(the_carrier(X3742)))
| ~ closed_subset(X3745,X3742)
| ~ subset(X3743,X3745)
| in(X3744,X3745)
| ~ in(X3744,the_carrier(X3742))
| ~ element(X3743,powerset(the_carrier(X3742)))
| ~ top_str(X3742) )
& ( element(esk430_3(X3742,X3743,X3744),powerset(the_carrier(X3742)))
| in(X3744,topstr_closure(X3742,X3743))
| ~ in(X3744,the_carrier(X3742))
| ~ element(X3743,powerset(the_carrier(X3742)))
| ~ top_str(X3742) )
& ( closed_subset(esk430_3(X3742,X3743,X3744),X3742)
| in(X3744,topstr_closure(X3742,X3743))
| ~ in(X3744,the_carrier(X3742))
| ~ element(X3743,powerset(the_carrier(X3742)))
| ~ top_str(X3742) )
& ( subset(X3743,esk430_3(X3742,X3743,X3744))
| in(X3744,topstr_closure(X3742,X3743))
| ~ in(X3744,the_carrier(X3742))
| ~ element(X3743,powerset(the_carrier(X3742)))
| ~ top_str(X3742) )
& ( ~ in(X3744,esk430_3(X3742,X3743,X3744))
| in(X3744,topstr_closure(X3742,X3743))
| ~ in(X3744,the_carrier(X3742))
| ~ element(X3743,powerset(the_carrier(X3742)))
| ~ top_str(X3742) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t45_pre_topc])])])])]) ).
cnf(i_0_1582,plain,
( latt_element_smaller(X1,esk51_3(X1,X2,X3),X2)
| X3 = join_of_latt_set(X1,X2)
| empty_carrier(X1)
| empty_carrier(X1)
| ~ latt_element_smaller(X1,X3,X2)
| ~ element(X3,the_carrier(X1))
| ~ lattice(X1)
| ~ complete_latt_str(X1)
| ~ latt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_749]) ).
cnf(i_0_1583,lemma,
( in(X1,X2)
| esk177_2(X2,X4) = esk181_2(X2,X4)
| empty(X2)
| ~ in(ordered_pair(X1,X3),esk182_2(X2,X4))
| ~ relation(X4) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1584,lemma,
( in(X1,X2)
| esk177_2(X2,X4) = esk180_2(X2,X4)
| empty(X2)
| ~ in(ordered_pair(X1,X3),esk182_2(X2,X4))
| ~ relation(X4) ),
inference(split_conjunct,[status(thm)],[i_0_690]) ).
cnf(i_0_1585,plain,
( element(esk449_0,powerset(powerset(succ(esk447_0))))
| in(esk446_1(X1),esk445_0)
| epred1_0
| ~ in(X1,esk445_0) ),
inference(split_conjunct,[status(thm)],[i_0_760]) ).
fof(i_0_1586,plain,
! [X1856,X1857,X1858] :
( ( function(X1858)
| ~ function(X1858)
| ~ quasi_total(X1858,X1856,X1857)
| ~ bijective(X1858,X1856,X1857)
| ~ relation_of2(X1858,X1856,X1857) )
& ( one_to_one(X1858)
| ~ function(X1858)
| ~ quasi_total(X1858,X1856,X1857)
| ~ bijective(X1858,X1856,X1857)
| ~ relation_of2(X1858,X1856,X1857) )
& ( quasi_total(X1858,X1856,X1857)
| ~ function(X1858)
| ~ quasi_total(X1858,X1856,X1857)
| ~ bijective(X1858,X1856,X1857)
| ~ relation_of2(X1858,X1856,X1857) )
& ( onto(X1858,X1856,X1857)
| ~ function(X1858)
| ~ quasi_total(X1858,X1856,X1857)
| ~ bijective(X1858,X1856,X1857)
| ~ relation_of2(X1858,X1856,X1857) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_funct_2])])]) ).
fof(i_0_1587,lemma,
! [X3400,X3401,X3403,X3405] :
( ( element(esk406_2(X3400,X3401),powerset(powerset(the_carrier(X3400))))
| ~ topological_space(X3400)
| ~ top_str(X3400)
| ~ element(X3401,powerset(the_carrier(X3400))) )
& ( element(esk407_3(X3400,X3401,X3403),powerset(the_carrier(X3400)))
| ~ in(X3403,esk406_2(X3400,X3401))
| ~ element(X3403,powerset(the_carrier(X3400)))
| ~ topological_space(X3400)
| ~ top_str(X3400)
| ~ element(X3401,powerset(the_carrier(X3400))) )
& ( esk407_3(X3400,X3401,X3403) = X3403
| ~ in(X3403,esk406_2(X3400,X3401))
| ~ element(X3403,powerset(the_carrier(X3400)))
| ~ topological_space(X3400)
| ~ top_str(X3400)
| ~ element(X3401,powerset(the_carrier(X3400))) )
& ( closed_subset(esk407_3(X3400,X3401,X3403),X3400)
| ~ in(X3403,esk406_2(X3400,X3401))
| ~ element(X3403,powerset(the_carrier(X3400)))
| ~ topological_space(X3400)
| ~ top_str(X3400)
| ~ element(X3401,powerset(the_carrier(X3400))) )
& ( subset(X3401,X3403)
| ~ in(X3403,esk406_2(X3400,X3401))
| ~ element(X3403,powerset(the_carrier(X3400)))
| ~ topological_space(X3400)
| ~ top_str(X3400)
| ~ element(X3401,powerset(the_carrier(X3400))) )
& ( ~ element(X3405,powerset(the_carrier(X3400)))
| X3405 != X3403
| ~ closed_subset(X3405,X3400)
| ~ subset(X3401,X3403)
| in(X3403,esk406_2(X3400,X3401))
| ~ element(X3403,powerset(the_carrier(X3400)))
| ~ topological_space(X3400)
| ~ top_str(X3400)
| ~ element(X3401,powerset(the_carrier(X3400))) ) ),
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)],[s3_subset_1__e1_40__pre_topc])])])])])]) ).
fof(i_0_1588,lemma,
! [X3878,X3879,X3880] :
( ( ~ below_refl(X3878,X3879,X3880)
| related_reflexive(poset_of_lattice(X3878),cast_to_el_of_LattPOSet(X3878,X3879),cast_to_el_of_LattPOSet(X3878,X3880))
| ~ element(X3880,the_carrier(X3878))
| ~ element(X3879,the_carrier(X3878))
| empty_carrier(X3878)
| ~ lattice(X3878)
| ~ latt_str(X3878) )
& ( ~ related_reflexive(poset_of_lattice(X3878),cast_to_el_of_LattPOSet(X3878,X3879),cast_to_el_of_LattPOSet(X3878,X3880))
| below_refl(X3878,X3879,X3880)
| ~ element(X3880,the_carrier(X3878))
| ~ element(X3879,the_carrier(X3878))
| empty_carrier(X3878)
| ~ lattice(X3878)
| ~ latt_str(X3878) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_761])])])]) ).
cnf(i_0_1589,plain,
( in(esk339_3(X1,X2,X3),succ(X2))
| ~ in(X3,esk338_2(X1,X2))
| esk334_2(X1,X2) != esk335_2(X1,X2)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_762]) ).
fof(i_0_1590,plain,
! [X1992,X1993,X1994] :
( ( meet(X1992,X1993,X1994) = X1993
| ~ element(X1994,the_carrier(X1992))
| X1993 != bottom_of_semilattstr(X1992)
| ~ element(X1993,the_carrier(X1992))
| ~ lower_bounded_semilattstr(X1992)
| empty_carrier(X1992)
| ~ meet_semilatt_str(X1992) )
& ( meet(X1992,X1994,X1993) = X1993
| ~ element(X1994,the_carrier(X1992))
| X1993 != bottom_of_semilattstr(X1992)
| ~ element(X1993,the_carrier(X1992))
| ~ lower_bounded_semilattstr(X1992)
| empty_carrier(X1992)
| ~ meet_semilatt_str(X1992) )
& ( element(esk23_2(X1992,X1993),the_carrier(X1992))
| X1993 = bottom_of_semilattstr(X1992)
| ~ element(X1993,the_carrier(X1992))
| ~ lower_bounded_semilattstr(X1992)
| empty_carrier(X1992)
| ~ meet_semilatt_str(X1992) )
& ( meet(X1992,X1993,esk23_2(X1992,X1993)) != X1993
| meet(X1992,esk23_2(X1992,X1993),X1993) != X1993
| X1993 = bottom_of_semilattstr(X1992)
| ~ element(X1993,the_carrier(X1992))
| ~ lower_bounded_semilattstr(X1992)
| empty_carrier(X1992)
| ~ meet_semilatt_str(X1992) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_763])])])])]) ).
fof(i_0_1591,lemma,
! [X3911,X3912] :
( empty_carrier(X3911)
| ~ one_sorted_str(X3911)
| ~ element(X3912,the_carrier(X3911))
| apply_as_element(the_carrier(X3911),the_carrier(X3911),identity_on_carrier(X3911),X3912) = X3912 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_764])])]) ).
cnf(i_0_1592,plain,
( element(esk449_0,powerset(powerset(succ(esk447_0))))
| epred1_0
| esk446_1(X1) != X1
| ~ in(X1,esk445_0) ),
inference(split_conjunct,[status(thm)],[i_0_760]) ).
cnf(i_0_1593,plain,
( in(esk339_3(X1,X2,X3),succ(X2))
| in(esk337_2(X1,X2),X1)
| ~ in(X3,esk338_2(X1,X2))
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_762]) ).
cnf(i_0_1594,plain,
( in(esk339_3(X1,X2,X3),succ(X2))
| in(esk336_2(X1,X2),X1)
| ~ in(X3,esk338_2(X1,X2))
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_762]) ).
cnf(i_0_1595,plain,
( in(ordered_pair(X2,X3),the_InternalRel(X1))
| ~ related(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_756]) ).
fof(i_0_1596,plain,
! [X2243,X2244,X2245,X2247,X2249] :
( ( in(esk75_3(X2243,X2244,X2245),X2245)
| ~ subset(X2245,X2244)
| X2245 = empty_set
| ~ is_well_founded_in(X2243,X2244)
| ~ relation(X2243) )
& ( disjoint(fiber(X2243,esk75_3(X2243,X2244,X2245)),X2245)
| ~ subset(X2245,X2244)
| X2245 = empty_set
| ~ is_well_founded_in(X2243,X2244)
| ~ relation(X2243) )
& ( subset(esk76_2(X2243,X2247),X2247)
| is_well_founded_in(X2243,X2247)
| ~ relation(X2243) )
& ( esk76_2(X2243,X2247) != empty_set
| is_well_founded_in(X2243,X2247)
| ~ relation(X2243) )
& ( ~ in(X2249,esk76_2(X2243,X2247))
| ~ disjoint(fiber(X2243,X2249),esk76_2(X2243,X2247))
| is_well_founded_in(X2243,X2247)
| ~ relation(X2243) ) ),
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)],[d3_wellord1])])])])])]) ).
cnf(i_0_1597,lemma,
( in(X1,X2)
| ~ in(ordered_pair(X1,X3),relation_composition(identity_relation(X2),X4))
| ~ relation(X4) ),
inference(split_conjunct,[status(thm)],[i_0_746]) ).
fof(i_0_1598,lemma,
! [X3751,X3752,X3753,X3754,X3755] :
( ( in(X3755,X3751)
| ~ in(X3755,relation_inverse_image(X3754,X3753))
| X3752 = empty_set
| ~ function(X3754)
| ~ quasi_total(X3754,X3751,X3752)
| ~ relation_of2_as_subset(X3754,X3751,X3752) )
& ( in(apply(X3754,X3755),X3753)
| ~ in(X3755,relation_inverse_image(X3754,X3753))
| X3752 = empty_set
| ~ function(X3754)
| ~ quasi_total(X3754,X3751,X3752)
| ~ relation_of2_as_subset(X3754,X3751,X3752) )
& ( ~ in(X3755,X3751)
| ~ in(apply(X3754,X3755),X3753)
| in(X3755,relation_inverse_image(X3754,X3753))
| X3752 = empty_set
| ~ function(X3754)
| ~ quasi_total(X3754,X3751,X3752)
| ~ relation_of2_as_subset(X3754,X3751,X3752) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t46_funct_2])])])]) ).
cnf(i_0_1599,plain,
( element(esk449_0,powerset(powerset(succ(esk447_0))))
| element(esk445_0,powerset(powerset(empty_set)))
| epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_760]) ).
fof(i_0_1600,plain,
! [X1947,X1949,X1950] :
( ( element(esk11_1(X1947),the_carrier(X1947))
| ~ lower_bounded_semilattstr(X1947)
| empty_carrier(X1947)
| ~ meet_semilatt_str(X1947) )
& ( meet(X1947,esk11_1(X1947),X1949) = esk11_1(X1947)
| ~ element(X1949,the_carrier(X1947))
| ~ lower_bounded_semilattstr(X1947)
| empty_carrier(X1947)
| ~ meet_semilatt_str(X1947) )
& ( meet(X1947,X1949,esk11_1(X1947)) = esk11_1(X1947)
| ~ element(X1949,the_carrier(X1947))
| ~ lower_bounded_semilattstr(X1947)
| empty_carrier(X1947)
| ~ meet_semilatt_str(X1947) )
& ( element(esk12_2(X1947,X1950),the_carrier(X1947))
| ~ element(X1950,the_carrier(X1947))
| lower_bounded_semilattstr(X1947)
| empty_carrier(X1947)
| ~ meet_semilatt_str(X1947) )
& ( meet(X1947,X1950,esk12_2(X1947,X1950)) != X1950
| meet(X1947,esk12_2(X1947,X1950),X1950) != X1950
| ~ element(X1950,the_carrier(X1947))
| lower_bounded_semilattstr(X1947)
| empty_carrier(X1947)
| ~ meet_semilatt_str(X1947) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_765])])])])]) ).
cnf(i_0_1601,plain,
( X2 = ordered_pair(esk37_2(X1,X2),esk38_2(X1,X2))
| ~ relation(X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_766]) ).
cnf(i_0_1602,plain,
( in(esk244_3(X1,X2,X3),X1)
| ordered_pair(esk240_1(X1),esk241_1(X1)) = esk237_1(X1)
| ~ in(X3,esk242_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_715]) ).
cnf(i_0_1603,plain,
( in(esk244_3(X1,X2,X3),X1)
| ordered_pair(esk238_1(X1),esk239_1(X1)) = esk236_1(X1)
| ~ in(X3,esk242_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_715]) ).
fof(i_0_1604,lemma,
! [X3321,X3322,X3323,X3325,X3326] :
( ( in(X3325,powerset(relation_dom(X3323)))
| ~ in(X3325,esk371_3(X3321,X3322,X3323))
| ~ element(X3322,powerset(powerset(X3321)))
| ~ relation(X3323)
| ~ function(X3323) )
& ( in(relation_image(X3323,X3325),X3322)
| ~ in(X3325,esk371_3(X3321,X3322,X3323))
| ~ element(X3322,powerset(powerset(X3321)))
| ~ relation(X3323)
| ~ function(X3323) )
& ( ~ in(X3326,powerset(relation_dom(X3323)))
| ~ in(relation_image(X3323,X3326),X3322)
| in(X3326,esk371_3(X3321,X3322,X3323))
| ~ element(X3322,powerset(powerset(X3321)))
| ~ relation(X3323)
| ~ function(X3323) ) ),
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)],[s1_xboole_0__e6_27__finset_1])])])])])]) ).
cnf(i_0_1605,plain,
( subset(X1,X2)
| ~ in(ordered_pair(X1,X2),X3)
| ~ in(X1,X4)
| ~ in(X2,X4)
| X3 != inclusion_relation(X4)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_719]) ).
fof(i_0_1606,plain,
! [X2345,X2346] :
( ( ~ closed_subset(X2346,X2345)
| open_subset(subset_difference(the_carrier(X2345),cast_as_carrier_subset(X2345),X2346),X2345)
| ~ element(X2346,powerset(the_carrier(X2345)))
| ~ top_str(X2345) )
& ( ~ open_subset(subset_difference(the_carrier(X2345),cast_as_carrier_subset(X2345),X2346),X2345)
| closed_subset(X2346,X2345)
| ~ element(X2346,powerset(the_carrier(X2345)))
| ~ top_str(X2345) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d6_pre_topc])])])]) ).
cnf(i_0_1607,plain,
( in(esk339_3(X1,X2,X3),succ(X2))
| ordinal(esk337_2(X1,X2))
| ~ in(X3,esk338_2(X1,X2))
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_762]) ).
cnf(i_0_1608,plain,
( in(esk339_3(X1,X2,X3),succ(X2))
| ordinal(esk336_2(X1,X2))
| ~ in(X3,esk338_2(X1,X2))
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_762]) ).
fof(i_0_1609,lemma,
! [X3555,X3556,X3557,X3558,X3559] :
( ~ function(X3558)
| ~ quasi_total(X3558,X3555,X3556)
| ~ relation_of2_as_subset(X3558,X3555,X3556)
| ~ relation(X3559)
| ~ function(X3559)
| ~ in(X3557,X3555)
| X3556 = empty_set
| apply(relation_composition(X3558,X3559),X3557) = apply(X3559,apply(X3558,X3557)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t21_funct_2])])]) ).
cnf(i_0_1610,plain,
( in(esk339_3(X1,X2,X3),succ(X2))
| esk335_2(X1,X2) = esk337_2(X1,X2)
| ~ in(X3,esk338_2(X1,X2))
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_762]) ).
cnf(i_0_1611,plain,
( in(esk339_3(X1,X2,X3),succ(X2))
| esk334_2(X1,X2) = esk336_2(X1,X2)
| ~ in(X3,esk338_2(X1,X2))
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_762]) ).
cnf(i_0_1612,plain,
( in(esk339_3(X1,X2,X3),succ(X2))
| esk333_2(X1,X2) = esk335_2(X1,X2)
| ~ in(X3,esk338_2(X1,X2))
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_762]) ).
cnf(i_0_1613,plain,
( in(esk339_3(X1,X2,X3),succ(X2))
| esk333_2(X1,X2) = esk334_2(X1,X2)
| ~ in(X3,esk338_2(X1,X2))
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_762]) ).
cnf(i_0_1614,plain,
( in(X1,X5)
| ~ in(ordered_pair(X1,X2),X3)
| ~ in(X2,X4)
| X5 != relation_inverse_image(X3,X4)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_704]) ).
cnf(i_0_1615,plain,
( in(X2,X5)
| ~ in(ordered_pair(X1,X2),X3)
| ~ in(X1,X4)
| X5 != relation_image(X3,X4)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_698]) ).
cnf(i_0_1616,plain,
( element(esk449_0,powerset(powerset(succ(esk447_0))))
| in(empty_set,omega)
| epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_760]) ).
fof(i_0_1617,plain,
! [X2168,X2169,X2170,X2171,X2172,X2173,X2174,X2175] :
( ( ~ in(X2171,X2170)
| X2171 = X2168
| X2171 = X2169
| X2170 != unordered_pair(X2168,X2169) )
& ( X2172 != X2168
| in(X2172,X2170)
| X2170 != unordered_pair(X2168,X2169) )
& ( X2172 != X2169
| in(X2172,X2170)
| X2170 != unordered_pair(X2168,X2169) )
& ( esk58_3(X2173,X2174,X2175) != X2173
| ~ in(esk58_3(X2173,X2174,X2175),X2175)
| X2175 = unordered_pair(X2173,X2174) )
& ( esk58_3(X2173,X2174,X2175) != X2174
| ~ in(esk58_3(X2173,X2174,X2175),X2175)
| X2175 = unordered_pair(X2173,X2174) )
& ( in(esk58_3(X2173,X2174,X2175),X2175)
| esk58_3(X2173,X2174,X2175) = X2173
| esk58_3(X2173,X2174,X2175) = X2174
| X2175 = unordered_pair(X2173,X2174) ) ),
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)],[d2_tarski])])])])])]) ).
cnf(i_0_1618,plain,
( in(X4,esk242_2(X2,X3))
| esk241_1(X2) = singleton(esk240_1(X2))
| ~ in(X1,cartesian_product2(X2,X3))
| X1 != X4
| ordered_pair(X5,X6) != X4
| ~ in(X5,X2)
| X6 != singleton(X5) ),
inference(split_conjunct,[status(thm)],[i_0_715]) ).
cnf(i_0_1619,plain,
( in(X4,esk242_2(X2,X3))
| esk239_1(X2) = singleton(esk238_1(X2))
| ~ in(X1,cartesian_product2(X2,X3))
| X1 != X4
| ordered_pair(X5,X6) != X4
| ~ in(X5,X2)
| X6 != singleton(X5) ),
inference(split_conjunct,[status(thm)],[i_0_715]) ).
cnf(i_0_1620,plain,
( X2 = apply(X3,X1)
| ~ in(ordered_pair(X1,X2),X3)
| ~ in(X1,relation_dom(X3))
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[i_0_767]) ).
cnf(i_0_1621,plain,
( element(esk51_3(X1,X2,X3),the_carrier(X1))
| X3 = join_of_latt_set(X1,X2)
| empty_carrier(X1)
| empty_carrier(X1)
| ~ latt_element_smaller(X1,X3,X2)
| ~ element(X3,the_carrier(X1))
| ~ lattice(X1)
| ~ complete_latt_str(X1)
| ~ latt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_749]) ).
cnf(i_0_1622,plain,
( in(X2,esk249_1(X1))
| esk253_3(X1,X2,X3) != empty_set
| ~ ordinal(X3)
| X2 != X3
| ~ in(X4,succ(X1))
| X4 != X2
| esk247_1(X1) != esk248_1(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_717]) ).
cnf(i_0_1623,plain,
( in(esk77_3(X1,X2,X3),X1)
| in(esk77_3(X1,X2,X3),X3)
| X3 = set_intersection2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_735]) ).
cnf(i_0_1624,plain,
( in(esk77_3(X1,X2,X3),X2)
| in(esk77_3(X1,X2,X3),X3)
| X3 = set_intersection2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_735]) ).
cnf(i_0_1625,plain,
( element(esk449_0,powerset(powerset(succ(esk447_0))))
| epred1_0
| esk445_0 != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_760]) ).
cnf(i_0_1626,lemma,
( X1 = singleton(X2)
| esk187_1(X3) = singleton(esk185_1(X3))
| ~ in(ordered_pair(X2,X1),esk188_1(X3)) ),
inference(split_conjunct,[status(thm)],[i_0_768]) ).
cnf(i_0_1627,lemma,
( X1 = singleton(X2)
| esk186_1(X3) = singleton(esk185_1(X3))
| ~ in(ordered_pair(X2,X1),esk188_1(X3)) ),
inference(split_conjunct,[status(thm)],[i_0_768]) ).
cnf(i_0_1628,lemma,
( in(X1,X2)
| ~ in(ordered_pair(X1,X3),cartesian_product2(X2,X4)) ),
inference(split_conjunct,[status(thm)],[i_0_769]) ).
cnf(i_0_1629,lemma,
( in(X1,X2)
| ~ in(ordered_pair(X1,X3),cartesian_product2(X2,X4)) ),
inference(split_conjunct,[status(thm)],[i_0_770]) ).
cnf(i_0_1630,lemma,
( in(X1,X2)
| ~ in(ordered_pair(X3,X1),cartesian_product2(X4,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_769]) ).
cnf(i_0_1631,lemma,
( in(X1,X2)
| ~ in(ordered_pair(X3,X1),cartesian_product2(X4,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_770]) ).
cnf(i_0_1632,lemma,
( in(X1,X2)
| esk187_1(X2) = singleton(esk185_1(X2))
| ~ in(ordered_pair(X1,X3),esk188_1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_768]) ).
cnf(i_0_1633,lemma,
( in(X1,X2)
| esk186_1(X2) = singleton(esk185_1(X2))
| ~ in(ordered_pair(X1,X3),esk188_1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_768]) ).
cnf(i_0_1634,plain,
( in(X4,esk242_2(X2,X3))
| in(esk240_1(X2),X2)
| ~ in(X1,cartesian_product2(X2,X3))
| X1 != X4
| ordered_pair(X5,X6) != X4
| ~ in(X5,X2)
| X6 != singleton(X5) ),
inference(split_conjunct,[status(thm)],[i_0_715]) ).
cnf(i_0_1635,plain,
( in(X4,esk242_2(X2,X3))
| in(esk238_1(X2),X2)
| ~ in(X1,cartesian_product2(X2,X3))
| X1 != X4
| ordered_pair(X5,X6) != X4
| ~ in(X5,X2)
| X6 != singleton(X5) ),
inference(split_conjunct,[status(thm)],[i_0_715]) ).
cnf(i_0_1636,plain,
( in(X1,X2)
| ~ in(ordered_pair(X3,X1),X4)
| X4 != relation_rng_restriction(X2,X5)
| ~ relation(X4)
| ~ relation(X5) ),
inference(split_conjunct,[status(thm)],[i_0_699]) ).
cnf(i_0_1637,plain,
( in(X1,X2)
| ~ in(ordered_pair(X1,X3),X4)
| X4 != relation_dom_restriction(X5,X2)
| ~ relation(X4)
| ~ relation(X5) ),
inference(split_conjunct,[status(thm)],[i_0_700]) ).
fof(i_0_1638,lemma,
! [X3271,X3272,X3274,X3275] :
( ( in(X3274,powerset(the_carrier(X3271)))
| ~ in(X3274,esk356_2(X3271,X3272))
| ~ topological_space(X3271)
| ~ top_str(X3271)
| ~ element(X3272,powerset(powerset(the_carrier(X3271)))) )
& ( in(set_difference(cast_as_carrier_subset(X3271),X3274),X3272)
| ~ in(X3274,esk356_2(X3271,X3272))
| ~ topological_space(X3271)
| ~ top_str(X3271)
| ~ element(X3272,powerset(powerset(the_carrier(X3271)))) )
& ( ~ in(X3275,powerset(the_carrier(X3271)))
| ~ in(set_difference(cast_as_carrier_subset(X3271),X3275),X3272)
| in(X3275,esk356_2(X3271,X3272))
| ~ topological_space(X3271)
| ~ top_str(X3271)
| ~ element(X3272,powerset(powerset(the_carrier(X3271)))) ) ),
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)],[s1_xboole_0__e2_37_1_1__pre_topc__1])])])])])]) ).
fof(i_0_1639,lemma,
! [X3406,X3407,X3409] :
( ( element(esk408_2(X3406,X3407),powerset(powerset(the_carrier(X3406))))
| ~ topological_space(X3406)
| ~ top_str(X3406)
| ~ element(X3407,powerset(powerset(the_carrier(X3406)))) )
& ( ~ in(X3409,esk408_2(X3406,X3407))
| in(set_difference(cast_as_carrier_subset(X3406),X3409),X3407)
| ~ element(X3409,powerset(the_carrier(X3406)))
| ~ topological_space(X3406)
| ~ top_str(X3406)
| ~ element(X3407,powerset(powerset(the_carrier(X3406)))) )
& ( ~ in(set_difference(cast_as_carrier_subset(X3406),X3409),X3407)
| in(X3409,esk408_2(X3406,X3407))
| ~ element(X3409,powerset(the_carrier(X3406)))
| ~ topological_space(X3406)
| ~ top_str(X3406)
| ~ element(X3407,powerset(powerset(the_carrier(X3406)))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[s3_subset_1__e2_37_1_1__pre_topc])])])])]) ).
cnf(i_0_1640,plain,
( X1 = X2
| in(X1,X4)
| ~ in(ordered_pair(X1,X2),X3)
| X4 != fiber(X3,X2)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_703]) ).
cnf(i_0_1641,plain,
( in(X3,esk338_2(X5,X2))
| ~ in(X1,succ(X2))
| X1 != X3
| ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X5)
| esk334_2(X5,X2) != esk335_2(X5,X2)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_762]) ).
cnf(i_0_1642,plain,
( in(X1,omega)
| in(X2,esk249_1(X4))
| epred2_3(esk248_1(X4),esk247_1(X4),esk246_1(X4))
| ~ ordinal(X1)
| X2 != X1
| ~ in(X3,succ(X4))
| X3 != X2
| ~ ordinal(X4) ),
inference(split_conjunct,[status(thm)],[i_0_717]) ).
cnf(i_0_1643,plain,
( in(X4,esk242_2(X2,X3))
| ~ in(X1,cartesian_product2(X2,X3))
| X1 != X4
| ordered_pair(X5,X6) != X4
| ~ in(X5,X2)
| X6 != singleton(X5)
| esk236_1(X2) != esk237_1(X2) ),
inference(split_conjunct,[status(thm)],[i_0_715]) ).
cnf(i_0_1644,lemma,
( X1 = singleton(X2)
| in(esk185_1(X3),X3)
| ~ in(ordered_pair(X2,X1),esk188_1(X3)) ),
inference(split_conjunct,[status(thm)],[i_0_768]) ).
cnf(i_0_1645,lemma,
( X1 = singleton(X2)
| in(esk185_1(X3),X3)
| ~ in(ordered_pair(X2,X1),esk188_1(X3)) ),
inference(split_conjunct,[status(thm)],[i_0_768]) ).
cnf(i_0_1646,lemma,
( in(X1,X2)
| in(esk185_1(X2),X2)
| ~ in(ordered_pair(X1,X3),esk188_1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_768]) ).
cnf(i_0_1647,lemma,
( in(X1,X2)
| in(esk185_1(X2),X2)
| ~ in(ordered_pair(X1,X3),esk188_1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_768]) ).
cnf(i_0_1648,plain,
( in(X3,esk338_2(X5,X2))
| in(esk337_2(X5,X2),X5)
| ~ in(X1,succ(X2))
| X1 != X3
| ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X5)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_762]) ).
cnf(i_0_1649,plain,
( in(X3,esk338_2(X5,X2))
| in(esk336_2(X5,X2),X5)
| ~ in(X1,succ(X2))
| X1 != X3
| ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X5)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_762]) ).
cnf(i_0_1650,lemma,
( in(X2,esk349_1(X1))
| esk352_3(X1,X2,X3) != empty_set
| ~ ordinal(X3)
| X2 != X3
| ~ in(X2,succ(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_721]) ).
cnf(i_0_1651,lemma,
( in(esk439_3(X1,X2,X3),relation_dom(X2))
| X2 = relation_dom_restriction(X3,X1)
| relation_dom(X2) != set_intersection2(relation_dom(X3),X1)
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_741]) ).
fof(i_0_1652,lemma,
! [X3264,X3265,X3267,X3269,X3270] :
( ( in(X3267,powerset(the_carrier(X3264)))
| ~ in(X3267,esk354_2(X3264,X3265))
| ~ topological_space(X3264)
| ~ top_str(X3264)
| ~ element(X3265,powerset(the_carrier(X3264))) )
& ( element(esk355_3(X3264,X3265,X3267),powerset(the_carrier(X3264)))
| ~ in(X3267,esk354_2(X3264,X3265))
| ~ topological_space(X3264)
| ~ top_str(X3264)
| ~ element(X3265,powerset(the_carrier(X3264))) )
& ( esk355_3(X3264,X3265,X3267) = X3267
| ~ in(X3267,esk354_2(X3264,X3265))
| ~ topological_space(X3264)
| ~ top_str(X3264)
| ~ element(X3265,powerset(the_carrier(X3264))) )
& ( closed_subset(esk355_3(X3264,X3265,X3267),X3264)
| ~ in(X3267,esk354_2(X3264,X3265))
| ~ topological_space(X3264)
| ~ top_str(X3264)
| ~ element(X3265,powerset(the_carrier(X3264))) )
& ( subset(X3265,X3267)
| ~ in(X3267,esk354_2(X3264,X3265))
| ~ topological_space(X3264)
| ~ top_str(X3264)
| ~ element(X3265,powerset(the_carrier(X3264))) )
& ( ~ in(X3269,powerset(the_carrier(X3264)))
| ~ element(X3270,powerset(the_carrier(X3264)))
| X3270 != X3269
| ~ closed_subset(X3270,X3264)
| ~ subset(X3265,X3269)
| in(X3269,esk354_2(X3264,X3265))
| ~ topological_space(X3264)
| ~ top_str(X3264)
| ~ element(X3265,powerset(the_carrier(X3264))) ) ),
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)],[s1_xboole_0__e1_40__pre_topc__1])])])])])]) ).
cnf(i_0_1653,plain,
( in(X4,esk242_2(X2,X3))
| esk235_1(X2) = esk237_1(X2)
| ~ in(X1,cartesian_product2(X2,X3))
| X1 != X4
| ordered_pair(X5,X6) != X4
| ~ in(X5,X2)
| X6 != singleton(X5) ),
inference(split_conjunct,[status(thm)],[i_0_715]) ).
cnf(i_0_1654,plain,
( in(X4,esk242_2(X2,X3))
| esk235_1(X2) = esk236_1(X2)
| ~ in(X1,cartesian_product2(X2,X3))
| X1 != X4
| ordered_pair(X5,X6) != X4
| ~ in(X5,X2)
| X6 != singleton(X5) ),
inference(split_conjunct,[status(thm)],[i_0_715]) ).
cnf(i_0_1655,lemma,
( X1 = singleton(X2)
| ~ in(ordered_pair(X2,X1),esk188_1(X3))
| esk186_1(X3) != esk187_1(X3) ),
inference(split_conjunct,[status(thm)],[i_0_768]) ).
cnf(i_0_1656,lemma,
( in(X1,X2)
| ~ in(ordered_pair(X1,X3),esk188_1(X2))
| esk186_1(X2) != esk187_1(X2) ),
inference(split_conjunct,[status(thm)],[i_0_768]) ).
cnf(i_0_1657,lemma,
( in(X1,relation_dom(X2))
| ~ in(ordered_pair(X1,X3),X2)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_771]) ).
cnf(i_0_1658,plain,
( in(X3,esk338_2(X5,X2))
| ordinal(esk337_2(X5,X2))
| ~ in(X1,succ(X2))
| X1 != X3
| ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X5)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_762]) ).
cnf(i_0_1659,plain,
( in(X3,esk338_2(X5,X2))
| ordinal(esk336_2(X5,X2))
| ~ in(X1,succ(X2))
| X1 != X3
| ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X5)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_762]) ).
fof(i_0_1660,lemma,
! [X3920,X3921,X3922,X3923] :
( ( function(X3923)
| X3921 = empty_set
| ~ subset(X3921,X3922)
| ~ function(X3923)
| ~ quasi_total(X3923,X3920,X3921)
| ~ relation_of2_as_subset(X3923,X3920,X3921) )
& ( quasi_total(X3923,X3920,X3922)
| X3921 = empty_set
| ~ subset(X3921,X3922)
| ~ function(X3923)
| ~ quasi_total(X3923,X3920,X3921)
| ~ relation_of2_as_subset(X3923,X3920,X3921) )
& ( relation_of2_as_subset(X3923,X3920,X3922)
| X3921 = empty_set
| ~ subset(X3921,X3922)
| ~ function(X3923)
| ~ quasi_total(X3923,X3920,X3921)
| ~ relation_of2_as_subset(X3923,X3920,X3921) )
& ( function(X3923)
| X3920 != empty_set
| ~ subset(X3921,X3922)
| ~ function(X3923)
| ~ quasi_total(X3923,X3920,X3921)
| ~ relation_of2_as_subset(X3923,X3920,X3921) )
& ( quasi_total(X3923,X3920,X3922)
| X3920 != empty_set
| ~ subset(X3921,X3922)
| ~ function(X3923)
| ~ quasi_total(X3923,X3920,X3921)
| ~ relation_of2_as_subset(X3923,X3920,X3921) )
& ( relation_of2_as_subset(X3923,X3920,X3922)
| X3920 != empty_set
| ~ subset(X3921,X3922)
| ~ function(X3923)
| ~ quasi_total(X3923,X3920,X3921)
| ~ relation_of2_as_subset(X3923,X3920,X3921) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t9_funct_2])])]) ).
fof(i_0_1661,lemma,
! [X3611,X3612,X3613] :
( empty_carrier(X3611)
| ~ join_commutative(X3611)
| ~ join_semilatt_str(X3611)
| ~ element(X3612,the_carrier(X3611))
| ~ element(X3613,the_carrier(X3611))
| ~ below(X3611,X3612,X3613)
| ~ below(X3611,X3613,X3612)
| X3612 = X3613 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_772])])]) ).
fof(i_0_1662,lemma,
! [X3656,X3657,X3658] :
( ( ~ relstr_set_smaller(poset_of_lattice(X3657),X3656,X3658)
| latt_element_smaller(X3657,cast_to_el_of_lattice(X3657,X3658),X3656)
| ~ element(X3658,the_carrier(poset_of_lattice(X3657)))
| empty_carrier(X3657)
| ~ lattice(X3657)
| ~ latt_str(X3657) )
& ( ~ latt_element_smaller(X3657,cast_to_el_of_lattice(X3657,X3658),X3656)
| relstr_set_smaller(poset_of_lattice(X3657),X3656,X3658)
| ~ element(X3658,the_carrier(poset_of_lattice(X3657)))
| empty_carrier(X3657)
| ~ lattice(X3657)
| ~ latt_str(X3657) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_773])])])]) ).
fof(i_0_1663,lemma,
! [X3632,X3633,X3634] :
( ( ~ relstr_element_smaller(poset_of_lattice(X3633),X3632,X3634)
| latt_set_smaller(X3633,cast_to_el_of_lattice(X3633,X3634),X3632)
| ~ element(X3634,the_carrier(poset_of_lattice(X3633)))
| empty_carrier(X3633)
| ~ lattice(X3633)
| ~ latt_str(X3633) )
& ( ~ latt_set_smaller(X3633,cast_to_el_of_lattice(X3633,X3634),X3632)
| relstr_element_smaller(poset_of_lattice(X3633),X3632,X3634)
| ~ element(X3634,the_carrier(poset_of_lattice(X3633)))
| empty_carrier(X3633)
| ~ lattice(X3633)
| ~ latt_str(X3633) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_774])])])]) ).
cnf(i_0_1664,plain,
( in(X3,esk338_2(X5,X2))
| esk335_2(X5,X2) = esk337_2(X5,X2)
| ~ in(X1,succ(X2))
| X1 != X3
| ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X5)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_762]) ).
cnf(i_0_1665,plain,
( in(X3,esk338_2(X5,X2))
| esk334_2(X5,X2) = esk336_2(X5,X2)
| ~ in(X1,succ(X2))
| X1 != X3
| ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X5)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_762]) ).
cnf(i_0_1666,plain,
( in(X3,esk338_2(X5,X2))
| esk333_2(X5,X2) = esk335_2(X5,X2)
| ~ in(X1,succ(X2))
| X1 != X3
| ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X5)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_762]) ).
cnf(i_0_1667,plain,
( in(X3,esk338_2(X5,X2))
| esk333_2(X5,X2) = esk334_2(X5,X2)
| ~ in(X1,succ(X2))
| X1 != X3
| ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X5)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_762]) ).
fof(i_0_1668,lemma,
! [X3569,X3570] :
( ~ one_sorted_str(X3569)
| ~ element(X3570,powerset(the_carrier(X3569)))
| subset_difference(the_carrier(X3569),cast_as_carrier_subset(X3569),subset_difference(the_carrier(X3569),cast_as_carrier_subset(X3569),X3570)) = X3570 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t22_pre_topc])])]) ).
cnf(i_0_1669,plain,
( in(X1,X2)
| ~ in(ordered_pair(X1,X3),X4)
| X4 != identity_relation(X2)
| ~ relation(X4) ),
inference(split_conjunct,[status(thm)],[i_0_720]) ).
cnf(i_0_1670,plain,
( in(X1,X4)
| ~ in(ordered_pair(X1,X2),X3)
| X4 != relation_dom(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_729]) ).
cnf(i_0_1671,plain,
( in(X2,X4)
| ~ in(ordered_pair(X1,X2),X3)
| X4 != relation_rng(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_710]) ).
cnf(i_0_1672,lemma,
( in(X1,esk346_2(X2,X3))
| ~ in(X1,cartesian_product2(X2,X3))
| ordered_pair(X4,X5) != X1
| ~ in(X4,X2)
| X5 != singleton(X4) ),
inference(split_conjunct,[status(thm)],[i_0_722]) ).
cnf(i_0_1673,lemma,
( X1 = apply(X2,X3)
| ~ in(ordered_pair(X3,X1),X2)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_771]) ).
cnf(i_0_1674,plain,
( below(X2,X4,X1)
| empty_carrier(X2)
| empty_carrier(X2)
| ~ element(X1,the_carrier(X2))
| ~ latt_element_smaller(X2,X1,X3)
| X4 != join_of_latt_set(X2,X3)
| ~ element(X4,the_carrier(X2))
| ~ lattice(X2)
| ~ complete_latt_str(X2)
| ~ latt_str(X2)
| ~ latt_str(X2) ),
inference(split_conjunct,[status(thm)],[i_0_749]) ).
cnf(i_0_1675,lemma,
( in(X1,relation_rng(X2))
| ~ in(ordered_pair(X3,X1),X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_775]) ).
cnf(i_0_1676,lemma,
( in(X1,relation_field(X2))
| ~ in(ordered_pair(X1,X3),X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_776]) ).
cnf(i_0_1677,lemma,
( in(X1,relation_field(X2))
| ~ in(ordered_pair(X3,X1),X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_776]) ).
cnf(i_0_1678,lemma,
( in(X1,relation_dom(X2))
| ~ in(ordered_pair(X1,X3),X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_775]) ).
fof(i_0_1679,lemma,
! [X3601,X3602,X3603] :
( ~ antisymmetric_relstr(X3601)
| ~ rel_str(X3601)
| ~ element(X3602,the_carrier(X3601))
| ~ element(X3603,the_carrier(X3601))
| ~ related(X3601,X3602,X3603)
| ~ related(X3601,X3603,X3602)
| X3602 = X3603 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t25_orders_2])])]) ).
cnf(i_0_1680,lemma,
( in(ordered_pair(esk135_1(X1),esk134_1(X1)),X1)
| antisymmetric(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_743]) ).
cnf(i_0_1681,lemma,
( in(ordered_pair(esk134_1(X1),esk135_1(X1)),X1)
| antisymmetric(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_743]) ).
cnf(i_0_1682,lemma,
( in(ordered_pair(esk131_1(X1),esk132_1(X1)),X1)
| transitive(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_737]) ).
cnf(i_0_1683,lemma,
( in(ordered_pair(esk130_1(X1),esk131_1(X1)),X1)
| transitive(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_737]) ).
cnf(i_0_1684,lemma,
( being_limit_ordinal(X1)
| ~ in(succ(esk427_1(X1)),X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_777]) ).
fof(i_0_1685,lemma,
! [X3583,X3584,X3585] :
( empty_carrier(X3583)
| ~ meet_commutative(X3583)
| ~ meet_absorbing(X3583)
| ~ latt_str(X3583)
| ~ element(X3584,the_carrier(X3583))
| ~ element(X3585,the_carrier(X3583))
| below(X3583,meet_commut(X3583,X3584,X3585),X3584) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_778])])]) ).
fof(i_0_1686,plain,
! [X2683,X2684,X2685,X2687,X2688] :
( ( element(esk128_3(X2683,X2684,X2685),the_carrier(X2684))
| ~ in(X2683,a_2_3_lattice3(X2684,X2685))
| empty_carrier(X2684)
| ~ lattice(X2684)
| ~ complete_latt_str(X2684)
| ~ latt_str(X2684) )
& ( X2683 = esk128_3(X2683,X2684,X2685)
| ~ in(X2683,a_2_3_lattice3(X2684,X2685))
| empty_carrier(X2684)
| ~ lattice(X2684)
| ~ complete_latt_str(X2684)
| ~ latt_str(X2684) )
& ( latt_set_smaller(X2684,esk128_3(X2683,X2684,X2685),X2685)
| ~ in(X2683,a_2_3_lattice3(X2684,X2685))
| empty_carrier(X2684)
| ~ lattice(X2684)
| ~ complete_latt_str(X2684)
| ~ latt_str(X2684) )
& ( ~ element(X2688,the_carrier(X2684))
| X2683 != X2688
| ~ latt_set_smaller(X2684,X2688,X2687)
| in(X2683,a_2_3_lattice3(X2684,X2687))
| empty_carrier(X2684)
| ~ lattice(X2684)
| ~ complete_latt_str(X2684)
| ~ latt_str(X2684) ) ),
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)],[i_0_779])])])])])]) ).
fof(i_0_1687,lemma,
! [X3856,X3857,X3858,X3859] :
( ~ function(X3859)
| ~ quasi_total(X3859,X3856,X3857)
| ~ relation_of2_as_subset(X3859,X3856,X3857)
| ~ in(X3858,X3856)
| X3857 = empty_set
| in(apply(X3859,X3858),relation_rng(X3859)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_funct_2])]) ).
cnf(i_0_1688,lemma,
( in(ordered_pair(esk437_1(X1),esk438_1(X1)),X1)
| X1 = empty_set
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_780]) ).
cnf(i_0_1689,plain,
( in(ordered_pair(esk27_1(X1),esk29_1(X1)),X1)
| function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_745]) ).
cnf(i_0_1690,plain,
( in(ordered_pair(esk27_1(X1),esk28_1(X1)),X1)
| function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_745]) ).
cnf(i_0_1691,plain,
( X1 = X2
| ~ in(ordered_pair(X1,X2),X3)
| X3 != identity_relation(X4)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_720]) ).
fof(i_0_1692,plain,
! [X1874,X1875,X1876] :
( ( function(X1876)
| ~ function(X1876)
| ~ quasi_total(X1876,X1874,X1875)
| ~ relation_of2(X1876,X1874,X1875)
| empty(X1874)
| empty(X1875) )
& ( ~ empty(X1876)
| ~ function(X1876)
| ~ quasi_total(X1876,X1874,X1875)
| ~ relation_of2(X1876,X1874,X1875)
| empty(X1874)
| empty(X1875) )
& ( v1_partfun1(X1876,X1874,X1875)
| ~ function(X1876)
| ~ quasi_total(X1876,X1874,X1875)
| ~ relation_of2(X1876,X1874,X1875)
| empty(X1874)
| empty(X1875) )
& ( quasi_total(X1876,X1874,X1875)
| ~ function(X1876)
| ~ quasi_total(X1876,X1874,X1875)
| ~ relation_of2(X1876,X1874,X1875)
| empty(X1874)
| empty(X1875) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_781])])])]) ).
fof(i_0_1693,lemma,
! [X3648,X3649,X3650] :
( ( ~ latt_element_smaller(X3649,X3650,X3648)
| relstr_set_smaller(poset_of_lattice(X3649),X3648,cast_to_el_of_LattPOSet(X3649,X3650))
| ~ element(X3650,the_carrier(X3649))
| empty_carrier(X3649)
| ~ lattice(X3649)
| ~ latt_str(X3649) )
& ( ~ relstr_set_smaller(poset_of_lattice(X3649),X3648,cast_to_el_of_LattPOSet(X3649,X3650))
| latt_element_smaller(X3649,X3650,X3648)
| ~ element(X3650,the_carrier(X3649))
| empty_carrier(X3649)
| ~ lattice(X3649)
| ~ latt_str(X3649) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_782])])])]) ).
fof(i_0_1694,lemma,
! [X3623,X3624,X3625] :
( ( ~ latt_set_smaller(X3624,X3625,X3623)
| relstr_element_smaller(poset_of_lattice(X3624),X3623,cast_to_el_of_LattPOSet(X3624,X3625))
| ~ element(X3625,the_carrier(X3624))
| empty_carrier(X3624)
| ~ lattice(X3624)
| ~ latt_str(X3624) )
& ( ~ relstr_element_smaller(poset_of_lattice(X3624),X3623,cast_to_el_of_LattPOSet(X3624,X3625))
| latt_set_smaller(X3624,X3625,X3623)
| ~ element(X3625,the_carrier(X3624))
| empty_carrier(X3624)
| ~ lattice(X3624)
| ~ latt_str(X3624) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_783])])])]) ).
cnf(i_0_1695,plain,
( in(esk243_3(X1,X2,X3),cartesian_product2(X1,X2))
| esk241_1(X1) = singleton(esk240_1(X1))
| ~ in(X3,esk242_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_715]) ).
cnf(i_0_1696,plain,
( in(esk243_3(X1,X2,X3),cartesian_product2(X1,X2))
| esk239_1(X1) = singleton(esk238_1(X1))
| ~ in(X3,esk242_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_715]) ).
fof(i_0_1697,plain,
! [X2880,X2881,X2882] :
( ( ~ below_refl(X2880,X2881,X2882)
| below(X2880,X2881,X2882)
| empty_carrier(X2880)
| ~ meet_commutative(X2880)
| ~ meet_absorbing(X2880)
| ~ join_absorbing(X2880)
| ~ latt_str(X2880)
| ~ element(X2881,the_carrier(X2880))
| ~ element(X2882,the_carrier(X2880)) )
& ( ~ below(X2880,X2881,X2882)
| below_refl(X2880,X2881,X2882)
| empty_carrier(X2880)
| ~ meet_commutative(X2880)
| ~ meet_absorbing(X2880)
| ~ join_absorbing(X2880)
| ~ latt_str(X2880)
| ~ element(X2881,the_carrier(X2880))
| ~ element(X2882,the_carrier(X2880)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_784])])]) ).
fof(i_0_1698,plain,
! [X1871,X1872,X1873] :
( ( function(X1873)
| ~ function(X1873)
| ~ quasi_total(X1873,X1871,X1872)
| ~ relation_of2(X1873,X1871,X1872)
| empty(X1872) )
& ( v1_partfun1(X1873,X1871,X1872)
| ~ function(X1873)
| ~ quasi_total(X1873,X1871,X1872)
| ~ relation_of2(X1873,X1871,X1872)
| empty(X1872) )
& ( quasi_total(X1873,X1871,X1872)
| ~ function(X1873)
| ~ quasi_total(X1873,X1871,X1872)
| ~ relation_of2(X1873,X1871,X1872)
| empty(X1872) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_785])])])]) ).
cnf(i_0_1699,plain,
( esk243_3(X1,X2,X3) = X3
| ordered_pair(esk240_1(X1),esk241_1(X1)) = esk237_1(X1)
| ~ in(X3,esk242_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_715]) ).
cnf(i_0_1700,plain,
( esk243_3(X1,X2,X3) = X3
| ordered_pair(esk238_1(X1),esk239_1(X1)) = esk236_1(X1)
| ~ in(X3,esk242_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_715]) ).
fof(i_0_1701,plain,
! [X2677,X2678,X2679,X2681,X2682] :
( ( element(esk127_3(X2677,X2678,X2679),the_carrier(X2678))
| ~ in(X2677,a_2_2_lattice3(X2678,X2679))
| empty_carrier(X2678)
| ~ latt_str(X2678) )
& ( X2677 = esk127_3(X2677,X2678,X2679)
| ~ in(X2677,a_2_2_lattice3(X2678,X2679))
| empty_carrier(X2678)
| ~ latt_str(X2678) )
& ( latt_set_smaller(X2678,esk127_3(X2677,X2678,X2679),X2679)
| ~ in(X2677,a_2_2_lattice3(X2678,X2679))
| empty_carrier(X2678)
| ~ latt_str(X2678) )
& ( ~ element(X2682,the_carrier(X2678))
| X2677 != X2682
| ~ latt_set_smaller(X2678,X2682,X2681)
| in(X2677,a_2_2_lattice3(X2678,X2681))
| empty_carrier(X2678)
| ~ latt_str(X2678) ) ),
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)],[i_0_786])])])])])]) ).
fof(i_0_1702,plain,
! [X1838,X1839,X1840] :
( ( function(X1840)
| ~ function(X1840)
| ~ v1_partfun1(X1840,X1838,X1839)
| ~ relation_of2(X1840,X1838,X1839) )
& ( quasi_total(X1840,X1838,X1839)
| ~ function(X1840)
| ~ v1_partfun1(X1840,X1838,X1839)
| ~ relation_of2(X1840,X1838,X1839) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_funct_2])])]) ).
fof(i_0_1703,plain,
! [X2214,X2215,X2218] :
( ( element(esk68_2(X2214,X2215),powerset(powerset(the_carrier(X2214))))
| ~ is_a_cover_of_carrier(X2214,X2215)
| ~ open_subsets(X2215,X2214)
| ~ element(X2215,powerset(powerset(the_carrier(X2214))))
| ~ compact_top_space(X2214)
| ~ top_str(X2214) )
& ( subset(esk68_2(X2214,X2215),X2215)
| ~ is_a_cover_of_carrier(X2214,X2215)
| ~ open_subsets(X2215,X2214)
| ~ element(X2215,powerset(powerset(the_carrier(X2214))))
| ~ compact_top_space(X2214)
| ~ top_str(X2214) )
& ( is_a_cover_of_carrier(X2214,esk68_2(X2214,X2215))
| ~ is_a_cover_of_carrier(X2214,X2215)
| ~ open_subsets(X2215,X2214)
| ~ element(X2215,powerset(powerset(the_carrier(X2214))))
| ~ compact_top_space(X2214)
| ~ top_str(X2214) )
& ( finite(esk68_2(X2214,X2215))
| ~ is_a_cover_of_carrier(X2214,X2215)
| ~ open_subsets(X2215,X2214)
| ~ element(X2215,powerset(powerset(the_carrier(X2214))))
| ~ compact_top_space(X2214)
| ~ top_str(X2214) )
& ( element(esk69_1(X2214),powerset(powerset(the_carrier(X2214))))
| compact_top_space(X2214)
| ~ top_str(X2214) )
& ( is_a_cover_of_carrier(X2214,esk69_1(X2214))
| compact_top_space(X2214)
| ~ top_str(X2214) )
& ( open_subsets(esk69_1(X2214),X2214)
| compact_top_space(X2214)
| ~ top_str(X2214) )
& ( ~ element(X2218,powerset(powerset(the_carrier(X2214))))
| ~ subset(X2218,esk69_1(X2214))
| ~ is_a_cover_of_carrier(X2214,X2218)
| ~ finite(X2218)
| compact_top_space(X2214)
| ~ top_str(X2214) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_compts_1])])])])]) ).
fof(i_0_1704,plain,
! [X2032,X2033,X2034] :
( ( ~ quasi_total(X2034,X2032,X2033)
| X2032 = relation_dom_as_subset(X2032,X2033,X2034)
| X2033 = empty_set
| ~ relation_of2_as_subset(X2034,X2032,X2033) )
& ( X2032 != relation_dom_as_subset(X2032,X2033,X2034)
| quasi_total(X2034,X2032,X2033)
| X2033 = empty_set
| ~ relation_of2_as_subset(X2034,X2032,X2033) )
& ( ~ quasi_total(X2034,X2032,X2033)
| X2032 = relation_dom_as_subset(X2032,X2033,X2034)
| X2032 != empty_set
| ~ relation_of2_as_subset(X2034,X2032,X2033) )
& ( X2032 != relation_dom_as_subset(X2032,X2033,X2034)
| quasi_total(X2034,X2032,X2033)
| X2032 != empty_set
| ~ relation_of2_as_subset(X2034,X2032,X2033) )
& ( ~ quasi_total(X2034,X2032,X2033)
| X2034 = empty_set
| X2032 = empty_set
| X2033 != empty_set
| ~ relation_of2_as_subset(X2034,X2032,X2033) )
& ( X2034 != empty_set
| quasi_total(X2034,X2032,X2033)
| X2032 = empty_set
| X2033 != empty_set
| ~ relation_of2_as_subset(X2034,X2032,X2033) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_funct_2])])]) ).
cnf(i_0_1705,plain,
( in(esk250_2(X1,X2),succ(X1))
| epred2_3(esk248_1(X1),esk247_1(X1),esk246_1(X1))
| ~ in(X2,esk249_1(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_717]) ).
fof(i_0_1706,plain,
! [X2006,X2007,X2008] :
( ( ~ point_neighbourhood(X2008,X2006,X2007)
| in(X2007,interior(X2006,X2008))
| ~ element(X2008,powerset(the_carrier(X2006)))
| ~ element(X2007,the_carrier(X2006))
| empty_carrier(X2006)
| ~ topological_space(X2006)
| ~ top_str(X2006) )
& ( ~ in(X2007,interior(X2006,X2008))
| point_neighbourhood(X2008,X2006,X2007)
| ~ element(X2008,powerset(the_carrier(X2006)))
| ~ element(X2007,the_carrier(X2006))
| empty_carrier(X2006)
| ~ topological_space(X2006)
| ~ top_str(X2006) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_787])])])]) ).
cnf(i_0_1707,plain,
( in(ordered_pair(X1,X2),X3)
| ~ subset(X1,X2)
| ~ in(X1,X4)
| ~ in(X2,X4)
| X3 != inclusion_relation(X4)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_719]) ).
cnf(i_0_1708,lemma,
( in(ordered_pair(X1,X3),esk188_1(X2))
| esk187_1(X2) = singleton(esk185_1(X2))
| ~ in(X1,X2)
| X3 != singleton(X1) ),
inference(split_conjunct,[status(thm)],[i_0_768]) ).
cnf(i_0_1709,lemma,
( in(ordered_pair(X1,X3),esk188_1(X2))
| esk186_1(X2) = singleton(esk185_1(X2))
| ~ in(X1,X2)
| X3 != singleton(X1) ),
inference(split_conjunct,[status(thm)],[i_0_768]) ).
cnf(i_0_1710,lemma,
( in(X1,esk372_2(X4,X2))
| ~ in(X1,succ(X2))
| ~ ordinal(X3)
| X1 != X3
| ~ in(X3,X4)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_788]) ).
fof(i_0_1711,plain,
! [X2883,X2884,X2885] :
( ( ~ related_reflexive(X2883,X2884,X2885)
| related(X2883,X2884,X2885)
| empty_carrier(X2883)
| ~ reflexive_relstr(X2883)
| ~ rel_str(X2883)
| ~ element(X2884,the_carrier(X2883))
| ~ element(X2885,the_carrier(X2883)) )
& ( ~ related(X2883,X2884,X2885)
| related_reflexive(X2883,X2884,X2885)
| empty_carrier(X2883)
| ~ reflexive_relstr(X2883)
| ~ rel_str(X2883)
| ~ element(X2884,the_carrier(X2883))
| ~ element(X2885,the_carrier(X2883)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_789])])]) ).
fof(i_0_1712,plain,
! [X2633,X2634] :
( ( strict_rel_str(rel_str_of(X2633,X2634))
| ~ reflexive(X2634)
| ~ antisymmetric(X2634)
| ~ transitive(X2634)
| ~ v1_partfun1(X2634,X2633,X2633)
| ~ relation_of2(X2634,X2633,X2633) )
& ( reflexive_relstr(rel_str_of(X2633,X2634))
| ~ reflexive(X2634)
| ~ antisymmetric(X2634)
| ~ transitive(X2634)
| ~ v1_partfun1(X2634,X2633,X2633)
| ~ relation_of2(X2634,X2633,X2633) )
& ( transitive_relstr(rel_str_of(X2633,X2634))
| ~ reflexive(X2634)
| ~ antisymmetric(X2634)
| ~ transitive(X2634)
| ~ v1_partfun1(X2634,X2633,X2633)
| ~ relation_of2(X2634,X2633,X2633) )
& ( antisymmetric_relstr(rel_str_of(X2633,X2634))
| ~ reflexive(X2634)
| ~ antisymmetric(X2634)
| ~ transitive(X2634)
| ~ v1_partfun1(X2634,X2633,X2633)
| ~ relation_of2(X2634,X2633,X2633) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc3_orders_2])])]) ).
fof(i_0_1713,lemma,
! [X3566,X3567,X3568] :
( ~ relation(X3567)
| ~ function(X3567)
| ~ relation(X3568)
| ~ function(X3568)
| ~ in(X3566,relation_dom(relation_composition(X3568,X3567)))
| apply(relation_composition(X3568,X3567),X3566) = apply(X3567,apply(X3568,X3566)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t22_funct_1])])]) ).
cnf(i_0_1714,plain,
( X1 = X3
| X1 != pair_first(X2)
| X2 != ordered_pair(X3,X4)
| X2 != ordered_pair(X5,X6) ),
inference(split_conjunct,[status(thm)],[i_0_754]) ).
cnf(i_0_1715,plain,
( X1 = X4
| X1 != pair_second(X2)
| X2 != ordered_pair(X3,X4)
| X2 != ordered_pair(X5,X6) ),
inference(split_conjunct,[status(thm)],[i_0_753]) ).
fof(i_0_1716,lemma,
! [X3735,X3736] :
( ( element(esk429_2(X3735,X3736),powerset(the_carrier(X3735)))
| closed_subset(meet_of_subsets(the_carrier(X3735),X3736),X3735)
| ~ element(X3736,powerset(powerset(the_carrier(X3735))))
| ~ topological_space(X3735)
| ~ top_str(X3735) )
& ( in(esk429_2(X3735,X3736),X3736)
| closed_subset(meet_of_subsets(the_carrier(X3735),X3736),X3735)
| ~ element(X3736,powerset(powerset(the_carrier(X3735))))
| ~ topological_space(X3735)
| ~ top_str(X3735) )
& ( ~ closed_subset(esk429_2(X3735,X3736),X3735)
| closed_subset(meet_of_subsets(the_carrier(X3735),X3736),X3735)
| ~ element(X3736,powerset(powerset(the_carrier(X3735))))
| ~ topological_space(X3735)
| ~ top_str(X3735) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t44_pre_topc])])])])]) ).
fof(i_0_1717,plain,
! [X2221,X2222,X2223] :
( ( ~ below(X2221,X2222,X2223)
| join(X2221,X2222,X2223) = X2223
| ~ element(X2223,the_carrier(X2221))
| ~ element(X2222,the_carrier(X2221))
| empty_carrier(X2221)
| ~ join_semilatt_str(X2221) )
& ( join(X2221,X2222,X2223) != X2223
| below(X2221,X2222,X2223)
| ~ element(X2223,the_carrier(X2221))
| ~ element(X2222,the_carrier(X2221))
| empty_carrier(X2221)
| ~ join_semilatt_str(X2221) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_790])])])]) ).
cnf(i_0_1718,lemma,
( in(ordered_pair(X1,X3),esk188_1(X2))
| in(esk185_1(X2),X2)
| ~ in(X1,X2)
| X3 != singleton(X1) ),
inference(split_conjunct,[status(thm)],[i_0_768]) ).
cnf(i_0_1719,lemma,
( in(ordered_pair(X1,X3),esk188_1(X2))
| in(esk185_1(X2),X2)
| ~ in(X1,X2)
| X3 != singleton(X1) ),
inference(split_conjunct,[status(thm)],[i_0_768]) ).
cnf(i_0_1720,lemma,
( in(ordered_pair(X1,X3),cartesian_product2(X2,X4))
| ~ in(X1,X2)
| ~ in(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_769]) ).
cnf(i_0_1721,lemma,
( in(ordered_pair(X1,X3),cartesian_product2(X2,X4))
| ~ in(X1,X2)
| ~ in(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_770]) ).
cnf(i_0_1722,plain,
( in(esk244_3(X1,X2,X3),X1)
| esk241_1(X1) = singleton(esk240_1(X1))
| ~ in(X3,esk242_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_715]) ).
cnf(i_0_1723,plain,
( in(esk244_3(X1,X2,X3),X1)
| esk239_1(X1) = singleton(esk238_1(X1))
| ~ in(X3,esk242_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_715]) ).
fof(i_0_1724,plain,
! [X2077,X2078,X2079,X2080,X2081,X2083,X2086,X2087,X2088,X2089] :
( ( ~ in(X2079,X2078)
| ~ in(X2080,X2077)
| in(X2079,X2080)
| X2078 != set_meet(X2077)
| X2077 = empty_set )
& ( in(esk41_3(X2077,X2078,X2081),X2077)
| in(X2081,X2078)
| X2078 != set_meet(X2077)
| X2077 = empty_set )
& ( ~ in(X2081,esk41_3(X2077,X2078,X2081))
| in(X2081,X2078)
| X2078 != set_meet(X2077)
| X2077 = empty_set )
& ( in(esk43_2(X2077,X2083),X2077)
| ~ in(esk42_2(X2077,X2083),X2083)
| X2083 = set_meet(X2077)
| X2077 = empty_set )
& ( ~ in(esk42_2(X2077,X2083),esk43_2(X2077,X2083))
| ~ in(esk42_2(X2077,X2083),X2083)
| X2083 = set_meet(X2077)
| X2077 = empty_set )
& ( in(esk42_2(X2077,X2083),X2083)
| ~ in(X2086,X2077)
| in(esk42_2(X2077,X2083),X2086)
| X2083 = set_meet(X2077)
| X2077 = empty_set )
& ( X2088 != set_meet(X2087)
| X2088 = empty_set
| X2087 != empty_set )
& ( X2089 != empty_set
| X2089 = set_meet(X2087)
| X2087 != 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)],[d1_setfam_1])])])])])]) ).
cnf(i_0_1725,lemma,
( in(ordered_pair(X1,X3),X2)
| ~ in(X1,relation_dom(X2))
| X3 != apply(X2,X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_771]) ).
cnf(i_0_1726,plain,
( in(ordered_pair(X3,X1),X2)
| X1 != apply(X2,X3)
| ~ in(X3,relation_dom(X2))
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_767]) ).
fof(i_0_1727,plain,
! [X2497,X2498,X2499] :
( ~ relation_of2(X2499,X2497,X2498)
| element(relation_rng_as_subset(X2497,X2498,X2499),powerset(X2498)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k5_relset_1])]) ).
fof(i_0_1728,plain,
! [X2486,X2487,X2488] :
( ~ relation_of2(X2488,X2486,X2487)
| element(relation_dom_as_subset(X2486,X2487,X2488),powerset(X2486)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k4_relset_1])]) ).
fof(i_0_1729,lemma,
! [X3638,X3639,X3640] :
( ( ~ below(boole_lattice(X3638),X3639,X3640)
| subset(X3639,X3640)
| ~ element(X3640,the_carrier(boole_lattice(X3638)))
| ~ element(X3639,the_carrier(boole_lattice(X3638))) )
& ( ~ subset(X3639,X3640)
| below(boole_lattice(X3638),X3639,X3640)
| ~ element(X3640,the_carrier(boole_lattice(X3638)))
| ~ element(X3639,the_carrier(boole_lattice(X3638))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_lattice3])])])]) ).
cnf(i_0_1730,plain,
( in(X1,omega)
| in(X2,esk249_1(X4))
| ~ ordinal(X1)
| X2 != X1
| ~ in(X3,succ(X4))
| X3 != X2
| esk247_1(X4) != esk248_1(X4)
| ~ ordinal(X4) ),
inference(split_conjunct,[status(thm)],[i_0_717]) ).
cnf(i_0_1731,plain,
( apply_binary(X1,X2,X3) = apply(X1,ordered_pair(X2,X3))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_791]) ).
fof(i_0_1732,plain,
! [X2482,X2483,X2484] :
( empty_carrier(X2482)
| ~ meet_commutative(X2482)
| ~ meet_semilatt_str(X2482)
| ~ element(X2483,the_carrier(X2482))
| ~ element(X2484,the_carrier(X2482))
| element(meet_commut(X2482,X2483,X2484),the_carrier(X2482)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_792])]) ).
fof(i_0_1733,plain,
! [X2475,X2476,X2477] :
( empty_carrier(X2475)
| ~ join_commutative(X2475)
| ~ join_semilatt_str(X2475)
| ~ element(X2476,the_carrier(X2475))
| ~ element(X2477,the_carrier(X2475))
| element(join_commut(X2475,X2476,X2477),the_carrier(X2475)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_793])]) ).
cnf(i_0_1734,plain,
~ empty(ordered_pair(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_794]) ).
cnf(i_0_1735,lemma,
( in(ordered_pair(X1,X3),esk188_1(X2))
| ~ in(X1,X2)
| X3 != singleton(X1)
| esk186_1(X2) != esk187_1(X2) ),
inference(split_conjunct,[status(thm)],[i_0_768]) ).
cnf(i_0_1736,lemma,
( X1 = X2
| ordered_pair(X1,X3) != ordered_pair(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_795]) ).
cnf(i_0_1737,lemma,
( X1 = X2
| ordered_pair(X3,X1) != ordered_pair(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_795]) ).
fof(i_0_1738,plain,
! [X2179,X2180,X2181] :
( ( ~ closed_subsets(X2180,X2179)
| ~ element(X2181,powerset(the_carrier(X2179)))
| ~ in(X2181,X2180)
| closed_subset(X2181,X2179)
| ~ element(X2180,powerset(powerset(the_carrier(X2179))))
| ~ top_str(X2179) )
& ( element(esk59_2(X2179,X2180),powerset(the_carrier(X2179)))
| closed_subsets(X2180,X2179)
| ~ element(X2180,powerset(powerset(the_carrier(X2179))))
| ~ top_str(X2179) )
& ( in(esk59_2(X2179,X2180),X2180)
| closed_subsets(X2180,X2179)
| ~ element(X2180,powerset(powerset(the_carrier(X2179))))
| ~ top_str(X2179) )
& ( ~ closed_subset(esk59_2(X2179,X2180),X2179)
| closed_subsets(X2180,X2179)
| ~ element(X2180,powerset(powerset(the_carrier(X2179))))
| ~ top_str(X2179) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d2_tops_2])])])])]) ).
fof(i_0_1739,plain,
! [X2100,X2101,X2102] :
( ( ~ open_subsets(X2101,X2100)
| ~ element(X2102,powerset(the_carrier(X2100)))
| ~ in(X2102,X2101)
| open_subset(X2102,X2100)
| ~ element(X2101,powerset(powerset(the_carrier(X2100))))
| ~ top_str(X2100) )
& ( element(esk45_2(X2100,X2101),powerset(the_carrier(X2100)))
| open_subsets(X2101,X2100)
| ~ element(X2101,powerset(powerset(the_carrier(X2100))))
| ~ top_str(X2100) )
& ( in(esk45_2(X2100,X2101),X2101)
| open_subsets(X2101,X2100)
| ~ element(X2101,powerset(powerset(the_carrier(X2100))))
| ~ top_str(X2100) )
& ( ~ open_subset(esk45_2(X2100,X2101),X2100)
| open_subsets(X2101,X2100)
| ~ element(X2101,powerset(powerset(the_carrier(X2100))))
| ~ top_str(X2100) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_tops_2])])])])]) ).
fof(i_0_1740,lemma,
! [X3552,X3553,X3554] :
( ( in(X3552,relation_dom(X3554))
| ~ in(X3552,relation_dom(relation_composition(X3554,X3553)))
| ~ relation(X3554)
| ~ function(X3554)
| ~ relation(X3553)
| ~ function(X3553) )
& ( in(apply(X3554,X3552),relation_dom(X3553))
| ~ in(X3552,relation_dom(relation_composition(X3554,X3553)))
| ~ relation(X3554)
| ~ function(X3554)
| ~ relation(X3553)
| ~ function(X3553) )
& ( ~ in(X3552,relation_dom(X3554))
| ~ in(apply(X3554,X3552),relation_dom(X3553))
| in(X3552,relation_dom(relation_composition(X3554,X3553)))
| ~ relation(X3554)
| ~ function(X3554)
| ~ relation(X3553)
| ~ function(X3553) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t21_funct_1])])])]) ).
fof(i_0_1741,plain,
! [X2451,X2452,X2453] :
( empty_carrier(X2451)
| ~ join_semilatt_str(X2451)
| ~ element(X2452,the_carrier(X2451))
| ~ element(X2453,the_carrier(X2451))
| element(join(X2451,X2452,X2453),the_carrier(X2451)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_796])]) ).
fof(i_0_1742,plain,
! [X2467,X2468,X2469] :
( empty_carrier(X2467)
| ~ meet_semilatt_str(X2467)
| ~ element(X2468,the_carrier(X2467))
| ~ element(X2469,the_carrier(X2467))
| element(meet(X2467,X2468,X2469),the_carrier(X2467)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_797])]) ).
cnf(i_0_1743,lemma,
( meet(boole_lattice(X1),X2,X3) = set_intersection2(X2,X3)
| ~ element(X3,the_carrier(boole_lattice(X1)))
| ~ element(X2,the_carrier(boole_lattice(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_798]) ).
fof(i_0_1744,lemma,
! [X3756,X3757,X3759] :
( ( element(esk431_2(X3756,X3757),powerset(powerset(the_carrier(X3756))))
| ~ element(X3757,powerset(the_carrier(X3756)))
| ~ topological_space(X3756)
| ~ top_str(X3756) )
& ( closed_subset(X3759,X3756)
| ~ in(X3759,esk431_2(X3756,X3757))
| ~ element(X3759,powerset(the_carrier(X3756)))
| ~ element(X3757,powerset(the_carrier(X3756)))
| ~ topological_space(X3756)
| ~ top_str(X3756) )
& ( subset(X3757,X3759)
| ~ in(X3759,esk431_2(X3756,X3757))
| ~ element(X3759,powerset(the_carrier(X3756)))
| ~ element(X3757,powerset(the_carrier(X3756)))
| ~ topological_space(X3756)
| ~ top_str(X3756) )
& ( ~ closed_subset(X3759,X3756)
| ~ subset(X3757,X3759)
| in(X3759,esk431_2(X3756,X3757))
| ~ element(X3759,powerset(the_carrier(X3756)))
| ~ element(X3757,powerset(the_carrier(X3756)))
| ~ topological_space(X3756)
| ~ top_str(X3756) )
& ( topstr_closure(X3756,X3757) = meet_of_subsets(the_carrier(X3756),esk431_2(X3756,X3757))
| ~ element(X3757,powerset(the_carrier(X3756)))
| ~ topological_space(X3756)
| ~ top_str(X3756) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t46_pre_topc])])])])]) ).
fof(i_0_1745,lemma,
! [X3827,X3828,X3829] :
( empty_carrier(X3827)
| ~ topological_space(X3827)
| ~ top_str(X3827)
| ~ element(X3828,powerset(the_carrier(X3827)))
| ~ element(X3829,the_carrier(X3827))
| ~ open_subset(X3828,X3827)
| ~ in(X3829,X3828)
| point_neighbourhood(X3828,X3827,X3829) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_799])])]) ).
fof(i_0_1746,lemma,
! [X2750,X2751,X2752] :
( ( ~ in(X2752,subset_complement(the_carrier(X2750),X2751))
| ~ in(X2752,X2751)
| ~ element(X2752,the_carrier(X2750))
| ~ element(X2751,powerset(the_carrier(X2750)))
| empty_carrier(X2750)
| ~ one_sorted_str(X2750) )
& ( in(X2752,X2751)
| in(X2752,subset_complement(the_carrier(X2750),X2751))
| ~ element(X2752,the_carrier(X2750))
| ~ element(X2751,powerset(the_carrier(X2750)))
| empty_carrier(X2750)
| ~ one_sorted_str(X2750) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_800])])])]) ).
cnf(i_0_1747,plain,
( in(ordered_pair(X1,X2),X3)
| ~ in(X1,X4)
| X4 != fiber(X3,X2)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_703]) ).
cnf(i_0_1748,plain,
( in(ordered_pair(X3,X3),X1)
| ~ is_reflexive_in(X1,X2)
| ~ in(X3,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_725]) ).
cnf(i_0_1749,lemma,
( in(X1,omega)
| in(X2,esk349_1(X3))
| ~ ordinal(X1)
| X2 != X1
| ~ in(X2,succ(X3))
| ~ ordinal(X3) ),
inference(split_conjunct,[status(thm)],[i_0_721]) ).
fof(i_0_1750,plain,
! [X2098,X2099] :
( ~ top_str(X2098)
| ~ element(X2099,powerset(the_carrier(X2098)))
| interior(X2098,X2099) = subset_complement(the_carrier(X2098),topstr_closure(X2098,subset_complement(the_carrier(X2098),X2099))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_tops_1])])]) ).
fof(i_0_1751,lemma,
! [X3506,X3507] :
( ( ~ closed_subsets(X3507,X3506)
| open_subsets(complements_of_subsets(the_carrier(X3506),X3507),X3506)
| ~ element(X3507,powerset(powerset(the_carrier(X3506))))
| ~ top_str(X3506) )
& ( ~ open_subsets(complements_of_subsets(the_carrier(X3506),X3507),X3506)
| closed_subsets(X3507,X3506)
| ~ element(X3507,powerset(powerset(the_carrier(X3506))))
| ~ top_str(X3506) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t16_tops_2])])])]) ).
fof(i_0_1752,lemma,
! [X3520,X3521] :
( ( ~ open_subsets(X3521,X3520)
| closed_subsets(complements_of_subsets(the_carrier(X3520),X3521),X3520)
| ~ element(X3521,powerset(powerset(the_carrier(X3520))))
| ~ top_str(X3520) )
& ( ~ closed_subsets(complements_of_subsets(the_carrier(X3520),X3521),X3520)
| open_subsets(X3521,X3520)
| ~ element(X3521,powerset(powerset(the_carrier(X3520))))
| ~ top_str(X3520) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t17_tops_2])])])]) ).
cnf(i_0_1753,lemma,
( subset(set_intersection2(X1,X3),set_intersection2(X2,X3))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_801]) ).
fof(i_0_1754,plain,
! [X2843,X2844,X2845] :
( empty_carrier(X2843)
| ~ join_commutative(X2843)
| ~ join_semilatt_str(X2843)
| ~ element(X2844,the_carrier(X2843))
| ~ element(X2845,the_carrier(X2843))
| join_commut(X2843,X2844,X2845) = join(X2843,X2844,X2845) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_802])]) ).
fof(i_0_1755,plain,
! [X2846,X2847,X2848] :
( empty_carrier(X2846)
| ~ meet_commutative(X2846)
| ~ meet_semilatt_str(X2846)
| ~ element(X2847,the_carrier(X2846))
| ~ element(X2848,the_carrier(X2846))
| meet_commut(X2846,X2847,X2848) = meet(X2846,X2847,X2848) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_803])]) ).
fof(i_0_1756,plain,
! [X1886,X1887,X1888] :
( empty_carrier(X1886)
| ~ meet_commutative(X1886)
| ~ meet_semilatt_str(X1886)
| ~ element(X1887,the_carrier(X1886))
| ~ element(X1888,the_carrier(X1886))
| meet_commut(X1886,X1887,X1888) = meet_commut(X1886,X1888,X1887) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_804])]) ).
fof(i_0_1757,plain,
! [X1881,X1882,X1883] :
( empty_carrier(X1881)
| ~ join_commutative(X1881)
| ~ join_semilatt_str(X1881)
| ~ element(X1882,the_carrier(X1881))
| ~ element(X1883,the_carrier(X1881))
| join_commut(X1881,X1882,X1883) = join_commut(X1881,X1883,X1882) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_805])]) ).
fof(i_0_1758,plain,
! [X2511,X2512,X2513] :
( ~ element(X2512,powerset(X2511))
| ~ element(X2513,powerset(X2511))
| element(subset_difference(X2511,X2512,X2513),powerset(X2511)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k6_subset_1])]) ).
fof(i_0_1759,plain,
! [X2502,X2503,X2504] :
( ~ element(X2503,powerset(X2502))
| ~ element(X2504,powerset(X2502))
| element(subset_intersection2(X2502,X2503,X2504),powerset(X2502)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k5_subset_1])]) ).
fof(i_0_1760,plain,
! [X2489,X2490,X2491] :
( ~ element(X2490,powerset(X2489))
| ~ element(X2491,powerset(X2489))
| element(subset_union2(X2489,X2490,X2491),powerset(X2489)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k4_subset_1])]) ).
cnf(i_0_1761,lemma,
( in(ordered_pair(X2,X2),X1)
| ~ reflexive(X1)
| ~ in(X2,relation_field(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_751]) ).
cnf(i_0_1762,plain,
( in(X5,X6)
| ~ in(X1,X2)
| ~ in(X3,X4)
| X5 != ordered_pair(X1,X3)
| X6 != cartesian_product2(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_702]) ).
cnf(i_0_1763,plain,
( in(ordered_pair(X1,X3),X4)
| ~ in(X1,X2)
| X1 != X3
| X4 != identity_relation(X2)
| ~ relation(X4) ),
inference(split_conjunct,[status(thm)],[i_0_720]) ).
fof(i_0_1764,lemma,
! [X3865,X3866,X3867] :
( ~ relation(X3867)
| ~ function(X3867)
| ~ in(X3866,relation_dom(relation_dom_restriction(X3867,X3865)))
| apply(relation_dom_restriction(X3867,X3865),X3866) = apply(X3867,X3866) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t70_funct_1])]) ).
fof(i_0_1765,lemma,
! [X3459,X3460] :
( ( ~ compact_top_space(X3459)
| ~ element(X3460,powerset(powerset(the_carrier(X3459))))
| ~ centered(X3460)
| ~ closed_subsets(X3460,X3459)
| meet_of_subsets(the_carrier(X3459),X3460) != empty_set
| empty_carrier(X3459)
| ~ topological_space(X3459)
| ~ top_str(X3459) )
& ( element(esk410_1(X3459),powerset(powerset(the_carrier(X3459))))
| compact_top_space(X3459)
| empty_carrier(X3459)
| ~ topological_space(X3459)
| ~ top_str(X3459) )
& ( centered(esk410_1(X3459))
| compact_top_space(X3459)
| empty_carrier(X3459)
| ~ topological_space(X3459)
| ~ top_str(X3459) )
& ( closed_subsets(esk410_1(X3459),X3459)
| compact_top_space(X3459)
| empty_carrier(X3459)
| ~ topological_space(X3459)
| ~ top_str(X3459) )
& ( meet_of_subsets(the_carrier(X3459),esk410_1(X3459)) = empty_set
| compact_top_space(X3459)
| empty_carrier(X3459)
| ~ topological_space(X3459)
| ~ top_str(X3459) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_806])])])])]) ).
fof(i_0_1766,lemma,
! [X3776,X3777,X3778] :
( ~ relation(X3776)
| ~ relation(X3777)
| ~ relation(X3778)
| ~ function(X3778)
| ~ relation_isomorphism(X3776,X3777,X3778)
| relation_isomorphism(X3777,X3776,function_inverse(X3778)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t49_wellord1])])]) ).
cnf(i_0_1767,lemma,
( in(X1,X2)
| ~ ordinal_subset(succ(X1),X2)
| ~ ordinal(X2)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_807]) ).
fof(i_0_1768,plain,
! [X1892,X1893,X1894] :
( ~ element(X1893,powerset(X1892))
| ~ element(X1894,powerset(X1892))
| subset_intersection2(X1892,X1893,X1894) = subset_intersection2(X1892,X1894,X1893) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[commutativity_k5_subset_1])]) ).
fof(i_0_1769,plain,
! [X1889,X1890,X1891] :
( ~ element(X1890,powerset(X1889))
| ~ element(X1891,powerset(X1889))
| subset_union2(X1889,X1890,X1891) = subset_union2(X1889,X1891,X1890) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[commutativity_k4_subset_1])]) ).
fof(i_0_1770,lemma,
! [X3485,X3486,X3487,X3488] :
( ~ relation_of2_as_subset(X3488,X3487,X3485)
| ~ subset(relation_rng(X3488),X3486)
| relation_of2_as_subset(X3488,X3487,X3486) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t14_relset_1])]) ).
cnf(i_0_1771,lemma,
( X1 = empty_set
| subset_difference(X2,cast_to_subset(X2),union_of_subsets(X2,X1)) = meet_of_subsets(X2,complements_of_subsets(X2,X1))
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_808]) ).
cnf(i_0_1772,plain,
cast_to_subset(X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_809]) ).
cnf(i_0_1773,lemma,
( X1 = empty_set
| union_of_subsets(X2,complements_of_subsets(X2,X1)) = subset_difference(X2,cast_to_subset(X2),meet_of_subsets(X2,X1))
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_810]) ).
fof(i_0_1774,plain,
! [X2310,X2311,X2312,X2314,X2315,X2316,X2318] :
( ( in(esk88_3(X2310,X2311,X2312),relation_dom(X2310))
| ~ in(X2312,X2311)
| X2311 != relation_rng(X2310)
| ~ relation(X2310)
| ~ function(X2310) )
& ( X2312 = apply(X2310,esk88_3(X2310,X2311,X2312))
| ~ in(X2312,X2311)
| X2311 != relation_rng(X2310)
| ~ relation(X2310)
| ~ function(X2310) )
& ( ~ in(X2315,relation_dom(X2310))
| X2314 != apply(X2310,X2315)
| in(X2314,X2311)
| X2311 != relation_rng(X2310)
| ~ relation(X2310)
| ~ function(X2310) )
& ( ~ in(esk89_2(X2310,X2316),X2316)
| ~ in(X2318,relation_dom(X2310))
| esk89_2(X2310,X2316) != apply(X2310,X2318)
| X2316 = relation_rng(X2310)
| ~ relation(X2310)
| ~ function(X2310) )
& ( in(esk90_2(X2310,X2316),relation_dom(X2310))
| in(esk89_2(X2310,X2316),X2316)
| X2316 = relation_rng(X2310)
| ~ relation(X2310)
| ~ function(X2310) )
& ( esk89_2(X2310,X2316) = apply(X2310,esk90_2(X2310,X2316))
| in(esk89_2(X2310,X2316),X2316)
| X2316 = relation_rng(X2310)
| ~ relation(X2310)
| ~ function(X2310) ) ),
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)],[d5_funct_1])])])])])]) ).
cnf(i_0_1775,plain,
( in(esk250_2(X1,X2),succ(X1))
| ~ in(X2,esk249_1(X1))
| esk247_1(X1) != esk248_1(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_717]) ).
fof(i_0_1776,plain,
! [X2533,X2534,X2535] :
( empty_carrier(X2533)
| ~ topological_space(X2533)
| ~ top_str(X2533)
| ~ element(X2534,the_carrier(X2533))
| ~ point_neighbourhood(X2535,X2533,X2534)
| element(X2535,powerset(the_carrier(X2533))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_811])])]) ).
fof(i_0_1777,lemma,
! [X3464,X3465] :
( ( ~ finite(complements_of_subsets(the_carrier(X3464),X3465))
| finite(X3465)
| ~ element(X3465,powerset(powerset(the_carrier(X3464))))
| ~ one_sorted_str(X3464) )
& ( ~ finite(X3465)
| finite(complements_of_subsets(the_carrier(X3464),X3465))
| ~ element(X3465,powerset(powerset(the_carrier(X3464))))
| ~ one_sorted_str(X3464) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t13_tops_2])])])]) ).
cnf(i_0_1778,lemma,
( ~ in(X1,set_intersection2(X2,X3))
| ~ disjoint(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_812]) ).
fof(i_0_1779,lemma,
! [X3502,X3503,X3504,X3505] :
( ~ relation_of2_as_subset(X3505,X3504,X3502)
| ~ subset(X3502,X3503)
| relation_of2_as_subset(X3505,X3504,X3503) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t16_relset_1])]) ).
fof(i_0_1780,lemma,
! [X3818,X3819,X3820,X3821] :
( ( ~ open_subset(X3821,X3819)
| interior(X3819,X3821) = X3821
| ~ element(X3821,powerset(the_carrier(X3819)))
| ~ element(X3820,powerset(the_carrier(X3818)))
| ~ top_str(X3819)
| ~ topological_space(X3818)
| ~ top_str(X3818) )
& ( interior(X3818,X3820) != X3820
| open_subset(X3820,X3818)
| ~ element(X3821,powerset(the_carrier(X3819)))
| ~ element(X3820,powerset(the_carrier(X3818)))
| ~ top_str(X3819)
| ~ topological_space(X3818)
| ~ top_str(X3818) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t55_tops_1])])])]) ).
cnf(i_0_1781,lemma,
( in(X1,succ(X2))
| ~ in(X1,esk372_2(X3,X2))
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_788]) ).
fof(i_0_1782,lemma,
! [X3526,X3527,X3529] :
( ( in(esk413_2(X3526,X3527),X3527)
| X3527 = empty_set
| ~ element(X3527,powerset(powerset(X3526)))
| ~ finite(X3526) )
& ( ~ in(X3529,X3527)
| ~ subset(esk413_2(X3526,X3527),X3529)
| X3529 = esk413_2(X3526,X3527)
| X3527 = empty_set
| ~ element(X3527,powerset(powerset(X3526)))
| ~ finite(X3526) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t18_finset_1])])])])]) ).
cnf(i_0_1783,plain,
( subset_intersection2(X2,X1,X3) = set_intersection2(X1,X3)
| ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_813]) ).
fof(i_0_1784,plain,
! [X2536,X2537,X2538] :
( ~ relation_of2_as_subset(X2538,X2536,X2537)
| element(X2538,powerset(cartesian_product2(X2536,X2537))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m2_relset_1])]) ).
fof(i_0_1785,negated_conjecture,
( rel_str(esk440_0)
& element(esk441_0,the_carrier(esk440_0))
& ( ~ relstr_set_smaller(esk440_0,empty_set,esk441_0)
| ~ relstr_element_smaller(esk440_0,empty_set,esk441_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_814])])]) ).
fof(i_0_1786,lemma,
! [X3635,X3636] :
( ( ~ closed_subset(X3636,X3635)
| open_subset(subset_complement(the_carrier(X3635),X3636),X3635)
| ~ element(X3636,powerset(the_carrier(X3635)))
| ~ top_str(X3635) )
& ( ~ open_subset(subset_complement(the_carrier(X3635),X3636),X3635)
| closed_subset(X3636,X3635)
| ~ element(X3636,powerset(the_carrier(X3635)))
| ~ top_str(X3635) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t29_tops_1])])])]) ).
fof(i_0_1787,lemma,
! [X3654,X3655] :
( ( ~ open_subset(X3655,X3654)
| closed_subset(subset_complement(the_carrier(X3654),X3655),X3654)
| ~ element(X3655,powerset(the_carrier(X3654)))
| ~ top_str(X3654) )
& ( ~ closed_subset(subset_complement(the_carrier(X3654),X3655),X3654)
| open_subset(X3655,X3654)
| ~ element(X3655,powerset(the_carrier(X3654)))
| ~ top_str(X3654) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t30_tops_1])])])]) ).
fof(i_0_1788,plain,
! [X2283,X2284,X2285,X2287,X2288,X2289,X2290,X2292] :
( ( in(X2285,esk83_3(X2283,X2284,X2285))
| ~ in(X2285,X2284)
| X2284 != union(X2283) )
& ( in(esk83_3(X2283,X2284,X2285),X2283)
| ~ in(X2285,X2284)
| X2284 != union(X2283) )
& ( ~ in(X2287,X2288)
| ~ in(X2288,X2283)
| in(X2287,X2284)
| X2284 != union(X2283) )
& ( ~ in(esk84_2(X2289,X2290),X2290)
| ~ in(esk84_2(X2289,X2290),X2292)
| ~ in(X2292,X2289)
| X2290 = union(X2289) )
& ( in(esk84_2(X2289,X2290),esk85_2(X2289,X2290))
| in(esk84_2(X2289,X2290),X2290)
| X2290 = union(X2289) )
& ( in(esk85_2(X2289,X2290),X2289)
| in(esk84_2(X2289,X2290),X2290)
| X2290 = union(X2289) ) ),
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)],[d4_tarski])])])])])]) ).
fof(i_0_1789,plain,
! [X2890,X2891,X2892] :
( empty_carrier(X2890)
| ~ meet_commutative(X2890)
| ~ meet_absorbing(X2890)
| ~ join_absorbing(X2890)
| ~ latt_str(X2890)
| ~ element(X2891,the_carrier(X2890))
| ~ element(X2892,the_carrier(X2890))
| below_refl(X2890,X2891,X2891) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_815])]) ).
fof(i_0_1790,plain,
! [X2392,X2393] :
( ( ~ is_a_cover_of_carrier(X2392,X2393)
| cast_as_carrier_subset(X2392) = union_of_subsets(the_carrier(X2392),X2393)
| ~ element(X2393,powerset(powerset(the_carrier(X2392))))
| ~ one_sorted_str(X2392) )
& ( cast_as_carrier_subset(X2392) != union_of_subsets(the_carrier(X2392),X2393)
| is_a_cover_of_carrier(X2392,X2393)
| ~ element(X2393,powerset(powerset(the_carrier(X2392))))
| ~ one_sorted_str(X2392) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_pre_topc])])])]) ).
cnf(i_0_1791,lemma,
( relation_image(X1,X2) = relation_image(X1,set_intersection2(relation_dom(X1),X2))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_816]) ).
cnf(i_0_1792,plain,
( esk243_3(X1,X2,X3) = X3
| esk241_1(X1) = singleton(esk240_1(X1))
| ~ in(X3,esk242_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_715]) ).
cnf(i_0_1793,plain,
( esk243_3(X1,X2,X3) = X3
| esk239_1(X1) = singleton(esk238_1(X1))
| ~ in(X3,esk242_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_715]) ).
fof(i_0_1794,lemma,
! [X2769,X2770,X2771] :
( ( in(X2770,relation_dom(X2771))
| ~ in(X2770,relation_dom(relation_dom_restriction(X2771,X2769)))
| ~ relation(X2771)
| ~ function(X2771) )
& ( in(X2770,X2769)
| ~ in(X2770,relation_dom(relation_dom_restriction(X2771,X2769)))
| ~ relation(X2771)
| ~ function(X2771) )
& ( ~ in(X2770,relation_dom(X2771))
| ~ in(X2770,X2769)
| in(X2770,relation_dom(relation_dom_restriction(X2771,X2769)))
| ~ relation(X2771)
| ~ function(X2771) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l82_funct_1])])]) ).
fof(i_0_1795,lemma,
! [X3518,X3519] :
( ~ one_sorted_str(X3518)
| ~ element(X3519,powerset(the_carrier(X3518)))
| subset_complement(the_carrier(X3518),X3519) = subset_difference(the_carrier(X3518),cast_as_carrier_subset(X3518),X3519) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t17_pre_topc])])]) ).
fof(i_0_1796,plain,
! [X2855,X2856,X2857] :
( ~ relation_of2(X2857,X2855,X2856)
| relation_rng_as_subset(X2855,X2856,X2857) = relation_rng(X2857) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k5_relset_1])]) ).
fof(i_0_1797,plain,
! [X2849,X2850,X2851] :
( ~ relation_of2(X2851,X2849,X2850)
| relation_dom_as_subset(X2849,X2850,X2851) = relation_dom(X2851) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k4_relset_1])]) ).
cnf(i_0_1798,plain,
( ~ empty(succ(X1))
| ~ ordinal(X1)
| ~ natural(X1) ),
inference(split_conjunct,[status(thm)],[i_0_817]) ).
fof(i_0_1799,lemma,
! [X3732,X3733,X3734] :
( ( ~ disjoint(X3733,X3734)
| subset(X3733,subset_complement(X3732,X3734))
| ~ element(X3734,powerset(X3732))
| ~ element(X3733,powerset(X3732)) )
& ( ~ subset(X3733,subset_complement(X3732,X3734))
| disjoint(X3733,X3734)
| ~ element(X3734,powerset(X3732))
| ~ element(X3733,powerset(X3732)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t43_subset_1])])])]) ).
fof(i_0_1800,lemma,
! [X3425,X3426,X3427] :
( ( in(X3425,X3426)
| ~ in(X3425,relation_rng(relation_rng_restriction(X3426,X3427)))
| ~ relation(X3427) )
& ( in(X3425,relation_rng(X3427))
| ~ in(X3425,relation_rng(relation_rng_restriction(X3426,X3427)))
| ~ relation(X3427) )
& ( ~ in(X3425,X3426)
| ~ in(X3425,relation_rng(X3427))
| in(X3425,relation_rng(relation_rng_restriction(X3426,X3427)))
| ~ relation(X3427) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t115_relat_1])])]) ).
fof(i_0_1801,lemma,
! [X3532,X3533,X3534] :
( ( in(X3532,relation_field(X3534))
| ~ in(X3532,relation_field(relation_restriction(X3534,X3533)))
| ~ relation(X3534) )
& ( in(X3532,X3533)
| ~ in(X3532,relation_field(relation_restriction(X3534,X3533)))
| ~ relation(X3534) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t19_wellord1])])]) ).
fof(i_0_1802,lemma,
! [X3892,X3893,X3894] :
( ( in(X3892,X3893)
| ~ in(X3892,relation_dom(relation_dom_restriction(X3894,X3893)))
| ~ relation(X3894) )
& ( in(X3892,relation_dom(X3894))
| ~ in(X3892,relation_dom(relation_dom_restriction(X3894,X3893)))
| ~ relation(X3894) )
& ( ~ in(X3892,X3893)
| ~ in(X3892,relation_dom(X3894))
| in(X3892,relation_dom(relation_dom_restriction(X3894,X3893)))
| ~ relation(X3894) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t86_relat_1])])]) ).
fof(i_0_1803,plain,
! [X2655,X2656] :
( ~ topological_space(X2655)
| ~ top_str(X2655)
| ~ open_subset(X2656,X2655)
| ~ element(X2656,powerset(the_carrier(X2655)))
| closed_subset(subset_complement(the_carrier(X2655),X2656),X2655) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc4_tops_1])]) ).
fof(i_0_1804,plain,
! [X2640,X2641] :
( ~ topological_space(X2640)
| ~ top_str(X2640)
| ~ closed_subset(X2641,X2640)
| ~ element(X2641,powerset(the_carrier(X2640)))
| open_subset(subset_complement(the_carrier(X2640),X2641),X2640) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc3_tops_1])]) ).
fof(i_0_1805,lemma,
! [X3580,X3581,X3582] :
( ~ relation(X3581)
| ~ function(X3581)
| ~ relation(X3582)
| ~ function(X3582)
| ~ in(X3580,relation_dom(X3581))
| apply(relation_composition(X3581,X3582),X3580) = apply(X3582,apply(X3581,X3580)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t23_funct_1])])]) ).
fof(i_0_1806,plain,
! [X2873,X2874,X2875] :
( ( ~ relation_of2_as_subset(X2875,X2873,X2874)
| relation_of2(X2875,X2873,X2874) )
& ( ~ relation_of2(X2875,X2873,X2874)
| relation_of2_as_subset(X2875,X2873,X2874) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])]) ).
fof(i_0_1807,plain,
! [X2183,X2184,X2187] :
( ( in(esk60_2(X2183,X2184),X2184)
| ~ subset(X2184,relation_field(X2183))
| X2184 = empty_set
| ~ well_founded_relation(X2183)
| ~ relation(X2183) )
& ( disjoint(fiber(X2183,esk60_2(X2183,X2184)),X2184)
| ~ subset(X2184,relation_field(X2183))
| X2184 = empty_set
| ~ well_founded_relation(X2183)
| ~ relation(X2183) )
& ( subset(esk61_1(X2183),relation_field(X2183))
| well_founded_relation(X2183)
| ~ relation(X2183) )
& ( esk61_1(X2183) != empty_set
| well_founded_relation(X2183)
| ~ relation(X2183) )
& ( ~ in(X2187,esk61_1(X2183))
| ~ disjoint(fiber(X2183,X2187),esk61_1(X2183))
| well_founded_relation(X2183)
| ~ relation(X2183) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d2_wellord1])])])])]) ).
fof(i_0_1808,plain,
! [X2578,X2579] :
( ( ~ empty_carrier(rel_str_of(X2578,X2579))
| empty(X2578)
| ~ relation_of2(X2579,X2578,X2578) )
& ( strict_rel_str(rel_str_of(X2578,X2579))
| empty(X2578)
| ~ relation_of2(X2579,X2578,X2578) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_818])])]) ).
fof(i_0_1809,plain,
! [X2893,X2894,X2895] :
( empty_carrier(X2893)
| ~ reflexive_relstr(X2893)
| ~ rel_str(X2893)
| ~ element(X2894,the_carrier(X2893))
| ~ element(X2895,the_carrier(X2893))
| related_reflexive(X2893,X2894,X2894) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_819])]) ).
cnf(i_0_1810,lemma,
( subset(X1,set_intersection2(X2,X3))
| ~ subset(X1,X2)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_820]) ).
cnf(i_0_1811,plain,
( latt_element_smaller(X1,X2,X3)
| empty_carrier(X1)
| empty_carrier(X1)
| X2 != join_of_latt_set(X1,X3)
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ complete_latt_str(X1)
| ~ latt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_749]) ).
cnf(i_0_1812,plain,
( ~ empty(succ(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_821]) ).
cnf(i_0_1813,lemma,
( in(succ(X2),X1)
| ~ being_limit_ordinal(X1)
| ~ ordinal(X2)
| ~ in(X2,X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_777]) ).
fof(i_0_1814,plain,
! [X2659] :
( ( relation(the_L_meet(X2659))
| empty_carrier(X2659)
| ~ meet_associative(X2659)
| ~ meet_semilatt_str(X2659) )
& ( function(the_L_meet(X2659))
| empty_carrier(X2659)
| ~ meet_associative(X2659)
| ~ meet_semilatt_str(X2659) )
& ( quasi_total(the_L_meet(X2659),cartesian_product2(the_carrier(X2659),the_carrier(X2659)),the_carrier(X2659))
| empty_carrier(X2659)
| ~ meet_associative(X2659)
| ~ meet_semilatt_str(X2659) )
& ( v2_binop_1(the_L_meet(X2659),the_carrier(X2659))
| empty_carrier(X2659)
| ~ meet_associative(X2659)
| ~ meet_semilatt_str(X2659) )
& ( v1_partfun1(the_L_meet(X2659),cartesian_product2(the_carrier(X2659),the_carrier(X2659)),the_carrier(X2659))
| empty_carrier(X2659)
| ~ meet_associative(X2659)
| ~ meet_semilatt_str(X2659) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_822])])]) ).
fof(i_0_1815,plain,
! [X2650] :
( ( relation(the_L_meet(X2650))
| empty_carrier(X2650)
| ~ meet_commutative(X2650)
| ~ meet_semilatt_str(X2650) )
& ( function(the_L_meet(X2650))
| empty_carrier(X2650)
| ~ meet_commutative(X2650)
| ~ meet_semilatt_str(X2650) )
& ( quasi_total(the_L_meet(X2650),cartesian_product2(the_carrier(X2650),the_carrier(X2650)),the_carrier(X2650))
| empty_carrier(X2650)
| ~ meet_commutative(X2650)
| ~ meet_semilatt_str(X2650) )
& ( v1_binop_1(the_L_meet(X2650),the_carrier(X2650))
| empty_carrier(X2650)
| ~ meet_commutative(X2650)
| ~ meet_semilatt_str(X2650) )
& ( v1_partfun1(the_L_meet(X2650),cartesian_product2(the_carrier(X2650),the_carrier(X2650)),the_carrier(X2650))
| empty_carrier(X2650)
| ~ meet_commutative(X2650)
| ~ meet_semilatt_str(X2650) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_823])])]) ).
fof(i_0_1816,plain,
! [X2629] :
( ( relation(the_L_join(X2629))
| empty_carrier(X2629)
| ~ join_associative(X2629)
| ~ join_semilatt_str(X2629) )
& ( function(the_L_join(X2629))
| empty_carrier(X2629)
| ~ join_associative(X2629)
| ~ join_semilatt_str(X2629) )
& ( quasi_total(the_L_join(X2629),cartesian_product2(the_carrier(X2629),the_carrier(X2629)),the_carrier(X2629))
| empty_carrier(X2629)
| ~ join_associative(X2629)
| ~ join_semilatt_str(X2629) )
& ( v2_binop_1(the_L_join(X2629),the_carrier(X2629))
| empty_carrier(X2629)
| ~ join_associative(X2629)
| ~ join_semilatt_str(X2629) )
& ( v1_partfun1(the_L_join(X2629),cartesian_product2(the_carrier(X2629),the_carrier(X2629)),the_carrier(X2629))
| empty_carrier(X2629)
| ~ join_associative(X2629)
| ~ join_semilatt_str(X2629) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_824])])]) ).
fof(i_0_1817,plain,
! [X2596] :
( ( relation(the_L_join(X2596))
| empty_carrier(X2596)
| ~ join_commutative(X2596)
| ~ join_semilatt_str(X2596) )
& ( function(the_L_join(X2596))
| empty_carrier(X2596)
| ~ join_commutative(X2596)
| ~ join_semilatt_str(X2596) )
& ( quasi_total(the_L_join(X2596),cartesian_product2(the_carrier(X2596),the_carrier(X2596)),the_carrier(X2596))
| empty_carrier(X2596)
| ~ join_commutative(X2596)
| ~ join_semilatt_str(X2596) )
& ( v1_binop_1(the_L_join(X2596),the_carrier(X2596))
| empty_carrier(X2596)
| ~ join_commutative(X2596)
| ~ join_semilatt_str(X2596) )
& ( v1_partfun1(the_L_join(X2596),cartesian_product2(the_carrier(X2596),the_carrier(X2596)),the_carrier(X2596))
| empty_carrier(X2596)
| ~ join_commutative(X2596)
| ~ join_semilatt_str(X2596) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_825])])]) ).
fof(i_0_1818,plain,
! [X2341,X2342] :
( ( is_reflexive_in(X2341,X2342)
| ~ well_orders(X2341,X2342)
| ~ relation(X2341) )
& ( is_transitive_in(X2341,X2342)
| ~ well_orders(X2341,X2342)
| ~ relation(X2341) )
& ( is_antisymmetric_in(X2341,X2342)
| ~ well_orders(X2341,X2342)
| ~ relation(X2341) )
& ( is_connected_in(X2341,X2342)
| ~ well_orders(X2341,X2342)
| ~ relation(X2341) )
& ( is_well_founded_in(X2341,X2342)
| ~ well_orders(X2341,X2342)
| ~ relation(X2341) )
& ( ~ is_reflexive_in(X2341,X2342)
| ~ is_transitive_in(X2341,X2342)
| ~ is_antisymmetric_in(X2341,X2342)
| ~ is_connected_in(X2341,X2342)
| ~ is_well_founded_in(X2341,X2342)
| well_orders(X2341,X2342)
| ~ relation(X2341) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_wellord1])])])]) ).
cnf(i_0_1819,lemma,
pair_second(ordered_pair(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[i_0_826]) ).
cnf(i_0_1820,lemma,
pair_first(ordered_pair(X1,X2)) = X1,
inference(split_conjunct,[status(thm)],[i_0_826]) ).
cnf(i_0_1821,plain,
( X1 = pair_second(X2)
| X1 != esk54_2(X2,X1)
| X2 != ordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_753]) ).
cnf(i_0_1822,plain,
( X1 = pair_first(X2)
| X1 != esk32_2(X2,X1)
| X2 != ordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_754]) ).
fof(i_0_1823,lemma,
! [X3508,X3509,X3510] :
( ( in(X3508,X3510)
| ~ in(X3508,relation_restriction(X3510,X3509))
| ~ relation(X3510) )
& ( in(X3508,cartesian_product2(X3509,X3509))
| ~ in(X3508,relation_restriction(X3510,X3509))
| ~ relation(X3510) )
& ( ~ in(X3508,X3510)
| ~ in(X3508,cartesian_product2(X3509,X3509))
| in(X3508,relation_restriction(X3510,X3509))
| ~ relation(X3510) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t16_wellord1])])]) ).
fof(i_0_1824,plain,
! [X2866,X2867,X2868] :
( ~ element(X2867,powerset(X2866))
| ~ element(X2868,powerset(X2866))
| subset_difference(X2866,X2867,X2868) = set_difference(X2867,X2868) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k6_subset_1])]) ).
fof(i_0_1825,plain,
! [X2852,X2853,X2854] :
( ~ element(X2853,powerset(X2852))
| ~ element(X2854,powerset(X2852))
| subset_union2(X2852,X2853,X2854) = set_union2(X2853,X2854) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k4_subset_1])]) ).
fof(i_0_1826,lemma,
! [X3443,X3444] :
( ~ element(X3444,powerset(powerset(X3443)))
| X3444 = empty_set
| meet_of_subsets(X3443,complements_of_subsets(X3443,X3444)) = subset_complement(X3443,union_of_subsets(X3443,X3444)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t11_tops_2])]) ).
fof(i_0_1827,lemma,
! [X3449,X3450] :
( ~ element(X3450,powerset(powerset(X3449)))
| X3450 = empty_set
| union_of_subsets(X3449,complements_of_subsets(X3449,X3450)) = subset_complement(X3449,meet_of_subsets(X3449,X3450)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_tops_2])]) ).
fof(i_0_1828,plain,
! [X2377,X2378,X2379] :
( ( ~ one_to_one(X2377)
| ~ in(X2378,relation_dom(X2377))
| ~ in(X2379,relation_dom(X2377))
| apply(X2377,X2378) != apply(X2377,X2379)
| X2378 = X2379
| ~ relation(X2377)
| ~ function(X2377) )
& ( in(esk101_1(X2377),relation_dom(X2377))
| one_to_one(X2377)
| ~ relation(X2377)
| ~ function(X2377) )
& ( in(esk102_1(X2377),relation_dom(X2377))
| one_to_one(X2377)
| ~ relation(X2377)
| ~ function(X2377) )
& ( apply(X2377,esk101_1(X2377)) = apply(X2377,esk102_1(X2377))
| one_to_one(X2377)
| ~ relation(X2377)
| ~ function(X2377) )
& ( esk101_1(X2377) != esk102_1(X2377)
| one_to_one(X2377)
| ~ relation(X2377)
| ~ function(X2377) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_funct_1])])])])]) ).
fof(i_0_1829,plain,
! [X2689,X2690,X2691,X2692] :
( ( X2689 = X2691
| rel_str_of(X2689,X2690) != rel_str_of(X2691,X2692)
| ~ relation_of2(X2690,X2689,X2689) )
& ( X2690 = X2692
| rel_str_of(X2689,X2690) != rel_str_of(X2691,X2692)
| ~ relation_of2(X2690,X2689,X2689) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[free_g1_orders_2])])])]) ).
cnf(i_0_1830,lemma,
( disjoint(X1,X2)
| in(esk432_2(X1,X2),set_intersection2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_812]) ).
fof(i_0_1831,plain,
! [X2122,X2123,X2124,X2125,X2126,X2127] :
( ( ~ in(X2124,X2123)
| subset(X2124,X2122)
| X2123 != powerset(X2122) )
& ( ~ subset(X2125,X2122)
| in(X2125,X2123)
| X2123 != powerset(X2122) )
& ( ~ in(esk50_2(X2126,X2127),X2127)
| ~ subset(esk50_2(X2126,X2127),X2126)
| X2127 = powerset(X2126) )
& ( in(esk50_2(X2126,X2127),X2127)
| subset(esk50_2(X2126,X2127),X2126)
| X2127 = powerset(X2126) ) ),
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)],[d1_zfmisc_1])])])])])]) ).
fof(i_0_1832,plain,
! [X2549,X2550] :
( empty_carrier(X2549)
| ~ topological_space(X2549)
| ~ top_str(X2549)
| ~ element(X2550,the_carrier(X2549))
| point_neighbourhood(esk121_2(X2549,X2550),X2549,X2550) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_827])])]) ).
fof(i_0_1833,lemma,
! [X3480,X3481] :
( ~ relation(X3481)
| ~ subset(X3480,relation_dom(X3481))
| subset(X3480,relation_inverse_image(X3481,relation_image(X3481,X3480))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t146_funct_1])]) ).
cnf(i_0_1834,lemma,
( in(X1,succ(X2))
| ~ in(X1,esk349_1(X2))
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_721]) ).
cnf(i_0_1835,lemma,
( apply(esk387_1(X2),X1) = singleton(X1)
| esk385_1(X2) = singleton(esk383_1(X2))
| ~ in(X1,X2)
| X3 != singleton(esk386_1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_828]) ).
cnf(i_0_1836,lemma,
( apply(esk387_1(X2),X1) = singleton(X1)
| esk384_1(X2) = singleton(esk383_1(X2))
| ~ in(X1,X2)
| X3 != singleton(esk386_1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_828]) ).
cnf(i_0_1837,plain,
( X1 = singleton(esk234_2(X2,X1))
| esk232_1(X2) = singleton(esk230_1(X2))
| ~ in(X1,esk233_1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_829]) ).
cnf(i_0_1838,plain,
( X1 = singleton(esk234_2(X2,X1))
| esk231_1(X2) = singleton(esk230_1(X2))
| ~ in(X1,esk233_1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_829]) ).
fof(i_0_1839,lemma,
! [X3798,X3799,X3800] :
( ~ relation(X3798)
| ~ relation(X3799)
| ~ relation(X3800)
| ~ function(X3800)
| ~ relation_isomorphism(X3798,X3799,X3800)
| epred3_2(X3799,X3798) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_830])])]) ).
cnf(i_0_1840,lemma,
( in(X3,X1)
| subset(X1,set_difference(X2,singleton(X3)))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_831]) ).
cnf(i_0_1841,plain,
~ empty(succ(X1)),
inference(split_conjunct,[status(thm)],[i_0_832]) ).
cnf(i_0_1842,lemma,
( ordinal_subset(succ(X1),X2)
| ~ in(X1,X2)
| ~ ordinal(X2)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_807]) ).
fof(i_0_1843,plain,
! [X3643,X3644] :
( ( ~ in(esk421_2(X3643,X3644),X3643)
| ~ in(esk421_2(X3643,X3644),X3644)
| X3643 = X3644 )
& ( in(esk421_2(X3643,X3644),X3643)
| in(esk421_2(X3643,X3644),X3644)
| X3643 = X3644 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_tarski])])])]) ).
fof(i_0_1844,lemma,
! [X3814,X3815,X3816] :
( ~ relation(X3814)
| ~ relation(X3815)
| ~ relation(X3816)
| ~ function(X3816)
| ~ well_ordering(X3814)
| ~ relation_isomorphism(X3814,X3815,X3816)
| well_ordering(X3815) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t54_wellord1])])]) ).
fof(i_0_1845,lemma,
! [X3835,X3836] :
( empty_carrier(X3835)
| ~ one_sorted_str(X3835)
| ~ element(X3836,powerset(powerset(the_carrier(X3835))))
| ~ is_a_cover_of_carrier(X3835,X3836)
| X3836 != empty_set ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_833])])]) ).
fof(i_0_1846,plain,
! [X2074,X2075,X2076] :
( ( ~ relation_of2(X2076,X2074,X2075)
| subset(X2076,cartesian_product2(X2074,X2075)) )
& ( ~ subset(X2076,cartesian_product2(X2074,X2075))
| relation_of2(X2076,X2074,X2075) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_relset_1])]) ).
fof(i_0_1847,lemma,
! [X3491,X3492] :
( ~ one_sorted_str(X3491)
| ~ element(X3492,powerset(the_carrier(X3491)))
| subset_intersection2(the_carrier(X3491),X3492,cast_as_carrier_subset(X3491)) = X3492 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t15_pre_topc])])]) ).
fof(i_0_1848,lemma,
! [X3563,X3564,X3565] :
( ~ relation(X3565)
| subset(fiber(relation_restriction(X3565,X3563),X3564),fiber(X3565,X3564)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t21_wellord1])]) ).
cnf(i_0_1849,plain,
( in(X1,X4)
| ~ in(X1,X2)
| ~ in(X1,X3)
| X4 != set_intersection2(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_735]) ).
fof(i_0_1850,plain,
! [X2539] :
( ( function(the_L_meet(X2539))
| ~ meet_semilatt_str(X2539) )
& ( quasi_total(the_L_meet(X2539),cartesian_product2(the_carrier(X2539),the_carrier(X2539)),the_carrier(X2539))
| ~ meet_semilatt_str(X2539) )
& ( relation_of2_as_subset(the_L_meet(X2539),cartesian_product2(the_carrier(X2539),the_carrier(X2539)),the_carrier(X2539))
| ~ meet_semilatt_str(X2539) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u1_lattices])])]) ).
fof(i_0_1851,plain,
! [X2542] :
( ( function(the_L_join(X2542))
| ~ join_semilatt_str(X2542) )
& ( quasi_total(the_L_join(X2542),cartesian_product2(the_carrier(X2542),the_carrier(X2542)),the_carrier(X2542))
| ~ join_semilatt_str(X2542) )
& ( relation_of2_as_subset(the_L_join(X2542),cartesian_product2(the_carrier(X2542),the_carrier(X2542)),the_carrier(X2542))
| ~ join_semilatt_str(X2542) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u2_lattices])])]) ).
cnf(i_0_1852,lemma,
( apply(esk387_1(X2),X1) = singleton(X1)
| in(esk383_1(X2),X2)
| ~ in(X1,X2)
| X3 != singleton(esk386_1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_828]) ).
fof(i_0_1853,plain,
! [X2704,X2705,X2706] :
( ~ element(X2705,powerset(X2704))
| ~ element(X2706,powerset(X2704))
| subset_intersection2(X2704,X2705,X2705) = X2705 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[idempotence_k5_subset_1])]) ).
fof(i_0_1854,plain,
! [X2701,X2702,X2703] :
( ~ element(X2702,powerset(X2701))
| ~ element(X2703,powerset(X2701))
| subset_union2(X2701,X2702,X2702) = X2702 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[idempotence_k4_subset_1])]) ).
cnf(i_0_1855,plain,
( X1 = singleton(esk234_2(X2,X1))
| in(esk230_1(X2),X2)
| ~ in(X1,esk233_1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_829]) ).
cnf(i_0_1856,plain,
( X1 = singleton(esk234_2(X2,X1))
| in(esk230_1(X2),X2)
| ~ in(X1,esk233_1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_829]) ).
fof(i_0_1857,lemma,
! [X3811,X3812,X3813] :
( ~ element(X3813,powerset(X3811))
| ~ in(X3812,subset_complement(X3811,X3813))
| ~ in(X3812,X3813) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t54_subset_1])]) ).
fof(i_0_1858,plain,
! [X1846,X1847,X1848] :
( ~ element(X1848,powerset(cartesian_product2(X1846,X1847)))
| relation(X1848) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relset_1])]) ).
fof(i_0_1859,plain,
! [X2456,X2457] :
( ~ top_str(X2456)
| ~ element(X2457,powerset(the_carrier(X2456)))
| element(interior(X2456,X2457),powerset(the_carrier(X2456))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_tops_1])]) ).
fof(i_0_1860,plain,
! [X2506,X2507] :
( ~ top_str(X2506)
| ~ element(X2507,powerset(the_carrier(X2506)))
| element(topstr_closure(X2506,X2507),powerset(the_carrier(X2506))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k6_pre_topc])]) ).
cnf(i_0_1861,plain,
( in(succ(esk447_0),omega)
| subset(X1,esk446_1(X1))
| epred1_0
| ~ in(X1,esk445_0) ),
inference(split_conjunct,[status(thm)],[i_0_760]) ).
fof(i_0_1862,plain,
! [X2492,X2493] :
( empty_carrier(X2492)
| ~ lattice(X2492)
| ~ latt_str(X2492)
| ~ element(X2493,the_carrier(poset_of_lattice(X2492)))
| element(cast_to_el_of_lattice(X2492,X2493),the_carrier(X2492)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_834])]) ).
fof(i_0_1863,plain,
! [X2433,X2434] :
( ( strict_rel_str(rel_str_of(X2433,X2434))
| ~ relation_of2(X2434,X2433,X2433) )
& ( rel_str(rel_str_of(X2433,X2434))
| ~ relation_of2(X2434,X2433,X2433) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_g1_orders_2])])]) ).
cnf(i_0_1864,plain,
( in(succ(esk447_0),omega)
| in(esk446_1(X1),esk445_0)
| epred1_0
| ~ in(X1,esk445_0) ),
inference(split_conjunct,[status(thm)],[i_0_760]) ).
cnf(i_0_1865,lemma,
( relation_dom(X1) = set_intersection2(relation_dom(X2),X3)
| X1 != relation_dom_restriction(X2,X3)
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_741]) ).
cnf(i_0_1866,plain,
( relation(X1)
| esk39_1(X1) != ordered_pair(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_766]) ).
cnf(i_0_1867,lemma,
( apply(esk387_1(X2),X1) = singleton(X1)
| ~ in(X1,X2)
| X3 != singleton(esk386_1(X2))
| esk384_1(X2) != esk385_1(X2) ),
inference(split_conjunct,[status(thm)],[i_0_828]) ).
fof(i_0_1868,lemma,
! [X3681,X3682,X3683] :
( ( relation_dom(X3682) = X3681
| X3682 != identity_relation(X3681)
| ~ relation(X3682)
| ~ function(X3682) )
& ( ~ in(X3683,X3681)
| apply(X3682,X3683) = X3683
| X3682 != identity_relation(X3681)
| ~ relation(X3682)
| ~ function(X3682) )
& ( in(esk424_2(X3681,X3682),X3681)
| relation_dom(X3682) != X3681
| X3682 = identity_relation(X3681)
| ~ relation(X3682)
| ~ function(X3682) )
& ( apply(X3682,esk424_2(X3681,X3682)) != esk424_2(X3681,X3682)
| relation_dom(X3682) != X3681
| X3682 = identity_relation(X3681)
| ~ relation(X3682)
| ~ function(X3682) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t34_funct_1])])])])]) ).
cnf(i_0_1869,plain,
( relation_restriction(X1,X2) = set_intersection2(X1,cartesian_product2(X2,X2))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_835]) ).
cnf(i_0_1870,plain,
( X1 = singleton(esk234_2(X2,X1))
| ~ in(X1,esk233_1(X2))
| esk231_1(X2) != esk232_1(X2) ),
inference(split_conjunct,[status(thm)],[i_0_829]) ).
fof(i_0_1871,lemma,
! [X3439,X3440,X3441,X3442] :
( ~ subset(X3439,X3440)
| ~ subset(X3441,X3442)
| subset(cartesian_product2(X3439,X3441),cartesian_product2(X3440,X3442)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t119_zfmisc_1])]) ).
fof(i_0_1872,lemma,
! [X3791,X3792,X3793] :
( X3791 = empty_set
| ~ element(X3792,powerset(X3791))
| ~ element(X3793,X3791)
| in(X3793,X3792)
| in(X3793,subset_complement(X3791,X3792)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_836])])]) ).
fof(i_0_1873,plain,
! [X2517,X2518] :
( ~ element(X2518,powerset(powerset(X2517)))
| element(complements_of_subsets(X2517,X2518),powerset(powerset(X2517))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k7_setfam_1])]) ).
fof(i_0_1874,plain,
! [X2480,X2481] :
( empty_carrier(X2480)
| ~ lattice(X2480)
| ~ latt_str(X2480)
| ~ element(X2481,the_carrier(X2480))
| element(cast_to_el_of_LattPOSet(X2480,X2481),the_carrier(poset_of_lattice(X2480))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_837])]) ).
fof(i_0_1875,plain,
! [X3883,X3884,X3886] :
( ( in(esk442_2(X3883,X3884),X3884)
| ~ in(X3883,X3884) )
& ( ~ in(X3886,X3884)
| ~ in(X3886,esk442_2(X3883,X3884))
| ~ in(X3883,X3884) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_tarski])])])])]) ).
cnf(i_0_1876,lemma,
( apply(esk387_1(X2),X1) = singleton(X1)
| in(esk386_1(X2),X2)
| esk385_1(X2) = singleton(esk383_1(X2))
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_828]) ).
cnf(i_0_1877,lemma,
( apply(esk387_1(X2),X1) = singleton(X1)
| in(esk386_1(X2),X2)
| esk384_1(X2) = singleton(esk383_1(X2))
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_828]) ).
fof(i_0_1878,lemma,
! [X3825,X3826] :
( ( X3825 = apply(X3826,apply(function_inverse(X3826),X3825))
| ~ one_to_one(X3826)
| ~ in(X3825,relation_rng(X3826))
| ~ relation(X3826)
| ~ function(X3826) )
& ( X3825 = apply(relation_composition(function_inverse(X3826),X3826),X3825)
| ~ one_to_one(X3826)
| ~ in(X3825,relation_rng(X3826))
| ~ relation(X3826)
| ~ function(X3826) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t57_funct_1])])]) ).
fof(i_0_1879,lemma,
! [X3446,X3447,X3448] :
( ( subset(relation_dom(X3448),X3446)
| ~ relation_of2_as_subset(X3448,X3446,X3447) )
& ( subset(relation_rng(X3448),X3447)
| ~ relation_of2_as_subset(X3448,X3446,X3447) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_relset_1])])]) ).
fof(i_0_1880,lemma,
! [X3476,X3477] :
( ~ relation(X3477)
| ~ function(X3477)
| subset(relation_image(X3477,relation_inverse_image(X3477,X3476)),X3476) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t145_funct_1])]) ).
cnf(i_0_1881,lemma,
( X1 = X2
| ~ subset(singleton(X1),singleton(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_838]) ).
fof(i_0_1882,plain,
! [X2604,X2605] :
( ~ topological_space(X2604)
| ~ top_str(X2604)
| ~ element(X2605,powerset(the_carrier(X2604)))
| closed_subset(topstr_closure(X2604,X2605),X2604) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc2_tops_1])]) ).
fof(i_0_1883,lemma,
! [X3794,X3795] :
( ~ topological_space(X3794)
| ~ top_str(X3794)
| ~ element(X3795,powerset(the_carrier(X3794)))
| open_subset(interior(X3794,X3795),X3794) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t51_tops_1])])]) ).
fof(i_0_1884,plain,
! [X2663,X2664] :
( ~ topological_space(X2663)
| ~ top_str(X2663)
| ~ element(X2664,powerset(the_carrier(X2663)))
| open_subset(interior(X2663,X2664),X2663) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc6_tops_1])]) ).
fof(i_0_1885,plain,
! [X2325,X2326] :
( ( ~ open_subset(X2326,X2325)
| in(X2326,the_topology(X2325))
| ~ element(X2326,powerset(the_carrier(X2325)))
| ~ top_str(X2325) )
& ( ~ in(X2326,the_topology(X2325))
| open_subset(X2326,X2325)
| ~ element(X2326,powerset(the_carrier(X2325)))
| ~ top_str(X2325) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_pre_topc])])])]) ).
cnf(i_0_1886,plain,
( in(succ(esk447_0),omega)
| epred1_0
| esk446_1(X1) != X1
| ~ in(X1,esk445_0) ),
inference(split_conjunct,[status(thm)],[i_0_760]) ).
fof(i_0_1887,lemma,
! [X3796,X3797] :
( ( ~ closed_subset(X3797,X3796)
| topstr_closure(X3796,X3797) = X3797
| ~ element(X3797,powerset(the_carrier(X3796)))
| ~ top_str(X3796) )
& ( ~ topological_space(X3796)
| topstr_closure(X3796,X3797) != X3797
| closed_subset(X3797,X3796)
| ~ element(X3797,powerset(the_carrier(X3796)))
| ~ top_str(X3796) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t52_pre_topc])])])]) ).
cnf(i_0_1888,plain,
( in(esk234_2(X1,X2),X1)
| esk232_1(X1) = singleton(esk230_1(X1))
| ~ in(X2,esk233_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_829]) ).
cnf(i_0_1889,plain,
( in(esk234_2(X1,X2),X1)
| esk231_1(X1) = singleton(esk230_1(X1))
| ~ in(X2,esk233_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_829]) ).
cnf(i_0_1890,plain,
( X2 = singleton(X1)
| ~ in(esk44_2(X1,X2),X2)
| esk44_2(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[i_0_839]) ).
fof(i_0_1891,plain,
! [X2598] :
( ( relation(the_InternalRel(X2598))
| ~ reflexive_relstr(X2598)
| ~ transitive_relstr(X2598)
| ~ antisymmetric_relstr(X2598)
| ~ rel_str(X2598) )
& ( reflexive(the_InternalRel(X2598))
| ~ reflexive_relstr(X2598)
| ~ transitive_relstr(X2598)
| ~ antisymmetric_relstr(X2598)
| ~ rel_str(X2598) )
& ( antisymmetric(the_InternalRel(X2598))
| ~ reflexive_relstr(X2598)
| ~ transitive_relstr(X2598)
| ~ antisymmetric_relstr(X2598)
| ~ rel_str(X2598) )
& ( transitive(the_InternalRel(X2598))
| ~ reflexive_relstr(X2598)
| ~ transitive_relstr(X2598)
| ~ antisymmetric_relstr(X2598)
| ~ rel_str(X2598) )
& ( v1_partfun1(the_InternalRel(X2598),the_carrier(X2598),the_carrier(X2598))
| ~ reflexive_relstr(X2598)
| ~ transitive_relstr(X2598)
| ~ antisymmetric_relstr(X2598)
| ~ rel_str(X2598) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc2_orders_2])])]) ).
cnf(i_0_1892,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_735]) ).
cnf(i_0_1893,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_735]) ).
fof(i_0_1894,lemma,
! [X3666,X3667,X3669] :
( ( ordinal(esk423_2(X3666,X3667))
| ~ subset(X3666,X3667)
| X3666 = empty_set
| ~ ordinal(X3667) )
& ( in(esk423_2(X3666,X3667),X3666)
| ~ subset(X3666,X3667)
| X3666 = empty_set
| ~ ordinal(X3667) )
& ( ~ ordinal(X3669)
| ~ in(X3669,X3666)
| ordinal_subset(esk423_2(X3666,X3667),X3669)
| ~ subset(X3666,X3667)
| X3666 = empty_set
| ~ ordinal(X3667) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t32_ordinal1])])])])]) ).
cnf(i_0_1895,plain,
( in(succ(esk447_0),omega)
| element(esk445_0,powerset(powerset(empty_set)))
| epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_760]) ).
fof(i_0_1896,lemma,
! [X3626,X3629] :
( ( relation(esk420_1(X3626))
| in(esk419_1(X3626),X3626)
| empty(X3626) )
& ( function(esk420_1(X3626))
| in(esk419_1(X3626),X3626)
| empty(X3626) )
& ( relation_dom(esk420_1(X3626)) = X3626
| in(esk419_1(X3626),X3626)
| empty(X3626) )
& ( ~ in(X3629,X3626)
| in(apply(esk420_1(X3626),X3629),X3629)
| in(esk419_1(X3626),X3626)
| empty(X3626) )
& ( relation(esk420_1(X3626))
| esk419_1(X3626) = empty_set
| empty(X3626) )
& ( function(esk420_1(X3626))
| esk419_1(X3626) = empty_set
| empty(X3626) )
& ( relation_dom(esk420_1(X3626)) = X3626
| esk419_1(X3626) = empty_set
| empty(X3626) )
& ( ~ in(X3629,X3626)
| in(apply(esk420_1(X3626),X3629),X3629)
| esk419_1(X3626) = empty_set
| empty(X3626) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_840])])])])]) ).
fof(i_0_1897,lemma,
! [X3740,X3741] :
( ~ top_str(X3740)
| ~ element(X3741,powerset(the_carrier(X3740)))
| subset(interior(X3740,X3741),X3741) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t44_tops_1])])]) ).
fof(i_0_1898,lemma,
! [X3770,X3771] :
( ~ top_str(X3770)
| ~ element(X3771,powerset(the_carrier(X3770)))
| subset(X3771,topstr_closure(X3770,X3771)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t48_pre_topc])])]) ).
cnf(i_0_1899,lemma,
( apply(esk387_1(X2),X1) = singleton(X1)
| in(esk386_1(X2),X2)
| in(esk383_1(X2),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_828]) ).
fof(i_0_1900,plain,
! [X2509,X2510] :
( ~ element(X2510,powerset(powerset(X2509)))
| element(meet_of_subsets(X2509,X2510),powerset(X2509)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k6_setfam_1])]) ).
fof(i_0_1901,plain,
! [X2500,X2501] :
( ~ element(X2501,powerset(powerset(X2500)))
| element(union_of_subsets(X2500,X2501),powerset(X2500)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k5_setfam_1])]) ).
cnf(i_0_1902,plain,
( in(X3,esk233_1(X2))
| esk232_1(X2) = singleton(esk230_1(X2))
| ~ in(X1,X2)
| X3 != singleton(X1) ),
inference(split_conjunct,[status(thm)],[i_0_829]) ).
cnf(i_0_1903,plain,
( in(X3,esk233_1(X2))
| esk231_1(X2) = singleton(esk230_1(X2))
| ~ in(X1,X2)
| X3 != singleton(X1) ),
inference(split_conjunct,[status(thm)],[i_0_829]) ).
cnf(i_0_1904,plain,
( relation(set_intersection2(X1,X2))
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_841]) ).
cnf(i_0_1905,plain,
( epsilon_connected(succ(X1))
| ~ ordinal(X1)
| ~ natural(X1) ),
inference(split_conjunct,[status(thm)],[i_0_817]) ).
cnf(i_0_1906,plain,
( epsilon_transitive(succ(X1))
| ~ ordinal(X1)
| ~ natural(X1) ),
inference(split_conjunct,[status(thm)],[i_0_817]) ).
cnf(i_0_1907,plain,
( ordinal(succ(X1))
| ~ ordinal(X1)
| ~ natural(X1) ),
inference(split_conjunct,[status(thm)],[i_0_817]) ).
cnf(i_0_1908,plain,
( natural(succ(X1))
| ~ ordinal(X1)
| ~ natural(X1) ),
inference(split_conjunct,[status(thm)],[i_0_817]) ).
fof(i_0_1909,lemma,
! [X3513,X3514,X3515] :
( ~ relation(X3515)
| ~ subset(X3513,X3514)
| subset(relation_inverse_image(X3515,X3513),relation_inverse_image(X3515,X3514)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t178_relat_1])]) ).
cnf(i_0_1910,lemma,
( relation_rng(relation_rng_restriction(X2,X1)) = set_intersection2(relation_rng(X1),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_842]) ).
cnf(i_0_1911,lemma,
( relation_dom(relation_dom_restriction(X1,X2)) = set_intersection2(relation_dom(X1),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_843]) ).
fof(i_0_1912,plain,
! [X3924,X3926,X3927,X3928,X3930,X3931] :
( in(X3924,esk443_1(X3924))
& ( ~ in(X3926,esk443_1(X3924))
| ~ subset(X3927,X3926)
| in(X3927,esk443_1(X3924)) )
& ( in(esk444_2(X3924,X3928),esk443_1(X3924))
| ~ in(X3928,esk443_1(X3924)) )
& ( ~ subset(X3930,X3928)
| in(X3930,esk444_2(X3924,X3928))
| ~ in(X3928,esk443_1(X3924)) )
& ( ~ subset(X3931,esk443_1(X3924))
| are_equipotent(X3931,esk443_1(X3924))
| in(X3931,esk443_1(X3924)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_844])])])])]) ).
fof(i_0_1913,lemma,
! [X3747,X3748] :
( ~ relation(X3747)
| ~ relation(X3748)
| subset(relation_rng(relation_composition(X3747,X3748)),relation_rng(X3748)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t45_relat_1])])]) ).
fof(i_0_1914,lemma,
! [X3738,X3739] :
( ~ relation(X3738)
| ~ relation(X3739)
| subset(relation_dom(relation_composition(X3738,X3739)),relation_dom(X3738)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t44_relat_1])])]) ).
fof(i_0_1915,plain,
! [X2710,X2711] :
( ~ element(X2711,powerset(powerset(X2710)))
| complements_of_subsets(X2710,complements_of_subsets(X2710,X2711)) = X2711 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[involutiveness_k7_setfam_1])]) ).
cnf(i_0_1916,lemma,
subset(set_intersection2(X1,X2),X1),
inference(split_conjunct,[status(thm)],[i_0_845]) ).
cnf(i_0_1917,lemma,
in(X1,succ(X1)),
inference(split_conjunct,[status(thm)],[i_0_846]) ).
fof(i_0_1918,plain,
! [X2466] :
( ( reflexive(k2_lattice3(X2466))
| empty_carrier(X2466)
| ~ lattice(X2466)
| ~ latt_str(X2466) )
& ( antisymmetric(k2_lattice3(X2466))
| empty_carrier(X2466)
| ~ lattice(X2466)
| ~ latt_str(X2466) )
& ( transitive(k2_lattice3(X2466))
| empty_carrier(X2466)
| ~ lattice(X2466)
| ~ latt_str(X2466) )
& ( v1_partfun1(k2_lattice3(X2466),the_carrier(X2466),the_carrier(X2466))
| empty_carrier(X2466)
| ~ lattice(X2466)
| ~ latt_str(X2466) )
& ( relation_of2_as_subset(k2_lattice3(X2466),the_carrier(X2466),the_carrier(X2466))
| empty_carrier(X2466)
| ~ lattice(X2466)
| ~ latt_str(X2466) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_847])])]) ).
fof(i_0_1919,lemma,
! [X3869,X3870,X3871] :
( ~ relation(X3871)
| ~ function(X3871)
| ~ in(X3870,X3869)
| apply(relation_dom_restriction(X3871,X3869),X3870) = apply(X3871,X3870) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t72_funct_1])]) ).
cnf(i_0_1920,lemma,
( apply(esk387_1(X2),X1) = singleton(X1)
| in(esk386_1(X2),X2)
| ~ in(X1,X2)
| esk384_1(X2) != esk385_1(X2) ),
inference(split_conjunct,[status(thm)],[i_0_828]) ).
fof(i_0_1921,lemma,
! [X3766,X3767] :
( ~ relation(X3766)
| ~ relation(X3767)
| ~ subset(relation_dom(X3766),relation_rng(X3767))
| relation_rng(relation_composition(X3767,X3766)) = relation_rng(X3766) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t47_relat_1])])]) ).
fof(i_0_1922,lemma,
! [X3760,X3761] :
( ~ relation(X3760)
| ~ relation(X3761)
| ~ subset(relation_rng(X3760),relation_dom(X3761))
| relation_dom(relation_composition(X3760,X3761)) = relation_dom(X3760) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t46_relat_1])])]) ).
cnf(i_0_1923,lemma,
( finite(set_intersection2(X1,X2))
| ~ finite(X1) ),
inference(split_conjunct,[status(thm)],[i_0_848]) ).
cnf(i_0_1924,plain,
( finite(set_intersection2(X1,X2))
| ~ finite(X1) ),
inference(split_conjunct,[status(thm)],[i_0_849]) ).
cnf(i_0_1925,plain,
( finite(set_intersection2(X2,X1))
| ~ finite(X1) ),
inference(split_conjunct,[status(thm)],[i_0_850]) ).
cnf(i_0_1926,plain,
( epsilon_connected(succ(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_821]) ).
cnf(i_0_1927,plain,
( epsilon_transitive(succ(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_821]) ).
cnf(i_0_1928,plain,
( ordinal(succ(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_821]) ).
cnf(i_0_1929,plain,
( v5_membered(set_intersection2(X1,X2))
| ~ v5_membered(X1) ),
inference(split_conjunct,[status(thm)],[i_0_851]) ).
cnf(i_0_1930,plain,
( v5_membered(set_intersection2(X1,X2))
| ~ v5_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_852]) ).
cnf(i_0_1931,plain,
( v4_membered(set_intersection2(X1,X2))
| ~ v5_membered(X1) ),
inference(split_conjunct,[status(thm)],[i_0_851]) ).
cnf(i_0_1932,plain,
( v4_membered(set_intersection2(X1,X2))
| ~ v5_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_852]) ).
cnf(i_0_1933,plain,
( v4_membered(set_intersection2(X1,X2))
| ~ v4_membered(X1) ),
inference(split_conjunct,[status(thm)],[i_0_853]) ).
cnf(i_0_1934,plain,
( v4_membered(set_intersection2(X1,X2))
| ~ v4_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_854]) ).
cnf(i_0_1935,plain,
( v3_membered(set_intersection2(X1,X2))
| ~ v5_membered(X1) ),
inference(split_conjunct,[status(thm)],[i_0_851]) ).
cnf(i_0_1936,plain,
( v3_membered(set_intersection2(X1,X2))
| ~ v5_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_852]) ).
cnf(i_0_1937,plain,
( v3_membered(set_intersection2(X1,X2))
| ~ v4_membered(X1) ),
inference(split_conjunct,[status(thm)],[i_0_853]) ).
cnf(i_0_1938,plain,
( v3_membered(set_intersection2(X1,X2))
| ~ v4_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_854]) ).
cnf(i_0_1939,plain,
( v3_membered(set_intersection2(X1,X2))
| ~ v3_membered(X1) ),
inference(split_conjunct,[status(thm)],[i_0_855]) ).
cnf(i_0_1940,plain,
( v3_membered(set_intersection2(X1,X2))
| ~ v3_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_856]) ).
cnf(i_0_1941,plain,
( v2_membered(set_intersection2(X1,X2))
| ~ v5_membered(X1) ),
inference(split_conjunct,[status(thm)],[i_0_851]) ).
cnf(i_0_1942,plain,
( v2_membered(set_intersection2(X1,X2))
| ~ v5_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_852]) ).
cnf(i_0_1943,plain,
( v2_membered(set_intersection2(X1,X2))
| ~ v4_membered(X1) ),
inference(split_conjunct,[status(thm)],[i_0_853]) ).
cnf(i_0_1944,plain,
( v2_membered(set_intersection2(X1,X2))
| ~ v4_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_854]) ).
cnf(i_0_1945,plain,
( v2_membered(set_intersection2(X1,X2))
| ~ v3_membered(X1) ),
inference(split_conjunct,[status(thm)],[i_0_855]) ).
cnf(i_0_1946,plain,
( v2_membered(set_intersection2(X1,X2))
| ~ v3_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_856]) ).
cnf(i_0_1947,plain,
( v2_membered(set_intersection2(X1,X2))
| ~ v2_membered(X1) ),
inference(split_conjunct,[status(thm)],[i_0_857]) ).
cnf(i_0_1948,plain,
( v2_membered(set_intersection2(X1,X2))
| ~ v2_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_858]) ).
cnf(i_0_1949,plain,
( v1_membered(set_intersection2(X1,X2))
| ~ v5_membered(X1) ),
inference(split_conjunct,[status(thm)],[i_0_851]) ).
cnf(i_0_1950,plain,
( v1_membered(set_intersection2(X1,X2))
| ~ v5_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_852]) ).
cnf(i_0_1951,plain,
( v1_membered(set_intersection2(X1,X2))
| ~ v4_membered(X1) ),
inference(split_conjunct,[status(thm)],[i_0_853]) ).
cnf(i_0_1952,plain,
( v1_membered(set_intersection2(X1,X2))
| ~ v4_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_854]) ).
cnf(i_0_1953,plain,
( v1_membered(set_intersection2(X1,X2))
| ~ v3_membered(X1) ),
inference(split_conjunct,[status(thm)],[i_0_855]) ).
cnf(i_0_1954,plain,
( v1_membered(set_intersection2(X1,X2))
| ~ v3_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_856]) ).
cnf(i_0_1955,plain,
( v1_membered(set_intersection2(X1,X2))
| ~ v2_membered(X1) ),
inference(split_conjunct,[status(thm)],[i_0_857]) ).
cnf(i_0_1956,plain,
( v1_membered(set_intersection2(X1,X2))
| ~ v2_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_858]) ).
cnf(i_0_1957,plain,
( v1_membered(set_intersection2(X1,X2))
| ~ v1_membered(X1) ),
inference(split_conjunct,[status(thm)],[i_0_859]) ).
cnf(i_0_1958,plain,
( v1_membered(set_intersection2(X2,X1))
| ~ v1_membered(X1) ),
inference(split_conjunct,[status(thm)],[i_0_860]) ).
fof(i_0_1959,lemma,
! [X3674,X3675,X3676] :
( ~ subset(X3674,X3675)
| subset(set_difference(X3674,X3676),set_difference(X3675,X3676)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t33_xboole_1])]) ).
fof(i_0_1960,lemma,
! [X3434,X3435,X3436] :
( ( subset(cartesian_product2(X3434,X3436),cartesian_product2(X3435,X3436))
| ~ subset(X3434,X3435) )
& ( subset(cartesian_product2(X3436,X3434),cartesian_product2(X3436,X3435))
| ~ subset(X3434,X3435) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t118_zfmisc_1])])]) ).
fof(i_0_1961,plain,
! [X1809] :
( ~ latt_str(X1809)
| ~ strict_latt_str(X1809)
| X1809 = latt_str_of(the_carrier(X1809),the_L_join(X1809),the_L_meet(X1809)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[abstractness_v3_lattices])]) ).
fof(i_0_1962,lemma,
! [X3483,X3484] :
( ~ relation(X3484)
| ~ function(X3484)
| ~ subset(X3483,relation_rng(X3484))
| relation_image(X3484,relation_inverse_image(X3484,X3483)) = X3483 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t147_funct_1])]) ).
cnf(i_0_1963,plain,
( in(X3,esk233_1(X2))
| in(esk230_1(X2),X2)
| ~ in(X1,X2)
| X3 != singleton(X1) ),
inference(split_conjunct,[status(thm)],[i_0_829]) ).
cnf(i_0_1964,plain,
( in(X3,esk233_1(X2))
| in(esk230_1(X2),X2)
| ~ in(X1,X2)
| X3 != singleton(X1) ),
inference(split_conjunct,[status(thm)],[i_0_829]) ).
cnf(i_0_1965,plain,
( in(succ(esk447_0),omega)
| in(empty_set,omega)
| epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_760]) ).
cnf(i_0_1966,lemma,
( set_difference(X1,singleton(X2)) != X1
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_861]) ).
fof(i_0_1967,lemma,
! [X3466,X3467,X3468] :
( ~ relation(X3468)
| relation_dom_restriction(relation_rng_restriction(X3466,X3468),X3467) = relation_rng_restriction(X3466,relation_dom_restriction(X3468,X3467)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t140_relat_1])]) ).
fof(i_0_1968,lemma,
! [X2734,X2735] :
( ( relation(esk133_2(X2734,X2735))
| ~ well_ordering(X2735)
| ~ equipotent(X2734,relation_field(X2735))
| ~ relation(X2735) )
& ( well_orders(esk133_2(X2734,X2735),X2734)
| ~ well_ordering(X2735)
| ~ equipotent(X2734,relation_field(X2735))
| ~ relation(X2735) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_862])])])]) ).
cnf(i_0_1969,lemma,
( ~ ordinal(X1)
| X2 != succ(X1)
| ~ being_limit_ordinal(X2)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_863]) ).
cnf(i_0_1970,lemma,
( ~ disjoint(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_864]) ).
fof(i_0_1971,lemma,
! [X3903,X3904,X3905] :
( ~ subset(X3903,X3904)
| ~ subset(X3905,X3904)
| subset(set_union2(X3903,X3905),X3904) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_xboole_1])]) ).
fof(i_0_1972,lemma,
! [X3700,X3701,X3702] :
( ( in(X3700,X3702)
| ~ subset(unordered_pair(X3700,X3701),X3702) )
& ( in(X3701,X3702)
| ~ subset(unordered_pair(X3700,X3701),X3702) )
& ( ~ in(X3700,X3702)
| ~ in(X3701,X3702)
| subset(unordered_pair(X3700,X3701),X3702) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t38_zfmisc_1])])]) ).
fof(i_0_1973,plain,
! [X2262,X2263] :
( empty_carrier(X2262)
| ~ lattice(X2262)
| ~ latt_str(X2262)
| ~ element(X2263,the_carrier(poset_of_lattice(X2262)))
| cast_to_el_of_lattice(X2262,X2263) = X2263 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_865])])]) ).
fof(i_0_1974,lemma,
! [X3432,X3433] :
( ~ relation(X3433)
| subset(relation_rng(relation_rng_restriction(X3432,X3433)),relation_rng(X3433)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t118_relat_1])]) ).
fof(i_0_1975,lemma,
! [X3917,X3918] :
( ~ relation(X3918)
| subset(relation_rng(relation_dom_restriction(X3918,X3917)),relation_rng(X3918)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t99_relat_1])]) ).
fof(i_0_1976,lemma,
! [X3550,X3551] :
( ( subset(relation_field(relation_restriction(X3551,X3550)),relation_field(X3551))
| ~ relation(X3551) )
& ( subset(relation_field(relation_restriction(X3551,X3550)),X3550)
| ~ relation(X3551) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t20_wellord1])])]) ).
fof(i_0_1977,lemma,
! [X2723,X2724] :
( ~ relation(X2724)
| subset(relation_dom(relation_rng_restriction(X2723,X2724)),relation_dom(X2724)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l29_wellord1])]) ).
cnf(i_0_1978,lemma,
( relation_dom(esk387_1(X1)) = X1
| esk385_1(X1) = singleton(esk383_1(X1))
| X2 != singleton(esk386_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_828]) ).
cnf(i_0_1979,lemma,
( relation_dom(esk387_1(X1)) = X1
| esk384_1(X1) = singleton(esk383_1(X1))
| X2 != singleton(esk386_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_828]) ).
cnf(i_0_1980,lemma,
( relation(esk387_1(X1))
| esk385_1(X1) = singleton(esk383_1(X1))
| X2 != singleton(esk386_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_828]) ).
cnf(i_0_1981,lemma,
( function(esk387_1(X1))
| esk385_1(X1) = singleton(esk383_1(X1))
| X2 != singleton(esk386_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_828]) ).
cnf(i_0_1982,lemma,
( relation(esk387_1(X1))
| esk384_1(X1) = singleton(esk383_1(X1))
| X2 != singleton(esk386_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_828]) ).
cnf(i_0_1983,lemma,
( function(esk387_1(X1))
| esk384_1(X1) = singleton(esk383_1(X1))
| X2 != singleton(esk386_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_828]) ).
fof(i_0_1984,lemma,
! [X2766,X2767] :
( ( in(esk138_2(X2766,X2767),X2766)
| element(X2766,powerset(X2767)) )
& ( ~ in(esk138_2(X2766,X2767),X2767)
| element(X2766,powerset(X2767)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l71_subset_1])])])]) ).
fof(i_0_1985,plain,
! [X2224,X2225,X2226,X2227] :
( ( ~ epsilon_connected(X2224)
| ~ in(X2225,X2224)
| ~ in(X2226,X2224)
| in(X2225,X2226)
| X2225 = X2226
| in(X2226,X2225) )
& ( in(esk70_1(X2227),X2227)
| epsilon_connected(X2227) )
& ( in(esk71_1(X2227),X2227)
| epsilon_connected(X2227) )
& ( ~ in(esk70_1(X2227),esk71_1(X2227))
| epsilon_connected(X2227) )
& ( esk70_1(X2227) != esk71_1(X2227)
| epsilon_connected(X2227) )
& ( ~ in(esk71_1(X2227),esk70_1(X2227))
| epsilon_connected(X2227) ) ),
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)],[i_0_866])])])])])]) ).
cnf(i_0_1986,lemma,
( X1 = succ(esk428_1(X1))
| being_limit_ordinal(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_863]) ).
fof(i_0_1987,plain,
! [X2557,X2558] : relation_of2_as_subset(esk124_2(X2557,X2558),X2557,X2558),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m2_relset_1])]) ).
fof(i_0_1988,plain,
! [X2775,X2776] :
( relation_of2(esk142_2(X2775,X2776),X2775,X2776)
& relation(esk142_2(X2775,X2776))
& function(esk142_2(X2775,X2776))
& quasi_total(esk142_2(X2775,X2776),X2775,X2776) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_funct_2])]) ).
fof(i_0_1989,plain,
! [X2796,X2797] :
( relation_of2(esk157_2(X2796,X2797),X2796,X2797)
& relation(esk157_2(X2796,X2797))
& function(esk157_2(X2796,X2797)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_partfun1])]) ).
fof(i_0_1990,plain,
! [X2552,X2553] : relation_of2(esk122_2(X2552,X2553),X2552,X2553),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_relset_1])]) ).
fof(i_0_1991,lemma,
! [X2951,X2952,X2954] :
( ( ordinal(esk199_1(X2951))
| ~ ordinal(X2952)
| ~ in(X2952,X2951) )
& ( in(esk199_1(X2951),X2951)
| ~ ordinal(X2952)
| ~ in(X2952,X2951) )
& ( ~ ordinal(X2954)
| ~ in(X2954,X2951)
| ordinal_subset(esk199_1(X2951),X2954)
| ~ ordinal(X2952)
| ~ in(X2952,X2951) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[s1_ordinal1__e8_6__wellord2])])])])]) ).
cnf(i_0_1992,plain,
( in(X3,esk233_1(X2))
| ~ in(X1,X2)
| X3 != singleton(X1)
| esk231_1(X2) != esk232_1(X2) ),
inference(split_conjunct,[status(thm)],[i_0_829]) ).
fof(i_0_1993,plain,
! [X2514] :
( ( function(identity_on_carrier(X2514))
| ~ one_sorted_str(X2514) )
& ( quasi_total(identity_on_carrier(X2514),the_carrier(X2514),the_carrier(X2514))
| ~ one_sorted_str(X2514) )
& ( relation_of2_as_subset(identity_on_carrier(X2514),the_carrier(X2514),the_carrier(X2514))
| ~ one_sorted_str(X2514) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k7_grcat_1])])]) ).
fof(i_0_1994,plain,
! [X2540] :
( ~ rel_str(X2540)
| relation_of2_as_subset(the_InternalRel(X2540),the_carrier(X2540),the_carrier(X2540)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u1_orders_2])]) ).
cnf(i_0_1995,lemma,
( X1 = empty_set
| X1 = singleton(X2)
| ~ subset(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_867]) ).
cnf(i_0_1996,lemma,
( X1 = empty_set
| X1 = singleton(X2)
| ~ subset(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_868]) ).
cnf(i_0_1997,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_869]) ).
fof(i_0_1998,lemma,
! [X3428,X3429] :
( ~ relation(X3429)
| subset(relation_rng(relation_rng_restriction(X3428,X3429)),X3428) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t116_relat_1])]) ).
fof(i_0_1999,plain,
! [X2478,X2479] :
( ~ element(X2479,powerset(X2478))
| element(subset_complement(X2478,X2479),powerset(X2478)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k3_subset_1])]) ).
fof(i_0_2000,lemma,
! [X3703,X3704] :
( ~ relation(X3704)
| ~ well_ordering(X3704)
| ~ subset(X3703,relation_field(X3704))
| relation_field(relation_restriction(X3704,X3703)) = X3703 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t39_wellord1])]) ).
fof(i_0_2001,plain,
! [X2237,X2238,X2239,X2240,X2241] :
( ( ~ subset(X2237,X2238)
| ~ in(X2239,X2237)
| in(X2239,X2238) )
& ( in(esk74_2(X2240,X2241),X2240)
| subset(X2240,X2241) )
& ( ~ in(esk74_2(X2240,X2241),X2241)
| subset(X2240,X2241) ) ),
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)],[d3_tarski])])])])])]) ).
cnf(i_0_2002,lemma,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_870]) ).
cnf(i_0_2003,lemma,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_871]) ).
cnf(i_0_2004,plain,
( disjoint(X1,X2)
| set_intersection2(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_872]) ).
cnf(i_0_2005,plain,
( in(succ(esk447_0),omega)
| epred1_0
| esk445_0 != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_760]) ).
fof(i_0_2006,lemma,
! [X3762,X3763] :
( ~ element(X3763,powerset(powerset(X3762)))
| X3763 = empty_set
| complements_of_subsets(X3762,X3763) != empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t46_setfam_1])]) ).
fof(i_0_2007,lemma,
! [X3419,X3420] :
( ( X3420 = empty_set
| complements_of_subsets(X3419,X3420) != empty_set
| ~ element(X3420,powerset(powerset(X3419))) )
& ( complements_of_subsets(X3419,X3420) = empty_set
| X3420 != empty_set
| ~ element(X3420,powerset(powerset(X3419))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t10_tops_2])])]) ).
fof(i_0_2008,plain,
! [X3198,X3200,X3202,X3203] :
( ( in(esk327_2(X3198,X3200),X3198)
| ~ in(X3200,esk326_1(X3198))
| esk323_0 = esk324_0 )
& ( esk327_2(X3198,X3200) = X3200
| ~ in(X3200,esk326_1(X3198))
| esk323_0 = esk324_0 )
& ( ordinal(X3200)
| ~ in(X3200,esk326_1(X3198))
| esk323_0 = esk324_0 )
& ( ~ in(X3203,X3198)
| X3203 != X3202
| ~ ordinal(X3202)
| in(X3202,esk326_1(X3198))
| esk323_0 = esk324_0 )
& ( in(esk327_2(X3198,X3200),X3198)
| ~ in(X3200,esk326_1(X3198))
| ordinal(esk324_0) )
& ( esk327_2(X3198,X3200) = X3200
| ~ in(X3200,esk326_1(X3198))
| ordinal(esk324_0) )
& ( ordinal(X3200)
| ~ in(X3200,esk326_1(X3198))
| ordinal(esk324_0) )
& ( ~ in(X3203,X3198)
| X3203 != X3202
| ~ ordinal(X3202)
| in(X3202,esk326_1(X3198))
| ordinal(esk324_0) )
& ( in(esk327_2(X3198,X3200),X3198)
| ~ in(X3200,esk326_1(X3198))
| esk323_0 = esk325_0 )
& ( esk327_2(X3198,X3200) = X3200
| ~ in(X3200,esk326_1(X3198))
| esk323_0 = esk325_0 )
& ( ordinal(X3200)
| ~ in(X3200,esk326_1(X3198))
| esk323_0 = esk325_0 )
& ( ~ in(X3203,X3198)
| X3203 != X3202
| ~ ordinal(X3202)
| in(X3202,esk326_1(X3198))
| esk323_0 = esk325_0 )
& ( in(esk327_2(X3198,X3200),X3198)
| ~ in(X3200,esk326_1(X3198))
| ordinal(esk325_0) )
& ( esk327_2(X3198,X3200) = X3200
| ~ in(X3200,esk326_1(X3198))
| ordinal(esk325_0) )
& ( ordinal(X3200)
| ~ in(X3200,esk326_1(X3198))
| ordinal(esk325_0) )
& ( ~ in(X3203,X3198)
| X3203 != X3202
| ~ ordinal(X3202)
| in(X3202,esk326_1(X3198))
| ordinal(esk325_0) )
& ( in(esk327_2(X3198,X3200),X3198)
| ~ in(X3200,esk326_1(X3198))
| esk324_0 != esk325_0 )
& ( esk327_2(X3198,X3200) = X3200
| ~ in(X3200,esk326_1(X3198))
| esk324_0 != esk325_0 )
& ( ordinal(X3200)
| ~ in(X3200,esk326_1(X3198))
| esk324_0 != esk325_0 )
& ( ~ in(X3203,X3198)
| X3203 != X3202
| ~ ordinal(X3202)
| in(X3202,esk326_1(X3198))
| esk324_0 != esk325_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)],[s1_tarski__e6_22__wellord2__1])])])])])]) ).
fof(i_0_2009,lemma,
! [X3453,X3455,X3456,X3457,X3458] :
( in(X3453,esk409_1(X3453))
& ( ~ in(X3455,esk409_1(X3453))
| ~ subset(X3456,X3455)
| in(X3456,esk409_1(X3453)) )
& ( ~ in(X3457,esk409_1(X3453))
| in(powerset(X3457),esk409_1(X3453)) )
& ( ~ subset(X3458,esk409_1(X3453))
| are_equipotent(X3458,esk409_1(X3453))
| in(X3458,esk409_1(X3453)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_873])])])]) ).
cnf(i_0_2010,lemma,
( relation_dom(esk387_1(X1)) = X1
| in(esk383_1(X1),X1)
| X2 != singleton(esk386_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_828]) ).
cnf(i_0_2011,lemma,
( relation(esk387_1(X1))
| in(esk383_1(X1),X1)
| X2 != singleton(esk386_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_828]) ).
cnf(i_0_2012,lemma,
( function(esk387_1(X1))
| in(esk383_1(X1),X1)
| X2 != singleton(esk386_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_828]) ).
fof(i_0_2013,plain,
! [X2707,X2708] :
( ~ element(X2708,powerset(X2707))
| subset_complement(X2707,subset_complement(X2707,X2708)) = X2708 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[involutiveness_k3_subset_1])]) ).
fof(i_0_2014,lemma,
! [X3562] :
( ~ relation(X3562)
| subset(X3562,cartesian_product2(relation_dom(X3562),relation_rng(X3562))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t21_relat_1])]) ).
cnf(i_0_2015,plain,
( in(esk44_2(X1,X2),X2)
| esk44_2(X1,X2) = X1
| X2 = singleton(X1) ),
inference(split_conjunct,[status(thm)],[i_0_839]) ).
fof(i_0_2016,plain,
! [X2541] :
( ~ top_str(X2541)
| element(the_topology(X2541),powerset(powerset(the_carrier(X2541)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u1_pre_topc])]) ).
fof(i_0_2017,plain,
! [X2864,X2865] :
( ~ element(X2865,powerset(powerset(X2864)))
| meet_of_subsets(X2864,X2865) = set_meet(X2865) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k6_setfam_1])]) ).
fof(i_0_2018,plain,
! [X2858,X2859] :
( ~ element(X2859,powerset(powerset(X2858)))
| union_of_subsets(X2858,X2859) = union(X2859) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k5_setfam_1])]) ).
fof(i_0_2019,plain,
! [X3780,X3781,X3782] :
( ~ in(X3780,X3781)
| ~ element(X3781,powerset(X3782))
| element(X3780,X3782) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).
fof(i_0_2020,lemma,
! [X2739,X2740,X2741] :
( ~ element(X2740,powerset(X2739))
| ~ in(X2741,X2740)
| in(X2741,X2739) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l3_subset_1])])]) ).
fof(i_0_2021,plain,
! [X2321,X2322,X2323] :
( ( in(empty_set,X2321)
| X2321 != omega )
& ( being_limit_ordinal(X2321)
| X2321 != omega )
& ( ordinal(X2321)
| X2321 != omega )
& ( ~ ordinal(X2322)
| ~ in(empty_set,X2322)
| ~ being_limit_ordinal(X2322)
| subset(X2321,X2322)
| X2321 != omega )
& ( ordinal(esk91_1(X2323))
| ~ in(empty_set,X2323)
| ~ being_limit_ordinal(X2323)
| ~ ordinal(X2323)
| X2323 = omega )
& ( in(empty_set,esk91_1(X2323))
| ~ in(empty_set,X2323)
| ~ being_limit_ordinal(X2323)
| ~ ordinal(X2323)
| X2323 = omega )
& ( being_limit_ordinal(esk91_1(X2323))
| ~ in(empty_set,X2323)
| ~ being_limit_ordinal(X2323)
| ~ ordinal(X2323)
| X2323 = omega )
& ( ~ subset(X2323,esk91_1(X2323))
| ~ in(empty_set,X2323)
| ~ being_limit_ordinal(X2323)
| ~ ordinal(X2323)
| X2323 = 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)],[d5_ordinal2])])])])])]) ).
fof(i_0_2022,lemma,
! [X3717,X3718,X3720,X3721,X3722] :
( ( in(esk426_2(X3717,X3718),X3717)
| disjoint(X3717,X3718) )
& ( in(esk426_2(X3717,X3718),X3718)
| disjoint(X3717,X3718) )
& ( ~ in(X3722,X3720)
| ~ in(X3722,X3721)
| ~ disjoint(X3720,X3721) ) ),
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)],[i_0_874])])])])])]) ).
fof(i_0_2023,lemma,
! [X3711,X3712,X3713] :
( ~ in(X3711,X3712)
| ~ in(X3712,X3713)
| ~ in(X3713,X3711) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_ordinal1])]) ).
fof(i_0_2024,lemma,
! [X3833,X3834] :
( ( ~ proper_element(X3834,powerset(X3833))
| X3834 != X3833
| ~ element(X3834,powerset(X3833)) )
& ( X3834 = X3833
| proper_element(X3834,powerset(X3833))
| ~ element(X3834,powerset(X3833)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_tex_2])])]) ).
cnf(i_0_2025,lemma,
( relation_dom(esk387_1(X1)) = X1
| X2 != singleton(esk386_1(X1))
| esk384_1(X1) != esk385_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_828]) ).
cnf(i_0_2026,lemma,
( relation(esk387_1(X1))
| X2 != singleton(esk386_1(X1))
| esk384_1(X1) != esk385_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_828]) ).
cnf(i_0_2027,lemma,
( function(esk387_1(X1))
| X2 != singleton(esk386_1(X1))
| esk384_1(X1) != esk385_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_828]) ).
fof(i_0_2028,plain,
! [X2219,X2220] :
( empty_carrier(X2219)
| ~ lattice(X2219)
| ~ latt_str(X2219)
| ~ element(X2220,the_carrier(X2219))
| cast_to_el_of_LattPOSet(X2219,X2220) = X2220 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_875])])]) ).
fof(i_0_2029,plain,
! [X2134,X2135] :
( empty_carrier(X2134)
| ~ latt_str(X2134)
| meet_of_latt_set(X2134,X2135) = join_of_latt_set(X2134,a_2_2_lattice3(X2134,X2135)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_876])])]) ).
fof(i_0_2030,lemma,
! [X3493,X3494] :
( ~ relation(X3493)
| ~ relation(X3494)
| relation_rng(relation_composition(X3493,X3494)) = relation_image(X3494,relation_rng(X3493)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t160_relat_1])])]) ).
cnf(i_0_2031,lemma,
( subset(X1,singleton(X2))
| X1 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[i_0_867]) ).
cnf(i_0_2032,lemma,
( subset(X1,singleton(X2))
| X1 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[i_0_868]) ).
cnf(i_0_2033,lemma,
( set_union2(singleton(X1),X2) = X2
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_877]) ).
cnf(i_0_2034,lemma,
( set_union2(singleton(X1),X2) = X2
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_878]) ).
cnf(i_0_2035,lemma,
( set_intersection2(X1,X2) = X1
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_879]) ).
fof(i_0_2036,lemma,
! [X3749,X3750] :
( ~ subset(X3749,X3750)
| X3750 = set_union2(X3749,set_difference(X3750,X3749)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t45_xboole_1])]) ).
fof(i_0_2037,lemma,
! [X3604,X3605] :
( ( subset(relation_dom(X3604),relation_dom(X3605))
| ~ subset(X3604,X3605)
| ~ relation(X3605)
| ~ relation(X3604) )
& ( subset(relation_rng(X3604),relation_rng(X3605))
| ~ subset(X3604,X3605)
| ~ relation(X3605)
| ~ relation(X3604) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t25_relat_1])])])]) ).
fof(i_0_2038,lemma,
! [X3511,X3512] :
( ~ relation(X3512)
| X3511 = empty_set
| ~ subset(X3511,relation_rng(X3512))
| relation_inverse_image(X3512,X3511) != empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t174_relat_1])]) ).
cnf(i_0_2039,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_870]) ).
cnf(i_0_2040,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_871]) ).
cnf(i_0_2041,plain,
( set_intersection2(X1,X2) = empty_set
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_872]) ).
cnf(i_0_2042,lemma,
( relation_dom(esk387_1(X1)) = X1
| in(esk386_1(X1),X1)
| esk385_1(X1) = singleton(esk383_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_828]) ).
cnf(i_0_2043,lemma,
( relation_dom(esk387_1(X1)) = X1
| in(esk386_1(X1),X1)
| esk384_1(X1) = singleton(esk383_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_828]) ).
fof(i_0_2044,plain,
! [X3830,X3831,X3832] :
( ~ in(X3830,X3831)
| ~ element(X3831,powerset(X3832))
| ~ empty(X3832) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
cnf(i_0_2045,lemma,
( relation(esk387_1(X1))
| in(esk386_1(X1),X1)
| esk385_1(X1) = singleton(esk383_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_828]) ).
cnf(i_0_2046,lemma,
( function(esk387_1(X1))
| in(esk386_1(X1),X1)
| esk385_1(X1) = singleton(esk383_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_828]) ).
cnf(i_0_2047,lemma,
( relation(esk387_1(X1))
| in(esk386_1(X1),X1)
| esk384_1(X1) = singleton(esk383_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_828]) ).
cnf(i_0_2048,lemma,
( function(esk387_1(X1))
| in(esk386_1(X1),X1)
| esk384_1(X1) = singleton(esk383_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_828]) ).
fof(i_0_2049,lemma,
! [X3522,X3523] :
( ~ relation(X3523)
| relation_restriction(X3523,X3522) = relation_dom_restriction(relation_rng_restriction(X3522,X3523),X3522) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t17_wellord1])]) ).
fof(i_0_2050,lemma,
! [X3530,X3531] :
( ~ relation(X3531)
| relation_restriction(X3531,X3530) = relation_rng_restriction(X3530,relation_dom_restriction(X3531,X3530)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t18_wellord1])]) ).
fof(i_0_2051,lemma,
! [X3608,X3609] :
( ( relation_field(relation_restriction(X3609,X3608)) = X3608
| ~ well_orders(X3609,X3608)
| ~ relation(X3609) )
& ( well_ordering(relation_restriction(X3609,X3608))
| ~ well_orders(X3609,X3608)
| ~ relation(X3609) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t25_wellord2])])]) ).
cnf(i_0_2052,plain,
relation_of2_as_subset(identity_as_relation_of(X1),X1,X1),
inference(split_conjunct,[status(thm)],[i_0_880]) ).
cnf(i_0_2053,plain,
identity_as_relation_of(X1) = identity_relation(X1),
inference(split_conjunct,[status(thm)],[i_0_881]) ).
fof(i_0_2054,plain,
! [X2792] :
( relation_of2(esk154_1(X2792),X2792,X2792)
& relation(esk154_1(X2792))
& function(esk154_1(X2792))
& one_to_one(esk154_1(X2792))
& quasi_total(esk154_1(X2792),X2792,X2792)
& onto(esk154_1(X2792),X2792,X2792)
& bijective(esk154_1(X2792),X2792,X2792) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_funct_2])]) ).
fof(i_0_2055,plain,
! [X2812] :
( relation_of2(esk167_1(X2812),X2812,X2812)
& relation(esk167_1(X2812))
& reflexive(esk167_1(X2812))
& symmetric(esk167_1(X2812))
& antisymmetric(esk167_1(X2812))
& transitive(esk167_1(X2812))
& v1_partfun1(esk167_1(X2812),X2812,X2812) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc3_partfun1])]) ).
cnf(i_0_2056,plain,
v1_partfun1(identity_as_relation_of(X1),X1,X1),
inference(split_conjunct,[status(thm)],[i_0_880]) ).
fof(i_0_2057,plain,
! [X2337,X2338] :
( ~ element(X2338,powerset(X2337))
| subset_complement(X2337,X2338) = set_difference(X2337,X2338) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_subset_1])]) ).
fof(i_0_2058,lemma,
! [X3842,X3843,X3844] :
( ~ subset(X3842,X3843)
| ~ disjoint(X3843,X3844)
| disjoint(X3842,X3844) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t63_xboole_1])]) ).
fof(i_0_2059,lemma,
! [X3544,X3545,X3546] :
( ~ subset(X3544,X3545)
| ~ subset(X3545,X3546)
| subset(X3544,X3546) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_xboole_1])]) ).
fof(i_0_2060,plain,
! [X1859] :
( ( ~ empty_carrier(X1859)
| empty_carrier(X1859)
| ~ join_commutative(X1859)
| ~ join_associative(X1859)
| ~ meet_commutative(X1859)
| ~ meet_associative(X1859)
| ~ meet_absorbing(X1859)
| ~ join_absorbing(X1859)
| ~ latt_str(X1859) )
& ( lattice(X1859)
| empty_carrier(X1859)
| ~ join_commutative(X1859)
| ~ join_associative(X1859)
| ~ meet_commutative(X1859)
| ~ meet_associative(X1859)
| ~ meet_absorbing(X1859)
| ~ join_absorbing(X1859)
| ~ latt_str(X1859) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_882])])]) ).
fof(i_0_2061,plain,
! [X2575,X2576] :
( ( relation(relation_composition(X2575,X2576))
| ~ relation(X2575)
| ~ function(X2575)
| ~ relation(X2576)
| ~ function(X2576) )
& ( function(relation_composition(X2575,X2576))
| ~ relation(X2575)
| ~ function(X2575)
| ~ relation(X2576)
| ~ function(X2576) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc1_funct_1])])]) ).
fof(i_0_2062,plain,
! [X2444,X2445] :
( empty_carrier(X2444)
| ~ latt_str(X2444)
| element(meet_of_latt_set(X2444,X2445),the_carrier(X2444)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_883])]) ).
fof(i_0_2063,plain,
! [X2442,X2443] :
( empty_carrier(X2442)
| ~ latt_str(X2442)
| element(join_of_latt_set(X2442,X2443),the_carrier(X2442)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_884])]) ).
fof(i_0_2064,plain,
! [X2824] :
( ( element(esk175_1(X2824),powerset(the_carrier(X2824)))
| empty_carrier(X2824)
| ~ topological_space(X2824)
| ~ top_str(X2824) )
& ( ~ empty(esk175_1(X2824))
| empty_carrier(X2824)
| ~ topological_space(X2824)
| ~ top_str(X2824) )
& ( closed_subset(esk175_1(X2824),X2824)
| empty_carrier(X2824)
| ~ topological_space(X2824)
| ~ top_str(X2824) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_885])])])]) ).
fof(i_0_2065,plain,
! [X2020,X2022,X2023] :
( ( relation(esk26_1(X2020))
| ~ finite(X2020) )
& ( function(esk26_1(X2020))
| ~ finite(X2020) )
& ( relation_rng(esk26_1(X2020)) = X2020
| ~ finite(X2020) )
& ( in(relation_dom(esk26_1(X2020)),omega)
| ~ finite(X2020) )
& ( ~ relation(X2023)
| ~ function(X2023)
| relation_rng(X2023) != X2022
| ~ in(relation_dom(X2023),omega)
| finite(X2022) ) ),
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)],[d1_finset_1])])])])])]) ).
fof(i_0_2066,plain,
! [X2653,X2654] :
( empty(X2653)
| empty(X2654)
| ~ empty(cartesian_product2(X2653,X2654)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_886])]) ).
cnf(i_0_2067,lemma,
( apply(esk405_1(X2),X1) = singleton(X1)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_887]) ).
cnf(i_0_2068,lemma,
( in(X1,X2)
| set_difference(X2,singleton(X1)) = X2 ),
inference(split_conjunct,[status(thm)],[i_0_861]) ).
cnf(i_0_2069,lemma,
( in(X1,X2)
| disjoint(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_888]) ).
fof(i_0_2070,lemma,
! [X3724,X3725] : set_difference(set_union2(X3724,X3725),X3725) = set_difference(X3724,X3725),
inference(variable_rename,[status(thm)],[t40_xboole_1]) ).
fof(i_0_2071,lemma,
! [X3705,X3706] : set_union2(X3705,set_difference(X3706,X3705)) = set_union2(X3705,X3706),
inference(variable_rename,[status(thm)],[t39_xboole_1]) ).
fof(i_0_2072,plain,
! [X2519,X2520] :
( ( strict_latt_str(k8_filter_1(X2519,X2520))
| empty_carrier(X2519)
| ~ latt_str(X2519)
| empty_carrier(X2520)
| ~ latt_str(X2520) )
& ( latt_str(k8_filter_1(X2519,X2520))
| empty_carrier(X2519)
| ~ latt_str(X2519)
| empty_carrier(X2520)
| ~ latt_str(X2520) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_889])])]) ).
fof(i_0_2073,plain,
! [X2295,X2296,X2298,X2299,X2300] :
( ( relation(esk86_2(X2295,X2296))
| ~ equipotent(X2295,X2296) )
& ( function(esk86_2(X2295,X2296))
| ~ equipotent(X2295,X2296) )
& ( one_to_one(esk86_2(X2295,X2296))
| ~ equipotent(X2295,X2296) )
& ( relation_dom(esk86_2(X2295,X2296)) = X2295
| ~ equipotent(X2295,X2296) )
& ( relation_rng(esk86_2(X2295,X2296)) = X2296
| ~ equipotent(X2295,X2296) )
& ( ~ relation(X2300)
| ~ function(X2300)
| ~ one_to_one(X2300)
| relation_dom(X2300) != X2298
| relation_rng(X2300) != X2299
| equipotent(X2298,X2299) ) ),
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)],[d4_wellord2])])])])])]) ).
fof(i_0_2074,plain,
! [X2177,X2178] :
( ( ~ proper_element(X2178,X2177)
| X2178 != union(X2177)
| ~ element(X2178,X2177) )
& ( X2178 = union(X2177)
| proper_element(X2178,X2177)
| ~ element(X2178,X2177) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d2_tex_2])])]) ).
fof(i_0_2075,lemma,
! [X3659] :
( ( in(esk422_1(X3659),X3659)
| ordinal(X3659) )
& ( ~ ordinal(esk422_1(X3659))
| ~ subset(esk422_1(X3659),X3659)
| ordinal(X3659) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t31_ordinal1])])])]) ).
fof(i_0_2076,plain,
! [X2343] :
( ( ~ antisymmetric_relstr(X2343)
| is_antisymmetric_in(the_InternalRel(X2343),the_carrier(X2343))
| ~ rel_str(X2343) )
& ( ~ is_antisymmetric_in(the_InternalRel(X2343),the_carrier(X2343))
| antisymmetric_relstr(X2343)
| ~ rel_str(X2343) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d6_orders_2])])]) ).
fof(i_0_2077,plain,
! [X2320] :
( ( ~ transitive_relstr(X2320)
| is_transitive_in(the_InternalRel(X2320),the_carrier(X2320))
| ~ rel_str(X2320) )
& ( ~ is_transitive_in(the_InternalRel(X2320),the_carrier(X2320))
| transitive_relstr(X2320)
| ~ rel_str(X2320) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_orders_2])])]) ).
fof(i_0_2078,lemma,
! [X3500,X3501] :
( ~ relation(X3501)
| subset(relation_inverse_image(X3501,X3500),relation_dom(X3501)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t167_relat_1])]) ).
fof(i_0_2079,lemma,
! [X3474,X3475] :
( ~ relation(X3475)
| subset(relation_image(X3475,X3474),relation_rng(X3475)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t144_relat_1])]) ).
fof(i_0_2080,plain,
! [X2822] :
( ( element(esk174_1(X2822),powerset(the_carrier(X2822)))
| ~ topological_space(X2822)
| ~ top_str(X2822) )
& ( closed_subset(esk174_1(X2822),X2822)
| ~ topological_space(X2822)
| ~ top_str(X2822) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[rc6_pre_topc])])])]) ).
fof(i_0_2081,plain,
! [X2804] :
( ( element(esk161_1(X2804),powerset(the_carrier(X2804)))
| ~ topological_space(X2804)
| ~ top_str(X2804) )
& ( open_subset(esk161_1(X2804),X2804)
| ~ topological_space(X2804)
| ~ top_str(X2804) )
& ( closed_subset(esk161_1(X2804),X2804)
| ~ topological_space(X2804)
| ~ top_str(X2804) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[rc2_tops_1])])])]) ).
fof(i_0_2082,plain,
! [X2786] :
( ( element(esk150_1(X2786),powerset(the_carrier(X2786)))
| ~ topological_space(X2786)
| ~ top_str(X2786) )
& ( open_subset(esk150_1(X2786),X2786)
| ~ topological_space(X2786)
| ~ top_str(X2786) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[rc1_tops_1])])])]) ).
fof(i_0_2083,plain,
! [X2606,X2607] :
( empty(X2606)
| ~ empty(set_union2(X2606,X2607)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_890])]) ).
fof(i_0_2084,plain,
! [X2642,X2643] :
( empty(X2642)
| ~ empty(set_union2(X2643,X2642)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_891])]) ).
fof(i_0_2085,lemma,
! [X3516,X3517] :
( ~ relation(X3517)
| ~ function(X3517)
| ~ finite(X3516)
| finite(relation_image(X3517,X3516)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t17_finset_1])]) ).
fof(i_0_2086,plain,
! [X2569,X2570] :
( ~ relation(X2569)
| ~ function(X2569)
| ~ finite(X2570)
| finite(relation_image(X2569,X2570)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc13_finset_1])]) ).
fof(i_0_2087,plain,
! [X2876,X2877] :
( ( ~ ordinal_subset(X2876,X2877)
| subset(X2876,X2877)
| ~ ordinal(X2876)
| ~ ordinal(X2877) )
& ( ~ subset(X2876,X2877)
| ordinal_subset(X2876,X2877)
| ~ ordinal(X2876)
| ~ ordinal(X2877) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_r1_ordinal1])])]) ).
fof(i_0_2088,lemma,
! [X3560,X3561] :
( ~ epsilon_transitive(X3560)
| ~ ordinal(X3561)
| ~ proper_subset(X3560,X3561)
| in(X3560,X3561) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t21_ordinal1])])]) ).
fof(i_0_2089,plain,
! [X2819] :
( ( element(esk172_1(X2819),powerset(the_carrier(X2819)))
| empty_carrier(X2819)
| ~ one_sorted_str(X2819) )
& ( ~ empty(esk172_1(X2819))
| empty_carrier(X2819)
| ~ one_sorted_str(X2819) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_892])])])]) ).
fof(i_0_2090,lemma,
! [X3317,X3319,X3320] :
( ( in(X3319,X3317)
| ~ in(X3319,esk370_1(X3317)) )
& ( ordinal(X3319)
| ~ in(X3319,esk370_1(X3317)) )
& ( ~ in(X3320,X3317)
| ~ ordinal(X3320)
| in(X3320,esk370_1(X3317)) ) ),
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)],[s1_xboole_0__e6_22__wellord2])])])])])]) ).
fof(i_0_2091,plain,
! [X2140] :
( empty_carrier(X2140)
| ~ lattice(X2140)
| ~ latt_str(X2140)
| poset_of_lattice(X2140) = rel_str_of(the_carrier(X2140),k2_lattice3(X2140)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_893])]) ).
cnf(i_0_2092,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[i_0_839]) ).
fof(i_0_2093,lemma,
! [X3421,X3422,X3423,X3424] :
( unordered_pair(X3421,X3422) != unordered_pair(X3423,X3424)
| X3421 = X3423
| X3421 = X3424 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t10_zfmisc_1])]) ).
cnf(i_0_2094,plain,
~ empty(singleton(X1)),
inference(split_conjunct,[status(thm)],[i_0_894]) ).
cnf(i_0_2095,plain,
~ empty(singleton(X1)),
inference(split_conjunct,[status(thm)],[i_0_895]) ).
fof(i_0_2096,plain,
! [X2638,X2639] : ~ empty(unordered_pair(X2638,X2639)),
inference(variable_rename,[status(thm)],[i_0_896]) ).
fof(i_0_2097,plain,
! [X1905,X1906] :
( ( subset(X1905,X1906)
| X1905 != X1906 )
& ( subset(X1906,X1905)
| X1905 != X1906 )
& ( ~ subset(X1905,X1906)
| ~ subset(X1906,X1905)
| X1905 = X1906 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])]) ).
fof(i_0_2098,plain,
! [X2294] :
( ( reflexive(X2294)
| ~ well_ordering(X2294)
| ~ relation(X2294) )
& ( transitive(X2294)
| ~ well_ordering(X2294)
| ~ relation(X2294) )
& ( antisymmetric(X2294)
| ~ well_ordering(X2294)
| ~ relation(X2294) )
& ( connected(X2294)
| ~ well_ordering(X2294)
| ~ relation(X2294) )
& ( well_founded_relation(X2294)
| ~ well_ordering(X2294)
| ~ relation(X2294) )
& ( ~ reflexive(X2294)
| ~ transitive(X2294)
| ~ antisymmetric(X2294)
| ~ connected(X2294)
| ~ well_founded_relation(X2294)
| well_ordering(X2294)
| ~ relation(X2294) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d4_wellord1])])]) ).
fof(i_0_2099,lemma,
! [X3430,X3431] :
( ~ relation(X3431)
| subset(relation_rng_restriction(X3430,X3431),X3431) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t117_relat_1])]) ).
fof(i_0_2100,lemma,
! [X3895,X3896] :
( ~ relation(X3896)
| subset(relation_dom_restriction(X3896,X3895),X3896) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t88_relat_1])]) ).
fof(i_0_2101,plain,
! [X3714,X3715] :
( ( ~ element(X3714,powerset(X3715))
| subset(X3714,X3715) )
& ( ~ subset(X3714,X3715)
| element(X3714,powerset(X3715)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
cnf(i_0_2102,lemma,
( X1 = X2
| singleton(X1) != unordered_pair(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_897]) ).
cnf(i_0_2103,lemma,
( X2 = X3
| singleton(X1) != unordered_pair(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_898]) ).
fof(i_0_2104,plain,
! [X2470] :
( ~ one_sorted_str(X2470)
| element(cast_as_carrier_subset(X2470),powerset(the_carrier(X2470))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_pre_topc])]) ).
fof(i_0_2105,plain,
! [X2455] :
( ~ one_sorted_str(X2455)
| element(empty_carrier_subset(X2455),powerset(the_carrier(X2455))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_pre_topc])]) ).
fof(i_0_2106,plain,
! [X2136,X2137,X2138] :
( ( X2136 != empty_set
| ~ centered(X2136) )
& ( X2137 = empty_set
| ~ subset(X2137,X2136)
| ~ finite(X2137)
| set_meet(X2137) != empty_set
| ~ centered(X2136) )
& ( esk52_1(X2138) != empty_set
| X2138 = empty_set
| centered(X2138) )
& ( subset(esk52_1(X2138),X2138)
| X2138 = empty_set
| centered(X2138) )
& ( finite(esk52_1(X2138))
| X2138 = empty_set
| centered(X2138) )
& ( set_meet(esk52_1(X2138)) = empty_set
| X2138 = empty_set
| centered(X2138) ) ),
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)],[d2_compts_1])])])])])]) ).
fof(i_0_2107,lemma,
! [X3597,X3598] :
( ~ ordinal(X3597)
| ~ ordinal(X3598)
| in(X3597,X3598)
| X3597 = X3598
| in(X3598,X3597) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_899])])]) ).
fof(i_0_2108,lemma,
! [X3839,X3840] :
( ~ subset(X3839,X3840)
| ~ proper_subset(X3840,X3839) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t60_xboole_1])]) ).
fof(i_0_2109,plain,
! [X1812,X1813] :
( ~ proper_subset(X1812,X1813)
| ~ proper_subset(X1813,X1812) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_900])]) ).
fof(i_0_2110,plain,
! [X1810,X1811] :
( ~ in(X1810,X1811)
| ~ in(X1811,X1810) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_901])]) ).
fof(i_0_2111,plain,
! [X2571,X2572] :
( ( relation(relation_dom_restriction(X2571,X2572))
| ~ relation(X2571)
| ~ relation_empty_yielding(X2571) )
& ( relation_empty_yielding(relation_dom_restriction(X2571,X2572))
| ~ relation(X2571)
| ~ relation_empty_yielding(X2571) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc13_relat_1])])]) ).
fof(i_0_2112,lemma,
! [X3670,X3671] :
( ~ relation(X3671)
| ~ well_ordering(X3671)
| well_ordering(relation_restriction(X3671,X3670)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t32_wellord1])]) ).
fof(i_0_2113,lemma,
! [X3661,X3662] :
( ~ relation(X3662)
| ~ well_founded_relation(X3662)
| well_founded_relation(relation_restriction(X3662,X3661)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t31_wellord1])]) ).
fof(i_0_2114,lemma,
! [X3595,X3596] :
( ~ relation(X3596)
| ~ connected(X3596)
| connected(relation_restriction(X3596,X3595)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t23_wellord1])]) ).
fof(i_0_2115,lemma,
! [X3606,X3607] :
( ~ relation(X3607)
| ~ antisymmetric(X3607)
| antisymmetric(relation_restriction(X3607,X3606)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t25_wellord1])]) ).
fof(i_0_2116,lemma,
! [X3578,X3579] :
( ~ relation(X3579)
| ~ reflexive(X3579)
| reflexive(relation_restriction(X3579,X3578)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t22_wellord1])]) ).
fof(i_0_2117,lemma,
! [X3599,X3600] :
( ~ relation(X3600)
| ~ transitive(X3600)
| transitive(relation_restriction(X3600,X3599)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t24_wellord1])]) ).
fof(i_0_2118,plain,
! [X2495,X2496] :
( ~ relation(X2495)
| ~ relation(X2496)
| relation(relation_composition(X2495,X2496)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k5_relat_1])]) ).
fof(i_0_2119,plain,
! [X2669,X2670] :
( ( empty(relation_composition(X2669,X2670))
| ~ empty(X2669)
| ~ relation(X2670) )
& ( relation(relation_composition(X2669,X2670))
| ~ empty(X2669)
| ~ relation(X2670) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc9_relat_1])])]) ).
fof(i_0_2120,plain,
! [X2562,X2563] :
( ( empty(relation_composition(X2563,X2562))
| ~ empty(X2562)
| ~ relation(X2563) )
& ( relation(relation_composition(X2563,X2562))
| ~ empty(X2562)
| ~ relation(X2563) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc10_relat_1])])]) ).
fof(i_0_2121,plain,
! [X2636,X2637] :
( ~ relation(X2636)
| ~ relation(X2637)
| relation(set_difference(X2636,X2637)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc3_relat_1])]) ).
fof(i_0_2122,plain,
! [X2657,X2658] :
( ( relation(relation_rng_restriction(X2657,X2658))
| ~ relation(X2658)
| ~ function(X2658) )
& ( function(relation_rng_restriction(X2657,X2658))
| ~ relation(X2658)
| ~ function(X2658) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc5_funct_1])])]) ).
fof(i_0_2123,plain,
! [X2648,X2649] :
( ( relation(relation_dom_restriction(X2648,X2649))
| ~ relation(X2648)
| ~ function(X2648) )
& ( function(relation_dom_restriction(X2648,X2649))
| ~ relation(X2648)
| ~ function(X2648) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc4_funct_1])])]) ).
fof(i_0_2124,plain,
! [X2601,X2602] :
( ~ relation(X2601)
| ~ relation(X2602)
| relation(set_union2(X2601,X2602)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc2_relat_1])]) ).
fof(i_0_2125,plain,
! [X2667,X2668] :
( ~ finite(X2667)
| ~ finite(X2668)
| finite(set_union2(X2667,X2668)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc9_finset_1])]) ).
fof(i_0_2126,plain,
! [X2153,X2154,X2155] :
( ( ~ epsilon_transitive(X2153)
| ~ in(X2154,X2153)
| subset(X2154,X2153) )
& ( in(esk55_1(X2155),X2155)
| epsilon_transitive(X2155) )
& ( ~ subset(esk55_1(X2155),X2155)
| epsilon_transitive(X2155) ) ),
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)],[d2_ordinal1])])])])])]) ).
fof(i_0_2127,lemma,
! [X3902] :
( ( ~ well_orders(X3902,relation_field(X3902))
| well_ordering(X3902)
| ~ relation(X3902) )
& ( ~ well_ordering(X3902)
| well_orders(X3902,relation_field(X3902))
| ~ relation(X3902) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_wellord1])])]) ).
fof(i_0_2128,lemma,
! [X3837] :
( ( ~ well_founded_relation(X3837)
| is_well_founded_in(X3837,relation_field(X3837))
| ~ relation(X3837) )
& ( ~ is_well_founded_in(X3837,relation_field(X3837))
| well_founded_relation(X3837)
| ~ relation(X3837) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_wellord1])])]) ).
fof(i_0_2129,plain,
! [X1985] :
( ( ~ connected(X1985)
| is_connected_in(X1985,relation_field(X1985))
| ~ relation(X1985) )
& ( ~ is_connected_in(X1985,relation_field(X1985))
| connected(X1985)
| ~ relation(X1985) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d14_relat_2])])]) ).
fof(i_0_2130,plain,
! [X1938] :
( ( ~ antisymmetric(X1938)
| is_antisymmetric_in(X1938,relation_field(X1938))
| ~ relation(X1938) )
& ( ~ is_antisymmetric_in(X1938,relation_field(X1938))
| antisymmetric(X1938)
| ~ relation(X1938) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d12_relat_2])])]) ).
fof(i_0_2131,plain,
! [X2432] :
( ( ~ reflexive(X2432)
| is_reflexive_in(X2432,relation_field(X2432))
| ~ relation(X2432) )
& ( ~ is_reflexive_in(X2432,relation_field(X2432))
| reflexive(X2432)
| ~ relation(X2432) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d9_relat_2])])]) ).
fof(i_0_2132,plain,
! [X1996] :
( ( ~ transitive(X1996)
| is_transitive_in(X1996,relation_field(X1996))
| ~ relation(X1996) )
& ( ~ is_transitive_in(X1996,relation_field(X1996))
| transitive(X1996)
| ~ relation(X1996) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d16_relat_2])])]) ).
fof(i_0_2133,plain,
! [X1852,X1853] :
( ~ finite(X1852)
| ~ element(X1853,powerset(X1852))
| finite(X1853) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_finset_1])])]) ).
fof(i_0_2134,plain,
! [X1849,X1850] :
( ( v1_membered(X1850)
| ~ element(X1850,powerset(X1849))
| ~ v5_membered(X1849) )
& ( v2_membered(X1850)
| ~ element(X1850,powerset(X1849))
| ~ v5_membered(X1849) )
& ( v3_membered(X1850)
| ~ element(X1850,powerset(X1849))
| ~ v5_membered(X1849) )
& ( v4_membered(X1850)
| ~ element(X1850,powerset(X1849))
| ~ v5_membered(X1849) )
& ( v5_membered(X1850)
| ~ element(X1850,powerset(X1849))
| ~ v5_membered(X1849) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc20_membered])])])]) ).
fof(i_0_2135,plain,
! [X1831,X1832] :
( ( v1_membered(X1832)
| ~ element(X1832,powerset(X1831))
| ~ v4_membered(X1831) )
& ( v2_membered(X1832)
| ~ element(X1832,powerset(X1831))
| ~ v4_membered(X1831) )
& ( v3_membered(X1832)
| ~ element(X1832,powerset(X1831))
| ~ v4_membered(X1831) )
& ( v4_membered(X1832)
| ~ element(X1832,powerset(X1831))
| ~ v4_membered(X1831) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc19_membered])])])]) ).
fof(i_0_2136,plain,
! [X1829,X1830] :
( ( v1_membered(X1830)
| ~ element(X1830,powerset(X1829))
| ~ v3_membered(X1829) )
& ( v2_membered(X1830)
| ~ element(X1830,powerset(X1829))
| ~ v3_membered(X1829) )
& ( v3_membered(X1830)
| ~ element(X1830,powerset(X1829))
| ~ v3_membered(X1829) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc18_membered])])])]) ).
fof(i_0_2137,plain,
! [X1827,X1828] :
( ( v1_membered(X1828)
| ~ element(X1828,powerset(X1827))
| ~ v2_membered(X1827) )
& ( v2_membered(X1828)
| ~ element(X1828,powerset(X1827))
| ~ v2_membered(X1827) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc17_membered])])])]) ).
fof(i_0_2138,plain,
! [X1825,X1826] :
( ~ v1_membered(X1825)
| ~ element(X1826,powerset(X1825))
| v1_membered(X1826) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc16_membered])])]) ).
fof(i_0_2139,lemma,
! [X3691,X3692] :
( ~ in(X3692,X3691)
| apply(identity_relation(X3691),X3692) = X3692 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t35_funct_1])]) ).
fof(i_0_2140,plain,
! [X1895,X1896] :
( ~ ordinal(X1895)
| ~ ordinal(X1896)
| ordinal_subset(X1895,X1896)
| ordinal_subset(X1896,X1895) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[connectedness_r1_ordinal1])]) ).
fof(i_0_2141,lemma,
! [X3913,X3914] :
( ~ in(X3913,X3914)
| subset(X3913,union(X3914)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t92_zfmisc_1])]) ).
fof(i_0_2142,lemma,
! [X2760,X2761] :
( ~ in(X2760,X2761)
| subset(X2760,union(X2761)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l50_zfmisc_1])]) ).
fof(i_0_2143,lemma,
! [X3790] :
( ( ~ empty_carrier(X3790)
| empty_carrier(X3790)
| ~ lattice(X3790)
| ~ complete_latt_str(X3790)
| ~ latt_str(X3790) )
& ( lattice(X3790)
| empty_carrier(X3790)
| ~ lattice(X3790)
| ~ complete_latt_str(X3790)
| ~ latt_str(X3790) )
& ( lower_bounded_semilattstr(X3790)
| empty_carrier(X3790)
| ~ lattice(X3790)
| ~ complete_latt_str(X3790)
| ~ latt_str(X3790) )
& ( latt_str(X3790)
| empty_carrier(X3790)
| ~ lattice(X3790)
| ~ complete_latt_str(X3790)
| ~ latt_str(X3790) )
& ( bottom_of_semilattstr(X3790) = join_of_latt_set(X3790,empty_set)
| empty_carrier(X3790)
| ~ lattice(X3790)
| ~ complete_latt_str(X3790)
| ~ latt_str(X3790) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_902])])]) ).
cnf(i_0_2144,lemma,
( subset(X1,singleton(X2))
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_867]) ).
cnf(i_0_2145,lemma,
( subset(X1,singleton(X2))
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_868]) ).
cnf(i_0_2146,plain,
( in(X1,X3)
| X1 != X2
| X3 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[i_0_839]) ).
fof(i_0_2147,plain,
! [X2802] :
( element(esk160_1(X2802),powerset(X2802))
& ~ proper_element(esk160_1(X2802),powerset(X2802)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_903])]) ).
fof(i_0_2148,lemma,
! [X3610] :
( ~ relation(X3610)
| ~ function(X3610)
| ~ finite(relation_dom(X3610))
| finite(relation_rng(X3610)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t26_finset_1])]) ).
fof(i_0_2149,plain,
! [X1808] :
( ~ rel_str(X1808)
| ~ strict_rel_str(X1808)
| X1808 = rel_str_of(the_carrier(X1808),the_InternalRel(X1808)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[abstractness_v1_orders_2])]) ).
fof(i_0_2150,plain,
! [X2166,X2167] :
( ( ~ element(X2167,X2166)
| in(X2167,X2166)
| empty(X2166) )
& ( ~ in(X2167,X2166)
| element(X2167,X2166)
| empty(X2166) )
& ( ~ element(X2167,X2166)
| empty(X2167)
| ~ empty(X2166) )
& ( ~ empty(X2167)
| element(X2167,X2166)
| ~ empty(X2166) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_904])])]) ).
fof(i_0_2151,plain,
! [X3641,X3642] :
( ~ element(X3641,X3642)
| empty(X3642)
| in(X3641,X3642) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(i_0_2152,lemma,
! [X3915,X3916] :
( ~ relation(X3916)
| relation_dom_restriction(X3916,X3915) = relation_composition(identity_relation(X3915),X3916) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t94_relat_1])]) ).
cnf(i_0_2153,lemma,
( relation(esk188_1(X1))
| esk187_1(X1) = singleton(esk185_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_768]) ).
cnf(i_0_2154,lemma,
( function(esk188_1(X1))
| esk187_1(X1) = singleton(esk185_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_768]) ).
cnf(i_0_2155,lemma,
( relation(esk188_1(X1))
| esk186_1(X1) = singleton(esk185_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_768]) ).
cnf(i_0_2156,lemma,
( function(esk188_1(X1))
| esk186_1(X1) = singleton(esk185_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_768]) ).
cnf(i_0_2157,plain,
set_intersection2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_905]) ).
fof(i_0_2158,lemma,
! [X3693,X3694] : subset(set_difference(X3693,X3694),X3693),
inference(variable_rename,[status(thm)],[t36_xboole_1]) ).
fof(i_0_2159,lemma,
! [X3888,X3889] : subset(X3888,set_union2(X3888,X3889)),
inference(variable_rename,[status(thm)],[t7_xboole_1]) ).
fof(i_0_2160,plain,
! [X2421,X2422] :
( ( subset(X2421,X2422)
| ~ proper_subset(X2421,X2422) )
& ( X2421 != X2422
| ~ proper_subset(X2421,X2422) )
& ( ~ subset(X2421,X2422)
| X2421 = X2422
| proper_subset(X2421,X2422) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_xboole_0])])]) ).
cnf(i_0_2161,plain,
element(k1_pcomps_1(X1),powerset(powerset(X1))),
inference(split_conjunct,[status(thm)],[i_0_906]) ).
cnf(i_0_2162,plain,
k1_pcomps_1(X1) = powerset(X1),
inference(split_conjunct,[status(thm)],[i_0_907]) ).
fof(i_0_2163,plain,
! [X2494] :
( empty_carrier(X2494)
| ~ meet_semilatt_str(X2494)
| element(bottom_of_semilattstr(X2494),the_carrier(X2494)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_908])]) ).
fof(i_0_2164,lemma,
! [X3890,X3891] :
( ( ~ disjoint(X3890,X3891)
| set_difference(X3890,X3891) = X3890 )
& ( set_difference(X3890,X3891) != X3890
| disjoint(X3890,X3891) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t83_xboole_1])]) ).
fof(i_0_2165,lemma,
! [X3451,X3452] :
( ~ subset(X3451,X3452)
| set_union2(X3451,X3452) = X3452 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_xboole_1])]) ).
fof(i_0_2166,plain,
! [X2347] :
( ~ relation(X2347)
| relation_field(X2347) = set_union2(relation_dom(X2347),relation_rng(X2347)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d6_relat_1])]) ).
fof(i_0_2167,plain,
! [X2472,X2473] :
( ~ relation(X2472)
| relation(relation_restriction(X2472,X2473)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_wellord1])]) ).
fof(i_0_2168,plain,
! [X2525,X2526] :
( ~ relation(X2526)
| relation(relation_rng_restriction(X2525,X2526)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k8_relat_1])]) ).
fof(i_0_2169,plain,
! [X2515,X2516] :
( ~ relation(X2515)
| relation(relation_dom_restriction(X2515,X2516)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k7_relat_1])]) ).
fof(i_0_2170,plain,
! [X2567,X2568] :
( ~ finite(X2567)
| finite(set_difference(X2567,X2568)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc12_finset_1])]) ).
fof(i_0_2171,plain,
! [X2646,X2647] :
( ( v1_membered(set_difference(X2646,X2647))
| ~ v5_membered(X2646) )
& ( v2_membered(set_difference(X2646,X2647))
| ~ v5_membered(X2646) )
& ( v3_membered(set_difference(X2646,X2647))
| ~ v5_membered(X2646) )
& ( v4_membered(set_difference(X2646,X2647))
| ~ v5_membered(X2646) )
& ( v5_membered(set_difference(X2646,X2647))
| ~ v5_membered(X2646) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc41_membered])])]) ).
fof(i_0_2172,plain,
! [X2644,X2645] :
( ( v1_membered(set_difference(X2644,X2645))
| ~ v4_membered(X2644) )
& ( v2_membered(set_difference(X2644,X2645))
| ~ v4_membered(X2644) )
& ( v3_membered(set_difference(X2644,X2645))
| ~ v4_membered(X2644) )
& ( v4_membered(set_difference(X2644,X2645))
| ~ v4_membered(X2644) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc40_membered])])]) ).
fof(i_0_2173,plain,
! [X2626,X2627] :
( ( v1_membered(set_difference(X2626,X2627))
| ~ v3_membered(X2626) )
& ( v2_membered(set_difference(X2626,X2627))
| ~ v3_membered(X2626) )
& ( v3_membered(set_difference(X2626,X2627))
| ~ v3_membered(X2626) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc39_membered])])]) ).
fof(i_0_2174,plain,
! [X2624,X2625] :
( ( v1_membered(set_difference(X2624,X2625))
| ~ v2_membered(X2624) )
& ( v2_membered(set_difference(X2624,X2625))
| ~ v2_membered(X2624) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc38_membered])])]) ).
fof(i_0_2175,plain,
! [X2622,X2623] :
( ~ v1_membered(X2622)
| v1_membered(set_difference(X2622,X2623)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc37_membered])]) ).
cnf(i_0_2176,plain,
set_intersection2(X1,empty_set) = empty_set,
inference(split_conjunct,[status(thm)],[i_0_909]) ).
fof(i_0_2177,plain,
! [X2878,X2879] :
( ( ~ equipotent(X2878,X2879)
| are_equipotent(X2878,X2879) )
& ( ~ are_equipotent(X2878,X2879)
| equipotent(X2878,X2879) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_r2_wellord2])]) ).
fof(i_0_2178,plain,
! [X3412,X3413] :
( ~ equipotent(X3412,X3413)
| equipotent(X3413,X3412) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_r2_wellord2])]) ).
fof(i_0_2179,plain,
! [X3410,X3411] :
( ~ disjoint(X3410,X3411)
| disjoint(X3411,X3410) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0])]) ).
fof(i_0_2180,plain,
! [X3542,X3543] :
( ~ in(X3542,X3543)
| element(X3542,X3543) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
fof(i_0_2181,lemma,
! [X3696,X3697] :
( ( set_difference(X3696,X3697) != empty_set
| subset(X3696,X3697) )
& ( ~ subset(X3696,X3697)
| set_difference(X3696,X3697) = empty_set ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t37_xboole_1])]) ).
fof(i_0_2182,lemma,
! [X2737,X2738] :
( ( set_difference(X2737,X2738) != empty_set
| subset(X2737,X2738) )
& ( ~ subset(X2737,X2738)
| set_difference(X2737,X2738) = empty_set ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l32_xboole_1])]) ).
fof(i_0_2183,lemma,
! [X3817] :
( ( relation_rng(X3817) = relation_dom(function_inverse(X3817))
| ~ one_to_one(X3817)
| ~ relation(X3817)
| ~ function(X3817) )
& ( relation_dom(X3817) = relation_rng(function_inverse(X3817))
| ~ one_to_one(X3817)
| ~ relation(X3817)
| ~ function(X3817) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t55_funct_1])])]) ).
fof(i_0_2184,plain,
! [X2651] :
( ( ~ empty_carrier(poset_of_lattice(X2651))
| empty_carrier(X2651)
| ~ lattice(X2651)
| ~ latt_str(X2651) )
& ( strict_rel_str(poset_of_lattice(X2651))
| empty_carrier(X2651)
| ~ lattice(X2651)
| ~ latt_str(X2651) )
& ( reflexive_relstr(poset_of_lattice(X2651))
| empty_carrier(X2651)
| ~ lattice(X2651)
| ~ latt_str(X2651) )
& ( transitive_relstr(poset_of_lattice(X2651))
| empty_carrier(X2651)
| ~ lattice(X2651)
| ~ latt_str(X2651) )
& ( antisymmetric_relstr(poset_of_lattice(X2651))
| empty_carrier(X2651)
| ~ lattice(X2651)
| ~ latt_str(X2651) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_910])])]) ).
fof(i_0_2185,plain,
! [X2660] :
( ~ topological_space(X2660)
| ~ top_str(X2660)
| closed_subset(cast_as_carrier_subset(X2660),X2660) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc5_pre_topc])]) ).
fof(i_0_2186,plain,
! [X3956,X3957] :
( ( ~ reflexive(X3956)
| reflexive(X3957)
| ~ epred3_2(X3957,X3956) )
& ( ~ transitive(X3956)
| transitive(X3957)
| ~ epred3_2(X3957,X3956) )
& ( ~ connected(X3956)
| connected(X3957)
| ~ epred3_2(X3957,X3956) )
& ( ~ antisymmetric(X3956)
| antisymmetric(X3957)
| ~ epred3_2(X3957,X3956) )
& ( ~ well_founded_relation(X3956)
| well_founded_relation(X3957)
| ~ epred3_2(X3957,X3956) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_911])])]) ).
fof(i_0_2187,lemma,
! [X3462,X3463] :
( ~ subset(X3462,X3463)
| ~ finite(X3463)
| finite(X3462) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t13_finset_1])]) ).
fof(i_0_2188,plain,
! [X1833,X1834] :
( ( epsilon_transitive(X1834)
| ~ element(X1834,X1833)
| ~ ordinal(X1833) )
& ( epsilon_connected(X1834)
| ~ element(X1834,X1833)
| ~ ordinal(X1833) )
& ( ordinal(X1834)
| ~ element(X1834,X1833)
| ~ ordinal(X1833) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_arytm_3])])])]) ).
fof(i_0_2189,lemma,
! [X3586,X3587] :
( ~ ordinal(X3587)
| ~ in(X3586,X3587)
| ordinal(X3586) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t23_ordinal1])]) ).
fof(i_0_2190,plain,
! [X1822,X1823] :
( ( v1_xcmplx_0(X1823)
| ~ element(X1823,X1822)
| ~ v5_membered(X1822) )
& ( natural(X1823)
| ~ element(X1823,X1822)
| ~ v5_membered(X1822) )
& ( v1_xreal_0(X1823)
| ~ element(X1823,X1822)
| ~ v5_membered(X1822) )
& ( v1_int_1(X1823)
| ~ element(X1823,X1822)
| ~ v5_membered(X1822) )
& ( v1_rat_1(X1823)
| ~ element(X1823,X1822)
| ~ v5_membered(X1822) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc14_membered])])])]) ).
fof(i_0_2191,plain,
! [X1820,X1821] :
( ( v1_xcmplx_0(X1821)
| ~ element(X1821,X1820)
| ~ v4_membered(X1820) )
& ( v1_xreal_0(X1821)
| ~ element(X1821,X1820)
| ~ v4_membered(X1820) )
& ( v1_int_1(X1821)
| ~ element(X1821,X1820)
| ~ v4_membered(X1820) )
& ( v1_rat_1(X1821)
| ~ element(X1821,X1820)
| ~ v4_membered(X1820) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc13_membered])])])]) ).
fof(i_0_2192,plain,
! [X1818,X1819] :
( ( v1_xcmplx_0(X1819)
| ~ element(X1819,X1818)
| ~ v3_membered(X1818) )
& ( v1_xreal_0(X1819)
| ~ element(X1819,X1818)
| ~ v3_membered(X1818) )
& ( v1_rat_1(X1819)
| ~ element(X1819,X1818)
| ~ v3_membered(X1818) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc12_membered])])])]) ).
fof(i_0_2193,plain,
! [X1816,X1817] :
( ( v1_xcmplx_0(X1817)
| ~ element(X1817,X1816)
| ~ v2_membered(X1816) )
& ( v1_xreal_0(X1817)
| ~ element(X1817,X1816)
| ~ v2_membered(X1816) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc11_membered])])])]) ).
fof(i_0_2194,plain,
! [X1814,X1815] :
( ~ v1_membered(X1814)
| ~ element(X1815,X1814)
| v1_xcmplx_0(X1815) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc10_membered])])]) ).
fof(i_0_2195,lemma,
! [X3841] :
( ~ relation(X3841)
| ~ function(X3841)
| ~ one_to_one(X3841)
| one_to_one(function_inverse(X3841)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t62_funct_1])]) ).
fof(i_0_2196,plain,
! [X2628] :
( ( relation(relation_inverse(X2628))
| ~ relation(X2628)
| ~ function(X2628)
| ~ one_to_one(X2628) )
& ( function(relation_inverse(X2628))
| ~ relation(X2628)
| ~ function(X2628)
| ~ one_to_one(X2628) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc3_funct_1])])]) ).
fof(i_0_2197,lemma,
! [X3482] :
( ~ relation(X3482)
| relation_image(X3482,relation_dom(X3482)) = relation_rng(X3482) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t146_relat_1])]) ).
fof(i_0_2198,plain,
! [X2816] :
( ( element(esk170_1(X2816),powerset(X2816))
| empty(X2816) )
& ( ~ empty(esk170_1(X2816))
| empty(X2816) )
& ( finite(esk170_1(X2816))
| empty(X2816) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_912])])])]) ).
fof(i_0_2199,plain,
! [X2807] :
( ( element(esk163_1(X2807),powerset(X2807))
| empty(X2807) )
& ( ~ empty(esk163_1(X2807))
| empty(X2807) )
& ( finite(esk163_1(X2807))
| empty(X2807) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_913])])])]) ).
fof(i_0_2200,plain,
! [X2784] :
( ( element(esk149_1(X2784),powerset(X2784))
| empty(X2784) )
& ( ~ empty(esk149_1(X2784))
| empty(X2784) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_914])])])]) ).
cnf(i_0_2201,plain,
finite(singleton(X1)),
inference(split_conjunct,[status(thm)],[i_0_895]) ).
fof(i_0_2202,plain,
! [X3876,X3877] :
( ~ in(X3876,X3877)
| ~ empty(X3877) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(i_0_2203,plain,
! [X2423] :
( ~ relation(X2423)
| ~ function(X2423)
| ~ one_to_one(X2423)
| function_inverse(X2423) = relation_inverse(X2423) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d9_funct_1])]) ).
fof(i_0_2204,plain,
! [X2474] :
( ( strict_rel_str(poset_of_lattice(X2474))
| empty_carrier(X2474)
| ~ lattice(X2474)
| ~ latt_str(X2474) )
& ( reflexive_relstr(poset_of_lattice(X2474))
| empty_carrier(X2474)
| ~ lattice(X2474)
| ~ latt_str(X2474) )
& ( transitive_relstr(poset_of_lattice(X2474))
| empty_carrier(X2474)
| ~ lattice(X2474)
| ~ latt_str(X2474) )
& ( antisymmetric_relstr(poset_of_lattice(X2474))
| empty_carrier(X2474)
| ~ lattice(X2474)
| ~ latt_str(X2474) )
& ( rel_str(poset_of_lattice(X2474))
| empty_carrier(X2474)
| ~ lattice(X2474)
| ~ latt_str(X2474) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_915])])]) ).
fof(i_0_2205,plain,
! [X2527] :
( empty_carrier(X2527)
| ~ lattice(X2527)
| ~ latt_str(X2527)
| relation(relation_of_lattice(X2527)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_916])]) ).
fof(i_0_2206,plain,
! [X2886,X2887] :
( ~ ordinal(X2886)
| ~ ordinal(X2887)
| ordinal_subset(X2886,X2886) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[reflexivity_r1_ordinal1])]) ).
fof(i_0_2207,plain,
! [X2600] :
( empty_carrier(X2600)
| ~ one_sorted_str(X2600)
| ~ empty(cast_as_carrier_subset(X2600)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_917])]) ).
fof(i_0_2208,plain,
! [X2584] :
( empty_carrier(X2584)
| ~ one_sorted_str(X2584)
| ~ empty(the_carrier(X2584)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_918])]) ).
fof(i_0_2209,plain,
! [X2090] :
( ( ~ empty_carrier(X2090)
| empty(the_carrier(X2090))
| ~ one_sorted_str(X2090) )
& ( ~ empty(the_carrier(X2090))
| empty_carrier(X2090)
| ~ one_sorted_str(X2090) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_struct_0])])]) ).
fof(i_0_2210,plain,
! [X2662] :
( empty(X2662)
| ~ relation(X2662)
| ~ empty(relation_rng(X2662)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_919])]) ).
fof(i_0_2211,plain,
! [X2661] :
( empty(X2661)
| ~ relation(X2661)
| ~ empty(relation_dom(X2661)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_920])]) ).
fof(i_0_2212,plain,
! [X1879,X1880] : set_union2(X1879,X1880) = set_union2(X1880,X1879),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(i_0_2213,plain,
! [X1877,X1878] : unordered_pair(X1877,X1878) = unordered_pair(X1878,X1877),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
fof(i_0_2214,plain,
! [X2376] :
( empty_carrier(X2376)
| ~ lattice(X2376)
| ~ latt_str(X2376)
| relation_of_lattice(X2376) = a_1_0_filter_1(X2376) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_921])]) ).
fof(i_0_2215,plain,
! [X2842] :
( empty_carrier(X2842)
| ~ lattice(X2842)
| ~ latt_str(X2842)
| k2_lattice3(X2842) = relation_of_lattice(X2842) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_922])]) ).
fof(i_0_2216,plain,
! [X2800] :
( element(esk159_1(X2800),powerset(X2800))
& empty(esk159_1(X2800)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_subset_1])]) ).
fof(i_0_2217,plain,
! [X2789] :
( element(esk152_1(X2789),powerset(X2789))
& empty(esk152_1(X2789))
& relation(esk152_1(X2789))
& function(esk152_1(X2789))
& one_to_one(esk152_1(X2789))
& epsilon_transitive(esk152_1(X2789))
& epsilon_connected(esk152_1(X2789))
& ordinal(esk152_1(X2789))
& natural(esk152_1(X2789))
& finite(esk152_1(X2789)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_finset_1])]) ).
fof(i_0_2218,plain,
! [X1855] :
( ( relation(X1855)
| ~ relation(X1855)
| ~ empty(X1855)
| ~ function(X1855) )
& ( function(X1855)
| ~ relation(X1855)
| ~ empty(X1855)
| ~ function(X1855) )
& ( one_to_one(X1855)
| ~ relation(X1855)
| ~ empty(X1855)
| ~ function(X1855) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_funct_1])])]) ).
fof(i_0_2219,plain,
! [X1844] :
( ( relation(X1844)
| ~ relation(X1844)
| ~ symmetric(X1844)
| ~ transitive(X1844) )
& ( reflexive(X1844)
| ~ relation(X1844)
| ~ symmetric(X1844)
| ~ transitive(X1844) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_partfun1])])]) ).
fof(i_0_2220,plain,
! [X2118,X2119,X2120] :
( ( X2118 != empty_set
| ~ in(X2119,X2118) )
& ( in(esk49_1(X2120),X2120)
| X2120 = 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)],[i_0_923])])])])]) ).
fof(i_0_2221,plain,
! [X2465] :
( ( relation(function_inverse(X2465))
| ~ relation(X2465)
| ~ function(X2465) )
& ( function(function_inverse(X2465))
| ~ relation(X2465)
| ~ function(X2465) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_funct_1])])]) ).
fof(i_0_2222,plain,
! [X1862] :
( ( epsilon_transitive(X1862)
| ~ element(X1862,omega) )
& ( epsilon_connected(X1862)
| ~ element(X1862,omega) )
& ( ordinal(X1862)
| ~ element(X1862,omega) )
& ( natural(X1862)
| ~ element(X1862,omega) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc3_arytm_3])])]) ).
fof(i_0_2223,plain,
! [X1841] :
( ( ~ empty_carrier(X1841)
| empty_carrier(X1841)
| ~ lattice(X1841)
| ~ latt_str(X1841) )
& ( join_commutative(X1841)
| empty_carrier(X1841)
| ~ lattice(X1841)
| ~ latt_str(X1841) )
& ( join_associative(X1841)
| empty_carrier(X1841)
| ~ lattice(X1841)
| ~ latt_str(X1841) )
& ( meet_commutative(X1841)
| empty_carrier(X1841)
| ~ lattice(X1841)
| ~ latt_str(X1841) )
& ( meet_associative(X1841)
| empty_carrier(X1841)
| ~ lattice(X1841)
| ~ latt_str(X1841) )
& ( meet_absorbing(X1841)
| empty_carrier(X1841)
| ~ lattice(X1841)
| ~ latt_str(X1841) )
& ( join_absorbing(X1841)
| empty_carrier(X1841)
| ~ lattice(X1841)
| ~ latt_str(X1841) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_924])])]) ).
fof(i_0_2224,plain,
! [X2712] : ~ proper_subset(X2712,X2712),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[i_0_925])]) ).
cnf(i_0_2225,lemma,
singleton(X1) != empty_set,
inference(split_conjunct,[status(thm)],[i_0_926]) ).
fof(i_0_2226,lemma,
! [X3723] :
( ~ subset(X3723,empty_set)
| X3723 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_xboole_1])]) ).
fof(i_0_2227,lemma,
! [X3695] :
( ( relation_rng(X3695) = relation_dom(relation_inverse(X3695))
| ~ relation(X3695) )
& ( relation_dom(X3695) = relation_rng(relation_inverse(X3695))
| ~ relation(X3695) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t37_relat_1])])]) ).
cnf(i_0_2228,plain,
( identity_on_carrier(X1) = identity_as_relation_of(the_carrier(X1))
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_927]) ).
fof(i_0_2229,lemma,
! [X3618] :
( relation(esk418_1(X3618))
& well_orders(esk418_1(X3618),X3618) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[t26_wellord2])]) ).
fof(i_0_2230,plain,
! [X2555] : element(esk123_1(X2555),X2555),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
cnf(i_0_2231,plain,
element(cast_to_subset(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_928]) ).
fof(i_0_2232,plain,
! [X1854] :
( ~ cup_closed(X1854)
| ~ diff_closed(X1854)
| preboolean(X1854) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_finsub_1])]) ).
fof(i_0_2233,plain,
! [X1851] :
( ( epsilon_transitive(X1851)
| ~ empty(X1851)
| ~ ordinal(X1851) )
& ( epsilon_connected(X1851)
| ~ empty(X1851)
| ~ ordinal(X1851) )
& ( ordinal(X1851)
| ~ empty(X1851)
| ~ ordinal(X1851) )
& ( natural(X1851)
| ~ empty(X1851)
| ~ ordinal(X1851) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_arytm_3])])]) ).
fof(i_0_2234,plain,
! [X2264] :
( ( epsilon_transitive(X2264)
| ~ ordinal(X2264) )
& ( epsilon_connected(X2264)
| ~ ordinal(X2264) )
& ( ~ epsilon_transitive(X2264)
| ~ epsilon_connected(X2264)
| ordinal(X2264) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d4_ordinal1])])]) ).
fof(i_0_2235,plain,
! [X1861] :
( ~ epsilon_transitive(X1861)
| ~ epsilon_connected(X1861)
| ordinal(X1861) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_ordinal1])]) ).
fof(i_0_2236,lemma,
! [X3846] :
( ( relation_dom(X3846) != empty_set
| relation_rng(X3846) = empty_set
| ~ relation(X3846) )
& ( relation_rng(X3846) != empty_set
| relation_dom(X3846) = empty_set
| ~ relation(X3846) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t65_relat_1])])]) ).
fof(i_0_2237,plain,
! [X2709] :
( ~ relation(X2709)
| relation_inverse(relation_inverse(X2709)) = X2709 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[involutiveness_k4_relat_1])]) ).
fof(i_0_2238,lemma,
! [X3887] :
( ~ ordinal(X3887)
| well_ordering(inclusion_relation(X3887)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_wellord2])]) ).
fof(i_0_2239,lemma,
! [X3860] :
( ~ ordinal(X3860)
| well_founded_relation(inclusion_relation(X3860)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_wellord2])]) ).
fof(i_0_2240,lemma,
! [X3783] :
( ~ ordinal(X3783)
| connected(inclusion_relation(X3783)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_wellord2])]) ).
fof(i_0_2241,plain,
! [X2485] :
( ~ relation(X2485)
| relation(relation_inverse(X2485)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k4_relat_1])]) ).
fof(i_0_2242,plain,
! [X2566] :
( ( empty(relation_inverse(X2566))
| ~ empty(X2566) )
& ( relation(relation_inverse(X2566))
| ~ empty(X2566) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc11_relat_1])])]) ).
fof(i_0_2243,plain,
! [X2666] :
( ( empty(relation_rng(X2666))
| ~ empty(X2666) )
& ( relation(relation_rng(X2666))
| ~ empty(X2666) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc8_relat_1])])]) ).
fof(i_0_2244,plain,
! [X2665] :
( ( empty(relation_dom(X2665))
| ~ empty(X2665) )
& ( relation(relation_dom(X2665))
| ~ empty(X2665) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc7_relat_1])])]) ).
fof(i_0_2245,plain,
! [X2652] :
( ( epsilon_transitive(union(X2652))
| ~ ordinal(X2652) )
& ( epsilon_connected(union(X2652))
| ~ ordinal(X2652) )
& ( ordinal(union(X2652))
| ~ ordinal(X2652) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc4_ordinal1])])]) ).
fof(i_0_2246,plain,
! [X2581] :
( ( empty(empty_carrier_subset(X2581))
| ~ one_sorted_str(X2581) )
& ( v1_membered(empty_carrier_subset(X2581))
| ~ one_sorted_str(X2581) )
& ( v2_membered(empty_carrier_subset(X2581))
| ~ one_sorted_str(X2581) )
& ( v3_membered(empty_carrier_subset(X2581))
| ~ one_sorted_str(X2581) )
& ( v4_membered(empty_carrier_subset(X2581))
| ~ one_sorted_str(X2581) )
& ( v5_membered(empty_carrier_subset(X2581))
| ~ one_sorted_str(X2581) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc1_pre_topc])])]) ).
fof(i_0_2247,plain,
! [X2597] :
( ~ empty_carrier(boole_lattice(X2597))
& strict_latt_str(boole_lattice(X2597))
& join_commutative(boole_lattice(X2597))
& join_associative(boole_lattice(X2597))
& meet_commutative(boole_lattice(X2597))
& meet_associative(boole_lattice(X2597))
& meet_absorbing(boole_lattice(X2597))
& join_absorbing(boole_lattice(X2597))
& lattice(boole_lattice(X2597)) ),
inference(variable_rename,[status(thm)],[i_0_929]) ).
fof(i_0_2248,plain,
! [X2577] :
( ~ empty_carrier(boole_lattice(X2577))
& strict_latt_str(boole_lattice(X2577)) ),
inference(variable_rename,[status(thm)],[i_0_930]) ).
fof(i_0_2249,plain,
! [X2585] : ~ empty(powerset(X2585)),
inference(variable_rename,[status(thm)],[i_0_931]) ).
fof(i_0_2250,plain,
! [X2574] :
( ~ empty(powerset(X2574))
& cup_closed(powerset(X2574))
& diff_closed(powerset(X2574))
& preboolean(powerset(X2574)) ),
inference(variable_rename,[status(thm)],[i_0_932]) ).
fof(i_0_2251,plain,
! [X3897,X3898] :
( ~ empty(X3897)
| X3897 = X3898
| ~ empty(X3898) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_boole])]) ).
fof(i_0_2252,lemma,
! [X3845] :
( ( relation_dom(X3845) != empty_set
| X3845 = empty_set
| ~ relation(X3845) )
& ( relation_rng(X3845) != empty_set
| X3845 = empty_set
| ~ relation(X3845) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t64_relat_1])])]) ).
fof(i_0_2253,lemma,
! [X3445] :
( ~ one_sorted_str(X3445)
| cast_as_carrier_subset(X3445) = the_carrier(X3445) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_pre_topc])]) ).
fof(i_0_2254,plain,
! [X2230] :
( ~ one_sorted_str(X2230)
| cast_as_carrier_subset(X2230) = the_carrier(X2230) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_pre_topc])]) ).
fof(i_0_2255,plain,
! [X2699] : set_union2(X2699,X2699) = X2699,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k2_xboole_0])]) ).
fof(i_0_2256,plain,
! [X2889] : equipotent(X2889,X2889),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r2_wellord2])]) ).
fof(i_0_2257,plain,
! [X2888] : subset(X2888,X2888),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(i_0_2258,lemma,
powerset(empty_set) = singleton(empty_set),
inference(split_conjunct,[status(thm)],[t1_zfmisc_1]) ).
fof(i_0_2259,plain,
! [X3709] : set_difference(X3709,empty_set) = X3709,
inference(variable_rename,[status(thm)],[t3_boole]) ).
fof(i_0_2260,plain,
! [X3538] : set_union2(X3538,empty_set) = X3538,
inference(variable_rename,[status(thm)],[t1_boole]) ).
fof(i_0_2261,plain,
! [X2344] :
( ( ~ being_limit_ordinal(X2344)
| X2344 = union(X2344) )
& ( X2344 != union(X2344)
| being_limit_ordinal(X2344) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d6_ordinal1])]) ).
fof(i_0_2262,lemma,
! [X3647] : subset(empty_set,X3647),
inference(variable_rename,[status(thm)],[t2_xboole_1]) ).
fof(i_0_2263,plain,
! [X3779] : set_difference(empty_set,X3779) = empty_set,
inference(variable_rename,[status(thm)],[t4_boole]) ).
fof(i_0_2264,plain,
! [X2530] :
( ~ top_str(X2530)
| one_sorted_str(X2530) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_pre_topc])]) ).
fof(i_0_2265,plain,
! [X2528] :
( ~ meet_semilatt_str(X2528)
| one_sorted_str(X2528) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_lattices])]) ).
fof(i_0_2266,plain,
! [X2531] :
( ~ join_semilatt_str(X2531)
| one_sorted_str(X2531) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l2_lattices])]) ).
fof(i_0_2267,plain,
! [X2529] :
( ~ rel_str(X2529)
| one_sorted_str(X2529) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_orders_2])]) ).
fof(i_0_2268,plain,
! [X2532] :
( ( meet_semilatt_str(X2532)
| ~ latt_str(X2532) )
& ( join_semilatt_str(X2532)
| ~ latt_str(X2532) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_lattices])])]) ).
fof(i_0_2269,plain,
! [X1845] :
( ~ empty(X1845)
| relation(X1845) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relat_1])]) ).
fof(i_0_2270,plain,
! [X1837] :
( ~ empty(X1837)
| function(X1837) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_funct_1])]) ).
fof(i_0_2271,plain,
! [X1836] :
( ( cup_closed(X1836)
| ~ preboolean(X1836) )
& ( diff_closed(X1836)
| ~ preboolean(X1836) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_finsub_1])])]) ).
fof(i_0_2272,plain,
! [X1835] :
( ~ empty(X1835)
| finite(X1835) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_finset_1])]) ).
fof(i_0_2273,plain,
! [X1843] :
( ( epsilon_transitive(X1843)
| ~ ordinal(X1843) )
& ( epsilon_connected(X1843)
| ~ ordinal(X1843) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_ordinal1])])]) ).
fof(i_0_2274,plain,
! [X1867] :
( ( epsilon_transitive(X1867)
| ~ empty(X1867) )
& ( epsilon_connected(X1867)
| ~ empty(X1867) )
& ( ordinal(X1867)
| ~ empty(X1867) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc3_ordinal1])])]) ).
fof(i_0_2275,plain,
! [X1824] :
( ( v1_membered(X1824)
| ~ empty(X1824) )
& ( v2_membered(X1824)
| ~ empty(X1824) )
& ( v3_membered(X1824)
| ~ empty(X1824) )
& ( v4_membered(X1824)
| ~ empty(X1824) )
& ( v5_membered(X1824)
| ~ empty(X1824) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc15_membered])])]) ).
fof(i_0_2276,plain,
! [X1842] :
( ~ v5_membered(X1842)
| v4_membered(X1842) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_membered])]) ).
fof(i_0_2277,plain,
! [X1860] :
( ~ v4_membered(X1860)
| v3_membered(X1860) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_membered])]) ).
fof(i_0_2278,plain,
! [X1866] :
( ~ v3_membered(X1866)
| v2_membered(X1866) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc3_membered])]) ).
fof(i_0_2279,plain,
! [X1870] :
( ~ v2_membered(X1870)
| v1_membered(X1870) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc4_membered])]) ).
fof(i_0_2280,plain,
! [X2157] :
( ~ one_sorted_str(X2157)
| empty_carrier_subset(X2157) = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d2_pre_topc])]) ).
fof(i_0_2281,lemma,
! [X3919] : union(powerset(X3919)) = X3919,
inference(variable_rename,[status(thm)],[t99_zfmisc_1]) ).
fof(i_0_2282,lemma,
! [X3868] :
( relation_dom(identity_relation(X3868)) = X3868
& relation_rng(identity_relation(X3868)) = X3868 ),
inference(variable_rename,[status(thm)],[t71_relat_1]) ).
fof(i_0_2283,lemma,
! [X3710] :
( lower_bounded_semilattstr(boole_lattice(X3710))
& bottom_of_semilattstr(boole_lattice(X3710)) = empty_set ),
inference(variable_rename,[status(thm)],[t3_lattice3]) ).
fof(i_0_2284,lemma,
! [X3838] : antisymmetric(inclusion_relation(X3838)),
inference(variable_rename,[status(thm)],[t5_wellord2]) ).
fof(i_0_2285,plain,
! [X2599] :
( relation(identity_relation(X2599))
& function(identity_relation(X2599))
& reflexive(identity_relation(X2599))
& symmetric(identity_relation(X2599))
& antisymmetric(identity_relation(X2599))
& transitive(identity_relation(X2599)) ),
inference(variable_rename,[status(thm)],[fc2_partfun1]) ).
fof(i_0_2286,lemma,
! [X3646] : reflexive(inclusion_relation(X3646)),
inference(variable_rename,[status(thm)],[t2_wellord2]) ).
fof(i_0_2287,lemma,
! [X3716] : transitive(inclusion_relation(X3716)),
inference(variable_rename,[status(thm)],[t3_wellord2]) ).
fof(i_0_2288,plain,
! [X2458] : relation(inclusion_relation(X2458)),
inference(variable_rename,[status(thm)],[dt_k1_wellord2]) ).
fof(i_0_2289,plain,
! [X2595] :
( relation(identity_relation(X2595))
& function(identity_relation(X2595)) ),
inference(variable_rename,[status(thm)],[fc2_funct_1]) ).
fof(i_0_2290,plain,
! [X2508] : relation(identity_relation(X2508)),
inference(variable_rename,[status(thm)],[dt_k6_relat_1]) ).
fof(i_0_2291,plain,
! [X2450] :
( strict_latt_str(boole_lattice(X2450))
& latt_str(boole_lattice(X2450)) ),
inference(variable_rename,[status(thm)],[dt_k1_lattice3]) ).
fof(i_0_2292,plain,
! [X3855] :
( ~ empty(X3855)
| X3855 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(i_0_2293,plain,
( latt_str(esk176_0)
& ~ empty_carrier(esk176_0)
& strict_latt_str(esk176_0)
& join_commutative(esk176_0)
& join_associative(esk176_0)
& meet_commutative(esk176_0)
& meet_associative(esk176_0)
& meet_absorbing(esk176_0)
& join_absorbing(esk176_0)
& lattice(esk176_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_933])]) ).
fof(i_0_2294,plain,
( latt_str(esk173_0)
& ~ empty_carrier(esk173_0)
& strict_latt_str(esk173_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_934])]) ).
fof(i_0_2295,plain,
( one_sorted_str(esk169_0)
& ~ empty_carrier(esk169_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_935])]) ).
fof(i_0_2296,plain,
( rel_str(esk155_0)
& ~ empty_carrier(esk155_0)
& strict_rel_str(esk155_0)
& reflexive_relstr(esk155_0)
& transitive_relstr(esk155_0)
& antisymmetric_relstr(esk155_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_936])]) ).
fof(i_0_2297,plain,
( ~ empty(esk166_0)
& epsilon_transitive(esk166_0)
& epsilon_connected(esk166_0)
& ordinal(esk166_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_937])]) ).
fof(i_0_2298,plain,
~ empty(esk162_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_938])]) ).
fof(i_0_2299,plain,
( ~ empty(esk158_0)
& relation(esk158_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_939])]) ).
fof(i_0_2300,plain,
( ~ empty(esk143_0)
& v1_membered(esk143_0)
& v2_membered(esk143_0)
& v3_membered(esk143_0)
& v4_membered(esk143_0)
& v5_membered(esk143_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_940])]) ).
fof(i_0_2301,plain,
( ~ empty(esk140_0)
& finite(esk140_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_941])]) ).
fof(i_0_2302,plain,
( ~ empty(esk139_0)
& epsilon_transitive(esk139_0)
& epsilon_connected(esk139_0)
& ordinal(esk139_0)
& natural(esk139_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_942])]) ).
fof(i_0_2303,plain,
( epsilon_transitive(omega)
& epsilon_connected(omega)
& ordinal(omega)
& ~ empty(omega) ),
inference(fof_simplification,[status(thm)],[fc1_ordinal2]) ).
fof(i_0_2304,plain,
( relation(esk171_0)
& relation_empty_yielding(esk171_0)
& function(esk171_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc4_funct_1])]) ).
fof(i_0_2305,plain,
( relation(esk168_0)
& relation_empty_yielding(esk168_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc3_relat_1])]) ).
fof(i_0_2306,plain,
( epsilon_transitive(esk146_0)
& epsilon_connected(esk146_0)
& ordinal(esk146_0)
& being_limit_ordinal(esk146_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_ordinal2])]) ).
fof(i_0_2307,plain,
top_str(esk117_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_l1_pre_topc])]) ).
fof(i_0_2308,plain,
one_sorted_str(esk118_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_l1_struct_0])]) ).
fof(i_0_2309,plain,
meet_semilatt_str(esk115_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_l1_lattices])]) ).
fof(i_0_2310,plain,
join_semilatt_str(esk119_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_l2_lattices])]) ).
fof(i_0_2311,plain,
( relation(esk164_0)
& function(esk164_0)
& one_to_one(esk164_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc3_funct_1])]) ).
fof(i_0_2312,plain,
( relation(esk156_0)
& function(esk156_0)
& one_to_one(esk156_0)
& empty(esk156_0)
& epsilon_transitive(esk156_0)
& epsilon_connected(esk156_0)
& ordinal(esk156_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_ordinal1])]) ).
fof(i_0_2313,plain,
( relation(esk147_0)
& function(esk147_0)
& one_to_one(esk147_0)
& empty(esk147_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_partfun1])]) ).
fof(i_0_2314,plain,
( relation(esk153_0)
& empty(esk153_0)
& function(esk153_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_funct_1])]) ).
fof(i_0_2315,plain,
( empty(esk148_0)
& relation(esk148_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_relat_1])]) ).
fof(i_0_2316,plain,
( relation(esk141_0)
& function(esk141_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_funct_1])]) ).
fof(i_0_2317,plain,
( epsilon_transitive(esk145_0)
& epsilon_connected(esk145_0)
& ordinal(esk145_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_ordinal1])]) ).
fof(i_0_2318,plain,
empty(esk151_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
fof(i_0_2319,plain,
( latt_str(esk165_0)
& strict_latt_str(esk165_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc3_lattices])]) ).
fof(i_0_2320,plain,
latt_str(esk120_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_l3_lattices])]) ).
fof(i_0_2321,plain,
( rel_str(esk144_0)
& strict_rel_str(esk144_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_orders_2])]) ).
fof(i_0_2322,plain,
rel_str(esk116_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_l1_orders_2])]) ).
cnf(i_0_2323,plain,
( empty(X2)
| in(X5,esk224_3(X2,X3,X4))
| in(unordered_pair(unordered_pair(esk222_2(X2,X3),X9),unordered_pair(esk222_2(X2,X3),esk222_2(X2,X3))),X3)
| X6 != X7
| X5 != X8
| unordered_pair(unordered_pair(X6,X1),unordered_pair(X6,X6)) != X5
| ~ relation(X3)
| ~ in(X6,X2)
| ~ in(X1,X7)
| ~ in(X9,esk223_2(X2,X3))
| ~ in(X8,cartesian_product2(X2,X4))
| ~ in(unordered_pair(unordered_pair(X1,esk229_7(X2,X3,X4,X5,X6,X1,X7)),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_943,c_0_944]),c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2324,plain,
( empty(X2)
| in(X5,esk224_3(X2,X3,X4))
| in(unordered_pair(unordered_pair(esk219_2(X2,X3),X9),unordered_pair(esk219_2(X2,X3),esk219_2(X2,X3))),X3)
| X6 != X7
| X5 != X8
| unordered_pair(unordered_pair(X6,X1),unordered_pair(X6,X6)) != X5
| ~ relation(X3)
| ~ in(X6,X2)
| ~ in(X1,X7)
| ~ in(X9,esk220_2(X2,X3))
| ~ in(X8,cartesian_product2(X2,X4))
| ~ in(unordered_pair(unordered_pair(X1,esk229_7(X2,X3,X4,X5,X6,X1,X7)),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_945,c_0_944]),c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2325,plain,
( unordered_pair(unordered_pair(esk221_2(X2,X3),esk222_2(X2,X3)),unordered_pair(esk221_2(X2,X3),esk221_2(X2,X3))) = esk217_2(X2,X3)
| empty(X2)
| in(X5,esk224_3(X2,X3,X4))
| X6 != X7
| X5 != X8
| unordered_pair(unordered_pair(X6,X1),unordered_pair(X6,X6)) != X5
| ~ relation(X3)
| ~ in(X6,X2)
| ~ in(X1,X7)
| ~ in(X8,cartesian_product2(X2,X4))
| ~ in(unordered_pair(unordered_pair(X1,esk229_7(X2,X3,X4,X5,X6,X1,X7)),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_946,c_0_944]),c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2326,plain,
( unordered_pair(unordered_pair(esk218_2(X2,X3),esk219_2(X2,X3)),unordered_pair(esk218_2(X2,X3),esk218_2(X2,X3))) = esk216_2(X2,X3)
| empty(X2)
| in(X5,esk224_3(X2,X3,X4))
| X6 != X7
| X5 != X8
| unordered_pair(unordered_pair(X6,X1),unordered_pair(X6,X6)) != X5
| ~ relation(X3)
| ~ in(X6,X2)
| ~ in(X1,X7)
| ~ in(X8,cartesian_product2(X2,X4))
| ~ in(unordered_pair(unordered_pair(X1,esk229_7(X2,X3,X4,X5,X6,X1,X7)),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_947,c_0_944]),c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2327,plain,
( empty(X2)
| in(X5,esk224_3(X2,X3,X4))
| in(esk222_2(X2,X3),esk223_2(X2,X3))
| X6 != X7
| X5 != X8
| unordered_pair(unordered_pair(X6,X1),unordered_pair(X6,X6)) != X5
| ~ relation(X3)
| ~ in(X6,X2)
| ~ in(X1,X7)
| ~ in(X8,cartesian_product2(X2,X4))
| ~ in(unordered_pair(unordered_pair(X1,esk229_7(X2,X3,X4,X5,X6,X1,X7)),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_948,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2328,plain,
( empty(X2)
| in(X5,esk224_3(X2,X3,X4))
| in(esk219_2(X2,X3),esk220_2(X2,X3))
| X6 != X7
| X5 != X8
| unordered_pair(unordered_pair(X6,X1),unordered_pair(X6,X6)) != X5
| ~ relation(X3)
| ~ in(X6,X2)
| ~ in(X1,X7)
| ~ in(X8,cartesian_product2(X2,X4))
| ~ in(unordered_pair(unordered_pair(X1,esk229_7(X2,X3,X4,X5,X6,X1,X7)),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_949,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2329,plain,
( empty(X2)
| in(X5,esk224_3(X2,X3,X4))
| X6 != X7
| X5 != X8
| esk217_2(X2,X3) != esk216_2(X2,X3)
| unordered_pair(unordered_pair(X6,X1),unordered_pair(X6,X6)) != X5
| ~ relation(X3)
| ~ in(X6,X2)
| ~ in(X1,X7)
| ~ in(X8,cartesian_product2(X2,X4))
| ~ in(unordered_pair(unordered_pair(X1,esk229_7(X2,X3,X4,X5,X6,X1,X7)),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_950,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2330,plain,
( empty(X2)
| in(esk221_2(X2,X3),X2)
| in(X5,esk224_3(X2,X3,X4))
| X6 != X7
| X5 != X8
| unordered_pair(unordered_pair(X6,X1),unordered_pair(X6,X6)) != X5
| ~ relation(X3)
| ~ in(X6,X2)
| ~ in(X1,X7)
| ~ in(X8,cartesian_product2(X2,X4))
| ~ in(unordered_pair(unordered_pair(X1,esk229_7(X2,X3,X4,X5,X6,X1,X7)),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_951,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2331,plain,
( empty(X2)
| in(esk218_2(X2,X3),X2)
| in(X5,esk224_3(X2,X3,X4))
| X6 != X7
| X5 != X8
| unordered_pair(unordered_pair(X6,X1),unordered_pair(X6,X6)) != X5
| ~ relation(X3)
| ~ in(X6,X2)
| ~ in(X1,X7)
| ~ in(X8,cartesian_product2(X2,X4))
| ~ in(unordered_pair(unordered_pair(X1,esk229_7(X2,X3,X4,X5,X6,X1,X7)),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_952,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2332,plain,
( esk223_2(X2,X3) = esk221_2(X2,X3)
| empty(X2)
| in(X5,esk224_3(X2,X3,X4))
| X6 != X7
| X5 != X8
| unordered_pair(unordered_pair(X6,X1),unordered_pair(X6,X6)) != X5
| ~ relation(X3)
| ~ in(X6,X2)
| ~ in(X1,X7)
| ~ in(X8,cartesian_product2(X2,X4))
| ~ in(unordered_pair(unordered_pair(X1,esk229_7(X2,X3,X4,X5,X6,X1,X7)),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_953,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2333,plain,
( esk220_2(X2,X3) = esk218_2(X2,X3)
| empty(X2)
| in(X5,esk224_3(X2,X3,X4))
| X6 != X7
| X5 != X8
| unordered_pair(unordered_pair(X6,X1),unordered_pair(X6,X6)) != X5
| ~ relation(X3)
| ~ in(X6,X2)
| ~ in(X1,X7)
| ~ in(X8,cartesian_product2(X2,X4))
| ~ in(unordered_pair(unordered_pair(X1,esk229_7(X2,X3,X4,X5,X6,X1,X7)),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_954,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2334,plain,
( esk217_2(X2,X3) = esk215_2(X2,X3)
| empty(X2)
| in(X5,esk224_3(X2,X3,X4))
| X6 != X7
| X5 != X8
| unordered_pair(unordered_pair(X6,X1),unordered_pair(X6,X6)) != X5
| ~ relation(X3)
| ~ in(X6,X2)
| ~ in(X1,X7)
| ~ in(X8,cartesian_product2(X2,X4))
| ~ in(unordered_pair(unordered_pair(X1,esk229_7(X2,X3,X4,X5,X6,X1,X7)),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_955,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2335,plain,
( esk216_2(X2,X3) = esk215_2(X2,X3)
| empty(X2)
| in(X5,esk224_3(X2,X3,X4))
| X6 != X7
| X5 != X8
| unordered_pair(unordered_pair(X6,X1),unordered_pair(X6,X6)) != X5
| ~ relation(X3)
| ~ in(X6,X2)
| ~ in(X1,X7)
| ~ in(X8,cartesian_product2(X2,X4))
| ~ in(unordered_pair(unordered_pair(X1,esk229_7(X2,X3,X4,X5,X6,X1,X7)),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_956,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2336,lemma,
( empty(X2)
| in(X5,esk341_3(X2,X3,X4))
| X6 != X7
| unordered_pair(unordered_pair(X6,X1),unordered_pair(X6,X6)) != X5
| ~ relation(X3)
| ~ in(X6,X2)
| ~ in(X1,X7)
| ~ in(X5,cartesian_product2(X2,X4))
| ~ in(unordered_pair(unordered_pair(X1,esk345_7(X2,X3,X4,X5,X6,X1,X7)),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_957,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2337,plain,
( empty(X1)
| in(X4,esk224_3(X1,X2,X3))
| in(esk229_7(X1,X2,X3,X4,X5,X6,X7),X7)
| in(unordered_pair(unordered_pair(esk222_2(X1,X2),X9),unordered_pair(esk222_2(X1,X2),esk222_2(X1,X2))),X2)
| X5 != X7
| X4 != X8
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ relation(X2)
| ~ in(X6,X7)
| ~ in(X5,X1)
| ~ in(X9,esk223_2(X1,X2))
| ~ in(X8,cartesian_product2(X1,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_958,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2338,plain,
( empty(X1)
| in(X4,esk224_3(X1,X2,X3))
| in(esk229_7(X1,X2,X3,X4,X5,X6,X7),X7)
| in(unordered_pair(unordered_pair(esk219_2(X1,X2),X9),unordered_pair(esk219_2(X1,X2),esk219_2(X1,X2))),X2)
| X5 != X7
| X4 != X8
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ relation(X2)
| ~ in(X6,X7)
| ~ in(X5,X1)
| ~ in(X9,esk220_2(X1,X2))
| ~ in(X8,cartesian_product2(X1,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_959,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2339,plain,
( unordered_pair(unordered_pair(esk221_2(X1,X2),esk222_2(X1,X2)),unordered_pair(esk221_2(X1,X2),esk221_2(X1,X2))) = esk217_2(X1,X2)
| empty(X1)
| in(X4,esk224_3(X1,X2,X3))
| in(esk229_7(X1,X2,X3,X4,X5,X6,X7),X7)
| X5 != X7
| X4 != X8
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ relation(X2)
| ~ in(X6,X7)
| ~ in(X5,X1)
| ~ in(X8,cartesian_product2(X1,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_960,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2340,plain,
( unordered_pair(unordered_pair(esk218_2(X1,X2),esk219_2(X1,X2)),unordered_pair(esk218_2(X1,X2),esk218_2(X1,X2))) = esk216_2(X1,X2)
| empty(X1)
| in(X4,esk224_3(X1,X2,X3))
| in(esk229_7(X1,X2,X3,X4,X5,X6,X7),X7)
| X5 != X7
| X4 != X8
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ relation(X2)
| ~ in(X6,X7)
| ~ in(X5,X1)
| ~ in(X8,cartesian_product2(X1,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_961,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2341,plain,
( empty(X1)
| in(X4,esk224_3(X1,X2,X3))
| in(esk222_2(X1,X2),esk223_2(X1,X2))
| in(esk229_7(X1,X2,X3,X4,X5,X6,X7),X7)
| X5 != X7
| X4 != X8
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ relation(X2)
| ~ in(X6,X7)
| ~ in(X5,X1)
| ~ in(X8,cartesian_product2(X1,X3)) ),
inference(rw,[status(thm)],[i_0_962,c_0_944]),
[final] ).
cnf(i_0_2342,plain,
( empty(X1)
| in(X4,esk224_3(X1,X2,X3))
| in(esk219_2(X1,X2),esk220_2(X1,X2))
| in(esk229_7(X1,X2,X3,X4,X5,X6,X7),X7)
| X5 != X7
| X4 != X8
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ relation(X2)
| ~ in(X6,X7)
| ~ in(X5,X1)
| ~ in(X8,cartesian_product2(X1,X3)) ),
inference(rw,[status(thm)],[i_0_963,c_0_944]),
[final] ).
cnf(i_0_2343,plain,
( empty(X1)
| in(X4,esk224_3(X1,X2,X3))
| in(esk229_7(X1,X2,X3,X4,X5,X6,X7),X7)
| X5 != X7
| X4 != X8
| esk217_2(X1,X2) != esk216_2(X1,X2)
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ relation(X2)
| ~ in(X6,X7)
| ~ in(X5,X1)
| ~ in(X8,cartesian_product2(X1,X3)) ),
inference(rw,[status(thm)],[i_0_964,c_0_944]),
[final] ).
cnf(i_0_2344,plain,
( empty(X1)
| in(esk221_2(X1,X2),X1)
| in(X4,esk224_3(X1,X2,X3))
| in(esk229_7(X1,X2,X3,X4,X5,X6,X7),X7)
| X5 != X7
| X4 != X8
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ relation(X2)
| ~ in(X6,X7)
| ~ in(X5,X1)
| ~ in(X8,cartesian_product2(X1,X3)) ),
inference(rw,[status(thm)],[i_0_965,c_0_944]),
[final] ).
cnf(i_0_2345,plain,
( empty(X1)
| in(esk218_2(X1,X2),X1)
| in(X4,esk224_3(X1,X2,X3))
| in(esk229_7(X1,X2,X3,X4,X5,X6,X7),X7)
| X5 != X7
| X4 != X8
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ relation(X2)
| ~ in(X6,X7)
| ~ in(X5,X1)
| ~ in(X8,cartesian_product2(X1,X3)) ),
inference(rw,[status(thm)],[i_0_966,c_0_944]),
[final] ).
cnf(i_0_2346,plain,
( esk223_2(X1,X2) = esk221_2(X1,X2)
| empty(X1)
| in(X4,esk224_3(X1,X2,X3))
| in(esk229_7(X1,X2,X3,X4,X5,X6,X7),X7)
| X5 != X7
| X4 != X8
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ relation(X2)
| ~ in(X6,X7)
| ~ in(X5,X1)
| ~ in(X8,cartesian_product2(X1,X3)) ),
inference(rw,[status(thm)],[i_0_967,c_0_944]),
[final] ).
cnf(i_0_2347,plain,
( esk220_2(X1,X2) = esk218_2(X1,X2)
| empty(X1)
| in(X4,esk224_3(X1,X2,X3))
| in(esk229_7(X1,X2,X3,X4,X5,X6,X7),X7)
| X5 != X7
| X4 != X8
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ relation(X2)
| ~ in(X6,X7)
| ~ in(X5,X1)
| ~ in(X8,cartesian_product2(X1,X3)) ),
inference(rw,[status(thm)],[i_0_968,c_0_944]),
[final] ).
cnf(i_0_2348,plain,
( esk217_2(X1,X2) = esk215_2(X1,X2)
| empty(X1)
| in(X4,esk224_3(X1,X2,X3))
| in(esk229_7(X1,X2,X3,X4,X5,X6,X7),X7)
| X5 != X7
| X4 != X8
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ relation(X2)
| ~ in(X6,X7)
| ~ in(X5,X1)
| ~ in(X8,cartesian_product2(X1,X3)) ),
inference(rw,[status(thm)],[i_0_969,c_0_944]),
[final] ).
cnf(i_0_2349,plain,
( esk216_2(X1,X2) = esk215_2(X1,X2)
| empty(X1)
| in(X4,esk224_3(X1,X2,X3))
| in(esk229_7(X1,X2,X3,X4,X5,X6,X7),X7)
| X5 != X7
| X4 != X8
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ relation(X2)
| ~ in(X6,X7)
| ~ in(X5,X1)
| ~ in(X8,cartesian_product2(X1,X3)) ),
inference(rw,[status(thm)],[i_0_970,c_0_944]),
[final] ).
cnf(i_0_2350,lemma,
( empty(X1)
| in(X4,esk341_3(X1,X2,X3))
| in(esk345_7(X1,X2,X3,X4,X5,X6,X7),X7)
| X5 != X7
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ relation(X2)
| ~ in(X6,X7)
| ~ in(X5,X1)
| ~ in(X4,cartesian_product2(X1,X3)) ),
inference(rw,[status(thm)],[i_0_971,c_0_944]),
[final] ).
cnf(i_0_2351,plain,
( in(unordered_pair(unordered_pair(esk106_5(X1,X2,X3,X4,X5),X5),unordered_pair(esk106_5(X1,X2,X3,X4,X5),esk106_5(X1,X2,X3,X4,X5))),X2)
| X3 != relation_composition(X1,X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_972,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2352,plain,
( in(unordered_pair(unordered_pair(apply(X1,esk317_3(X2,X3,X1)),apply(X1,esk318_3(X2,X3,X1))),unordered_pair(apply(X1,esk317_3(X2,X3,X1)),apply(X1,esk317_3(X2,X3,X1)))),X3)
| in(unordered_pair(unordered_pair(apply(X1,esk321_4(X2,X3,X1,X4)),apply(X1,esk322_4(X2,X3,X1,X4))),unordered_pair(apply(X1,esk321_4(X2,X3,X1,X4)),apply(X1,esk321_4(X2,X3,X1,X4)))),X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ in(X4,esk319_3(X2,X3,X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_973,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2353,plain,
( in(unordered_pair(unordered_pair(apply(X1,esk315_3(X2,X3,X1)),apply(X1,esk316_3(X2,X3,X1))),unordered_pair(apply(X1,esk315_3(X2,X3,X1)),apply(X1,esk315_3(X2,X3,X1)))),X3)
| in(unordered_pair(unordered_pair(apply(X1,esk321_4(X2,X3,X1,X4)),apply(X1,esk322_4(X2,X3,X1,X4))),unordered_pair(apply(X1,esk321_4(X2,X3,X1,X4)),apply(X1,esk321_4(X2,X3,X1,X4)))),X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ in(X4,esk319_3(X2,X3,X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_974,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2354,plain,
( unordered_pair(unordered_pair(esk287_2(X2,X3),esk288_2(X2,X3)),unordered_pair(esk287_2(X2,X3),esk287_2(X2,X3))) = esk284_2(X2,X3)
| in(X5,esk289_3(X2,X3,X4))
| X5 != X7
| unordered_pair(unordered_pair(X6,X1),unordered_pair(X6,X6)) != X5
| X1 != subset_complement(the_carrier(X2),esk293_6(X2,X3,X4,X5,X6,X1))
| ~ one_sorted_str(X2)
| ~ in(X6,complements_of_subsets(the_carrier(X2),X3))
| ~ element(X3,powerset(powerset(the_carrier(X2))))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X2),X3),X4)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_975,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2355,plain,
( unordered_pair(unordered_pair(esk285_2(X2,X3),esk286_2(X2,X3)),unordered_pair(esk285_2(X2,X3),esk285_2(X2,X3))) = esk283_2(X2,X3)
| in(X5,esk289_3(X2,X3,X4))
| X5 != X7
| unordered_pair(unordered_pair(X6,X1),unordered_pair(X6,X6)) != X5
| X1 != subset_complement(the_carrier(X2),esk293_6(X2,X3,X4,X5,X6,X1))
| ~ one_sorted_str(X2)
| ~ in(X6,complements_of_subsets(the_carrier(X2),X3))
| ~ element(X3,powerset(powerset(the_carrier(X2))))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X2),X3),X4)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_976,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2356,plain,
( esk288_2(X2,X3) = subset_complement(the_carrier(X2),X8)
| in(X5,esk289_3(X2,X3,X4))
| X5 != X7
| X8 != esk287_2(X2,X3)
| unordered_pair(unordered_pair(X6,X1),unordered_pair(X6,X6)) != X5
| X1 != subset_complement(the_carrier(X2),esk293_6(X2,X3,X4,X5,X6,X1))
| ~ one_sorted_str(X2)
| ~ element(X8,powerset(the_carrier(X2)))
| ~ in(X6,complements_of_subsets(the_carrier(X2),X3))
| ~ element(X3,powerset(powerset(the_carrier(X2))))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X2),X3),X4)) ),
inference(rw,[status(thm)],[i_0_977,c_0_944]),
[final] ).
cnf(i_0_2357,plain,
( esk286_2(X2,X3) = subset_complement(the_carrier(X2),X8)
| in(X5,esk289_3(X2,X3,X4))
| X5 != X7
| X8 != esk285_2(X2,X3)
| unordered_pair(unordered_pair(X6,X1),unordered_pair(X6,X6)) != X5
| X1 != subset_complement(the_carrier(X2),esk293_6(X2,X3,X4,X5,X6,X1))
| ~ one_sorted_str(X2)
| ~ element(X8,powerset(the_carrier(X2)))
| ~ in(X6,complements_of_subsets(the_carrier(X2),X3))
| ~ element(X3,powerset(powerset(the_carrier(X2))))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X2),X3),X4)) ),
inference(rw,[status(thm)],[i_0_978,c_0_944]),
[final] ).
cnf(i_0_2358,plain,
( unordered_pair(unordered_pair(esk305_2(X2,X3),esk306_2(X2,X3)),unordered_pair(esk305_2(X2,X3),esk305_2(X2,X3))) = esk302_2(X2,X3)
| in(X5,esk307_3(X2,X3,X4))
| X5 != X7
| unordered_pair(unordered_pair(X6,X1),unordered_pair(X6,X6)) != X5
| X1 != subset_complement(the_carrier(X2),esk311_6(X2,X3,X4,X5,X6,X1))
| ~ one_sorted_str(X2)
| ~ in(X6,X3)
| ~ in(X7,cartesian_product2(X3,X4))
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_979,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2359,plain,
( unordered_pair(unordered_pair(esk303_2(X2,X3),esk304_2(X2,X3)),unordered_pair(esk303_2(X2,X3),esk303_2(X2,X3))) = esk301_2(X2,X3)
| in(X5,esk307_3(X2,X3,X4))
| X5 != X7
| unordered_pair(unordered_pair(X6,X1),unordered_pair(X6,X6)) != X5
| X1 != subset_complement(the_carrier(X2),esk311_6(X2,X3,X4,X5,X6,X1))
| ~ one_sorted_str(X2)
| ~ in(X6,X3)
| ~ in(X7,cartesian_product2(X3,X4))
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_980,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2360,plain,
( in(X5,esk289_3(X2,X3,X4))
| in(esk287_2(X2,X3),complements_of_subsets(the_carrier(X2),X3))
| X5 != X7
| unordered_pair(unordered_pair(X6,X1),unordered_pair(X6,X6)) != X5
| X1 != subset_complement(the_carrier(X2),esk293_6(X2,X3,X4,X5,X6,X1))
| ~ one_sorted_str(X2)
| ~ in(X6,complements_of_subsets(the_carrier(X2),X3))
| ~ element(X3,powerset(powerset(the_carrier(X2))))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X2),X3),X4)) ),
inference(rw,[status(thm)],[i_0_981,c_0_944]),
[final] ).
cnf(i_0_2361,plain,
( in(X5,esk289_3(X2,X3,X4))
| in(esk285_2(X2,X3),complements_of_subsets(the_carrier(X2),X3))
| X5 != X7
| unordered_pair(unordered_pair(X6,X1),unordered_pair(X6,X6)) != X5
| X1 != subset_complement(the_carrier(X2),esk293_6(X2,X3,X4,X5,X6,X1))
| ~ one_sorted_str(X2)
| ~ in(X6,complements_of_subsets(the_carrier(X2),X3))
| ~ element(X3,powerset(powerset(the_carrier(X2))))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X2),X3),X4)) ),
inference(rw,[status(thm)],[i_0_982,c_0_944]),
[final] ).
cnf(i_0_2362,plain,
( in(X5,esk289_3(X2,X3,X4))
| X5 != X7
| esk284_2(X2,X3) != esk283_2(X2,X3)
| unordered_pair(unordered_pair(X6,X1),unordered_pair(X6,X6)) != X5
| X1 != subset_complement(the_carrier(X2),esk293_6(X2,X3,X4,X5,X6,X1))
| ~ one_sorted_str(X2)
| ~ in(X6,complements_of_subsets(the_carrier(X2),X3))
| ~ element(X3,powerset(powerset(the_carrier(X2))))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X2),X3),X4)) ),
inference(rw,[status(thm)],[i_0_983,c_0_944]),
[final] ).
cnf(i_0_2363,plain,
( esk284_2(X2,X3) = esk282_2(X2,X3)
| in(X5,esk289_3(X2,X3,X4))
| X5 != X7
| unordered_pair(unordered_pair(X6,X1),unordered_pair(X6,X6)) != X5
| X1 != subset_complement(the_carrier(X2),esk293_6(X2,X3,X4,X5,X6,X1))
| ~ one_sorted_str(X2)
| ~ in(X6,complements_of_subsets(the_carrier(X2),X3))
| ~ element(X3,powerset(powerset(the_carrier(X2))))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X2),X3),X4)) ),
inference(rw,[status(thm)],[i_0_984,c_0_944]),
[final] ).
cnf(i_0_2364,plain,
( esk283_2(X2,X3) = esk282_2(X2,X3)
| in(X5,esk289_3(X2,X3,X4))
| X5 != X7
| unordered_pair(unordered_pair(X6,X1),unordered_pair(X6,X6)) != X5
| X1 != subset_complement(the_carrier(X2),esk293_6(X2,X3,X4,X5,X6,X1))
| ~ one_sorted_str(X2)
| ~ in(X6,complements_of_subsets(the_carrier(X2),X3))
| ~ element(X3,powerset(powerset(the_carrier(X2))))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X2),X3),X4)) ),
inference(rw,[status(thm)],[i_0_985,c_0_944]),
[final] ).
cnf(i_0_2365,lemma,
( in(X5,esk359_3(X2,X3,X4))
| unordered_pair(unordered_pair(X6,X1),unordered_pair(X6,X6)) != X5
| X1 != subset_complement(the_carrier(X2),esk362_6(X2,X3,X4,X5,X6,X1))
| ~ one_sorted_str(X2)
| ~ in(X6,complements_of_subsets(the_carrier(X2),X3))
| ~ element(X3,powerset(powerset(the_carrier(X2))))
| ~ in(X5,cartesian_product2(complements_of_subsets(the_carrier(X2),X3),X4)) ),
inference(rw,[status(thm)],[i_0_986,c_0_944]),
[final] ).
cnf(i_0_2366,plain,
( esk306_2(X2,X3) = subset_complement(the_carrier(X2),X8)
| in(X5,esk307_3(X2,X3,X4))
| X5 != X7
| X8 != esk305_2(X2,X3)
| unordered_pair(unordered_pair(X6,X1),unordered_pair(X6,X6)) != X5
| X1 != subset_complement(the_carrier(X2),esk311_6(X2,X3,X4,X5,X6,X1))
| ~ one_sorted_str(X2)
| ~ in(X6,X3)
| ~ in(X7,cartesian_product2(X3,X4))
| ~ element(X8,powerset(the_carrier(X2)))
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(rw,[status(thm)],[i_0_987,c_0_944]),
[final] ).
cnf(i_0_2367,plain,
( esk304_2(X2,X3) = subset_complement(the_carrier(X2),X8)
| in(X5,esk307_3(X2,X3,X4))
| X5 != X7
| X8 != esk303_2(X2,X3)
| unordered_pair(unordered_pair(X6,X1),unordered_pair(X6,X6)) != X5
| X1 != subset_complement(the_carrier(X2),esk311_6(X2,X3,X4,X5,X6,X1))
| ~ one_sorted_str(X2)
| ~ in(X6,X3)
| ~ in(X7,cartesian_product2(X3,X4))
| ~ element(X8,powerset(the_carrier(X2)))
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(rw,[status(thm)],[i_0_988,c_0_944]),
[final] ).
cnf(i_0_2368,plain,
( in(X5,esk307_3(X2,X3,X4))
| X5 != X7
| esk302_2(X2,X3) != esk301_2(X2,X3)
| unordered_pair(unordered_pair(X6,X1),unordered_pair(X6,X6)) != X5
| X1 != subset_complement(the_carrier(X2),esk311_6(X2,X3,X4,X5,X6,X1))
| ~ one_sorted_str(X2)
| ~ in(X6,X3)
| ~ in(X7,cartesian_product2(X3,X4))
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(rw,[status(thm)],[i_0_989,c_0_944]),
[final] ).
cnf(i_0_2369,plain,
( in(esk305_2(X2,X3),X3)
| in(X5,esk307_3(X2,X3,X4))
| X5 != X7
| unordered_pair(unordered_pair(X6,X1),unordered_pair(X6,X6)) != X5
| X1 != subset_complement(the_carrier(X2),esk311_6(X2,X3,X4,X5,X6,X1))
| ~ one_sorted_str(X2)
| ~ in(X6,X3)
| ~ in(X7,cartesian_product2(X3,X4))
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(rw,[status(thm)],[i_0_990,c_0_944]),
[final] ).
cnf(i_0_2370,plain,
( in(esk303_2(X2,X3),X3)
| in(X5,esk307_3(X2,X3,X4))
| X5 != X7
| unordered_pair(unordered_pair(X6,X1),unordered_pair(X6,X6)) != X5
| X1 != subset_complement(the_carrier(X2),esk311_6(X2,X3,X4,X5,X6,X1))
| ~ one_sorted_str(X2)
| ~ in(X6,X3)
| ~ in(X7,cartesian_product2(X3,X4))
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(rw,[status(thm)],[i_0_991,c_0_944]),
[final] ).
cnf(i_0_2371,plain,
( esk302_2(X2,X3) = esk300_2(X2,X3)
| in(X5,esk307_3(X2,X3,X4))
| X5 != X7
| unordered_pair(unordered_pair(X6,X1),unordered_pair(X6,X6)) != X5
| X1 != subset_complement(the_carrier(X2),esk311_6(X2,X3,X4,X5,X6,X1))
| ~ one_sorted_str(X2)
| ~ in(X6,X3)
| ~ in(X7,cartesian_product2(X3,X4))
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(rw,[status(thm)],[i_0_992,c_0_944]),
[final] ).
cnf(i_0_2372,plain,
( esk301_2(X2,X3) = esk300_2(X2,X3)
| in(X5,esk307_3(X2,X3,X4))
| X5 != X7
| unordered_pair(unordered_pair(X6,X1),unordered_pair(X6,X6)) != X5
| X1 != subset_complement(the_carrier(X2),esk311_6(X2,X3,X4,X5,X6,X1))
| ~ one_sorted_str(X2)
| ~ in(X6,X3)
| ~ in(X7,cartesian_product2(X3,X4))
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(rw,[status(thm)],[i_0_993,c_0_944]),
[final] ).
cnf(i_0_2373,lemma,
( in(X5,esk363_3(X2,X3,X4))
| unordered_pair(unordered_pair(X6,X1),unordered_pair(X6,X6)) != X5
| X1 != subset_complement(the_carrier(X2),esk366_6(X2,X3,X4,X5,X6,X1))
| ~ one_sorted_str(X2)
| ~ in(X6,X3)
| ~ in(X5,cartesian_product2(X3,X4))
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(rw,[status(thm)],[i_0_994,c_0_944]),
[final] ).
cnf(i_0_2374,plain,
( esk314_3(X2,X3,X1) = unordered_pair(unordered_pair(esk317_3(X2,X3,X1),esk318_3(X2,X3,X1)),unordered_pair(esk317_3(X2,X3,X1),esk317_3(X2,X3,X1)))
| in(unordered_pair(unordered_pair(apply(X1,esk321_4(X2,X3,X1,X4)),apply(X1,esk322_4(X2,X3,X1,X4))),unordered_pair(apply(X1,esk321_4(X2,X3,X1,X4)),apply(X1,esk321_4(X2,X3,X1,X4)))),X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ in(X4,esk319_3(X2,X3,X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_995,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2375,plain,
( esk313_3(X2,X3,X1) = unordered_pair(unordered_pair(esk315_3(X2,X3,X1),esk316_3(X2,X3,X1)),unordered_pair(esk315_3(X2,X3,X1),esk315_3(X2,X3,X1)))
| in(unordered_pair(unordered_pair(apply(X1,esk321_4(X2,X3,X1,X4)),apply(X1,esk322_4(X2,X3,X1,X4))),unordered_pair(apply(X1,esk321_4(X2,X3,X1,X4)),apply(X1,esk321_4(X2,X3,X1,X4)))),X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ in(X4,esk319_3(X2,X3,X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_996,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2376,plain,
( in(unordered_pair(unordered_pair(apply(X1,esk321_4(X2,X3,X1,X4)),apply(X1,esk322_4(X2,X3,X1,X4))),unordered_pair(apply(X1,esk321_4(X2,X3,X1,X4)),apply(X1,esk321_4(X2,X3,X1,X4)))),X3)
| esk314_3(X2,X3,X1) != esk313_3(X2,X3,X1)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ in(X4,esk319_3(X2,X3,X1)) ),
inference(rw,[status(thm)],[i_0_997,c_0_944]),
[final] ).
cnf(i_0_2377,plain,
( esk314_3(X2,X3,X1) = esk312_3(X2,X3,X1)
| in(unordered_pair(unordered_pair(apply(X1,esk321_4(X2,X3,X1,X4)),apply(X1,esk322_4(X2,X3,X1,X4))),unordered_pair(apply(X1,esk321_4(X2,X3,X1,X4)),apply(X1,esk321_4(X2,X3,X1,X4)))),X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ in(X4,esk319_3(X2,X3,X1)) ),
inference(rw,[status(thm)],[i_0_998,c_0_944]),
[final] ).
cnf(i_0_2378,plain,
( esk313_3(X2,X3,X1) = esk312_3(X2,X3,X1)
| in(unordered_pair(unordered_pair(apply(X1,esk321_4(X2,X3,X1,X4)),apply(X1,esk322_4(X2,X3,X1,X4))),unordered_pair(apply(X1,esk321_4(X2,X3,X1,X4)),apply(X1,esk321_4(X2,X3,X1,X4)))),X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ in(X4,esk319_3(X2,X3,X1)) ),
inference(rw,[status(thm)],[i_0_999,c_0_944]),
[final] ).
cnf(i_0_2379,lemma,
( in(unordered_pair(unordered_pair(apply(X1,esk368_4(X2,X3,X1,X4)),apply(X1,esk369_4(X2,X3,X1,X4))),unordered_pair(apply(X1,esk368_4(X2,X3,X1,X4)),apply(X1,esk368_4(X2,X3,X1,X4)))),X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ in(X4,esk367_3(X2,X3,X1)) ),
inference(rw,[status(thm)],[i_0_1000,c_0_944]),
[final] ).
cnf(i_0_2380,lemma,
( empty(X2)
| in(unordered_pair(unordered_pair(X4,X1),unordered_pair(X4,X4)),esk182_2(X2,X3))
| in(unordered_pair(unordered_pair(esk179_2(X2,X3),X6),unordered_pair(esk179_2(X2,X3),esk179_2(X2,X3))),X3)
| X4 != X5
| ~ relation(X3)
| ~ in(X4,X2)
| ~ in(X1,X5)
| ~ in(X6,esk181_2(X2,X3))
| ~ in(unordered_pair(unordered_pair(X1,esk184_5(X2,X3,X4,X1,X5)),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1001,c_0_944]),c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2381,lemma,
( empty(X2)
| in(unordered_pair(unordered_pair(X4,X1),unordered_pair(X4,X4)),esk182_2(X2,X3))
| in(unordered_pair(unordered_pair(esk178_2(X2,X3),X6),unordered_pair(esk178_2(X2,X3),esk178_2(X2,X3))),X3)
| X4 != X5
| ~ relation(X3)
| ~ in(X4,X2)
| ~ in(X1,X5)
| ~ in(X6,esk180_2(X2,X3))
| ~ in(unordered_pair(unordered_pair(X1,esk184_5(X2,X3,X4,X1,X5)),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1002,c_0_944]),c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2382,plain,
( empty(X2)
| in(X1,esk211_2(X2,X3))
| in(unordered_pair(unordered_pair(esk208_2(X2,X3),X6),unordered_pair(esk208_2(X2,X3),esk208_2(X2,X3))),X3)
| X4 != X5
| ~ relation(X3)
| ~ in(X4,X2)
| ~ in(X1,X5)
| ~ in(X6,esk210_2(X2,X3))
| ~ in(unordered_pair(unordered_pair(X1,esk214_5(X2,X3,X1,X4,X5)),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1003,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2383,plain,
( empty(X2)
| in(X1,esk211_2(X2,X3))
| in(unordered_pair(unordered_pair(esk207_2(X2,X3),X6),unordered_pair(esk207_2(X2,X3),esk207_2(X2,X3))),X3)
| X4 != X5
| ~ relation(X3)
| ~ in(X4,X2)
| ~ in(X1,X5)
| ~ in(X6,esk209_2(X2,X3))
| ~ in(unordered_pair(unordered_pair(X1,esk214_5(X2,X3,X1,X4,X5)),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1004,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2384,lemma,
( empty(X2)
| in(esk179_2(X2,X3),esk181_2(X2,X3))
| in(unordered_pair(unordered_pair(X4,X1),unordered_pair(X4,X4)),esk182_2(X2,X3))
| X4 != X5
| ~ relation(X3)
| ~ in(X4,X2)
| ~ in(X1,X5)
| ~ in(unordered_pair(unordered_pair(X1,esk184_5(X2,X3,X4,X1,X5)),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1005,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2385,lemma,
( empty(X2)
| in(esk178_2(X2,X3),esk180_2(X2,X3))
| in(unordered_pair(unordered_pair(X4,X1),unordered_pair(X4,X4)),esk182_2(X2,X3))
| X4 != X5
| ~ relation(X3)
| ~ in(X4,X2)
| ~ in(X1,X5)
| ~ in(unordered_pair(unordered_pair(X1,esk184_5(X2,X3,X4,X1,X5)),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1006,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2386,lemma,
( empty(X2)
| in(unordered_pair(unordered_pair(X4,X1),unordered_pair(X4,X4)),esk182_2(X2,X3))
| X4 != X5
| esk179_2(X2,X3) != esk178_2(X2,X3)
| ~ relation(X3)
| ~ in(X4,X2)
| ~ in(X1,X5)
| ~ in(unordered_pair(unordered_pair(X1,esk184_5(X2,X3,X4,X1,X5)),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1007,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2387,lemma,
( empty(X2)
| in(esk177_2(X2,X3),X2)
| in(unordered_pair(unordered_pair(X4,X1),unordered_pair(X4,X4)),esk182_2(X2,X3))
| X4 != X5
| ~ relation(X3)
| ~ in(X4,X2)
| ~ in(X1,X5)
| ~ in(unordered_pair(unordered_pair(X1,esk184_5(X2,X3,X4,X1,X5)),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1008,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2388,lemma,
( empty(X2)
| in(esk177_2(X2,X3),X2)
| in(unordered_pair(unordered_pair(X4,X1),unordered_pair(X4,X4)),esk182_2(X2,X3))
| X4 != X5
| ~ relation(X3)
| ~ in(X4,X2)
| ~ in(X1,X5)
| ~ in(unordered_pair(unordered_pair(X1,esk184_5(X2,X3,X4,X1,X5)),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1009,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2389,lemma,
( esk181_2(X2,X3) = esk177_2(X2,X3)
| empty(X2)
| in(unordered_pair(unordered_pair(X4,X1),unordered_pair(X4,X4)),esk182_2(X2,X3))
| X4 != X5
| ~ relation(X3)
| ~ in(X4,X2)
| ~ in(X1,X5)
| ~ in(unordered_pair(unordered_pair(X1,esk184_5(X2,X3,X4,X1,X5)),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1010,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2390,lemma,
( esk180_2(X2,X3) = esk177_2(X2,X3)
| empty(X2)
| in(unordered_pair(unordered_pair(X4,X1),unordered_pair(X4,X4)),esk182_2(X2,X3))
| X4 != X5
| ~ relation(X3)
| ~ in(X4,X2)
| ~ in(X1,X5)
| ~ in(unordered_pair(unordered_pair(X1,esk184_5(X2,X3,X4,X1,X5)),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1011,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2391,plain,
( empty(X2)
| in(X1,esk211_2(X2,X3))
| in(esk208_2(X2,X3),esk210_2(X2,X3))
| X4 != X5
| ~ relation(X3)
| ~ in(X4,X2)
| ~ in(X1,X5)
| ~ in(unordered_pair(unordered_pair(X1,esk214_5(X2,X3,X1,X4,X5)),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[i_0_1012,c_0_944]),
[final] ).
cnf(i_0_2392,plain,
( empty(X2)
| in(X1,esk211_2(X2,X3))
| in(esk207_2(X2,X3),esk209_2(X2,X3))
| X4 != X5
| ~ relation(X3)
| ~ in(X4,X2)
| ~ in(X1,X5)
| ~ in(unordered_pair(unordered_pair(X1,esk214_5(X2,X3,X1,X4,X5)),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[i_0_1013,c_0_944]),
[final] ).
cnf(i_0_2393,plain,
( empty(X2)
| in(X1,esk211_2(X2,X3))
| X4 != X5
| esk208_2(X2,X3) != esk207_2(X2,X3)
| ~ relation(X3)
| ~ in(X4,X2)
| ~ in(X1,X5)
| ~ in(unordered_pair(unordered_pair(X1,esk214_5(X2,X3,X1,X4,X5)),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[i_0_1014,c_0_944]),
[final] ).
cnf(i_0_2394,plain,
( empty(X2)
| in(X1,esk211_2(X2,X3))
| in(esk206_2(X2,X3),X2)
| X4 != X5
| ~ relation(X3)
| ~ in(X4,X2)
| ~ in(X1,X5)
| ~ in(unordered_pair(unordered_pair(X1,esk214_5(X2,X3,X1,X4,X5)),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[i_0_1015,c_0_944]),
[final] ).
cnf(i_0_2395,plain,
( empty(X2)
| in(X1,esk211_2(X2,X3))
| in(esk206_2(X2,X3),X2)
| X4 != X5
| ~ relation(X3)
| ~ in(X4,X2)
| ~ in(X1,X5)
| ~ in(unordered_pair(unordered_pair(X1,esk214_5(X2,X3,X1,X4,X5)),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[i_0_1016,c_0_944]),
[final] ).
cnf(i_0_2396,plain,
( esk210_2(X2,X3) = esk206_2(X2,X3)
| empty(X2)
| in(X1,esk211_2(X2,X3))
| X4 != X5
| ~ relation(X3)
| ~ in(X4,X2)
| ~ in(X1,X5)
| ~ in(unordered_pair(unordered_pair(X1,esk214_5(X2,X3,X1,X4,X5)),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[i_0_1017,c_0_944]),
[final] ).
cnf(i_0_2397,plain,
( esk209_2(X2,X3) = esk206_2(X2,X3)
| empty(X2)
| in(X1,esk211_2(X2,X3))
| X4 != X5
| ~ relation(X3)
| ~ in(X4,X2)
| ~ in(X1,X5)
| ~ in(unordered_pair(unordered_pair(X1,esk214_5(X2,X3,X1,X4,X5)),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[i_0_1018,c_0_944]),
[final] ).
cnf(i_0_2398,plain,
( unordered_pair(unordered_pair(esk287_2(X1,X2),esk288_2(X1,X2)),unordered_pair(esk287_2(X1,X2),esk287_2(X1,X2))) = esk284_2(X1,X2)
| in(X4,esk289_3(X1,X2,X3))
| element(esk293_6(X1,X2,X3,X4,X5,X6),powerset(the_carrier(X1)))
| X4 != X7
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ one_sorted_str(X1)
| ~ in(X5,complements_of_subsets(the_carrier(X1),X2))
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1019,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2399,plain,
( unordered_pair(unordered_pair(esk285_2(X1,X2),esk286_2(X1,X2)),unordered_pair(esk285_2(X1,X2),esk285_2(X1,X2))) = esk283_2(X1,X2)
| in(X4,esk289_3(X1,X2,X3))
| element(esk293_6(X1,X2,X3,X4,X5,X6),powerset(the_carrier(X1)))
| X4 != X7
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ one_sorted_str(X1)
| ~ in(X5,complements_of_subsets(the_carrier(X1),X2))
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1020,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2400,plain,
( esk288_2(X1,X2) = subset_complement(the_carrier(X1),X8)
| in(X4,esk289_3(X1,X2,X3))
| element(esk293_6(X1,X2,X3,X4,X5,X6),powerset(the_carrier(X1)))
| X4 != X7
| X8 != esk287_2(X1,X2)
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ one_sorted_str(X1)
| ~ element(X8,powerset(the_carrier(X1)))
| ~ in(X5,complements_of_subsets(the_carrier(X1),X2))
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3)) ),
inference(rw,[status(thm)],[i_0_1021,c_0_944]),
[final] ).
cnf(i_0_2401,plain,
( esk286_2(X1,X2) = subset_complement(the_carrier(X1),X8)
| in(X4,esk289_3(X1,X2,X3))
| element(esk293_6(X1,X2,X3,X4,X5,X6),powerset(the_carrier(X1)))
| X4 != X7
| X8 != esk285_2(X1,X2)
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ one_sorted_str(X1)
| ~ element(X8,powerset(the_carrier(X1)))
| ~ in(X5,complements_of_subsets(the_carrier(X1),X2))
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3)) ),
inference(rw,[status(thm)],[i_0_1022,c_0_944]),
[final] ).
cnf(i_0_2402,plain,
( unordered_pair(unordered_pair(esk305_2(X1,X2),esk306_2(X1,X2)),unordered_pair(esk305_2(X1,X2),esk305_2(X1,X2))) = esk302_2(X1,X2)
| in(X4,esk307_3(X1,X2,X3))
| element(esk311_6(X1,X2,X3,X4,X5,X6),powerset(the_carrier(X1)))
| X4 != X7
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ one_sorted_str(X1)
| ~ in(X5,X2)
| ~ in(X7,cartesian_product2(X2,X3))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1023,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2403,plain,
( unordered_pair(unordered_pair(esk303_2(X1,X2),esk304_2(X1,X2)),unordered_pair(esk303_2(X1,X2),esk303_2(X1,X2))) = esk301_2(X1,X2)
| in(X4,esk307_3(X1,X2,X3))
| element(esk311_6(X1,X2,X3,X4,X5,X6),powerset(the_carrier(X1)))
| X4 != X7
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ one_sorted_str(X1)
| ~ in(X5,X2)
| ~ in(X7,cartesian_product2(X2,X3))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1024,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2404,plain,
( in(X4,esk289_3(X1,X2,X3))
| in(esk287_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| element(esk293_6(X1,X2,X3,X4,X5,X6),powerset(the_carrier(X1)))
| X4 != X7
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ one_sorted_str(X1)
| ~ in(X5,complements_of_subsets(the_carrier(X1),X2))
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3)) ),
inference(rw,[status(thm)],[i_0_1025,c_0_944]),
[final] ).
cnf(i_0_2405,plain,
( in(X4,esk289_3(X1,X2,X3))
| in(esk285_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| element(esk293_6(X1,X2,X3,X4,X5,X6),powerset(the_carrier(X1)))
| X4 != X7
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ one_sorted_str(X1)
| ~ in(X5,complements_of_subsets(the_carrier(X1),X2))
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3)) ),
inference(rw,[status(thm)],[i_0_1026,c_0_944]),
[final] ).
cnf(i_0_2406,plain,
( in(X4,esk289_3(X1,X2,X3))
| element(esk293_6(X1,X2,X3,X4,X5,X6),powerset(the_carrier(X1)))
| X4 != X7
| esk284_2(X1,X2) != esk283_2(X1,X2)
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ one_sorted_str(X1)
| ~ in(X5,complements_of_subsets(the_carrier(X1),X2))
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3)) ),
inference(rw,[status(thm)],[i_0_1027,c_0_944]),
[final] ).
cnf(i_0_2407,plain,
( esk284_2(X1,X2) = esk282_2(X1,X2)
| in(X4,esk289_3(X1,X2,X3))
| element(esk293_6(X1,X2,X3,X4,X5,X6),powerset(the_carrier(X1)))
| X4 != X7
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ one_sorted_str(X1)
| ~ in(X5,complements_of_subsets(the_carrier(X1),X2))
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3)) ),
inference(rw,[status(thm)],[i_0_1028,c_0_944]),
[final] ).
cnf(i_0_2408,plain,
( esk283_2(X1,X2) = esk282_2(X1,X2)
| in(X4,esk289_3(X1,X2,X3))
| element(esk293_6(X1,X2,X3,X4,X5,X6),powerset(the_carrier(X1)))
| X4 != X7
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ one_sorted_str(X1)
| ~ in(X5,complements_of_subsets(the_carrier(X1),X2))
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3)) ),
inference(rw,[status(thm)],[i_0_1029,c_0_944]),
[final] ).
cnf(i_0_2409,lemma,
( in(X4,esk359_3(X1,X2,X3))
| element(esk362_6(X1,X2,X3,X4,X5,X6),powerset(the_carrier(X1)))
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ one_sorted_str(X1)
| ~ in(X5,complements_of_subsets(the_carrier(X1),X2))
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ in(X4,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3)) ),
inference(rw,[status(thm)],[i_0_1030,c_0_944]),
[final] ).
cnf(i_0_2410,plain,
( esk306_2(X1,X2) = subset_complement(the_carrier(X1),X8)
| in(X4,esk307_3(X1,X2,X3))
| element(esk311_6(X1,X2,X3,X4,X5,X6),powerset(the_carrier(X1)))
| X4 != X7
| X8 != esk305_2(X1,X2)
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ one_sorted_str(X1)
| ~ in(X5,X2)
| ~ in(X7,cartesian_product2(X2,X3))
| ~ element(X8,powerset(the_carrier(X1)))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1031,c_0_944]),
[final] ).
cnf(i_0_2411,plain,
( esk304_2(X1,X2) = subset_complement(the_carrier(X1),X8)
| in(X4,esk307_3(X1,X2,X3))
| element(esk311_6(X1,X2,X3,X4,X5,X6),powerset(the_carrier(X1)))
| X4 != X7
| X8 != esk303_2(X1,X2)
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ one_sorted_str(X1)
| ~ in(X5,X2)
| ~ in(X7,cartesian_product2(X2,X3))
| ~ element(X8,powerset(the_carrier(X1)))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1032,c_0_944]),
[final] ).
cnf(i_0_2412,plain,
( in(X4,esk307_3(X1,X2,X3))
| element(esk311_6(X1,X2,X3,X4,X5,X6),powerset(the_carrier(X1)))
| X4 != X7
| esk302_2(X1,X2) != esk301_2(X1,X2)
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ one_sorted_str(X1)
| ~ in(X5,X2)
| ~ in(X7,cartesian_product2(X2,X3))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1033,c_0_944]),
[final] ).
cnf(i_0_2413,plain,
( in(esk305_2(X1,X2),X2)
| in(X4,esk307_3(X1,X2,X3))
| element(esk311_6(X1,X2,X3,X4,X5,X6),powerset(the_carrier(X1)))
| X4 != X7
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ one_sorted_str(X1)
| ~ in(X5,X2)
| ~ in(X7,cartesian_product2(X2,X3))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1034,c_0_944]),
[final] ).
cnf(i_0_2414,plain,
( in(esk303_2(X1,X2),X2)
| in(X4,esk307_3(X1,X2,X3))
| element(esk311_6(X1,X2,X3,X4,X5,X6),powerset(the_carrier(X1)))
| X4 != X7
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ one_sorted_str(X1)
| ~ in(X5,X2)
| ~ in(X7,cartesian_product2(X2,X3))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1035,c_0_944]),
[final] ).
cnf(i_0_2415,plain,
( esk302_2(X1,X2) = esk300_2(X1,X2)
| in(X4,esk307_3(X1,X2,X3))
| element(esk311_6(X1,X2,X3,X4,X5,X6),powerset(the_carrier(X1)))
| X4 != X7
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ one_sorted_str(X1)
| ~ in(X5,X2)
| ~ in(X7,cartesian_product2(X2,X3))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1036,c_0_944]),
[final] ).
cnf(i_0_2416,plain,
( esk301_2(X1,X2) = esk300_2(X1,X2)
| in(X4,esk307_3(X1,X2,X3))
| element(esk311_6(X1,X2,X3,X4,X5,X6),powerset(the_carrier(X1)))
| X4 != X7
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ one_sorted_str(X1)
| ~ in(X5,X2)
| ~ in(X7,cartesian_product2(X2,X3))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1037,c_0_944]),
[final] ).
cnf(i_0_2417,lemma,
( in(X4,esk363_3(X1,X2,X3))
| element(esk366_6(X1,X2,X3,X4,X5,X6),powerset(the_carrier(X1)))
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ one_sorted_str(X1)
| ~ in(X5,X2)
| ~ in(X4,cartesian_product2(X2,X3))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1038,c_0_944]),
[final] ).
cnf(i_0_2418,plain,
( empty(X1)
| empty(X2)
| element(apply_binary_as_element(X1,X2,X4,X3,X5,X6),X4)
| ~ function(X3)
| ~ quasi_total(X3,cartesian_product2(X1,X2),X4)
| ~ relation_of2(X3,cartesian_product2(X1,X2),X4)
| ~ element(X5,X1)
| ~ element(X6,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1039]),
[final] ).
cnf(i_0_2419,plain,
( in(unordered_pair(unordered_pair(X1,esk106_5(X2,X3,X4,X1,X5)),unordered_pair(X1,X1)),X2)
| X4 != relation_composition(X2,X3)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X1,X5),unordered_pair(X1,X1)),X4) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1040,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2420,plain,
( relation_isomorphism(X1,X2,X3)
| relation_field(X1) != relation_dom(X3)
| relation_rng(X3) != relation_field(X2)
| ~ function(X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| ~ one_to_one(X3)
| ~ in(esk99_3(X1,X2,X3),relation_field(X1))
| ~ in(esk100_3(X1,X2,X3),relation_field(X1))
| ~ in(unordered_pair(unordered_pair(esk99_3(X1,X2,X3),esk100_3(X1,X2,X3)),unordered_pair(esk99_3(X1,X2,X3),esk99_3(X1,X2,X3))),X1)
| ~ in(unordered_pair(unordered_pair(apply(X3,esk99_3(X1,X2,X3)),apply(X3,esk100_3(X1,X2,X3))),unordered_pair(apply(X3,esk99_3(X1,X2,X3)),apply(X3,esk99_3(X1,X2,X3)))),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1041,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2421,plain,
( X1 = unordered_pair(unordered_pair(esk321_4(X2,X3,X4,X1),esk322_4(X2,X3,X4,X1)),unordered_pair(esk321_4(X2,X3,X4,X1),esk321_4(X2,X3,X4,X1)))
| in(unordered_pair(unordered_pair(apply(X4,esk317_3(X2,X3,X4)),apply(X4,esk318_3(X2,X3,X4))),unordered_pair(apply(X4,esk317_3(X2,X3,X4)),apply(X4,esk317_3(X2,X3,X4)))),X3)
| ~ function(X4)
| ~ relation(X4)
| ~ relation(X3)
| ~ in(X1,esk319_3(X2,X3,X4)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1042,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2422,plain,
( X1 = unordered_pair(unordered_pair(esk321_4(X2,X3,X4,X1),esk322_4(X2,X3,X4,X1)),unordered_pair(esk321_4(X2,X3,X4,X1),esk321_4(X2,X3,X4,X1)))
| in(unordered_pair(unordered_pair(apply(X4,esk315_3(X2,X3,X4)),apply(X4,esk316_3(X2,X3,X4))),unordered_pair(apply(X4,esk315_3(X2,X3,X4)),apply(X4,esk315_3(X2,X3,X4)))),X3)
| ~ function(X4)
| ~ relation(X4)
| ~ relation(X3)
| ~ in(X1,esk319_3(X2,X3,X4)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1043,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2423,plain,
( empty(X2)
| in(unordered_pair(unordered_pair(esk222_2(X2,X3),X6),unordered_pair(esk222_2(X2,X3),esk222_2(X2,X3))),X3)
| in(unordered_pair(unordered_pair(esk227_4(X2,X3,X4,X5),X1),unordered_pair(esk227_4(X2,X3,X4,X5),esk227_4(X2,X3,X4,X5))),X3)
| ~ relation(X3)
| ~ in(X6,esk223_2(X2,X3))
| ~ in(X5,esk224_3(X2,X3,X4))
| ~ in(X1,esk228_4(X2,X3,X4,X5)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1044,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2424,plain,
( empty(X2)
| in(unordered_pair(unordered_pair(esk219_2(X2,X3),X6),unordered_pair(esk219_2(X2,X3),esk219_2(X2,X3))),X3)
| in(unordered_pair(unordered_pair(esk227_4(X2,X3,X4,X5),X1),unordered_pair(esk227_4(X2,X3,X4,X5),esk227_4(X2,X3,X4,X5))),X3)
| ~ relation(X3)
| ~ in(X6,esk220_2(X2,X3))
| ~ in(X5,esk224_3(X2,X3,X4))
| ~ in(X1,esk228_4(X2,X3,X4,X5)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1045,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2425,plain,
( unordered_pair(unordered_pair(esk221_2(X2,X3),esk222_2(X2,X3)),unordered_pair(esk221_2(X2,X3),esk221_2(X2,X3))) = esk217_2(X2,X3)
| empty(X2)
| in(unordered_pair(unordered_pair(esk227_4(X2,X3,X4,X5),X1),unordered_pair(esk227_4(X2,X3,X4,X5),esk227_4(X2,X3,X4,X5))),X3)
| ~ relation(X3)
| ~ in(X5,esk224_3(X2,X3,X4))
| ~ in(X1,esk228_4(X2,X3,X4,X5)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1046,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2426,plain,
( unordered_pair(unordered_pair(esk218_2(X2,X3),esk219_2(X2,X3)),unordered_pair(esk218_2(X2,X3),esk218_2(X2,X3))) = esk216_2(X2,X3)
| empty(X2)
| in(unordered_pair(unordered_pair(esk227_4(X2,X3,X4,X5),X1),unordered_pair(esk227_4(X2,X3,X4,X5),esk227_4(X2,X3,X4,X5))),X3)
| ~ relation(X3)
| ~ in(X5,esk224_3(X2,X3,X4))
| ~ in(X1,esk228_4(X2,X3,X4,X5)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1047,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2427,plain,
( empty(X2)
| in(esk222_2(X2,X3),esk223_2(X2,X3))
| in(unordered_pair(unordered_pair(esk227_4(X2,X3,X4,X5),X1),unordered_pair(esk227_4(X2,X3,X4,X5),esk227_4(X2,X3,X4,X5))),X3)
| ~ relation(X3)
| ~ in(X5,esk224_3(X2,X3,X4))
| ~ in(X1,esk228_4(X2,X3,X4,X5)) ),
inference(rw,[status(thm)],[i_0_1048,c_0_944]),
[final] ).
cnf(i_0_2428,plain,
( empty(X2)
| in(esk219_2(X2,X3),esk220_2(X2,X3))
| in(unordered_pair(unordered_pair(esk227_4(X2,X3,X4,X5),X1),unordered_pair(esk227_4(X2,X3,X4,X5),esk227_4(X2,X3,X4,X5))),X3)
| ~ relation(X3)
| ~ in(X5,esk224_3(X2,X3,X4))
| ~ in(X1,esk228_4(X2,X3,X4,X5)) ),
inference(rw,[status(thm)],[i_0_1049,c_0_944]),
[final] ).
cnf(i_0_2429,plain,
( empty(X2)
| in(unordered_pair(unordered_pair(esk227_4(X2,X3,X4,X5),X1),unordered_pair(esk227_4(X2,X3,X4,X5),esk227_4(X2,X3,X4,X5))),X3)
| esk217_2(X2,X3) != esk216_2(X2,X3)
| ~ relation(X3)
| ~ in(X5,esk224_3(X2,X3,X4))
| ~ in(X1,esk228_4(X2,X3,X4,X5)) ),
inference(rw,[status(thm)],[i_0_1050,c_0_944]),
[final] ).
cnf(i_0_2430,plain,
( empty(X2)
| in(esk221_2(X2,X3),X2)
| in(unordered_pair(unordered_pair(esk227_4(X2,X3,X4,X5),X1),unordered_pair(esk227_4(X2,X3,X4,X5),esk227_4(X2,X3,X4,X5))),X3)
| ~ relation(X3)
| ~ in(X5,esk224_3(X2,X3,X4))
| ~ in(X1,esk228_4(X2,X3,X4,X5)) ),
inference(rw,[status(thm)],[i_0_1051,c_0_944]),
[final] ).
cnf(i_0_2431,plain,
( empty(X2)
| in(esk218_2(X2,X3),X2)
| in(unordered_pair(unordered_pair(esk227_4(X2,X3,X4,X5),X1),unordered_pair(esk227_4(X2,X3,X4,X5),esk227_4(X2,X3,X4,X5))),X3)
| ~ relation(X3)
| ~ in(X5,esk224_3(X2,X3,X4))
| ~ in(X1,esk228_4(X2,X3,X4,X5)) ),
inference(rw,[status(thm)],[i_0_1052,c_0_944]),
[final] ).
cnf(i_0_2432,plain,
( esk223_2(X2,X3) = esk221_2(X2,X3)
| empty(X2)
| in(unordered_pair(unordered_pair(esk227_4(X2,X3,X4,X5),X1),unordered_pair(esk227_4(X2,X3,X4,X5),esk227_4(X2,X3,X4,X5))),X3)
| ~ relation(X3)
| ~ in(X5,esk224_3(X2,X3,X4))
| ~ in(X1,esk228_4(X2,X3,X4,X5)) ),
inference(rw,[status(thm)],[i_0_1053,c_0_944]),
[final] ).
cnf(i_0_2433,plain,
( esk220_2(X2,X3) = esk218_2(X2,X3)
| empty(X2)
| in(unordered_pair(unordered_pair(esk227_4(X2,X3,X4,X5),X1),unordered_pair(esk227_4(X2,X3,X4,X5),esk227_4(X2,X3,X4,X5))),X3)
| ~ relation(X3)
| ~ in(X5,esk224_3(X2,X3,X4))
| ~ in(X1,esk228_4(X2,X3,X4,X5)) ),
inference(rw,[status(thm)],[i_0_1054,c_0_944]),
[final] ).
cnf(i_0_2434,plain,
( esk217_2(X2,X3) = esk215_2(X2,X3)
| empty(X2)
| in(unordered_pair(unordered_pair(esk227_4(X2,X3,X4,X5),X1),unordered_pair(esk227_4(X2,X3,X4,X5),esk227_4(X2,X3,X4,X5))),X3)
| ~ relation(X3)
| ~ in(X5,esk224_3(X2,X3,X4))
| ~ in(X1,esk228_4(X2,X3,X4,X5)) ),
inference(rw,[status(thm)],[i_0_1055,c_0_944]),
[final] ).
cnf(i_0_2435,plain,
( esk216_2(X2,X3) = esk215_2(X2,X3)
| empty(X2)
| in(unordered_pair(unordered_pair(esk227_4(X2,X3,X4,X5),X1),unordered_pair(esk227_4(X2,X3,X4,X5),esk227_4(X2,X3,X4,X5))),X3)
| ~ relation(X3)
| ~ in(X5,esk224_3(X2,X3,X4))
| ~ in(X1,esk228_4(X2,X3,X4,X5)) ),
inference(rw,[status(thm)],[i_0_1056,c_0_944]),
[final] ).
cnf(i_0_2436,lemma,
( empty(X2)
| in(unordered_pair(unordered_pair(esk343_4(X2,X3,X4,X5),X1),unordered_pair(esk343_4(X2,X3,X4,X5),esk343_4(X2,X3,X4,X5))),X3)
| ~ relation(X3)
| ~ in(X5,esk341_3(X2,X3,X4))
| ~ in(X1,esk344_4(X2,X3,X4,X5)) ),
inference(rw,[status(thm)],[i_0_1057,c_0_944]),
[final] ).
cnf(i_0_2437,plain,
( esk293_6(X1,X2,X3,X4,X5,X6) = X5
| unordered_pair(unordered_pair(esk287_2(X1,X2),esk288_2(X1,X2)),unordered_pair(esk287_2(X1,X2),esk287_2(X1,X2))) = esk284_2(X1,X2)
| in(X4,esk289_3(X1,X2,X3))
| X4 != X7
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ one_sorted_str(X1)
| ~ in(X5,complements_of_subsets(the_carrier(X1),X2))
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1058,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2438,plain,
( esk293_6(X1,X2,X3,X4,X5,X6) = X5
| unordered_pair(unordered_pair(esk285_2(X1,X2),esk286_2(X1,X2)),unordered_pair(esk285_2(X1,X2),esk285_2(X1,X2))) = esk283_2(X1,X2)
| in(X4,esk289_3(X1,X2,X3))
| X4 != X7
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ one_sorted_str(X1)
| ~ in(X5,complements_of_subsets(the_carrier(X1),X2))
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1059,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2439,plain,
( esk293_6(X1,X2,X3,X4,X5,X6) = X5
| esk288_2(X1,X2) = subset_complement(the_carrier(X1),X8)
| in(X4,esk289_3(X1,X2,X3))
| X4 != X7
| X8 != esk287_2(X1,X2)
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ one_sorted_str(X1)
| ~ element(X8,powerset(the_carrier(X1)))
| ~ in(X5,complements_of_subsets(the_carrier(X1),X2))
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3)) ),
inference(rw,[status(thm)],[i_0_1060,c_0_944]),
[final] ).
cnf(i_0_2440,plain,
( esk293_6(X1,X2,X3,X4,X5,X6) = X5
| esk286_2(X1,X2) = subset_complement(the_carrier(X1),X8)
| in(X4,esk289_3(X1,X2,X3))
| X4 != X7
| X8 != esk285_2(X1,X2)
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ one_sorted_str(X1)
| ~ element(X8,powerset(the_carrier(X1)))
| ~ in(X5,complements_of_subsets(the_carrier(X1),X2))
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3)) ),
inference(rw,[status(thm)],[i_0_1061,c_0_944]),
[final] ).
cnf(i_0_2441,plain,
( esk311_6(X1,X2,X3,X4,X5,X6) = X5
| unordered_pair(unordered_pair(esk305_2(X1,X2),esk306_2(X1,X2)),unordered_pair(esk305_2(X1,X2),esk305_2(X1,X2))) = esk302_2(X1,X2)
| in(X4,esk307_3(X1,X2,X3))
| X4 != X7
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ one_sorted_str(X1)
| ~ in(X5,X2)
| ~ in(X7,cartesian_product2(X2,X3))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1062,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2442,plain,
( esk311_6(X1,X2,X3,X4,X5,X6) = X5
| unordered_pair(unordered_pair(esk303_2(X1,X2),esk304_2(X1,X2)),unordered_pair(esk303_2(X1,X2),esk303_2(X1,X2))) = esk301_2(X1,X2)
| in(X4,esk307_3(X1,X2,X3))
| X4 != X7
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ one_sorted_str(X1)
| ~ in(X5,X2)
| ~ in(X7,cartesian_product2(X2,X3))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1063,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2443,plain,
( esk293_6(X1,X2,X3,X4,X5,X6) = X5
| in(X4,esk289_3(X1,X2,X3))
| in(esk287_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| X4 != X7
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ one_sorted_str(X1)
| ~ in(X5,complements_of_subsets(the_carrier(X1),X2))
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3)) ),
inference(rw,[status(thm)],[i_0_1064,c_0_944]),
[final] ).
cnf(i_0_2444,plain,
( esk293_6(X1,X2,X3,X4,X5,X6) = X5
| in(X4,esk289_3(X1,X2,X3))
| in(esk285_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| X4 != X7
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ one_sorted_str(X1)
| ~ in(X5,complements_of_subsets(the_carrier(X1),X2))
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3)) ),
inference(rw,[status(thm)],[i_0_1065,c_0_944]),
[final] ).
cnf(i_0_2445,plain,
( esk293_6(X1,X2,X3,X4,X5,X6) = X5
| in(X4,esk289_3(X1,X2,X3))
| X4 != X7
| esk284_2(X1,X2) != esk283_2(X1,X2)
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ one_sorted_str(X1)
| ~ in(X5,complements_of_subsets(the_carrier(X1),X2))
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3)) ),
inference(rw,[status(thm)],[i_0_1066,c_0_944]),
[final] ).
cnf(i_0_2446,plain,
( esk284_2(X1,X2) = esk282_2(X1,X2)
| esk293_6(X1,X2,X3,X4,X5,X6) = X5
| in(X4,esk289_3(X1,X2,X3))
| X4 != X7
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ one_sorted_str(X1)
| ~ in(X5,complements_of_subsets(the_carrier(X1),X2))
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3)) ),
inference(rw,[status(thm)],[i_0_1067,c_0_944]),
[final] ).
cnf(i_0_2447,plain,
( esk283_2(X1,X2) = esk282_2(X1,X2)
| esk293_6(X1,X2,X3,X4,X5,X6) = X5
| in(X4,esk289_3(X1,X2,X3))
| X4 != X7
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ one_sorted_str(X1)
| ~ in(X5,complements_of_subsets(the_carrier(X1),X2))
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3)) ),
inference(rw,[status(thm)],[i_0_1068,c_0_944]),
[final] ).
cnf(i_0_2448,lemma,
( esk362_6(X1,X2,X3,X4,X5,X6) = X5
| in(X4,esk359_3(X1,X2,X3))
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ one_sorted_str(X1)
| ~ in(X5,complements_of_subsets(the_carrier(X1),X2))
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ in(X4,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3)) ),
inference(rw,[status(thm)],[i_0_1069,c_0_944]),
[final] ).
cnf(i_0_2449,plain,
( esk311_6(X1,X2,X3,X4,X5,X6) = X5
| esk306_2(X1,X2) = subset_complement(the_carrier(X1),X8)
| in(X4,esk307_3(X1,X2,X3))
| X4 != X7
| X8 != esk305_2(X1,X2)
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ one_sorted_str(X1)
| ~ in(X5,X2)
| ~ in(X7,cartesian_product2(X2,X3))
| ~ element(X8,powerset(the_carrier(X1)))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1070,c_0_944]),
[final] ).
cnf(i_0_2450,plain,
( esk311_6(X1,X2,X3,X4,X5,X6) = X5
| esk304_2(X1,X2) = subset_complement(the_carrier(X1),X8)
| in(X4,esk307_3(X1,X2,X3))
| X4 != X7
| X8 != esk303_2(X1,X2)
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ one_sorted_str(X1)
| ~ in(X5,X2)
| ~ in(X7,cartesian_product2(X2,X3))
| ~ element(X8,powerset(the_carrier(X1)))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1071,c_0_944]),
[final] ).
cnf(i_0_2451,plain,
( esk311_6(X1,X2,X3,X4,X5,X6) = X5
| in(X4,esk307_3(X1,X2,X3))
| X4 != X7
| esk302_2(X1,X2) != esk301_2(X1,X2)
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ one_sorted_str(X1)
| ~ in(X5,X2)
| ~ in(X7,cartesian_product2(X2,X3))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1072,c_0_944]),
[final] ).
cnf(i_0_2452,plain,
( esk311_6(X1,X2,X3,X4,X5,X6) = X5
| in(esk305_2(X1,X2),X2)
| in(X4,esk307_3(X1,X2,X3))
| X4 != X7
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ one_sorted_str(X1)
| ~ in(X5,X2)
| ~ in(X7,cartesian_product2(X2,X3))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1073,c_0_944]),
[final] ).
cnf(i_0_2453,plain,
( esk311_6(X1,X2,X3,X4,X5,X6) = X5
| in(esk303_2(X1,X2),X2)
| in(X4,esk307_3(X1,X2,X3))
| X4 != X7
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ one_sorted_str(X1)
| ~ in(X5,X2)
| ~ in(X7,cartesian_product2(X2,X3))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1074,c_0_944]),
[final] ).
cnf(i_0_2454,plain,
( esk302_2(X1,X2) = esk300_2(X1,X2)
| esk311_6(X1,X2,X3,X4,X5,X6) = X5
| in(X4,esk307_3(X1,X2,X3))
| X4 != X7
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ one_sorted_str(X1)
| ~ in(X5,X2)
| ~ in(X7,cartesian_product2(X2,X3))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1075,c_0_944]),
[final] ).
cnf(i_0_2455,plain,
( esk301_2(X1,X2) = esk300_2(X1,X2)
| esk311_6(X1,X2,X3,X4,X5,X6) = X5
| in(X4,esk307_3(X1,X2,X3))
| X4 != X7
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ one_sorted_str(X1)
| ~ in(X5,X2)
| ~ in(X7,cartesian_product2(X2,X3))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1076,c_0_944]),
[final] ).
cnf(i_0_2456,lemma,
( esk366_6(X1,X2,X3,X4,X5,X6) = X5
| in(X4,esk363_3(X1,X2,X3))
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ one_sorted_str(X1)
| ~ in(X5,X2)
| ~ in(X4,cartesian_product2(X2,X3))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1077,c_0_944]),
[final] ).
cnf(i_0_2457,plain,
( empty(X1)
| empty(X2)
| apply_binary_as_element(X1,X2,X4,X3,X5,X6) = apply_binary(X3,X5,X6)
| ~ function(X3)
| ~ quasi_total(X3,cartesian_product2(X1,X2),X4)
| ~ relation_of2(X3,cartesian_product2(X1,X2),X4)
| ~ element(X5,X1)
| ~ element(X6,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1078]),
[final] ).
cnf(i_0_2458,lemma,
( in(unordered_pair(unordered_pair(esk417_4(X1,X2,X3,X4),X4),unordered_pair(esk417_4(X1,X2,X3,X4),esk417_4(X1,X2,X3,X4))),X3)
| relation_rng_as_subset(X1,X2,X3) != X2
| ~ in(X4,X2)
| ~ relation_of2_as_subset(X3,X1,X2) ),
inference(rw,[status(thm)],[i_0_1079,c_0_944]),
[final] ).
cnf(i_0_2459,plain,
( empty_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)
| ~ join_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1080]),
[final] ).
cnf(i_0_2460,plain,
( empty_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)
| ~ meet_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1081]),
[final] ).
cnf(i_0_2461,plain,
( in(unordered_pair(unordered_pair(esk16_4(X1,X2,X3,X4),X4),unordered_pair(esk16_4(X1,X2,X3,X4),esk16_4(X1,X2,X3,X4))),X1)
| X3 != relation_image(X1,X2)
| ~ relation(X1)
| ~ in(X4,X3) ),
inference(rw,[status(thm)],[i_0_1082,c_0_944]),
[final] ).
cnf(i_0_2462,plain,
( X3 = relation_composition(X1,X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(X4,esk108_3(X1,X2,X3)),unordered_pair(X4,X4)),X2)
| ~ in(unordered_pair(unordered_pair(esk107_3(X1,X2,X3),X4),unordered_pair(esk107_3(X1,X2,X3),esk107_3(X1,X2,X3))),X1)
| ~ in(unordered_pair(unordered_pair(esk107_3(X1,X2,X3),esk108_3(X1,X2,X3)),unordered_pair(esk107_3(X1,X2,X3),esk107_3(X1,X2,X3))),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1083,c_0_944]),c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2463,plain,
( X3 = relation_rng_restriction(X1,X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(esk9_3(X1,X2,X3),X1)
| ~ in(unordered_pair(unordered_pair(esk8_3(X1,X2,X3),esk9_3(X1,X2,X3)),unordered_pair(esk8_3(X1,X2,X3),esk8_3(X1,X2,X3))),X3)
| ~ in(unordered_pair(unordered_pair(esk8_3(X1,X2,X3),esk9_3(X1,X2,X3)),unordered_pair(esk8_3(X1,X2,X3),esk8_3(X1,X2,X3))),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1084,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2464,plain,
( X3 = relation_dom_restriction(X1,X2)
| ~ relation(X3)
| ~ relation(X1)
| ~ in(esk3_3(X1,X2,X3),X2)
| ~ in(unordered_pair(unordered_pair(esk3_3(X1,X2,X3),esk4_3(X1,X2,X3)),unordered_pair(esk3_3(X1,X2,X3),esk3_3(X1,X2,X3))),X3)
| ~ in(unordered_pair(unordered_pair(esk3_3(X1,X2,X3),esk4_3(X1,X2,X3)),unordered_pair(esk3_3(X1,X2,X3),esk3_3(X1,X2,X3))),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1085,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2465,plain,
( relation_isomorphism(X2,X3,X1)
| in(unordered_pair(unordered_pair(esk99_3(X2,X3,X1),esk100_3(X2,X3,X1)),unordered_pair(esk99_3(X2,X3,X1),esk99_3(X2,X3,X1))),X2)
| in(unordered_pair(unordered_pair(apply(X1,esk99_3(X2,X3,X1)),apply(X1,esk100_3(X2,X3,X1))),unordered_pair(apply(X1,esk99_3(X2,X3,X1)),apply(X1,esk99_3(X2,X3,X1)))),X3)
| relation_field(X2) != relation_dom(X1)
| relation_rng(X1) != relation_field(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| ~ one_to_one(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1086,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2466,plain,
( X1 = unordered_pair(unordered_pair(esk321_4(X2,X3,X4,X1),esk322_4(X2,X3,X4,X1)),unordered_pair(esk321_4(X2,X3,X4,X1),esk321_4(X2,X3,X4,X1)))
| esk314_3(X2,X3,X4) = unordered_pair(unordered_pair(esk317_3(X2,X3,X4),esk318_3(X2,X3,X4)),unordered_pair(esk317_3(X2,X3,X4),esk317_3(X2,X3,X4)))
| ~ function(X4)
| ~ relation(X4)
| ~ relation(X3)
| ~ in(X1,esk319_3(X2,X3,X4)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1087,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2467,plain,
( X1 = unordered_pair(unordered_pair(esk321_4(X2,X3,X4,X1),esk322_4(X2,X3,X4,X1)),unordered_pair(esk321_4(X2,X3,X4,X1),esk321_4(X2,X3,X4,X1)))
| esk313_3(X2,X3,X4) = unordered_pair(unordered_pair(esk315_3(X2,X3,X4),esk316_3(X2,X3,X4)),unordered_pair(esk315_3(X2,X3,X4),esk315_3(X2,X3,X4)))
| ~ function(X4)
| ~ relation(X4)
| ~ relation(X3)
| ~ in(X1,esk319_3(X2,X3,X4)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1088,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2468,lemma,
( empty(X2)
| in(unordered_pair(unordered_pair(esk376_2(X2,X3),X7),unordered_pair(esk376_2(X2,X3),esk376_2(X2,X3))),X3)
| in(unordered_pair(unordered_pair(apply(esk381_2(X2,X3),X4),X1),unordered_pair(apply(esk381_2(X2,X3),X4),apply(esk381_2(X2,X3),X4))),X3)
| esk379_2(X2,X3) != X6
| ~ relation(X3)
| ~ in(X5,X6)
| ~ in(X4,X2)
| ~ in(X7,esk378_2(X2,X3))
| ~ in(X1,esk382_3(X2,X3,X4))
| ~ in(unordered_pair(unordered_pair(X5,esk380_4(X2,X3,X5,X6)),unordered_pair(X5,X5)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1089,c_0_944]),c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2469,lemma,
( empty(X2)
| in(unordered_pair(unordered_pair(esk375_2(X2,X3),X7),unordered_pair(esk375_2(X2,X3),esk375_2(X2,X3))),X3)
| in(unordered_pair(unordered_pair(apply(esk381_2(X2,X3),X4),X1),unordered_pair(apply(esk381_2(X2,X3),X4),apply(esk381_2(X2,X3),X4))),X3)
| esk379_2(X2,X3) != X6
| ~ relation(X3)
| ~ in(X5,X6)
| ~ in(X4,X2)
| ~ in(X7,esk377_2(X2,X3))
| ~ in(X1,esk382_3(X2,X3,X4))
| ~ in(unordered_pair(unordered_pair(X5,esk380_4(X2,X3,X5,X6)),unordered_pair(X5,X5)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1090,c_0_944]),c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2470,plain,
( in(X3,esk319_3(X2,X7,X6))
| in(unordered_pair(unordered_pair(apply(X6,esk317_3(X2,X7,X6)),apply(X6,esk318_3(X2,X7,X6))),unordered_pair(apply(X6,esk317_3(X2,X7,X6)),apply(X6,esk317_3(X2,X7,X6)))),X7)
| X1 != X3
| X3 != unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4))
| ~ function(X6)
| ~ relation(X7)
| ~ relation(X6)
| ~ in(X1,cartesian_product2(X2,X2))
| ~ in(unordered_pair(unordered_pair(apply(X6,X4),apply(X6,X5)),unordered_pair(apply(X6,X4),apply(X6,X4))),X7) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1091,c_0_944]),c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2471,plain,
( in(X3,esk319_3(X2,X7,X6))
| in(unordered_pair(unordered_pair(apply(X6,esk315_3(X2,X7,X6)),apply(X6,esk316_3(X2,X7,X6))),unordered_pair(apply(X6,esk315_3(X2,X7,X6)),apply(X6,esk315_3(X2,X7,X6)))),X7)
| X1 != X3
| X3 != unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4))
| ~ function(X6)
| ~ relation(X7)
| ~ relation(X6)
| ~ in(X1,cartesian_product2(X2,X2))
| ~ in(unordered_pair(unordered_pair(apply(X6,X4),apply(X6,X5)),unordered_pair(apply(X6,X4),apply(X6,X4))),X7) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1092,c_0_944]),c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2472,lemma,
( empty(X2)
| in(esk376_2(X2,X3),esk378_2(X2,X3))
| in(unordered_pair(unordered_pair(apply(esk381_2(X2,X3),X4),X1),unordered_pair(apply(esk381_2(X2,X3),X4),apply(esk381_2(X2,X3),X4))),X3)
| esk379_2(X2,X3) != X6
| ~ relation(X3)
| ~ in(X5,X6)
| ~ in(X4,X2)
| ~ in(X1,esk382_3(X2,X3,X4))
| ~ in(unordered_pair(unordered_pair(X5,esk380_4(X2,X3,X5,X6)),unordered_pair(X5,X5)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1093,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2473,lemma,
( empty(X2)
| in(esk375_2(X2,X3),esk377_2(X2,X3))
| in(unordered_pair(unordered_pair(apply(esk381_2(X2,X3),X4),X1),unordered_pair(apply(esk381_2(X2,X3),X4),apply(esk381_2(X2,X3),X4))),X3)
| esk379_2(X2,X3) != X6
| ~ relation(X3)
| ~ in(X5,X6)
| ~ in(X4,X2)
| ~ in(X1,esk382_3(X2,X3,X4))
| ~ in(unordered_pair(unordered_pair(X5,esk380_4(X2,X3,X5,X6)),unordered_pair(X5,X5)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1094,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2474,plain,
( unordered_pair(unordered_pair(esk226_4(X1,X2,X3,X4),esk227_4(X1,X2,X3,X4)),unordered_pair(esk226_4(X1,X2,X3,X4),esk226_4(X1,X2,X3,X4))) = X4
| empty(X1)
| in(unordered_pair(unordered_pair(esk222_2(X1,X2),X5),unordered_pair(esk222_2(X1,X2),esk222_2(X1,X2))),X2)
| ~ relation(X2)
| ~ in(X5,esk223_2(X1,X2))
| ~ in(X4,esk224_3(X1,X2,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1095,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2475,plain,
( unordered_pair(unordered_pair(esk226_4(X1,X2,X3,X4),esk227_4(X1,X2,X3,X4)),unordered_pair(esk226_4(X1,X2,X3,X4),esk226_4(X1,X2,X3,X4))) = X4
| empty(X1)
| in(unordered_pair(unordered_pair(esk219_2(X1,X2),X5),unordered_pair(esk219_2(X1,X2),esk219_2(X1,X2))),X2)
| ~ relation(X2)
| ~ in(X5,esk220_2(X1,X2))
| ~ in(X4,esk224_3(X1,X2,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1096,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2476,plain,
( in(esk320_4(X1,X2,X3,X4),cartesian_product2(X1,X1))
| in(unordered_pair(unordered_pair(apply(X3,esk317_3(X1,X2,X3)),apply(X3,esk318_3(X1,X2,X3))),unordered_pair(apply(X3,esk317_3(X1,X2,X3)),apply(X3,esk317_3(X1,X2,X3)))),X2)
| ~ function(X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(X4,esk319_3(X1,X2,X3)) ),
inference(rw,[status(thm)],[i_0_1097,c_0_944]),
[final] ).
cnf(i_0_2477,plain,
( in(esk320_4(X1,X2,X3,X4),cartesian_product2(X1,X1))
| in(unordered_pair(unordered_pair(apply(X3,esk315_3(X1,X2,X3)),apply(X3,esk316_3(X1,X2,X3))),unordered_pair(apply(X3,esk315_3(X1,X2,X3)),apply(X3,esk315_3(X1,X2,X3)))),X2)
| ~ function(X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(X4,esk319_3(X1,X2,X3)) ),
inference(rw,[status(thm)],[i_0_1098,c_0_944]),
[final] ).
cnf(i_0_2478,lemma,
( empty(X2)
| in(unordered_pair(unordered_pair(apply(esk381_2(X2,X3),X4),X1),unordered_pair(apply(esk381_2(X2,X3),X4),apply(esk381_2(X2,X3),X4))),X3)
| esk379_2(X2,X3) != X6
| esk376_2(X2,X3) != esk375_2(X2,X3)
| ~ relation(X3)
| ~ in(X5,X6)
| ~ in(X4,X2)
| ~ in(X1,esk382_3(X2,X3,X4))
| ~ in(unordered_pair(unordered_pair(X5,esk380_4(X2,X3,X5,X6)),unordered_pair(X5,X5)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1099,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2479,lemma,
( empty(X2)
| in(esk374_2(X2,X3),X2)
| in(unordered_pair(unordered_pair(apply(esk381_2(X2,X3),X4),X1),unordered_pair(apply(esk381_2(X2,X3),X4),apply(esk381_2(X2,X3),X4))),X3)
| esk379_2(X2,X3) != X6
| ~ relation(X3)
| ~ in(X5,X6)
| ~ in(X4,X2)
| ~ in(X1,esk382_3(X2,X3,X4))
| ~ in(unordered_pair(unordered_pair(X5,esk380_4(X2,X3,X5,X6)),unordered_pair(X5,X5)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1100,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2480,lemma,
( esk378_2(X2,X3) = esk374_2(X2,X3)
| empty(X2)
| in(unordered_pair(unordered_pair(apply(esk381_2(X2,X3),X4),X1),unordered_pair(apply(esk381_2(X2,X3),X4),apply(esk381_2(X2,X3),X4))),X3)
| esk379_2(X2,X3) != X6
| ~ relation(X3)
| ~ in(X5,X6)
| ~ in(X4,X2)
| ~ in(X1,esk382_3(X2,X3,X4))
| ~ in(unordered_pair(unordered_pair(X5,esk380_4(X2,X3,X5,X6)),unordered_pair(X5,X5)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1101,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2481,lemma,
( esk377_2(X2,X3) = esk374_2(X2,X3)
| empty(X2)
| in(unordered_pair(unordered_pair(apply(esk381_2(X2,X3),X4),X1),unordered_pair(apply(esk381_2(X2,X3),X4),apply(esk381_2(X2,X3),X4))),X3)
| esk379_2(X2,X3) != X6
| ~ relation(X3)
| ~ in(X5,X6)
| ~ in(X4,X2)
| ~ in(X1,esk382_3(X2,X3,X4))
| ~ in(unordered_pair(unordered_pair(X5,esk380_4(X2,X3,X5,X6)),unordered_pair(X5,X5)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1102,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2482,plain,
( unordered_pair(unordered_pair(esk305_2(X1,X2),esk306_2(X1,X2)),unordered_pair(esk305_2(X1,X2),esk305_2(X1,X2))) = esk302_2(X1,X2)
| unordered_pair(unordered_pair(esk309_4(X1,X2,X3,X4),esk310_4(X1,X2,X3,X4)),unordered_pair(esk309_4(X1,X2,X3,X4),esk309_4(X1,X2,X3,X4))) = X4
| ~ one_sorted_str(X1)
| ~ in(X4,esk307_3(X1,X2,X3))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1103,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2483,plain,
( unordered_pair(unordered_pair(esk303_2(X1,X2),esk304_2(X1,X2)),unordered_pair(esk303_2(X1,X2),esk303_2(X1,X2))) = esk301_2(X1,X2)
| unordered_pair(unordered_pair(esk309_4(X1,X2,X3,X4),esk310_4(X1,X2,X3,X4)),unordered_pair(esk309_4(X1,X2,X3,X4),esk309_4(X1,X2,X3,X4))) = X4
| ~ one_sorted_str(X1)
| ~ in(X4,esk307_3(X1,X2,X3))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1104,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2484,plain,
( unordered_pair(unordered_pair(esk287_2(X1,X2),esk288_2(X1,X2)),unordered_pair(esk287_2(X1,X2),esk287_2(X1,X2))) = esk284_2(X1,X2)
| unordered_pair(unordered_pair(esk291_4(X1,X2,X3,X4),esk292_4(X1,X2,X3,X4)),unordered_pair(esk291_4(X1,X2,X3,X4),esk291_4(X1,X2,X3,X4))) = X4
| ~ one_sorted_str(X1)
| ~ in(X4,esk289_3(X1,X2,X3))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1105,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2485,plain,
( unordered_pair(unordered_pair(esk285_2(X1,X2),esk286_2(X1,X2)),unordered_pair(esk285_2(X1,X2),esk285_2(X1,X2))) = esk283_2(X1,X2)
| unordered_pair(unordered_pair(esk291_4(X1,X2,X3,X4),esk292_4(X1,X2,X3,X4)),unordered_pair(esk291_4(X1,X2,X3,X4),esk291_4(X1,X2,X3,X4))) = X4
| ~ one_sorted_str(X1)
| ~ in(X4,esk289_3(X1,X2,X3))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1106,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2486,plain,
( unordered_pair(unordered_pair(esk221_2(X1,X2),esk222_2(X1,X2)),unordered_pair(esk221_2(X1,X2),esk221_2(X1,X2))) = esk217_2(X1,X2)
| unordered_pair(unordered_pair(esk226_4(X1,X2,X3,X4),esk227_4(X1,X2,X3,X4)),unordered_pair(esk226_4(X1,X2,X3,X4),esk226_4(X1,X2,X3,X4))) = X4
| empty(X1)
| ~ relation(X2)
| ~ in(X4,esk224_3(X1,X2,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1107,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2487,plain,
( unordered_pair(unordered_pair(esk218_2(X1,X2),esk219_2(X1,X2)),unordered_pair(esk218_2(X1,X2),esk218_2(X1,X2))) = esk216_2(X1,X2)
| unordered_pair(unordered_pair(esk226_4(X1,X2,X3,X4),esk227_4(X1,X2,X3,X4)),unordered_pair(esk226_4(X1,X2,X3,X4),esk226_4(X1,X2,X3,X4))) = X4
| empty(X1)
| ~ relation(X2)
| ~ in(X4,esk224_3(X1,X2,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1108,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2488,plain,
( esk320_4(X1,X2,X3,X4) = X4
| in(unordered_pair(unordered_pair(apply(X3,esk317_3(X1,X2,X3)),apply(X3,esk318_3(X1,X2,X3))),unordered_pair(apply(X3,esk317_3(X1,X2,X3)),apply(X3,esk317_3(X1,X2,X3)))),X2)
| ~ function(X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(X4,esk319_3(X1,X2,X3)) ),
inference(rw,[status(thm)],[i_0_1109,c_0_944]),
[final] ).
cnf(i_0_2489,plain,
( esk320_4(X1,X2,X3,X4) = X4
| in(unordered_pair(unordered_pair(apply(X3,esk315_3(X1,X2,X3)),apply(X3,esk316_3(X1,X2,X3))),unordered_pair(apply(X3,esk315_3(X1,X2,X3)),apply(X3,esk315_3(X1,X2,X3)))),X2)
| ~ function(X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(X4,esk319_3(X1,X2,X3)) ),
inference(rw,[status(thm)],[i_0_1110,c_0_944]),
[final] ).
cnf(i_0_2490,plain,
( esk306_2(X1,X2) = subset_complement(the_carrier(X1),X5)
| unordered_pair(unordered_pair(esk309_4(X1,X2,X3,X4),esk310_4(X1,X2,X3,X4)),unordered_pair(esk309_4(X1,X2,X3,X4),esk309_4(X1,X2,X3,X4))) = X4
| X5 != esk305_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X5,powerset(the_carrier(X1)))
| ~ in(X4,esk307_3(X1,X2,X3))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1111,c_0_944]),
[final] ).
cnf(i_0_2491,plain,
( esk304_2(X1,X2) = subset_complement(the_carrier(X1),X5)
| unordered_pair(unordered_pair(esk309_4(X1,X2,X3,X4),esk310_4(X1,X2,X3,X4)),unordered_pair(esk309_4(X1,X2,X3,X4),esk309_4(X1,X2,X3,X4))) = X4
| X5 != esk303_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X5,powerset(the_carrier(X1)))
| ~ in(X4,esk307_3(X1,X2,X3))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1112,c_0_944]),
[final] ).
cnf(i_0_2492,plain,
( esk288_2(X1,X2) = subset_complement(the_carrier(X1),X5)
| unordered_pair(unordered_pair(esk291_4(X1,X2,X3,X4),esk292_4(X1,X2,X3,X4)),unordered_pair(esk291_4(X1,X2,X3,X4),esk291_4(X1,X2,X3,X4))) = X4
| X5 != esk287_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X5,powerset(the_carrier(X1)))
| ~ in(X4,esk289_3(X1,X2,X3))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1113,c_0_944]),
[final] ).
cnf(i_0_2493,plain,
( esk286_2(X1,X2) = subset_complement(the_carrier(X1),X5)
| unordered_pair(unordered_pair(esk291_4(X1,X2,X3,X4),esk292_4(X1,X2,X3,X4)),unordered_pair(esk291_4(X1,X2,X3,X4),esk291_4(X1,X2,X3,X4))) = X4
| X5 != esk285_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X5,powerset(the_carrier(X1)))
| ~ in(X4,esk289_3(X1,X2,X3))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1114,c_0_944]),
[final] ).
cnf(i_0_2494,plain,
( X1 = unordered_pair(unordered_pair(esk321_4(X2,X3,X4,X1),esk322_4(X2,X3,X4,X1)),unordered_pair(esk321_4(X2,X3,X4,X1),esk321_4(X2,X3,X4,X1)))
| esk314_3(X2,X3,X4) != esk313_3(X2,X3,X4)
| ~ function(X4)
| ~ relation(X4)
| ~ relation(X3)
| ~ in(X1,esk319_3(X2,X3,X4)) ),
inference(rw,[status(thm)],[i_0_1115,c_0_944]),
[final] ).
cnf(i_0_2495,plain,
( unordered_pair(unordered_pair(esk291_4(X1,X2,X3,X4),esk292_4(X1,X2,X3,X4)),unordered_pair(esk291_4(X1,X2,X3,X4),esk291_4(X1,X2,X3,X4))) = X4
| in(esk287_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| ~ one_sorted_str(X1)
| ~ in(X4,esk289_3(X1,X2,X3))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1116,c_0_944]),
[final] ).
cnf(i_0_2496,plain,
( unordered_pair(unordered_pair(esk291_4(X1,X2,X3,X4),esk292_4(X1,X2,X3,X4)),unordered_pair(esk291_4(X1,X2,X3,X4),esk291_4(X1,X2,X3,X4))) = X4
| in(esk285_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| ~ one_sorted_str(X1)
| ~ in(X4,esk289_3(X1,X2,X3))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1117,c_0_944]),
[final] ).
cnf(i_0_2497,plain,
( unordered_pair(unordered_pair(esk309_4(X1,X2,X3,X4),esk310_4(X1,X2,X3,X4)),unordered_pair(esk309_4(X1,X2,X3,X4),esk309_4(X1,X2,X3,X4))) = X4
| esk302_2(X1,X2) != esk301_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ in(X4,esk307_3(X1,X2,X3))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1118,c_0_944]),
[final] ).
cnf(i_0_2498,plain,
( unordered_pair(unordered_pair(esk291_4(X1,X2,X3,X4),esk292_4(X1,X2,X3,X4)),unordered_pair(esk291_4(X1,X2,X3,X4),esk291_4(X1,X2,X3,X4))) = X4
| esk284_2(X1,X2) != esk283_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ in(X4,esk289_3(X1,X2,X3))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1119,c_0_944]),
[final] ).
cnf(i_0_2499,plain,
( unordered_pair(unordered_pair(esk309_4(X1,X2,X3,X4),esk310_4(X1,X2,X3,X4)),unordered_pair(esk309_4(X1,X2,X3,X4),esk309_4(X1,X2,X3,X4))) = X4
| in(esk305_2(X1,X2),X2)
| ~ one_sorted_str(X1)
| ~ in(X4,esk307_3(X1,X2,X3))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1120,c_0_944]),
[final] ).
cnf(i_0_2500,plain,
( unordered_pair(unordered_pair(esk309_4(X1,X2,X3,X4),esk310_4(X1,X2,X3,X4)),unordered_pair(esk309_4(X1,X2,X3,X4),esk309_4(X1,X2,X3,X4))) = X4
| in(esk303_2(X1,X2),X2)
| ~ one_sorted_str(X1)
| ~ in(X4,esk307_3(X1,X2,X3))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1121,c_0_944]),
[final] ).
cnf(i_0_2501,plain,
( esk314_3(X2,X3,X4) = esk312_3(X2,X3,X4)
| X1 = unordered_pair(unordered_pair(esk321_4(X2,X3,X4,X1),esk322_4(X2,X3,X4,X1)),unordered_pair(esk321_4(X2,X3,X4,X1),esk321_4(X2,X3,X4,X1)))
| ~ function(X4)
| ~ relation(X4)
| ~ relation(X3)
| ~ in(X1,esk319_3(X2,X3,X4)) ),
inference(rw,[status(thm)],[i_0_1122,c_0_944]),
[final] ).
cnf(i_0_2502,plain,
( esk313_3(X2,X3,X4) = esk312_3(X2,X3,X4)
| X1 = unordered_pair(unordered_pair(esk321_4(X2,X3,X4,X1),esk322_4(X2,X3,X4,X1)),unordered_pair(esk321_4(X2,X3,X4,X1),esk321_4(X2,X3,X4,X1)))
| ~ function(X4)
| ~ relation(X4)
| ~ relation(X3)
| ~ in(X1,esk319_3(X2,X3,X4)) ),
inference(rw,[status(thm)],[i_0_1123,c_0_944]),
[final] ).
cnf(i_0_2503,plain,
( esk302_2(X1,X2) = esk300_2(X1,X2)
| unordered_pair(unordered_pair(esk309_4(X1,X2,X3,X4),esk310_4(X1,X2,X3,X4)),unordered_pair(esk309_4(X1,X2,X3,X4),esk309_4(X1,X2,X3,X4))) = X4
| ~ one_sorted_str(X1)
| ~ in(X4,esk307_3(X1,X2,X3))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1124,c_0_944]),
[final] ).
cnf(i_0_2504,plain,
( esk301_2(X1,X2) = esk300_2(X1,X2)
| unordered_pair(unordered_pair(esk309_4(X1,X2,X3,X4),esk310_4(X1,X2,X3,X4)),unordered_pair(esk309_4(X1,X2,X3,X4),esk309_4(X1,X2,X3,X4))) = X4
| ~ one_sorted_str(X1)
| ~ in(X4,esk307_3(X1,X2,X3))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1125,c_0_944]),
[final] ).
cnf(i_0_2505,plain,
( esk284_2(X1,X2) = esk282_2(X1,X2)
| unordered_pair(unordered_pair(esk291_4(X1,X2,X3,X4),esk292_4(X1,X2,X3,X4)),unordered_pair(esk291_4(X1,X2,X3,X4),esk291_4(X1,X2,X3,X4))) = X4
| ~ one_sorted_str(X1)
| ~ in(X4,esk289_3(X1,X2,X3))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1126,c_0_944]),
[final] ).
cnf(i_0_2506,plain,
( esk283_2(X1,X2) = esk282_2(X1,X2)
| unordered_pair(unordered_pair(esk291_4(X1,X2,X3,X4),esk292_4(X1,X2,X3,X4)),unordered_pair(esk291_4(X1,X2,X3,X4),esk291_4(X1,X2,X3,X4))) = X4
| ~ one_sorted_str(X1)
| ~ in(X4,esk289_3(X1,X2,X3))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1127,c_0_944]),
[final] ).
cnf(i_0_2507,lemma,
( unordered_pair(unordered_pair(esk364_4(X1,X2,X3,X4),esk365_4(X1,X2,X3,X4)),unordered_pair(esk364_4(X1,X2,X3,X4),esk364_4(X1,X2,X3,X4))) = X4
| ~ one_sorted_str(X1)
| ~ in(X4,esk363_3(X1,X2,X3))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1128,c_0_944]),
[final] ).
cnf(i_0_2508,lemma,
( unordered_pair(unordered_pair(esk360_4(X1,X2,X3,X4),esk361_4(X1,X2,X3,X4)),unordered_pair(esk360_4(X1,X2,X3,X4),esk360_4(X1,X2,X3,X4))) = X4
| ~ one_sorted_str(X1)
| ~ in(X4,esk359_3(X1,X2,X3))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1129,c_0_944]),
[final] ).
cnf(i_0_2509,plain,
( unordered_pair(unordered_pair(esk226_4(X1,X2,X3,X4),esk227_4(X1,X2,X3,X4)),unordered_pair(esk226_4(X1,X2,X3,X4),esk226_4(X1,X2,X3,X4))) = X4
| empty(X1)
| in(esk222_2(X1,X2),esk223_2(X1,X2))
| ~ relation(X2)
| ~ in(X4,esk224_3(X1,X2,X3)) ),
inference(rw,[status(thm)],[i_0_1130,c_0_944]),
[final] ).
cnf(i_0_2510,plain,
( unordered_pair(unordered_pair(esk226_4(X1,X2,X3,X4),esk227_4(X1,X2,X3,X4)),unordered_pair(esk226_4(X1,X2,X3,X4),esk226_4(X1,X2,X3,X4))) = X4
| empty(X1)
| in(esk219_2(X1,X2),esk220_2(X1,X2))
| ~ relation(X2)
| ~ in(X4,esk224_3(X1,X2,X3)) ),
inference(rw,[status(thm)],[i_0_1131,c_0_944]),
[final] ).
cnf(i_0_2511,plain,
( unordered_pair(unordered_pair(esk226_4(X1,X2,X3,X4),esk227_4(X1,X2,X3,X4)),unordered_pair(esk226_4(X1,X2,X3,X4),esk226_4(X1,X2,X3,X4))) = X4
| empty(X1)
| esk217_2(X1,X2) != esk216_2(X1,X2)
| ~ relation(X2)
| ~ in(X4,esk224_3(X1,X2,X3)) ),
inference(rw,[status(thm)],[i_0_1132,c_0_944]),
[final] ).
cnf(i_0_2512,plain,
( unordered_pair(unordered_pair(esk226_4(X1,X2,X3,X4),esk227_4(X1,X2,X3,X4)),unordered_pair(esk226_4(X1,X2,X3,X4),esk226_4(X1,X2,X3,X4))) = X4
| empty(X1)
| in(esk221_2(X1,X2),X1)
| ~ relation(X2)
| ~ in(X4,esk224_3(X1,X2,X3)) ),
inference(rw,[status(thm)],[i_0_1133,c_0_944]),
[final] ).
cnf(i_0_2513,plain,
( unordered_pair(unordered_pair(esk226_4(X1,X2,X3,X4),esk227_4(X1,X2,X3,X4)),unordered_pair(esk226_4(X1,X2,X3,X4),esk226_4(X1,X2,X3,X4))) = X4
| empty(X1)
| in(esk218_2(X1,X2),X1)
| ~ relation(X2)
| ~ in(X4,esk224_3(X1,X2,X3)) ),
inference(rw,[status(thm)],[i_0_1134,c_0_944]),
[final] ).
cnf(i_0_2514,plain,
( esk223_2(X1,X2) = esk221_2(X1,X2)
| unordered_pair(unordered_pair(esk226_4(X1,X2,X3,X4),esk227_4(X1,X2,X3,X4)),unordered_pair(esk226_4(X1,X2,X3,X4),esk226_4(X1,X2,X3,X4))) = X4
| empty(X1)
| ~ relation(X2)
| ~ in(X4,esk224_3(X1,X2,X3)) ),
inference(rw,[status(thm)],[i_0_1135,c_0_944]),
[final] ).
cnf(i_0_2515,plain,
( esk220_2(X1,X2) = esk218_2(X1,X2)
| unordered_pair(unordered_pair(esk226_4(X1,X2,X3,X4),esk227_4(X1,X2,X3,X4)),unordered_pair(esk226_4(X1,X2,X3,X4),esk226_4(X1,X2,X3,X4))) = X4
| empty(X1)
| ~ relation(X2)
| ~ in(X4,esk224_3(X1,X2,X3)) ),
inference(rw,[status(thm)],[i_0_1136,c_0_944]),
[final] ).
cnf(i_0_2516,plain,
( esk217_2(X1,X2) = esk215_2(X1,X2)
| unordered_pair(unordered_pair(esk226_4(X1,X2,X3,X4),esk227_4(X1,X2,X3,X4)),unordered_pair(esk226_4(X1,X2,X3,X4),esk226_4(X1,X2,X3,X4))) = X4
| empty(X1)
| ~ relation(X2)
| ~ in(X4,esk224_3(X1,X2,X3)) ),
inference(rw,[status(thm)],[i_0_1137,c_0_944]),
[final] ).
cnf(i_0_2517,plain,
( esk216_2(X1,X2) = esk215_2(X1,X2)
| unordered_pair(unordered_pair(esk226_4(X1,X2,X3,X4),esk227_4(X1,X2,X3,X4)),unordered_pair(esk226_4(X1,X2,X3,X4),esk226_4(X1,X2,X3,X4))) = X4
| empty(X1)
| ~ relation(X2)
| ~ in(X4,esk224_3(X1,X2,X3)) ),
inference(rw,[status(thm)],[i_0_1138,c_0_944]),
[final] ).
cnf(i_0_2518,lemma,
( X1 = unordered_pair(unordered_pair(esk368_4(X2,X3,X4,X1),esk369_4(X2,X3,X4,X1)),unordered_pair(esk368_4(X2,X3,X4,X1),esk368_4(X2,X3,X4,X1)))
| ~ function(X4)
| ~ relation(X4)
| ~ relation(X3)
| ~ in(X1,esk367_3(X2,X3,X4)) ),
inference(rw,[status(thm)],[i_0_1139,c_0_944]),
[final] ).
cnf(i_0_2519,lemma,
( unordered_pair(unordered_pair(esk342_4(X1,X2,X3,X4),esk343_4(X1,X2,X3,X4)),unordered_pair(esk342_4(X1,X2,X3,X4),esk342_4(X1,X2,X3,X4))) = X4
| empty(X1)
| ~ relation(X2)
| ~ in(X4,esk341_3(X1,X2,X3)) ),
inference(rw,[status(thm)],[i_0_1140,c_0_944]),
[final] ).
cnf(i_0_2520,lemma,
( empty(X1)
| in(apply(esk381_2(X1,X2),X3),esk382_3(X1,X2,X3))
| in(unordered_pair(unordered_pair(esk376_2(X1,X2),X6),unordered_pair(esk376_2(X1,X2),esk376_2(X1,X2))),X2)
| esk379_2(X1,X2) != X5
| ~ relation(X2)
| ~ in(X4,X5)
| ~ in(X3,X1)
| ~ in(X6,esk378_2(X1,X2))
| ~ in(unordered_pair(unordered_pair(X4,esk380_4(X1,X2,X4,X5)),unordered_pair(X4,X4)),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1141,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2521,lemma,
( empty(X1)
| in(apply(esk381_2(X1,X2),X3),esk382_3(X1,X2,X3))
| in(unordered_pair(unordered_pair(esk375_2(X1,X2),X6),unordered_pair(esk375_2(X1,X2),esk375_2(X1,X2))),X2)
| esk379_2(X1,X2) != X5
| ~ relation(X2)
| ~ in(X4,X5)
| ~ in(X3,X1)
| ~ in(X6,esk377_2(X1,X2))
| ~ in(unordered_pair(unordered_pair(X4,esk380_4(X1,X2,X4,X5)),unordered_pair(X4,X4)),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1142,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2522,plain,
( X1 = unordered_pair(unordered_pair(esk63_4(X2,X3,X4,X1),esk64_4(X2,X3,X4,X1)),unordered_pair(esk63_4(X2,X3,X4,X1),esk63_4(X2,X3,X4,X1)))
| X4 != cartesian_product2(X2,X3)
| ~ in(X1,X4) ),
inference(rw,[status(thm)],[i_0_1143,c_0_944]),
[final] ).
cnf(i_0_2523,lemma,
( X1 = esk382_3(X2,X3,X1)
| empty(X2)
| in(unordered_pair(unordered_pair(esk376_2(X2,X3),X6),unordered_pair(esk376_2(X2,X3),esk376_2(X2,X3))),X3)
| esk379_2(X2,X3) != X5
| ~ relation(X3)
| ~ in(X4,X5)
| ~ in(X1,X2)
| ~ in(X6,esk378_2(X2,X3))
| ~ in(unordered_pair(unordered_pair(X4,esk380_4(X2,X3,X4,X5)),unordered_pair(X4,X4)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1144,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2524,lemma,
( X1 = esk382_3(X2,X3,X1)
| empty(X2)
| in(unordered_pair(unordered_pair(esk375_2(X2,X3),X6),unordered_pair(esk375_2(X2,X3),esk375_2(X2,X3))),X3)
| esk379_2(X2,X3) != X5
| ~ relation(X3)
| ~ in(X4,X5)
| ~ in(X1,X2)
| ~ in(X6,esk377_2(X2,X3))
| ~ in(unordered_pair(unordered_pair(X4,esk380_4(X2,X3,X4,X5)),unordered_pair(X4,X4)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1145,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2525,lemma,
( relation_dom(esk381_2(X1,X2)) = X1
| empty(X1)
| in(unordered_pair(unordered_pair(esk376_2(X1,X2),X5),unordered_pair(esk376_2(X1,X2),esk376_2(X1,X2))),X2)
| esk379_2(X1,X2) != X4
| ~ relation(X2)
| ~ in(X3,X4)
| ~ in(X5,esk378_2(X1,X2))
| ~ in(unordered_pair(unordered_pair(X3,esk380_4(X1,X2,X3,X4)),unordered_pair(X3,X3)),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1146,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2526,lemma,
( relation_dom(esk381_2(X1,X2)) = X1
| empty(X1)
| in(unordered_pair(unordered_pair(esk375_2(X1,X2),X5),unordered_pair(esk375_2(X1,X2),esk375_2(X1,X2))),X2)
| esk379_2(X1,X2) != X4
| ~ relation(X2)
| ~ in(X3,X4)
| ~ in(X5,esk377_2(X1,X2))
| ~ in(unordered_pair(unordered_pair(X3,esk380_4(X1,X2,X3,X4)),unordered_pair(X3,X3)),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1147,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2527,lemma,
( empty(X1)
| relation(esk381_2(X1,X2))
| in(unordered_pair(unordered_pair(esk376_2(X1,X2),X5),unordered_pair(esk376_2(X1,X2),esk376_2(X1,X2))),X2)
| esk379_2(X1,X2) != X4
| ~ relation(X2)
| ~ in(X3,X4)
| ~ in(X5,esk378_2(X1,X2))
| ~ in(unordered_pair(unordered_pair(X3,esk380_4(X1,X2,X3,X4)),unordered_pair(X3,X3)),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1148,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2528,lemma,
( empty(X1)
| relation(esk381_2(X1,X2))
| in(unordered_pair(unordered_pair(esk375_2(X1,X2),X5),unordered_pair(esk375_2(X1,X2),esk375_2(X1,X2))),X2)
| esk379_2(X1,X2) != X4
| ~ relation(X2)
| ~ in(X3,X4)
| ~ in(X5,esk377_2(X1,X2))
| ~ in(unordered_pair(unordered_pair(X3,esk380_4(X1,X2,X3,X4)),unordered_pair(X3,X3)),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1149,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2529,lemma,
( empty(X1)
| function(esk381_2(X1,X2))
| in(unordered_pair(unordered_pair(esk376_2(X1,X2),X5),unordered_pair(esk376_2(X1,X2),esk376_2(X1,X2))),X2)
| esk379_2(X1,X2) != X4
| ~ relation(X2)
| ~ in(X3,X4)
| ~ in(X5,esk378_2(X1,X2))
| ~ in(unordered_pair(unordered_pair(X3,esk380_4(X1,X2,X3,X4)),unordered_pair(X3,X3)),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1150,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2530,lemma,
( empty(X1)
| function(esk381_2(X1,X2))
| in(unordered_pair(unordered_pair(esk375_2(X1,X2),X5),unordered_pair(esk375_2(X1,X2),esk375_2(X1,X2))),X2)
| esk379_2(X1,X2) != X4
| ~ relation(X2)
| ~ in(X3,X4)
| ~ in(X5,esk377_2(X1,X2))
| ~ in(unordered_pair(unordered_pair(X3,esk380_4(X1,X2,X3,X4)),unordered_pair(X3,X3)),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1151,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2531,plain,
( X3 = relation_composition(X1,X2)
| in(unordered_pair(unordered_pair(esk107_3(X1,X2,X3),esk108_3(X1,X2,X3)),unordered_pair(esk107_3(X1,X2,X3),esk107_3(X1,X2,X3))),X3)
| in(unordered_pair(unordered_pair(esk109_3(X1,X2,X3),esk108_3(X1,X2,X3)),unordered_pair(esk109_3(X1,X2,X3),esk109_3(X1,X2,X3))),X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1152,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2532,plain,
( X3 = relation_composition(X1,X2)
| in(unordered_pair(unordered_pair(esk107_3(X1,X2,X3),esk108_3(X1,X2,X3)),unordered_pair(esk107_3(X1,X2,X3),esk107_3(X1,X2,X3))),X3)
| in(unordered_pair(unordered_pair(esk107_3(X1,X2,X3),esk109_3(X1,X2,X3)),unordered_pair(esk107_3(X1,X2,X3),esk107_3(X1,X2,X3))),X1)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1153,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2533,plain,
( X3 = relation_rng_restriction(X1,X2)
| in(unordered_pair(unordered_pair(esk8_3(X1,X2,X3),esk9_3(X1,X2,X3)),unordered_pair(esk8_3(X1,X2,X3),esk8_3(X1,X2,X3))),X3)
| in(unordered_pair(unordered_pair(esk8_3(X1,X2,X3),esk9_3(X1,X2,X3)),unordered_pair(esk8_3(X1,X2,X3),esk8_3(X1,X2,X3))),X2)
| ~ relation(X3)
| ~ relation(X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1154,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2534,plain,
( X3 = relation_dom_restriction(X1,X2)
| in(unordered_pair(unordered_pair(esk3_3(X1,X2,X3),esk4_3(X1,X2,X3)),unordered_pair(esk3_3(X1,X2,X3),esk3_3(X1,X2,X3))),X3)
| in(unordered_pair(unordered_pair(esk3_3(X1,X2,X3),esk4_3(X1,X2,X3)),unordered_pair(esk3_3(X1,X2,X3),esk3_3(X1,X2,X3))),X1)
| ~ relation(X3)
| ~ relation(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1155,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2535,lemma,
( empty(X1)
| in(esk376_2(X1,X2),esk378_2(X1,X2))
| in(apply(esk381_2(X1,X2),X3),esk382_3(X1,X2,X3))
| esk379_2(X1,X2) != X5
| ~ relation(X2)
| ~ in(X4,X5)
| ~ in(X3,X1)
| ~ in(unordered_pair(unordered_pair(X4,esk380_4(X1,X2,X4,X5)),unordered_pair(X4,X4)),X2) ),
inference(rw,[status(thm)],[i_0_1156,c_0_944]),
[final] ).
cnf(i_0_2536,lemma,
( empty(X1)
| in(esk375_2(X1,X2),esk377_2(X1,X2))
| in(apply(esk381_2(X1,X2),X3),esk382_3(X1,X2,X3))
| esk379_2(X1,X2) != X5
| ~ relation(X2)
| ~ in(X4,X5)
| ~ in(X3,X1)
| ~ in(unordered_pair(unordered_pair(X4,esk380_4(X1,X2,X4,X5)),unordered_pair(X4,X4)),X2) ),
inference(rw,[status(thm)],[i_0_1157,c_0_944]),
[final] ).
cnf(i_0_2537,lemma,
( empty(X1)
| in(apply(esk381_2(X1,X2),X3),esk382_3(X1,X2,X3))
| esk379_2(X1,X2) != X5
| esk376_2(X1,X2) != esk375_2(X1,X2)
| ~ relation(X2)
| ~ in(X4,X5)
| ~ in(X3,X1)
| ~ in(unordered_pair(unordered_pair(X4,esk380_4(X1,X2,X4,X5)),unordered_pair(X4,X4)),X2) ),
inference(rw,[status(thm)],[i_0_1158,c_0_944]),
[final] ).
cnf(i_0_2538,lemma,
( empty(X1)
| in(esk374_2(X1,X2),X1)
| in(apply(esk381_2(X1,X2),X3),esk382_3(X1,X2,X3))
| esk379_2(X1,X2) != X5
| ~ relation(X2)
| ~ in(X4,X5)
| ~ in(X3,X1)
| ~ in(unordered_pair(unordered_pair(X4,esk380_4(X1,X2,X4,X5)),unordered_pair(X4,X4)),X2) ),
inference(rw,[status(thm)],[i_0_1159,c_0_944]),
[final] ).
cnf(i_0_2539,lemma,
( esk378_2(X1,X2) = esk374_2(X1,X2)
| empty(X1)
| in(apply(esk381_2(X1,X2),X3),esk382_3(X1,X2,X3))
| esk379_2(X1,X2) != X5
| ~ relation(X2)
| ~ in(X4,X5)
| ~ in(X3,X1)
| ~ in(unordered_pair(unordered_pair(X4,esk380_4(X1,X2,X4,X5)),unordered_pair(X4,X4)),X2) ),
inference(rw,[status(thm)],[i_0_1160,c_0_944]),
[final] ).
cnf(i_0_2540,lemma,
( esk377_2(X1,X2) = esk374_2(X1,X2)
| empty(X1)
| in(apply(esk381_2(X1,X2),X3),esk382_3(X1,X2,X3))
| esk379_2(X1,X2) != X5
| ~ relation(X2)
| ~ in(X4,X5)
| ~ in(X3,X1)
| ~ in(unordered_pair(unordered_pair(X4,esk380_4(X1,X2,X4,X5)),unordered_pair(X4,X4)),X2) ),
inference(rw,[status(thm)],[i_0_1161,c_0_944]),
[final] ).
cnf(i_0_2541,lemma,
( X1 = esk382_3(X2,X3,X1)
| empty(X2)
| in(esk376_2(X2,X3),esk378_2(X2,X3))
| esk379_2(X2,X3) != X5
| ~ relation(X3)
| ~ in(X4,X5)
| ~ in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X4,esk380_4(X2,X3,X4,X5)),unordered_pair(X4,X4)),X3) ),
inference(rw,[status(thm)],[i_0_1162,c_0_944]),
[final] ).
cnf(i_0_2542,lemma,
( X1 = esk382_3(X2,X3,X1)
| empty(X2)
| in(esk375_2(X2,X3),esk377_2(X2,X3))
| esk379_2(X2,X3) != X5
| ~ relation(X3)
| ~ in(X4,X5)
| ~ in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X4,esk380_4(X2,X3,X4,X5)),unordered_pair(X4,X4)),X3) ),
inference(rw,[status(thm)],[i_0_1163,c_0_944]),
[final] ).
cnf(i_0_2543,lemma,
( X1 = esk382_3(X2,X3,X1)
| empty(X2)
| esk379_2(X2,X3) != X5
| esk376_2(X2,X3) != esk375_2(X2,X3)
| ~ relation(X3)
| ~ in(X4,X5)
| ~ in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X4,esk380_4(X2,X3,X4,X5)),unordered_pair(X4,X4)),X3) ),
inference(rw,[status(thm)],[i_0_1164,c_0_944]),
[final] ).
cnf(i_0_2544,lemma,
( X1 = esk382_3(X2,X3,X1)
| empty(X2)
| in(esk374_2(X2,X3),X2)
| esk379_2(X2,X3) != X5
| ~ relation(X3)
| ~ in(X4,X5)
| ~ in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X4,esk380_4(X2,X3,X4,X5)),unordered_pair(X4,X4)),X3) ),
inference(rw,[status(thm)],[i_0_1165,c_0_944]),
[final] ).
cnf(i_0_2545,lemma,
( X1 = esk382_3(X2,X3,X1)
| esk378_2(X2,X3) = esk374_2(X2,X3)
| empty(X2)
| esk379_2(X2,X3) != X5
| ~ relation(X3)
| ~ in(X4,X5)
| ~ in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X4,esk380_4(X2,X3,X4,X5)),unordered_pair(X4,X4)),X3) ),
inference(rw,[status(thm)],[i_0_1166,c_0_944]),
[final] ).
cnf(i_0_2546,lemma,
( X1 = esk382_3(X2,X3,X1)
| esk377_2(X2,X3) = esk374_2(X2,X3)
| empty(X2)
| esk379_2(X2,X3) != X5
| ~ relation(X3)
| ~ in(X4,X5)
| ~ in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X4,esk380_4(X2,X3,X4,X5)),unordered_pair(X4,X4)),X3) ),
inference(rw,[status(thm)],[i_0_1167,c_0_944]),
[final] ).
cnf(i_0_2547,lemma,
( relation_dom(esk381_2(X1,X2)) = X1
| empty(X1)
| in(esk376_2(X1,X2),esk378_2(X1,X2))
| esk379_2(X1,X2) != X4
| ~ relation(X2)
| ~ in(X3,X4)
| ~ in(unordered_pair(unordered_pair(X3,esk380_4(X1,X2,X3,X4)),unordered_pair(X3,X3)),X2) ),
inference(rw,[status(thm)],[i_0_1168,c_0_944]),
[final] ).
cnf(i_0_2548,lemma,
( relation_dom(esk381_2(X1,X2)) = X1
| empty(X1)
| in(esk375_2(X1,X2),esk377_2(X1,X2))
| esk379_2(X1,X2) != X4
| ~ relation(X2)
| ~ in(X3,X4)
| ~ in(unordered_pair(unordered_pair(X3,esk380_4(X1,X2,X3,X4)),unordered_pair(X3,X3)),X2) ),
inference(rw,[status(thm)],[i_0_1169,c_0_944]),
[final] ).
cnf(i_0_2549,lemma,
( empty(X1)
| relation(esk381_2(X1,X2))
| in(esk376_2(X1,X2),esk378_2(X1,X2))
| esk379_2(X1,X2) != X4
| ~ relation(X2)
| ~ in(X3,X4)
| ~ in(unordered_pair(unordered_pair(X3,esk380_4(X1,X2,X3,X4)),unordered_pair(X3,X3)),X2) ),
inference(rw,[status(thm)],[i_0_1170,c_0_944]),
[final] ).
cnf(i_0_2550,lemma,
( empty(X1)
| relation(esk381_2(X1,X2))
| in(esk375_2(X1,X2),esk377_2(X1,X2))
| esk379_2(X1,X2) != X4
| ~ relation(X2)
| ~ in(X3,X4)
| ~ in(unordered_pair(unordered_pair(X3,esk380_4(X1,X2,X3,X4)),unordered_pair(X3,X3)),X2) ),
inference(rw,[status(thm)],[i_0_1171,c_0_944]),
[final] ).
cnf(i_0_2551,lemma,
( empty(X1)
| function(esk381_2(X1,X2))
| in(esk376_2(X1,X2),esk378_2(X1,X2))
| esk379_2(X1,X2) != X4
| ~ relation(X2)
| ~ in(X3,X4)
| ~ in(unordered_pair(unordered_pair(X3,esk380_4(X1,X2,X3,X4)),unordered_pair(X3,X3)),X2) ),
inference(rw,[status(thm)],[i_0_1172,c_0_944]),
[final] ).
cnf(i_0_2552,lemma,
( empty(X1)
| function(esk381_2(X1,X2))
| in(esk375_2(X1,X2),esk377_2(X1,X2))
| esk379_2(X1,X2) != X4
| ~ relation(X2)
| ~ in(X3,X4)
| ~ in(unordered_pair(unordered_pair(X3,esk380_4(X1,X2,X3,X4)),unordered_pair(X3,X3)),X2) ),
inference(rw,[status(thm)],[i_0_1173,c_0_944]),
[final] ).
cnf(i_0_2553,lemma,
( relation_dom(esk381_2(X1,X2)) = X1
| empty(X1)
| esk379_2(X1,X2) != X4
| esk376_2(X1,X2) != esk375_2(X1,X2)
| ~ relation(X2)
| ~ in(X3,X4)
| ~ in(unordered_pair(unordered_pair(X3,esk380_4(X1,X2,X3,X4)),unordered_pair(X3,X3)),X2) ),
inference(rw,[status(thm)],[i_0_1174,c_0_944]),
[final] ).
cnf(i_0_2554,lemma,
( empty(X1)
| relation(esk381_2(X1,X2))
| esk379_2(X1,X2) != X4
| esk376_2(X1,X2) != esk375_2(X1,X2)
| ~ relation(X2)
| ~ in(X3,X4)
| ~ in(unordered_pair(unordered_pair(X3,esk380_4(X1,X2,X3,X4)),unordered_pair(X3,X3)),X2) ),
inference(rw,[status(thm)],[i_0_1175,c_0_944]),
[final] ).
cnf(i_0_2555,lemma,
( empty(X1)
| function(esk381_2(X1,X2))
| esk379_2(X1,X2) != X4
| esk376_2(X1,X2) != esk375_2(X1,X2)
| ~ relation(X2)
| ~ in(X3,X4)
| ~ in(unordered_pair(unordered_pair(X3,esk380_4(X1,X2,X3,X4)),unordered_pair(X3,X3)),X2) ),
inference(rw,[status(thm)],[i_0_1176,c_0_944]),
[final] ).
cnf(i_0_2556,lemma,
( relation_dom(esk381_2(X1,X2)) = X1
| empty(X1)
| in(esk374_2(X1,X2),X1)
| esk379_2(X1,X2) != X4
| ~ relation(X2)
| ~ in(X3,X4)
| ~ in(unordered_pair(unordered_pair(X3,esk380_4(X1,X2,X3,X4)),unordered_pair(X3,X3)),X2) ),
inference(rw,[status(thm)],[i_0_1177,c_0_944]),
[final] ).
cnf(i_0_2557,lemma,
( empty(X1)
| relation(esk381_2(X1,X2))
| in(esk374_2(X1,X2),X1)
| esk379_2(X1,X2) != X4
| ~ relation(X2)
| ~ in(X3,X4)
| ~ in(unordered_pair(unordered_pair(X3,esk380_4(X1,X2,X3,X4)),unordered_pair(X3,X3)),X2) ),
inference(rw,[status(thm)],[i_0_1178,c_0_944]),
[final] ).
cnf(i_0_2558,lemma,
( empty(X1)
| function(esk381_2(X1,X2))
| in(esk374_2(X1,X2),X1)
| esk379_2(X1,X2) != X4
| ~ relation(X2)
| ~ in(X3,X4)
| ~ in(unordered_pair(unordered_pair(X3,esk380_4(X1,X2,X3,X4)),unordered_pair(X3,X3)),X2) ),
inference(rw,[status(thm)],[i_0_1179,c_0_944]),
[final] ).
cnf(i_0_2559,lemma,
( relation_dom(esk381_2(X1,X2)) = X1
| esk378_2(X1,X2) = esk374_2(X1,X2)
| empty(X1)
| esk379_2(X1,X2) != X4
| ~ relation(X2)
| ~ in(X3,X4)
| ~ in(unordered_pair(unordered_pair(X3,esk380_4(X1,X2,X3,X4)),unordered_pair(X3,X3)),X2) ),
inference(rw,[status(thm)],[i_0_1180,c_0_944]),
[final] ).
cnf(i_0_2560,lemma,
( relation_dom(esk381_2(X1,X2)) = X1
| esk377_2(X1,X2) = esk374_2(X1,X2)
| empty(X1)
| esk379_2(X1,X2) != X4
| ~ relation(X2)
| ~ in(X3,X4)
| ~ in(unordered_pair(unordered_pair(X3,esk380_4(X1,X2,X3,X4)),unordered_pair(X3,X3)),X2) ),
inference(rw,[status(thm)],[i_0_1181,c_0_944]),
[final] ).
cnf(i_0_2561,lemma,
( esk378_2(X1,X2) = esk374_2(X1,X2)
| empty(X1)
| relation(esk381_2(X1,X2))
| esk379_2(X1,X2) != X4
| ~ relation(X2)
| ~ in(X3,X4)
| ~ in(unordered_pair(unordered_pair(X3,esk380_4(X1,X2,X3,X4)),unordered_pair(X3,X3)),X2) ),
inference(rw,[status(thm)],[i_0_1182,c_0_944]),
[final] ).
cnf(i_0_2562,lemma,
( esk378_2(X1,X2) = esk374_2(X1,X2)
| empty(X1)
| function(esk381_2(X1,X2))
| esk379_2(X1,X2) != X4
| ~ relation(X2)
| ~ in(X3,X4)
| ~ in(unordered_pair(unordered_pair(X3,esk380_4(X1,X2,X3,X4)),unordered_pair(X3,X3)),X2) ),
inference(rw,[status(thm)],[i_0_1183,c_0_944]),
[final] ).
cnf(i_0_2563,lemma,
( esk377_2(X1,X2) = esk374_2(X1,X2)
| empty(X1)
| relation(esk381_2(X1,X2))
| esk379_2(X1,X2) != X4
| ~ relation(X2)
| ~ in(X3,X4)
| ~ in(unordered_pair(unordered_pair(X3,esk380_4(X1,X2,X3,X4)),unordered_pair(X3,X3)),X2) ),
inference(rw,[status(thm)],[i_0_1184,c_0_944]),
[final] ).
cnf(i_0_2564,lemma,
( esk377_2(X1,X2) = esk374_2(X1,X2)
| empty(X1)
| function(esk381_2(X1,X2))
| esk379_2(X1,X2) != X4
| ~ relation(X2)
| ~ in(X3,X4)
| ~ in(unordered_pair(unordered_pair(X3,esk380_4(X1,X2,X3,X4)),unordered_pair(X3,X3)),X2) ),
inference(rw,[status(thm)],[i_0_1185,c_0_944]),
[final] ).
cnf(i_0_2565,lemma,
( empty(X1)
| in(esk184_5(X1,X2,X3,X4,X5),X5)
| in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),esk182_2(X1,X2))
| in(unordered_pair(unordered_pair(esk179_2(X1,X2),X6),unordered_pair(esk179_2(X1,X2),esk179_2(X1,X2))),X2)
| X3 != X5
| ~ relation(X2)
| ~ in(X4,X5)
| ~ in(X3,X1)
| ~ in(X6,esk181_2(X1,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1186,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2566,lemma,
( empty(X1)
| in(esk184_5(X1,X2,X3,X4,X5),X5)
| in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),esk182_2(X1,X2))
| in(unordered_pair(unordered_pair(esk178_2(X1,X2),X6),unordered_pair(esk178_2(X1,X2),esk178_2(X1,X2))),X2)
| X3 != X5
| ~ relation(X2)
| ~ in(X4,X5)
| ~ in(X3,X1)
| ~ in(X6,esk180_2(X1,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1187,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2567,plain,
( empty(X1)
| in(X3,esk211_2(X1,X2))
| in(esk214_5(X1,X2,X3,X4,X5),X5)
| in(unordered_pair(unordered_pair(esk208_2(X1,X2),X6),unordered_pair(esk208_2(X1,X2),esk208_2(X1,X2))),X2)
| X4 != X5
| ~ relation(X2)
| ~ in(X4,X1)
| ~ in(X3,X5)
| ~ in(X6,esk210_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1188,c_0_944]),
[final] ).
cnf(i_0_2568,plain,
( empty(X1)
| in(X3,esk211_2(X1,X2))
| in(esk214_5(X1,X2,X3,X4,X5),X5)
| in(unordered_pair(unordered_pair(esk207_2(X1,X2),X6),unordered_pair(esk207_2(X1,X2),esk207_2(X1,X2))),X2)
| X4 != X5
| ~ relation(X2)
| ~ in(X4,X1)
| ~ in(X3,X5)
| ~ in(X6,esk209_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1189,c_0_944]),
[final] ).
cnf(i_0_2569,lemma,
( empty(X1)
| in(esk179_2(X1,X2),esk181_2(X1,X2))
| in(esk184_5(X1,X2,X3,X4,X5),X5)
| in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),esk182_2(X1,X2))
| X3 != X5
| ~ relation(X2)
| ~ in(X4,X5)
| ~ in(X3,X1) ),
inference(rw,[status(thm)],[i_0_1190,c_0_944]),
[final] ).
cnf(i_0_2570,lemma,
( empty(X1)
| in(esk178_2(X1,X2),esk180_2(X1,X2))
| in(esk184_5(X1,X2,X3,X4,X5),X5)
| in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),esk182_2(X1,X2))
| X3 != X5
| ~ relation(X2)
| ~ in(X4,X5)
| ~ in(X3,X1) ),
inference(rw,[status(thm)],[i_0_1191,c_0_944]),
[final] ).
cnf(i_0_2571,lemma,
( empty(X1)
| in(esk184_5(X1,X2,X3,X4,X5),X5)
| in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),esk182_2(X1,X2))
| X3 != X5
| esk179_2(X1,X2) != esk178_2(X1,X2)
| ~ relation(X2)
| ~ in(X4,X5)
| ~ in(X3,X1) ),
inference(rw,[status(thm)],[i_0_1192,c_0_944]),
[final] ).
cnf(i_0_2572,lemma,
( empty(X1)
| in(esk177_2(X1,X2),X1)
| in(esk184_5(X1,X2,X3,X4,X5),X5)
| in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),esk182_2(X1,X2))
| X3 != X5
| ~ relation(X2)
| ~ in(X4,X5)
| ~ in(X3,X1) ),
inference(rw,[status(thm)],[i_0_1193,c_0_944]),
[final] ).
cnf(i_0_2573,lemma,
( empty(X1)
| in(esk177_2(X1,X2),X1)
| in(esk184_5(X1,X2,X3,X4,X5),X5)
| in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),esk182_2(X1,X2))
| X3 != X5
| ~ relation(X2)
| ~ in(X4,X5)
| ~ in(X3,X1) ),
inference(rw,[status(thm)],[i_0_1194,c_0_944]),
[final] ).
cnf(i_0_2574,lemma,
( esk181_2(X1,X2) = esk177_2(X1,X2)
| empty(X1)
| in(esk184_5(X1,X2,X3,X4,X5),X5)
| in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),esk182_2(X1,X2))
| X3 != X5
| ~ relation(X2)
| ~ in(X4,X5)
| ~ in(X3,X1) ),
inference(rw,[status(thm)],[i_0_1195,c_0_944]),
[final] ).
cnf(i_0_2575,lemma,
( esk180_2(X1,X2) = esk177_2(X1,X2)
| empty(X1)
| in(esk184_5(X1,X2,X3,X4,X5),X5)
| in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),esk182_2(X1,X2))
| X3 != X5
| ~ relation(X2)
| ~ in(X4,X5)
| ~ in(X3,X1) ),
inference(rw,[status(thm)],[i_0_1196,c_0_944]),
[final] ).
cnf(i_0_2576,plain,
( in(esk214_5(X1,X2,X3,X4,X5),X5)
| in(X3,esk211_2(X1,X2))
| in(esk208_2(X1,X2),esk210_2(X1,X2))
| empty(X1)
| X4 != X5
| ~ in(X3,X5)
| ~ in(X4,X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_691]),
[final] ).
cnf(i_0_2577,plain,
( in(esk214_5(X1,X2,X3,X4,X5),X5)
| in(X3,esk211_2(X1,X2))
| in(esk207_2(X1,X2),esk209_2(X1,X2))
| empty(X1)
| X4 != X5
| ~ in(X3,X5)
| ~ in(X4,X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_691]),
[final] ).
cnf(i_0_2578,plain,
( in(esk214_5(X1,X2,X3,X4,X5),X5)
| in(X3,esk211_2(X1,X2))
| empty(X1)
| X4 != X5
| ~ in(X3,X5)
| ~ in(X4,X1)
| esk207_2(X1,X2) != esk208_2(X1,X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_691]),
[final] ).
cnf(i_0_2579,plain,
( in(esk214_5(X1,X2,X3,X4,X5),X5)
| in(X3,esk211_2(X1,X2))
| in(esk206_2(X1,X2),X1)
| empty(X1)
| X4 != X5
| ~ in(X3,X5)
| ~ in(X4,X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_691]),
[final] ).
cnf(i_0_2580,plain,
( in(esk214_5(X1,X2,X3,X4,X5),X5)
| in(X3,esk211_2(X1,X2))
| in(esk206_2(X1,X2),X1)
| empty(X1)
| X4 != X5
| ~ in(X3,X5)
| ~ in(X4,X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_691]),
[final] ).
cnf(i_0_2581,plain,
( in(esk214_5(X1,X2,X3,X4,X5),X5)
| in(X3,esk211_2(X1,X2))
| esk206_2(X1,X2) = esk210_2(X1,X2)
| empty(X1)
| X4 != X5
| ~ in(X3,X5)
| ~ in(X4,X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_691]),
[final] ).
cnf(i_0_2582,plain,
( in(esk214_5(X1,X2,X3,X4,X5),X5)
| in(X3,esk211_2(X1,X2))
| esk206_2(X1,X2) = esk209_2(X1,X2)
| empty(X1)
| X4 != X5
| ~ in(X3,X5)
| ~ in(X4,X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_691]),
[final] ).
cnf(i_0_2583,plain,
( X3 = fiber(X1,X2)
| esk46_3(X1,X2,X3) = X2
| ~ relation(X1)
| ~ in(esk46_3(X1,X2,X3),X3)
| ~ in(unordered_pair(unordered_pair(esk46_3(X1,X2,X3),X2),unordered_pair(esk46_3(X1,X2,X3),esk46_3(X1,X2,X3))),X1) ),
inference(rw,[status(thm)],[i_0_1197,c_0_944]),
[final] ).
cnf(i_0_2584,plain,
( X3 = relation_inverse_image(X1,X2)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(esk20_3(X1,X2,X3),X3)
| ~ in(unordered_pair(unordered_pair(esk20_3(X1,X2,X3),X4),unordered_pair(esk20_3(X1,X2,X3),esk20_3(X1,X2,X3))),X1) ),
inference(rw,[status(thm)],[i_0_1198,c_0_944]),
[final] ).
cnf(i_0_2585,lemma,
( relation_dom_as_subset(X2,X1,X3) = X2
| ~ relation_of2_as_subset(X3,X2,X1)
| ~ in(unordered_pair(unordered_pair(esk414_3(X1,X2,X3),X4),unordered_pair(esk414_3(X1,X2,X3),esk414_3(X1,X2,X3))),X3) ),
inference(rw,[status(thm)],[i_0_1199,c_0_944]),
[final] ).
cnf(i_0_2586,lemma,
( empty(X2)
| in(esk380_4(X2,X3,X5,X6),X6)
| in(unordered_pair(unordered_pair(esk376_2(X2,X3),X7),unordered_pair(esk376_2(X2,X3),esk376_2(X2,X3))),X3)
| in(unordered_pair(unordered_pair(apply(esk381_2(X2,X3),X4),X1),unordered_pair(apply(esk381_2(X2,X3),X4),apply(esk381_2(X2,X3),X4))),X3)
| esk379_2(X2,X3) != X6
| ~ relation(X3)
| ~ in(X5,X6)
| ~ in(X4,X2)
| ~ in(X7,esk378_2(X2,X3))
| ~ in(X1,esk382_3(X2,X3,X4)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1200,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2587,lemma,
( empty(X2)
| in(esk380_4(X2,X3,X5,X6),X6)
| in(unordered_pair(unordered_pair(esk375_2(X2,X3),X7),unordered_pair(esk375_2(X2,X3),esk375_2(X2,X3))),X3)
| in(unordered_pair(unordered_pair(apply(esk381_2(X2,X3),X4),X1),unordered_pair(apply(esk381_2(X2,X3),X4),apply(esk381_2(X2,X3),X4))),X3)
| esk379_2(X2,X3) != X6
| ~ relation(X3)
| ~ in(X5,X6)
| ~ in(X4,X2)
| ~ in(X7,esk377_2(X2,X3))
| ~ in(X1,esk382_3(X2,X3,X4)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1201,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2588,lemma,
( in(unordered_pair(unordered_pair(X4,esk415_4(X2,X1,X3,X4)),unordered_pair(X4,X4)),X3)
| relation_dom_as_subset(X1,X2,X3) != X1
| ~ in(X4,X1)
| ~ relation_of2_as_subset(X3,X1,X2) ),
inference(rw,[status(thm)],[i_0_1202,c_0_944]),
[final] ).
cnf(i_0_2589,plain,
( in(unordered_pair(unordered_pair(X1,esk19_4(X2,X3,X4,X1)),unordered_pair(X1,X1)),X2)
| X4 != relation_inverse_image(X2,X3)
| ~ relation(X2)
| ~ in(X1,X4) ),
inference(rw,[status(thm)],[i_0_1203,c_0_944]),
[final] ).
cnf(i_0_2590,plain,
( esk314_3(X2,X7,X6) = unordered_pair(unordered_pair(esk317_3(X2,X7,X6),esk318_3(X2,X7,X6)),unordered_pair(esk317_3(X2,X7,X6),esk317_3(X2,X7,X6)))
| in(X3,esk319_3(X2,X7,X6))
| X1 != X3
| X3 != unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4))
| ~ function(X6)
| ~ relation(X7)
| ~ relation(X6)
| ~ in(X1,cartesian_product2(X2,X2))
| ~ in(unordered_pair(unordered_pair(apply(X6,X4),apply(X6,X5)),unordered_pair(apply(X6,X4),apply(X6,X4))),X7) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1204,c_0_944]),c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2591,plain,
( esk313_3(X2,X7,X6) = unordered_pair(unordered_pair(esk315_3(X2,X7,X6),esk316_3(X2,X7,X6)),unordered_pair(esk315_3(X2,X7,X6),esk315_3(X2,X7,X6)))
| in(X3,esk319_3(X2,X7,X6))
| X1 != X3
| X3 != unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4))
| ~ function(X6)
| ~ relation(X7)
| ~ relation(X6)
| ~ in(X1,cartesian_product2(X2,X2))
| ~ in(unordered_pair(unordered_pair(apply(X6,X4),apply(X6,X5)),unordered_pair(apply(X6,X4),apply(X6,X4))),X7) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1205,c_0_944]),c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2592,plain,
( relation_isomorphism(X1,X2,X3)
| in(esk100_3(X1,X2,X3),relation_field(X1))
| in(unordered_pair(unordered_pair(esk99_3(X1,X2,X3),esk100_3(X1,X2,X3)),unordered_pair(esk99_3(X1,X2,X3),esk99_3(X1,X2,X3))),X1)
| relation_field(X1) != relation_dom(X3)
| relation_rng(X3) != relation_field(X2)
| ~ function(X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| ~ one_to_one(X3) ),
inference(rw,[status(thm)],[i_0_1206,c_0_944]),
[final] ).
cnf(i_0_2593,plain,
( relation_isomorphism(X1,X2,X3)
| in(esk99_3(X1,X2,X3),relation_field(X1))
| in(unordered_pair(unordered_pair(esk99_3(X1,X2,X3),esk100_3(X1,X2,X3)),unordered_pair(esk99_3(X1,X2,X3),esk99_3(X1,X2,X3))),X1)
| relation_field(X1) != relation_dom(X3)
| relation_rng(X3) != relation_field(X2)
| ~ function(X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| ~ one_to_one(X3) ),
inference(rw,[status(thm)],[i_0_1207,c_0_944]),
[final] ).
cnf(i_0_2594,plain,
( X1 = esk454_4(X3,X4,X5,X2)
| X2 = empty_set
| ~ in(X1,X2)
| ~ subset(esk454_4(X3,X4,X5,X2),X1)
| ~ element(X2,powerset(powerset(esk453_3(X3,X4,X5))))
| ~ in(esk453_3(X3,X4,X5),omega)
| ~ epred2_3(X5,X4,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1208]),
[final] ).
cnf(i_0_2595,plain,
( X1 = esk452_4(X3,X4,X5,X2)
| X2 = empty_set
| ~ in(X1,X2)
| ~ subset(esk452_4(X3,X4,X5,X2),X1)
| ~ element(X2,powerset(powerset(esk451_3(X3,X4,X5))))
| ~ in(esk451_3(X3,X4,X5),omega)
| ~ epred2_3(X5,X4,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1208]),
[final] ).
cnf(i_0_2596,plain,
( X3 = relation_rng_restriction(X1,X2)
| in(esk9_3(X1,X2,X3),X1)
| in(unordered_pair(unordered_pair(esk8_3(X1,X2,X3),esk9_3(X1,X2,X3)),unordered_pair(esk8_3(X1,X2,X3),esk8_3(X1,X2,X3))),X3)
| ~ relation(X3)
| ~ relation(X2) ),
inference(rw,[status(thm)],[i_0_1209,c_0_944]),
[final] ).
cnf(i_0_2597,plain,
( X3 = relation_dom_restriction(X1,X2)
| in(esk3_3(X1,X2,X3),X2)
| in(unordered_pair(unordered_pair(esk3_3(X1,X2,X3),esk4_3(X1,X2,X3)),unordered_pair(esk3_3(X1,X2,X3),esk3_3(X1,X2,X3))),X3)
| ~ relation(X3)
| ~ relation(X1) ),
inference(rw,[status(thm)],[i_0_1210,c_0_944]),
[final] ).
cnf(i_0_2598,plain,
( X3 = relation_inverse_image(X1,X2)
| in(esk20_3(X1,X2,X3),X3)
| in(unordered_pair(unordered_pair(esk20_3(X1,X2,X3),esk21_3(X1,X2,X3)),unordered_pair(esk20_3(X1,X2,X3),esk20_3(X1,X2,X3))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[i_0_1211,c_0_944]),
[final] ).
cnf(i_0_2599,plain,
( X3 = relation_image(X1,X2)
| in(esk17_3(X1,X2,X3),X3)
| in(unordered_pair(unordered_pair(esk18_3(X1,X2,X3),esk17_3(X1,X2,X3)),unordered_pair(esk18_3(X1,X2,X3),esk18_3(X1,X2,X3))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[i_0_1212,c_0_944]),
[final] ).
cnf(i_0_2600,lemma,
( empty(X2)
| in(esk380_4(X2,X3,X5,X6),X6)
| in(esk376_2(X2,X3),esk378_2(X2,X3))
| in(unordered_pair(unordered_pair(apply(esk381_2(X2,X3),X4),X1),unordered_pair(apply(esk381_2(X2,X3),X4),apply(esk381_2(X2,X3),X4))),X3)
| esk379_2(X2,X3) != X6
| ~ relation(X3)
| ~ in(X5,X6)
| ~ in(X4,X2)
| ~ in(X1,esk382_3(X2,X3,X4)) ),
inference(rw,[status(thm)],[i_0_1213,c_0_944]),
[final] ).
cnf(i_0_2601,lemma,
( empty(X2)
| in(esk380_4(X2,X3,X5,X6),X6)
| in(esk375_2(X2,X3),esk377_2(X2,X3))
| in(unordered_pair(unordered_pair(apply(esk381_2(X2,X3),X4),X1),unordered_pair(apply(esk381_2(X2,X3),X4),apply(esk381_2(X2,X3),X4))),X3)
| esk379_2(X2,X3) != X6
| ~ relation(X3)
| ~ in(X5,X6)
| ~ in(X4,X2)
| ~ in(X1,esk382_3(X2,X3,X4)) ),
inference(rw,[status(thm)],[i_0_1214,c_0_944]),
[final] ).
cnf(i_0_2602,lemma,
( empty(X2)
| in(esk380_4(X2,X3,X5,X6),X6)
| in(unordered_pair(unordered_pair(apply(esk381_2(X2,X3),X4),X1),unordered_pair(apply(esk381_2(X2,X3),X4),apply(esk381_2(X2,X3),X4))),X3)
| esk379_2(X2,X3) != X6
| esk376_2(X2,X3) != esk375_2(X2,X3)
| ~ relation(X3)
| ~ in(X5,X6)
| ~ in(X4,X2)
| ~ in(X1,esk382_3(X2,X3,X4)) ),
inference(rw,[status(thm)],[i_0_1215,c_0_944]),
[final] ).
cnf(i_0_2603,lemma,
( empty(X2)
| in(esk374_2(X2,X3),X2)
| in(esk380_4(X2,X3,X5,X6),X6)
| in(unordered_pair(unordered_pair(apply(esk381_2(X2,X3),X4),X1),unordered_pair(apply(esk381_2(X2,X3),X4),apply(esk381_2(X2,X3),X4))),X3)
| esk379_2(X2,X3) != X6
| ~ relation(X3)
| ~ in(X5,X6)
| ~ in(X4,X2)
| ~ in(X1,esk382_3(X2,X3,X4)) ),
inference(rw,[status(thm)],[i_0_1216,c_0_944]),
[final] ).
cnf(i_0_2604,lemma,
( esk378_2(X2,X3) = esk374_2(X2,X3)
| empty(X2)
| in(esk380_4(X2,X3,X5,X6),X6)
| in(unordered_pair(unordered_pair(apply(esk381_2(X2,X3),X4),X1),unordered_pair(apply(esk381_2(X2,X3),X4),apply(esk381_2(X2,X3),X4))),X3)
| esk379_2(X2,X3) != X6
| ~ relation(X3)
| ~ in(X5,X6)
| ~ in(X4,X2)
| ~ in(X1,esk382_3(X2,X3,X4)) ),
inference(rw,[status(thm)],[i_0_1217,c_0_944]),
[final] ).
cnf(i_0_2605,lemma,
( esk377_2(X2,X3) = esk374_2(X2,X3)
| empty(X2)
| in(esk380_4(X2,X3,X5,X6),X6)
| in(unordered_pair(unordered_pair(apply(esk381_2(X2,X3),X4),X1),unordered_pair(apply(esk381_2(X2,X3),X4),apply(esk381_2(X2,X3),X4))),X3)
| esk379_2(X2,X3) != X6
| ~ relation(X3)
| ~ in(X5,X6)
| ~ in(X4,X2)
| ~ in(X1,esk382_3(X2,X3,X4)) ),
inference(rw,[status(thm)],[i_0_1218,c_0_944]),
[final] ).
cnf(i_0_2606,lemma,
( empty(X2)
| in(esk379_2(X2,X3),X2)
| in(unordered_pair(unordered_pair(esk376_2(X2,X3),X5),unordered_pair(esk376_2(X2,X3),esk376_2(X2,X3))),X3)
| in(unordered_pair(unordered_pair(apply(esk381_2(X2,X3),X4),X1),unordered_pair(apply(esk381_2(X2,X3),X4),apply(esk381_2(X2,X3),X4))),X3)
| ~ relation(X3)
| ~ in(X4,X2)
| ~ in(X5,esk378_2(X2,X3))
| ~ in(X1,esk382_3(X2,X3,X4)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1219,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2607,lemma,
( empty(X2)
| in(esk379_2(X2,X3),X2)
| in(unordered_pair(unordered_pair(esk375_2(X2,X3),X5),unordered_pair(esk375_2(X2,X3),esk375_2(X2,X3))),X3)
| in(unordered_pair(unordered_pair(apply(esk381_2(X2,X3),X4),X1),unordered_pair(apply(esk381_2(X2,X3),X4),apply(esk381_2(X2,X3),X4))),X3)
| ~ relation(X3)
| ~ in(X4,X2)
| ~ in(X5,esk377_2(X2,X3))
| ~ in(X1,esk382_3(X2,X3,X4)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1220,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2608,plain,
( X2 = relation_inverse(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(esk97_2(X1,X2),esk98_2(X1,X2)),unordered_pair(esk97_2(X1,X2),esk97_2(X1,X2))),X2)
| ~ in(unordered_pair(unordered_pair(esk98_2(X1,X2),esk97_2(X1,X2)),unordered_pair(esk98_2(X1,X2),esk98_2(X1,X2))),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1221,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2609,plain,
( X1 = X2
| ~ relation(X2)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(esk56_2(X1,X2),esk57_2(X1,X2)),unordered_pair(esk56_2(X1,X2),esk56_2(X1,X2))),X2)
| ~ in(unordered_pair(unordered_pair(esk56_2(X1,X2),esk57_2(X1,X2)),unordered_pair(esk56_2(X1,X2),esk56_2(X1,X2))),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1222,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2610,lemma,
( empty(X2)
| in(unordered_pair(unordered_pair(X5,X1),unordered_pair(X5,X5)),X3)
| in(unordered_pair(unordered_pair(esk179_2(X2,X3),X6),unordered_pair(esk179_2(X2,X3),esk179_2(X2,X3))),X3)
| ~ relation(X3)
| ~ in(X6,esk181_2(X2,X3))
| ~ in(X1,esk183_4(X2,X3,X4,X5))
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),esk182_2(X2,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1223,c_0_944]),c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2611,lemma,
( empty(X2)
| in(unordered_pair(unordered_pair(X5,X1),unordered_pair(X5,X5)),X3)
| in(unordered_pair(unordered_pair(esk178_2(X2,X3),X6),unordered_pair(esk178_2(X2,X3),esk178_2(X2,X3))),X3)
| ~ relation(X3)
| ~ in(X6,esk180_2(X2,X3))
| ~ in(X1,esk183_4(X2,X3,X4,X5))
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),esk182_2(X2,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1224,c_0_944]),c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2612,plain,
( empty(X1)
| in(esk227_4(X1,X2,X3,X4),esk228_4(X1,X2,X3,X4))
| in(unordered_pair(unordered_pair(esk222_2(X1,X2),X5),unordered_pair(esk222_2(X1,X2),esk222_2(X1,X2))),X2)
| ~ relation(X2)
| ~ in(X5,esk223_2(X1,X2))
| ~ in(X4,esk224_3(X1,X2,X3)) ),
inference(rw,[status(thm)],[i_0_1225,c_0_944]),
[final] ).
cnf(i_0_2613,plain,
( empty(X1)
| in(esk227_4(X1,X2,X3,X4),esk228_4(X1,X2,X3,X4))
| in(unordered_pair(unordered_pair(esk219_2(X1,X2),X5),unordered_pair(esk219_2(X1,X2),esk219_2(X1,X2))),X2)
| ~ relation(X2)
| ~ in(X5,esk220_2(X1,X2))
| ~ in(X4,esk224_3(X1,X2,X3)) ),
inference(rw,[status(thm)],[i_0_1226,c_0_944]),
[final] ).
cnf(i_0_2614,plain,
( esk314_3(X1,X2,X3) = unordered_pair(unordered_pair(esk317_3(X1,X2,X3),esk318_3(X1,X2,X3)),unordered_pair(esk317_3(X1,X2,X3),esk317_3(X1,X2,X3)))
| in(esk320_4(X1,X2,X3,X4),cartesian_product2(X1,X1))
| ~ function(X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(X4,esk319_3(X1,X2,X3)) ),
inference(rw,[status(thm)],[i_0_1227,c_0_944]),
[final] ).
cnf(i_0_2615,plain,
( esk313_3(X1,X2,X3) = unordered_pair(unordered_pair(esk315_3(X1,X2,X3),esk316_3(X1,X2,X3)),unordered_pair(esk315_3(X1,X2,X3),esk315_3(X1,X2,X3)))
| in(esk320_4(X1,X2,X3,X4),cartesian_product2(X1,X1))
| ~ function(X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(X4,esk319_3(X1,X2,X3)) ),
inference(rw,[status(thm)],[i_0_1228,c_0_944]),
[final] ).
cnf(i_0_2616,plain,
( X3 = fiber(X1,X2)
| in(esk46_3(X1,X2,X3),X3)
| in(unordered_pair(unordered_pair(esk46_3(X1,X2,X3),X2),unordered_pair(esk46_3(X1,X2,X3),esk46_3(X1,X2,X3))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[i_0_1229,c_0_944]),
[final] ).
cnf(i_0_2617,plain,
( in(esk454_4(X1,X2,X3,X4),X4)
| X4 = empty_set
| ~ element(X4,powerset(powerset(esk453_3(X1,X2,X3))))
| ~ in(esk453_3(X1,X2,X3),omega)
| ~ epred2_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1208]),
[final] ).
cnf(i_0_2618,plain,
( in(esk452_4(X1,X2,X3,X4),X4)
| X4 = empty_set
| ~ element(X4,powerset(powerset(esk451_3(X1,X2,X3))))
| ~ in(esk451_3(X1,X2,X3),omega)
| ~ epred2_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1208]),
[final] ).
cnf(i_0_2619,lemma,
( in(unordered_pair(unordered_pair(esk411_3(X1,X2,X3),X1),unordered_pair(esk411_3(X1,X2,X3),esk411_3(X1,X2,X3))),X3)
| ~ relation(X3)
| ~ in(X1,relation_image(X3,X2)) ),
inference(rw,[status(thm)],[i_0_1230,c_0_944]),
[final] ).
cnf(i_0_2620,plain,
( unordered_pair(unordered_pair(esk221_2(X1,X2),esk222_2(X1,X2)),unordered_pair(esk221_2(X1,X2),esk221_2(X1,X2))) = esk217_2(X1,X2)
| empty(X1)
| in(esk227_4(X1,X2,X3,X4),esk228_4(X1,X2,X3,X4))
| ~ relation(X2)
| ~ in(X4,esk224_3(X1,X2,X3)) ),
inference(rw,[status(thm)],[i_0_1231,c_0_944]),
[final] ).
cnf(i_0_2621,plain,
( unordered_pair(unordered_pair(esk218_2(X1,X2),esk219_2(X1,X2)),unordered_pair(esk218_2(X1,X2),esk218_2(X1,X2))) = esk216_2(X1,X2)
| empty(X1)
| in(esk227_4(X1,X2,X3,X4),esk228_4(X1,X2,X3,X4))
| ~ relation(X2)
| ~ in(X4,esk224_3(X1,X2,X3)) ),
inference(rw,[status(thm)],[i_0_1232,c_0_944]),
[final] ).
cnf(i_0_2622,plain,
( in(unordered_pair(unordered_pair(esk92_3(X3,X2,X1),X1),unordered_pair(esk92_3(X3,X2,X1),esk92_3(X3,X2,X1))),X3)
| X2 != relation_rng(X3)
| ~ relation(X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_1233,c_0_944]),
[final] ).
cnf(i_0_2623,plain,
( esk320_4(X1,X2,X3,X4) = X4
| esk314_3(X1,X2,X3) = unordered_pair(unordered_pair(esk317_3(X1,X2,X3),esk318_3(X1,X2,X3)),unordered_pair(esk317_3(X1,X2,X3),esk317_3(X1,X2,X3)))
| ~ function(X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(X4,esk319_3(X1,X2,X3)) ),
inference(rw,[status(thm)],[i_0_1234,c_0_944]),
[final] ).
cnf(i_0_2624,plain,
( esk320_4(X1,X2,X3,X4) = X4
| esk313_3(X1,X2,X3) = unordered_pair(unordered_pair(esk315_3(X1,X2,X3),esk316_3(X1,X2,X3)),unordered_pair(esk315_3(X1,X2,X3),esk315_3(X1,X2,X3)))
| ~ function(X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(X4,esk319_3(X1,X2,X3)) ),
inference(rw,[status(thm)],[i_0_1235,c_0_944]),
[final] ).
cnf(i_0_2625,lemma,
( empty(X2)
| in(esk379_2(X2,X3),X2)
| in(esk376_2(X2,X3),esk378_2(X2,X3))
| in(unordered_pair(unordered_pair(apply(esk381_2(X2,X3),X4),X1),unordered_pair(apply(esk381_2(X2,X3),X4),apply(esk381_2(X2,X3),X4))),X3)
| ~ relation(X3)
| ~ in(X4,X2)
| ~ in(X1,esk382_3(X2,X3,X4)) ),
inference(rw,[status(thm)],[i_0_1236,c_0_944]),
[final] ).
cnf(i_0_2626,lemma,
( empty(X2)
| in(esk379_2(X2,X3),X2)
| in(esk375_2(X2,X3),esk377_2(X2,X3))
| in(unordered_pair(unordered_pair(apply(esk381_2(X2,X3),X4),X1),unordered_pair(apply(esk381_2(X2,X3),X4),apply(esk381_2(X2,X3),X4))),X3)
| ~ relation(X3)
| ~ in(X4,X2)
| ~ in(X1,esk382_3(X2,X3,X4)) ),
inference(rw,[status(thm)],[i_0_1237,c_0_944]),
[final] ).
cnf(i_0_2627,lemma,
( empty(X2)
| in(esk379_2(X2,X3),X2)
| in(unordered_pair(unordered_pair(apply(esk381_2(X2,X3),X4),X1),unordered_pair(apply(esk381_2(X2,X3),X4),apply(esk381_2(X2,X3),X4))),X3)
| esk376_2(X2,X3) != esk375_2(X2,X3)
| ~ relation(X3)
| ~ in(X4,X2)
| ~ in(X1,esk382_3(X2,X3,X4)) ),
inference(rw,[status(thm)],[i_0_1238,c_0_944]),
[final] ).
cnf(i_0_2628,lemma,
( empty(X2)
| in(esk374_2(X2,X3),X2)
| in(esk379_2(X2,X3),X2)
| in(unordered_pair(unordered_pair(apply(esk381_2(X2,X3),X4),X1),unordered_pair(apply(esk381_2(X2,X3),X4),apply(esk381_2(X2,X3),X4))),X3)
| ~ relation(X3)
| ~ in(X4,X2)
| ~ in(X1,esk382_3(X2,X3,X4)) ),
inference(rw,[status(thm)],[i_0_1239,c_0_944]),
[final] ).
cnf(i_0_2629,lemma,
( esk378_2(X2,X3) = esk374_2(X2,X3)
| empty(X2)
| in(esk379_2(X2,X3),X2)
| in(unordered_pair(unordered_pair(apply(esk381_2(X2,X3),X4),X1),unordered_pair(apply(esk381_2(X2,X3),X4),apply(esk381_2(X2,X3),X4))),X3)
| ~ relation(X3)
| ~ in(X4,X2)
| ~ in(X1,esk382_3(X2,X3,X4)) ),
inference(rw,[status(thm)],[i_0_1240,c_0_944]),
[final] ).
cnf(i_0_2630,lemma,
( esk377_2(X2,X3) = esk374_2(X2,X3)
| empty(X2)
| in(esk379_2(X2,X3),X2)
| in(unordered_pair(unordered_pair(apply(esk381_2(X2,X3),X4),X1),unordered_pair(apply(esk381_2(X2,X3),X4),apply(esk381_2(X2,X3),X4))),X3)
| ~ relation(X3)
| ~ in(X4,X2)
| ~ in(X1,esk382_3(X2,X3,X4)) ),
inference(rw,[status(thm)],[i_0_1241,c_0_944]),
[final] ).
cnf(i_0_2631,plain,
( in(X3,esk319_3(X2,X7,X6))
| X1 != X3
| esk314_3(X2,X7,X6) != esk313_3(X2,X7,X6)
| X3 != unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4))
| ~ function(X6)
| ~ relation(X7)
| ~ relation(X6)
| ~ in(X1,cartesian_product2(X2,X2))
| ~ in(unordered_pair(unordered_pair(apply(X6,X4),apply(X6,X5)),unordered_pair(apply(X6,X4),apply(X6,X4))),X7) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1242,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2632,plain,
( in(esk25_4(X1,X2,X3,X4),X4)
| esk25_4(X1,X2,X3,X4) = X1
| esk25_4(X1,X2,X3,X4) = X2
| esk25_4(X1,X2,X3,X4) = X3
| X4 = unordered_triple(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1243]),
[final] ).
cnf(i_0_2633,lemma,
( empty(X1)
| in(esk380_4(X1,X2,X4,X5),X5)
| in(apply(esk381_2(X1,X2),X3),esk382_3(X1,X2,X3))
| in(unordered_pair(unordered_pair(esk376_2(X1,X2),X6),unordered_pair(esk376_2(X1,X2),esk376_2(X1,X2))),X2)
| esk379_2(X1,X2) != X5
| ~ relation(X2)
| ~ in(X4,X5)
| ~ in(X3,X1)
| ~ in(X6,esk378_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1244,c_0_944]),
[final] ).
cnf(i_0_2634,lemma,
( empty(X1)
| in(esk380_4(X1,X2,X4,X5),X5)
| in(apply(esk381_2(X1,X2),X3),esk382_3(X1,X2,X3))
| in(unordered_pair(unordered_pair(esk375_2(X1,X2),X6),unordered_pair(esk375_2(X1,X2),esk375_2(X1,X2))),X2)
| esk379_2(X1,X2) != X5
| ~ relation(X2)
| ~ in(X4,X5)
| ~ in(X3,X1)
| ~ in(X6,esk377_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1245,c_0_944]),
[final] ).
cnf(i_0_2635,lemma,
( empty(X2)
| in(X1,esk183_4(X2,X3,X4,X1))
| in(unordered_pair(unordered_pair(esk179_2(X2,X3),X5),unordered_pair(esk179_2(X2,X3),esk179_2(X2,X3))),X3)
| ~ relation(X3)
| ~ in(X5,esk181_2(X2,X3))
| ~ in(unordered_pair(unordered_pair(X4,X1),unordered_pair(X4,X4)),esk182_2(X2,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1246,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2636,lemma,
( empty(X2)
| in(X1,esk183_4(X2,X3,X4,X1))
| in(unordered_pair(unordered_pair(esk178_2(X2,X3),X5),unordered_pair(esk178_2(X2,X3),esk178_2(X2,X3))),X3)
| ~ relation(X3)
| ~ in(X5,esk180_2(X2,X3))
| ~ in(unordered_pair(unordered_pair(X4,X1),unordered_pair(X4,X4)),esk182_2(X2,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1247,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2637,plain,
( esk314_3(X2,X7,X6) = esk312_3(X2,X7,X6)
| in(X3,esk319_3(X2,X7,X6))
| X1 != X3
| X3 != unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4))
| ~ function(X6)
| ~ relation(X7)
| ~ relation(X6)
| ~ in(X1,cartesian_product2(X2,X2))
| ~ in(unordered_pair(unordered_pair(apply(X6,X4),apply(X6,X5)),unordered_pair(apply(X6,X4),apply(X6,X4))),X7) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1248,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2638,plain,
( esk313_3(X2,X7,X6) = esk312_3(X2,X7,X6)
| in(X3,esk319_3(X2,X7,X6))
| X1 != X3
| X3 != unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4))
| ~ function(X6)
| ~ relation(X7)
| ~ relation(X6)
| ~ in(X1,cartesian_product2(X2,X2))
| ~ in(unordered_pair(unordered_pair(apply(X6,X4),apply(X6,X5)),unordered_pair(apply(X6,X4),apply(X6,X4))),X7) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1249,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2639,lemma,
( empty(X2)
| in(esk179_2(X2,X3),esk181_2(X2,X3))
| in(unordered_pair(unordered_pair(X5,X1),unordered_pair(X5,X5)),X3)
| ~ relation(X3)
| ~ in(X1,esk183_4(X2,X3,X4,X5))
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),esk182_2(X2,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1250,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2640,lemma,
( empty(X2)
| in(esk178_2(X2,X3),esk180_2(X2,X3))
| in(unordered_pair(unordered_pair(X5,X1),unordered_pair(X5,X5)),X3)
| ~ relation(X3)
| ~ in(X1,esk183_4(X2,X3,X4,X5))
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),esk182_2(X2,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1251,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2641,plain,
( esk310_4(X2,X3,X4,X5) = subset_complement(the_carrier(X2),X1)
| unordered_pair(unordered_pair(esk305_2(X2,X3),esk306_2(X2,X3)),unordered_pair(esk305_2(X2,X3),esk305_2(X2,X3))) = esk302_2(X2,X3)
| X1 != esk309_4(X2,X3,X4,X5)
| ~ one_sorted_str(X2)
| ~ element(X1,powerset(the_carrier(X2)))
| ~ in(X5,esk307_3(X2,X3,X4))
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(rw,[status(thm)],[i_0_1252,c_0_944]),
[final] ).
cnf(i_0_2642,plain,
( esk310_4(X2,X3,X4,X5) = subset_complement(the_carrier(X2),X1)
| unordered_pair(unordered_pair(esk303_2(X2,X3),esk304_2(X2,X3)),unordered_pair(esk303_2(X2,X3),esk303_2(X2,X3))) = esk301_2(X2,X3)
| X1 != esk309_4(X2,X3,X4,X5)
| ~ one_sorted_str(X2)
| ~ element(X1,powerset(the_carrier(X2)))
| ~ in(X5,esk307_3(X2,X3,X4))
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(rw,[status(thm)],[i_0_1253,c_0_944]),
[final] ).
cnf(i_0_2643,plain,
( esk292_4(X2,X3,X4,X5) = subset_complement(the_carrier(X2),X1)
| unordered_pair(unordered_pair(esk287_2(X2,X3),esk288_2(X2,X3)),unordered_pair(esk287_2(X2,X3),esk287_2(X2,X3))) = esk284_2(X2,X3)
| X1 != esk291_4(X2,X3,X4,X5)
| ~ one_sorted_str(X2)
| ~ element(X1,powerset(the_carrier(X2)))
| ~ in(X5,esk289_3(X2,X3,X4))
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(rw,[status(thm)],[i_0_1254,c_0_944]),
[final] ).
cnf(i_0_2644,plain,
( esk292_4(X2,X3,X4,X5) = subset_complement(the_carrier(X2),X1)
| unordered_pair(unordered_pair(esk285_2(X2,X3),esk286_2(X2,X3)),unordered_pair(esk285_2(X2,X3),esk285_2(X2,X3))) = esk283_2(X2,X3)
| X1 != esk291_4(X2,X3,X4,X5)
| ~ one_sorted_str(X2)
| ~ element(X1,powerset(the_carrier(X2)))
| ~ in(X5,esk289_3(X2,X3,X4))
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(rw,[status(thm)],[i_0_1255,c_0_944]),
[final] ).
cnf(i_0_2645,plain,
( in(esk227_4(X1,X2,X3,X4),esk228_4(X1,X2,X3,X4))
| in(esk222_2(X1,X2),esk223_2(X1,X2))
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]),
[final] ).
cnf(i_0_2646,plain,
( in(esk227_4(X1,X2,X3,X4),esk228_4(X1,X2,X3,X4))
| in(esk219_2(X1,X2),esk220_2(X1,X2))
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]),
[final] ).
cnf(i_0_2647,lemma,
( esk191_2(X2,X3) = subset_complement(the_carrier(X2),X5)
| in(unordered_pair(unordered_pair(X4,X1),unordered_pair(X4,X4)),esk192_2(X2,X3))
| X5 != esk189_2(X2,X3)
| X1 != subset_complement(the_carrier(X2),esk193_4(X2,X3,X4,X1))
| ~ one_sorted_str(X2)
| ~ element(X5,powerset(the_carrier(X2)))
| ~ in(X4,complements_of_subsets(the_carrier(X2),X3))
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(rw,[status(thm)],[i_0_1256,c_0_944]),
[final] ).
cnf(i_0_2648,lemma,
( esk190_2(X2,X3) = subset_complement(the_carrier(X2),X5)
| in(unordered_pair(unordered_pair(X4,X1),unordered_pair(X4,X4)),esk192_2(X2,X3))
| X5 != esk189_2(X2,X3)
| X1 != subset_complement(the_carrier(X2),esk193_4(X2,X3,X4,X1))
| ~ one_sorted_str(X2)
| ~ element(X5,powerset(the_carrier(X2)))
| ~ in(X4,complements_of_subsets(the_carrier(X2),X3))
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(rw,[status(thm)],[i_0_1257,c_0_944]),
[final] ).
cnf(i_0_2649,lemma,
( empty(X2)
| in(unordered_pair(unordered_pair(X5,X1),unordered_pair(X5,X5)),X3)
| esk179_2(X2,X3) != esk178_2(X2,X3)
| ~ relation(X3)
| ~ in(X1,esk183_4(X2,X3,X4,X5))
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),esk182_2(X2,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1258,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2650,lemma,
( empty(X2)
| in(esk177_2(X2,X3),X2)
| in(unordered_pair(unordered_pair(X5,X1),unordered_pair(X5,X5)),X3)
| ~ relation(X3)
| ~ in(X1,esk183_4(X2,X3,X4,X5))
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),esk182_2(X2,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1259,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2651,lemma,
( empty(X2)
| in(esk177_2(X2,X3),X2)
| in(unordered_pair(unordered_pair(X5,X1),unordered_pair(X5,X5)),X3)
| ~ relation(X3)
| ~ in(X1,esk183_4(X2,X3,X4,X5))
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),esk182_2(X2,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1260,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2652,plain,
( empty(X1)
| in(esk225_4(X1,X2,X3,X4),cartesian_product2(X1,X3))
| in(unordered_pair(unordered_pair(esk222_2(X1,X2),X5),unordered_pair(esk222_2(X1,X2),esk222_2(X1,X2))),X2)
| ~ relation(X2)
| ~ in(X5,esk223_2(X1,X2))
| ~ in(X4,esk224_3(X1,X2,X3)) ),
inference(rw,[status(thm)],[i_0_1261,c_0_944]),
[final] ).
cnf(i_0_2653,plain,
( empty(X1)
| in(esk225_4(X1,X2,X3,X4),cartesian_product2(X1,X3))
| in(unordered_pair(unordered_pair(esk219_2(X1,X2),X5),unordered_pair(esk219_2(X1,X2),esk219_2(X1,X2))),X2)
| ~ relation(X2)
| ~ in(X5,esk220_2(X1,X2))
| ~ in(X4,esk224_3(X1,X2,X3)) ),
inference(rw,[status(thm)],[i_0_1262,c_0_944]),
[final] ).
cnf(i_0_2654,lemma,
( esk181_2(X2,X3) = esk177_2(X2,X3)
| empty(X2)
| in(unordered_pair(unordered_pair(X5,X1),unordered_pair(X5,X5)),X3)
| ~ relation(X3)
| ~ in(X1,esk183_4(X2,X3,X4,X5))
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),esk182_2(X2,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1263,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2655,lemma,
( esk180_2(X2,X3) = esk177_2(X2,X3)
| empty(X2)
| in(unordered_pair(unordered_pair(X5,X1),unordered_pair(X5,X5)),X3)
| ~ relation(X3)
| ~ in(X1,esk183_4(X2,X3,X4,X5))
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),esk182_2(X2,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1264,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2656,plain,
( in(esk227_4(X1,X2,X3,X4),esk228_4(X1,X2,X3,X4))
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| esk216_2(X1,X2) != esk217_2(X1,X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]),
[final] ).
cnf(i_0_2657,plain,
( X4 = unordered_triple(X1,X2,X3)
| esk25_4(X1,X2,X3,X4) != X1
| ~ in(esk25_4(X1,X2,X3,X4),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1243]),
[final] ).
cnf(i_0_2658,plain,
( X4 = unordered_triple(X1,X2,X3)
| esk25_4(X1,X2,X3,X4) != X2
| ~ in(esk25_4(X1,X2,X3,X4),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1243]),
[final] ).
cnf(i_0_2659,plain,
( X4 = unordered_triple(X1,X2,X3)
| esk25_4(X1,X2,X3,X4) != X3
| ~ in(esk25_4(X1,X2,X3,X4),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1243]),
[final] ).
cnf(i_0_2660,plain,
( in(esk227_4(X1,X2,X3,X4),esk228_4(X1,X2,X3,X4))
| in(esk221_2(X1,X2),X1)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]),
[final] ).
cnf(i_0_2661,plain,
( in(esk227_4(X1,X2,X3,X4),esk228_4(X1,X2,X3,X4))
| in(esk218_2(X1,X2),X1)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]),
[final] ).
cnf(i_0_2662,lemma,
( in(esk189_2(X2,X3),complements_of_subsets(the_carrier(X2),X3))
| in(unordered_pair(unordered_pair(X4,X1),unordered_pair(X4,X4)),esk192_2(X2,X3))
| X1 != subset_complement(the_carrier(X2),esk193_4(X2,X3,X4,X1))
| ~ one_sorted_str(X2)
| ~ in(X4,complements_of_subsets(the_carrier(X2),X3))
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(rw,[status(thm)],[i_0_1265,c_0_944]),
[final] ).
cnf(i_0_2663,lemma,
( in(esk189_2(X2,X3),complements_of_subsets(the_carrier(X2),X3))
| in(unordered_pair(unordered_pair(X4,X1),unordered_pair(X4,X4)),esk192_2(X2,X3))
| X1 != subset_complement(the_carrier(X2),esk193_4(X2,X3,X4,X1))
| ~ one_sorted_str(X2)
| ~ in(X4,complements_of_subsets(the_carrier(X2),X3))
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(rw,[status(thm)],[i_0_1266,c_0_944]),
[final] ).
cnf(i_0_2664,plain,
( in(esk227_4(X1,X2,X3,X4),esk228_4(X1,X2,X3,X4))
| esk221_2(X1,X2) = esk223_2(X1,X2)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]),
[final] ).
cnf(i_0_2665,plain,
( in(esk227_4(X1,X2,X3,X4),esk228_4(X1,X2,X3,X4))
| esk218_2(X1,X2) = esk220_2(X1,X2)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]),
[final] ).
cnf(i_0_2666,plain,
( in(esk227_4(X1,X2,X3,X4),esk228_4(X1,X2,X3,X4))
| esk215_2(X1,X2) = esk217_2(X1,X2)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]),
[final] ).
cnf(i_0_2667,plain,
( in(esk227_4(X1,X2,X3,X4),esk228_4(X1,X2,X3,X4))
| esk215_2(X1,X2) = esk216_2(X1,X2)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]),
[final] ).
cnf(i_0_2668,plain,
( empty(X1)
| in(esk226_4(X1,X2,X3,X4),X1)
| in(unordered_pair(unordered_pair(esk222_2(X1,X2),X5),unordered_pair(esk222_2(X1,X2),esk222_2(X1,X2))),X2)
| ~ relation(X2)
| ~ in(X5,esk223_2(X1,X2))
| ~ in(X4,esk224_3(X1,X2,X3)) ),
inference(rw,[status(thm)],[i_0_1267,c_0_944]),
[final] ).
cnf(i_0_2669,plain,
( empty(X1)
| in(esk226_4(X1,X2,X3,X4),X1)
| in(unordered_pair(unordered_pair(esk219_2(X1,X2),X5),unordered_pair(esk219_2(X1,X2),esk219_2(X1,X2))),X2)
| ~ relation(X2)
| ~ in(X5,esk220_2(X1,X2))
| ~ in(X4,esk224_3(X1,X2,X3)) ),
inference(rw,[status(thm)],[i_0_1268,c_0_944]),
[final] ).
cnf(i_0_2670,plain,
( esk228_4(X1,X2,X3,X4) = esk226_4(X1,X2,X3,X4)
| empty(X1)
| in(unordered_pair(unordered_pair(esk222_2(X1,X2),X5),unordered_pair(esk222_2(X1,X2),esk222_2(X1,X2))),X2)
| ~ relation(X2)
| ~ in(X5,esk223_2(X1,X2))
| ~ in(X4,esk224_3(X1,X2,X3)) ),
inference(rw,[status(thm)],[i_0_1269,c_0_944]),
[final] ).
cnf(i_0_2671,plain,
( esk228_4(X1,X2,X3,X4) = esk226_4(X1,X2,X3,X4)
| empty(X1)
| in(unordered_pair(unordered_pair(esk219_2(X1,X2),X5),unordered_pair(esk219_2(X1,X2),esk219_2(X1,X2))),X2)
| ~ relation(X2)
| ~ in(X5,esk220_2(X1,X2))
| ~ in(X4,esk224_3(X1,X2,X3)) ),
inference(rw,[status(thm)],[i_0_1270,c_0_944]),
[final] ).
cnf(i_0_2672,lemma,
( esk196_2(X2,X3) = subset_complement(the_carrier(X2),X5)
| in(unordered_pair(unordered_pair(X4,X1),unordered_pair(X4,X4)),esk197_2(X2,X3))
| X5 != esk194_2(X2,X3)
| X1 != subset_complement(the_carrier(X2),esk198_4(X2,X3,X4,X1))
| ~ one_sorted_str(X2)
| ~ in(X4,X3)
| ~ element(X5,powerset(the_carrier(X2)))
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(rw,[status(thm)],[i_0_1271,c_0_944]),
[final] ).
cnf(i_0_2673,lemma,
( esk195_2(X2,X3) = subset_complement(the_carrier(X2),X5)
| in(unordered_pair(unordered_pair(X4,X1),unordered_pair(X4,X4)),esk197_2(X2,X3))
| X5 != esk194_2(X2,X3)
| X1 != subset_complement(the_carrier(X2),esk198_4(X2,X3,X4,X1))
| ~ one_sorted_str(X2)
| ~ in(X4,X3)
| ~ element(X5,powerset(the_carrier(X2)))
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(rw,[status(thm)],[i_0_1272,c_0_944]),
[final] ).
cnf(i_0_2674,plain,
( in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),X2)
| ~ function(X4)
| ~ relation(X5)
| ~ relation(X4)
| ~ relation(X2)
| ~ relation_isomorphism(X2,X5,X4)
| ~ in(X3,relation_field(X2))
| ~ in(X1,relation_field(X2))
| ~ in(unordered_pair(unordered_pair(apply(X4,X1),apply(X4,X3)),unordered_pair(apply(X4,X1),apply(X4,X1))),X5) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1273,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2675,lemma,
( in(esk343_4(X1,X2,X3,X4),esk344_4(X1,X2,X3,X4))
| empty(X1)
| ~ in(X4,esk341_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_682]),
[final] ).
cnf(i_0_2676,lemma,
( in(unordered_pair(unordered_pair(X4,X1),unordered_pair(X4,X4)),esk192_2(X2,X3))
| esk191_2(X2,X3) != esk190_2(X2,X3)
| X1 != subset_complement(the_carrier(X2),esk193_4(X2,X3,X4,X1))
| ~ one_sorted_str(X2)
| ~ in(X4,complements_of_subsets(the_carrier(X2),X3))
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(rw,[status(thm)],[i_0_1274,c_0_944]),
[final] ).
cnf(i_0_2677,lemma,
( in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),esk205_3(X2,X5,X4))
| ~ function(X4)
| ~ relation(X5)
| ~ relation(X4)
| ~ in(X3,X2)
| ~ in(X1,X2)
| ~ in(unordered_pair(unordered_pair(apply(X4,X1),apply(X4,X3)),unordered_pair(apply(X4,X1),apply(X4,X1))),X5) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1275,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2678,lemma,
( in(X1,esk367_3(X2,X6,X5))
| X1 != unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3))
| ~ function(X5)
| ~ relation(X6)
| ~ relation(X5)
| ~ in(X1,cartesian_product2(X2,X2))
| ~ in(unordered_pair(unordered_pair(apply(X5,X3),apply(X5,X4)),unordered_pair(apply(X5,X3),apply(X5,X3))),X6) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1276,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2679,plain,
( unordered_pair(unordered_pair(esk287_2(X1,X2),esk288_2(X1,X2)),unordered_pair(esk287_2(X1,X2),esk287_2(X1,X2))) = esk284_2(X1,X2)
| in(esk290_4(X1,X2,X3,X4),cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| ~ one_sorted_str(X1)
| ~ in(X4,esk289_3(X1,X2,X3))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1277,c_0_944]),
[final] ).
cnf(i_0_2680,plain,
( unordered_pair(unordered_pair(esk285_2(X1,X2),esk286_2(X1,X2)),unordered_pair(esk285_2(X1,X2),esk285_2(X1,X2))) = esk283_2(X1,X2)
| in(esk290_4(X1,X2,X3,X4),cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| ~ one_sorted_str(X1)
| ~ in(X4,esk289_3(X1,X2,X3))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1278,c_0_944]),
[final] ).
cnf(i_0_2681,lemma,
( X1 = esk382_3(X2,X3,X1)
| empty(X2)
| in(esk380_4(X2,X3,X4,X5),X5)
| in(unordered_pair(unordered_pair(esk376_2(X2,X3),X6),unordered_pair(esk376_2(X2,X3),esk376_2(X2,X3))),X3)
| esk379_2(X2,X3) != X5
| ~ relation(X3)
| ~ in(X4,X5)
| ~ in(X1,X2)
| ~ in(X6,esk378_2(X2,X3)) ),
inference(rw,[status(thm)],[i_0_1279,c_0_944]),
[final] ).
cnf(i_0_2682,lemma,
( X1 = esk382_3(X2,X3,X1)
| empty(X2)
| in(esk380_4(X2,X3,X4,X5),X5)
| in(unordered_pair(unordered_pair(esk375_2(X2,X3),X6),unordered_pair(esk375_2(X2,X3),esk375_2(X2,X3))),X3)
| esk379_2(X2,X3) != X5
| ~ relation(X3)
| ~ in(X4,X5)
| ~ in(X1,X2)
| ~ in(X6,esk377_2(X2,X3)) ),
inference(rw,[status(thm)],[i_0_1280,c_0_944]),
[final] ).
cnf(i_0_2683,lemma,
( in(unordered_pair(unordered_pair(X4,X1),unordered_pair(X4,X4)),esk197_2(X2,X3))
| esk196_2(X2,X3) != esk195_2(X2,X3)
| X1 != subset_complement(the_carrier(X2),esk198_4(X2,X3,X4,X1))
| ~ one_sorted_str(X2)
| ~ in(X4,X3)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(rw,[status(thm)],[i_0_1281,c_0_944]),
[final] ).
cnf(i_0_2684,lemma,
( in(esk194_2(X2,X3),X3)
| in(unordered_pair(unordered_pair(X4,X1),unordered_pair(X4,X4)),esk197_2(X2,X3))
| X1 != subset_complement(the_carrier(X2),esk198_4(X2,X3,X4,X1))
| ~ one_sorted_str(X2)
| ~ in(X4,X3)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(rw,[status(thm)],[i_0_1282,c_0_944]),
[final] ).
cnf(i_0_2685,lemma,
( in(esk194_2(X2,X3),X3)
| in(unordered_pair(unordered_pair(X4,X1),unordered_pair(X4,X4)),esk197_2(X2,X3))
| X1 != subset_complement(the_carrier(X2),esk198_4(X2,X3,X4,X1))
| ~ one_sorted_str(X2)
| ~ in(X4,X3)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(rw,[status(thm)],[i_0_1283,c_0_944]),
[final] ).
cnf(i_0_2686,plain,
( in(X1,esk279_2(X2,X3))
| esk278_2(X2,X3) = subset_complement(the_carrier(X2),X5)
| X1 != subset_complement(the_carrier(X2),esk281_4(X2,X3,X1,X4))
| ~ in(X4,complements_of_subsets(the_carrier(X2),X3))
| ~ element(X5,powerset(the_carrier(X2)))
| X5 != esk276_2(X2,X3)
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1284]),
[final] ).
cnf(i_0_2687,plain,
( in(X1,esk279_2(X2,X3))
| esk277_2(X2,X3) = subset_complement(the_carrier(X2),X5)
| X1 != subset_complement(the_carrier(X2),esk281_4(X2,X3,X1,X4))
| ~ in(X4,complements_of_subsets(the_carrier(X2),X3))
| ~ element(X5,powerset(the_carrier(X2)))
| X5 != esk276_2(X2,X3)
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1284]),
[final] ).
cnf(i_0_2688,plain,
( X2 = relation_inverse(X1)
| in(unordered_pair(unordered_pair(esk97_2(X1,X2),esk98_2(X1,X2)),unordered_pair(esk97_2(X1,X2),esk97_2(X1,X2))),X2)
| in(unordered_pair(unordered_pair(esk98_2(X1,X2),esk97_2(X1,X2)),unordered_pair(esk98_2(X1,X2),esk98_2(X1,X2))),X1)
| ~ relation(X2)
| ~ relation(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1285,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2689,plain,
( X1 = X2
| in(unordered_pair(unordered_pair(esk56_2(X1,X2),esk57_2(X1,X2)),unordered_pair(esk56_2(X1,X2),esk56_2(X1,X2))),X2)
| in(unordered_pair(unordered_pair(esk56_2(X1,X2),esk57_2(X1,X2)),unordered_pair(esk56_2(X1,X2),esk56_2(X1,X2))),X1)
| ~ relation(X2)
| ~ relation(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1286,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2690,plain,
( X3 = relation_image(X1,X2)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(esk17_3(X1,X2,X3),X3)
| ~ in(unordered_pair(unordered_pair(X4,esk17_3(X1,X2,X3)),unordered_pair(X4,X4)),X1) ),
inference(rw,[status(thm)],[i_0_1287,c_0_944]),
[final] ).
cnf(i_0_2691,plain,
( unordered_pair(unordered_pair(esk287_2(X1,X2),esk288_2(X1,X2)),unordered_pair(esk287_2(X1,X2),esk287_2(X1,X2))) = esk284_2(X1,X2)
| in(esk291_4(X1,X2,X3,X4),complements_of_subsets(the_carrier(X1),X2))
| ~ one_sorted_str(X1)
| ~ in(X4,esk289_3(X1,X2,X3))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1288,c_0_944]),
[final] ).
cnf(i_0_2692,plain,
( unordered_pair(unordered_pair(esk285_2(X1,X2),esk286_2(X1,X2)),unordered_pair(esk285_2(X1,X2),esk285_2(X1,X2))) = esk283_2(X1,X2)
| in(esk291_4(X1,X2,X3,X4),complements_of_subsets(the_carrier(X1),X2))
| ~ one_sorted_str(X1)
| ~ in(X4,esk289_3(X1,X2,X3))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1289,c_0_944]),
[final] ).
cnf(i_0_2693,lemma,
( relation_dom(esk381_2(X1,X2)) = X1
| empty(X1)
| in(esk380_4(X1,X2,X3,X4),X4)
| in(unordered_pair(unordered_pair(esk376_2(X1,X2),X5),unordered_pair(esk376_2(X1,X2),esk376_2(X1,X2))),X2)
| esk379_2(X1,X2) != X4
| ~ relation(X2)
| ~ in(X3,X4)
| ~ in(X5,esk378_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1290,c_0_944]),
[final] ).
cnf(i_0_2694,lemma,
( relation_dom(esk381_2(X1,X2)) = X1
| empty(X1)
| in(esk380_4(X1,X2,X3,X4),X4)
| in(unordered_pair(unordered_pair(esk375_2(X1,X2),X5),unordered_pair(esk375_2(X1,X2),esk375_2(X1,X2))),X2)
| esk379_2(X1,X2) != X4
| ~ relation(X2)
| ~ in(X3,X4)
| ~ in(X5,esk377_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1291,c_0_944]),
[final] ).
cnf(i_0_2695,lemma,
( empty(X1)
| relation(esk381_2(X1,X2))
| in(esk380_4(X1,X2,X3,X4),X4)
| in(unordered_pair(unordered_pair(esk376_2(X1,X2),X5),unordered_pair(esk376_2(X1,X2),esk376_2(X1,X2))),X2)
| esk379_2(X1,X2) != X4
| ~ relation(X2)
| ~ in(X3,X4)
| ~ in(X5,esk378_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1292,c_0_944]),
[final] ).
cnf(i_0_2696,lemma,
( empty(X1)
| relation(esk381_2(X1,X2))
| in(esk380_4(X1,X2,X3,X4),X4)
| in(unordered_pair(unordered_pair(esk375_2(X1,X2),X5),unordered_pair(esk375_2(X1,X2),esk375_2(X1,X2))),X2)
| esk379_2(X1,X2) != X4
| ~ relation(X2)
| ~ in(X3,X4)
| ~ in(X5,esk377_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1293,c_0_944]),
[final] ).
cnf(i_0_2697,lemma,
( empty(X1)
| function(esk381_2(X1,X2))
| in(esk380_4(X1,X2,X3,X4),X4)
| in(unordered_pair(unordered_pair(esk376_2(X1,X2),X5),unordered_pair(esk376_2(X1,X2),esk376_2(X1,X2))),X2)
| esk379_2(X1,X2) != X4
| ~ relation(X2)
| ~ in(X3,X4)
| ~ in(X5,esk378_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1294,c_0_944]),
[final] ).
cnf(i_0_2698,lemma,
( empty(X1)
| function(esk381_2(X1,X2))
| in(esk380_4(X1,X2,X3,X4),X4)
| in(unordered_pair(unordered_pair(esk375_2(X1,X2),X5),unordered_pair(esk375_2(X1,X2),esk375_2(X1,X2))),X2)
| esk379_2(X1,X2) != X4
| ~ relation(X2)
| ~ in(X3,X4)
| ~ in(X5,esk377_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1295,c_0_944]),
[final] ).
cnf(i_0_2699,plain,
( X3 = cartesian_product2(X1,X2)
| esk65_3(X1,X2,X3) = unordered_pair(unordered_pair(esk66_3(X1,X2,X3),esk67_3(X1,X2,X3)),unordered_pair(esk66_3(X1,X2,X3),esk66_3(X1,X2,X3)))
| in(esk65_3(X1,X2,X3),X3) ),
inference(rw,[status(thm)],[i_0_1296,c_0_944]),
[final] ).
cnf(i_0_2700,plain,
( unordered_pair(unordered_pair(esk305_2(X1,X2),esk306_2(X1,X2)),unordered_pair(esk305_2(X1,X2),esk305_2(X1,X2))) = esk302_2(X1,X2)
| in(esk308_4(X1,X2,X3,X4),cartesian_product2(X2,X3))
| ~ one_sorted_str(X1)
| ~ in(X4,esk307_3(X1,X2,X3))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1297,c_0_944]),
[final] ).
cnf(i_0_2701,plain,
( unordered_pair(unordered_pair(esk303_2(X1,X2),esk304_2(X1,X2)),unordered_pair(esk303_2(X1,X2),esk303_2(X1,X2))) = esk301_2(X1,X2)
| in(esk308_4(X1,X2,X3,X4),cartesian_product2(X2,X3))
| ~ one_sorted_str(X1)
| ~ in(X4,esk307_3(X1,X2,X3))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1298,c_0_944]),
[final] ).
cnf(i_0_2702,plain,
( esk310_4(X2,X3,X4,X5) = subset_complement(the_carrier(X2),X1)
| esk306_2(X2,X3) = subset_complement(the_carrier(X2),X6)
| ~ element(X1,powerset(the_carrier(X2)))
| X1 != esk309_4(X2,X3,X4,X5)
| ~ in(X5,esk307_3(X2,X3,X4))
| ~ element(X6,powerset(the_carrier(X2)))
| X6 != esk305_2(X2,X3)
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]),
[final] ).
cnf(i_0_2703,plain,
( esk310_4(X2,X3,X4,X5) = subset_complement(the_carrier(X2),X1)
| esk304_2(X2,X3) = subset_complement(the_carrier(X2),X6)
| ~ element(X1,powerset(the_carrier(X2)))
| X1 != esk309_4(X2,X3,X4,X5)
| ~ in(X5,esk307_3(X2,X3,X4))
| ~ element(X6,powerset(the_carrier(X2)))
| X6 != esk303_2(X2,X3)
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]),
[final] ).
cnf(i_0_2704,plain,
( esk292_4(X2,X3,X4,X5) = subset_complement(the_carrier(X2),X1)
| esk288_2(X2,X3) = subset_complement(the_carrier(X2),X6)
| ~ element(X1,powerset(the_carrier(X2)))
| X1 != esk291_4(X2,X3,X4,X5)
| ~ in(X5,esk289_3(X2,X3,X4))
| ~ element(X6,powerset(the_carrier(X2)))
| X6 != esk287_2(X2,X3)
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]),
[final] ).
cnf(i_0_2705,plain,
( esk292_4(X2,X3,X4,X5) = subset_complement(the_carrier(X2),X1)
| esk286_2(X2,X3) = subset_complement(the_carrier(X2),X6)
| ~ element(X1,powerset(the_carrier(X2)))
| X1 != esk291_4(X2,X3,X4,X5)
| ~ in(X5,esk289_3(X2,X3,X4))
| ~ element(X6,powerset(the_carrier(X2)))
| X6 != esk285_2(X2,X3)
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]),
[final] ).
cnf(i_0_2706,plain,
( in(X1,esk279_2(X2,X3))
| in(esk276_2(X2,X3),complements_of_subsets(the_carrier(X2),X3))
| X1 != subset_complement(the_carrier(X2),esk281_4(X2,X3,X1,X4))
| ~ in(X4,complements_of_subsets(the_carrier(X2),X3))
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1284]),
[final] ).
cnf(i_0_2707,plain,
( in(X1,esk279_2(X2,X3))
| in(esk276_2(X2,X3),complements_of_subsets(the_carrier(X2),X3))
| X1 != subset_complement(the_carrier(X2),esk281_4(X2,X3,X1,X4))
| ~ in(X4,complements_of_subsets(the_carrier(X2),X3))
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1284]),
[final] ).
cnf(i_0_2708,plain,
( unordered_pair(unordered_pair(esk240_1(X1),esk241_1(X1)),unordered_pair(esk240_1(X1),esk240_1(X1))) = esk237_1(X1)
| unordered_pair(unordered_pair(esk244_3(X1,X2,X3),esk245_3(X1,X2,X3)),unordered_pair(esk244_3(X1,X2,X3),esk244_3(X1,X2,X3))) = X3
| ~ in(X3,esk242_2(X1,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1299,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2709,plain,
( unordered_pair(unordered_pair(esk238_1(X1),esk239_1(X1)),unordered_pair(esk238_1(X1),esk238_1(X1))) = esk236_1(X1)
| unordered_pair(unordered_pair(esk244_3(X1,X2,X3),esk245_3(X1,X2,X3)),unordered_pair(esk244_3(X1,X2,X3),esk244_3(X1,X2,X3))) = X3
| ~ in(X3,esk242_2(X1,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1300,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2710,plain,
( unordered_pair(unordered_pair(esk305_2(X1,X2),esk306_2(X1,X2)),unordered_pair(esk305_2(X1,X2),esk305_2(X1,X2))) = esk302_2(X1,X2)
| in(esk309_4(X1,X2,X3,X4),X2)
| ~ one_sorted_str(X1)
| ~ in(X4,esk307_3(X1,X2,X3))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1301,c_0_944]),
[final] ).
cnf(i_0_2711,plain,
( unordered_pair(unordered_pair(esk303_2(X1,X2),esk304_2(X1,X2)),unordered_pair(esk303_2(X1,X2),esk303_2(X1,X2))) = esk301_2(X1,X2)
| in(esk309_4(X1,X2,X3,X4),X2)
| ~ one_sorted_str(X1)
| ~ in(X4,esk307_3(X1,X2,X3))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1302,c_0_944]),
[final] ).
cnf(i_0_2712,plain,
( in(X1,esk297_2(X2,X3))
| esk296_2(X2,X3) = subset_complement(the_carrier(X2),X5)
| X1 != subset_complement(the_carrier(X2),esk299_4(X2,X3,X1,X4))
| ~ in(X4,X3)
| ~ element(X5,powerset(the_carrier(X2)))
| X5 != esk294_2(X2,X3)
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1303]),
[final] ).
cnf(i_0_2713,plain,
( in(X1,esk297_2(X2,X3))
| esk295_2(X2,X3) = subset_complement(the_carrier(X2),X5)
| X1 != subset_complement(the_carrier(X2),esk299_4(X2,X3,X1,X4))
| ~ in(X4,X3)
| ~ element(X5,powerset(the_carrier(X2)))
| X5 != esk294_2(X2,X3)
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1303]),
[final] ).
cnf(i_0_2714,plain,
( esk292_4(X2,X3,X4,X5) = subset_complement(the_carrier(X2),X1)
| in(esk287_2(X2,X3),complements_of_subsets(the_carrier(X2),X3))
| ~ element(X1,powerset(the_carrier(X2)))
| X1 != esk291_4(X2,X3,X4,X5)
| ~ in(X5,esk289_3(X2,X3,X4))
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]),
[final] ).
cnf(i_0_2715,plain,
( esk292_4(X2,X3,X4,X5) = subset_complement(the_carrier(X2),X1)
| in(esk285_2(X2,X3),complements_of_subsets(the_carrier(X2),X3))
| ~ element(X1,powerset(the_carrier(X2)))
| X1 != esk291_4(X2,X3,X4,X5)
| ~ in(X5,esk289_3(X2,X3,X4))
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]),
[final] ).
cnf(i_0_2716,plain,
( in(X1,esk279_2(X2,X3))
| X1 != subset_complement(the_carrier(X2),esk281_4(X2,X3,X1,X4))
| ~ in(X4,complements_of_subsets(the_carrier(X2),X3))
| esk277_2(X2,X3) != esk278_2(X2,X3)
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1284]),
[final] ).
cnf(i_0_2717,plain,
( in(X2,esk249_1(X1))
| epred2_3(esk248_1(X1),esk247_1(X1),esk246_1(X1))
| in(esk254_4(X1,X2,X3,X4),esk253_3(X1,X2,X3))
| X2 != X5
| X2 != X3
| ~ ordinal(X3)
| ~ ordinal(X1)
| ~ in(X4,esk253_3(X1,X2,X3))
| ~ in(X5,set_union2(X1,unordered_pair(X1,X1))) ),
inference(rw,[status(thm)],[i_0_1304,c_0_1305]),
[final] ).
cnf(i_0_2718,lemma,
( X1 = esk183_4(X2,X3,X1,X4)
| empty(X2)
| in(unordered_pair(unordered_pair(esk179_2(X2,X3),X5),unordered_pair(esk179_2(X2,X3),esk179_2(X2,X3))),X3)
| ~ relation(X3)
| ~ in(X5,esk181_2(X2,X3))
| ~ in(unordered_pair(unordered_pair(X1,X4),unordered_pair(X1,X1)),esk182_2(X2,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1306,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2719,lemma,
( X1 = esk183_4(X2,X3,X1,X4)
| empty(X2)
| in(unordered_pair(unordered_pair(esk178_2(X2,X3),X5),unordered_pair(esk178_2(X2,X3),esk178_2(X2,X3))),X3)
| ~ relation(X3)
| ~ in(X5,esk180_2(X2,X3))
| ~ in(unordered_pair(unordered_pair(X1,X4),unordered_pair(X1,X1)),esk182_2(X2,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1307,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2720,plain,
( esk310_4(X2,X3,X4,X5) = subset_complement(the_carrier(X2),X1)
| ~ element(X1,powerset(the_carrier(X2)))
| X1 != esk309_4(X2,X3,X4,X5)
| ~ in(X5,esk307_3(X2,X3,X4))
| esk301_2(X2,X3) != esk302_2(X2,X3)
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]),
[final] ).
cnf(i_0_2721,plain,
( esk292_4(X2,X3,X4,X5) = subset_complement(the_carrier(X2),X1)
| ~ element(X1,powerset(the_carrier(X2)))
| X1 != esk291_4(X2,X3,X4,X5)
| ~ in(X5,esk289_3(X2,X3,X4))
| esk283_2(X2,X3) != esk284_2(X2,X3)
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]),
[final] ).
cnf(i_0_2722,lemma,
( relation_rng_as_subset(X2,X3,X4) = X3
| ~ relation_of2_as_subset(X4,X2,X3)
| ~ in(unordered_pair(unordered_pair(X1,esk416_3(X2,X3,X4)),unordered_pair(X1,X1)),X4) ),
inference(rw,[status(thm)],[i_0_1308,c_0_944]),
[final] ).
cnf(i_0_2723,plain,
( esk310_4(X2,X3,X4,X5) = subset_complement(the_carrier(X2),X1)
| in(esk305_2(X2,X3),X3)
| ~ element(X1,powerset(the_carrier(X2)))
| X1 != esk309_4(X2,X3,X4,X5)
| ~ in(X5,esk307_3(X2,X3,X4))
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]),
[final] ).
cnf(i_0_2724,plain,
( esk310_4(X2,X3,X4,X5) = subset_complement(the_carrier(X2),X1)
| in(esk303_2(X2,X3),X3)
| ~ element(X1,powerset(the_carrier(X2)))
| X1 != esk309_4(X2,X3,X4,X5)
| ~ in(X5,esk307_3(X2,X3,X4))
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]),
[final] ).
cnf(i_0_2725,plain,
( in(esk332_4(X1,X2,X3,X4),powerset(relation_dom(X3)))
| in(relation_image(X3,esk330_3(X1,X2,X3)),X2)
| ~ in(X4,esk331_3(X1,X2,X3))
| ~ element(X2,powerset(powerset(X1)))
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1309]),
[final] ).
cnf(i_0_2726,plain,
( in(esk332_4(X1,X2,X3,X4),powerset(relation_dom(X3)))
| in(relation_image(X3,esk329_3(X1,X2,X3)),X2)
| ~ in(X4,esk331_3(X1,X2,X3))
| ~ element(X2,powerset(powerset(X1)))
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1309]),
[final] ).
cnf(i_0_2727,plain,
( esk310_4(X2,X3,X4,X5) = subset_complement(the_carrier(X2),X1)
| esk300_2(X2,X3) = esk302_2(X2,X3)
| ~ element(X1,powerset(the_carrier(X2)))
| X1 != esk309_4(X2,X3,X4,X5)
| ~ in(X5,esk307_3(X2,X3,X4))
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]),
[final] ).
cnf(i_0_2728,plain,
( esk310_4(X2,X3,X4,X5) = subset_complement(the_carrier(X2),X1)
| esk300_2(X2,X3) = esk301_2(X2,X3)
| ~ element(X1,powerset(the_carrier(X2)))
| X1 != esk309_4(X2,X3,X4,X5)
| ~ in(X5,esk307_3(X2,X3,X4))
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]),
[final] ).
cnf(i_0_2729,plain,
( esk292_4(X2,X3,X4,X5) = subset_complement(the_carrier(X2),X1)
| esk282_2(X2,X3) = esk284_2(X2,X3)
| ~ element(X1,powerset(the_carrier(X2)))
| X1 != esk291_4(X2,X3,X4,X5)
| ~ in(X5,esk289_3(X2,X3,X4))
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]),
[final] ).
cnf(i_0_2730,plain,
( esk292_4(X2,X3,X4,X5) = subset_complement(the_carrier(X2),X1)
| esk282_2(X2,X3) = esk283_2(X2,X3)
| ~ element(X1,powerset(the_carrier(X2)))
| X1 != esk291_4(X2,X3,X4,X5)
| ~ in(X5,esk289_3(X2,X3,X4))
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]),
[final] ).
cnf(i_0_2731,plain,
( unordered_pair(unordered_pair(esk221_2(X1,X2),esk222_2(X1,X2)),unordered_pair(esk221_2(X1,X2),esk221_2(X1,X2))) = esk217_2(X1,X2)
| empty(X1)
| in(esk225_4(X1,X2,X3,X4),cartesian_product2(X1,X3))
| ~ relation(X2)
| ~ in(X4,esk224_3(X1,X2,X3)) ),
inference(rw,[status(thm)],[i_0_1310,c_0_944]),
[final] ).
cnf(i_0_2732,plain,
( unordered_pair(unordered_pair(esk218_2(X1,X2),esk219_2(X1,X2)),unordered_pair(esk218_2(X1,X2),esk218_2(X1,X2))) = esk216_2(X1,X2)
| empty(X1)
| in(esk225_4(X1,X2,X3,X4),cartesian_product2(X1,X3))
| ~ relation(X2)
| ~ in(X4,esk224_3(X1,X2,X3)) ),
inference(rw,[status(thm)],[i_0_1311,c_0_944]),
[final] ).
cnf(i_0_2733,plain,
( esk241_1(X1) = unordered_pair(esk240_1(X1),esk240_1(X1))
| unordered_pair(unordered_pair(esk244_3(X1,X2,X3),esk245_3(X1,X2,X3)),unordered_pair(esk244_3(X1,X2,X3),esk244_3(X1,X2,X3))) = X3
| ~ in(X3,esk242_2(X1,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1312,c_0_681]),c_0_944]),
[final] ).
cnf(i_0_2734,plain,
( esk239_1(X1) = unordered_pair(esk238_1(X1),esk238_1(X1))
| unordered_pair(unordered_pair(esk244_3(X1,X2,X3),esk245_3(X1,X2,X3)),unordered_pair(esk244_3(X1,X2,X3),esk244_3(X1,X2,X3))) = X3
| ~ in(X3,esk242_2(X1,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1313,c_0_681]),c_0_944]),
[final] ).
cnf(i_0_2735,plain,
( in(X1,esk297_2(X2,X3))
| X1 != subset_complement(the_carrier(X2),esk299_4(X2,X3,X1,X4))
| ~ in(X4,X3)
| esk295_2(X2,X3) != esk296_2(X2,X3)
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1303]),
[final] ).
cnf(i_0_2736,plain,
( in(X1,esk297_2(X2,X3))
| in(esk294_2(X2,X3),X3)
| X1 != subset_complement(the_carrier(X2),esk299_4(X2,X3,X1,X4))
| ~ in(X4,X3)
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1303]),
[final] ).
cnf(i_0_2737,plain,
( in(X1,esk297_2(X2,X3))
| in(esk294_2(X2,X3),X3)
| X1 != subset_complement(the_carrier(X2),esk299_4(X2,X3,X1,X4))
| ~ in(X4,X3)
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1303]),
[final] ).
cnf(i_0_2738,plain,
( in(esk290_4(X1,X2,X3,X4),cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| esk288_2(X1,X2) = subset_complement(the_carrier(X1),X5)
| ~ in(X4,esk289_3(X1,X2,X3))
| ~ element(X5,powerset(the_carrier(X1)))
| X5 != esk287_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]),
[final] ).
cnf(i_0_2739,plain,
( in(esk290_4(X1,X2,X3,X4),cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| esk286_2(X1,X2) = subset_complement(the_carrier(X1),X5)
| ~ in(X4,esk289_3(X1,X2,X3))
| ~ element(X5,powerset(the_carrier(X1)))
| X5 != esk285_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]),
[final] ).
cnf(i_0_2740,plain,
( unordered_pair(unordered_pair(esk244_3(X1,X2,X3),esk245_3(X1,X2,X3)),unordered_pair(esk244_3(X1,X2,X3),esk244_3(X1,X2,X3))) = X3
| in(esk240_1(X1),X1)
| ~ in(X3,esk242_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1314,c_0_944]),
[final] ).
cnf(i_0_2741,plain,
( unordered_pair(unordered_pair(esk244_3(X1,X2,X3),esk245_3(X1,X2,X3)),unordered_pair(esk244_3(X1,X2,X3),esk244_3(X1,X2,X3))) = X3
| in(esk238_1(X1),X1)
| ~ in(X3,esk242_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1315,c_0_944]),
[final] ).
cnf(i_0_2742,plain,
( in(X2,esk249_1(X1))
| in(esk254_4(X1,X2,X3,X4),esk253_3(X1,X2,X3))
| X2 != X5
| X2 != X3
| esk248_1(X1) != esk247_1(X1)
| ~ ordinal(X3)
| ~ ordinal(X1)
| ~ in(X4,esk253_3(X1,X2,X3))
| ~ in(X5,set_union2(X1,unordered_pair(X1,X1))) ),
inference(rw,[status(thm)],[i_0_1316,c_0_1305]),
[final] ).
cnf(i_0_2743,plain,
( X2 = inclusion_relation(X1)
| relation_field(X2) != X1
| ~ relation(X2)
| ~ subset(esk47_2(X1,X2),esk48_2(X1,X2))
| ~ in(unordered_pair(unordered_pair(esk47_2(X1,X2),esk48_2(X1,X2)),unordered_pair(esk47_2(X1,X2),esk47_2(X1,X2))),X2) ),
inference(rw,[status(thm)],[i_0_1317,c_0_944]),
[final] ).
cnf(i_0_2744,plain,
( X2 = identity_relation(X1)
| esk2_2(X1,X2) != esk1_2(X1,X2)
| ~ relation(X2)
| ~ in(esk1_2(X1,X2),X1)
| ~ in(unordered_pair(unordered_pair(esk1_2(X1,X2),esk2_2(X1,X2)),unordered_pair(esk1_2(X1,X2),esk1_2(X1,X2))),X2) ),
inference(rw,[status(thm)],[i_0_1318,c_0_944]),
[final] ).
cnf(i_0_2745,plain,
( unordered_pair(unordered_pair(esk244_3(X1,X2,X3),esk245_3(X1,X2,X3)),unordered_pair(esk244_3(X1,X2,X3),esk244_3(X1,X2,X3))) = X3
| esk237_1(X1) != esk236_1(X1)
| ~ in(X3,esk242_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1319,c_0_944]),
[final] ).
cnf(i_0_2746,lemma,
( esk365_4(X2,X3,X4,X5) = subset_complement(the_carrier(X2),X1)
| ~ element(X1,powerset(the_carrier(X2)))
| X1 != esk364_4(X2,X3,X4,X5)
| ~ in(X5,esk363_3(X2,X3,X4))
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_688]),
[final] ).
cnf(i_0_2747,lemma,
( esk361_4(X2,X3,X4,X5) = subset_complement(the_carrier(X2),X1)
| ~ element(X1,powerset(the_carrier(X2)))
| X1 != esk360_4(X2,X3,X4,X5)
| ~ in(X5,esk359_3(X2,X3,X4))
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_687]),
[final] ).
cnf(i_0_2748,plain,
( unordered_pair(unordered_pair(esk221_2(X1,X2),esk222_2(X1,X2)),unordered_pair(esk221_2(X1,X2),esk221_2(X1,X2))) = esk217_2(X1,X2)
| empty(X1)
| in(esk226_4(X1,X2,X3,X4),X1)
| ~ relation(X2)
| ~ in(X4,esk224_3(X1,X2,X3)) ),
inference(rw,[status(thm)],[i_0_1320,c_0_944]),
[final] ).
cnf(i_0_2749,plain,
( unordered_pair(unordered_pair(esk218_2(X1,X2),esk219_2(X1,X2)),unordered_pair(esk218_2(X1,X2),esk218_2(X1,X2))) = esk216_2(X1,X2)
| empty(X1)
| in(esk226_4(X1,X2,X3,X4),X1)
| ~ relation(X2)
| ~ in(X4,esk224_3(X1,X2,X3)) ),
inference(rw,[status(thm)],[i_0_1321,c_0_944]),
[final] ).
cnf(i_0_2750,plain,
( esk237_1(X1) = esk235_1(X1)
| unordered_pair(unordered_pair(esk244_3(X1,X2,X3),esk245_3(X1,X2,X3)),unordered_pair(esk244_3(X1,X2,X3),esk244_3(X1,X2,X3))) = X3
| ~ in(X3,esk242_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1322,c_0_944]),
[final] ).
cnf(i_0_2751,plain,
( esk236_1(X1) = esk235_1(X1)
| unordered_pair(unordered_pair(esk244_3(X1,X2,X3),esk245_3(X1,X2,X3)),unordered_pair(esk244_3(X1,X2,X3),esk244_3(X1,X2,X3))) = X3
| ~ in(X3,esk242_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1323,c_0_944]),
[final] ).
cnf(i_0_2752,lemma,
( in(X2,esk349_1(X1))
| in(esk353_4(X1,X2,X3,X4),esk352_3(X1,X2,X3))
| X2 != X3
| ~ ordinal(X3)
| ~ ordinal(X1)
| ~ in(X4,esk352_3(X1,X2,X3))
| ~ in(X2,set_union2(X1,unordered_pair(X1,X1))) ),
inference(rw,[status(thm)],[i_0_1324,c_0_1305]),
[final] ).
cnf(i_0_2753,lemma,
( esk191_2(X1,X2) = subset_complement(the_carrier(X1),X5)
| element(esk193_4(X1,X2,X3,X4),powerset(the_carrier(X1)))
| in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),esk192_2(X1,X2))
| X5 != esk189_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X5,powerset(the_carrier(X1)))
| ~ in(X3,complements_of_subsets(the_carrier(X1),X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1325,c_0_944]),
[final] ).
cnf(i_0_2754,lemma,
( esk190_2(X1,X2) = subset_complement(the_carrier(X1),X5)
| element(esk193_4(X1,X2,X3,X4),powerset(the_carrier(X1)))
| in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),esk192_2(X1,X2))
| X5 != esk189_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X5,powerset(the_carrier(X1)))
| ~ in(X3,complements_of_subsets(the_carrier(X1),X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1326,c_0_944]),
[final] ).
cnf(i_0_2755,plain,
( esk228_4(X1,X2,X3,X4) = esk226_4(X1,X2,X3,X4)
| unordered_pair(unordered_pair(esk221_2(X1,X2),esk222_2(X1,X2)),unordered_pair(esk221_2(X1,X2),esk221_2(X1,X2))) = esk217_2(X1,X2)
| empty(X1)
| ~ relation(X2)
| ~ in(X4,esk224_3(X1,X2,X3)) ),
inference(rw,[status(thm)],[i_0_1327,c_0_944]),
[final] ).
cnf(i_0_2756,plain,
( esk228_4(X1,X2,X3,X4) = esk226_4(X1,X2,X3,X4)
| unordered_pair(unordered_pair(esk218_2(X1,X2),esk219_2(X1,X2)),unordered_pair(esk218_2(X1,X2),esk218_2(X1,X2))) = esk216_2(X1,X2)
| empty(X1)
| ~ relation(X2)
| ~ in(X4,esk224_3(X1,X2,X3)) ),
inference(rw,[status(thm)],[i_0_1328,c_0_944]),
[final] ).
cnf(i_0_2757,lemma,
( unordered_pair(unordered_pair(esk347_3(X1,X2,X3),esk348_3(X1,X2,X3)),unordered_pair(esk347_3(X1,X2,X3),esk347_3(X1,X2,X3))) = X3
| ~ in(X3,esk346_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1329,c_0_944]),
[final] ).
cnf(i_0_2758,lemma,
( below_refl(X1,X2,X3)
| empty_carrier(X1)
| ~ in(ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3),relation_of_lattice(X1))
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1330]),
[final] ).
cnf(i_0_2759,plain,
( in(esk290_4(X1,X2,X3,X4),cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| in(esk287_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| ~ in(X4,esk289_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]),
[final] ).
cnf(i_0_2760,plain,
( in(esk290_4(X1,X2,X3,X4),cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| in(esk285_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| ~ in(X4,esk289_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]),
[final] ).
cnf(i_0_2761,lemma,
( in(unordered_pair(unordered_pair(apply(X1,X2),apply(X1,X3)),unordered_pair(apply(X1,X2),apply(X1,X2))),X4)
| ~ function(X1)
| ~ relation(X4)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),esk205_3(X5,X4,X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1331,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2762,plain,
( esk225_4(X1,X2,X3,X4) = X4
| empty(X1)
| in(unordered_pair(unordered_pair(esk222_2(X1,X2),X5),unordered_pair(esk222_2(X1,X2),esk222_2(X1,X2))),X2)
| ~ relation(X2)
| ~ in(X5,esk223_2(X1,X2))
| ~ in(X4,esk224_3(X1,X2,X3)) ),
inference(rw,[status(thm)],[i_0_1332,c_0_944]),
[final] ).
cnf(i_0_2763,plain,
( esk225_4(X1,X2,X3,X4) = X4
| empty(X1)
| in(unordered_pair(unordered_pair(esk219_2(X1,X2),X5),unordered_pair(esk219_2(X1,X2),esk219_2(X1,X2))),X2)
| ~ relation(X2)
| ~ in(X5,esk220_2(X1,X2))
| ~ in(X4,esk224_3(X1,X2,X3)) ),
inference(rw,[status(thm)],[i_0_1333,c_0_944]),
[final] ).
cnf(i_0_2764,plain,
( in(X3,esk249_1(X2))
| subset(X1,esk254_4(X2,X3,X4,X1))
| epred2_3(esk248_1(X2),esk247_1(X2),esk246_1(X2))
| X3 != X5
| X3 != X4
| ~ ordinal(X4)
| ~ ordinal(X2)
| ~ in(X1,esk253_3(X2,X3,X4))
| ~ in(X5,set_union2(X2,unordered_pair(X2,X2))) ),
inference(rw,[status(thm)],[i_0_1334,c_0_1305]),
[final] ).
cnf(i_0_2765,lemma,
( in(esk189_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| element(esk193_4(X1,X2,X3,X4),powerset(the_carrier(X1)))
| in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),esk192_2(X1,X2))
| ~ one_sorted_str(X1)
| ~ in(X3,complements_of_subsets(the_carrier(X1),X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1335,c_0_944]),
[final] ).
cnf(i_0_2766,lemma,
( in(esk189_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| element(esk193_4(X1,X2,X3,X4),powerset(the_carrier(X1)))
| in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),esk192_2(X1,X2))
| ~ one_sorted_str(X1)
| ~ in(X3,complements_of_subsets(the_carrier(X1),X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1336,c_0_944]),
[final] ).
cnf(i_0_2767,plain,
( in(esk332_4(X1,X2,X3,X4),powerset(relation_dom(X3)))
| ~ in(X4,esk331_3(X1,X2,X3))
| esk329_3(X1,X2,X3) != esk330_3(X1,X2,X3)
| ~ element(X2,powerset(powerset(X1)))
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1309]),
[final] ).
cnf(i_0_2768,plain,
( in(esk291_4(X1,X2,X3,X4),complements_of_subsets(the_carrier(X1),X2))
| esk288_2(X1,X2) = subset_complement(the_carrier(X1),X5)
| ~ in(X4,esk289_3(X1,X2,X3))
| ~ element(X5,powerset(the_carrier(X1)))
| X5 != esk287_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]),
[final] ).
cnf(i_0_2769,plain,
( in(esk291_4(X1,X2,X3,X4),complements_of_subsets(the_carrier(X1),X2))
| esk286_2(X1,X2) = subset_complement(the_carrier(X1),X5)
| ~ in(X4,esk289_3(X1,X2,X3))
| ~ element(X5,powerset(the_carrier(X1)))
| X5 != esk285_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]),
[final] ).
cnf(i_0_2770,plain,
( in(esk290_4(X1,X2,X3,X4),cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| ~ in(X4,esk289_3(X1,X2,X3))
| esk283_2(X1,X2) != esk284_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]),
[final] ).
cnf(i_0_2771,plain,
( in(esk308_4(X1,X2,X3,X4),cartesian_product2(X2,X3))
| esk306_2(X1,X2) = subset_complement(the_carrier(X1),X5)
| ~ in(X4,esk307_3(X1,X2,X3))
| ~ element(X5,powerset(the_carrier(X1)))
| X5 != esk305_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]),
[final] ).
cnf(i_0_2772,plain,
( in(esk308_4(X1,X2,X3,X4),cartesian_product2(X2,X3))
| esk304_2(X1,X2) = subset_complement(the_carrier(X1),X5)
| ~ in(X4,esk307_3(X1,X2,X3))
| ~ element(X5,powerset(the_carrier(X1)))
| X5 != esk303_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]),
[final] ).
cnf(i_0_2773,plain,
( empty(X2)
| in(unordered_pair(unordered_pair(X4,X1),unordered_pair(X4,X4)),X3)
| in(unordered_pair(unordered_pair(esk208_2(X2,X3),X5),unordered_pair(esk208_2(X2,X3),esk208_2(X2,X3))),X3)
| ~ relation(X3)
| ~ in(X5,esk210_2(X2,X3))
| ~ in(X4,esk211_2(X2,X3))
| ~ in(X1,esk213_3(X2,X3,X4)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1337,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2774,plain,
( empty(X2)
| in(unordered_pair(unordered_pair(X4,X1),unordered_pair(X4,X4)),X3)
| in(unordered_pair(unordered_pair(esk207_2(X2,X3),X5),unordered_pair(esk207_2(X2,X3),esk207_2(X2,X3))),X3)
| ~ relation(X3)
| ~ in(X5,esk209_2(X2,X3))
| ~ in(X4,esk211_2(X2,X3))
| ~ in(X1,esk213_3(X2,X3,X4)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1338,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2775,lemma,
( esk196_2(X1,X2) = subset_complement(the_carrier(X1),X5)
| element(esk198_4(X1,X2,X3,X4),powerset(the_carrier(X1)))
| in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),esk197_2(X1,X2))
| X5 != esk194_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ in(X3,X2)
| ~ element(X5,powerset(the_carrier(X1)))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1339,c_0_944]),
[final] ).
cnf(i_0_2776,lemma,
( esk195_2(X1,X2) = subset_complement(the_carrier(X1),X5)
| element(esk198_4(X1,X2,X3,X4),powerset(the_carrier(X1)))
| in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),esk197_2(X1,X2))
| X5 != esk194_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ in(X3,X2)
| ~ element(X5,powerset(the_carrier(X1)))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1340,c_0_944]),
[final] ).
cnf(i_0_2777,plain,
( in(esk290_4(X1,X2,X3,X4),cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| esk282_2(X1,X2) = esk284_2(X1,X2)
| ~ in(X4,esk289_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]),
[final] ).
cnf(i_0_2778,plain,
( in(esk290_4(X1,X2,X3,X4),cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| esk282_2(X1,X2) = esk283_2(X1,X2)
| ~ in(X4,esk289_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]),
[final] ).
cnf(i_0_2779,lemma,
( element(esk193_4(X1,X2,X3,X4),powerset(the_carrier(X1)))
| in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),esk192_2(X1,X2))
| esk191_2(X1,X2) != esk190_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ in(X3,complements_of_subsets(the_carrier(X1),X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1341,c_0_944]),
[final] ).
cnf(i_0_2780,plain,
( in(esk320_4(X1,X2,X3,X4),cartesian_product2(X1,X1))
| ~ in(X4,esk319_3(X1,X2,X3))
| esk313_3(X1,X2,X3) != esk314_3(X1,X2,X3)
| ~ relation(X2)
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[i_0_684]),
[final] ).
cnf(i_0_2781,plain,
( in(esk291_4(X1,X2,X3,X4),complements_of_subsets(the_carrier(X1),X2))
| in(esk287_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| ~ in(X4,esk289_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]),
[final] ).
cnf(i_0_2782,plain,
( in(esk291_4(X1,X2,X3,X4),complements_of_subsets(the_carrier(X1),X2))
| in(esk285_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| ~ in(X4,esk289_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]),
[final] ).
cnf(i_0_2783,plain,
( subset(X1,X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(esk72_2(X1,X2),esk73_2(X1,X2)),unordered_pair(esk72_2(X1,X2),esk72_2(X1,X2))),X2) ),
inference(rw,[status(thm)],[i_0_1342,c_0_944]),
[final] ).
cnf(i_0_2784,plain,
( in(esk309_4(X1,X2,X3,X4),X2)
| esk306_2(X1,X2) = subset_complement(the_carrier(X1),X5)
| ~ in(X4,esk307_3(X1,X2,X3))
| ~ element(X5,powerset(the_carrier(X1)))
| X5 != esk305_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]),
[final] ).
cnf(i_0_2785,plain,
( in(esk309_4(X1,X2,X3,X4),X2)
| esk304_2(X1,X2) = subset_complement(the_carrier(X1),X5)
| ~ in(X4,esk307_3(X1,X2,X3))
| ~ element(X5,powerset(the_carrier(X1)))
| X5 != esk303_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]),
[final] ).
cnf(i_0_2786,plain,
( in(unordered_pair(unordered_pair(apply(X1,X2),apply(X1,X3)),unordered_pair(apply(X1,X2),apply(X1,X2))),X4)
| ~ function(X1)
| ~ relation(X5)
| ~ relation(X4)
| ~ relation(X1)
| ~ relation_isomorphism(X5,X4,X1)
| ~ in(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),X5) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1343,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2787,plain,
( is_reflexive_in(X1,X2)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(esk40_2(X1,X2),esk40_2(X1,X2)),unordered_pair(esk40_2(X1,X2),esk40_2(X1,X2))),X1) ),
inference(rw,[status(thm)],[i_0_1344,c_0_944]),
[final] ).
cnf(i_0_2788,plain,
( is_transitive_in(X1,X2)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(esk110_2(X1,X2),esk112_2(X1,X2)),unordered_pair(esk110_2(X1,X2),esk110_2(X1,X2))),X1) ),
inference(rw,[status(thm)],[i_0_1345,c_0_944]),
[final] ).
cnf(i_0_2789,plain,
( is_connected_in(X1,X2)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(esk96_2(X1,X2),esk95_2(X1,X2)),unordered_pair(esk96_2(X1,X2),esk96_2(X1,X2))),X1) ),
inference(rw,[status(thm)],[i_0_1346,c_0_944]),
[final] ).
cnf(i_0_2790,plain,
( is_connected_in(X1,X2)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(esk95_2(X1,X2),esk96_2(X1,X2)),unordered_pair(esk95_2(X1,X2),esk95_2(X1,X2))),X1) ),
inference(rw,[status(thm)],[i_0_1347,c_0_944]),
[final] ).
cnf(i_0_2791,plain,
( in(X3,esk249_1(X2))
| subset(X1,esk254_4(X2,X3,X4,X1))
| X3 != X5
| X3 != X4
| esk248_1(X2) != esk247_1(X2)
| ~ ordinal(X4)
| ~ ordinal(X2)
| ~ in(X1,esk253_3(X2,X3,X4))
| ~ in(X5,set_union2(X2,unordered_pair(X2,X2))) ),
inference(rw,[status(thm)],[i_0_1348,c_0_1305]),
[final] ).
cnf(i_0_2792,plain,
( in(esk332_4(X1,X2,X3,X4),powerset(relation_dom(X3)))
| esk328_3(X1,X2,X3) = esk330_3(X1,X2,X3)
| ~ in(X4,esk331_3(X1,X2,X3))
| ~ element(X2,powerset(powerset(X1)))
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1309]),
[final] ).
cnf(i_0_2793,plain,
( in(esk332_4(X1,X2,X3,X4),powerset(relation_dom(X3)))
| esk328_3(X1,X2,X3) = esk329_3(X1,X2,X3)
| ~ in(X4,esk331_3(X1,X2,X3))
| ~ element(X2,powerset(powerset(X1)))
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1309]),
[final] ).
cnf(i_0_2794,lemma,
( in(X3,esk349_1(X2))
| subset(X1,esk353_4(X2,X3,X4,X1))
| X3 != X4
| ~ ordinal(X4)
| ~ ordinal(X2)
| ~ in(X1,esk352_3(X2,X3,X4))
| ~ in(X3,set_union2(X2,unordered_pair(X2,X2))) ),
inference(rw,[status(thm)],[i_0_1349,c_0_1305]),
[final] ).
cnf(i_0_2795,plain,
( in(esk291_4(X1,X2,X3,X4),complements_of_subsets(the_carrier(X1),X2))
| ~ in(X4,esk289_3(X1,X2,X3))
| esk283_2(X1,X2) != esk284_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]),
[final] ).
cnf(i_0_2796,plain,
( in(esk308_4(X1,X2,X3,X4),cartesian_product2(X2,X3))
| ~ in(X4,esk307_3(X1,X2,X3))
| esk301_2(X1,X2) != esk302_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]),
[final] ).
cnf(i_0_2797,plain,
( in(esk291_4(X1,X2,X3,X4),complements_of_subsets(the_carrier(X1),X2))
| esk282_2(X1,X2) = esk284_2(X1,X2)
| ~ in(X4,esk289_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]),
[final] ).
cnf(i_0_2798,plain,
( in(esk291_4(X1,X2,X3,X4),complements_of_subsets(the_carrier(X1),X2))
| esk282_2(X1,X2) = esk283_2(X1,X2)
| ~ in(X4,esk289_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]),
[final] ).
cnf(i_0_2799,plain,
( in(esk308_4(X1,X2,X3,X4),cartesian_product2(X2,X3))
| in(esk305_2(X1,X2),X2)
| ~ in(X4,esk307_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]),
[final] ).
cnf(i_0_2800,plain,
( in(esk308_4(X1,X2,X3,X4),cartesian_product2(X2,X3))
| in(esk303_2(X1,X2),X2)
| ~ in(X4,esk307_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]),
[final] ).
cnf(i_0_2801,lemma,
( element(esk198_4(X1,X2,X3,X4),powerset(the_carrier(X1)))
| in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),esk197_2(X1,X2))
| esk196_2(X1,X2) != esk195_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ in(X3,X2)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1350,c_0_944]),
[final] ).
cnf(i_0_2802,lemma,
( in(esk194_2(X1,X2),X2)
| element(esk198_4(X1,X2,X3,X4),powerset(the_carrier(X1)))
| in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),esk197_2(X1,X2))
| ~ one_sorted_str(X1)
| ~ in(X3,X2)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1351,c_0_944]),
[final] ).
cnf(i_0_2803,lemma,
( in(esk194_2(X1,X2),X2)
| element(esk198_4(X1,X2,X3,X4),powerset(the_carrier(X1)))
| in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),esk197_2(X1,X2))
| ~ one_sorted_str(X1)
| ~ in(X3,X2)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1352,c_0_944]),
[final] ).
cnf(i_0_2804,plain,
( element(esk281_4(X1,X2,X3,X4),powerset(the_carrier(X1)))
| in(X3,esk279_2(X1,X2))
| esk278_2(X1,X2) = subset_complement(the_carrier(X1),X5)
| ~ in(X4,complements_of_subsets(the_carrier(X1),X2))
| ~ element(X5,powerset(the_carrier(X1)))
| X5 != esk276_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1284]),
[final] ).
cnf(i_0_2805,plain,
( element(esk281_4(X1,X2,X3,X4),powerset(the_carrier(X1)))
| in(X3,esk279_2(X1,X2))
| esk277_2(X1,X2) = subset_complement(the_carrier(X1),X5)
| ~ in(X4,complements_of_subsets(the_carrier(X1),X2))
| ~ element(X5,powerset(the_carrier(X1)))
| X5 != esk276_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1284]),
[final] ).
cnf(i_0_2806,plain,
( in(esk320_4(X1,X2,X3,X4),cartesian_product2(X1,X1))
| esk312_3(X1,X2,X3) = esk314_3(X1,X2,X3)
| ~ in(X4,esk319_3(X1,X2,X3))
| ~ relation(X2)
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[i_0_684]),
[final] ).
cnf(i_0_2807,plain,
( in(esk320_4(X1,X2,X3,X4),cartesian_product2(X1,X1))
| esk312_3(X1,X2,X3) = esk313_3(X1,X2,X3)
| ~ in(X4,esk319_3(X1,X2,X3))
| ~ relation(X2)
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[i_0_684]),
[final] ).
cnf(i_0_2808,lemma,
( in(apply(esk381_2(X1,X2),X3),esk382_3(X1,X2,X3))
| in(esk380_4(X1,X2,X4,X5),X5)
| in(esk376_2(X1,X2),esk378_2(X1,X2))
| empty(X1)
| ~ in(X3,X1)
| esk379_2(X1,X2) != X5
| ~ in(X4,X5)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_2809,lemma,
( in(apply(esk381_2(X1,X2),X3),esk382_3(X1,X2,X3))
| in(esk380_4(X1,X2,X4,X5),X5)
| in(esk375_2(X1,X2),esk377_2(X1,X2))
| empty(X1)
| ~ in(X3,X1)
| esk379_2(X1,X2) != X5
| ~ in(X4,X5)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_2810,lemma,
( empty(X2)
| in(X1,esk183_4(X2,X3,X4,X1))
| in(esk179_2(X2,X3),esk181_2(X2,X3))
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X4,X1),unordered_pair(X4,X4)),esk182_2(X2,X3)) ),
inference(rw,[status(thm)],[i_0_1353,c_0_944]),
[final] ).
cnf(i_0_2811,lemma,
( empty(X2)
| in(X1,esk183_4(X2,X3,X4,X1))
| in(esk178_2(X2,X3),esk180_2(X2,X3))
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X4,X1),unordered_pair(X4,X4)),esk182_2(X2,X3)) ),
inference(rw,[status(thm)],[i_0_1354,c_0_944]),
[final] ).
cnf(i_0_2812,plain,
( in(esk308_4(X1,X2,X3,X4),cartesian_product2(X2,X3))
| esk300_2(X1,X2) = esk302_2(X1,X2)
| ~ in(X4,esk307_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]),
[final] ).
cnf(i_0_2813,plain,
( in(esk308_4(X1,X2,X3,X4),cartesian_product2(X2,X3))
| esk300_2(X1,X2) = esk301_2(X1,X2)
| ~ in(X4,esk307_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]),
[final] ).
cnf(i_0_2814,plain,
( in(X2,esk249_1(X1))
| epred2_3(esk248_1(X1),esk247_1(X1),esk246_1(X1))
| X2 != X5
| X2 != X3
| esk254_4(X1,X2,X3,X4) != X4
| ~ ordinal(X3)
| ~ ordinal(X1)
| ~ in(X4,esk253_3(X1,X2,X3))
| ~ in(X5,set_union2(X1,unordered_pair(X1,X1))) ),
inference(rw,[status(thm)],[i_0_1355,c_0_1305]),
[final] ).
cnf(i_0_2815,plain,
( X1 = set_difference(esk275_3(X2,X3,X1),unordered_pair(X2,X2))
| esk270_2(X2,X3) = set_difference(esk272_2(X2,X3),unordered_pair(X2,X2))
| ~ ordinal(X2)
| ~ in(X1,esk273_2(X2,X3))
| ~ element(X3,powerset(powerset(set_union2(X2,unordered_pair(X2,X2))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1356,c_0_681]),c_0_681]),c_0_1305]),
[final] ).
cnf(i_0_2816,plain,
( X1 = set_difference(esk275_3(X2,X3,X1),unordered_pair(X2,X2))
| esk269_2(X2,X3) = set_difference(esk271_2(X2,X3),unordered_pair(X2,X2))
| ~ ordinal(X2)
| ~ in(X1,esk273_2(X2,X3))
| ~ element(X3,powerset(powerset(set_union2(X2,unordered_pair(X2,X2))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1357,c_0_681]),c_0_681]),c_0_1305]),
[final] ).
cnf(i_0_2817,plain,
( in(esk309_4(X1,X2,X3,X4),X2)
| ~ in(X4,esk307_3(X1,X2,X3))
| esk301_2(X1,X2) != esk302_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]),
[final] ).
cnf(i_0_2818,plain,
( in(esk309_4(X1,X2,X3,X4),X2)
| in(esk305_2(X1,X2),X2)
| ~ in(X4,esk307_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]),
[final] ).
cnf(i_0_2819,plain,
( in(esk309_4(X1,X2,X3,X4),X2)
| in(esk303_2(X1,X2),X2)
| ~ in(X4,esk307_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]),
[final] ).
cnf(i_0_2820,lemma,
( in(esk360_4(X1,X2,X3,X4),complements_of_subsets(the_carrier(X1),X2))
| ~ in(X4,esk359_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_687]),
[final] ).
cnf(i_0_2821,lemma,
( in(apply(esk381_2(X1,X2),X3),esk382_3(X1,X2,X3))
| in(esk380_4(X1,X2,X4,X5),X5)
| empty(X1)
| ~ in(X3,X1)
| esk379_2(X1,X2) != X5
| ~ in(X4,X5)
| esk375_2(X1,X2) != esk376_2(X1,X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_2822,lemma,
( empty(X2)
| in(X1,esk183_4(X2,X3,X4,X1))
| esk179_2(X2,X3) != esk178_2(X2,X3)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X4,X1),unordered_pair(X4,X4)),esk182_2(X2,X3)) ),
inference(rw,[status(thm)],[i_0_1358,c_0_944]),
[final] ).
cnf(i_0_2823,lemma,
( in(apply(esk381_2(X1,X2),X3),esk382_3(X1,X2,X3))
| in(esk380_4(X1,X2,X4,X5),X5)
| in(esk374_2(X1,X2),X1)
| empty(X1)
| ~ in(X3,X1)
| esk379_2(X1,X2) != X5
| ~ in(X4,X5)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_2824,lemma,
( empty(X2)
| in(esk177_2(X2,X3),X2)
| in(X1,esk183_4(X2,X3,X4,X1))
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X4,X1),unordered_pair(X4,X4)),esk182_2(X2,X3)) ),
inference(rw,[status(thm)],[i_0_1359,c_0_944]),
[final] ).
cnf(i_0_2825,lemma,
( empty(X2)
| in(esk177_2(X2,X3),X2)
| in(X1,esk183_4(X2,X3,X4,X1))
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X4,X1),unordered_pair(X4,X4)),esk182_2(X2,X3)) ),
inference(rw,[status(thm)],[i_0_1360,c_0_944]),
[final] ).
cnf(i_0_2826,plain,
( element(esk281_4(X1,X2,X3,X4),powerset(the_carrier(X1)))
| in(X3,esk279_2(X1,X2))
| in(esk276_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| ~ in(X4,complements_of_subsets(the_carrier(X1),X2))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1284]),
[final] ).
cnf(i_0_2827,plain,
( element(esk281_4(X1,X2,X3,X4),powerset(the_carrier(X1)))
| in(X3,esk279_2(X1,X2))
| in(esk276_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| ~ in(X4,complements_of_subsets(the_carrier(X1),X2))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1284]),
[final] ).
cnf(i_0_2828,plain,
( esk308_4(X1,X2,X3,X4) = X4
| unordered_pair(unordered_pair(esk305_2(X1,X2),esk306_2(X1,X2)),unordered_pair(esk305_2(X1,X2),esk305_2(X1,X2))) = esk302_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ in(X4,esk307_3(X1,X2,X3))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1361,c_0_944]),
[final] ).
cnf(i_0_2829,plain,
( esk308_4(X1,X2,X3,X4) = X4
| unordered_pair(unordered_pair(esk303_2(X1,X2),esk304_2(X1,X2)),unordered_pair(esk303_2(X1,X2),esk303_2(X1,X2))) = esk301_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ in(X4,esk307_3(X1,X2,X3))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1362,c_0_944]),
[final] ).
cnf(i_0_2830,plain,
( esk290_4(X1,X2,X3,X4) = X4
| unordered_pair(unordered_pair(esk287_2(X1,X2),esk288_2(X1,X2)),unordered_pair(esk287_2(X1,X2),esk287_2(X1,X2))) = esk284_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ in(X4,esk289_3(X1,X2,X3))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1363,c_0_944]),
[final] ).
cnf(i_0_2831,plain,
( esk290_4(X1,X2,X3,X4) = X4
| unordered_pair(unordered_pair(esk285_2(X1,X2),esk286_2(X1,X2)),unordered_pair(esk285_2(X1,X2),esk285_2(X1,X2))) = esk283_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ in(X4,esk289_3(X1,X2,X3))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1364,c_0_944]),
[final] ).
cnf(i_0_2832,plain,
( in(esk309_4(X1,X2,X3,X4),X2)
| esk300_2(X1,X2) = esk302_2(X1,X2)
| ~ in(X4,esk307_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]),
[final] ).
cnf(i_0_2833,plain,
( in(esk309_4(X1,X2,X3,X4),X2)
| esk300_2(X1,X2) = esk301_2(X1,X2)
| ~ in(X4,esk307_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]),
[final] ).
cnf(i_0_2834,plain,
( X3 = relation_inverse_image(X1,X2)
| ~ in(esk10_3(X1,X2,X3),X3)
| ~ in(esk10_3(X1,X2,X3),relation_dom(X1))
| ~ in(apply(X1,esk10_3(X1,X2,X3)),X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1365]),
[final] ).
cnf(i_0_2835,plain,
( esk270_2(X1,X2) = set_difference(esk272_2(X1,X2),unordered_pair(X1,X1))
| in(esk274_3(X1,X2,X3),powerset(X1))
| ~ ordinal(X1)
| ~ in(X3,esk273_2(X1,X2))
| ~ element(X2,powerset(powerset(set_union2(X1,unordered_pair(X1,X1))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1366,c_0_681]),c_0_1305]),
[final] ).
cnf(i_0_2836,plain,
( esk269_2(X1,X2) = set_difference(esk271_2(X1,X2),unordered_pair(X1,X1))
| in(esk274_3(X1,X2,X3),powerset(X1))
| ~ ordinal(X1)
| ~ in(X3,esk273_2(X1,X2))
| ~ element(X2,powerset(powerset(set_union2(X1,unordered_pair(X1,X1))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1367,c_0_681]),c_0_1305]),
[final] ).
cnf(i_0_2837,lemma,
( in(apply(esk381_2(X1,X2),X3),esk382_3(X1,X2,X3))
| in(esk380_4(X1,X2,X4,X5),X5)
| esk374_2(X1,X2) = esk378_2(X1,X2)
| empty(X1)
| ~ in(X3,X1)
| esk379_2(X1,X2) != X5
| ~ in(X4,X5)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_2838,lemma,
( in(apply(esk381_2(X1,X2),X3),esk382_3(X1,X2,X3))
| in(esk380_4(X1,X2,X4,X5),X5)
| esk374_2(X1,X2) = esk377_2(X1,X2)
| empty(X1)
| ~ in(X3,X1)
| esk379_2(X1,X2) != X5
| ~ in(X4,X5)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_2839,lemma,
( esk181_2(X2,X3) = esk177_2(X2,X3)
| empty(X2)
| in(X1,esk183_4(X2,X3,X4,X1))
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X4,X1),unordered_pair(X4,X4)),esk182_2(X2,X3)) ),
inference(rw,[status(thm)],[i_0_1368,c_0_944]),
[final] ).
cnf(i_0_2840,lemma,
( esk180_2(X2,X3) = esk177_2(X2,X3)
| empty(X2)
| in(X1,esk183_4(X2,X3,X4,X1))
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X4,X1),unordered_pair(X4,X4)),esk182_2(X2,X3)) ),
inference(rw,[status(thm)],[i_0_1369,c_0_944]),
[final] ).
cnf(i_0_2841,plain,
( esk270_2(X1,X2) = set_difference(esk272_2(X1,X2),unordered_pair(X1,X1))
| in(esk275_3(X1,X2,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,esk273_2(X1,X2))
| ~ element(X2,powerset(powerset(set_union2(X1,unordered_pair(X1,X1))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1370,c_0_681]),c_0_1305]),
[final] ).
cnf(i_0_2842,plain,
( esk269_2(X1,X2) = set_difference(esk271_2(X1,X2),unordered_pair(X1,X1))
| in(esk275_3(X1,X2,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,esk273_2(X1,X2))
| ~ element(X2,powerset(powerset(set_union2(X1,unordered_pair(X1,X1))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1371,c_0_681]),c_0_1305]),
[final] ).
cnf(i_0_2843,lemma,
( empty(X2)
| in(X1,X2)
| in(unordered_pair(unordered_pair(esk179_2(X2,X4),X5),unordered_pair(esk179_2(X2,X4),esk179_2(X2,X4))),X4)
| ~ relation(X4)
| ~ in(X5,esk181_2(X2,X4))
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),esk182_2(X2,X4)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1372,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2844,lemma,
( empty(X2)
| in(X1,X2)
| in(unordered_pair(unordered_pair(esk178_2(X2,X4),X5),unordered_pair(esk178_2(X2,X4),esk178_2(X2,X4))),X4)
| ~ relation(X4)
| ~ in(X5,esk180_2(X2,X4))
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),esk182_2(X2,X4)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1373,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2845,plain,
( X1 = set_difference(esk275_3(X2,X3,X1),unordered_pair(X2,X2))
| esk270_2(X2,X3) != esk269_2(X2,X3)
| ~ ordinal(X2)
| ~ in(X1,esk273_2(X2,X3))
| ~ element(X3,powerset(powerset(set_union2(X2,unordered_pair(X2,X2))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1374,c_0_681]),c_0_1305]),
[final] ).
cnf(i_0_2846,plain,
( in(esk225_4(X1,X2,X3,X4),cartesian_product2(X1,X3))
| in(esk222_2(X1,X2),esk223_2(X1,X2))
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]),
[final] ).
cnf(i_0_2847,plain,
( in(esk225_4(X1,X2,X3,X4),cartesian_product2(X1,X3))
| in(esk219_2(X1,X2),esk220_2(X1,X2))
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]),
[final] ).
cnf(i_0_2848,plain,
( X1 = set_difference(esk275_3(X2,X3,X1),unordered_pair(X2,X2))
| in(esk272_2(X2,X3),X3)
| ~ ordinal(X2)
| ~ in(X1,esk273_2(X2,X3))
| ~ element(X3,powerset(powerset(set_union2(X2,unordered_pair(X2,X2))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1375,c_0_681]),c_0_1305]),
[final] ).
cnf(i_0_2849,plain,
( X1 = set_difference(esk275_3(X2,X3,X1),unordered_pair(X2,X2))
| in(esk271_2(X2,X3),X3)
| ~ ordinal(X2)
| ~ in(X1,esk273_2(X2,X3))
| ~ element(X3,powerset(powerset(set_union2(X2,unordered_pair(X2,X2))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1376,c_0_681]),c_0_1305]),
[final] ).
cnf(i_0_2850,plain,
( element(esk299_4(X1,X2,X3,X4),powerset(the_carrier(X1)))
| in(X3,esk297_2(X1,X2))
| esk296_2(X1,X2) = subset_complement(the_carrier(X1),X5)
| ~ in(X4,X2)
| ~ element(X5,powerset(the_carrier(X1)))
| X5 != esk294_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1303]),
[final] ).
cnf(i_0_2851,plain,
( element(esk299_4(X1,X2,X3,X4),powerset(the_carrier(X1)))
| in(X3,esk297_2(X1,X2))
| esk295_2(X1,X2) = subset_complement(the_carrier(X1),X5)
| ~ in(X4,X2)
| ~ element(X5,powerset(the_carrier(X1)))
| X5 != esk294_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1303]),
[final] ).
cnf(i_0_2852,lemma,
( in(esk364_4(X1,X2,X3,X4),X2)
| ~ in(X4,esk363_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_688]),
[final] ).
cnf(i_0_2853,lemma,
( empty(X1)
| in(esk379_2(X1,X2),X1)
| in(apply(esk381_2(X1,X2),X3),esk382_3(X1,X2,X3))
| in(unordered_pair(unordered_pair(esk376_2(X1,X2),X4),unordered_pair(esk376_2(X1,X2),esk376_2(X1,X2))),X2)
| ~ relation(X2)
| ~ in(X3,X1)
| ~ in(X4,esk378_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1377,c_0_944]),
[final] ).
cnf(i_0_2854,lemma,
( empty(X1)
| in(esk379_2(X1,X2),X1)
| in(apply(esk381_2(X1,X2),X3),esk382_3(X1,X2,X3))
| in(unordered_pair(unordered_pair(esk375_2(X1,X2),X4),unordered_pair(esk375_2(X1,X2),esk375_2(X1,X2))),X2)
| ~ relation(X2)
| ~ in(X3,X1)
| ~ in(X4,esk377_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1378,c_0_944]),
[final] ).
cnf(i_0_2855,plain,
( esk270_2(X2,X5) = set_difference(esk272_2(X2,X5),unordered_pair(X2,X2))
| in(X3,esk273_2(X2,X5))
| X1 != X3
| X3 != set_difference(X4,unordered_pair(X2,X2))
| ~ ordinal(X2)
| ~ in(X4,X5)
| ~ in(X1,powerset(X2))
| ~ element(X5,powerset(powerset(set_union2(X2,unordered_pair(X2,X2))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1379,c_0_681]),c_0_681]),c_0_1305]),
[final] ).
cnf(i_0_2856,plain,
( esk269_2(X2,X5) = set_difference(esk271_2(X2,X5),unordered_pair(X2,X2))
| in(X3,esk273_2(X2,X5))
| X1 != X3
| X3 != set_difference(X4,unordered_pair(X2,X2))
| ~ ordinal(X2)
| ~ in(X4,X5)
| ~ in(X1,powerset(X2))
| ~ element(X5,powerset(powerset(set_union2(X2,unordered_pair(X2,X2))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1380,c_0_681]),c_0_681]),c_0_1305]),
[final] ).
cnf(i_0_2857,plain,
( X2 = relation_dom(X1)
| ~ relation(X1)
| ~ in(esk79_2(X1,X2),X2)
| ~ in(unordered_pair(unordered_pair(esk79_2(X1,X2),X3),unordered_pair(esk79_2(X1,X2),esk79_2(X1,X2))),X1) ),
inference(rw,[status(thm)],[i_0_1381,c_0_944]),
[final] ).
cnf(i_0_2858,plain,
( element(esk281_4(X1,X2,X3,X4),powerset(the_carrier(X1)))
| in(X3,esk279_2(X1,X2))
| ~ in(X4,complements_of_subsets(the_carrier(X1),X2))
| esk277_2(X1,X2) != esk278_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1284]),
[final] ).
cnf(i_0_2859,plain,
( esk270_2(X2,X3) = esk268_2(X2,X3)
| X1 = set_difference(esk275_3(X2,X3,X1),unordered_pair(X2,X2))
| ~ ordinal(X2)
| ~ in(X1,esk273_2(X2,X3))
| ~ element(X3,powerset(powerset(set_union2(X2,unordered_pair(X2,X2))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1382,c_0_681]),c_0_1305]),
[final] ).
cnf(i_0_2860,plain,
( esk269_2(X2,X3) = esk268_2(X2,X3)
| X1 = set_difference(esk275_3(X2,X3,X1),unordered_pair(X2,X2))
| ~ ordinal(X2)
| ~ in(X1,esk273_2(X2,X3))
| ~ element(X3,powerset(powerset(set_union2(X2,unordered_pair(X2,X2))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1383,c_0_681]),c_0_1305]),
[final] ).
cnf(i_0_2861,plain,
( in(esk274_3(X1,X2,X3),powerset(X1))
| esk270_2(X1,X2) != esk269_2(X1,X2)
| ~ ordinal(X1)
| ~ in(X3,esk273_2(X1,X2))
| ~ element(X2,powerset(powerset(set_union2(X1,unordered_pair(X1,X1))))) ),
inference(rw,[status(thm)],[i_0_1384,c_0_1305]),
[final] ).
cnf(i_0_2862,plain,
( in(X2,esk249_1(X1))
| X2 != X5
| X2 != X3
| esk248_1(X1) != esk247_1(X1)
| esk254_4(X1,X2,X3,X4) != X4
| ~ ordinal(X3)
| ~ ordinal(X1)
| ~ in(X4,esk253_3(X1,X2,X3))
| ~ in(X5,set_union2(X1,unordered_pair(X1,X1))) ),
inference(rw,[status(thm)],[i_0_1385,c_0_1305]),
[final] ).
cnf(i_0_2863,plain,
( in(esk225_4(X1,X2,X3,X4),cartesian_product2(X1,X3))
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| esk216_2(X1,X2) != esk217_2(X1,X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]),
[final] ).
cnf(i_0_2864,plain,
( in(esk272_2(X1,X2),X2)
| in(esk274_3(X1,X2,X3),powerset(X1))
| ~ ordinal(X1)
| ~ in(X3,esk273_2(X1,X2))
| ~ element(X2,powerset(powerset(set_union2(X1,unordered_pair(X1,X1))))) ),
inference(rw,[status(thm)],[i_0_1386,c_0_1305]),
[final] ).
cnf(i_0_2865,plain,
( in(esk271_2(X1,X2),X2)
| in(esk274_3(X1,X2,X3),powerset(X1))
| ~ ordinal(X1)
| ~ in(X3,esk273_2(X1,X2))
| ~ element(X2,powerset(powerset(set_union2(X1,unordered_pair(X1,X1))))) ),
inference(rw,[status(thm)],[i_0_1387,c_0_1305]),
[final] ).
cnf(i_0_2866,plain,
( in(esk275_3(X1,X2,X3),X2)
| esk270_2(X1,X2) != esk269_2(X1,X2)
| ~ ordinal(X1)
| ~ in(X3,esk273_2(X1,X2))
| ~ element(X2,powerset(powerset(set_union2(X1,unordered_pair(X1,X1))))) ),
inference(rw,[status(thm)],[i_0_1388,c_0_1305]),
[final] ).
cnf(i_0_2867,plain,
( in(esk226_4(X1,X2,X3,X4),X1)
| in(esk222_2(X1,X2),esk223_2(X1,X2))
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]),
[final] ).
cnf(i_0_2868,plain,
( in(esk226_4(X1,X2,X3,X4),X1)
| in(esk219_2(X1,X2),esk220_2(X1,X2))
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]),
[final] ).
cnf(i_0_2869,plain,
( in(esk225_4(X1,X2,X3,X4),cartesian_product2(X1,X3))
| in(esk221_2(X1,X2),X1)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]),
[final] ).
cnf(i_0_2870,plain,
( in(esk225_4(X1,X2,X3,X4),cartesian_product2(X1,X3))
| in(esk218_2(X1,X2),X1)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]),
[final] ).
cnf(i_0_2871,plain,
( in(esk272_2(X1,X2),X2)
| in(esk275_3(X1,X2,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,esk273_2(X1,X2))
| ~ element(X2,powerset(powerset(set_union2(X1,unordered_pair(X1,X1))))) ),
inference(rw,[status(thm)],[i_0_1389,c_0_1305]),
[final] ).
cnf(i_0_2872,plain,
( in(esk271_2(X1,X2),X2)
| in(esk275_3(X1,X2,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,esk273_2(X1,X2))
| ~ element(X2,powerset(powerset(set_union2(X1,unordered_pair(X1,X1))))) ),
inference(rw,[status(thm)],[i_0_1390,c_0_1305]),
[final] ).
cnf(i_0_2873,plain,
( esk270_2(X1,X2) = esk268_2(X1,X2)
| in(esk274_3(X1,X2,X3),powerset(X1))
| ~ ordinal(X1)
| ~ in(X3,esk273_2(X1,X2))
| ~ element(X2,powerset(powerset(set_union2(X1,unordered_pair(X1,X1))))) ),
inference(rw,[status(thm)],[i_0_1391,c_0_1305]),
[final] ).
cnf(i_0_2874,plain,
( esk269_2(X1,X2) = esk268_2(X1,X2)
| in(esk274_3(X1,X2,X3),powerset(X1))
| ~ ordinal(X1)
| ~ in(X3,esk273_2(X1,X2))
| ~ element(X2,powerset(powerset(set_union2(X1,unordered_pair(X1,X1))))) ),
inference(rw,[status(thm)],[i_0_1392,c_0_1305]),
[final] ).
cnf(i_0_2875,lemma,
( in(X2,esk349_1(X1))
| X2 != X3
| esk353_4(X1,X2,X3,X4) != X4
| ~ ordinal(X3)
| ~ ordinal(X1)
| ~ in(X4,esk352_3(X1,X2,X3))
| ~ in(X2,set_union2(X1,unordered_pair(X1,X1))) ),
inference(rw,[status(thm)],[i_0_1393,c_0_1305]),
[final] ).
cnf(i_0_2876,plain,
( esk226_4(X1,X2,X3,X4) = esk228_4(X1,X2,X3,X4)
| in(esk222_2(X1,X2),esk223_2(X1,X2))
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]),
[final] ).
cnf(i_0_2877,plain,
( esk226_4(X1,X2,X3,X4) = esk228_4(X1,X2,X3,X4)
| in(esk219_2(X1,X2),esk220_2(X1,X2))
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]),
[final] ).
cnf(i_0_2878,plain,
( in(esk225_4(X1,X2,X3,X4),cartesian_product2(X1,X3))
| esk221_2(X1,X2) = esk223_2(X1,X2)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]),
[final] ).
cnf(i_0_2879,plain,
( in(esk225_4(X1,X2,X3,X4),cartesian_product2(X1,X3))
| esk218_2(X1,X2) = esk220_2(X1,X2)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]),
[final] ).
cnf(i_0_2880,plain,
( in(esk225_4(X1,X2,X3,X4),cartesian_product2(X1,X3))
| esk215_2(X1,X2) = esk217_2(X1,X2)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]),
[final] ).
cnf(i_0_2881,plain,
( in(esk225_4(X1,X2,X3,X4),cartesian_product2(X1,X3))
| esk215_2(X1,X2) = esk216_2(X1,X2)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]),
[final] ).
cnf(i_0_2882,plain,
( esk270_2(X1,X2) = esk268_2(X1,X2)
| in(esk275_3(X1,X2,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,esk273_2(X1,X2))
| ~ element(X2,powerset(powerset(set_union2(X1,unordered_pair(X1,X1))))) ),
inference(rw,[status(thm)],[i_0_1394,c_0_1305]),
[final] ).
cnf(i_0_2883,plain,
( esk269_2(X1,X2) = esk268_2(X1,X2)
| in(esk275_3(X1,X2,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,esk273_2(X1,X2))
| ~ element(X2,powerset(powerset(set_union2(X1,unordered_pair(X1,X1))))) ),
inference(rw,[status(thm)],[i_0_1395,c_0_1305]),
[final] ).
cnf(i_0_2884,lemma,
( X1 = set_difference(esk358_3(X2,X3,X1),unordered_pair(X2,X2))
| ~ ordinal(X2)
| ~ in(X1,esk357_2(X2,X3))
| ~ element(X3,powerset(powerset(set_union2(X2,unordered_pair(X2,X2))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1396,c_0_681]),c_0_1305]),
[final] ).
cnf(i_0_2885,plain,
( esk332_4(X1,X2,X3,X4) = X4
| in(relation_image(X3,esk330_3(X1,X2,X3)),X2)
| ~ in(X4,esk331_3(X1,X2,X3))
| ~ element(X2,powerset(powerset(X1)))
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1309]),
[final] ).
cnf(i_0_2886,plain,
( esk332_4(X1,X2,X3,X4) = X4
| in(relation_image(X3,esk329_3(X1,X2,X3)),X2)
| ~ in(X4,esk331_3(X1,X2,X3))
| ~ element(X2,powerset(powerset(X1)))
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1309]),
[final] ).
cnf(i_0_2887,plain,
( in(X3,esk273_2(X2,X5))
| X1 != X3
| X3 != set_difference(X4,unordered_pair(X2,X2))
| esk270_2(X2,X5) != esk269_2(X2,X5)
| ~ ordinal(X2)
| ~ in(X4,X5)
| ~ in(X1,powerset(X2))
| ~ element(X5,powerset(powerset(set_union2(X2,unordered_pair(X2,X2))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1397,c_0_681]),c_0_1305]),
[final] ).
cnf(i_0_2888,plain,
( in(esk226_4(X1,X2,X3,X4),X1)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| esk216_2(X1,X2) != esk217_2(X1,X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]),
[final] ).
cnf(i_0_2889,plain,
( in(X3,esk273_2(X2,X5))
| in(esk272_2(X2,X5),X5)
| X1 != X3
| X3 != set_difference(X4,unordered_pair(X2,X2))
| ~ ordinal(X2)
| ~ in(X4,X5)
| ~ in(X1,powerset(X2))
| ~ element(X5,powerset(powerset(set_union2(X2,unordered_pair(X2,X2))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1398,c_0_681]),c_0_1305]),
[final] ).
cnf(i_0_2890,plain,
( in(X3,esk273_2(X2,X5))
| in(esk271_2(X2,X5),X5)
| X1 != X3
| X3 != set_difference(X4,unordered_pair(X2,X2))
| ~ ordinal(X2)
| ~ in(X4,X5)
| ~ in(X1,powerset(X2))
| ~ element(X5,powerset(powerset(set_union2(X2,unordered_pair(X2,X2))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1399,c_0_681]),c_0_1305]),
[final] ).
cnf(i_0_2891,plain,
( in(esk226_4(X1,X2,X3,X4),X1)
| in(esk221_2(X1,X2),X1)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]),
[final] ).
cnf(i_0_2892,plain,
( in(esk226_4(X1,X2,X3,X4),X1)
| in(esk218_2(X1,X2),X1)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]),
[final] ).
cnf(i_0_2893,plain,
( esk274_3(X1,X2,X3) = X3
| esk270_2(X1,X2) = set_difference(esk272_2(X1,X2),unordered_pair(X1,X1))
| ~ ordinal(X1)
| ~ in(X3,esk273_2(X1,X2))
| ~ element(X2,powerset(powerset(set_union2(X1,unordered_pair(X1,X1))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1400,c_0_681]),c_0_1305]),
[final] ).
cnf(i_0_2894,plain,
( esk274_3(X1,X2,X3) = X3
| esk269_2(X1,X2) = set_difference(esk271_2(X1,X2),unordered_pair(X1,X1))
| ~ ordinal(X1)
| ~ in(X3,esk273_2(X1,X2))
| ~ element(X2,powerset(powerset(set_union2(X1,unordered_pair(X1,X1))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1401,c_0_681]),c_0_1305]),
[final] ).
cnf(i_0_2895,plain,
( esk226_4(X1,X2,X3,X4) = esk228_4(X1,X2,X3,X4)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| esk216_2(X1,X2) != esk217_2(X1,X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]),
[final] ).
cnf(i_0_2896,plain,
( esk270_2(X2,X5) = esk268_2(X2,X5)
| in(X3,esk273_2(X2,X5))
| X1 != X3
| X3 != set_difference(X4,unordered_pair(X2,X2))
| ~ ordinal(X2)
| ~ in(X4,X5)
| ~ in(X1,powerset(X2))
| ~ element(X5,powerset(powerset(set_union2(X2,unordered_pair(X2,X2))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1402,c_0_681]),c_0_1305]),
[final] ).
cnf(i_0_2897,plain,
( esk269_2(X2,X5) = esk268_2(X2,X5)
| in(X3,esk273_2(X2,X5))
| X1 != X3
| X3 != set_difference(X4,unordered_pair(X2,X2))
| ~ ordinal(X2)
| ~ in(X4,X5)
| ~ in(X1,powerset(X2))
| ~ element(X5,powerset(powerset(set_union2(X2,unordered_pair(X2,X2))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1403,c_0_681]),c_0_1305]),
[final] ).
cnf(i_0_2898,plain,
( esk225_4(X1,X2,X3,X4) = X4
| unordered_pair(unordered_pair(esk221_2(X1,X2),esk222_2(X1,X2)),unordered_pair(esk221_2(X1,X2),esk221_2(X1,X2))) = esk217_2(X1,X2)
| empty(X1)
| ~ relation(X2)
| ~ in(X4,esk224_3(X1,X2,X3)) ),
inference(rw,[status(thm)],[i_0_1404,c_0_944]),
[final] ).
cnf(i_0_2899,plain,
( esk225_4(X1,X2,X3,X4) = X4
| unordered_pair(unordered_pair(esk218_2(X1,X2),esk219_2(X1,X2)),unordered_pair(esk218_2(X1,X2),esk218_2(X1,X2))) = esk216_2(X1,X2)
| empty(X1)
| ~ relation(X2)
| ~ in(X4,esk224_3(X1,X2,X3)) ),
inference(rw,[status(thm)],[i_0_1405,c_0_944]),
[final] ).
cnf(i_0_2900,plain,
( esk226_4(X1,X2,X3,X4) = esk228_4(X1,X2,X3,X4)
| in(esk221_2(X1,X2),X1)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]),
[final] ).
cnf(i_0_2901,plain,
( esk226_4(X1,X2,X3,X4) = esk228_4(X1,X2,X3,X4)
| in(esk218_2(X1,X2),X1)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]),
[final] ).
cnf(i_0_2902,plain,
( in(esk226_4(X1,X2,X3,X4),X1)
| esk221_2(X1,X2) = esk223_2(X1,X2)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]),
[final] ).
cnf(i_0_2903,plain,
( in(esk226_4(X1,X2,X3,X4),X1)
| esk218_2(X1,X2) = esk220_2(X1,X2)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]),
[final] ).
cnf(i_0_2904,plain,
( in(esk226_4(X1,X2,X3,X4),X1)
| esk215_2(X1,X2) = esk217_2(X1,X2)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]),
[final] ).
cnf(i_0_2905,plain,
( in(esk226_4(X1,X2,X3,X4),X1)
| esk215_2(X1,X2) = esk216_2(X1,X2)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]),
[final] ).
cnf(i_0_2906,lemma,
( in(esk358_3(X1,X2,X3),X2)
| ~ ordinal(X1)
| ~ in(X3,esk357_2(X1,X2))
| ~ element(X2,powerset(powerset(set_union2(X1,unordered_pair(X1,X1))))) ),
inference(rw,[status(thm)],[i_0_1406,c_0_1305]),
[final] ).
cnf(i_0_2907,plain,
( element(esk299_4(X1,X2,X3,X4),powerset(the_carrier(X1)))
| in(X3,esk297_2(X1,X2))
| ~ in(X4,X2)
| esk295_2(X1,X2) != esk296_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1303]),
[final] ).
cnf(i_0_2908,plain,
( element(esk299_4(X1,X2,X3,X4),powerset(the_carrier(X1)))
| in(X3,esk297_2(X1,X2))
| in(esk294_2(X1,X2),X2)
| ~ in(X4,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1303]),
[final] ).
cnf(i_0_2909,plain,
( element(esk299_4(X1,X2,X3,X4),powerset(the_carrier(X1)))
| in(X3,esk297_2(X1,X2))
| in(esk294_2(X1,X2),X2)
| ~ in(X4,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1303]),
[final] ).
cnf(i_0_2910,plain,
( esk226_4(X1,X2,X3,X4) = esk228_4(X1,X2,X3,X4)
| esk221_2(X1,X2) = esk223_2(X1,X2)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]),
[final] ).
cnf(i_0_2911,plain,
( esk226_4(X1,X2,X3,X4) = esk228_4(X1,X2,X3,X4)
| esk218_2(X1,X2) = esk220_2(X1,X2)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]),
[final] ).
cnf(i_0_2912,plain,
( esk226_4(X1,X2,X3,X4) = esk228_4(X1,X2,X3,X4)
| esk215_2(X1,X2) = esk217_2(X1,X2)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]),
[final] ).
cnf(i_0_2913,plain,
( esk226_4(X1,X2,X3,X4) = esk228_4(X1,X2,X3,X4)
| esk215_2(X1,X2) = esk216_2(X1,X2)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]),
[final] ).
cnf(i_0_2914,plain,
( X1 = boole_lattice(X2)
| apply_binary(the_L_join(X1),esk30_2(X2,X1),esk31_2(X2,X1)) != subset_union2(X2,esk30_2(X2,X1),esk31_2(X2,X1))
| apply_binary(the_L_meet(X1),esk30_2(X2,X1),esk31_2(X2,X1)) != subset_intersection2(X2,esk30_2(X2,X1),esk31_2(X2,X1))
| the_carrier(X1) != powerset(X2)
| ~ strict_latt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1407]),
[final] ).
cnf(i_0_2915,plain,
( empty(X1)
| in(esk212_3(X1,X2,X3),X1)
| in(unordered_pair(unordered_pair(esk208_2(X1,X2),X4),unordered_pair(esk208_2(X1,X2),esk208_2(X1,X2))),X2)
| ~ relation(X2)
| ~ in(X4,esk210_2(X1,X2))
| ~ in(X3,esk211_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1408,c_0_944]),
[final] ).
cnf(i_0_2916,plain,
( empty(X1)
| in(esk212_3(X1,X2,X3),X1)
| in(unordered_pair(unordered_pair(esk207_2(X1,X2),X4),unordered_pair(esk207_2(X1,X2),esk207_2(X1,X2))),X2)
| ~ relation(X2)
| ~ in(X4,esk209_2(X1,X2))
| ~ in(X3,esk211_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1409,c_0_944]),
[final] ).
cnf(i_0_2917,plain,
( empty(X2)
| in(X1,esk213_3(X2,X3,X1))
| in(unordered_pair(unordered_pair(esk208_2(X2,X3),X4),unordered_pair(esk208_2(X2,X3),esk208_2(X2,X3))),X3)
| ~ relation(X3)
| ~ in(X4,esk210_2(X2,X3))
| ~ in(X1,esk211_2(X2,X3)) ),
inference(rw,[status(thm)],[i_0_1410,c_0_944]),
[final] ).
cnf(i_0_2918,plain,
( empty(X2)
| in(X1,esk213_3(X2,X3,X1))
| in(unordered_pair(unordered_pair(esk207_2(X2,X3),X4),unordered_pair(esk207_2(X2,X3),esk207_2(X2,X3))),X3)
| ~ relation(X3)
| ~ in(X4,esk209_2(X2,X3))
| ~ in(X1,esk211_2(X2,X3)) ),
inference(rw,[status(thm)],[i_0_1411,c_0_944]),
[final] ).
cnf(i_0_2919,plain,
( empty(X1)
| element(apply_as_element(X1,X3,X2,X4),X3)
| ~ function(X2)
| ~ quasi_total(X2,X1,X3)
| ~ relation_of2(X2,X1,X3)
| ~ element(X4,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1412]),
[final] ).
cnf(i_0_2920,plain,
( esk274_3(X1,X2,X3) = X3
| esk270_2(X1,X2) != esk269_2(X1,X2)
| ~ ordinal(X1)
| ~ in(X3,esk273_2(X1,X2))
| ~ element(X2,powerset(powerset(set_union2(X1,unordered_pair(X1,X1))))) ),
inference(rw,[status(thm)],[i_0_1413,c_0_1305]),
[final] ).
cnf(i_0_2921,lemma,
( X1 = esk382_3(X2,X3,X1)
| in(esk380_4(X2,X3,X4,X5),X5)
| in(esk376_2(X2,X3),esk378_2(X2,X3))
| empty(X2)
| ~ in(X1,X2)
| esk379_2(X2,X3) != X5
| ~ in(X4,X5)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_2922,lemma,
( X1 = esk382_3(X2,X3,X1)
| in(esk380_4(X2,X3,X4,X5),X5)
| in(esk375_2(X2,X3),esk377_2(X2,X3))
| empty(X2)
| ~ in(X1,X2)
| esk379_2(X2,X3) != X5
| ~ in(X4,X5)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_2923,lemma,
( in(esk342_4(X1,X2,X3,X4),X1)
| empty(X1)
| ~ in(X4,esk341_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_682]),
[final] ).
cnf(i_0_2924,lemma,
( esk193_4(X1,X2,X3,X4) = X3
| esk191_2(X1,X2) = subset_complement(the_carrier(X1),X5)
| in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),esk192_2(X1,X2))
| X5 != esk189_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X5,powerset(the_carrier(X1)))
| ~ in(X3,complements_of_subsets(the_carrier(X1),X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1414,c_0_944]),
[final] ).
cnf(i_0_2925,lemma,
( esk193_4(X1,X2,X3,X4) = X3
| esk190_2(X1,X2) = subset_complement(the_carrier(X1),X5)
| in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),esk192_2(X1,X2))
| X5 != esk189_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X5,powerset(the_carrier(X1)))
| ~ in(X3,complements_of_subsets(the_carrier(X1),X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1415,c_0_944]),
[final] ).
cnf(i_0_2926,lemma,
( in(X1,esk357_2(X2,X4))
| X1 != set_difference(X3,unordered_pair(X2,X2))
| ~ ordinal(X2)
| ~ in(X3,X4)
| ~ in(X1,powerset(X2))
| ~ element(X4,powerset(powerset(set_union2(X2,unordered_pair(X2,X2))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1416,c_0_681]),c_0_1305]),
[final] ).
cnf(i_0_2927,plain,
( X3 = complements_of_subsets(X1,X2)
| ~ in(esk113_3(X1,X2,X3),X3)
| ~ in(subset_complement(X1,esk113_3(X1,X2,X3)),X2)
| ~ element(X3,powerset(powerset(X1)))
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1417]),
[final] ).
cnf(i_0_2928,lemma,
( in(ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3),relation_of_lattice(X1))
| empty_carrier(X1)
| ~ below_refl(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1330]),
[final] ).
cnf(i_0_2929,plain,
( esk274_3(X1,X2,X3) = X3
| in(esk272_2(X1,X2),X2)
| ~ ordinal(X1)
| ~ in(X3,esk273_2(X1,X2))
| ~ element(X2,powerset(powerset(set_union2(X1,unordered_pair(X1,X1))))) ),
inference(rw,[status(thm)],[i_0_1418,c_0_1305]),
[final] ).
cnf(i_0_2930,plain,
( esk274_3(X1,X2,X3) = X3
| in(esk271_2(X1,X2),X2)
| ~ ordinal(X1)
| ~ in(X3,esk273_2(X1,X2))
| ~ element(X2,powerset(powerset(set_union2(X1,unordered_pair(X1,X1))))) ),
inference(rw,[status(thm)],[i_0_1419,c_0_1305]),
[final] ).
cnf(i_0_2931,plain,
( element(esk13_4(X1,X2,X3,X4),powerset(the_carrier(X1)))
| in(X4,X3)
| ~ in(X4,the_carrier(X1))
| X3 != topstr_closure(X1,X2)
| ~ element(X3,powerset(the_carrier(X1)))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1420]),
[final] ).
cnf(i_0_2932,plain,
( esk213_3(X1,X2,X3) = esk212_3(X1,X2,X3)
| empty(X1)
| in(unordered_pair(unordered_pair(esk208_2(X1,X2),X4),unordered_pair(esk208_2(X1,X2),esk208_2(X1,X2))),X2)
| ~ relation(X2)
| ~ in(X4,esk210_2(X1,X2))
| ~ in(X3,esk211_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1421,c_0_944]),
[final] ).
cnf(i_0_2933,plain,
( esk213_3(X1,X2,X3) = esk212_3(X1,X2,X3)
| empty(X1)
| in(unordered_pair(unordered_pair(esk207_2(X1,X2),X4),unordered_pair(esk207_2(X1,X2),esk207_2(X1,X2))),X2)
| ~ relation(X2)
| ~ in(X4,esk209_2(X1,X2))
| ~ in(X3,esk211_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1422,c_0_944]),
[final] ).
cnf(i_0_2934,plain,
( empty(X1)
| ~ empty_carrier(latt_str_of(X1,X2,X3))
| ~ function(X2)
| ~ quasi_total(X2,cartesian_product2(X1,X1),X1)
| ~ relation_of2(X2,cartesian_product2(X1,X1),X1)
| ~ function(X3)
| ~ quasi_total(X3,cartesian_product2(X1,X1),X1)
| ~ relation_of2(X3,cartesian_product2(X1,X1),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1423]),
[final] ).
cnf(i_0_2935,lemma,
( esk342_4(X1,X2,X3,X4) = esk344_4(X1,X2,X3,X4)
| empty(X1)
| ~ in(X4,esk341_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_682]),
[final] ).
cnf(i_0_2936,plain,
( X1 = X2
| latt_str_of(X1,X3,X4) != latt_str_of(X2,X5,X6)
| ~ function(X3)
| ~ quasi_total(X3,cartesian_product2(X1,X1),X1)
| ~ relation_of2(X3,cartesian_product2(X1,X1),X1)
| ~ function(X4)
| ~ quasi_total(X4,cartesian_product2(X1,X1),X1)
| ~ relation_of2(X4,cartesian_product2(X1,X1),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1424]),
[final] ).
cnf(i_0_2937,plain,
( X1 = X2
| latt_str_of(X3,X1,X4) != latt_str_of(X5,X2,X6)
| ~ function(X1)
| ~ quasi_total(X1,cartesian_product2(X3,X3),X3)
| ~ relation_of2(X1,cartesian_product2(X3,X3),X3)
| ~ function(X4)
| ~ quasi_total(X4,cartesian_product2(X3,X3),X3)
| ~ relation_of2(X4,cartesian_product2(X3,X3),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1424]),
[final] ).
cnf(i_0_2938,plain,
( X1 = X2
| latt_str_of(X3,X4,X1) != latt_str_of(X5,X6,X2)
| ~ function(X4)
| ~ quasi_total(X4,cartesian_product2(X3,X3),X3)
| ~ relation_of2(X4,cartesian_product2(X3,X3),X3)
| ~ function(X1)
| ~ quasi_total(X1,cartesian_product2(X3,X3),X3)
| ~ relation_of2(X1,cartesian_product2(X3,X3),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1424]),
[final] ).
cnf(i_0_2939,plain,
( in(unordered_pair(unordered_pair(X3,X5),unordered_pair(X3,X3)),X1)
| ~ relation(X1)
| ~ in(X5,X2)
| ~ in(X4,X2)
| ~ in(X3,X2)
| ~ is_transitive_in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1)
| ~ in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1425,c_0_944]),c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2940,plain,
( esk274_3(X1,X2,X3) = X3
| esk270_2(X1,X2) = esk268_2(X1,X2)
| ~ ordinal(X1)
| ~ in(X3,esk273_2(X1,X2))
| ~ element(X2,powerset(powerset(set_union2(X1,unordered_pair(X1,X1))))) ),
inference(rw,[status(thm)],[i_0_1426,c_0_1305]),
[final] ).
cnf(i_0_2941,plain,
( esk274_3(X1,X2,X3) = X3
| esk269_2(X1,X2) = esk268_2(X1,X2)
| ~ ordinal(X1)
| ~ in(X3,esk273_2(X1,X2))
| ~ element(X2,powerset(powerset(set_union2(X1,unordered_pair(X1,X1))))) ),
inference(rw,[status(thm)],[i_0_1427,c_0_1305]),
[final] ).
cnf(i_0_2942,lemma,
( X1 = esk382_3(X2,X3,X1)
| in(esk380_4(X2,X3,X4,X5),X5)
| empty(X2)
| ~ in(X1,X2)
| esk379_2(X2,X3) != X5
| ~ in(X4,X5)
| esk375_2(X2,X3) != esk376_2(X2,X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_2943,plain,
( open_subset(esk13_4(X1,X2,X3,X4),X1)
| in(X4,X3)
| ~ in(X4,the_carrier(X1))
| X3 != topstr_closure(X1,X2)
| ~ element(X3,powerset(the_carrier(X1)))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1420]),
[final] ).
cnf(i_0_2944,plain,
( in(X1,esk13_4(X2,X3,X4,X1))
| in(X1,X4)
| ~ in(X1,the_carrier(X2))
| X4 != topstr_closure(X2,X3)
| ~ element(X4,powerset(the_carrier(X2)))
| ~ element(X3,powerset(the_carrier(X2)))
| ~ top_str(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1420]),
[final] ).
cnf(i_0_2945,plain,
( disjoint(X1,esk13_4(X2,X1,X3,X4))
| in(X4,X3)
| ~ in(X4,the_carrier(X2))
| X3 != topstr_closure(X2,X1)
| ~ element(X3,powerset(the_carrier(X2)))
| ~ element(X1,powerset(the_carrier(X2)))
| ~ top_str(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1420]),
[final] ).
cnf(i_0_2946,lemma,
( X1 = esk382_3(X2,X3,X1)
| in(esk380_4(X2,X3,X4,X5),X5)
| in(esk374_2(X2,X3),X2)
| empty(X2)
| ~ in(X1,X2)
| esk379_2(X2,X3) != X5
| ~ in(X4,X5)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_2947,lemma,
( esk193_4(X1,X2,X3,X4) = X3
| in(esk189_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),esk192_2(X1,X2))
| ~ one_sorted_str(X1)
| ~ in(X3,complements_of_subsets(the_carrier(X1),X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1428,c_0_944]),
[final] ).
cnf(i_0_2948,lemma,
( esk193_4(X1,X2,X3,X4) = X3
| in(esk189_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),esk192_2(X1,X2))
| ~ one_sorted_str(X1)
| ~ in(X3,complements_of_subsets(the_carrier(X1),X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1429,c_0_944]),
[final] ).
cnf(i_0_2949,plain,
( esk332_4(X1,X2,X3,X4) = X4
| ~ in(X4,esk331_3(X1,X2,X3))
| esk329_3(X1,X2,X3) != esk330_3(X1,X2,X3)
| ~ element(X2,powerset(powerset(X1)))
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1309]),
[final] ).
cnf(i_0_2950,lemma,
( X1 = esk382_3(X2,X3,X1)
| in(esk380_4(X2,X3,X4,X5),X5)
| esk374_2(X2,X3) = esk378_2(X2,X3)
| empty(X2)
| ~ in(X1,X2)
| esk379_2(X2,X3) != X5
| ~ in(X4,X5)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_2951,lemma,
( X1 = esk382_3(X2,X3,X1)
| in(esk380_4(X2,X3,X4,X5),X5)
| esk374_2(X2,X3) = esk377_2(X2,X3)
| empty(X2)
| ~ in(X1,X2)
| esk379_2(X2,X3) != X5
| ~ in(X4,X5)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_2952,plain,
( empty_carrier(X1)
| empty_carrier(X2)
| element(k10_filter_1(X1,X2,X3,X4),the_carrier(k8_filter_1(X1,X2)))
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ lattice(X2)
| ~ latt_str(X2)
| ~ element(X3,the_carrier(X1))
| ~ element(X4,the_carrier(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1430]),
[final] ).
cnf(i_0_2953,lemma,
( relation_dom(esk381_2(X1,X2)) = X1
| in(esk380_4(X1,X2,X3,X4),X4)
| in(esk376_2(X1,X2),esk378_2(X1,X2))
| empty(X1)
| esk379_2(X1,X2) != X4
| ~ in(X3,X4)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_2954,lemma,
( relation_dom(esk381_2(X1,X2)) = X1
| in(esk380_4(X1,X2,X3,X4),X4)
| in(esk375_2(X1,X2),esk377_2(X1,X2))
| empty(X1)
| esk379_2(X1,X2) != X4
| ~ in(X3,X4)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_2955,lemma,
( relation(esk381_2(X1,X2))
| in(esk380_4(X1,X2,X3,X4),X4)
| in(esk376_2(X1,X2),esk378_2(X1,X2))
| empty(X1)
| esk379_2(X1,X2) != X4
| ~ in(X3,X4)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_2956,lemma,
( relation(esk381_2(X1,X2))
| in(esk380_4(X1,X2,X3,X4),X4)
| in(esk375_2(X1,X2),esk377_2(X1,X2))
| empty(X1)
| esk379_2(X1,X2) != X4
| ~ in(X3,X4)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_2957,lemma,
( function(esk381_2(X1,X2))
| in(esk380_4(X1,X2,X3,X4),X4)
| in(esk376_2(X1,X2),esk378_2(X1,X2))
| empty(X1)
| esk379_2(X1,X2) != X4
| ~ in(X3,X4)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_2958,lemma,
( function(esk381_2(X1,X2))
| in(esk380_4(X1,X2,X3,X4),X4)
| in(esk375_2(X1,X2),esk377_2(X1,X2))
| empty(X1)
| esk379_2(X1,X2) != X4
| ~ in(X3,X4)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_2959,plain,
( X1 = esk252_3(X3,X4,X2)
| X2 = empty_set
| epred2_3(esk248_1(X3),esk247_1(X3),esk246_1(X3))
| ~ in(X1,X2)
| ~ subset(esk252_3(X3,X4,X2),X1)
| ~ element(X2,powerset(powerset(esk251_2(X3,X4))))
| ~ in(esk251_2(X3,X4),omega)
| ~ in(X4,esk249_1(X3))
| ~ ordinal(X3) ),
inference(split_conjunct,[status(thm)],[i_0_717]),
[final] ).
cnf(i_0_2960,lemma,
( X1 = esk382_3(X2,X3,X1)
| empty(X2)
| in(esk379_2(X2,X3),X2)
| in(unordered_pair(unordered_pair(esk376_2(X2,X3),X4),unordered_pair(esk376_2(X2,X3),esk376_2(X2,X3))),X3)
| ~ relation(X3)
| ~ in(X1,X2)
| ~ in(X4,esk378_2(X2,X3)) ),
inference(rw,[status(thm)],[i_0_1431,c_0_944]),
[final] ).
cnf(i_0_2961,lemma,
( X1 = esk382_3(X2,X3,X1)
| empty(X2)
| in(esk379_2(X2,X3),X2)
| in(unordered_pair(unordered_pair(esk375_2(X2,X3),X4),unordered_pair(esk375_2(X2,X3),esk375_2(X2,X3))),X3)
| ~ relation(X3)
| ~ in(X1,X2)
| ~ in(X4,esk377_2(X2,X3)) ),
inference(rw,[status(thm)],[i_0_1432,c_0_944]),
[final] ).
cnf(i_0_2962,lemma,
( esk198_4(X1,X2,X3,X4) = X3
| esk196_2(X1,X2) = subset_complement(the_carrier(X1),X5)
| in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),esk197_2(X1,X2))
| X5 != esk194_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ in(X3,X2)
| ~ element(X5,powerset(the_carrier(X1)))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1433,c_0_944]),
[final] ).
cnf(i_0_2963,lemma,
( esk198_4(X1,X2,X3,X4) = X3
| esk195_2(X1,X2) = subset_complement(the_carrier(X1),X5)
| in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),esk197_2(X1,X2))
| X5 != esk194_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ in(X3,X2)
| ~ element(X5,powerset(the_carrier(X1)))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1434,c_0_944]),
[final] ).
cnf(i_0_2964,plain,
( X2 = inclusion_relation(X1)
| subset(esk47_2(X1,X2),esk48_2(X1,X2))
| in(unordered_pair(unordered_pair(esk47_2(X1,X2),esk48_2(X1,X2)),unordered_pair(esk47_2(X1,X2),esk47_2(X1,X2))),X2)
| relation_field(X2) != X1
| ~ relation(X2) ),
inference(rw,[status(thm)],[i_0_1435,c_0_944]),
[final] ).
cnf(i_0_2965,plain,
( esk308_4(X1,X2,X3,X4) = X4
| esk306_2(X1,X2) = subset_complement(the_carrier(X1),X5)
| ~ in(X4,esk307_3(X1,X2,X3))
| ~ element(X5,powerset(the_carrier(X1)))
| X5 != esk305_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]),
[final] ).
cnf(i_0_2966,plain,
( esk308_4(X1,X2,X3,X4) = X4
| esk304_2(X1,X2) = subset_complement(the_carrier(X1),X5)
| ~ in(X4,esk307_3(X1,X2,X3))
| ~ element(X5,powerset(the_carrier(X1)))
| X5 != esk303_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]),
[final] ).
cnf(i_0_2967,plain,
( esk290_4(X1,X2,X3,X4) = X4
| esk288_2(X1,X2) = subset_complement(the_carrier(X1),X5)
| ~ in(X4,esk289_3(X1,X2,X3))
| ~ element(X5,powerset(the_carrier(X1)))
| X5 != esk287_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]),
[final] ).
cnf(i_0_2968,plain,
( esk290_4(X1,X2,X3,X4) = X4
| esk286_2(X1,X2) = subset_complement(the_carrier(X1),X5)
| ~ in(X4,esk289_3(X1,X2,X3))
| ~ element(X5,powerset(the_carrier(X1)))
| X5 != esk285_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]),
[final] ).
cnf(i_0_2969,lemma,
( esk193_4(X1,X2,X3,X4) = X3
| in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),esk192_2(X1,X2))
| esk191_2(X1,X2) != esk190_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ in(X3,complements_of_subsets(the_carrier(X1),X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1436,c_0_944]),
[final] ).
cnf(i_0_2970,plain,
( in(unordered_pair(unordered_pair(X1,X4),unordered_pair(X1,X1)),X6)
| X6 != relation_composition(X3,X5)
| ~ relation(X6)
| ~ relation(X5)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X2,X4),unordered_pair(X2,X2)),X5)
| ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1437,c_0_944]),c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2971,lemma,
( in(unordered_pair(unordered_pair(X1,esk412_3(X1,X2,X3)),unordered_pair(X1,X1)),X3)
| ~ relation(X3)
| ~ in(X1,relation_inverse_image(X3,X2)) ),
inference(rw,[status(thm)],[i_0_1438,c_0_944]),
[final] ).
cnf(i_0_2972,lemma,
( relation_dom(esk381_2(X1,X2)) = X1
| in(esk380_4(X1,X2,X3,X4),X4)
| empty(X1)
| esk379_2(X1,X2) != X4
| ~ in(X3,X4)
| esk375_2(X1,X2) != esk376_2(X1,X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_2973,lemma,
( relation(esk381_2(X1,X2))
| in(esk380_4(X1,X2,X3,X4),X4)
| empty(X1)
| esk379_2(X1,X2) != X4
| ~ in(X3,X4)
| esk375_2(X1,X2) != esk376_2(X1,X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_2974,lemma,
( function(esk381_2(X1,X2))
| in(esk380_4(X1,X2,X3,X4),X4)
| empty(X1)
| esk379_2(X1,X2) != X4
| ~ in(X3,X4)
| esk375_2(X1,X2) != esk376_2(X1,X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_2975,plain,
( strict_latt_str(latt_str_of(X1,X2,X3))
| empty(X1)
| ~ function(X2)
| ~ quasi_total(X2,cartesian_product2(X1,X1),X1)
| ~ relation_of2(X2,cartesian_product2(X1,X1),X1)
| ~ function(X3)
| ~ quasi_total(X3,cartesian_product2(X1,X1),X1)
| ~ relation_of2(X3,cartesian_product2(X1,X1),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1423]),
[final] ).
cnf(i_0_2976,lemma,
( relation_dom(esk381_2(X1,X2)) = X1
| in(esk380_4(X1,X2,X3,X4),X4)
| in(esk374_2(X1,X2),X1)
| empty(X1)
| esk379_2(X1,X2) != X4
| ~ in(X3,X4)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_2977,lemma,
( relation(esk381_2(X1,X2))
| in(esk380_4(X1,X2,X3,X4),X4)
| in(esk374_2(X1,X2),X1)
| empty(X1)
| esk379_2(X1,X2) != X4
| ~ in(X3,X4)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_2978,lemma,
( function(esk381_2(X1,X2))
| in(esk380_4(X1,X2,X3,X4),X4)
| in(esk374_2(X1,X2),X1)
| empty(X1)
| esk379_2(X1,X2) != X4
| ~ in(X3,X4)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_2979,plain,
( strict_latt_str(latt_str_of(X1,X2,X3))
| ~ function(X2)
| ~ quasi_total(X2,cartesian_product2(X1,X1),X1)
| ~ relation_of2(X2,cartesian_product2(X1,X1),X1)
| ~ function(X3)
| ~ quasi_total(X3,cartesian_product2(X1,X1),X1)
| ~ relation_of2(X3,cartesian_product2(X1,X1),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1439]),
[final] ).
cnf(i_0_2980,plain,
( latt_str(latt_str_of(X1,X2,X3))
| ~ function(X2)
| ~ quasi_total(X2,cartesian_product2(X1,X1),X1)
| ~ relation_of2(X2,cartesian_product2(X1,X1),X1)
| ~ function(X3)
| ~ quasi_total(X3,cartesian_product2(X1,X1),X1)
| ~ relation_of2(X3,cartesian_product2(X1,X1),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1439]),
[final] ).
cnf(i_0_2981,plain,
( esk320_4(X1,X2,X3,X4) = X4
| ~ in(X4,esk319_3(X1,X2,X3))
| esk313_3(X1,X2,X3) != esk314_3(X1,X2,X3)
| ~ relation(X2)
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[i_0_684]),
[final] ).
cnf(i_0_2982,lemma,
( in(X1,powerset(X2))
| ~ ordinal(X2)
| ~ in(X1,esk357_2(X2,X3))
| ~ element(X3,powerset(powerset(set_union2(X2,unordered_pair(X2,X2))))) ),
inference(rw,[status(thm)],[i_0_1440,c_0_1305]),
[final] ).
cnf(i_0_2983,lemma,
( relation_dom(esk381_2(X1,X2)) = X1
| in(esk380_4(X1,X2,X3,X4),X4)
| esk374_2(X1,X2) = esk378_2(X1,X2)
| empty(X1)
| esk379_2(X1,X2) != X4
| ~ in(X3,X4)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_2984,lemma,
( relation_dom(esk381_2(X1,X2)) = X1
| in(esk380_4(X1,X2,X3,X4),X4)
| esk374_2(X1,X2) = esk377_2(X1,X2)
| empty(X1)
| esk379_2(X1,X2) != X4
| ~ in(X3,X4)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_2985,lemma,
( relation(esk381_2(X1,X2))
| in(esk380_4(X1,X2,X3,X4),X4)
| esk374_2(X1,X2) = esk378_2(X1,X2)
| empty(X1)
| esk379_2(X1,X2) != X4
| ~ in(X3,X4)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_2986,lemma,
( function(esk381_2(X1,X2))
| in(esk380_4(X1,X2,X3,X4),X4)
| esk374_2(X1,X2) = esk378_2(X1,X2)
| empty(X1)
| esk379_2(X1,X2) != X4
| ~ in(X3,X4)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_2987,lemma,
( relation(esk381_2(X1,X2))
| in(esk380_4(X1,X2,X3,X4),X4)
| esk374_2(X1,X2) = esk377_2(X1,X2)
| empty(X1)
| esk379_2(X1,X2) != X4
| ~ in(X3,X4)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_2988,lemma,
( function(esk381_2(X1,X2))
| in(esk380_4(X1,X2,X3,X4),X4)
| esk374_2(X1,X2) = esk377_2(X1,X2)
| empty(X1)
| esk379_2(X1,X2) != X4
| ~ in(X3,X4)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_2989,plain,
( esk290_4(X1,X2,X3,X4) = X4
| in(esk287_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| ~ in(X4,esk289_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]),
[final] ).
cnf(i_0_2990,plain,
( esk290_4(X1,X2,X3,X4) = X4
| in(esk285_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| ~ in(X4,esk289_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]),
[final] ).
cnf(i_0_2991,plain,
( esk332_4(X1,X2,X3,X4) = X4
| esk328_3(X1,X2,X3) = esk330_3(X1,X2,X3)
| ~ in(X4,esk331_3(X1,X2,X3))
| ~ element(X2,powerset(powerset(X1)))
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1309]),
[final] ).
cnf(i_0_2992,plain,
( esk332_4(X1,X2,X3,X4) = X4
| esk328_3(X1,X2,X3) = esk329_3(X1,X2,X3)
| ~ in(X4,esk331_3(X1,X2,X3))
| ~ element(X2,powerset(powerset(X1)))
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1309]),
[final] ).
cnf(i_0_2993,plain,
( X3 = set_difference(X1,set_difference(X1,X2))
| ~ in(esk77_3(X1,X2,X3),X3)
| ~ in(esk77_3(X1,X2,X3),X2)
| ~ in(esk77_3(X1,X2,X3),X1) ),
inference(rw,[status(thm)],[i_0_1441,c_0_1442]),
[final] ).
cnf(i_0_2994,plain,
( X2 = relation_rng(X1)
| in(esk93_2(X1,X2),X2)
| in(unordered_pair(unordered_pair(esk94_2(X1,X2),esk93_2(X1,X2)),unordered_pair(esk94_2(X1,X2),esk94_2(X1,X2))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[i_0_1443,c_0_944]),
[final] ).
cnf(i_0_2995,plain,
( X2 = relation_dom(X1)
| in(esk79_2(X1,X2),X2)
| in(unordered_pair(unordered_pair(esk79_2(X1,X2),esk80_2(X1,X2)),unordered_pair(esk79_2(X1,X2),esk79_2(X1,X2))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[i_0_1444,c_0_944]),
[final] ).
cnf(i_0_2996,plain,
( X2 = identity_relation(X1)
| in(esk1_2(X1,X2),X1)
| in(unordered_pair(unordered_pair(esk1_2(X1,X2),esk2_2(X1,X2)),unordered_pair(esk1_2(X1,X2),esk1_2(X1,X2))),X2)
| ~ relation(X2) ),
inference(rw,[status(thm)],[i_0_1445,c_0_944]),
[final] ).
cnf(i_0_2997,lemma,
( in(unordered_pair(unordered_pair(X2,X4),unordered_pair(X2,X2)),X1)
| ~ relation(X1)
| ~ transitive(X1)
| ~ in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),X1)
| ~ in(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1446,c_0_944]),c_0_944]),c_0_944]),
[final] ).
cnf(i_0_2998,plain,
( in(unordered_pair(unordered_pair(X1,esk78_3(X3,X2,X1)),unordered_pair(X1,X1)),X3)
| X2 != relation_dom(X3)
| ~ relation(X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_1447,c_0_944]),
[final] ).
cnf(i_0_2999,lemma,
( apply(esk393_2(X2,X3),X1) = subset_complement(the_carrier(X2),X4)
| esk390_2(X2,X3) = subset_complement(the_carrier(X2),X6)
| ~ in(X1,complements_of_subsets(the_carrier(X2),X3))
| ~ element(X4,powerset(the_carrier(X2)))
| X4 != X1
| X5 != subset_complement(the_carrier(X2),esk392_3(X2,X3,X5))
| ~ element(X6,powerset(the_carrier(X2)))
| X6 != esk388_2(X2,X3)
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3000,lemma,
( apply(esk393_2(X2,X3),X1) = subset_complement(the_carrier(X2),X4)
| esk389_2(X2,X3) = subset_complement(the_carrier(X2),X6)
| ~ in(X1,complements_of_subsets(the_carrier(X2),X3))
| ~ element(X4,powerset(the_carrier(X2)))
| X4 != X1
| X5 != subset_complement(the_carrier(X2),esk392_3(X2,X3,X5))
| ~ element(X6,powerset(the_carrier(X2)))
| X6 != esk388_2(X2,X3)
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3001,lemma,
( relation_dom(esk381_2(X1,X2)) = X1
| empty(X1)
| in(esk379_2(X1,X2),X1)
| in(unordered_pair(unordered_pair(esk376_2(X1,X2),X3),unordered_pair(esk376_2(X1,X2),esk376_2(X1,X2))),X2)
| ~ relation(X2)
| ~ in(X3,esk378_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1449,c_0_944]),
[final] ).
cnf(i_0_3002,lemma,
( relation_dom(esk381_2(X1,X2)) = X1
| empty(X1)
| in(esk379_2(X1,X2),X1)
| in(unordered_pair(unordered_pair(esk375_2(X1,X2),X3),unordered_pair(esk375_2(X1,X2),esk375_2(X1,X2))),X2)
| ~ relation(X2)
| ~ in(X3,esk377_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1450,c_0_944]),
[final] ).
cnf(i_0_3003,lemma,
( empty(X1)
| relation(esk381_2(X1,X2))
| in(esk379_2(X1,X2),X1)
| in(unordered_pair(unordered_pair(esk376_2(X1,X2),X3),unordered_pair(esk376_2(X1,X2),esk376_2(X1,X2))),X2)
| ~ relation(X2)
| ~ in(X3,esk378_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1451,c_0_944]),
[final] ).
cnf(i_0_3004,lemma,
( empty(X1)
| relation(esk381_2(X1,X2))
| in(esk379_2(X1,X2),X1)
| in(unordered_pair(unordered_pair(esk375_2(X1,X2),X3),unordered_pair(esk375_2(X1,X2),esk375_2(X1,X2))),X2)
| ~ relation(X2)
| ~ in(X3,esk377_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1452,c_0_944]),
[final] ).
cnf(i_0_3005,lemma,
( empty(X1)
| function(esk381_2(X1,X2))
| in(esk379_2(X1,X2),X1)
| in(unordered_pair(unordered_pair(esk376_2(X1,X2),X3),unordered_pair(esk376_2(X1,X2),esk376_2(X1,X2))),X2)
| ~ relation(X2)
| ~ in(X3,esk378_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1453,c_0_944]),
[final] ).
cnf(i_0_3006,lemma,
( empty(X1)
| function(esk381_2(X1,X2))
| in(esk379_2(X1,X2),X1)
| in(unordered_pair(unordered_pair(esk375_2(X1,X2),X3),unordered_pair(esk375_2(X1,X2),esk375_2(X1,X2))),X2)
| ~ relation(X2)
| ~ in(X3,esk377_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1454,c_0_944]),
[final] ).
cnf(i_0_3007,plain,
( in(X4,a_1_0_filter_1(X2))
| empty_carrier(X2)
| ~ element(X1,the_carrier(X2))
| ~ element(X3,the_carrier(X2))
| X4 != ordered_pair_as_product_element(the_carrier(X2),the_carrier(X2),X1,X3)
| ~ below_refl(X2,X1,X3)
| ~ lattice(X2)
| ~ latt_str(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1455]),
[final] ).
cnf(i_0_3008,plain,
( X2 = identity_relation(X1)
| esk2_2(X1,X2) = esk1_2(X1,X2)
| in(unordered_pair(unordered_pair(esk1_2(X1,X2),esk2_2(X1,X2)),unordered_pair(esk1_2(X1,X2),esk1_2(X1,X2))),X2)
| ~ relation(X2) ),
inference(rw,[status(thm)],[i_0_1456,c_0_944]),
[final] ).
cnf(i_0_3009,plain,
( X1 = esk252_3(X3,X4,X2)
| X2 = empty_set
| ~ in(X1,X2)
| ~ subset(esk252_3(X3,X4,X2),X1)
| ~ element(X2,powerset(powerset(esk251_2(X3,X4))))
| ~ in(esk251_2(X3,X4),omega)
| ~ in(X4,esk249_1(X3))
| esk247_1(X3) != esk248_1(X3)
| ~ ordinal(X3) ),
inference(split_conjunct,[status(thm)],[i_0_717]),
[final] ).
cnf(i_0_3010,lemma,
( X1 = esk183_4(X2,X3,X1,X4)
| empty(X2)
| in(esk179_2(X2,X3),esk181_2(X2,X3))
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X1,X4),unordered_pair(X1,X1)),esk182_2(X2,X3)) ),
inference(rw,[status(thm)],[i_0_1457,c_0_944]),
[final] ).
cnf(i_0_3011,lemma,
( X1 = esk183_4(X2,X3,X1,X4)
| empty(X2)
| in(esk178_2(X2,X3),esk180_2(X2,X3))
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X1,X4),unordered_pair(X1,X1)),esk182_2(X2,X3)) ),
inference(rw,[status(thm)],[i_0_1458,c_0_944]),
[final] ).
cnf(i_0_3012,plain,
( subset(X1,X2)
| in(unordered_pair(unordered_pair(esk72_2(X1,X2),esk73_2(X1,X2)),unordered_pair(esk72_2(X1,X2),esk72_2(X1,X2))),X1)
| ~ relation(X2)
| ~ relation(X1) ),
inference(rw,[status(thm)],[i_0_1459,c_0_944]),
[final] ).
cnf(i_0_3013,plain,
( empty(X1)
| empty(X2)
| element(ordered_pair_as_product_element(X1,X2,X3,X4),cartesian_product2(X1,X2))
| ~ element(X3,X1)
| ~ element(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1460]),
[final] ).
cnf(i_0_3014,lemma,
( X1 = esk351_3(X3,X4,X2)
| X2 = empty_set
| ~ in(X1,X2)
| ~ subset(esk351_3(X3,X4,X2),X1)
| ~ element(X2,powerset(powerset(esk350_2(X3,X4))))
| ~ in(esk350_2(X3,X4),omega)
| ~ in(X4,esk349_1(X3))
| ~ ordinal(X3) ),
inference(split_conjunct,[status(thm)],[i_0_721]),
[final] ).
cnf(i_0_3015,lemma,
( esk198_4(X1,X2,X3,X4) = X3
| in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),esk197_2(X1,X2))
| esk196_2(X1,X2) != esk195_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ in(X3,X2)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1461,c_0_944]),
[final] ).
cnf(i_0_3016,plain,
( is_transitive_in(X1,X2)
| in(unordered_pair(unordered_pair(esk111_2(X1,X2),esk112_2(X1,X2)),unordered_pair(esk111_2(X1,X2),esk111_2(X1,X2))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[i_0_1462,c_0_944]),
[final] ).
cnf(i_0_3017,plain,
( is_transitive_in(X1,X2)
| in(unordered_pair(unordered_pair(esk110_2(X1,X2),esk111_2(X1,X2)),unordered_pair(esk110_2(X1,X2),esk110_2(X1,X2))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[i_0_1463,c_0_944]),
[final] ).
cnf(i_0_3018,plain,
( is_antisymmetric_in(X1,X2)
| in(unordered_pair(unordered_pair(esk82_2(X1,X2),esk81_2(X1,X2)),unordered_pair(esk82_2(X1,X2),esk82_2(X1,X2))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[i_0_1464,c_0_944]),
[final] ).
cnf(i_0_3019,plain,
( is_antisymmetric_in(X1,X2)
| in(unordered_pair(unordered_pair(esk81_2(X1,X2),esk82_2(X1,X2)),unordered_pair(esk81_2(X1,X2),esk81_2(X1,X2))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[i_0_1465,c_0_944]),
[final] ).
cnf(i_0_3020,plain,
( esk308_4(X1,X2,X3,X4) = X4
| ~ in(X4,esk307_3(X1,X2,X3))
| esk301_2(X1,X2) != esk302_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]),
[final] ).
cnf(i_0_3021,plain,
( esk290_4(X1,X2,X3,X4) = X4
| ~ in(X4,esk289_3(X1,X2,X3))
| esk283_2(X1,X2) != esk284_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]),
[final] ).
cnf(i_0_3022,lemma,
( esk198_4(X1,X2,X3,X4) = X3
| in(esk194_2(X1,X2),X2)
| in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),esk197_2(X1,X2))
| ~ one_sorted_str(X1)
| ~ in(X3,X2)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1466,c_0_944]),
[final] ).
cnf(i_0_3023,lemma,
( esk198_4(X1,X2,X3,X4) = X3
| in(esk194_2(X1,X2),X2)
| in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),esk197_2(X1,X2))
| ~ one_sorted_str(X1)
| ~ in(X3,X2)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(rw,[status(thm)],[i_0_1467,c_0_944]),
[final] ).
cnf(i_0_3024,plain,
( esk281_4(X1,X2,X3,X4) = X4
| in(X3,esk279_2(X1,X2))
| esk278_2(X1,X2) = subset_complement(the_carrier(X1),X5)
| ~ in(X4,complements_of_subsets(the_carrier(X1),X2))
| ~ element(X5,powerset(the_carrier(X1)))
| X5 != esk276_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1284]),
[final] ).
cnf(i_0_3025,plain,
( esk281_4(X1,X2,X3,X4) = X4
| in(X3,esk279_2(X1,X2))
| esk277_2(X1,X2) = subset_complement(the_carrier(X1),X5)
| ~ in(X4,complements_of_subsets(the_carrier(X1),X2))
| ~ element(X5,powerset(the_carrier(X1)))
| X5 != esk276_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1284]),
[final] ).
cnf(i_0_3026,plain,
( esk308_4(X1,X2,X3,X4) = X4
| in(esk305_2(X1,X2),X2)
| ~ in(X4,esk307_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]),
[final] ).
cnf(i_0_3027,plain,
( esk308_4(X1,X2,X3,X4) = X4
| in(esk303_2(X1,X2),X2)
| ~ in(X4,esk307_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]),
[final] ).
cnf(i_0_3028,lemma,
( apply(esk393_2(X2,X3),X1) = subset_complement(the_carrier(X2),X4)
| in(esk388_2(X2,X3),complements_of_subsets(the_carrier(X2),X3))
| ~ in(X1,complements_of_subsets(the_carrier(X2),X3))
| ~ element(X4,powerset(the_carrier(X2)))
| X4 != X1
| X5 != subset_complement(the_carrier(X2),esk392_3(X2,X3,X5))
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3029,plain,
( in(esk5_4(X1,X2,X3,X4),relation_dom(X1))
| ~ in(X4,X3)
| X3 != relation_image(X1,X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1468]),
[final] ).
cnf(i_0_3030,lemma,
( X1 = esk183_4(X2,X3,X1,X4)
| empty(X2)
| esk179_2(X2,X3) != esk178_2(X2,X3)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X1,X4),unordered_pair(X1,X1)),esk182_2(X2,X3)) ),
inference(rw,[status(thm)],[i_0_1469,c_0_944]),
[final] ).
cnf(i_0_3031,plain,
( esk320_4(X1,X2,X3,X4) = X4
| esk312_3(X1,X2,X3) = esk314_3(X1,X2,X3)
| ~ in(X4,esk319_3(X1,X2,X3))
| ~ relation(X2)
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[i_0_684]),
[final] ).
cnf(i_0_3032,plain,
( esk320_4(X1,X2,X3,X4) = X4
| esk312_3(X1,X2,X3) = esk313_3(X1,X2,X3)
| ~ in(X4,esk319_3(X1,X2,X3))
| ~ relation(X2)
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[i_0_684]),
[final] ).
cnf(i_0_3033,plain,
( X1 = apply(X2,esk5_4(X2,X3,X4,X1))
| ~ in(X1,X4)
| X4 != relation_image(X2,X3)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1468]),
[final] ).
cnf(i_0_3034,plain,
( in(esk5_4(X1,X2,X3,X4),X2)
| ~ in(X4,X3)
| X3 != relation_image(X1,X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1468]),
[final] ).
cnf(i_0_3035,lemma,
( X1 = esk183_4(X2,X3,X1,X4)
| empty(X2)
| in(esk177_2(X2,X3),X2)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X1,X4),unordered_pair(X1,X1)),esk182_2(X2,X3)) ),
inference(rw,[status(thm)],[i_0_1470,c_0_944]),
[final] ).
cnf(i_0_3036,lemma,
( X1 = esk183_4(X2,X3,X1,X4)
| empty(X2)
| in(esk177_2(X2,X3),X2)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X1,X4),unordered_pair(X1,X1)),esk182_2(X2,X3)) ),
inference(rw,[status(thm)],[i_0_1471,c_0_944]),
[final] ).
cnf(i_0_3037,plain,
( esk308_4(X1,X2,X3,X4) = X4
| esk300_2(X1,X2) = esk302_2(X1,X2)
| ~ in(X4,esk307_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]),
[final] ).
cnf(i_0_3038,plain,
( esk308_4(X1,X2,X3,X4) = X4
| esk300_2(X1,X2) = esk301_2(X1,X2)
| ~ in(X4,esk307_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_686]),
[final] ).
cnf(i_0_3039,plain,
( esk290_4(X1,X2,X3,X4) = X4
| esk282_2(X1,X2) = esk284_2(X1,X2)
| ~ in(X4,esk289_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]),
[final] ).
cnf(i_0_3040,plain,
( esk290_4(X1,X2,X3,X4) = X4
| esk282_2(X1,X2) = esk283_2(X1,X2)
| ~ in(X4,esk289_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_685]),
[final] ).
cnf(i_0_3041,plain,
( in(esk19_4(X1,X2,X3,X4),X2)
| ~ in(X4,X3)
| X3 != relation_inverse_image(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_704]),
[final] ).
cnf(i_0_3042,plain,
( in(esk16_4(X1,X2,X3,X4),X2)
| ~ in(X4,X3)
| X3 != relation_image(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_698]),
[final] ).
cnf(i_0_3043,lemma,
( empty(X1)
| relation(esk182_2(X1,X2))
| in(unordered_pair(unordered_pair(esk179_2(X1,X2),X3),unordered_pair(esk179_2(X1,X2),esk179_2(X1,X2))),X2)
| ~ relation(X2)
| ~ in(X3,esk181_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1472,c_0_944]),
[final] ).
cnf(i_0_3044,lemma,
( empty(X1)
| relation(esk182_2(X1,X2))
| in(unordered_pair(unordered_pair(esk178_2(X1,X2),X3),unordered_pair(esk178_2(X1,X2),esk178_2(X1,X2))),X2)
| ~ relation(X2)
| ~ in(X3,esk180_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1473,c_0_944]),
[final] ).
cnf(i_0_3045,lemma,
( empty(X1)
| function(esk182_2(X1,X2))
| in(unordered_pair(unordered_pair(esk179_2(X1,X2),X3),unordered_pair(esk179_2(X1,X2),esk179_2(X1,X2))),X2)
| ~ relation(X2)
| ~ in(X3,esk181_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1474,c_0_944]),
[final] ).
cnf(i_0_3046,lemma,
( empty(X1)
| function(esk182_2(X1,X2))
| in(unordered_pair(unordered_pair(esk178_2(X1,X2),X3),unordered_pair(esk178_2(X1,X2),esk178_2(X1,X2))),X2)
| ~ relation(X2)
| ~ in(X3,esk180_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1475,c_0_944]),
[final] ).
cnf(i_0_3047,plain,
( in(X3,esk331_3(X5,X4,X2))
| in(relation_image(X2,esk330_3(X5,X4,X2)),X4)
| ~ in(X1,powerset(relation_dom(X2)))
| X1 != X3
| ~ in(relation_image(X2,X3),X4)
| ~ element(X4,powerset(powerset(X5)))
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1309]),
[final] ).
cnf(i_0_3048,plain,
( in(X3,esk331_3(X5,X4,X2))
| in(relation_image(X2,esk329_3(X5,X4,X2)),X4)
| ~ in(X1,powerset(relation_dom(X2)))
| X1 != X3
| ~ in(relation_image(X2,X3),X4)
| ~ element(X4,powerset(powerset(X5)))
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1309]),
[final] ).
cnf(i_0_3049,lemma,
( X1 = esk183_4(X2,X3,X1,X4)
| esk181_2(X2,X3) = esk177_2(X2,X3)
| empty(X2)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X1,X4),unordered_pair(X1,X1)),esk182_2(X2,X3)) ),
inference(rw,[status(thm)],[i_0_1476,c_0_944]),
[final] ).
cnf(i_0_3050,lemma,
( X1 = esk183_4(X2,X3,X1,X4)
| esk180_2(X2,X3) = esk177_2(X2,X3)
| empty(X2)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X1,X4),unordered_pair(X1,X1)),esk182_2(X2,X3)) ),
inference(rw,[status(thm)],[i_0_1477,c_0_944]),
[final] ).
cnf(i_0_3051,plain,
( in(esk64_4(X1,X2,X3,X4),X2)
| ~ in(X4,X3)
| X3 != cartesian_product2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_702]),
[final] ).
cnf(i_0_3052,plain,
( in(esk63_4(X1,X2,X3,X4),X1)
| ~ in(X4,X3)
| X3 != cartesian_product2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_702]),
[final] ).
cnf(i_0_3053,plain,
( in(relation_image(X1,X2),X3)
| in(relation_image(X1,esk330_3(X4,X3,X1)),X3)
| ~ in(X2,esk331_3(X4,X3,X1))
| ~ element(X3,powerset(powerset(X4)))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1309]),
[final] ).
cnf(i_0_3054,plain,
( in(relation_image(X1,X2),X3)
| in(relation_image(X1,esk329_3(X4,X3,X1)),X3)
| ~ in(X2,esk331_3(X4,X3,X1))
| ~ element(X3,powerset(powerset(X4)))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1309]),
[final] ).
cnf(i_0_3055,lemma,
( X4 = subset_complement(the_carrier(X2),X1)
| esk196_2(X2,X5) = subset_complement(the_carrier(X2),X6)
| X1 != X3
| X6 != esk194_2(X2,X5)
| ~ one_sorted_str(X2)
| ~ element(X6,powerset(the_carrier(X2)))
| ~ element(X1,powerset(the_carrier(X2)))
| ~ element(X5,powerset(powerset(the_carrier(X2))))
| ~ in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),esk197_2(X2,X5)) ),
inference(rw,[status(thm)],[i_0_1478,c_0_944]),
[final] ).
cnf(i_0_3056,lemma,
( X4 = subset_complement(the_carrier(X2),X1)
| esk195_2(X2,X5) = subset_complement(the_carrier(X2),X6)
| X1 != X3
| X6 != esk194_2(X2,X5)
| ~ one_sorted_str(X2)
| ~ element(X6,powerset(the_carrier(X2)))
| ~ element(X1,powerset(the_carrier(X2)))
| ~ element(X5,powerset(powerset(the_carrier(X2))))
| ~ in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),esk197_2(X2,X5)) ),
inference(rw,[status(thm)],[i_0_1479,c_0_944]),
[final] ).
cnf(i_0_3057,lemma,
( X4 = subset_complement(the_carrier(X2),X1)
| esk191_2(X2,X5) = subset_complement(the_carrier(X2),X6)
| X1 != X3
| X6 != esk189_2(X2,X5)
| ~ one_sorted_str(X2)
| ~ element(X6,powerset(the_carrier(X2)))
| ~ element(X1,powerset(the_carrier(X2)))
| ~ element(X5,powerset(powerset(the_carrier(X2))))
| ~ in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),esk192_2(X2,X5)) ),
inference(rw,[status(thm)],[i_0_1480,c_0_944]),
[final] ).
cnf(i_0_3058,lemma,
( X4 = subset_complement(the_carrier(X2),X1)
| esk190_2(X2,X5) = subset_complement(the_carrier(X2),X6)
| X1 != X3
| X6 != esk189_2(X2,X5)
| ~ one_sorted_str(X2)
| ~ element(X6,powerset(the_carrier(X2)))
| ~ element(X1,powerset(the_carrier(X2)))
| ~ element(X5,powerset(powerset(the_carrier(X2))))
| ~ in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),esk192_2(X2,X5)) ),
inference(rw,[status(thm)],[i_0_1481,c_0_944]),
[final] ).
cnf(i_0_3059,plain,
( esk281_4(X1,X2,X3,X4) = X4
| in(X3,esk279_2(X1,X2))
| in(esk276_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| ~ in(X4,complements_of_subsets(the_carrier(X1),X2))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1284]),
[final] ).
cnf(i_0_3060,plain,
( esk281_4(X1,X2,X3,X4) = X4
| in(X3,esk279_2(X1,X2))
| in(esk276_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| ~ in(X4,complements_of_subsets(the_carrier(X1),X2))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1284]),
[final] ).
cnf(i_0_3061,lemma,
( apply(esk399_2(X4,X2),X1) = subset_complement(the_carrier(X4),X3)
| esk396_2(X4,X2) = subset_complement(the_carrier(X4),X6)
| ~ in(X1,X2)
| ~ element(X3,powerset(the_carrier(X4)))
| X3 != X1
| X5 != subset_complement(the_carrier(X4),esk398_3(X4,X2,X5))
| ~ element(X6,powerset(the_carrier(X4)))
| X6 != esk394_2(X4,X2)
| ~ one_sorted_str(X4)
| ~ element(X2,powerset(powerset(the_carrier(X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3062,lemma,
( apply(esk399_2(X4,X2),X1) = subset_complement(the_carrier(X4),X3)
| esk395_2(X4,X2) = subset_complement(the_carrier(X4),X6)
| ~ in(X1,X2)
| ~ element(X3,powerset(the_carrier(X4)))
| X3 != X1
| X5 != subset_complement(the_carrier(X4),esk398_3(X4,X2,X5))
| ~ element(X6,powerset(the_carrier(X4)))
| X6 != esk394_2(X4,X2)
| ~ one_sorted_str(X4)
| ~ element(X2,powerset(powerset(the_carrier(X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3063,lemma,
( apply(esk393_2(X2,X3),X1) = subset_complement(the_carrier(X2),X4)
| element(esk392_3(X2,X3,X5),powerset(the_carrier(X2)))
| esk390_2(X2,X3) = subset_complement(the_carrier(X2),X6)
| ~ in(X1,complements_of_subsets(the_carrier(X2),X3))
| ~ element(X4,powerset(the_carrier(X2)))
| X4 != X1
| ~ element(X6,powerset(the_carrier(X2)))
| X6 != esk388_2(X2,X3)
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3064,lemma,
( apply(esk393_2(X2,X3),X1) = subset_complement(the_carrier(X2),X4)
| element(esk392_3(X2,X3,X5),powerset(the_carrier(X2)))
| esk389_2(X2,X3) = subset_complement(the_carrier(X2),X6)
| ~ in(X1,complements_of_subsets(the_carrier(X2),X3))
| ~ element(X4,powerset(the_carrier(X2)))
| X4 != X1
| ~ element(X6,powerset(the_carrier(X2)))
| X6 != esk388_2(X2,X3)
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3065,plain,
( in(esk14_3(X1,X2,X3),esk15_3(X1,X2,X3))
| X3 = topstr_closure(X1,X2)
| ~ in(esk14_3(X1,X2,X3),X3)
| ~ element(X3,powerset(the_carrier(X1)))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1420]),
[final] ).
cnf(i_0_3066,lemma,
( apply(esk393_2(X2,X3),X1) = subset_complement(the_carrier(X2),X4)
| ~ in(X1,complements_of_subsets(the_carrier(X2),X3))
| ~ element(X4,powerset(the_carrier(X2)))
| X4 != X1
| X5 != subset_complement(the_carrier(X2),esk392_3(X2,X3,X5))
| esk389_2(X2,X3) != esk390_2(X2,X3)
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3067,plain,
( in(esk14_3(X1,X2,X3),X3)
| X3 = topstr_closure(X1,X2)
| ~ element(X4,powerset(the_carrier(X1)))
| ~ open_subset(X4,X1)
| ~ in(esk14_3(X1,X2,X3),X4)
| ~ disjoint(X2,X4)
| ~ element(X3,powerset(the_carrier(X1)))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1420]),
[final] ).
cnf(i_0_3068,plain,
( X3 = X4
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X3,X2)
| ~ is_antisymmetric_in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X4,X3),unordered_pair(X4,X4)),X1)
| ~ in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1483,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_3069,lemma,
( esk191_2(X2,X3) = subset_complement(the_carrier(X2),X5)
| in(X1,complements_of_subsets(the_carrier(X2),X3))
| X5 != esk189_2(X2,X3)
| ~ one_sorted_str(X2)
| ~ element(X5,powerset(the_carrier(X2)))
| ~ element(X3,powerset(powerset(the_carrier(X2))))
| ~ in(unordered_pair(unordered_pair(X1,X4),unordered_pair(X1,X1)),esk192_2(X2,X3)) ),
inference(rw,[status(thm)],[i_0_1484,c_0_944]),
[final] ).
cnf(i_0_3070,lemma,
( esk190_2(X2,X3) = subset_complement(the_carrier(X2),X5)
| in(X1,complements_of_subsets(the_carrier(X2),X3))
| X5 != esk189_2(X2,X3)
| ~ one_sorted_str(X2)
| ~ element(X5,powerset(the_carrier(X2)))
| ~ element(X3,powerset(powerset(the_carrier(X2))))
| ~ in(unordered_pair(unordered_pair(X1,X4),unordered_pair(X1,X1)),esk192_2(X2,X3)) ),
inference(rw,[status(thm)],[i_0_1485,c_0_944]),
[final] ).
cnf(i_0_3071,lemma,
( X1 = relation_dom_restriction(X3,X2)
| relation_dom(X1) != set_difference(relation_dom(X3),set_difference(relation_dom(X3),X2))
| apply(X1,esk439_3(X2,X1,X3)) != apply(X3,esk439_3(X2,X1,X3))
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1) ),
inference(rw,[status(thm)],[i_0_1486,c_0_1442]),
[final] ).
cnf(i_0_3072,lemma,
( X4 = subset_complement(the_carrier(X2),X1)
| in(esk189_2(X2,X5),complements_of_subsets(the_carrier(X2),X5))
| X1 != X3
| ~ one_sorted_str(X2)
| ~ element(X1,powerset(the_carrier(X2)))
| ~ element(X5,powerset(powerset(the_carrier(X2))))
| ~ in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),esk192_2(X2,X5)) ),
inference(rw,[status(thm)],[i_0_1487,c_0_944]),
[final] ).
cnf(i_0_3073,lemma,
( X4 = subset_complement(the_carrier(X2),X1)
| in(esk189_2(X2,X5),complements_of_subsets(the_carrier(X2),X5))
| X1 != X3
| ~ one_sorted_str(X2)
| ~ element(X1,powerset(the_carrier(X2)))
| ~ element(X5,powerset(powerset(the_carrier(X2))))
| ~ in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),esk192_2(X2,X5)) ),
inference(rw,[status(thm)],[i_0_1488,c_0_944]),
[final] ).
cnf(i_0_3074,plain,
( esk299_4(X1,X2,X3,X4) = X4
| in(X3,esk297_2(X1,X2))
| esk296_2(X1,X2) = subset_complement(the_carrier(X1),X5)
| ~ in(X4,X2)
| ~ element(X5,powerset(the_carrier(X1)))
| X5 != esk294_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1303]),
[final] ).
cnf(i_0_3075,plain,
( esk299_4(X1,X2,X3,X4) = X4
| in(X3,esk297_2(X1,X2))
| esk295_2(X1,X2) = subset_complement(the_carrier(X1),X5)
| ~ in(X4,X2)
| ~ element(X5,powerset(the_carrier(X1)))
| X5 != esk294_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1303]),
[final] ).
cnf(i_0_3076,plain,
( in(esk87_3(X1,X2,X3),X2)
| X3 = set_difference(X1,X2)
| ~ in(esk87_3(X1,X2,X3),X3)
| ~ in(esk87_3(X1,X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1489]),
[final] ).
cnf(i_0_3077,plain,
( esk225_4(X1,X2,X3,X4) = X4
| in(esk222_2(X1,X2),esk223_2(X1,X2))
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]),
[final] ).
cnf(i_0_3078,plain,
( esk225_4(X1,X2,X3,X4) = X4
| in(esk219_2(X1,X2),esk220_2(X1,X2))
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]),
[final] ).
cnf(i_0_3079,lemma,
( apply(esk393_2(X2,X3),X1) = subset_complement(the_carrier(X2),X4)
| element(esk392_3(X2,X3,X5),powerset(the_carrier(X2)))
| in(esk388_2(X2,X3),complements_of_subsets(the_carrier(X2),X3))
| ~ in(X1,complements_of_subsets(the_carrier(X2),X3))
| ~ element(X4,powerset(the_carrier(X2)))
| X4 != X1
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3080,plain,
( esk281_4(X1,X2,X3,X4) = X4
| in(X3,esk279_2(X1,X2))
| ~ in(X4,complements_of_subsets(the_carrier(X1),X2))
| esk277_2(X1,X2) != esk278_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1284]),
[final] ).
cnf(i_0_3081,plain,
( in(esk252_3(X1,X2,X3),X3)
| X3 = empty_set
| epred2_3(esk248_1(X1),esk247_1(X1),esk246_1(X1))
| ~ element(X3,powerset(powerset(esk251_2(X1,X2))))
| ~ in(esk251_2(X1,X2),omega)
| ~ in(X2,esk249_1(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_717]),
[final] ).
cnf(i_0_3082,lemma,
( in(X1,complements_of_subsets(the_carrier(X2),X3))
| in(esk189_2(X2,X3),complements_of_subsets(the_carrier(X2),X3))
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2))))
| ~ in(unordered_pair(unordered_pair(X1,X4),unordered_pair(X1,X1)),esk192_2(X2,X3)) ),
inference(rw,[status(thm)],[i_0_1490,c_0_944]),
[final] ).
cnf(i_0_3083,lemma,
( in(X1,complements_of_subsets(the_carrier(X2),X3))
| in(esk189_2(X2,X3),complements_of_subsets(the_carrier(X2),X3))
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2))))
| ~ in(unordered_pair(unordered_pair(X1,X4),unordered_pair(X1,X1)),esk192_2(X2,X3)) ),
inference(rw,[status(thm)],[i_0_1491,c_0_944]),
[final] ).
cnf(i_0_3084,plain,
( esk225_4(X1,X2,X3,X4) = X4
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| esk216_2(X1,X2) != esk217_2(X1,X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]),
[final] ).
cnf(i_0_3085,plain,
( in(esk113_3(X1,X2,X3),X3)
| in(subset_complement(X1,esk113_3(X1,X2,X3)),X2)
| X3 = complements_of_subsets(X1,X2)
| ~ element(X3,powerset(powerset(X1)))
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1417]),
[final] ).
cnf(i_0_3086,plain,
( esk225_4(X1,X2,X3,X4) = X4
| in(esk221_2(X1,X2),X1)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]),
[final] ).
cnf(i_0_3087,plain,
( esk225_4(X1,X2,X3,X4) = X4
| in(esk218_2(X1,X2),X1)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]),
[final] ).
cnf(i_0_3088,lemma,
( esk196_2(X4,X2) = subset_complement(the_carrier(X4),X5)
| in(X1,X2)
| X5 != esk194_2(X4,X2)
| ~ one_sorted_str(X4)
| ~ element(X5,powerset(the_carrier(X4)))
| ~ element(X2,powerset(powerset(the_carrier(X4))))
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),esk197_2(X4,X2)) ),
inference(rw,[status(thm)],[i_0_1492,c_0_944]),
[final] ).
cnf(i_0_3089,lemma,
( esk195_2(X4,X2) = subset_complement(the_carrier(X4),X5)
| in(X1,X2)
| X5 != esk194_2(X4,X2)
| ~ one_sorted_str(X4)
| ~ element(X5,powerset(the_carrier(X4)))
| ~ element(X2,powerset(powerset(the_carrier(X4))))
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),esk197_2(X4,X2)) ),
inference(rw,[status(thm)],[i_0_1493,c_0_944]),
[final] ).
cnf(i_0_3090,lemma,
( X4 = subset_complement(the_carrier(X2),X1)
| X1 != X3
| esk196_2(X2,X5) != esk195_2(X2,X5)
| ~ one_sorted_str(X2)
| ~ element(X1,powerset(the_carrier(X2)))
| ~ element(X5,powerset(powerset(the_carrier(X2))))
| ~ in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),esk197_2(X2,X5)) ),
inference(rw,[status(thm)],[i_0_1494,c_0_944]),
[final] ).
cnf(i_0_3091,lemma,
( X4 = subset_complement(the_carrier(X2),X1)
| X1 != X3
| esk191_2(X2,X5) != esk190_2(X2,X5)
| ~ one_sorted_str(X2)
| ~ element(X1,powerset(the_carrier(X2)))
| ~ element(X5,powerset(powerset(the_carrier(X2))))
| ~ in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),esk192_2(X2,X5)) ),
inference(rw,[status(thm)],[i_0_1495,c_0_944]),
[final] ).
cnf(i_0_3092,lemma,
( apply(esk399_2(X4,X2),X1) = subset_complement(the_carrier(X4),X3)
| element(esk398_3(X4,X2,X5),powerset(the_carrier(X4)))
| esk396_2(X4,X2) = subset_complement(the_carrier(X4),X6)
| ~ in(X1,X2)
| ~ element(X3,powerset(the_carrier(X4)))
| X3 != X1
| ~ element(X6,powerset(the_carrier(X4)))
| X6 != esk394_2(X4,X2)
| ~ one_sorted_str(X4)
| ~ element(X2,powerset(powerset(the_carrier(X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3093,lemma,
( apply(esk399_2(X4,X2),X1) = subset_complement(the_carrier(X4),X3)
| element(esk398_3(X4,X2,X5),powerset(the_carrier(X4)))
| esk395_2(X4,X2) = subset_complement(the_carrier(X4),X6)
| ~ in(X1,X2)
| ~ element(X3,powerset(the_carrier(X4)))
| X3 != X1
| ~ element(X6,powerset(the_carrier(X4)))
| X6 != esk394_2(X4,X2)
| ~ one_sorted_str(X4)
| ~ element(X2,powerset(powerset(the_carrier(X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3094,lemma,
( apply(esk393_2(X2,X3),X1) = subset_complement(the_carrier(X2),X4)
| in(esk391_2(X2,X3),complements_of_subsets(the_carrier(X2),X3))
| esk390_2(X2,X3) = subset_complement(the_carrier(X2),X5)
| ~ in(X1,complements_of_subsets(the_carrier(X2),X3))
| ~ element(X4,powerset(the_carrier(X2)))
| X4 != X1
| ~ element(X5,powerset(the_carrier(X2)))
| X5 != esk388_2(X2,X3)
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3095,lemma,
( apply(esk393_2(X2,X3),X1) = subset_complement(the_carrier(X2),X4)
| in(esk391_2(X2,X3),complements_of_subsets(the_carrier(X2),X3))
| esk389_2(X2,X3) = subset_complement(the_carrier(X2),X5)
| ~ in(X1,complements_of_subsets(the_carrier(X2),X3))
| ~ element(X4,powerset(the_carrier(X2)))
| X4 != X1
| ~ element(X5,powerset(the_carrier(X2)))
| X5 != esk388_2(X2,X3)
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3096,lemma,
( X4 = subset_complement(the_carrier(X2),X1)
| in(esk194_2(X2,X5),X5)
| X1 != X3
| ~ one_sorted_str(X2)
| ~ element(X1,powerset(the_carrier(X2)))
| ~ element(X5,powerset(powerset(the_carrier(X2))))
| ~ in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),esk197_2(X2,X5)) ),
inference(rw,[status(thm)],[i_0_1496,c_0_944]),
[final] ).
cnf(i_0_3097,lemma,
( X4 = subset_complement(the_carrier(X2),X1)
| in(esk194_2(X2,X5),X5)
| X1 != X3
| ~ one_sorted_str(X2)
| ~ element(X1,powerset(the_carrier(X2)))
| ~ element(X5,powerset(powerset(the_carrier(X2))))
| ~ in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),esk197_2(X2,X5)) ),
inference(rw,[status(thm)],[i_0_1497,c_0_944]),
[final] ).
cnf(i_0_3098,lemma,
( apply(esk399_2(X4,X2),X1) = subset_complement(the_carrier(X4),X3)
| ~ in(X1,X2)
| ~ element(X3,powerset(the_carrier(X4)))
| X3 != X1
| X5 != subset_complement(the_carrier(X4),esk398_3(X4,X2,X5))
| esk395_2(X4,X2) != esk396_2(X4,X2)
| ~ one_sorted_str(X4)
| ~ element(X2,powerset(powerset(the_carrier(X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3099,plain,
( esk225_4(X1,X2,X3,X4) = X4
| esk221_2(X1,X2) = esk223_2(X1,X2)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]),
[final] ).
cnf(i_0_3100,plain,
( esk225_4(X1,X2,X3,X4) = X4
| esk218_2(X1,X2) = esk220_2(X1,X2)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]),
[final] ).
cnf(i_0_3101,plain,
( esk225_4(X1,X2,X3,X4) = X4
| esk215_2(X1,X2) = esk217_2(X1,X2)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]),
[final] ).
cnf(i_0_3102,plain,
( esk225_4(X1,X2,X3,X4) = X4
| esk215_2(X1,X2) = esk216_2(X1,X2)
| empty(X1)
| ~ in(X4,esk224_3(X1,X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_679]),
[final] ).
cnf(i_0_3103,lemma,
( apply(esk393_2(X2,X3),X1) = subset_complement(the_carrier(X2),X4)
| element(esk392_3(X2,X3,X5),powerset(the_carrier(X2)))
| ~ in(X1,complements_of_subsets(the_carrier(X2),X3))
| ~ element(X4,powerset(the_carrier(X2)))
| X4 != X1
| esk389_2(X2,X3) != esk390_2(X2,X3)
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3104,plain,
( in(X3,esk331_3(X5,X4,X2))
| ~ in(X1,powerset(relation_dom(X2)))
| X1 != X3
| ~ in(relation_image(X2,X3),X4)
| esk329_3(X5,X4,X2) != esk330_3(X5,X4,X2)
| ~ element(X4,powerset(powerset(X5)))
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1309]),
[final] ).
cnf(i_0_3105,lemma,
( apply(esk399_2(X4,X2),X1) = subset_complement(the_carrier(X4),X3)
| in(esk394_2(X4,X2),X2)
| ~ in(X1,X2)
| ~ element(X3,powerset(the_carrier(X4)))
| X3 != X1
| X5 != subset_complement(the_carrier(X4),esk398_3(X4,X2,X5))
| ~ one_sorted_str(X4)
| ~ element(X2,powerset(powerset(the_carrier(X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3106,plain,
( empty(X2)
| in(esk208_2(X2,X3),esk210_2(X2,X3))
| in(unordered_pair(unordered_pair(X4,X1),unordered_pair(X4,X4)),X3)
| ~ relation(X3)
| ~ in(X4,esk211_2(X2,X3))
| ~ in(X1,esk213_3(X2,X3,X4)) ),
inference(rw,[status(thm)],[i_0_1498,c_0_944]),
[final] ).
cnf(i_0_3107,plain,
( empty(X2)
| in(esk207_2(X2,X3),esk209_2(X2,X3))
| in(unordered_pair(unordered_pair(X4,X1),unordered_pair(X4,X4)),X3)
| ~ relation(X3)
| ~ in(X4,esk211_2(X2,X3))
| ~ in(X1,esk213_3(X2,X3,X4)) ),
inference(rw,[status(thm)],[i_0_1499,c_0_944]),
[final] ).
cnf(i_0_3108,lemma,
( apply(esk393_2(X2,X3),X1) = subset_complement(the_carrier(X2),X4)
| esk392_3(X2,X3,X5) = esk391_2(X2,X3)
| esk390_2(X2,X3) = subset_complement(the_carrier(X2),X6)
| ~ in(X1,complements_of_subsets(the_carrier(X2),X3))
| ~ element(X4,powerset(the_carrier(X2)))
| X4 != X1
| ~ element(X6,powerset(the_carrier(X2)))
| X6 != esk388_2(X2,X3)
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3109,lemma,
( apply(esk393_2(X2,X3),X1) = subset_complement(the_carrier(X2),X4)
| esk392_3(X2,X3,X5) = esk391_2(X2,X3)
| esk389_2(X2,X3) = subset_complement(the_carrier(X2),X6)
| ~ in(X1,complements_of_subsets(the_carrier(X2),X3))
| ~ element(X4,powerset(the_carrier(X2)))
| X4 != X1
| ~ element(X6,powerset(the_carrier(X2)))
| X6 != esk388_2(X2,X3)
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3110,lemma,
( X2 = X3
| ~ relation(X1)
| ~ antisymmetric(X1)
| ~ in(unordered_pair(unordered_pair(X3,X2),unordered_pair(X3,X3)),X1)
| ~ in(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1500,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_3111,plain,
( empty(X1)
| apply_as_element(X1,X3,X2,X4) = apply(X2,X4)
| ~ function(X2)
| ~ quasi_total(X2,X1,X3)
| ~ relation_of2(X2,X1,X3)
| ~ element(X4,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1501]),
[final] ).
cnf(i_0_3112,plain,
( in(relation_image(X1,X2),X3)
| ~ in(X2,esk331_3(X4,X3,X1))
| esk329_3(X4,X3,X1) != esk330_3(X4,X3,X1)
| ~ element(X3,powerset(powerset(X4)))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1309]),
[final] ).
cnf(i_0_3113,plain,
( X2 = relation_rng(X1)
| ~ relation(X1)
| ~ in(esk93_2(X1,X2),X2)
| ~ in(unordered_pair(unordered_pair(X3,esk93_2(X1,X2)),unordered_pair(X3,X3)),X1) ),
inference(rw,[status(thm)],[i_0_1502,c_0_944]),
[final] ).
cnf(i_0_3114,plain,
( esk245_3(X1,X2,X3) = unordered_pair(esk244_3(X1,X2,X3),esk244_3(X1,X2,X3))
| unordered_pair(unordered_pair(esk240_1(X1),esk241_1(X1)),unordered_pair(esk240_1(X1),esk240_1(X1))) = esk237_1(X1)
| ~ in(X3,esk242_2(X1,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1503,c_0_681]),c_0_944]),
[final] ).
cnf(i_0_3115,plain,
( esk245_3(X1,X2,X3) = unordered_pair(esk244_3(X1,X2,X3),esk244_3(X1,X2,X3))
| unordered_pair(unordered_pair(esk238_1(X1),esk239_1(X1)),unordered_pair(esk238_1(X1),esk238_1(X1))) = esk236_1(X1)
| ~ in(X3,esk242_2(X1,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1504,c_0_681]),c_0_944]),
[final] ).
cnf(i_0_3116,plain,
( X3 = X4
| ~ function(X1)
| ~ in(unordered_pair(unordered_pair(X2,X4),unordered_pair(X2,X2)),X1)
| ~ in(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1505,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_3117,lemma,
( in(X1,complements_of_subsets(the_carrier(X2),X3))
| esk191_2(X2,X3) != esk190_2(X2,X3)
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2))))
| ~ in(unordered_pair(unordered_pair(X1,X4),unordered_pair(X1,X1)),esk192_2(X2,X3)) ),
inference(rw,[status(thm)],[i_0_1506,c_0_944]),
[final] ).
cnf(i_0_3118,lemma,
( relation_dom(esk393_2(X1,X2)) = complements_of_subsets(the_carrier(X1),X2)
| esk390_2(X1,X2) = subset_complement(the_carrier(X1),X4)
| X3 != subset_complement(the_carrier(X1),esk392_3(X1,X2,X3))
| ~ element(X4,powerset(the_carrier(X1)))
| X4 != esk388_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3119,lemma,
( relation_dom(esk393_2(X1,X2)) = complements_of_subsets(the_carrier(X1),X2)
| esk389_2(X1,X2) = subset_complement(the_carrier(X1),X4)
| X3 != subset_complement(the_carrier(X1),esk392_3(X1,X2,X3))
| ~ element(X4,powerset(the_carrier(X1)))
| X4 != esk388_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3120,plain,
( element(esk15_3(X1,X2,X3),powerset(the_carrier(X1)))
| X3 = topstr_closure(X1,X2)
| ~ in(esk14_3(X1,X2,X3),X3)
| ~ element(X3,powerset(the_carrier(X1)))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1420]),
[final] ).
cnf(i_0_3121,plain,
( empty(X2)
| in(unordered_pair(unordered_pair(X4,X1),unordered_pair(X4,X4)),X3)
| esk208_2(X2,X3) != esk207_2(X2,X3)
| ~ relation(X3)
| ~ in(X4,esk211_2(X2,X3))
| ~ in(X1,esk213_3(X2,X3,X4)) ),
inference(rw,[status(thm)],[i_0_1507,c_0_944]),
[final] ).
cnf(i_0_3122,plain,
( esk299_4(X1,X2,X3,X4) = X4
| in(X3,esk297_2(X1,X2))
| ~ in(X4,X2)
| esk295_2(X1,X2) != esk296_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1303]),
[final] ).
cnf(i_0_3123,lemma,
( apply(esk393_2(X2,X3),X1) = subset_complement(the_carrier(X2),X4)
| in(esk391_2(X2,X3),complements_of_subsets(the_carrier(X2),X3))
| in(esk388_2(X2,X3),complements_of_subsets(the_carrier(X2),X3))
| ~ in(X1,complements_of_subsets(the_carrier(X2),X3))
| ~ element(X4,powerset(the_carrier(X2)))
| X4 != X1
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3124,plain,
( in(esk252_3(X1,X2,X3),X3)
| X3 = empty_set
| ~ element(X3,powerset(powerset(esk251_2(X1,X2))))
| ~ in(esk251_2(X1,X2),omega)
| ~ in(X2,esk249_1(X1))
| esk247_1(X1) != esk248_1(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_717]),
[final] ).
cnf(i_0_3125,plain,
( empty(X2)
| in(esk206_2(X2,X3),X2)
| in(unordered_pair(unordered_pair(X4,X1),unordered_pair(X4,X4)),X3)
| ~ relation(X3)
| ~ in(X4,esk211_2(X2,X3))
| ~ in(X1,esk213_3(X2,X3,X4)) ),
inference(rw,[status(thm)],[i_0_1508,c_0_944]),
[final] ).
cnf(i_0_3126,plain,
( empty(X2)
| in(esk206_2(X2,X3),X2)
| in(unordered_pair(unordered_pair(X4,X1),unordered_pair(X4,X4)),X3)
| ~ relation(X3)
| ~ in(X4,esk211_2(X2,X3))
| ~ in(X1,esk213_3(X2,X3,X4)) ),
inference(rw,[status(thm)],[i_0_1509,c_0_944]),
[final] ).
cnf(i_0_3127,plain,
( esk299_4(X1,X2,X3,X4) = X4
| in(X3,esk297_2(X1,X2))
| in(esk294_2(X1,X2),X2)
| ~ in(X4,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1303]),
[final] ).
cnf(i_0_3128,plain,
( esk299_4(X1,X2,X3,X4) = X4
| in(X3,esk297_2(X1,X2))
| in(esk294_2(X1,X2),X2)
| ~ in(X4,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1303]),
[final] ).
cnf(i_0_3129,lemma,
( apply(esk393_2(X2,X3),X1) = subset_complement(the_carrier(X2),X4)
| esk392_3(X2,X3,X5) = esk391_2(X2,X3)
| in(esk388_2(X2,X3),complements_of_subsets(the_carrier(X2),X3))
| ~ in(X1,complements_of_subsets(the_carrier(X2),X3))
| ~ element(X4,powerset(the_carrier(X2)))
| X4 != X1
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3130,plain,
( X3 = cartesian_product2(X1,X2)
| esk65_3(X1,X2,X3) != unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4))
| ~ in(X5,X2)
| ~ in(X4,X1)
| ~ in(esk65_3(X1,X2,X3),X3) ),
inference(rw,[status(thm)],[i_0_1510,c_0_944]),
[final] ).
cnf(i_0_3131,lemma,
( relation_dom(esk399_2(X1,X2)) = X2
| esk396_2(X1,X2) = subset_complement(the_carrier(X1),X4)
| X3 != subset_complement(the_carrier(X1),esk398_3(X1,X2,X3))
| ~ element(X4,powerset(the_carrier(X1)))
| X4 != esk394_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3132,lemma,
( relation_dom(esk399_2(X1,X2)) = X2
| esk395_2(X1,X2) = subset_complement(the_carrier(X1),X4)
| X3 != subset_complement(the_carrier(X1),esk398_3(X1,X2,X3))
| ~ element(X4,powerset(the_carrier(X1)))
| X4 != esk394_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3133,lemma,
( relation(esk399_2(X1,X2))
| esk396_2(X1,X2) = subset_complement(the_carrier(X1),X4)
| X3 != subset_complement(the_carrier(X1),esk398_3(X1,X2,X3))
| ~ element(X4,powerset(the_carrier(X1)))
| X4 != esk394_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3134,lemma,
( function(esk399_2(X1,X2))
| esk396_2(X1,X2) = subset_complement(the_carrier(X1),X4)
| X3 != subset_complement(the_carrier(X1),esk398_3(X1,X2,X3))
| ~ element(X4,powerset(the_carrier(X1)))
| X4 != esk394_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3135,lemma,
( relation(esk399_2(X1,X2))
| esk395_2(X1,X2) = subset_complement(the_carrier(X1),X4)
| X3 != subset_complement(the_carrier(X1),esk398_3(X1,X2,X3))
| ~ element(X4,powerset(the_carrier(X1)))
| X4 != esk394_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3136,lemma,
( function(esk399_2(X1,X2))
| esk395_2(X1,X2) = subset_complement(the_carrier(X1),X4)
| X3 != subset_complement(the_carrier(X1),esk398_3(X1,X2,X3))
| ~ element(X4,powerset(the_carrier(X1)))
| X4 != esk394_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3137,lemma,
( relation(esk393_2(X1,X2))
| esk390_2(X1,X2) = subset_complement(the_carrier(X1),X4)
| X3 != subset_complement(the_carrier(X1),esk392_3(X1,X2,X3))
| ~ element(X4,powerset(the_carrier(X1)))
| X4 != esk388_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3138,lemma,
( function(esk393_2(X1,X2))
| esk390_2(X1,X2) = subset_complement(the_carrier(X1),X4)
| X3 != subset_complement(the_carrier(X1),esk392_3(X1,X2,X3))
| ~ element(X4,powerset(the_carrier(X1)))
| X4 != esk388_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3139,lemma,
( relation(esk393_2(X1,X2))
| esk389_2(X1,X2) = subset_complement(the_carrier(X1),X4)
| X3 != subset_complement(the_carrier(X1),esk392_3(X1,X2,X3))
| ~ element(X4,powerset(the_carrier(X1)))
| X4 != esk388_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3140,lemma,
( function(esk393_2(X1,X2))
| esk389_2(X1,X2) = subset_complement(the_carrier(X1),X4)
| X3 != subset_complement(the_carrier(X1),esk392_3(X1,X2,X3))
| ~ element(X4,powerset(the_carrier(X1)))
| X4 != esk388_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3141,lemma,
( in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),relation_composition(identity_relation(X2),X4))
| ~ relation(X4)
| ~ in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),X4) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1511,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_3142,plain,
( esk210_2(X2,X3) = esk206_2(X2,X3)
| empty(X2)
| in(unordered_pair(unordered_pair(X4,X1),unordered_pair(X4,X4)),X3)
| ~ relation(X3)
| ~ in(X4,esk211_2(X2,X3))
| ~ in(X1,esk213_3(X2,X3,X4)) ),
inference(rw,[status(thm)],[i_0_1512,c_0_944]),
[final] ).
cnf(i_0_3143,plain,
( esk209_2(X2,X3) = esk206_2(X2,X3)
| empty(X2)
| in(unordered_pair(unordered_pair(X4,X1),unordered_pair(X4,X4)),X3)
| ~ relation(X3)
| ~ in(X4,esk211_2(X2,X3))
| ~ in(X1,esk213_3(X2,X3,X4)) ),
inference(rw,[status(thm)],[i_0_1513,c_0_944]),
[final] ).
cnf(i_0_3144,lemma,
( in(esk351_3(X1,X2,X3),X3)
| X3 = empty_set
| ~ element(X3,powerset(powerset(esk350_2(X1,X2))))
| ~ in(esk350_2(X1,X2),omega)
| ~ in(X2,esk349_1(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_721]),
[final] ).
cnf(i_0_3145,lemma,
( in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),relation_composition(identity_relation(X4),X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1514,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_3146,plain,
( open_subset(esk15_3(X1,X2,X3),X1)
| X3 = topstr_closure(X1,X2)
| ~ in(esk14_3(X1,X2,X3),X3)
| ~ element(X3,powerset(the_carrier(X1)))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1420]),
[final] ).
cnf(i_0_3147,plain,
( disjoint(X1,esk15_3(X2,X1,X3))
| X3 = topstr_closure(X2,X1)
| ~ in(esk14_3(X2,X1,X3),X3)
| ~ element(X3,powerset(the_carrier(X2)))
| ~ element(X1,powerset(the_carrier(X2)))
| ~ top_str(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1420]),
[final] ).
cnf(i_0_3148,plain,
( in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),X5)
| X5 != relation_dom_restriction(X4,X2)
| ~ relation(X5)
| ~ relation(X4)
| ~ in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),X4) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1515,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_3149,plain,
( in(unordered_pair(unordered_pair(X3,X1),unordered_pair(X3,X3)),X5)
| X5 != relation_rng_restriction(X2,X4)
| ~ relation(X5)
| ~ relation(X4)
| ~ in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X3,X1),unordered_pair(X3,X3)),X4) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1516,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_3150,plain,
( X4 = subset_complement(the_carrier(X2),X1)
| esk296_2(X2,X3) = subset_complement(the_carrier(X2),X5)
| ~ element(X1,powerset(the_carrier(X2)))
| X1 != esk298_3(X2,X3,X4)
| ~ in(X4,esk297_2(X2,X3))
| ~ element(X5,powerset(the_carrier(X2)))
| X5 != esk294_2(X2,X3)
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1303]),
[final] ).
cnf(i_0_3151,plain,
( X4 = subset_complement(the_carrier(X2),X1)
| esk295_2(X2,X3) = subset_complement(the_carrier(X2),X5)
| ~ element(X1,powerset(the_carrier(X2)))
| X1 != esk298_3(X2,X3,X4)
| ~ in(X4,esk297_2(X2,X3))
| ~ element(X5,powerset(the_carrier(X2)))
| X5 != esk294_2(X2,X3)
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1303]),
[final] ).
cnf(i_0_3152,plain,
( X4 = subset_complement(the_carrier(X2),X1)
| esk278_2(X2,X3) = subset_complement(the_carrier(X2),X5)
| ~ element(X1,powerset(the_carrier(X2)))
| X1 != esk280_3(X2,X3,X4)
| ~ in(X4,esk279_2(X2,X3))
| ~ element(X5,powerset(the_carrier(X2)))
| X5 != esk276_2(X2,X3)
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1284]),
[final] ).
cnf(i_0_3153,plain,
( X4 = subset_complement(the_carrier(X2),X1)
| esk277_2(X2,X3) = subset_complement(the_carrier(X2),X5)
| ~ element(X1,powerset(the_carrier(X2)))
| X1 != esk280_3(X2,X3,X4)
| ~ in(X4,esk279_2(X2,X3))
| ~ element(X5,powerset(the_carrier(X2)))
| X5 != esk276_2(X2,X3)
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1284]),
[final] ).
cnf(i_0_3154,lemma,
( in(X1,X2)
| ~ function(X5)
| ~ relation(X5)
| ~ relation(X4)
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),esk205_3(X2,X4,X5)) ),
inference(rw,[status(thm)],[i_0_1517,c_0_944]),
[final] ).
cnf(i_0_3155,lemma,
( in(X1,X2)
| ~ function(X5)
| ~ relation(X5)
| ~ relation(X4)
| ~ in(unordered_pair(unordered_pair(X3,X1),unordered_pair(X3,X3)),esk205_3(X2,X4,X5)) ),
inference(rw,[status(thm)],[i_0_1518,c_0_944]),
[final] ).
cnf(i_0_3156,plain,
( in(esk280_3(X1,X2,X3),complements_of_subsets(the_carrier(X1),X2))
| esk278_2(X1,X2) = subset_complement(the_carrier(X1),X4)
| ~ in(X3,esk279_2(X1,X2))
| ~ element(X4,powerset(the_carrier(X1)))
| X4 != esk276_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1284]),
[final] ).
cnf(i_0_3157,plain,
( in(esk280_3(X1,X2,X3),complements_of_subsets(the_carrier(X1),X2))
| esk277_2(X1,X2) = subset_complement(the_carrier(X1),X4)
| ~ in(X3,esk279_2(X1,X2))
| ~ element(X4,powerset(the_carrier(X1)))
| X4 != esk276_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1284]),
[final] ).
cnf(i_0_3158,lemma,
( relation_dom(esk393_2(X1,X2)) = complements_of_subsets(the_carrier(X1),X2)
| in(esk388_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| X3 != subset_complement(the_carrier(X1),esk392_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3159,lemma,
( in(X1,X2)
| esk196_2(X4,X2) != esk195_2(X4,X2)
| ~ one_sorted_str(X4)
| ~ element(X2,powerset(powerset(the_carrier(X4))))
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),esk197_2(X4,X2)) ),
inference(rw,[status(thm)],[i_0_1519,c_0_944]),
[final] ).
cnf(i_0_3160,plain,
( topological_space(X1)
| ~ in(subset_intersection2(the_carrier(X1),esk35_1(X1),esk36_1(X1)),the_topology(X1))
| ~ in(union_of_subsets(the_carrier(X1),esk34_1(X1)),the_topology(X1))
| ~ in(the_carrier(X1),the_topology(X1))
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1520]),
[final] ).
cnf(i_0_3161,lemma,
( in(X1,X2)
| in(esk194_2(X4,X2),X2)
| ~ one_sorted_str(X4)
| ~ element(X2,powerset(powerset(the_carrier(X4))))
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),esk197_2(X4,X2)) ),
inference(rw,[status(thm)],[i_0_1521,c_0_944]),
[final] ).
cnf(i_0_3162,lemma,
( in(X1,X2)
| in(esk194_2(X4,X2),X2)
| ~ one_sorted_str(X4)
| ~ element(X2,powerset(powerset(the_carrier(X4))))
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),esk197_2(X4,X2)) ),
inference(rw,[status(thm)],[i_0_1522,c_0_944]),
[final] ).
cnf(i_0_3163,lemma,
( apply(esk399_2(X4,X2),X1) = subset_complement(the_carrier(X4),X3)
| element(esk398_3(X4,X2,X5),powerset(the_carrier(X4)))
| ~ in(X1,X2)
| ~ element(X3,powerset(the_carrier(X4)))
| X3 != X1
| esk395_2(X4,X2) != esk396_2(X4,X2)
| ~ one_sorted_str(X4)
| ~ element(X2,powerset(powerset(the_carrier(X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3164,lemma,
( apply(esk393_2(X2,X3),X1) = subset_complement(the_carrier(X2),X4)
| in(esk391_2(X2,X3),complements_of_subsets(the_carrier(X2),X3))
| ~ in(X1,complements_of_subsets(the_carrier(X2),X3))
| ~ element(X4,powerset(the_carrier(X2)))
| X4 != X1
| esk389_2(X2,X3) != esk390_2(X2,X3)
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3165,plain,
( k10_filter_1(X1,X2,X3,X4) = unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3))
| empty_carrier(X2)
| empty_carrier(X1)
| ~ latt_str(X2)
| ~ latt_str(X1)
| ~ lattice(X2)
| ~ lattice(X1)
| ~ element(X4,the_carrier(X2))
| ~ element(X3,the_carrier(X1)) ),
inference(rw,[status(thm)],[i_0_1523,c_0_944]),
[final] ).
cnf(i_0_3166,lemma,
( apply(esk399_2(X4,X2),X1) = subset_complement(the_carrier(X4),X3)
| element(esk398_3(X4,X2,X5),powerset(the_carrier(X4)))
| in(esk394_2(X4,X2),X2)
| ~ in(X1,X2)
| ~ element(X3,powerset(the_carrier(X4)))
| X3 != X1
| ~ one_sorted_str(X4)
| ~ element(X2,powerset(powerset(the_carrier(X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3167,plain,
( in(X3,esk331_3(X5,X4,X2))
| esk328_3(X5,X4,X2) = esk330_3(X5,X4,X2)
| ~ in(X1,powerset(relation_dom(X2)))
| X1 != X3
| ~ in(relation_image(X2,X3),X4)
| ~ element(X4,powerset(powerset(X5)))
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1309]),
[final] ).
cnf(i_0_3168,plain,
( in(X3,esk331_3(X5,X4,X2))
| esk328_3(X5,X4,X2) = esk329_3(X5,X4,X2)
| ~ in(X1,powerset(relation_dom(X2)))
| X1 != X3
| ~ in(relation_image(X2,X3),X4)
| ~ element(X4,powerset(powerset(X5)))
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1309]),
[final] ).
cnf(i_0_3169,lemma,
( X2 = meet_of_latt_set(X1,X3)
| empty_carrier(X1)
| ~ below_refl(X1,esk425_3(X1,X2,X3),X2)
| ~ latt_set_smaller(X1,X2,X3)
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ complete_latt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1524]),
[final] ).
cnf(i_0_3170,plain,
( X2 = join_of_latt_set(X1,X3)
| empty_carrier(X1)
| ~ latt_str(X1)
| ~ lattice(X1)
| ~ complete_latt_str(X1)
| ~ latt_element_smaller(X1,X2,X3)
| ~ element(X2,the_carrier(X1))
| ~ below(X1,X2,esk51_3(X1,X3,X2)) ),
inference(cn,[status(thm)],[i_0_1525]),
[final] ).
cnf(i_0_3171,lemma,
( apply(esk399_2(X4,X2),X1) = subset_complement(the_carrier(X4),X3)
| esk398_3(X4,X2,X5) = esk397_2(X4,X2)
| esk396_2(X4,X2) = subset_complement(the_carrier(X4),X6)
| ~ in(X1,X2)
| ~ element(X3,powerset(the_carrier(X4)))
| X3 != X1
| ~ element(X6,powerset(the_carrier(X4)))
| X6 != esk394_2(X4,X2)
| ~ one_sorted_str(X4)
| ~ element(X2,powerset(powerset(the_carrier(X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3172,lemma,
( apply(esk399_2(X4,X2),X1) = subset_complement(the_carrier(X4),X3)
| esk398_3(X4,X2,X5) = esk397_2(X4,X2)
| esk395_2(X4,X2) = subset_complement(the_carrier(X4),X6)
| ~ in(X1,X2)
| ~ element(X3,powerset(the_carrier(X4)))
| X3 != X1
| ~ element(X6,powerset(the_carrier(X4)))
| X6 != esk394_2(X4,X2)
| ~ one_sorted_str(X4)
| ~ element(X2,powerset(powerset(the_carrier(X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3173,plain,
( in(esk267_3(X1,X2,X3),powerset(the_carrier(X1)))
| in(set_difference(cast_as_carrier_subset(X1),esk265_2(X1,X2)),X2)
| ~ in(X3,esk266_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1526]),
[final] ).
cnf(i_0_3174,plain,
( in(esk267_3(X1,X2,X3),powerset(the_carrier(X1)))
| in(set_difference(cast_as_carrier_subset(X1),esk264_2(X1,X2)),X2)
| ~ in(X3,esk266_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1526]),
[final] ).
cnf(i_0_3175,plain,
( in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3)
| X4 != relation_rng_restriction(X5,X3)
| ~ relation(X4)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X4) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1527,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_3176,plain,
( in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3)
| X4 != relation_dom_restriction(X3,X5)
| ~ relation(X4)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X4) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1528,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_3177,lemma,
( apply(esk393_2(X2,X3),X1) = subset_complement(the_carrier(X2),X4)
| esk392_3(X2,X3,X5) = esk391_2(X2,X3)
| ~ in(X1,complements_of_subsets(the_carrier(X2),X3))
| ~ element(X4,powerset(the_carrier(X2)))
| X4 != X1
| esk389_2(X2,X3) != esk390_2(X2,X3)
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3178,plain,
( in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ subset(X1,X2)
| ~ in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1529,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_3179,lemma,
( relation(esk393_2(X1,X2))
| in(esk388_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| X3 != subset_complement(the_carrier(X1),esk392_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3180,lemma,
( function(esk393_2(X1,X2))
| in(esk388_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| X3 != subset_complement(the_carrier(X1),esk392_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3181,plain,
( in(relation_image(X1,X2),X3)
| esk328_3(X4,X3,X1) = esk330_3(X4,X3,X1)
| ~ in(X2,esk331_3(X4,X3,X1))
| ~ element(X3,powerset(powerset(X4)))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1309]),
[final] ).
cnf(i_0_3182,plain,
( in(relation_image(X1,X2),X3)
| esk328_3(X4,X3,X1) = esk329_3(X4,X3,X1)
| ~ in(X2,esk331_3(X4,X3,X1))
| ~ element(X3,powerset(powerset(X4)))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1309]),
[final] ).
cnf(i_0_3183,plain,
( in(apply(X1,esk10_3(X1,X2,X3)),X2)
| in(esk10_3(X1,X2,X3),X3)
| X3 = relation_inverse_image(X1,X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1365]),
[final] ).
cnf(i_0_3184,lemma,
( in(X1,cartesian_product2(complements_of_subsets(the_carrier(X2),X3),X4))
| ~ in(X1,esk359_3(X2,X3,X4))
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_687]),
[final] ).
cnf(i_0_3185,plain,
( in(X2,esk249_1(X1))
| epred2_3(esk248_1(X1),esk247_1(X1),esk246_1(X1))
| element(esk253_3(X1,X2,X3),powerset(powerset(X3)))
| X2 != X4
| X2 != X3
| ~ ordinal(X3)
| ~ ordinal(X1)
| ~ in(X4,set_union2(X1,unordered_pair(X1,X1))) ),
inference(rw,[status(thm)],[i_0_1530,c_0_1305]),
[final] ).
cnf(i_0_3186,plain,
( X4 = subset_complement(the_carrier(X2),X1)
| in(esk276_2(X2,X3),complements_of_subsets(the_carrier(X2),X3))
| ~ element(X1,powerset(the_carrier(X2)))
| X1 != esk280_3(X2,X3,X4)
| ~ in(X4,esk279_2(X2,X3))
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1284]),
[final] ).
cnf(i_0_3187,plain,
( X4 = subset_complement(the_carrier(X2),X1)
| in(esk276_2(X2,X3),complements_of_subsets(the_carrier(X2),X3))
| ~ element(X1,powerset(the_carrier(X2)))
| X1 != esk280_3(X2,X3,X4)
| ~ in(X4,esk279_2(X2,X3))
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1284]),
[final] ).
cnf(i_0_3188,plain,
( in(esk280_3(X1,X2,X3),complements_of_subsets(the_carrier(X1),X2))
| in(esk276_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| ~ in(X3,esk279_2(X1,X2))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1284]),
[final] ).
cnf(i_0_3189,plain,
( in(esk280_3(X1,X2,X3),complements_of_subsets(the_carrier(X1),X2))
| in(esk276_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| ~ in(X3,esk279_2(X1,X2))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1284]),
[final] ).
cnf(i_0_3190,lemma,
( relation_dom(esk393_2(X1,X2)) = complements_of_subsets(the_carrier(X1),X2)
| element(esk392_3(X1,X2,X3),powerset(the_carrier(X1)))
| esk390_2(X1,X2) = subset_complement(the_carrier(X1),X4)
| ~ element(X4,powerset(the_carrier(X1)))
| X4 != esk388_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3191,lemma,
( relation_dom(esk393_2(X1,X2)) = complements_of_subsets(the_carrier(X1),X2)
| element(esk392_3(X1,X2,X3),powerset(the_carrier(X1)))
| esk389_2(X1,X2) = subset_complement(the_carrier(X1),X4)
| ~ element(X4,powerset(the_carrier(X1)))
| X4 != esk388_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3192,plain,
( X3 = set_union2(X1,X2)
| ~ in(esk62_3(X1,X2,X3),X1)
| ~ in(esk62_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_3193,plain,
( X3 = set_union2(X1,X2)
| ~ in(esk62_3(X1,X2,X3),X2)
| ~ in(esk62_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_3194,plain,
( in(unordered_pair(unordered_pair(X2,X1),unordered_pair(X2,X2)),X4)
| X3 != relation_inverse(X4)
| ~ relation(X4)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1532,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_3195,plain,
( in(unordered_pair(unordered_pair(X2,X1),unordered_pair(X2,X2)),X4)
| X4 != relation_inverse(X3)
| ~ relation(X4)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1533,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_3196,lemma,
( relation_dom(esk393_2(X1,X2)) = complements_of_subsets(the_carrier(X1),X2)
| X3 != subset_complement(the_carrier(X1),esk392_3(X1,X2,X3))
| esk389_2(X1,X2) != esk390_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3197,plain,
( in(esk298_3(X1,X2,X3),X2)
| esk296_2(X1,X2) = subset_complement(the_carrier(X1),X4)
| ~ in(X3,esk297_2(X1,X2))
| ~ element(X4,powerset(the_carrier(X1)))
| X4 != esk294_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1303]),
[final] ).
cnf(i_0_3198,plain,
( in(esk298_3(X1,X2,X3),X2)
| esk295_2(X1,X2) = subset_complement(the_carrier(X1),X4)
| ~ in(X3,esk297_2(X1,X2))
| ~ element(X4,powerset(the_carrier(X1)))
| X4 != esk294_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1303]),
[final] ).
cnf(i_0_3199,lemma,
( connected(X1)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(esk137_1(X1),esk136_1(X1)),unordered_pair(esk137_1(X1),esk137_1(X1))),X1) ),
inference(rw,[status(thm)],[i_0_1534,c_0_944]),
[final] ).
cnf(i_0_3200,lemma,
( connected(X1)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(esk136_1(X1),esk137_1(X1)),unordered_pair(esk136_1(X1),esk136_1(X1))),X1) ),
inference(rw,[status(thm)],[i_0_1535,c_0_944]),
[final] ).
cnf(i_0_3201,lemma,
( reflexive(X1)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(esk129_1(X1),esk129_1(X1)),unordered_pair(esk129_1(X1),esk129_1(X1))),X1) ),
inference(rw,[status(thm)],[i_0_1536,c_0_944]),
[final] ).
cnf(i_0_3202,lemma,
( transitive(X1)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(esk130_1(X1),esk132_1(X1)),unordered_pair(esk130_1(X1),esk130_1(X1))),X1) ),
inference(rw,[status(thm)],[i_0_1537,c_0_944]),
[final] ).
cnf(i_0_3203,plain,
( in(X3,esk266_2(X2,X4))
| in(set_difference(cast_as_carrier_subset(X2),esk265_2(X2,X4)),X4)
| ~ in(X1,powerset(the_carrier(X2)))
| X1 != X3
| ~ in(set_difference(cast_as_carrier_subset(X2),X3),X4)
| ~ topological_space(X2)
| ~ top_str(X2)
| ~ element(X4,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1526]),
[final] ).
cnf(i_0_3204,plain,
( in(X3,esk266_2(X2,X4))
| in(set_difference(cast_as_carrier_subset(X2),esk264_2(X2,X4)),X4)
| ~ in(X1,powerset(the_carrier(X2)))
| X1 != X3
| ~ in(set_difference(cast_as_carrier_subset(X2),X3),X4)
| ~ topological_space(X2)
| ~ top_str(X2)
| ~ element(X4,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1526]),
[final] ).
cnf(i_0_3205,lemma,
( X1 = esk204_2(X3,X2)
| X2 = empty_set
| X4 = esk201_2(X6,X5)
| X5 = empty_set
| ~ in(X1,X2)
| ~ subset(esk204_2(X3,X2),X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X3,omega)
| ~ ordinal(X3)
| ~ in(X4,X5)
| ~ subset(esk201_2(X6,X5),X4)
| ~ element(X5,powerset(powerset(X6)))
| ~ in(X6,omega)
| ~ in(X6,esk200_0)
| ~ ordinal(X6)
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_1538]),
[final] ).
cnf(i_0_3206,lemma,
( apply(esk399_2(X4,X2),X1) = subset_complement(the_carrier(X4),X3)
| in(esk397_2(X4,X2),X2)
| esk396_2(X4,X2) = subset_complement(the_carrier(X4),X5)
| ~ in(X1,X2)
| ~ element(X3,powerset(the_carrier(X4)))
| X3 != X1
| ~ element(X5,powerset(the_carrier(X4)))
| X5 != esk394_2(X4,X2)
| ~ one_sorted_str(X4)
| ~ element(X2,powerset(powerset(the_carrier(X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3207,lemma,
( apply(esk399_2(X4,X2),X1) = subset_complement(the_carrier(X4),X3)
| in(esk397_2(X4,X2),X2)
| esk395_2(X4,X2) = subset_complement(the_carrier(X4),X5)
| ~ in(X1,X2)
| ~ element(X3,powerset(the_carrier(X4)))
| X3 != X1
| ~ element(X5,powerset(the_carrier(X4)))
| X5 != esk394_2(X4,X2)
| ~ one_sorted_str(X4)
| ~ element(X2,powerset(powerset(the_carrier(X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3208,plain,
( X2 = pair_second(X1)
| X1 = unordered_pair(unordered_pair(esk53_2(X1,X2),esk54_2(X1,X2)),unordered_pair(esk53_2(X1,X2),esk53_2(X1,X2)))
| X1 != unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1539,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_3209,plain,
( X2 = pair_first(X1)
| X1 = unordered_pair(unordered_pair(esk32_2(X1,X2),esk33_2(X1,X2)),unordered_pair(esk32_2(X1,X2),esk32_2(X1,X2)))
| X1 != unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1540,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_3210,lemma,
( X1 = esk404_2(X3,X2)
| X2 = empty_set
| X4 = esk401_2(X6,X5)
| X5 = empty_set
| ~ in(X1,X2)
| ~ subset(esk404_2(X3,X2),X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X3,omega)
| ~ ordinal(X3)
| ~ in(X4,X5)
| ~ subset(esk401_2(X6,X5),X4)
| ~ element(X5,powerset(powerset(X6)))
| ~ in(X6,omega)
| ~ in(X6,esk400_0)
| ~ ordinal(X6) ),
inference(split_conjunct,[status(thm)],[i_0_1541]),
[final] ).
cnf(i_0_3211,plain,
( X3 = relation_image(X1,X2)
| ~ in(esk6_3(X1,X2,X3),X3)
| ~ in(X4,relation_dom(X1))
| ~ in(X4,X2)
| esk6_3(X1,X2,X3) != apply(X1,X4)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1468]),
[final] ).
cnf(i_0_3212,plain,
( in(esk62_3(X1,X2,X3),X3)
| in(esk62_3(X1,X2,X3),X1)
| in(esk62_3(X1,X2,X3),X2)
| X3 = set_union2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_3213,plain,
( unordered_pair(unordered_pair(esk240_1(X2),esk241_1(X2)),unordered_pair(esk240_1(X2),esk240_1(X2))) = esk237_1(X2)
| in(X4,esk242_2(X2,X3))
| X1 != X4
| X6 != unordered_pair(X5,X5)
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ in(X5,X2)
| ~ in(X1,cartesian_product2(X2,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1542,c_0_681]),c_0_944]),c_0_944]),
[final] ).
cnf(i_0_3214,plain,
( unordered_pair(unordered_pair(esk238_1(X2),esk239_1(X2)),unordered_pair(esk238_1(X2),esk238_1(X2))) = esk236_1(X2)
| in(X4,esk242_2(X2,X3))
| X1 != X4
| X6 != unordered_pair(X5,X5)
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ in(X5,X2)
| ~ in(X1,cartesian_product2(X2,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1543,c_0_681]),c_0_944]),c_0_944]),
[final] ).
cnf(i_0_3215,lemma,
( relation_dom(esk399_2(X1,X2)) = X2
| element(esk398_3(X1,X2,X3),powerset(the_carrier(X1)))
| esk396_2(X1,X2) = subset_complement(the_carrier(X1),X4)
| ~ element(X4,powerset(the_carrier(X1)))
| X4 != esk394_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3216,lemma,
( relation_dom(esk399_2(X1,X2)) = X2
| element(esk398_3(X1,X2,X3),powerset(the_carrier(X1)))
| esk395_2(X1,X2) = subset_complement(the_carrier(X1),X4)
| ~ element(X4,powerset(the_carrier(X1)))
| X4 != esk394_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3217,lemma,
( relation(esk399_2(X1,X2))
| element(esk398_3(X1,X2,X3),powerset(the_carrier(X1)))
| esk396_2(X1,X2) = subset_complement(the_carrier(X1),X4)
| ~ element(X4,powerset(the_carrier(X1)))
| X4 != esk394_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3218,lemma,
( function(esk399_2(X1,X2))
| element(esk398_3(X1,X2,X3),powerset(the_carrier(X1)))
| esk396_2(X1,X2) = subset_complement(the_carrier(X1),X4)
| ~ element(X4,powerset(the_carrier(X1)))
| X4 != esk394_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3219,lemma,
( relation(esk399_2(X1,X2))
| element(esk398_3(X1,X2,X3),powerset(the_carrier(X1)))
| esk395_2(X1,X2) = subset_complement(the_carrier(X1),X4)
| ~ element(X4,powerset(the_carrier(X1)))
| X4 != esk394_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3220,lemma,
( function(esk399_2(X1,X2))
| element(esk398_3(X1,X2,X3),powerset(the_carrier(X1)))
| esk395_2(X1,X2) = subset_complement(the_carrier(X1),X4)
| ~ element(X4,powerset(the_carrier(X1)))
| X4 != esk394_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3221,lemma,
( relation(esk393_2(X1,X2))
| element(esk392_3(X1,X2,X3),powerset(the_carrier(X1)))
| esk390_2(X1,X2) = subset_complement(the_carrier(X1),X4)
| ~ element(X4,powerset(the_carrier(X1)))
| X4 != esk388_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3222,lemma,
( function(esk393_2(X1,X2))
| element(esk392_3(X1,X2,X3),powerset(the_carrier(X1)))
| esk390_2(X1,X2) = subset_complement(the_carrier(X1),X4)
| ~ element(X4,powerset(the_carrier(X1)))
| X4 != esk388_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3223,lemma,
( relation(esk393_2(X1,X2))
| element(esk392_3(X1,X2,X3),powerset(the_carrier(X1)))
| esk389_2(X1,X2) = subset_complement(the_carrier(X1),X4)
| ~ element(X4,powerset(the_carrier(X1)))
| X4 != esk388_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3224,lemma,
( function(esk393_2(X1,X2))
| element(esk392_3(X1,X2,X3),powerset(the_carrier(X1)))
| esk389_2(X1,X2) = subset_complement(the_carrier(X1),X4)
| ~ element(X4,powerset(the_carrier(X1)))
| X4 != esk388_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3225,plain,
( esk241_1(X1) = unordered_pair(esk240_1(X1),esk240_1(X1))
| esk245_3(X1,X2,X3) = unordered_pair(esk244_3(X1,X2,X3),esk244_3(X1,X2,X3))
| ~ in(X3,esk242_2(X1,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1544,c_0_681]),c_0_681]),
[final] ).
cnf(i_0_3226,plain,
( esk239_1(X1) = unordered_pair(esk238_1(X1),esk238_1(X1))
| esk245_3(X1,X2,X3) = unordered_pair(esk244_3(X1,X2,X3),esk244_3(X1,X2,X3))
| ~ in(X3,esk242_2(X1,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1545,c_0_681]),c_0_681]),
[final] ).
cnf(i_0_3227,plain,
( element(esk34_1(X1),powerset(powerset(the_carrier(X1))))
| topological_space(X1)
| ~ in(subset_intersection2(the_carrier(X1),esk35_1(X1),esk36_1(X1)),the_topology(X1))
| ~ in(the_carrier(X1),the_topology(X1))
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1520]),
[final] ).
cnf(i_0_3228,lemma,
( relation_dom(esk399_2(X1,X2)) = X2
| X3 != subset_complement(the_carrier(X1),esk398_3(X1,X2,X3))
| esk395_2(X1,X2) != esk396_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3229,lemma,
( relation(esk399_2(X1,X2))
| X3 != subset_complement(the_carrier(X1),esk398_3(X1,X2,X3))
| esk395_2(X1,X2) != esk396_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3230,lemma,
( relation(esk393_2(X1,X2))
| X3 != subset_complement(the_carrier(X1),esk392_3(X1,X2,X3))
| esk389_2(X1,X2) != esk390_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3231,lemma,
( function(esk399_2(X1,X2))
| X3 != subset_complement(the_carrier(X1),esk398_3(X1,X2,X3))
| esk395_2(X1,X2) != esk396_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3232,lemma,
( function(esk393_2(X1,X2))
| X3 != subset_complement(the_carrier(X1),esk392_3(X1,X2,X3))
| esk389_2(X1,X2) != esk390_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3233,lemma,
( X2 = function_inverse(X1)
| ~ in(esk435_2(X1,X2),relation_rng(X1))
| esk436_2(X1,X2) != apply(X2,esk435_2(X1,X2))
| ~ in(esk434_2(X1,X2),relation_dom(X1))
| esk433_2(X1,X2) != apply(X1,esk434_2(X1,X2))
| relation_dom(X2) != relation_rng(X1)
| ~ relation(X2)
| ~ function(X2)
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1546]),
[final] ).
cnf(i_0_3234,lemma,
( relation_dom(esk399_2(X1,X2)) = X2
| in(esk394_2(X1,X2),X2)
| X3 != subset_complement(the_carrier(X1),esk398_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3235,lemma,
( X2 = X3
| in(unordered_pair(unordered_pair(X3,X2),unordered_pair(X3,X3)),X1)
| in(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),X1)
| ~ relation(X1)
| ~ connected(X1)
| ~ in(X3,relation_field(X1))
| ~ in(X2,relation_field(X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1547,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_3236,lemma,
( relation(esk399_2(X1,X2))
| in(esk394_2(X1,X2),X2)
| X3 != subset_complement(the_carrier(X1),esk398_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3237,lemma,
( function(esk399_2(X1,X2))
| in(esk394_2(X1,X2),X2)
| X3 != subset_complement(the_carrier(X1),esk398_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3238,plain,
( ordered_pair_as_product_element(X1,X2,X3,X4) = unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3))
| empty(X2)
| empty(X1)
| ~ element(X4,X2)
| ~ element(X3,X1) ),
inference(rw,[status(thm)],[i_0_1548,c_0_944]),
[final] ).
cnf(i_0_3239,plain,
( esk245_3(X1,X2,X3) = unordered_pair(esk244_3(X1,X2,X3),esk244_3(X1,X2,X3))
| in(esk240_1(X1),X1)
| ~ in(X3,esk242_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1549,c_0_681]),
[final] ).
cnf(i_0_3240,plain,
( esk245_3(X1,X2,X3) = unordered_pair(esk244_3(X1,X2,X3),esk244_3(X1,X2,X3))
| in(esk238_1(X1),X1)
| ~ in(X3,esk242_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1550,c_0_681]),
[final] ).
cnf(i_0_3241,plain,
( X3 = X4
| in(unordered_pair(unordered_pair(X4,X3),unordered_pair(X4,X4)),X1)
| in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),X1)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X3,X2)
| ~ is_connected_in(X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1551,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_3242,lemma,
( relation_dom(esk393_2(X1,X2)) = complements_of_subsets(the_carrier(X1),X2)
| element(esk392_3(X1,X2,X3),powerset(the_carrier(X1)))
| in(esk388_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3243,plain,
( X4 = subset_complement(the_carrier(X2),X1)
| ~ element(X1,powerset(the_carrier(X2)))
| X1 != esk298_3(X2,X3,X4)
| ~ in(X4,esk297_2(X2,X3))
| esk295_2(X2,X3) != esk296_2(X2,X3)
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1303]),
[final] ).
cnf(i_0_3244,plain,
( X4 = subset_complement(the_carrier(X2),X1)
| ~ element(X1,powerset(the_carrier(X2)))
| X1 != esk280_3(X2,X3,X4)
| ~ in(X4,esk279_2(X2,X3))
| esk277_2(X2,X3) != esk278_2(X2,X3)
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1284]),
[final] ).
cnf(i_0_3245,plain,
( in(esk280_3(X1,X2,X3),complements_of_subsets(the_carrier(X1),X2))
| ~ in(X3,esk279_2(X1,X2))
| esk277_2(X1,X2) != esk278_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1284]),
[final] ).
cnf(i_0_3246,plain,
( X1 = ordered_pair_as_product_element(the_carrier(X2),the_carrier(X2),esk125_2(X1,X2),esk126_2(X1,X2))
| empty_carrier(X2)
| ~ in(X1,a_1_0_filter_1(X2))
| ~ lattice(X2)
| ~ latt_str(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1455]),
[final] ).
cnf(i_0_3247,plain,
( related(X3,X1,X2)
| ~ rel_str(X3)
| ~ element(X2,the_carrier(X3))
| ~ element(X1,the_carrier(X3))
| ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),the_InternalRel(X3)) ),
inference(rw,[status(thm)],[i_0_1552,c_0_944]),
[final] ).
cnf(i_0_3248,plain,
( in(X1,relation_field(X2))
| ~ function(X5)
| ~ relation(X5)
| ~ relation(X4)
| ~ relation(X2)
| ~ relation_isomorphism(X2,X4,X5)
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),X2) ),
inference(rw,[status(thm)],[i_0_1553,c_0_944]),
[final] ).
cnf(i_0_3249,plain,
( in(X1,relation_field(X2))
| ~ function(X5)
| ~ relation(X5)
| ~ relation(X4)
| ~ relation(X2)
| ~ relation_isomorphism(X2,X4,X5)
| ~ in(unordered_pair(unordered_pair(X3,X1),unordered_pair(X3,X3)),X2) ),
inference(rw,[status(thm)],[i_0_1554,c_0_944]),
[final] ).
cnf(i_0_3250,plain,
( X4 = subset_complement(the_carrier(X2),X1)
| in(esk294_2(X2,X3),X3)
| ~ element(X1,powerset(the_carrier(X2)))
| X1 != esk298_3(X2,X3,X4)
| ~ in(X4,esk297_2(X2,X3))
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1303]),
[final] ).
cnf(i_0_3251,plain,
( X4 = subset_complement(the_carrier(X2),X1)
| in(esk294_2(X2,X3),X3)
| ~ element(X1,powerset(the_carrier(X2)))
| X1 != esk298_3(X2,X3,X4)
| ~ in(X4,esk297_2(X2,X3))
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1303]),
[final] ).
cnf(i_0_3252,lemma,
( empty(X2)
| in(X1,X2)
| in(esk179_2(X2,X4),esk181_2(X2,X4))
| ~ relation(X4)
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),esk182_2(X2,X4)) ),
inference(rw,[status(thm)],[i_0_1555,c_0_944]),
[final] ).
cnf(i_0_3253,lemma,
( empty(X2)
| in(X1,X2)
| in(esk178_2(X2,X4),esk180_2(X2,X4))
| ~ relation(X4)
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),esk182_2(X2,X4)) ),
inference(rw,[status(thm)],[i_0_1556,c_0_944]),
[final] ).
cnf(i_0_3254,plain,
( esk245_3(X1,X2,X3) = unordered_pair(esk244_3(X1,X2,X3),esk244_3(X1,X2,X3))
| esk237_1(X1) != esk236_1(X1)
| ~ in(X3,esk242_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1557,c_0_681]),
[final] ).
cnf(i_0_3255,plain,
( esk237_1(X1) = esk235_1(X1)
| esk245_3(X1,X2,X3) = unordered_pair(esk244_3(X1,X2,X3),esk244_3(X1,X2,X3))
| ~ in(X3,esk242_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1558,c_0_681]),
[final] ).
cnf(i_0_3256,plain,
( esk236_1(X1) = esk235_1(X1)
| esk245_3(X1,X2,X3) = unordered_pair(esk244_3(X1,X2,X3),esk244_3(X1,X2,X3))
| ~ in(X3,esk242_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1559,c_0_681]),
[final] ).
cnf(i_0_3257,plain,
( latt_element_smaller(X1,X2,X3)
| empty_carrier(X1)
| ~ below(X1,esk24_3(X1,X2,X3),X2)
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1560]),
[final] ).
cnf(i_0_3258,plain,
( latt_set_smaller(X1,X2,X3)
| empty_carrier(X1)
| ~ below(X1,X2,esk22_3(X1,X2,X3))
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1561]),
[final] ).
cnf(i_0_3259,plain,
( in(esk267_3(X1,X2,X3),powerset(the_carrier(X1)))
| ~ in(X3,esk266_2(X1,X2))
| esk264_2(X1,X2) != esk265_2(X1,X2)
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1526]),
[final] ).
cnf(i_0_3260,plain,
( relstr_set_smaller(X1,X2,X3)
| ~ related(X1,esk114_3(X1,X2,X3),X3)
| ~ element(X3,the_carrier(X1))
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1562]),
[final] ).
cnf(i_0_3261,plain,
( relstr_element_smaller(X1,X3,X2)
| ~ related(X1,X2,esk103_3(X1,X3,X2))
| ~ element(X2,the_carrier(X1))
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1563]),
[final] ).
cnf(i_0_3262,lemma,
( apply(esk399_2(X4,X2),X1) = subset_complement(the_carrier(X4),X3)
| esk398_3(X4,X2,X5) = esk397_2(X4,X2)
| ~ in(X1,X2)
| ~ element(X3,powerset(the_carrier(X4)))
| X3 != X1
| esk395_2(X4,X2) != esk396_2(X4,X2)
| ~ one_sorted_str(X4)
| ~ element(X2,powerset(powerset(the_carrier(X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3263,plain,
( in(X2,esk249_1(X1))
| epred2_3(esk248_1(X1),esk247_1(X1),esk246_1(X1))
| X2 != X4
| X2 != X3
| esk253_3(X1,X2,X3) != empty_set
| ~ ordinal(X3)
| ~ ordinal(X1)
| ~ in(X4,set_union2(X1,unordered_pair(X1,X1))) ),
inference(rw,[status(thm)],[i_0_1564,c_0_1305]),
[final] ).
cnf(i_0_3264,lemma,
( relation(esk393_2(X1,X2))
| element(esk392_3(X1,X2,X3),powerset(the_carrier(X1)))
| in(esk388_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3265,lemma,
( function(esk393_2(X1,X2))
| element(esk392_3(X1,X2,X3),powerset(the_carrier(X1)))
| in(esk388_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3266,lemma,
( esk348_3(X1,X2,X3) = unordered_pair(esk347_3(X1,X2,X3),esk347_3(X1,X2,X3))
| ~ in(X3,esk346_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1565,c_0_681]),
[final] ).
cnf(i_0_3267,lemma,
( apply(esk399_2(X4,X2),X1) = subset_complement(the_carrier(X4),X3)
| esk398_3(X4,X2,X5) = esk397_2(X4,X2)
| in(esk394_2(X4,X2),X2)
| ~ in(X1,X2)
| ~ element(X3,powerset(the_carrier(X4)))
| X3 != X1
| ~ one_sorted_str(X4)
| ~ element(X2,powerset(powerset(the_carrier(X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3268,lemma,
( in(apply(esk381_2(X1,X2),X3),esk382_3(X1,X2,X3))
| in(esk379_2(X1,X2),X1)
| in(esk376_2(X1,X2),esk378_2(X1,X2))
| empty(X1)
| ~ in(X3,X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_3269,lemma,
( in(apply(esk381_2(X1,X2),X3),esk382_3(X1,X2,X3))
| in(esk379_2(X1,X2),X1)
| in(esk375_2(X1,X2),esk377_2(X1,X2))
| empty(X1)
| ~ in(X3,X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_3270,plain,
( in(X2,esk249_1(X1))
| element(esk253_3(X1,X2,X3),powerset(powerset(X3)))
| X2 != X4
| X2 != X3
| esk248_1(X1) != esk247_1(X1)
| ~ ordinal(X3)
| ~ ordinal(X1)
| ~ in(X4,set_union2(X1,unordered_pair(X1,X1))) ),
inference(rw,[status(thm)],[i_0_1566,c_0_1305]),
[final] ).
cnf(i_0_3271,lemma,
( related(X1,X2,X4)
| ~ transitive_relstr(X1)
| ~ rel_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ~ element(X4,the_carrier(X1))
| ~ related(X1,X2,X3)
| ~ related(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1567]),
[final] ).
cnf(i_0_3272,plain,
( subset(esk34_1(X1),the_topology(X1))
| topological_space(X1)
| ~ in(subset_intersection2(the_carrier(X1),esk35_1(X1),esk36_1(X1)),the_topology(X1))
| ~ in(the_carrier(X1),the_topology(X1))
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1520]),
[final] ).
cnf(i_0_3273,lemma,
( empty(X2)
| in(X1,X2)
| esk179_2(X2,X4) != esk178_2(X2,X4)
| ~ relation(X4)
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),esk182_2(X2,X4)) ),
inference(rw,[status(thm)],[i_0_1568,c_0_944]),
[final] ).
cnf(i_0_3274,lemma,
( relation_dom(esk393_2(X1,X2)) = complements_of_subsets(the_carrier(X1),X2)
| in(esk391_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| esk390_2(X1,X2) = subset_complement(the_carrier(X1),X3)
| ~ element(X3,powerset(the_carrier(X1)))
| X3 != esk388_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3275,lemma,
( relation_dom(esk393_2(X1,X2)) = complements_of_subsets(the_carrier(X1),X2)
| in(esk391_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| esk389_2(X1,X2) = subset_complement(the_carrier(X1),X3)
| ~ element(X3,powerset(the_carrier(X1)))
| X3 != esk388_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3276,plain,
( in(esk267_3(X1,X2,X3),powerset(the_carrier(X1)))
| esk263_2(X1,X2) = esk265_2(X1,X2)
| ~ in(X3,esk266_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1526]),
[final] ).
cnf(i_0_3277,plain,
( in(esk267_3(X1,X2,X3),powerset(the_carrier(X1)))
| esk263_2(X1,X2) = esk264_2(X1,X2)
| ~ in(X3,esk266_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1526]),
[final] ).
cnf(i_0_3278,lemma,
( empty(X2)
| in(X1,X2)
| in(esk177_2(X2,X4),X2)
| ~ relation(X4)
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),esk182_2(X2,X4)) ),
inference(rw,[status(thm)],[i_0_1569,c_0_944]),
[final] ).
cnf(i_0_3279,lemma,
( empty(X2)
| in(X1,X2)
| in(esk177_2(X2,X4),X2)
| ~ relation(X4)
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),esk182_2(X2,X4)) ),
inference(rw,[status(thm)],[i_0_1570,c_0_944]),
[final] ).
cnf(i_0_3280,lemma,
( relation_dom(esk393_2(X1,X2)) = complements_of_subsets(the_carrier(X1),X2)
| element(esk392_3(X1,X2,X3),powerset(the_carrier(X1)))
| esk389_2(X1,X2) != esk390_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3281,plain,
( unordered_pair(unordered_pair(esk240_1(X1),esk241_1(X1)),unordered_pair(esk240_1(X1),esk240_1(X1))) = esk237_1(X1)
| in(esk243_3(X1,X2,X3),cartesian_product2(X1,X2))
| ~ in(X3,esk242_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1571,c_0_944]),
[final] ).
cnf(i_0_3282,plain,
( unordered_pair(unordered_pair(esk238_1(X1),esk239_1(X1)),unordered_pair(esk238_1(X1),esk238_1(X1))) = esk236_1(X1)
| in(esk243_3(X1,X2,X3),cartesian_product2(X1,X2))
| ~ in(X3,esk242_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1572,c_0_944]),
[final] ).
cnf(i_0_3283,lemma,
( in(X3,relation_inverse_image(X2,X4))
| ~ relation(X2)
| ~ in(X1,X4)
| ~ in(X1,relation_rng(X2))
| ~ in(unordered_pair(unordered_pair(X3,X1),unordered_pair(X3,X3)),X2) ),
inference(rw,[status(thm)],[i_0_1573,c_0_944]),
[final] ).
cnf(i_0_3284,lemma,
( in(X3,relation_image(X2,X4))
| ~ relation(X2)
| ~ in(X1,X4)
| ~ in(X1,relation_dom(X2))
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),X2) ),
inference(rw,[status(thm)],[i_0_1574,c_0_944]),
[final] ).
cnf(i_0_3285,plain,
( onto(X1,X2,X2)
| ~ function(X1)
| ~ v1_partfun1(X1,X2,X2)
| ~ reflexive(X1)
| ~ quasi_total(X1,X2,X2)
| ~ relation_of2(X1,X2,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1575]),
[final] ).
cnf(i_0_3286,plain,
( bijective(X1,X2,X2)
| ~ function(X1)
| ~ v1_partfun1(X1,X2,X2)
| ~ reflexive(X1)
| ~ quasi_total(X1,X2,X2)
| ~ relation_of2(X1,X2,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1575]),
[final] ).
cnf(i_0_3287,plain,
( bijective(X1,X2,X3)
| ~ function(X1)
| ~ one_to_one(X1)
| ~ quasi_total(X1,X2,X3)
| ~ onto(X1,X2,X3)
| ~ relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1576]),
[final] ).
cnf(i_0_3288,lemma,
( in(X1,cartesian_product2(X2,X3))
| ~ in(X1,esk363_3(X4,X2,X3))
| ~ one_sorted_str(X4)
| ~ element(X2,powerset(powerset(the_carrier(X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_688]),
[final] ).
cnf(i_0_3289,plain,
( esk267_3(X1,X2,X3) = X3
| in(set_difference(cast_as_carrier_subset(X1),esk265_2(X1,X2)),X2)
| ~ in(X3,esk266_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1526]),
[final] ).
cnf(i_0_3290,plain,
( esk267_3(X1,X2,X3) = X3
| in(set_difference(cast_as_carrier_subset(X1),esk264_2(X1,X2)),X2)
| ~ in(X3,esk266_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1526]),
[final] ).
cnf(i_0_3291,plain,
( element(esk262_3(X1,X2,X3),powerset(the_carrier(X1)))
| element(esk259_2(X1,X2),powerset(the_carrier(X1)))
| ~ in(X3,esk260_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3292,plain,
( in(esk261_3(X1,X2,X3),powerset(the_carrier(X1)))
| element(esk259_2(X1,X2),powerset(the_carrier(X1)))
| ~ in(X3,esk260_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3293,plain,
( element(esk262_3(X1,X2,X3),powerset(the_carrier(X1)))
| element(esk258_2(X1,X2),powerset(the_carrier(X1)))
| ~ in(X3,esk260_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3294,plain,
( in(esk261_3(X1,X2,X3),powerset(the_carrier(X1)))
| element(esk258_2(X1,X2),powerset(the_carrier(X1)))
| ~ in(X3,esk260_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3295,plain,
( in(esk87_3(X1,X2,X3),X3)
| X3 = set_difference(X1,X2)
| ~ in(esk87_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1489]),
[final] ).
cnf(i_0_3296,plain,
( in(X3,esk266_2(X2,X4))
| ~ in(X1,powerset(the_carrier(X2)))
| X1 != X3
| ~ in(set_difference(cast_as_carrier_subset(X2),X3),X4)
| esk264_2(X2,X4) != esk265_2(X2,X4)
| ~ topological_space(X2)
| ~ top_str(X2)
| ~ element(X4,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1526]),
[final] ).
cnf(i_0_3297,plain,
( esk6_3(X1,X2,X3) = apply(X1,esk7_3(X1,X2,X3))
| in(esk6_3(X1,X2,X3),X3)
| X3 = relation_image(X1,X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1468]),
[final] ).
cnf(i_0_3298,plain,
( in(esk298_3(X1,X2,X3),X2)
| ~ in(X3,esk297_2(X1,X2))
| esk295_2(X1,X2) != esk296_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1303]),
[final] ).
cnf(i_0_3299,lemma,
( relation_dom(esk393_2(X1,X2)) = complements_of_subsets(the_carrier(X1),X2)
| esk392_3(X1,X2,X3) = esk391_2(X1,X2)
| esk390_2(X1,X2) = subset_complement(the_carrier(X1),X4)
| ~ element(X4,powerset(the_carrier(X1)))
| X4 != esk388_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3300,lemma,
( relation_dom(esk393_2(X1,X2)) = complements_of_subsets(the_carrier(X1),X2)
| esk392_3(X1,X2,X3) = esk391_2(X1,X2)
| esk389_2(X1,X2) = subset_complement(the_carrier(X1),X4)
| ~ element(X4,powerset(the_carrier(X1)))
| X4 != esk388_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3301,plain,
( in(set_difference(cast_as_carrier_subset(X1),X2),X3)
| in(set_difference(cast_as_carrier_subset(X1),esk265_2(X1,X3)),X3)
| ~ in(X2,esk266_2(X1,X3))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X3,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1526]),
[final] ).
cnf(i_0_3302,plain,
( in(set_difference(cast_as_carrier_subset(X1),X2),X3)
| in(set_difference(cast_as_carrier_subset(X1),esk264_2(X1,X3)),X3)
| ~ in(X2,esk266_2(X1,X3))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X3,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1526]),
[final] ).
cnf(i_0_3303,lemma,
( in(esk204_2(X1,X2),X2)
| X2 = empty_set
| X3 = esk201_2(X5,X4)
| X4 = empty_set
| ~ element(X2,powerset(powerset(X1)))
| ~ in(X1,omega)
| ~ ordinal(X1)
| ~ in(X3,X4)
| ~ subset(esk201_2(X5,X4),X3)
| ~ element(X4,powerset(powerset(X5)))
| ~ in(X5,omega)
| ~ in(X5,esk200_0)
| ~ ordinal(X5)
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_1538]),
[final] ).
cnf(i_0_3304,lemma,
( X1 = esk204_2(X3,X2)
| X2 = empty_set
| in(esk201_2(X4,X5),X5)
| X5 = empty_set
| ~ in(X1,X2)
| ~ subset(esk204_2(X3,X2),X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X3,omega)
| ~ ordinal(X3)
| ~ element(X5,powerset(powerset(X4)))
| ~ in(X4,omega)
| ~ in(X4,esk200_0)
| ~ ordinal(X4)
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_1538]),
[final] ).
cnf(i_0_3305,plain,
( meet_absorbing(X1)
| empty_carrier(X1)
| join(X1,meet(X1,esk104_1(X1),esk105_1(X1)),esk105_1(X1)) != esk105_1(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1578]),
[final] ).
cnf(i_0_3306,lemma,
( in(esk404_2(X1,X2),X2)
| X2 = empty_set
| X3 = esk401_2(X5,X4)
| X4 = empty_set
| ~ element(X2,powerset(powerset(X1)))
| ~ in(X1,omega)
| ~ ordinal(X1)
| ~ in(X3,X4)
| ~ subset(esk401_2(X5,X4),X3)
| ~ element(X4,powerset(powerset(X5)))
| ~ in(X5,omega)
| ~ in(X5,esk400_0)
| ~ ordinal(X5) ),
inference(split_conjunct,[status(thm)],[i_0_1541]),
[final] ).
cnf(i_0_3307,lemma,
( X1 = esk404_2(X3,X2)
| X2 = empty_set
| in(esk401_2(X4,X5),X5)
| X5 = empty_set
| ~ in(X1,X2)
| ~ subset(esk404_2(X3,X2),X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X3,omega)
| ~ ordinal(X3)
| ~ element(X5,powerset(powerset(X4)))
| ~ in(X4,omega)
| ~ in(X4,esk400_0)
| ~ ordinal(X4) ),
inference(split_conjunct,[status(thm)],[i_0_1541]),
[final] ).
cnf(i_0_3308,lemma,
( in(X2,esk349_1(X1))
| element(esk352_3(X1,X2,X3),powerset(powerset(X3)))
| X2 != X3
| ~ ordinal(X3)
| ~ ordinal(X1)
| ~ in(X2,set_union2(X1,unordered_pair(X1,X1))) ),
inference(rw,[status(thm)],[i_0_1579,c_0_1305]),
[final] ).
cnf(i_0_3309,plain,
( epred1_0
| subset(X1,esk446_1(X1))
| element(esk449_0,powerset(powerset(set_union2(esk447_0,unordered_pair(esk447_0,esk447_0)))))
| ~ in(X1,esk445_0) ),
inference(rw,[status(thm)],[i_0_1580,c_0_1305]),
[final] ).
cnf(i_0_3310,plain,
( in(esk298_3(X1,X2,X3),X2)
| in(esk294_2(X1,X2),X2)
| ~ in(X3,esk297_2(X1,X2))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1303]),
[final] ).
cnf(i_0_3311,plain,
( in(esk298_3(X1,X2,X3),X2)
| in(esk294_2(X1,X2),X2)
| ~ in(X3,esk297_2(X1,X2))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1303]),
[final] ).
cnf(i_0_3312,lemma,
( in(X1,topstr_closure(X2,X3))
| ~ in(X1,esk430_3(X2,X3,X1))
| ~ in(X1,the_carrier(X2))
| ~ element(X3,powerset(the_carrier(X2)))
| ~ top_str(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1581]),
[final] ).
cnf(i_0_3313,plain,
( in(subset_intersection2(the_carrier(X2),X1,X3),the_topology(X2))
| ~ element(X1,powerset(the_carrier(X2)))
| ~ element(X3,powerset(the_carrier(X2)))
| ~ in(X1,the_topology(X2))
| ~ in(X3,the_topology(X2))
| ~ topological_space(X2)
| ~ top_str(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1520]),
[final] ).
cnf(i_0_3314,lemma,
( latt_set_smaller(X1,esk425_3(X1,X2,X3),X3)
| X2 = meet_of_latt_set(X1,X3)
| empty_carrier(X1)
| ~ latt_set_smaller(X1,X2,X3)
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ complete_latt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1524]),
[final] ).
cnf(i_0_3315,plain,
( X3 = join_of_latt_set(X1,X2)
| empty_carrier(X1)
| latt_element_smaller(X1,esk51_3(X1,X2,X3),X2)
| ~ latt_str(X1)
| ~ lattice(X1)
| ~ complete_latt_str(X1)
| ~ latt_element_smaller(X1,X3,X2)
| ~ element(X3,the_carrier(X1)) ),
inference(cn,[status(thm)],[i_0_1582]),
[final] ).
cnf(i_0_3316,lemma,
( esk181_2(X2,X4) = esk177_2(X2,X4)
| empty(X2)
| in(X1,X2)
| ~ relation(X4)
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),esk182_2(X2,X4)) ),
inference(rw,[status(thm)],[i_0_1583,c_0_944]),
[final] ).
cnf(i_0_3317,lemma,
( esk180_2(X2,X4) = esk177_2(X2,X4)
| empty(X2)
| in(X1,X2)
| ~ relation(X4)
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),esk182_2(X2,X4)) ),
inference(rw,[status(thm)],[i_0_1584,c_0_944]),
[final] ).
cnf(i_0_3318,plain,
( epred1_0
| in(esk446_1(X1),esk445_0)
| element(esk449_0,powerset(powerset(set_union2(esk447_0,unordered_pair(esk447_0,esk447_0)))))
| ~ in(X1,esk445_0) ),
inference(rw,[status(thm)],[i_0_1585,c_0_1305]),
[final] ).
cnf(i_0_3319,plain,
( onto(X1,X2,X3)
| ~ function(X1)
| ~ quasi_total(X1,X2,X3)
| ~ bijective(X1,X2,X3)
| ~ relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1586]),
[final] ).
cnf(i_0_3320,plain,
( in(X3,esk260_2(X2,X5))
| element(esk259_2(X2,X5),powerset(the_carrier(X2)))
| ~ in(X1,powerset(the_carrier(X2)))
| X1 != X3
| ~ element(X4,powerset(the_carrier(X2)))
| X4 != X3
| ~ closed_subset(X4,X2)
| ~ subset(X5,X3)
| ~ topological_space(X2)
| ~ top_str(X2)
| ~ element(X5,powerset(the_carrier(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3321,plain,
( in(X3,esk260_2(X2,X5))
| element(esk258_2(X2,X5),powerset(the_carrier(X2)))
| ~ in(X1,powerset(the_carrier(X2)))
| X1 != X3
| ~ element(X4,powerset(the_carrier(X2)))
| X4 != X3
| ~ closed_subset(X4,X2)
| ~ subset(X5,X3)
| ~ topological_space(X2)
| ~ top_str(X2)
| ~ element(X5,powerset(the_carrier(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3322,lemma,
( element(esk407_3(X1,X2,X3),powerset(the_carrier(X1)))
| ~ in(X3,esk406_2(X1,X2))
| ~ element(X3,powerset(the_carrier(X1)))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1587]),
[final] ).
cnf(i_0_3323,lemma,
( apply(esk399_2(X4,X2),X1) = subset_complement(the_carrier(X4),X3)
| in(esk397_2(X4,X2),X2)
| ~ in(X1,X2)
| ~ element(X3,powerset(the_carrier(X4)))
| X3 != X1
| esk395_2(X4,X2) != esk396_2(X4,X2)
| ~ one_sorted_str(X4)
| ~ element(X2,powerset(powerset(the_carrier(X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3324,lemma,
( in(apply(esk381_2(X1,X2),X3),esk382_3(X1,X2,X3))
| in(esk379_2(X1,X2),X1)
| empty(X1)
| ~ in(X3,X1)
| esk375_2(X1,X2) != esk376_2(X1,X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_3325,lemma,
( apply(esk399_2(X4,X2),X1) = subset_complement(the_carrier(X4),X3)
| in(esk397_2(X4,X2),X2)
| in(esk394_2(X4,X2),X2)
| ~ in(X1,X2)
| ~ element(X3,powerset(the_carrier(X4)))
| X3 != X1
| ~ one_sorted_str(X4)
| ~ element(X2,powerset(powerset(the_carrier(X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3326,lemma,
( below_refl(X1,X2,X3)
| empty_carrier(X1)
| ~ related_reflexive(poset_of_lattice(X1),cast_to_el_of_LattPOSet(X1,X2),cast_to_el_of_LattPOSet(X1,X3))
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1588]),
[final] ).
cnf(i_0_3327,lemma,
( relation(esk393_2(X1,X2))
| in(esk391_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| esk390_2(X1,X2) = subset_complement(the_carrier(X1),X3)
| ~ element(X3,powerset(the_carrier(X1)))
| X3 != esk388_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3328,lemma,
( function(esk393_2(X1,X2))
| in(esk391_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| esk390_2(X1,X2) = subset_complement(the_carrier(X1),X3)
| ~ element(X3,powerset(the_carrier(X1)))
| X3 != esk388_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3329,lemma,
( relation(esk393_2(X1,X2))
| in(esk391_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| esk389_2(X1,X2) = subset_complement(the_carrier(X1),X3)
| ~ element(X3,powerset(the_carrier(X1)))
| X3 != esk388_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3330,lemma,
( function(esk393_2(X1,X2))
| in(esk391_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| esk389_2(X1,X2) = subset_complement(the_carrier(X1),X3)
| ~ element(X3,powerset(the_carrier(X1)))
| X3 != esk388_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3331,lemma,
( in(apply(esk381_2(X1,X2),X3),esk382_3(X1,X2,X3))
| in(esk379_2(X1,X2),X1)
| in(esk374_2(X1,X2),X1)
| empty(X1)
| ~ in(X3,X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_3332,plain,
( in(esk339_3(X1,X2,X3),set_union2(X2,unordered_pair(X2,X2)))
| esk335_2(X1,X2) != esk334_2(X1,X2)
| ~ ordinal(X2)
| ~ in(X3,esk338_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1589,c_0_1305]),
[final] ).
cnf(i_0_3333,plain,
( element(esk262_3(X1,X2,X3),powerset(the_carrier(X1)))
| ~ in(X3,esk260_2(X1,X2))
| esk256_2(X1,X2) != esk257_2(X1,X2)
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3334,plain,
( in(esk261_3(X1,X2,X3),powerset(the_carrier(X1)))
| ~ in(X3,esk260_2(X1,X2))
| esk256_2(X1,X2) != esk257_2(X1,X2)
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3335,plain,
( X2 = bottom_of_semilattstr(X1)
| empty_carrier(X1)
| meet(X1,X2,esk23_2(X1,X2)) != X2
| meet(X1,esk23_2(X1,X2),X2) != X2
| ~ element(X2,the_carrier(X1))
| ~ lower_bounded_semilattstr(X1)
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1590]),
[final] ).
cnf(i_0_3336,lemma,
( relation_dom(esk399_2(X1,X2)) = X2
| element(esk398_3(X1,X2,X3),powerset(the_carrier(X1)))
| esk395_2(X1,X2) != esk396_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3337,lemma,
( relation(esk399_2(X1,X2))
| element(esk398_3(X1,X2,X3),powerset(the_carrier(X1)))
| esk395_2(X1,X2) != esk396_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3338,lemma,
( relation(esk393_2(X1,X2))
| element(esk392_3(X1,X2,X3),powerset(the_carrier(X1)))
| esk389_2(X1,X2) != esk390_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3339,lemma,
( function(esk399_2(X1,X2))
| element(esk398_3(X1,X2,X3),powerset(the_carrier(X1)))
| esk395_2(X1,X2) != esk396_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3340,lemma,
( function(esk393_2(X1,X2))
| element(esk392_3(X1,X2,X3),powerset(the_carrier(X1)))
| esk389_2(X1,X2) != esk390_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3341,lemma,
( empty_carrier(X1)
| apply_as_element(the_carrier(X1),the_carrier(X1),identity_on_carrier(X1),X2) = X2
| ~ one_sorted_str(X1)
| ~ element(X2,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1591]),
[final] ).
cnf(i_0_3342,plain,
( epred1_0
| element(esk449_0,powerset(powerset(set_union2(esk447_0,unordered_pair(esk447_0,esk447_0)))))
| esk446_1(X1) != X1
| ~ in(X1,esk445_0) ),
inference(rw,[status(thm)],[i_0_1592,c_0_1305]),
[final] ).
cnf(i_0_3343,plain,
( in(X3,esk266_2(X2,X4))
| esk263_2(X2,X4) = esk265_2(X2,X4)
| ~ in(X1,powerset(the_carrier(X2)))
| X1 != X3
| ~ in(set_difference(cast_as_carrier_subset(X2),X3),X4)
| ~ topological_space(X2)
| ~ top_str(X2)
| ~ element(X4,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1526]),
[final] ).
cnf(i_0_3344,plain,
( in(X3,esk266_2(X2,X4))
| esk263_2(X2,X4) = esk264_2(X2,X4)
| ~ in(X1,powerset(the_carrier(X2)))
| X1 != X3
| ~ in(set_difference(cast_as_carrier_subset(X2),X3),X4)
| ~ topological_space(X2)
| ~ top_str(X2)
| ~ element(X4,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1526]),
[final] ).
cnf(i_0_3345,plain,
( in(esk337_2(X1,X2),X1)
| in(esk339_3(X1,X2,X3),set_union2(X2,unordered_pair(X2,X2)))
| ~ ordinal(X2)
| ~ in(X3,esk338_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1593,c_0_1305]),
[final] ).
cnf(i_0_3346,plain,
( in(esk336_2(X1,X2),X1)
| in(esk339_3(X1,X2,X3),set_union2(X2,unordered_pair(X2,X2)))
| ~ ordinal(X2)
| ~ in(X3,esk338_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1594,c_0_1305]),
[final] ).
cnf(i_0_3347,plain,
( closed_subset(esk262_3(X1,X2,X3),X1)
| element(esk259_2(X1,X2),powerset(the_carrier(X1)))
| ~ in(X3,esk260_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3348,plain,
( closed_subset(esk262_3(X1,X2,X3),X1)
| element(esk258_2(X1,X2),powerset(the_carrier(X1)))
| ~ in(X3,esk260_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3349,plain,
( element(esk262_3(X1,X2,X3),powerset(the_carrier(X1)))
| closed_subset(esk259_2(X1,X2),X1)
| ~ in(X3,esk260_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3350,plain,
( in(esk261_3(X1,X2,X3),powerset(the_carrier(X1)))
| closed_subset(esk259_2(X1,X2),X1)
| ~ in(X3,esk260_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3351,plain,
( element(esk262_3(X1,X2,X3),powerset(the_carrier(X1)))
| closed_subset(esk258_2(X1,X2),X1)
| ~ in(X3,esk260_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3352,plain,
( in(esk261_3(X1,X2,X3),powerset(the_carrier(X1)))
| closed_subset(esk258_2(X1,X2),X1)
| ~ in(X3,esk260_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3353,plain,
( element(esk262_3(X1,X2,X3),powerset(the_carrier(X1)))
| subset(X2,esk257_2(X1,X2))
| ~ in(X3,esk260_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3354,plain,
( in(esk261_3(X1,X2,X3),powerset(the_carrier(X1)))
| subset(X2,esk257_2(X1,X2))
| ~ in(X3,esk260_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3355,plain,
( element(esk262_3(X1,X2,X3),powerset(the_carrier(X1)))
| subset(X2,esk256_2(X1,X2))
| ~ in(X3,esk260_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3356,plain,
( in(esk261_3(X1,X2,X3),powerset(the_carrier(X1)))
| subset(X2,esk256_2(X1,X2))
| ~ in(X3,esk260_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3357,plain,
( ~ in(X1,X2)
| ~ element(X3,powerset(the_carrier(X4)))
| ~ open_subset(X3,X4)
| ~ in(X1,X3)
| ~ disjoint(X5,X3)
| ~ in(X1,the_carrier(X4))
| X2 != topstr_closure(X4,X5)
| ~ element(X2,powerset(the_carrier(X4)))
| ~ element(X5,powerset(the_carrier(X4)))
| ~ top_str(X4) ),
inference(split_conjunct,[status(thm)],[i_0_1420]),
[final] ).
cnf(i_0_3358,plain,
( in(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),the_InternalRel(X1))
| ~ rel_str(X1)
| ~ related(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1)) ),
inference(rw,[status(thm)],[i_0_1595,c_0_944]),
[final] ).
cnf(i_0_3359,lemma,
( relation_dom(esk399_2(X1,X2)) = X2
| element(esk398_3(X1,X2,X3),powerset(the_carrier(X1)))
| in(esk394_2(X1,X2),X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3360,plain,
( disjoint(fiber(X1,esk75_3(X1,X2,X3)),X3)
| X3 = empty_set
| ~ subset(X3,X2)
| ~ is_well_founded_in(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1596]),
[final] ).
cnf(i_0_3361,lemma,
( in(X1,X2)
| ~ relation(X4)
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),relation_composition(identity_relation(X2),X4)) ),
inference(rw,[status(thm)],[i_0_1597,c_0_944]),
[final] ).
cnf(i_0_3362,lemma,
( in(X1,relation_inverse_image(X3,X4))
| X5 = empty_set
| ~ in(X1,X2)
| ~ in(apply(X3,X1),X4)
| ~ function(X3)
| ~ quasi_total(X3,X2,X5)
| ~ relation_of2_as_subset(X3,X2,X5) ),
inference(split_conjunct,[status(thm)],[i_0_1598]),
[final] ).
cnf(i_0_3363,lemma,
( relation(esk399_2(X1,X2))
| element(esk398_3(X1,X2,X3),powerset(the_carrier(X1)))
| in(esk394_2(X1,X2),X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3364,lemma,
( function(esk399_2(X1,X2))
| element(esk398_3(X1,X2,X3),powerset(the_carrier(X1)))
| in(esk394_2(X1,X2),X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3365,plain,
( epred1_0
| element(esk445_0,powerset(powerset(empty_set)))
| element(esk449_0,powerset(powerset(set_union2(esk447_0,unordered_pair(esk447_0,esk447_0))))) ),
inference(rw,[status(thm)],[i_0_1599,c_0_1305]),
[final] ).
cnf(i_0_3366,lemma,
( relation_dom(esk399_2(X1,X2)) = X2
| esk398_3(X1,X2,X3) = esk397_2(X1,X2)
| esk396_2(X1,X2) = subset_complement(the_carrier(X1),X4)
| ~ element(X4,powerset(the_carrier(X1)))
| X4 != esk394_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3367,lemma,
( relation_dom(esk399_2(X1,X2)) = X2
| esk398_3(X1,X2,X3) = esk397_2(X1,X2)
| esk395_2(X1,X2) = subset_complement(the_carrier(X1),X4)
| ~ element(X4,powerset(the_carrier(X1)))
| X4 != esk394_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3368,plain,
( in(X3,esk260_2(X2,X5))
| ~ in(X1,powerset(the_carrier(X2)))
| X1 != X3
| ~ element(X4,powerset(the_carrier(X2)))
| X4 != X3
| ~ closed_subset(X4,X2)
| ~ subset(X5,X3)
| esk256_2(X2,X5) != esk257_2(X2,X5)
| ~ topological_space(X2)
| ~ top_str(X2)
| ~ element(X5,powerset(the_carrier(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3369,lemma,
( relation(esk399_2(X1,X2))
| esk398_3(X1,X2,X3) = esk397_2(X1,X2)
| esk396_2(X1,X2) = subset_complement(the_carrier(X1),X4)
| ~ element(X4,powerset(the_carrier(X1)))
| X4 != esk394_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3370,lemma,
( function(esk399_2(X1,X2))
| esk398_3(X1,X2,X3) = esk397_2(X1,X2)
| esk396_2(X1,X2) = subset_complement(the_carrier(X1),X4)
| ~ element(X4,powerset(the_carrier(X1)))
| X4 != esk394_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3371,lemma,
( relation(esk399_2(X1,X2))
| esk398_3(X1,X2,X3) = esk397_2(X1,X2)
| esk395_2(X1,X2) = subset_complement(the_carrier(X1),X4)
| ~ element(X4,powerset(the_carrier(X1)))
| X4 != esk394_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3372,lemma,
( function(esk399_2(X1,X2))
| esk398_3(X1,X2,X3) = esk397_2(X1,X2)
| esk395_2(X1,X2) = subset_complement(the_carrier(X1),X4)
| ~ element(X4,powerset(the_carrier(X1)))
| X4 != esk394_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3373,lemma,
( relation(esk393_2(X1,X2))
| esk392_3(X1,X2,X3) = esk391_2(X1,X2)
| esk390_2(X1,X2) = subset_complement(the_carrier(X1),X4)
| ~ element(X4,powerset(the_carrier(X1)))
| X4 != esk388_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3374,lemma,
( function(esk393_2(X1,X2))
| esk392_3(X1,X2,X3) = esk391_2(X1,X2)
| esk390_2(X1,X2) = subset_complement(the_carrier(X1),X4)
| ~ element(X4,powerset(the_carrier(X1)))
| X4 != esk388_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3375,lemma,
( relation(esk393_2(X1,X2))
| esk392_3(X1,X2,X3) = esk391_2(X1,X2)
| esk389_2(X1,X2) = subset_complement(the_carrier(X1),X4)
| ~ element(X4,powerset(the_carrier(X1)))
| X4 != esk388_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3376,lemma,
( function(esk393_2(X1,X2))
| esk392_3(X1,X2,X3) = esk391_2(X1,X2)
| esk389_2(X1,X2) = subset_complement(the_carrier(X1),X4)
| ~ element(X4,powerset(the_carrier(X1)))
| X4 != esk388_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3377,plain,
( lower_bounded_semilattstr(X1)
| empty_carrier(X1)
| meet(X1,X2,esk12_2(X1,X2)) != X2
| meet(X1,esk12_2(X1,X2),X2) != X2
| ~ element(X2,the_carrier(X1))
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1600]),
[final] ).
cnf(i_0_3378,lemma,
( relation_dom(esk393_2(X1,X2)) = complements_of_subsets(the_carrier(X1),X2)
| in(esk391_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| in(esk388_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3379,plain,
( X2 = unordered_pair(unordered_pair(esk37_2(X1,X2),esk38_2(X1,X2)),unordered_pair(esk37_2(X1,X2),esk37_2(X1,X2)))
| ~ relation(X1)
| ~ in(X2,X1) ),
inference(rw,[status(thm)],[i_0_1601,c_0_944]),
[final] ).
cnf(i_0_3380,plain,
( unordered_pair(unordered_pair(esk240_1(X1),esk241_1(X1)),unordered_pair(esk240_1(X1),esk240_1(X1))) = esk237_1(X1)
| in(esk244_3(X1,X2,X3),X1)
| ~ in(X3,esk242_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1602,c_0_944]),
[final] ).
cnf(i_0_3381,plain,
( unordered_pair(unordered_pair(esk238_1(X1),esk239_1(X1)),unordered_pair(esk238_1(X1),esk238_1(X1))) = esk236_1(X1)
| in(esk244_3(X1,X2,X3),X1)
| ~ in(X3,esk242_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1603,c_0_944]),
[final] ).
cnf(i_0_3382,plain,
( in(X3,esk260_2(X2,X5))
| closed_subset(esk259_2(X2,X5),X2)
| ~ in(X1,powerset(the_carrier(X2)))
| X1 != X3
| ~ element(X4,powerset(the_carrier(X2)))
| X4 != X3
| ~ closed_subset(X4,X2)
| ~ subset(X5,X3)
| ~ topological_space(X2)
| ~ top_str(X2)
| ~ element(X5,powerset(the_carrier(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3383,plain,
( in(X3,esk260_2(X2,X5))
| closed_subset(esk258_2(X2,X5),X2)
| ~ in(X1,powerset(the_carrier(X2)))
| X1 != X3
| ~ element(X4,powerset(the_carrier(X2)))
| X4 != X3
| ~ closed_subset(X4,X2)
| ~ subset(X5,X3)
| ~ topological_space(X2)
| ~ top_str(X2)
| ~ element(X5,powerset(the_carrier(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3384,plain,
( in(X3,esk260_2(X2,X5))
| subset(X5,esk257_2(X2,X5))
| ~ in(X1,powerset(the_carrier(X2)))
| X1 != X3
| ~ element(X4,powerset(the_carrier(X2)))
| X4 != X3
| ~ closed_subset(X4,X2)
| ~ subset(X5,X3)
| ~ topological_space(X2)
| ~ top_str(X2)
| ~ element(X5,powerset(the_carrier(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3385,plain,
( in(X3,esk260_2(X2,X5))
| subset(X5,esk256_2(X2,X5))
| ~ in(X1,powerset(the_carrier(X2)))
| X1 != X3
| ~ element(X4,powerset(the_carrier(X2)))
| X4 != X3
| ~ closed_subset(X4,X2)
| ~ subset(X5,X3)
| ~ topological_space(X2)
| ~ top_str(X2)
| ~ element(X5,powerset(the_carrier(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3386,lemma,
( closed_subset(esk407_3(X1,X2,X3),X1)
| ~ in(X3,esk406_2(X1,X2))
| ~ element(X3,powerset(the_carrier(X1)))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1587]),
[final] ).
cnf(i_0_3387,lemma,
( in(X1,esk371_3(X4,X3,X2))
| ~ in(X1,powerset(relation_dom(X2)))
| ~ in(relation_image(X2,X1),X3)
| ~ element(X3,powerset(powerset(X4)))
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_3388,lemma,
( in(apply(esk381_2(X1,X2),X3),esk382_3(X1,X2,X3))
| in(esk379_2(X1,X2),X1)
| esk374_2(X1,X2) = esk378_2(X1,X2)
| empty(X1)
| ~ in(X3,X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_3389,lemma,
( in(apply(esk381_2(X1,X2),X3),esk382_3(X1,X2,X3))
| in(esk379_2(X1,X2),X1)
| esk374_2(X1,X2) = esk377_2(X1,X2)
| empty(X1)
| ~ in(X3,X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_3390,plain,
( subset(X1,X2)
| X3 != inclusion_relation(X4)
| ~ relation(X3)
| ~ in(X2,X4)
| ~ in(X1,X4)
| ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[i_0_1605,c_0_944]),
[final] ).
cnf(i_0_3391,plain,
( closed_subset(X2,X1)
| ~ open_subset(subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),X2),X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1606]),
[final] ).
cnf(i_0_3392,plain,
( ordinal(esk337_2(X1,X2))
| in(esk339_3(X1,X2,X3),set_union2(X2,unordered_pair(X2,X2)))
| ~ ordinal(X2)
| ~ in(X3,esk338_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1607,c_0_1305]),
[final] ).
cnf(i_0_3393,plain,
( ordinal(esk336_2(X1,X2))
| in(esk339_3(X1,X2,X3),set_union2(X2,unordered_pair(X2,X2)))
| ~ ordinal(X2)
| ~ in(X3,esk338_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1608,c_0_1305]),
[final] ).
cnf(i_0_3394,lemma,
( X3 = empty_set
| apply(relation_composition(X1,X4),X5) = apply(X4,apply(X1,X5))
| ~ function(X1)
| ~ quasi_total(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3)
| ~ relation(X4)
| ~ function(X4)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1609]),
[final] ).
cnf(i_0_3395,plain,
( esk337_2(X1,X2) = esk335_2(X1,X2)
| in(esk339_3(X1,X2,X3),set_union2(X2,unordered_pair(X2,X2)))
| ~ ordinal(X2)
| ~ in(X3,esk338_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1610,c_0_1305]),
[final] ).
cnf(i_0_3396,plain,
( esk336_2(X1,X2) = esk334_2(X1,X2)
| in(esk339_3(X1,X2,X3),set_union2(X2,unordered_pair(X2,X2)))
| ~ ordinal(X2)
| ~ in(X3,esk338_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1611,c_0_1305]),
[final] ).
cnf(i_0_3397,plain,
( esk335_2(X1,X2) = esk333_2(X1,X2)
| in(esk339_3(X1,X2,X3),set_union2(X2,unordered_pair(X2,X2)))
| ~ ordinal(X2)
| ~ in(X3,esk338_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1612,c_0_1305]),
[final] ).
cnf(i_0_3398,plain,
( esk334_2(X1,X2) = esk333_2(X1,X2)
| in(esk339_3(X1,X2,X3),set_union2(X2,unordered_pair(X2,X2)))
| ~ ordinal(X2)
| ~ in(X3,esk338_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1613,c_0_1305]),
[final] ).
cnf(i_0_3399,plain,
( element(esk262_3(X1,X2,X3),powerset(the_carrier(X1)))
| esk259_2(X1,X2) = esk257_2(X1,X2)
| ~ in(X3,esk260_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3400,plain,
( in(esk261_3(X1,X2,X3),powerset(the_carrier(X1)))
| esk259_2(X1,X2) = esk257_2(X1,X2)
| ~ in(X3,esk260_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3401,plain,
( element(esk262_3(X1,X2,X3),powerset(the_carrier(X1)))
| esk258_2(X1,X2) = esk256_2(X1,X2)
| ~ in(X3,esk260_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3402,plain,
( in(esk261_3(X1,X2,X3),powerset(the_carrier(X1)))
| esk258_2(X1,X2) = esk256_2(X1,X2)
| ~ in(X3,esk260_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3403,plain,
( element(esk262_3(X1,X2,X3),powerset(the_carrier(X1)))
| esk255_2(X1,X2) = esk257_2(X1,X2)
| ~ in(X3,esk260_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3404,plain,
( in(esk261_3(X1,X2,X3),powerset(the_carrier(X1)))
| esk255_2(X1,X2) = esk257_2(X1,X2)
| ~ in(X3,esk260_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3405,plain,
( element(esk262_3(X1,X2,X3),powerset(the_carrier(X1)))
| esk255_2(X1,X2) = esk256_2(X1,X2)
| ~ in(X3,esk260_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3406,plain,
( in(esk261_3(X1,X2,X3),powerset(the_carrier(X1)))
| esk255_2(X1,X2) = esk256_2(X1,X2)
| ~ in(X3,esk260_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3407,lemma,
( in(relation_image(X1,X2),X3)
| ~ in(X2,esk371_3(X4,X3,X1))
| ~ element(X3,powerset(powerset(X4)))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_3408,plain,
( closed_subset(esk262_3(X1,X2,X3),X1)
| ~ in(X3,esk260_2(X1,X2))
| esk256_2(X1,X2) != esk257_2(X1,X2)
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3409,plain,
( in(X1,X5)
| X5 != relation_inverse_image(X3,X4)
| ~ relation(X3)
| ~ in(X2,X4)
| ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[i_0_1614,c_0_944]),
[final] ).
cnf(i_0_3410,plain,
( in(X2,X5)
| X5 != relation_image(X3,X4)
| ~ relation(X3)
| ~ in(X1,X4)
| ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[i_0_1615,c_0_944]),
[final] ).
cnf(i_0_3411,lemma,
( relation_dom(esk393_2(X1,X2)) = complements_of_subsets(the_carrier(X1),X2)
| esk392_3(X1,X2,X3) = esk391_2(X1,X2)
| in(esk388_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3412,plain,
( epred1_0
| in(empty_set,omega)
| element(esk449_0,powerset(powerset(set_union2(esk447_0,unordered_pair(esk447_0,esk447_0))))) ),
inference(rw,[status(thm)],[i_0_1616,c_0_1305]),
[final] ).
cnf(i_0_3413,plain,
( X3 = unordered_pair(X1,X2)
| esk58_3(X1,X2,X3) != X1
| ~ in(esk58_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1617]),
[final] ).
cnf(i_0_3414,plain,
( X3 = unordered_pair(X1,X2)
| esk58_3(X1,X2,X3) != X2
| ~ in(esk58_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1617]),
[final] ).
cnf(i_0_3415,plain,
( closed_subset(esk262_3(X1,X2,X3),X1)
| closed_subset(esk259_2(X1,X2),X1)
| ~ in(X3,esk260_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3416,plain,
( closed_subset(esk262_3(X1,X2,X3),X1)
| closed_subset(esk258_2(X1,X2),X1)
| ~ in(X3,esk260_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3417,plain,
( closed_subset(esk262_3(X1,X2,X3),X1)
| subset(X2,esk257_2(X1,X2))
| ~ in(X3,esk260_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3418,plain,
( closed_subset(esk262_3(X1,X2,X3),X1)
| subset(X2,esk256_2(X1,X2))
| ~ in(X3,esk260_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3419,plain,
( in(X3,esk260_2(X2,X5))
| esk259_2(X2,X5) = esk257_2(X2,X5)
| ~ in(X1,powerset(the_carrier(X2)))
| X1 != X3
| ~ element(X4,powerset(the_carrier(X2)))
| X4 != X3
| ~ closed_subset(X4,X2)
| ~ subset(X5,X3)
| ~ topological_space(X2)
| ~ top_str(X2)
| ~ element(X5,powerset(the_carrier(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3420,plain,
( in(X3,esk260_2(X2,X5))
| esk258_2(X2,X5) = esk256_2(X2,X5)
| ~ in(X1,powerset(the_carrier(X2)))
| X1 != X3
| ~ element(X4,powerset(the_carrier(X2)))
| X4 != X3
| ~ closed_subset(X4,X2)
| ~ subset(X5,X3)
| ~ topological_space(X2)
| ~ top_str(X2)
| ~ element(X5,powerset(the_carrier(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3421,plain,
( in(X3,esk260_2(X2,X5))
| esk255_2(X2,X5) = esk257_2(X2,X5)
| ~ in(X1,powerset(the_carrier(X2)))
| X1 != X3
| ~ element(X4,powerset(the_carrier(X2)))
| X4 != X3
| ~ closed_subset(X4,X2)
| ~ subset(X5,X3)
| ~ topological_space(X2)
| ~ top_str(X2)
| ~ element(X5,powerset(the_carrier(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3422,plain,
( in(X3,esk260_2(X2,X5))
| esk255_2(X2,X5) = esk256_2(X2,X5)
| ~ in(X1,powerset(the_carrier(X2)))
| X1 != X3
| ~ element(X4,powerset(the_carrier(X2)))
| X4 != X3
| ~ closed_subset(X4,X2)
| ~ subset(X5,X3)
| ~ topological_space(X2)
| ~ top_str(X2)
| ~ element(X5,powerset(the_carrier(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3423,plain,
( esk241_1(X2) = unordered_pair(esk240_1(X2),esk240_1(X2))
| in(X4,esk242_2(X2,X3))
| X1 != X4
| X6 != unordered_pair(X5,X5)
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ in(X5,X2)
| ~ in(X1,cartesian_product2(X2,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1618,c_0_681]),c_0_681]),c_0_944]),
[final] ).
cnf(i_0_3424,plain,
( esk239_1(X2) = unordered_pair(esk238_1(X2),esk238_1(X2))
| in(X4,esk242_2(X2,X3))
| X1 != X4
| X6 != unordered_pair(X5,X5)
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ in(X5,X2)
| ~ in(X1,cartesian_product2(X2,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1619,c_0_681]),c_0_681]),c_0_944]),
[final] ).
cnf(i_0_3425,lemma,
( in(X1,powerset(relation_dom(X2)))
| ~ in(X1,esk371_3(X3,X4,X2))
| ~ element(X4,powerset(powerset(X3)))
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_3426,plain,
( X2 = apply(X3,X1)
| ~ function(X3)
| ~ relation(X3)
| ~ in(X1,relation_dom(X3))
| ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[i_0_1620,c_0_944]),
[final] ).
cnf(i_0_3427,lemma,
( element(esk425_3(X1,X2,X3),the_carrier(X1))
| X2 = meet_of_latt_set(X1,X3)
| empty_carrier(X1)
| ~ latt_set_smaller(X1,X2,X3)
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ complete_latt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1524]),
[final] ).
cnf(i_0_3428,plain,
( X3 = join_of_latt_set(X1,X2)
| empty_carrier(X1)
| element(esk51_3(X1,X2,X3),the_carrier(X1))
| ~ latt_str(X1)
| ~ lattice(X1)
| ~ complete_latt_str(X1)
| ~ latt_element_smaller(X1,X3,X2)
| ~ element(X3,the_carrier(X1)) ),
inference(cn,[status(thm)],[i_0_1621]),
[final] ).
cnf(i_0_3429,plain,
( in(X2,esk249_1(X1))
| X2 != X4
| X2 != X3
| esk248_1(X1) != esk247_1(X1)
| esk253_3(X1,X2,X3) != empty_set
| ~ ordinal(X3)
| ~ ordinal(X1)
| ~ in(X4,set_union2(X1,unordered_pair(X1,X1))) ),
inference(rw,[status(thm)],[i_0_1622,c_0_1305]),
[final] ).
cnf(i_0_3430,lemma,
( in(apply(X1,X2),X3)
| X4 = empty_set
| ~ in(X2,relation_inverse_image(X1,X3))
| ~ function(X1)
| ~ quasi_total(X1,X5,X4)
| ~ relation_of2_as_subset(X1,X5,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1598]),
[final] ).
cnf(i_0_3431,lemma,
( relation(esk393_2(X1,X2))
| in(esk391_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| in(esk388_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3432,lemma,
( function(esk393_2(X1,X2))
| in(esk391_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| in(esk388_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3433,plain,
( X3 = set_difference(X1,set_difference(X1,X2))
| in(esk77_3(X1,X2,X3),X3)
| in(esk77_3(X1,X2,X3),X1) ),
inference(rw,[status(thm)],[i_0_1623,c_0_1442]),
[final] ).
cnf(i_0_3434,plain,
( X3 = set_difference(X1,set_difference(X1,X2))
| in(esk77_3(X1,X2,X3),X3)
| in(esk77_3(X1,X2,X3),X2) ),
inference(rw,[status(thm)],[i_0_1624,c_0_1442]),
[final] ).
cnf(i_0_3435,plain,
( epred1_0
| element(esk449_0,powerset(powerset(set_union2(esk447_0,unordered_pair(esk447_0,esk447_0)))))
| esk445_0 != empty_set ),
inference(rw,[status(thm)],[i_0_1625,c_0_1305]),
[final] ).
cnf(i_0_3436,lemma,
( related_reflexive(poset_of_lattice(X1),cast_to_el_of_LattPOSet(X1,X2),cast_to_el_of_LattPOSet(X1,X3))
| empty_carrier(X1)
| ~ below_refl(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1588]),
[final] ).
cnf(i_0_3437,lemma,
( X1 = unordered_pair(X2,X2)
| esk187_1(X3) = unordered_pair(esk185_1(X3),esk185_1(X3))
| ~ in(unordered_pair(unordered_pair(X2,X1),unordered_pair(X2,X2)),esk188_1(X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1626,c_0_681]),c_0_681]),c_0_944]),
[final] ).
cnf(i_0_3438,lemma,
( X1 = unordered_pair(X2,X2)
| esk186_1(X3) = unordered_pair(esk185_1(X3),esk185_1(X3))
| ~ in(unordered_pair(unordered_pair(X2,X1),unordered_pair(X2,X2)),esk188_1(X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1627,c_0_681]),c_0_681]),c_0_944]),
[final] ).
cnf(i_0_3439,lemma,
( in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),cartesian_product2(X2,X4)) ),
inference(rw,[status(thm)],[i_0_1628,c_0_944]),
[final] ).
cnf(i_0_3440,lemma,
( in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),cartesian_product2(X2,X4)) ),
inference(rw,[status(thm)],[i_0_1629,c_0_944]),
[final] ).
cnf(i_0_3441,lemma,
( in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X3,X1),unordered_pair(X3,X3)),cartesian_product2(X4,X2)) ),
inference(rw,[status(thm)],[i_0_1630,c_0_944]),
[final] ).
cnf(i_0_3442,lemma,
( in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X3,X1),unordered_pair(X3,X3)),cartesian_product2(X4,X2)) ),
inference(rw,[status(thm)],[i_0_1631,c_0_944]),
[final] ).
cnf(i_0_3443,lemma,
( esk187_1(X2) = unordered_pair(esk185_1(X2),esk185_1(X2))
| in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),esk188_1(X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1632,c_0_681]),c_0_944]),
[final] ).
cnf(i_0_3444,lemma,
( esk186_1(X2) = unordered_pair(esk185_1(X2),esk185_1(X2))
| in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),esk188_1(X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1633,c_0_681]),c_0_944]),
[final] ).
cnf(i_0_3445,plain,
( in(esk240_1(X2),X2)
| in(X4,esk242_2(X2,X3))
| X1 != X4
| X6 != unordered_pair(X5,X5)
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ in(X5,X2)
| ~ in(X1,cartesian_product2(X2,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1634,c_0_681]),c_0_944]),
[final] ).
cnf(i_0_3446,plain,
( in(esk238_1(X2),X2)
| in(X4,esk242_2(X2,X3))
| X1 != X4
| X6 != unordered_pair(X5,X5)
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ in(X5,X2)
| ~ in(X1,cartesian_product2(X2,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1635,c_0_681]),c_0_944]),
[final] ).
cnf(i_0_3447,plain,
( in(X1,X2)
| X4 != relation_rng_restriction(X2,X5)
| ~ relation(X5)
| ~ relation(X4)
| ~ in(unordered_pair(unordered_pair(X3,X1),unordered_pair(X3,X3)),X4) ),
inference(rw,[status(thm)],[i_0_1636,c_0_944]),
[final] ).
cnf(i_0_3448,plain,
( in(X1,X2)
| X4 != relation_dom_restriction(X5,X2)
| ~ relation(X5)
| ~ relation(X4)
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),X4) ),
inference(rw,[status(thm)],[i_0_1637,c_0_944]),
[final] ).
cnf(i_0_3449,lemma,
( in(X1,esk356_2(X2,X3))
| ~ in(X1,powerset(the_carrier(X2)))
| ~ in(set_difference(cast_as_carrier_subset(X2),X1),X3)
| ~ topological_space(X2)
| ~ top_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1638]),
[final] ).
cnf(i_0_3450,lemma,
( in(X2,esk408_2(X1,X3))
| ~ in(set_difference(cast_as_carrier_subset(X1),X2),X3)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X3,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1639]),
[final] ).
cnf(i_0_3451,plain,
( closed_subset(esk262_3(X1,X2,X3),X1)
| esk259_2(X1,X2) = esk257_2(X1,X2)
| ~ in(X3,esk260_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3452,plain,
( closed_subset(esk262_3(X1,X2,X3),X1)
| esk258_2(X1,X2) = esk256_2(X1,X2)
| ~ in(X3,esk260_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3453,plain,
( closed_subset(esk262_3(X1,X2,X3),X1)
| esk255_2(X1,X2) = esk257_2(X1,X2)
| ~ in(X3,esk260_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3454,plain,
( closed_subset(esk262_3(X1,X2,X3),X1)
| esk255_2(X1,X2) = esk256_2(X1,X2)
| ~ in(X3,esk260_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3455,lemma,
( relation_dom(esk399_2(X1,X2)) = X2
| in(esk397_2(X1,X2),X2)
| esk396_2(X1,X2) = subset_complement(the_carrier(X1),X3)
| ~ element(X3,powerset(the_carrier(X1)))
| X3 != esk394_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3456,lemma,
( relation_dom(esk399_2(X1,X2)) = X2
| in(esk397_2(X1,X2),X2)
| esk395_2(X1,X2) = subset_complement(the_carrier(X1),X3)
| ~ element(X3,powerset(the_carrier(X1)))
| X3 != esk394_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3457,plain,
( in(esk10_3(X1,X2,X3),relation_dom(X1))
| in(esk10_3(X1,X2,X3),X3)
| X3 = relation_inverse_image(X1,X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1365]),
[final] ).
cnf(i_0_3458,plain,
( in(esk7_3(X1,X2,X3),relation_dom(X1))
| in(esk6_3(X1,X2,X3),X3)
| X3 = relation_image(X1,X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1468]),
[final] ).
cnf(i_0_3459,plain,
( one_to_one(X1)
| ~ function(X1)
| ~ v1_partfun1(X1,X2,X2)
| ~ reflexive(X1)
| ~ quasi_total(X1,X2,X2)
| ~ relation_of2(X1,X2,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1575]),
[final] ).
cnf(i_0_3460,lemma,
( relation(esk399_2(X1,X2))
| in(esk397_2(X1,X2),X2)
| esk396_2(X1,X2) = subset_complement(the_carrier(X1),X3)
| ~ element(X3,powerset(the_carrier(X1)))
| X3 != esk394_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3461,lemma,
( function(esk399_2(X1,X2))
| in(esk397_2(X1,X2),X2)
| esk396_2(X1,X2) = subset_complement(the_carrier(X1),X3)
| ~ element(X3,powerset(the_carrier(X1)))
| X3 != esk394_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3462,lemma,
( relation(esk399_2(X1,X2))
| in(esk397_2(X1,X2),X2)
| esk395_2(X1,X2) = subset_complement(the_carrier(X1),X3)
| ~ element(X3,powerset(the_carrier(X1)))
| X3 != esk394_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3463,lemma,
( function(esk399_2(X1,X2))
| in(esk397_2(X1,X2),X2)
| esk395_2(X1,X2) = subset_complement(the_carrier(X1),X3)
| ~ element(X3,powerset(the_carrier(X1)))
| X3 != esk394_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3464,lemma,
( relation(esk393_2(X1,X2))
| esk392_3(X1,X2,X3) = esk391_2(X1,X2)
| in(esk388_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3465,lemma,
( function(esk393_2(X1,X2))
| esk392_3(X1,X2,X3) = esk391_2(X1,X2)
| in(esk388_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3466,plain,
( X1 = X2
| in(X1,X4)
| X4 != fiber(X3,X2)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[i_0_1640,c_0_944]),
[final] ).
cnf(i_0_3467,plain,
( in(X3,esk338_2(X5,X2))
| X3 != X4
| X1 != X3
| esk335_2(X5,X2) != esk334_2(X5,X2)
| ~ ordinal(X4)
| ~ ordinal(X2)
| ~ in(X4,X5)
| ~ in(X1,set_union2(X2,unordered_pair(X2,X2))) ),
inference(rw,[status(thm)],[i_0_1641,c_0_1305]),
[final] ).
cnf(i_0_3468,plain,
( in(X1,omega)
| in(X2,esk249_1(X4))
| epred2_3(esk248_1(X4),esk247_1(X4),esk246_1(X4))
| X2 != X3
| X1 != X2
| ~ ordinal(X4)
| ~ ordinal(X1)
| ~ in(X3,set_union2(X4,unordered_pair(X4,X4))) ),
inference(rw,[status(thm)],[i_0_1642,c_0_1305]),
[final] ).
cnf(i_0_3469,plain,
( in(X4,esk242_2(X2,X3))
| X1 != X4
| X6 != unordered_pair(X5,X5)
| esk237_1(X2) != esk236_1(X2)
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ in(X5,X2)
| ~ in(X1,cartesian_product2(X2,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1643,c_0_681]),c_0_944]),
[final] ).
cnf(i_0_3470,plain,
( in(esk7_3(X1,X2,X3),X2)
| in(esk6_3(X1,X2,X3),X3)
| X3 = relation_image(X1,X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1468]),
[final] ).
cnf(i_0_3471,lemma,
( in(set_difference(cast_as_carrier_subset(X2),X1),X3)
| ~ in(X1,esk408_2(X2,X3))
| ~ element(X1,powerset(the_carrier(X2)))
| ~ topological_space(X2)
| ~ top_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1639]),
[final] ).
cnf(i_0_3472,lemma,
( X1 = unordered_pair(X2,X2)
| in(esk185_1(X3),X3)
| ~ in(unordered_pair(unordered_pair(X2,X1),unordered_pair(X2,X2)),esk188_1(X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1644,c_0_681]),c_0_944]),
[final] ).
cnf(i_0_3473,lemma,
( X1 = unordered_pair(X2,X2)
| in(esk185_1(X3),X3)
| ~ in(unordered_pair(unordered_pair(X2,X1),unordered_pair(X2,X2)),esk188_1(X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1645,c_0_681]),c_0_944]),
[final] ).
cnf(i_0_3474,lemma,
( in(X1,X2)
| in(esk185_1(X2),X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),esk188_1(X2)) ),
inference(rw,[status(thm)],[i_0_1646,c_0_944]),
[final] ).
cnf(i_0_3475,lemma,
( in(X1,X2)
| in(esk185_1(X2),X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),esk188_1(X2)) ),
inference(rw,[status(thm)],[i_0_1647,c_0_944]),
[final] ).
cnf(i_0_3476,lemma,
( element(esk430_3(X1,X2,X3),powerset(the_carrier(X1)))
| in(X3,topstr_closure(X1,X2))
| ~ in(X3,the_carrier(X1))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1581]),
[final] ).
cnf(i_0_3477,plain,
( one_to_one(X1)
| ~ function(X1)
| ~ quasi_total(X1,X2,X3)
| ~ bijective(X1,X2,X3)
| ~ relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1586]),
[final] ).
cnf(i_0_3478,lemma,
( relation_dom(esk393_2(X1,X2)) = complements_of_subsets(the_carrier(X1),X2)
| in(esk391_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| esk389_2(X1,X2) != esk390_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3479,plain,
( in(X3,esk338_2(X5,X2))
| in(esk337_2(X5,X2),X5)
| X3 != X4
| X1 != X3
| ~ ordinal(X4)
| ~ ordinal(X2)
| ~ in(X4,X5)
| ~ in(X1,set_union2(X2,unordered_pair(X2,X2))) ),
inference(rw,[status(thm)],[i_0_1648,c_0_1305]),
[final] ).
cnf(i_0_3480,plain,
( in(X3,esk338_2(X5,X2))
| in(esk336_2(X5,X2),X5)
| X3 != X4
| X1 != X3
| ~ ordinal(X4)
| ~ ordinal(X2)
| ~ in(X4,X5)
| ~ in(X1,set_union2(X2,unordered_pair(X2,X2))) ),
inference(rw,[status(thm)],[i_0_1649,c_0_1305]),
[final] ).
cnf(i_0_3481,lemma,
( in(X2,esk349_1(X1))
| X2 != X3
| esk352_3(X1,X2,X3) != empty_set
| ~ ordinal(X3)
| ~ ordinal(X1)
| ~ in(X2,set_union2(X1,unordered_pair(X1,X1))) ),
inference(rw,[status(thm)],[i_0_1650,c_0_1305]),
[final] ).
cnf(i_0_3482,lemma,
( X2 = relation_dom_restriction(X3,X1)
| in(esk439_3(X1,X2,X3),relation_dom(X2))
| relation_dom(X2) != set_difference(relation_dom(X3),set_difference(relation_dom(X3),X1))
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2) ),
inference(rw,[status(thm)],[i_0_1651,c_0_1442]),
[final] ).
cnf(i_0_3483,lemma,
( element(esk355_3(X1,X2,X3),powerset(the_carrier(X1)))
| ~ in(X3,esk354_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1652]),
[final] ).
cnf(i_0_3484,plain,
( esk237_1(X2) = esk235_1(X2)
| in(X4,esk242_2(X2,X3))
| X1 != X4
| X6 != unordered_pair(X5,X5)
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ in(X5,X2)
| ~ in(X1,cartesian_product2(X2,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1653,c_0_681]),c_0_944]),
[final] ).
cnf(i_0_3485,plain,
( esk236_1(X2) = esk235_1(X2)
| in(X4,esk242_2(X2,X3))
| X1 != X4
| X6 != unordered_pair(X5,X5)
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ in(X5,X2)
| ~ in(X1,cartesian_product2(X2,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1654,c_0_681]),c_0_944]),
[final] ).
cnf(i_0_3486,plain,
( esk267_3(X1,X2,X3) = X3
| ~ in(X3,esk266_2(X1,X2))
| esk264_2(X1,X2) != esk265_2(X1,X2)
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1526]),
[final] ).
cnf(i_0_3487,lemma,
( esk435_2(X1,X2) = apply(X1,esk436_2(X1,X2))
| X2 = function_inverse(X1)
| ~ in(esk434_2(X1,X2),relation_dom(X1))
| esk433_2(X1,X2) != apply(X1,esk434_2(X1,X2))
| relation_dom(X2) != relation_rng(X1)
| ~ relation(X2)
| ~ function(X2)
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1546]),
[final] ).
cnf(i_0_3488,lemma,
( esk434_2(X1,X2) = apply(X2,esk433_2(X1,X2))
| X2 = function_inverse(X1)
| ~ in(esk435_2(X1,X2),relation_rng(X1))
| esk436_2(X1,X2) != apply(X2,esk435_2(X1,X2))
| relation_dom(X2) != relation_rng(X1)
| ~ relation(X2)
| ~ function(X2)
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1546]),
[final] ).
cnf(i_0_3489,lemma,
( in(X1,X4)
| ~ in(X1,topstr_closure(X2,X3))
| ~ element(X4,powerset(the_carrier(X2)))
| ~ closed_subset(X4,X2)
| ~ subset(X3,X4)
| ~ in(X1,the_carrier(X2))
| ~ element(X3,powerset(the_carrier(X2)))
| ~ top_str(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1581]),
[final] ).
cnf(i_0_3490,plain,
( in(esk21_3(X1,X2,X3),X2)
| in(esk20_3(X1,X2,X3),X3)
| X3 = relation_inverse_image(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_704]),
[final] ).
cnf(i_0_3491,plain,
( in(esk18_3(X1,X2,X3),X2)
| in(esk17_3(X1,X2,X3),X3)
| X3 = relation_image(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_698]),
[final] ).
cnf(i_0_3492,plain,
( in(set_difference(cast_as_carrier_subset(X1),X2),X3)
| ~ in(X2,esk266_2(X1,X3))
| esk264_2(X1,X3) != esk265_2(X1,X3)
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X3,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1526]),
[final] ).
cnf(i_0_3493,lemma,
( X1 = unordered_pair(X2,X2)
| esk187_1(X3) != esk186_1(X3)
| ~ in(unordered_pair(unordered_pair(X2,X1),unordered_pair(X2,X2)),esk188_1(X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1655,c_0_681]),c_0_944]),
[final] ).
cnf(i_0_3494,lemma,
( in(X1,X2)
| esk187_1(X2) != esk186_1(X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),esk188_1(X2)) ),
inference(rw,[status(thm)],[i_0_1656,c_0_944]),
[final] ).
cnf(i_0_3495,lemma,
( in(esk204_2(X1,X2),X2)
| X2 = empty_set
| in(esk201_2(X3,X4),X4)
| X4 = empty_set
| ~ element(X2,powerset(powerset(X1)))
| ~ in(X1,omega)
| ~ ordinal(X1)
| ~ element(X4,powerset(powerset(X3)))
| ~ in(X3,omega)
| ~ in(X3,esk200_0)
| ~ ordinal(X3)
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_1538]),
[final] ).
cnf(i_0_3496,lemma,
( in(esk416_3(X1,X2,X3),X2)
| relation_rng_as_subset(X1,X2,X3) = X2
| ~ relation_of2_as_subset(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_695]),
[final] ).
cnf(i_0_3497,lemma,
( in(esk414_3(X1,X2,X3),X2)
| relation_dom_as_subset(X2,X1,X3) = X2
| ~ relation_of2_as_subset(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_705]),
[final] ).
cnf(i_0_3498,plain,
( in(esk212_3(X1,X2,X3),X1)
| in(esk208_2(X1,X2),esk210_2(X1,X2))
| empty(X1)
| ~ in(X3,esk211_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_691]),
[final] ).
cnf(i_0_3499,plain,
( in(esk212_3(X1,X2,X3),X1)
| in(esk207_2(X1,X2),esk209_2(X1,X2))
| empty(X1)
| ~ in(X3,esk211_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_691]),
[final] ).
cnf(i_0_3500,plain,
( in(X1,esk213_3(X2,X3,X1))
| in(esk208_2(X2,X3),esk210_2(X2,X3))
| empty(X2)
| ~ in(X1,esk211_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_691]),
[final] ).
cnf(i_0_3501,plain,
( in(X1,esk213_3(X2,X3,X1))
| in(esk207_2(X2,X3),esk209_2(X2,X3))
| empty(X2)
| ~ in(X1,esk211_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_691]),
[final] ).
cnf(i_0_3502,lemma,
( in(esk404_2(X1,X2),X2)
| X2 = empty_set
| in(esk401_2(X3,X4),X4)
| X4 = empty_set
| ~ element(X2,powerset(powerset(X1)))
| ~ in(X1,omega)
| ~ ordinal(X1)
| ~ element(X4,powerset(powerset(X3)))
| ~ in(X3,omega)
| ~ in(X3,esk400_0)
| ~ ordinal(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1541]),
[final] ).
cnf(i_0_3503,lemma,
( in(X1,relation_dom(X2))
| ~ function(X2)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),X2) ),
inference(rw,[status(thm)],[i_0_1657,c_0_944]),
[final] ).
cnf(i_0_3504,lemma,
( relation_dom(esk393_2(X1,X2)) = complements_of_subsets(the_carrier(X1),X2)
| esk392_3(X1,X2,X3) = esk391_2(X1,X2)
| esk389_2(X1,X2) != esk390_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3505,plain,
( ordinal(esk337_2(X5,X2))
| in(X3,esk338_2(X5,X2))
| X3 != X4
| X1 != X3
| ~ ordinal(X4)
| ~ ordinal(X2)
| ~ in(X4,X5)
| ~ in(X1,set_union2(X2,unordered_pair(X2,X2))) ),
inference(rw,[status(thm)],[i_0_1658,c_0_1305]),
[final] ).
cnf(i_0_3506,plain,
( ordinal(esk336_2(X5,X2))
| in(X3,esk338_2(X5,X2))
| X3 != X4
| X1 != X3
| ~ ordinal(X4)
| ~ ordinal(X2)
| ~ in(X4,X5)
| ~ in(X1,set_union2(X2,unordered_pair(X2,X2))) ),
inference(rw,[status(thm)],[i_0_1659,c_0_1305]),
[final] ).
cnf(i_0_3507,lemma,
( relation_of2_as_subset(X1,X2,X3)
| X2 != empty_set
| ~ subset(X4,X3)
| ~ function(X1)
| ~ quasi_total(X1,X2,X4)
| ~ relation_of2_as_subset(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1660]),
[final] ).
cnf(i_0_3508,lemma,
( quasi_total(X1,X2,X3)
| X2 != empty_set
| ~ subset(X4,X3)
| ~ function(X1)
| ~ quasi_total(X1,X2,X4)
| ~ relation_of2_as_subset(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1660]),
[final] ).
cnf(i_0_3509,lemma,
( in(X1,X2)
| X5 = empty_set
| ~ in(X1,relation_inverse_image(X3,X4))
| ~ function(X3)
| ~ quasi_total(X3,X2,X5)
| ~ relation_of2_as_subset(X3,X2,X5) ),
inference(split_conjunct,[status(thm)],[i_0_1598]),
[final] ).
cnf(i_0_3510,lemma,
( in(esk436_2(X1,X2),relation_dom(X1))
| X2 = function_inverse(X1)
| ~ in(esk434_2(X1,X2),relation_dom(X1))
| esk433_2(X1,X2) != apply(X1,esk434_2(X1,X2))
| relation_dom(X2) != relation_rng(X1)
| ~ relation(X2)
| ~ function(X2)
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1546]),
[final] ).
cnf(i_0_3511,lemma,
( in(esk433_2(X1,X2),relation_rng(X1))
| X2 = function_inverse(X1)
| ~ in(esk435_2(X1,X2),relation_rng(X1))
| esk436_2(X1,X2) != apply(X2,esk435_2(X1,X2))
| relation_dom(X2) != relation_rng(X1)
| ~ relation(X2)
| ~ function(X2)
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1546]),
[final] ).
cnf(i_0_3512,lemma,
( relation_of2_as_subset(X1,X2,X3)
| X4 = empty_set
| ~ subset(X4,X3)
| ~ function(X1)
| ~ quasi_total(X1,X2,X4)
| ~ relation_of2_as_subset(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1660]),
[final] ).
cnf(i_0_3513,lemma,
( quasi_total(X1,X2,X3)
| X4 = empty_set
| ~ subset(X4,X3)
| ~ function(X1)
| ~ quasi_total(X1,X2,X4)
| ~ relation_of2_as_subset(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1660]),
[final] ).
cnf(i_0_3514,lemma,
( in(X1,esk354_2(X2,X4))
| ~ in(X1,powerset(the_carrier(X2)))
| ~ element(X3,powerset(the_carrier(X2)))
| X3 != X1
| ~ closed_subset(X3,X2)
| ~ subset(X4,X1)
| ~ topological_space(X2)
| ~ top_str(X2)
| ~ element(X4,powerset(the_carrier(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1652]),
[final] ).
cnf(i_0_3515,lemma,
( in(X3,esk406_2(X2,X4))
| ~ element(X1,powerset(the_carrier(X2)))
| X1 != X3
| ~ closed_subset(X1,X2)
| ~ subset(X4,X3)
| ~ element(X3,powerset(the_carrier(X2)))
| ~ topological_space(X2)
| ~ top_str(X2)
| ~ element(X4,powerset(the_carrier(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1587]),
[final] ).
cnf(i_0_3516,lemma,
( empty_carrier(X1)
| X2 = X3
| ~ join_commutative(X1)
| ~ join_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ~ below(X1,X2,X3)
| ~ below(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1661]),
[final] ).
cnf(i_0_3517,lemma,
( relstr_set_smaller(poset_of_lattice(X1),X3,X2)
| empty_carrier(X1)
| ~ latt_element_smaller(X1,cast_to_el_of_lattice(X1,X2),X3)
| ~ element(X2,the_carrier(poset_of_lattice(X1)))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1662]),
[final] ).
cnf(i_0_3518,lemma,
( relstr_element_smaller(poset_of_lattice(X1),X3,X2)
| empty_carrier(X1)
| ~ latt_set_smaller(X1,cast_to_el_of_lattice(X1,X2),X3)
| ~ element(X2,the_carrier(poset_of_lattice(X1)))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1663]),
[final] ).
cnf(i_0_3519,plain,
( esk337_2(X5,X2) = esk335_2(X5,X2)
| in(X3,esk338_2(X5,X2))
| X3 != X4
| X1 != X3
| ~ ordinal(X4)
| ~ ordinal(X2)
| ~ in(X4,X5)
| ~ in(X1,set_union2(X2,unordered_pair(X2,X2))) ),
inference(rw,[status(thm)],[i_0_1664,c_0_1305]),
[final] ).
cnf(i_0_3520,plain,
( esk336_2(X5,X2) = esk334_2(X5,X2)
| in(X3,esk338_2(X5,X2))
| X3 != X4
| X1 != X3
| ~ ordinal(X4)
| ~ ordinal(X2)
| ~ in(X4,X5)
| ~ in(X1,set_union2(X2,unordered_pair(X2,X2))) ),
inference(rw,[status(thm)],[i_0_1665,c_0_1305]),
[final] ).
cnf(i_0_3521,plain,
( esk335_2(X5,X2) = esk333_2(X5,X2)
| in(X3,esk338_2(X5,X2))
| X3 != X4
| X1 != X3
| ~ ordinal(X4)
| ~ ordinal(X2)
| ~ in(X4,X5)
| ~ in(X1,set_union2(X2,unordered_pair(X2,X2))) ),
inference(rw,[status(thm)],[i_0_1666,c_0_1305]),
[final] ).
cnf(i_0_3522,plain,
( esk334_2(X5,X2) = esk333_2(X5,X2)
| in(X3,esk338_2(X5,X2))
| X3 != X4
| X1 != X3
| ~ ordinal(X4)
| ~ ordinal(X2)
| ~ in(X4,X5)
| ~ in(X1,set_union2(X2,unordered_pair(X2,X2))) ),
inference(rw,[status(thm)],[i_0_1667,c_0_1305]),
[final] ).
cnf(i_0_3523,lemma,
( subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),X2)) = X2
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1668]),
[final] ).
cnf(i_0_3524,plain,
( in(esk87_3(X1,X2,X3),X1)
| in(esk87_3(X1,X2,X3),X3)
| X3 = set_difference(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1489]),
[final] ).
cnf(i_0_3525,plain,
( in(esk67_3(X1,X2,X3),X2)
| in(esk65_3(X1,X2,X3),X3)
| X3 = cartesian_product2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_702]),
[final] ).
cnf(i_0_3526,plain,
( in(esk66_3(X1,X2,X3),X1)
| in(esk65_3(X1,X2,X3),X3)
| X3 = cartesian_product2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_702]),
[final] ).
cnf(i_0_3527,plain,
( in(X1,X2)
| X4 != identity_relation(X2)
| ~ relation(X4)
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),X4) ),
inference(rw,[status(thm)],[i_0_1669,c_0_944]),
[final] ).
cnf(i_0_3528,plain,
( in(X1,X4)
| X4 != relation_dom(X3)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[i_0_1670,c_0_944]),
[final] ).
cnf(i_0_3529,plain,
( in(X2,X4)
| X4 != relation_rng(X3)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[i_0_1671,c_0_944]),
[final] ).
cnf(i_0_3530,lemma,
( in(X1,esk346_2(X2,X3))
| X5 != unordered_pair(X4,X4)
| unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)) != X1
| ~ in(X4,X2)
| ~ in(X1,cartesian_product2(X2,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1672,c_0_681]),c_0_944]),
[final] ).
cnf(i_0_3531,lemma,
( X1 = apply(X2,X3)
| ~ function(X2)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X3,X1),unordered_pair(X3,X3)),X2) ),
inference(rw,[status(thm)],[i_0_1673,c_0_944]),
[final] ).
cnf(i_0_3532,lemma,
( below_refl(X2,X1,X4)
| empty_carrier(X2)
| ~ element(X1,the_carrier(X2))
| ~ latt_set_smaller(X2,X1,X3)
| X4 != meet_of_latt_set(X2,X3)
| ~ element(X4,the_carrier(X2))
| ~ lattice(X2)
| ~ complete_latt_str(X2)
| ~ latt_str(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1524]),
[final] ).
cnf(i_0_3533,plain,
( empty_carrier(X2)
| below(X2,X4,X1)
| X4 != join_of_latt_set(X2,X3)
| ~ latt_str(X2)
| ~ lattice(X2)
| ~ complete_latt_str(X2)
| ~ latt_element_smaller(X2,X1,X3)
| ~ element(X4,the_carrier(X2))
| ~ element(X1,the_carrier(X2)) ),
inference(cn,[status(thm)],[i_0_1674]),
[final] ).
cnf(i_0_3534,lemma,
( in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X3,X1),unordered_pair(X3,X3)),X2) ),
inference(rw,[status(thm)],[i_0_1675,c_0_944]),
[final] ).
cnf(i_0_3535,lemma,
( in(X1,relation_field(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),X2) ),
inference(rw,[status(thm)],[i_0_1676,c_0_944]),
[final] ).
cnf(i_0_3536,lemma,
( in(X1,relation_field(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X3,X1),unordered_pair(X3,X3)),X2) ),
inference(rw,[status(thm)],[i_0_1677,c_0_944]),
[final] ).
cnf(i_0_3537,lemma,
( in(X1,relation_dom(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),X2) ),
inference(rw,[status(thm)],[i_0_1678,c_0_944]),
[final] ).
cnf(i_0_3538,lemma,
( X2 = X3
| ~ antisymmetric_relstr(X1)
| ~ rel_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ~ related(X1,X2,X3)
| ~ related(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1679]),
[final] ).
cnf(i_0_3539,lemma,
( antisymmetric(X1)
| in(unordered_pair(unordered_pair(esk135_1(X1),esk134_1(X1)),unordered_pair(esk135_1(X1),esk135_1(X1))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[i_0_1680,c_0_944]),
[final] ).
cnf(i_0_3540,lemma,
( antisymmetric(X1)
| in(unordered_pair(unordered_pair(esk134_1(X1),esk135_1(X1)),unordered_pair(esk134_1(X1),esk134_1(X1))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[i_0_1681,c_0_944]),
[final] ).
cnf(i_0_3541,lemma,
( transitive(X1)
| in(unordered_pair(unordered_pair(esk131_1(X1),esk132_1(X1)),unordered_pair(esk131_1(X1),esk131_1(X1))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[i_0_1682,c_0_944]),
[final] ).
cnf(i_0_3542,lemma,
( transitive(X1)
| in(unordered_pair(unordered_pair(esk130_1(X1),esk131_1(X1)),unordered_pair(esk130_1(X1),esk130_1(X1))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[i_0_1683,c_0_944]),
[final] ).
cnf(i_0_3543,plain,
( in(esk14_3(X1,X2,X3),the_carrier(X1))
| X3 = topstr_closure(X1,X2)
| ~ element(X3,powerset(the_carrier(X1)))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1420]),
[final] ).
cnf(i_0_3544,lemma,
( closed_subset(esk430_3(X1,X2,X3),X1)
| in(X3,topstr_closure(X1,X2))
| ~ in(X3,the_carrier(X1))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1581]),
[final] ).
cnf(i_0_3545,lemma,
( subset(X1,esk430_3(X2,X1,X3))
| in(X3,topstr_closure(X2,X1))
| ~ in(X3,the_carrier(X2))
| ~ element(X1,powerset(the_carrier(X2)))
| ~ top_str(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1581]),
[final] ).
cnf(i_0_3546,lemma,
( being_limit_ordinal(X1)
| ~ ordinal(X1)
| ~ in(set_union2(esk427_1(X1),unordered_pair(esk427_1(X1),esk427_1(X1))),X1) ),
inference(rw,[status(thm)],[i_0_1684,c_0_1305]),
[final] ).
cnf(i_0_3547,lemma,
( empty_carrier(X1)
| below(X1,meet_commut(X1,X2,X3),X2)
| ~ meet_commutative(X1)
| ~ meet_absorbing(X1)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1685]),
[final] ).
cnf(i_0_3548,lemma,
( in(X1,cartesian_product2(X2,X2))
| ~ in(X1,esk367_3(X2,X3,X4))
| ~ relation(X3)
| ~ relation(X4)
| ~ function(X4) ),
inference(split_conjunct,[status(thm)],[i_0_689]),
[final] ).
cnf(i_0_3549,plain,
( esk267_3(X1,X2,X3) = X3
| esk263_2(X1,X2) = esk265_2(X1,X2)
| ~ in(X3,esk266_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1526]),
[final] ).
cnf(i_0_3550,plain,
( esk267_3(X1,X2,X3) = X3
| esk263_2(X1,X2) = esk264_2(X1,X2)
| ~ in(X3,esk266_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1526]),
[final] ).
cnf(i_0_3551,plain,
( latt_set_smaller(X1,esk128_3(X2,X1,X3),X3)
| empty_carrier(X1)
| ~ in(X2,a_2_3_lattice3(X1,X3))
| ~ lattice(X1)
| ~ complete_latt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1686]),
[final] ).
cnf(i_0_3552,lemma,
( closed_subset(esk355_3(X1,X2,X3),X1)
| ~ in(X3,esk354_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1652]),
[final] ).
cnf(i_0_3553,plain,
( esk212_3(X1,X2,X3) = esk213_3(X1,X2,X3)
| in(esk208_2(X1,X2),esk210_2(X1,X2))
| empty(X1)
| ~ in(X3,esk211_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_691]),
[final] ).
cnf(i_0_3554,plain,
( esk212_3(X1,X2,X3) = esk213_3(X1,X2,X3)
| in(esk207_2(X1,X2),esk209_2(X1,X2))
| empty(X1)
| ~ in(X3,esk211_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_691]),
[final] ).
cnf(i_0_3555,lemma,
( X3 = empty_set
| in(apply(X1,X4),relation_rng(X1))
| ~ function(X1)
| ~ quasi_total(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1687]),
[final] ).
cnf(i_0_3556,lemma,
( relation(esk393_2(X1,X2))
| in(esk391_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| esk389_2(X1,X2) != esk390_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3557,lemma,
( function(esk393_2(X1,X2))
| in(esk391_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| esk389_2(X1,X2) != esk390_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3558,lemma,
( X1 = empty_set
| in(unordered_pair(unordered_pair(esk437_1(X1),esk438_1(X1)),unordered_pair(esk437_1(X1),esk437_1(X1))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[i_0_1688,c_0_944]),
[final] ).
cnf(i_0_3559,plain,
( in(set_difference(cast_as_carrier_subset(X1),X2),X3)
| esk263_2(X1,X3) = esk265_2(X1,X3)
| ~ in(X2,esk266_2(X1,X3))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X3,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1526]),
[final] ).
cnf(i_0_3560,plain,
( in(set_difference(cast_as_carrier_subset(X1),X2),X3)
| esk263_2(X1,X3) = esk264_2(X1,X3)
| ~ in(X2,esk266_2(X1,X3))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X3,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1526]),
[final] ).
cnf(i_0_3561,plain,
( in(esk58_3(X1,X2,X3),X3)
| esk58_3(X1,X2,X3) = X1
| esk58_3(X1,X2,X3) = X2
| X3 = unordered_pair(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1617]),
[final] ).
cnf(i_0_3562,lemma,
( latt_element_smaller(X1,cast_to_el_of_lattice(X1,X3),X2)
| empty_carrier(X1)
| ~ relstr_set_smaller(poset_of_lattice(X1),X2,X3)
| ~ element(X3,the_carrier(poset_of_lattice(X1)))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1662]),
[final] ).
cnf(i_0_3563,lemma,
( latt_set_smaller(X1,cast_to_el_of_lattice(X1,X3),X2)
| empty_carrier(X1)
| ~ relstr_element_smaller(poset_of_lattice(X1),X2,X3)
| ~ element(X3,the_carrier(poset_of_lattice(X1)))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1663]),
[final] ).
cnf(i_0_3564,plain,
( function(X1)
| in(unordered_pair(unordered_pair(esk27_1(X1),esk29_1(X1)),unordered_pair(esk27_1(X1),esk27_1(X1))),X1) ),
inference(rw,[status(thm)],[i_0_1689,c_0_944]),
[final] ).
cnf(i_0_3565,plain,
( function(X1)
| in(unordered_pair(unordered_pair(esk27_1(X1),esk28_1(X1)),unordered_pair(esk27_1(X1),esk27_1(X1))),X1) ),
inference(rw,[status(thm)],[i_0_1690,c_0_944]),
[final] ).
cnf(i_0_3566,plain,
( join(X1,meet(X1,X2,X3),X3) = X3
| empty_carrier(X1)
| ~ meet_absorbing(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1578]),
[final] ).
cnf(i_0_3567,plain,
( element(esk113_3(X1,X2,X3),powerset(X1))
| X3 = complements_of_subsets(X1,X2)
| ~ element(X3,powerset(powerset(X1)))
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1417]),
[final] ).
cnf(i_0_3568,plain,
( X1 = X2
| X3 != identity_relation(X4)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[i_0_1691,c_0_944]),
[final] ).
cnf(i_0_3569,plain,
( esk262_3(X1,X2,X3) = X3
| element(esk259_2(X1,X2),powerset(the_carrier(X1)))
| ~ in(X3,esk260_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3570,plain,
( esk262_3(X1,X2,X3) = X3
| element(esk258_2(X1,X2),powerset(the_carrier(X1)))
| ~ in(X3,esk260_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3571,plain,
( esk261_3(X1,X2,X3) = X3
| element(esk259_2(X1,X2),powerset(the_carrier(X1)))
| ~ in(X3,esk260_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3572,plain,
( esk261_3(X1,X2,X3) = X3
| element(esk258_2(X1,X2),powerset(the_carrier(X1)))
| ~ in(X3,esk260_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3573,plain,
( v1_partfun1(X1,X2,X3)
| empty(X2)
| empty(X3)
| ~ function(X1)
| ~ quasi_total(X1,X2,X3)
| ~ relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1692]),
[final] ).
cnf(i_0_3574,lemma,
( latt_element_smaller(X1,X3,X2)
| empty_carrier(X1)
| ~ relstr_set_smaller(poset_of_lattice(X1),X2,cast_to_el_of_LattPOSet(X1,X3))
| ~ element(X3,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1693]),
[final] ).
cnf(i_0_3575,lemma,
( latt_set_smaller(X1,X3,X2)
| empty_carrier(X1)
| ~ relstr_element_smaller(poset_of_lattice(X1),X2,cast_to_el_of_LattPOSet(X1,X3))
| ~ element(X3,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1694]),
[final] ).
cnf(i_0_3576,lemma,
( in(X1,cartesian_product2(X2,X3))
| empty(X2)
| ~ in(X1,esk341_3(X2,X4,X3))
| ~ relation(X4) ),
inference(split_conjunct,[status(thm)],[i_0_682]),
[final] ).
cnf(i_0_3577,lemma,
( relation_dom(esk399_2(X1,X2)) = X2
| esk398_3(X1,X2,X3) = esk397_2(X1,X2)
| esk395_2(X1,X2) != esk396_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3578,plain,
( esk241_1(X1) = unordered_pair(esk240_1(X1),esk240_1(X1))
| in(esk243_3(X1,X2,X3),cartesian_product2(X1,X2))
| ~ in(X3,esk242_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1695,c_0_681]),
[final] ).
cnf(i_0_3579,plain,
( esk239_1(X1) = unordered_pair(esk238_1(X1),esk238_1(X1))
| in(esk243_3(X1,X2,X3),cartesian_product2(X1,X2))
| ~ in(X3,esk242_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1696,c_0_681]),
[final] ).
cnf(i_0_3580,plain,
( in(esk212_3(X1,X2,X3),X1)
| empty(X1)
| ~ in(X3,esk211_2(X1,X2))
| esk207_2(X1,X2) != esk208_2(X1,X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_691]),
[final] ).
cnf(i_0_3581,plain,
( in(X1,esk213_3(X2,X3,X1))
| empty(X2)
| ~ in(X1,esk211_2(X2,X3))
| esk207_2(X2,X3) != esk208_2(X2,X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_691]),
[final] ).
cnf(i_0_3582,lemma,
( relation(esk399_2(X1,X2))
| esk398_3(X1,X2,X3) = esk397_2(X1,X2)
| esk395_2(X1,X2) != esk396_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3583,lemma,
( function(esk399_2(X1,X2))
| esk398_3(X1,X2,X3) = esk397_2(X1,X2)
| esk395_2(X1,X2) != esk396_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3584,lemma,
( relation(esk393_2(X1,X2))
| esk392_3(X1,X2,X3) = esk391_2(X1,X2)
| esk389_2(X1,X2) != esk390_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3585,lemma,
( function(esk393_2(X1,X2))
| esk392_3(X1,X2,X3) = esk391_2(X1,X2)
| esk389_2(X1,X2) != esk390_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_3586,plain,
( below(X1,X2,X4)
| empty_carrier(X1)
| ~ latt_set_smaller(X1,X2,X3)
| ~ element(X4,the_carrier(X1))
| ~ in(X4,X3)
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1561]),
[final] ).
cnf(i_0_3587,plain,
( below(X1,X4,X2)
| empty_carrier(X1)
| ~ latt_element_smaller(X1,X2,X3)
| ~ element(X4,the_carrier(X1))
| ~ in(X4,X3)
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1560]),
[final] ).
cnf(i_0_3588,plain,
( below_refl(X1,X2,X3)
| empty_carrier(X1)
| ~ below(X1,X2,X3)
| ~ meet_commutative(X1)
| ~ meet_absorbing(X1)
| ~ join_absorbing(X1)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1697]),
[final] ).
cnf(i_0_3589,plain,
( below(X1,X2,X3)
| empty_carrier(X1)
| ~ below_refl(X1,X2,X3)
| ~ meet_commutative(X1)
| ~ meet_absorbing(X1)
| ~ join_absorbing(X1)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1697]),
[final] ).
cnf(i_0_3590,plain,
( v1_partfun1(X1,X2,X3)
| empty(X3)
| ~ function(X1)
| ~ quasi_total(X1,X2,X3)
| ~ relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1698]),
[final] ).
cnf(i_0_3591,plain,
( esk243_3(X1,X2,X3) = X3
| unordered_pair(unordered_pair(esk240_1(X1),esk241_1(X1)),unordered_pair(esk240_1(X1),esk240_1(X1))) = esk237_1(X1)
| ~ in(X3,esk242_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1699,c_0_944]),
[final] ).
cnf(i_0_3592,plain,
( esk243_3(X1,X2,X3) = X3
| unordered_pair(unordered_pair(esk238_1(X1),esk239_1(X1)),unordered_pair(esk238_1(X1),esk238_1(X1))) = esk236_1(X1)
| ~ in(X3,esk242_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1700,c_0_944]),
[final] ).
cnf(i_0_3593,plain,
( in(X2,X4)
| ~ in(subset_complement(X1,X2),X3)
| ~ element(X2,powerset(X1))
| X4 != complements_of_subsets(X1,X3)
| ~ element(X4,powerset(powerset(X1)))
| ~ element(X3,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1417]),
[final] ).
cnf(i_0_3594,lemma,
( relation(esk197_2(X1,X2))
| esk196_2(X1,X2) = subset_complement(the_carrier(X1),X3)
| ~ element(X3,powerset(the_carrier(X1)))
| X3 != esk194_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_712]),
[final] ).
cnf(i_0_3595,lemma,
( function(esk197_2(X1,X2))
| esk196_2(X1,X2) = subset_complement(the_carrier(X1),X3)
| ~ element(X3,powerset(the_carrier(X1)))
| X3 != esk194_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_712]),
[final] ).
cnf(i_0_3596,lemma,
( relation(esk197_2(X1,X2))
| esk195_2(X1,X2) = subset_complement(the_carrier(X1),X3)
| ~ element(X3,powerset(the_carrier(X1)))
| X3 != esk194_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_712]),
[final] ).
cnf(i_0_3597,lemma,
( function(esk197_2(X1,X2))
| esk195_2(X1,X2) = subset_complement(the_carrier(X1),X3)
| ~ element(X3,powerset(the_carrier(X1)))
| X3 != esk194_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_712]),
[final] ).
cnf(i_0_3598,lemma,
( relation(esk192_2(X1,X2))
| esk191_2(X1,X2) = subset_complement(the_carrier(X1),X3)
| ~ element(X3,powerset(the_carrier(X1)))
| X3 != esk189_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_711]),
[final] ).
cnf(i_0_3599,lemma,
( function(esk192_2(X1,X2))
| esk191_2(X1,X2) = subset_complement(the_carrier(X1),X3)
| ~ element(X3,powerset(the_carrier(X1)))
| X3 != esk189_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_711]),
[final] ).
cnf(i_0_3600,lemma,
( relation(esk192_2(X1,X2))
| esk190_2(X1,X2) = subset_complement(the_carrier(X1),X3)
| ~ element(X3,powerset(the_carrier(X1)))
| X3 != esk189_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_711]),
[final] ).
cnf(i_0_3601,lemma,
( function(esk192_2(X1,X2))
| esk190_2(X1,X2) = subset_complement(the_carrier(X1),X3)
| ~ element(X3,powerset(the_carrier(X1)))
| X3 != esk189_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_711]),
[final] ).
cnf(i_0_3602,lemma,
( relation_dom(esk399_2(X1,X2)) = X2
| esk398_3(X1,X2,X3) = esk397_2(X1,X2)
| in(esk394_2(X1,X2),X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3603,plain,
( in(esk212_3(X1,X2,X3),X1)
| in(esk206_2(X1,X2),X1)
| empty(X1)
| ~ in(X3,esk211_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_691]),
[final] ).
cnf(i_0_3604,plain,
( in(esk212_3(X1,X2,X3),X1)
| in(esk206_2(X1,X2),X1)
| empty(X1)
| ~ in(X3,esk211_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_691]),
[final] ).
cnf(i_0_3605,plain,
( in(X1,esk213_3(X2,X3,X1))
| in(esk206_2(X2,X3),X2)
| empty(X2)
| ~ in(X1,esk211_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_691]),
[final] ).
cnf(i_0_3606,plain,
( in(X1,esk213_3(X2,X3,X1))
| in(esk206_2(X2,X3),X2)
| empty(X2)
| ~ in(X1,esk211_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_691]),
[final] ).
cnf(i_0_3607,plain,
( latt_set_smaller(X1,esk127_3(X2,X1,X3),X3)
| empty_carrier(X1)
| ~ in(X2,a_2_2_lattice3(X1,X3))
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1701]),
[final] ).
cnf(i_0_3608,lemma,
( esk407_3(X1,X2,X3) = X3
| ~ in(X3,esk406_2(X1,X2))
| ~ element(X3,powerset(the_carrier(X1)))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1587]),
[final] ).
cnf(i_0_3609,lemma,
( relation(esk399_2(X1,X2))
| esk398_3(X1,X2,X3) = esk397_2(X1,X2)
| in(esk394_2(X1,X2),X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3610,lemma,
( function(esk399_2(X1,X2))
| esk398_3(X1,X2,X3) = esk397_2(X1,X2)
| in(esk394_2(X1,X2),X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3611,plain,
( in(esk340_3(X1,X2,X3),X1)
| ~ in(X3,esk338_2(X1,X2))
| esk334_2(X1,X2) != esk335_2(X1,X2)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_762]),
[final] ).
cnf(i_0_3612,plain,
( related(X1,X3,X4)
| ~ relstr_element_smaller(X1,X2,X3)
| ~ element(X4,the_carrier(X1))
| ~ in(X4,X2)
| ~ element(X3,the_carrier(X1))
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1563]),
[final] ).
cnf(i_0_3613,plain,
( related(X1,X4,X3)
| ~ relstr_set_smaller(X1,X2,X3)
| ~ element(X4,the_carrier(X1))
| ~ in(X4,X2)
| ~ element(X3,the_carrier(X1))
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1562]),
[final] ).
cnf(i_0_3614,plain,
( quasi_total(X1,X2,X3)
| ~ function(X1)
| ~ v1_partfun1(X1,X2,X3)
| ~ relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1702]),
[final] ).
cnf(i_0_3615,plain,
( element(esk68_2(X1,X2),powerset(powerset(the_carrier(X1))))
| ~ is_a_cover_of_carrier(X1,X2)
| ~ open_subsets(X2,X1)
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ compact_top_space(X1)
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1703]),
[final] ).
cnf(i_0_3616,plain,
( in(esk340_3(X1,X2,X3),X1)
| in(esk337_2(X1,X2),X1)
| ~ in(X3,esk338_2(X1,X2))
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_762]),
[final] ).
cnf(i_0_3617,plain,
( in(esk340_3(X1,X2,X3),X1)
| in(esk336_2(X1,X2),X1)
| ~ in(X3,esk338_2(X1,X2))
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_762]),
[final] ).
cnf(i_0_3618,plain,
( in(esk243_3(X1,X2,X3),cartesian_product2(X1,X2))
| in(esk240_1(X1),X1)
| ~ in(X3,esk242_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_715]),
[final] ).
cnf(i_0_3619,plain,
( in(esk243_3(X1,X2,X3),cartesian_product2(X1,X2))
| in(esk238_1(X1),X1)
| ~ in(X3,esk242_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_715]),
[final] ).
cnf(i_0_3620,plain,
( in(esk46_3(X1,X2,X3),X3)
| X3 = fiber(X1,X2)
| esk46_3(X1,X2,X3) != X2
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_703]),
[final] ).
cnf(i_0_3621,plain,
( quasi_total(X3,X1,X2)
| X1 != relation_dom_as_subset(X1,X2,X3)
| X1 != empty_set
| ~ relation_of2_as_subset(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1704]),
[final] ).
cnf(i_0_3622,plain,
( epred2_3(esk248_1(X1),esk247_1(X1),esk246_1(X1))
| in(esk250_2(X1,X2),set_union2(X1,unordered_pair(X1,X1)))
| ~ ordinal(X1)
| ~ in(X2,esk249_1(X1)) ),
inference(rw,[status(thm)],[i_0_1705,c_0_1305]),
[final] ).
cnf(i_0_3623,plain,
( X2 = relation_dom_as_subset(X2,X3,X1)
| ~ quasi_total(X1,X2,X3)
| X2 != empty_set
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1704]),
[final] ).
cnf(i_0_3624,plain,
( quasi_total(X3,X1,X2)
| X2 = empty_set
| X1 != relation_dom_as_subset(X1,X2,X3)
| ~ relation_of2_as_subset(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1704]),
[final] ).
cnf(i_0_3625,plain,
( X2 = relation_dom_as_subset(X2,X3,X1)
| X3 = empty_set
| ~ quasi_total(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1704]),
[final] ).
cnf(i_0_3626,plain,
( in(X3,interior(X2,X1))
| empty_carrier(X2)
| ~ point_neighbourhood(X1,X2,X3)
| ~ element(X1,powerset(the_carrier(X2)))
| ~ element(X3,the_carrier(X2))
| ~ topological_space(X2)
| ~ top_str(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1706]),
[final] ).
cnf(i_0_3627,plain,
( esk262_3(X1,X2,X3) = X3
| ~ in(X3,esk260_2(X1,X2))
| esk256_2(X1,X2) != esk257_2(X1,X2)
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3628,plain,
( esk261_3(X1,X2,X3) = X3
| ~ in(X3,esk260_2(X1,X2))
| esk256_2(X1,X2) != esk257_2(X1,X2)
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3629,plain,
( esk212_3(X1,X2,X3) = esk213_3(X1,X2,X3)
| empty(X1)
| ~ in(X3,esk211_2(X1,X2))
| esk207_2(X1,X2) != esk208_2(X1,X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_691]),
[final] ).
cnf(i_0_3630,plain,
( in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3)
| X3 != inclusion_relation(X4)
| ~ relation(X3)
| ~ in(X2,X4)
| ~ in(X1,X4)
| ~ subset(X1,X2) ),
inference(rw,[status(thm)],[i_0_1707,c_0_944]),
[final] ).
cnf(i_0_3631,lemma,
( esk187_1(X2) = unordered_pair(esk185_1(X2),esk185_1(X2))
| in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),esk188_1(X2))
| X3 != unordered_pair(X1,X1)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1708,c_0_681]),c_0_681]),c_0_944]),
[final] ).
cnf(i_0_3632,lemma,
( esk186_1(X2) = unordered_pair(esk185_1(X2),esk185_1(X2))
| in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),esk188_1(X2))
| X3 != unordered_pair(X1,X1)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1709,c_0_681]),c_0_681]),c_0_944]),
[final] ).
cnf(i_0_3633,plain,
( open_subset(subset_difference(the_carrier(X2),cast_as_carrier_subset(X2),X1),X2)
| ~ closed_subset(X1,X2)
| ~ element(X1,powerset(the_carrier(X2)))
| ~ top_str(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1606]),
[final] ).
cnf(i_0_3634,plain,
( ordinal(esk340_3(X1,X2,X3))
| ~ in(X3,esk338_2(X1,X2))
| esk334_2(X1,X2) != esk335_2(X1,X2)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_762]),
[final] ).
cnf(i_0_3635,plain,
( element(esk24_3(X1,X2,X3),the_carrier(X1))
| latt_element_smaller(X1,X2,X3)
| empty_carrier(X1)
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1560]),
[final] ).
cnf(i_0_3636,plain,
( element(esk22_3(X1,X2,X3),the_carrier(X1))
| latt_set_smaller(X1,X2,X3)
| empty_carrier(X1)
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1561]),
[final] ).
cnf(i_0_3637,lemma,
( in(X1,esk372_2(X4,X2))
| X1 != X3
| ~ ordinal(X3)
| ~ ordinal(X2)
| ~ in(X3,X4)
| ~ in(X1,set_union2(X2,unordered_pair(X2,X2))) ),
inference(rw,[status(thm)],[i_0_1710,c_0_1305]),
[final] ).
cnf(i_0_3638,plain,
( esk262_3(X1,X2,X3) = X3
| closed_subset(esk259_2(X1,X2),X1)
| ~ in(X3,esk260_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3639,plain,
( esk262_3(X1,X2,X3) = X3
| closed_subset(esk258_2(X1,X2),X1)
| ~ in(X3,esk260_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3640,plain,
( esk261_3(X1,X2,X3) = X3
| closed_subset(esk259_2(X1,X2),X1)
| ~ in(X3,esk260_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3641,plain,
( esk261_3(X1,X2,X3) = X3
| closed_subset(esk258_2(X1,X2),X1)
| ~ in(X3,esk260_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3642,plain,
( esk262_3(X1,X2,X3) = X3
| subset(X2,esk257_2(X1,X2))
| ~ in(X3,esk260_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3643,plain,
( esk262_3(X1,X2,X3) = X3
| subset(X2,esk256_2(X1,X2))
| ~ in(X3,esk260_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3644,plain,
( esk261_3(X1,X2,X3) = X3
| subset(X2,esk257_2(X1,X2))
| ~ in(X3,esk260_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3645,plain,
( esk261_3(X1,X2,X3) = X3
| subset(X2,esk256_2(X1,X2))
| ~ in(X3,esk260_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3646,plain,
( related_reflexive(X1,X2,X3)
| empty_carrier(X1)
| ~ related(X1,X2,X3)
| ~ reflexive_relstr(X1)
| ~ rel_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1711]),
[final] ).
cnf(i_0_3647,plain,
( related(X1,X2,X3)
| empty_carrier(X1)
| ~ related_reflexive(X1,X2,X3)
| ~ reflexive_relstr(X1)
| ~ rel_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1711]),
[final] ).
cnf(i_0_3648,plain,
( esk212_3(X1,X2,X3) = esk213_3(X1,X2,X3)
| in(esk206_2(X1,X2),X1)
| empty(X1)
| ~ in(X3,esk211_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_691]),
[final] ).
cnf(i_0_3649,plain,
( esk212_3(X1,X2,X3) = esk213_3(X1,X2,X3)
| in(esk206_2(X1,X2),X1)
| empty(X1)
| ~ in(X3,esk211_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_691]),
[final] ).
cnf(i_0_3650,plain,
( in(esk212_3(X1,X2,X3),X1)
| esk206_2(X1,X2) = esk210_2(X1,X2)
| empty(X1)
| ~ in(X3,esk211_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_691]),
[final] ).
cnf(i_0_3651,plain,
( in(esk212_3(X1,X2,X3),X1)
| esk206_2(X1,X2) = esk209_2(X1,X2)
| empty(X1)
| ~ in(X3,esk211_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_691]),
[final] ).
cnf(i_0_3652,plain,
( in(X1,esk213_3(X2,X3,X1))
| esk206_2(X2,X3) = esk210_2(X2,X3)
| empty(X2)
| ~ in(X1,esk211_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_691]),
[final] ).
cnf(i_0_3653,plain,
( in(X1,esk213_3(X2,X3,X1))
| esk206_2(X2,X3) = esk209_2(X2,X3)
| empty(X2)
| ~ in(X1,esk211_2(X2,X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_691]),
[final] ).
cnf(i_0_3654,plain,
( reflexive_relstr(rel_str_of(X1,X2))
| ~ reflexive(X2)
| ~ antisymmetric(X2)
| ~ transitive(X2)
| ~ v1_partfun1(X2,X1,X1)
| ~ relation_of2(X2,X1,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1712]),
[final] ).
cnf(i_0_3655,plain,
( antisymmetric_relstr(rel_str_of(X1,X2))
| ~ reflexive(X2)
| ~ antisymmetric(X2)
| ~ transitive(X2)
| ~ v1_partfun1(X2,X1,X1)
| ~ relation_of2(X2,X1,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1712]),
[final] ).
cnf(i_0_3656,plain,
( transitive_relstr(rel_str_of(X1,X2))
| ~ reflexive(X2)
| ~ antisymmetric(X2)
| ~ transitive(X2)
| ~ v1_partfun1(X2,X1,X1)
| ~ relation_of2(X2,X1,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1712]),
[final] ).
cnf(i_0_3657,plain,
( strict_rel_str(rel_str_of(X1,X2))
| ~ reflexive(X2)
| ~ antisymmetric(X2)
| ~ transitive(X2)
| ~ v1_partfun1(X2,X1,X1)
| ~ relation_of2(X2,X1,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1712]),
[final] ).
cnf(i_0_3658,lemma,
( relstr_set_smaller(poset_of_lattice(X1),X3,cast_to_el_of_LattPOSet(X1,X2))
| empty_carrier(X1)
| ~ latt_element_smaller(X1,X2,X3)
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1693]),
[final] ).
cnf(i_0_3659,lemma,
( relstr_element_smaller(poset_of_lattice(X1),X3,cast_to_el_of_LattPOSet(X1,X2))
| empty_carrier(X1)
| ~ latt_set_smaller(X1,X2,X3)
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1694]),
[final] ).
cnf(i_0_3660,lemma,
( X1 = esk204_2(X3,X2)
| X2 = empty_set
| subset(X4,esk203_1(X4))
| ~ in(X1,X2)
| ~ subset(esk204_2(X3,X2),X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X3,omega)
| ~ ordinal(X3)
| ~ in(X4,esk202_0)
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_1538]),
[final] ).
cnf(i_0_3661,plain,
( in(esk243_3(X1,X2,X3),cartesian_product2(X1,X2))
| ~ in(X3,esk242_2(X1,X2))
| esk236_1(X1) != esk237_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_715]),
[final] ).
cnf(i_0_3662,lemma,
( X1 = esk404_2(X3,X2)
| X2 = empty_set
| subset(X4,esk403_1(X4))
| ~ in(X1,X2)
| ~ subset(esk404_2(X3,X2),X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X3,omega)
| ~ ordinal(X3)
| ~ in(X4,esk402_0) ),
inference(split_conjunct,[status(thm)],[i_0_1541]),
[final] ).
cnf(i_0_3663,lemma,
( X1 = esk204_2(X3,X2)
| X2 = empty_set
| in(esk203_1(X4),esk202_0)
| ~ in(X1,X2)
| ~ subset(esk204_2(X3,X2),X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X3,omega)
| ~ ordinal(X3)
| ~ in(X4,esk202_0)
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_1538]),
[final] ).
cnf(i_0_3664,lemma,
( apply(relation_composition(X2,X1),X3) = apply(X1,apply(X2,X3))
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X2)
| ~ function(X2)
| ~ in(X3,relation_dom(relation_composition(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1713]),
[final] ).
cnf(i_0_3665,plain,
( in(subset_complement(X3,X1),X4)
| ~ in(X1,X2)
| ~ element(X1,powerset(X3))
| X2 != complements_of_subsets(X3,X4)
| ~ element(X2,powerset(powerset(X3)))
| ~ element(X4,powerset(powerset(X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1417]),
[final] ).
cnf(i_0_3666,plain,
( ordinal(esk340_3(X1,X2,X3))
| in(esk337_2(X1,X2),X1)
| ~ in(X3,esk338_2(X1,X2))
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_762]),
[final] ).
cnf(i_0_3667,plain,
( ordinal(esk340_3(X1,X2,X3))
| in(esk336_2(X1,X2),X1)
| ~ in(X3,esk338_2(X1,X2))
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_762]),
[final] ).
cnf(i_0_3668,plain,
( in(esk340_3(X1,X2,X3),X1)
| ordinal(esk337_2(X1,X2))
| ~ in(X3,esk338_2(X1,X2))
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_762]),
[final] ).
cnf(i_0_3669,plain,
( in(esk340_3(X1,X2,X3),X1)
| ordinal(esk336_2(X1,X2))
| ~ in(X3,esk338_2(X1,X2))
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_762]),
[final] ).
cnf(i_0_3670,plain,
( element(esk114_3(X1,X2,X3),the_carrier(X1))
| relstr_set_smaller(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1562]),
[final] ).
cnf(i_0_3671,plain,
( element(esk103_3(X1,X2,X3),the_carrier(X1))
| relstr_element_smaller(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1563]),
[final] ).
cnf(i_0_3672,lemma,
( X1 = esk404_2(X3,X2)
| X2 = empty_set
| in(esk403_1(X4),esk402_0)
| ~ in(X1,X2)
| ~ subset(esk404_2(X3,X2),X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X3,omega)
| ~ ordinal(X3)
| ~ in(X4,esk402_0) ),
inference(split_conjunct,[status(thm)],[i_0_1541]),
[final] ).
cnf(i_0_3673,plain,
( X1 = X3
| X1 != pair_first(X2)
| X2 != unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5))
| X2 != unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1714,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_3674,plain,
( X1 = X4
| X1 != pair_second(X2)
| X2 != unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5))
| X2 != unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1715,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_3675,plain,
( point_neighbourhood(X3,X2,X1)
| empty_carrier(X2)
| ~ in(X1,interior(X2,X3))
| ~ element(X3,powerset(the_carrier(X2)))
| ~ element(X1,the_carrier(X2))
| ~ topological_space(X2)
| ~ top_str(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1706]),
[final] ).
cnf(i_0_3676,lemma,
( closed_subset(meet_of_subsets(the_carrier(X1),X2),X1)
| ~ closed_subset(esk429_2(X1,X2),X1)
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ topological_space(X1)
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1716]),
[final] ).
cnf(i_0_3677,lemma,
( in(set_difference(cast_as_carrier_subset(X1),X2),X3)
| ~ in(X2,esk356_2(X1,X3))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X3,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1638]),
[final] ).
cnf(i_0_3678,plain,
( in(esk24_3(X1,X2,X3),X3)
| latt_element_smaller(X1,X2,X3)
| empty_carrier(X1)
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1560]),
[final] ).
cnf(i_0_3679,plain,
( in(esk22_3(X1,X2,X3),X3)
| latt_set_smaller(X1,X2,X3)
| empty_carrier(X1)
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1561]),
[final] ).
cnf(i_0_3680,plain,
( in(esk340_3(X1,X2,X3),X1)
| esk335_2(X1,X2) = esk337_2(X1,X2)
| ~ in(X3,esk338_2(X1,X2))
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_762]),
[final] ).
cnf(i_0_3681,plain,
( in(esk340_3(X1,X2,X3),X1)
| esk334_2(X1,X2) = esk336_2(X1,X2)
| ~ in(X3,esk338_2(X1,X2))
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_762]),
[final] ).
cnf(i_0_3682,plain,
( in(esk340_3(X1,X2,X3),X1)
| esk333_2(X1,X2) = esk335_2(X1,X2)
| ~ in(X3,esk338_2(X1,X2))
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_762]),
[final] ).
cnf(i_0_3683,plain,
( in(esk340_3(X1,X2,X3),X1)
| esk333_2(X1,X2) = esk334_2(X1,X2)
| ~ in(X3,esk338_2(X1,X2))
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_762]),
[final] ).
cnf(i_0_3684,plain,
( in(esk243_3(X1,X2,X3),cartesian_product2(X1,X2))
| esk235_1(X1) = esk237_1(X1)
| ~ in(X3,esk242_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_715]),
[final] ).
cnf(i_0_3685,plain,
( in(esk243_3(X1,X2,X3),cartesian_product2(X1,X2))
| esk235_1(X1) = esk236_1(X1)
| ~ in(X3,esk242_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_715]),
[final] ).
cnf(i_0_3686,plain,
( below(X1,X2,X3)
| empty_carrier(X1)
| join(X1,X2,X3) != X3
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1717]),
[final] ).
cnf(i_0_3687,plain,
( join(X1,X2,X3) = X3
| empty_carrier(X1)
| ~ below(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1717]),
[final] ).
cnf(i_0_3688,lemma,
( in(esk185_1(X2),X2)
| in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),esk188_1(X2))
| X3 != unordered_pair(X1,X1)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1718,c_0_681]),c_0_944]),
[final] ).
cnf(i_0_3689,lemma,
( in(esk185_1(X2),X2)
| in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),esk188_1(X2))
| X3 != unordered_pair(X1,X1)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1719,c_0_681]),c_0_944]),
[final] ).
cnf(i_0_3690,plain,
( element(esk128_3(X1,X2,X3),the_carrier(X2))
| empty_carrier(X2)
| ~ in(X1,a_2_3_lattice3(X2,X3))
| ~ lattice(X2)
| ~ complete_latt_str(X2)
| ~ latt_str(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1686]),
[final] ).
cnf(i_0_3691,plain,
( in(esk114_3(X1,X2,X3),X2)
| relstr_set_smaller(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1562]),
[final] ).
cnf(i_0_3692,plain,
( in(esk103_3(X1,X2,X3),X2)
| relstr_element_smaller(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1563]),
[final] ).
cnf(i_0_3693,lemma,
( element(esk429_2(X1,X2),powerset(the_carrier(X1)))
| closed_subset(meet_of_subsets(the_carrier(X1),X2),X1)
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ topological_space(X1)
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1716]),
[final] ).
cnf(i_0_3694,lemma,
( in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),cartesian_product2(X2,X4))
| ~ in(X3,X4)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_1720,c_0_944]),
[final] ).
cnf(i_0_3695,lemma,
( in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),cartesian_product2(X2,X4))
| ~ in(X3,X4)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_1721,c_0_944]),
[final] ).
cnf(i_0_3696,plain,
( esk241_1(X1) = unordered_pair(esk240_1(X1),esk240_1(X1))
| in(esk244_3(X1,X2,X3),X1)
| ~ in(X3,esk242_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1722,c_0_681]),
[final] ).
cnf(i_0_3697,plain,
( esk239_1(X1) = unordered_pair(esk238_1(X1),esk238_1(X1))
| in(esk244_3(X1,X2,X3),X1)
| ~ in(X3,esk242_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1723,c_0_681]),
[final] ).
cnf(i_0_3698,plain,
( in(X1,X3)
| X2 = empty_set
| ~ in(X1,esk41_3(X2,X3,X1))
| X3 != set_meet(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1724]),
[final] ).
cnf(i_0_3699,lemma,
( in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),X2)
| X3 != apply(X2,X1)
| ~ function(X2)
| ~ relation(X2)
| ~ in(X1,relation_dom(X2)) ),
inference(rw,[status(thm)],[i_0_1725,c_0_944]),
[final] ).
cnf(i_0_3700,plain,
( in(unordered_pair(unordered_pair(X3,X1),unordered_pair(X3,X3)),X2)
| X1 != apply(X2,X3)
| ~ function(X2)
| ~ relation(X2)
| ~ in(X3,relation_dom(X2)) ),
inference(rw,[status(thm)],[i_0_1726,c_0_944]),
[final] ).
cnf(i_0_3701,plain,
( element(relation_rng_as_subset(X2,X3,X1),powerset(X3))
| ~ relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1727]),
[final] ).
cnf(i_0_3702,plain,
( element(relation_dom_as_subset(X2,X3,X1),powerset(X2))
| ~ relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1728]),
[final] ).
cnf(i_0_3703,lemma,
( subset(X2,X3)
| ~ below(boole_lattice(X1),X2,X3)
| ~ element(X3,the_carrier(boole_lattice(X1)))
| ~ element(X2,the_carrier(boole_lattice(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1729]),
[final] ).
cnf(i_0_3704,plain,
( in(X1,omega)
| in(X2,esk249_1(X4))
| X2 != X3
| X1 != X2
| esk248_1(X4) != esk247_1(X4)
| ~ ordinal(X4)
| ~ ordinal(X1)
| ~ in(X3,set_union2(X4,unordered_pair(X4,X4))) ),
inference(rw,[status(thm)],[i_0_1730,c_0_1305]),
[final] ).
cnf(i_0_3705,plain,
( esk262_3(X1,X2,X3) = X3
| esk259_2(X1,X2) = esk257_2(X1,X2)
| ~ in(X3,esk260_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3706,plain,
( esk262_3(X1,X2,X3) = X3
| esk258_2(X1,X2) = esk256_2(X1,X2)
| ~ in(X3,esk260_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3707,plain,
( esk262_3(X1,X2,X3) = X3
| esk255_2(X1,X2) = esk257_2(X1,X2)
| ~ in(X3,esk260_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3708,plain,
( esk262_3(X1,X2,X3) = X3
| esk255_2(X1,X2) = esk256_2(X1,X2)
| ~ in(X3,esk260_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3709,plain,
( esk261_3(X1,X2,X3) = X3
| esk259_2(X1,X2) = esk257_2(X1,X2)
| ~ in(X3,esk260_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3710,plain,
( esk261_3(X1,X2,X3) = X3
| esk258_2(X1,X2) = esk256_2(X1,X2)
| ~ in(X3,esk260_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3711,plain,
( esk261_3(X1,X2,X3) = X3
| esk255_2(X1,X2) = esk257_2(X1,X2)
| ~ in(X3,esk260_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3712,plain,
( esk261_3(X1,X2,X3) = X3
| esk255_2(X1,X2) = esk256_2(X1,X2)
| ~ in(X3,esk260_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3713,lemma,
( relation_dom(esk399_2(X1,X2)) = X2
| in(esk397_2(X1,X2),X2)
| esk395_2(X1,X2) != esk396_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3714,plain,
( apply_binary(X1,X2,X3) = apply(X1,unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)))
| ~ function(X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[i_0_1731,c_0_944]),
[final] ).
cnf(i_0_3715,plain,
( esk212_3(X1,X2,X3) = esk213_3(X1,X2,X3)
| esk206_2(X1,X2) = esk210_2(X1,X2)
| empty(X1)
| ~ in(X3,esk211_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_691]),
[final] ).
cnf(i_0_3716,plain,
( esk212_3(X1,X2,X3) = esk213_3(X1,X2,X3)
| esk206_2(X1,X2) = esk209_2(X1,X2)
| empty(X1)
| ~ in(X3,esk211_2(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_691]),
[final] ).
cnf(i_0_3717,plain,
( ordinal(esk340_3(X1,X2,X3))
| ordinal(esk337_2(X1,X2))
| ~ in(X3,esk338_2(X1,X2))
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_762]),
[final] ).
cnf(i_0_3718,plain,
( ordinal(esk340_3(X1,X2,X3))
| ordinal(esk336_2(X1,X2))
| ~ in(X3,esk338_2(X1,X2))
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_762]),
[final] ).
cnf(i_0_3719,lemma,
( relation(esk399_2(X1,X2))
| in(esk397_2(X1,X2),X2)
| esk395_2(X1,X2) != esk396_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3720,lemma,
( function(esk399_2(X1,X2))
| in(esk397_2(X1,X2),X2)
| esk395_2(X1,X2) != esk396_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3721,lemma,
( X1 = esk204_2(X3,X2)
| X2 = empty_set
| ~ in(X1,X2)
| ~ subset(esk204_2(X3,X2),X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X3,omega)
| ~ ordinal(X3)
| esk203_1(X4) != X4
| ~ in(X4,esk202_0)
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_1538]),
[final] ).
cnf(i_0_3722,plain,
( empty_carrier(X1)
| element(meet_commut(X1,X2,X3),the_carrier(X1))
| ~ meet_commutative(X1)
| ~ meet_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1732]),
[final] ).
cnf(i_0_3723,plain,
( empty_carrier(X1)
| element(join_commut(X1,X2,X3),the_carrier(X1))
| ~ join_commutative(X1)
| ~ join_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1733]),
[final] ).
cnf(i_0_3724,plain,
~ empty(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1))),
inference(rw,[status(thm)],[i_0_1734,c_0_944]),
[final] ).
cnf(i_0_3725,lemma,
( X1 = esk404_2(X3,X2)
| X2 = empty_set
| ~ in(X1,X2)
| ~ subset(esk404_2(X3,X2),X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X3,omega)
| ~ ordinal(X3)
| esk403_1(X4) != X4
| ~ in(X4,esk402_0) ),
inference(split_conjunct,[status(thm)],[i_0_1541]),
[final] ).
cnf(i_0_3726,plain,
( ordinal(esk340_3(X1,X2,X3))
| esk335_2(X1,X2) = esk337_2(X1,X2)
| ~ in(X3,esk338_2(X1,X2))
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_762]),
[final] ).
cnf(i_0_3727,plain,
( ordinal(esk340_3(X1,X2,X3))
| esk334_2(X1,X2) = esk336_2(X1,X2)
| ~ in(X3,esk338_2(X1,X2))
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_762]),
[final] ).
cnf(i_0_3728,plain,
( ordinal(esk340_3(X1,X2,X3))
| esk333_2(X1,X2) = esk335_2(X1,X2)
| ~ in(X3,esk338_2(X1,X2))
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_762]),
[final] ).
cnf(i_0_3729,plain,
( ordinal(esk340_3(X1,X2,X3))
| esk333_2(X1,X2) = esk334_2(X1,X2)
| ~ in(X3,esk338_2(X1,X2))
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_762]),
[final] ).
cnf(i_0_3730,lemma,
( in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),esk188_1(X2))
| X3 != unordered_pair(X1,X1)
| esk187_1(X2) != esk186_1(X2)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1735,c_0_681]),c_0_944]),
[final] ).
cnf(i_0_3731,lemma,
( X1 = X2
| unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)) != unordered_pair(unordered_pair(X2,X4),unordered_pair(X2,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1736,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_3732,lemma,
( X1 = X2
| unordered_pair(unordered_pair(X3,X1),unordered_pair(X3,X3)) != unordered_pair(unordered_pair(X4,X2),unordered_pair(X4,X4)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1737,c_0_944]),c_0_944]),
[final] ).
cnf(i_0_3733,lemma,
( relation_dom(esk399_2(X1,X2)) = X2
| in(esk397_2(X1,X2),X2)
| in(esk394_2(X1,X2),X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3734,plain,
( closed_subset(X3,X2)
| ~ closed_subsets(X1,X2)
| ~ element(X3,powerset(the_carrier(X2)))
| ~ in(X3,X1)
| ~ element(X1,powerset(powerset(the_carrier(X2))))
| ~ top_str(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1738]),
[final] ).
cnf(i_0_3735,plain,
( open_subset(X3,X2)
| ~ open_subsets(X1,X2)
| ~ element(X3,powerset(the_carrier(X2)))
| ~ in(X3,X1)
| ~ element(X1,powerset(powerset(the_carrier(X2))))
| ~ top_str(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1739]),
[final] ).
cnf(i_0_3736,lemma,
( X1 = esk204_2(X3,X2)
| X2 = empty_set
| element(esk202_0,powerset(powerset(esk200_0)))
| ~ in(X1,X2)
| ~ subset(esk204_2(X3,X2),X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X3,omega)
| ~ ordinal(X3)
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_1538]),
[final] ).
cnf(i_0_3737,lemma,
( relation(esk399_2(X1,X2))
| in(esk397_2(X1,X2),X2)
| in(esk394_2(X1,X2),X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3738,lemma,
( function(esk399_2(X1,X2))
| in(esk397_2(X1,X2),X2)
| in(esk394_2(X1,X2),X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_3739,lemma,
( X1 = esk404_2(X3,X2)
| X2 = empty_set
| element(esk402_0,powerset(powerset(esk400_0)))
| ~ in(X1,X2)
| ~ subset(esk404_2(X3,X2),X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X3,omega)
| ~ ordinal(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1541]),
[final] ).
cnf(i_0_3740,lemma,
( in(X1,relation_dom(relation_composition(X2,X3)))
| ~ in(X1,relation_dom(X2))
| ~ in(apply(X2,X1),relation_dom(X3))
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1740]),
[final] ).
cnf(i_0_3741,lemma,
( relation(esk192_2(X1,X2))
| in(esk189_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_711]),
[final] ).
cnf(i_0_3742,lemma,
( relation(esk192_2(X1,X2))
| in(esk189_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_711]),
[final] ).
cnf(i_0_3743,lemma,
( function(esk192_2(X1,X2))
| in(esk189_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_711]),
[final] ).
cnf(i_0_3744,lemma,
( function(esk192_2(X1,X2))
| in(esk189_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_711]),
[final] ).
cnf(i_0_3745,plain,
( in(esk244_3(X1,X2,X3),X1)
| in(esk240_1(X1),X1)
| ~ in(X3,esk242_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_715]),
[final] ).
cnf(i_0_3746,plain,
( in(esk244_3(X1,X2,X3),X1)
| in(esk238_1(X1),X1)
| ~ in(X3,esk242_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_715]),
[final] ).
cnf(i_0_3747,plain,
( element(esk36_1(X1),powerset(the_carrier(X1)))
| topological_space(X1)
| ~ in(union_of_subsets(the_carrier(X1),esk34_1(X1)),the_topology(X1))
| ~ in(the_carrier(X1),the_topology(X1))
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1520]),
[final] ).
cnf(i_0_3748,plain,
( element(esk35_1(X1),powerset(the_carrier(X1)))
| topological_space(X1)
| ~ in(union_of_subsets(the_carrier(X1),esk34_1(X1)),the_topology(X1))
| ~ in(the_carrier(X1),the_topology(X1))
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1520]),
[final] ).
cnf(i_0_3749,plain,
( empty_carrier(X1)
| element(join(X1,X2,X3),the_carrier(X1))
| ~ join_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1741]),
[final] ).
cnf(i_0_3750,plain,
( empty_carrier(X1)
| element(meet(X1,X2,X3),the_carrier(X1))
| ~ meet_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1742]),
[final] ).
cnf(i_0_3751,lemma,
( meet(boole_lattice(X1),X2,X3) = set_difference(X2,set_difference(X2,X3))
| ~ element(X3,the_carrier(boole_lattice(X1)))
| ~ element(X2,the_carrier(boole_lattice(X1))) ),
inference(rw,[status(thm)],[i_0_1743,c_0_1442]),
[final] ).
cnf(i_0_3752,lemma,
( in(X1,esk431_2(X2,X3))
| ~ closed_subset(X1,X2)
| ~ subset(X3,X1)
| ~ element(X1,powerset(the_carrier(X2)))
| ~ element(X3,powerset(the_carrier(X2)))
| ~ topological_space(X2)
| ~ top_str(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1744]),
[final] ).
cnf(i_0_3753,lemma,
( empty_carrier(X1)
| point_neighbourhood(X2,X1,X3)
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ element(X3,the_carrier(X1))
| ~ open_subset(X2,X1)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1745]),
[final] ).
cnf(i_0_3754,plain,
( apply_binary(the_L_meet(X1),X2,X3) = subset_intersection2(X4,X2,X3)
| ~ element(X3,powerset(X4))
| ~ element(X2,powerset(X4))
| X1 != boole_lattice(X4)
| ~ strict_latt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1407]),
[final] ).
cnf(i_0_3755,plain,
( apply_binary(the_L_join(X1),X2,X3) = subset_union2(X4,X2,X3)
| ~ element(X3,powerset(X4))
| ~ element(X2,powerset(X4))
| X1 != boole_lattice(X4)
| ~ strict_latt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1407]),
[final] ).
cnf(i_0_3756,plain,
( subset(X1,X2)
| element(esk259_2(X3,X1),powerset(the_carrier(X3)))
| ~ in(X2,esk260_2(X3,X1))
| ~ topological_space(X3)
| ~ top_str(X3)
| ~ element(X1,powerset(the_carrier(X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3757,plain,
( subset(X1,X2)
| element(esk258_2(X3,X1),powerset(the_carrier(X3)))
| ~ in(X2,esk260_2(X3,X1))
| ~ topological_space(X3)
| ~ top_str(X3)
| ~ element(X1,powerset(the_carrier(X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3758,plain,
( element(esk127_3(X1,X2,X3),the_carrier(X2))
| empty_carrier(X2)
| ~ in(X1,a_2_2_lattice3(X2,X3))
| ~ latt_str(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1701]),
[final] ).
cnf(i_0_3759,lemma,
( empty_carrier(X2)
| ~ in(X1,subset_complement(the_carrier(X2),X3))
| ~ in(X1,X3)
| ~ element(X1,the_carrier(X2))
| ~ element(X3,powerset(the_carrier(X2)))
| ~ one_sorted_str(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1746]),
[final] ).
cnf(i_0_3760,lemma,
( in(X1,powerset(the_carrier(X2)))
| ~ in(X1,esk356_2(X2,X3))
| ~ topological_space(X2)
| ~ top_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1638]),
[final] ).
cnf(i_0_3761,plain,
( in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3)
| X4 != fiber(X3,X2)
| ~ relation(X3)
| ~ in(X1,X4) ),
inference(rw,[status(thm)],[i_0_1747,c_0_944]),
[final] ).
cnf(i_0_3762,lemma,
( in(esk412_3(X1,X2,X3),relation_rng(X3))
| ~ in(X1,relation_inverse_image(X3,X2))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_734]),
[final] ).
cnf(i_0_3763,lemma,
( in(esk411_3(X1,X2,X3),relation_dom(X3))
| ~ in(X1,relation_image(X3,X2))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_709]),
[final] ).
cnf(i_0_3764,plain,
( in(esk244_3(X1,X2,X3),X1)
| ~ in(X3,esk242_2(X1,X2))
| esk236_1(X1) != esk237_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_715]),
[final] ).
cnf(i_0_3765,plain,
( ordinal(esk453_3(X1,X2,X3))
| ~ epred2_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1208]),
[final] ).
cnf(i_0_3766,plain,
( ordinal(esk451_3(X1,X2,X3))
| ~ epred2_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1208]),
[final] ).
cnf(i_0_3767,lemma,
( in(esk429_2(X1,X2),X2)
| closed_subset(meet_of_subsets(the_carrier(X1),X2),X1)
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ topological_space(X1)
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1716]),
[final] ).
cnf(i_0_3768,lemma,
( X1 = esk382_3(X2,X3,X1)
| in(esk379_2(X2,X3),X2)
| in(esk376_2(X2,X3),esk378_2(X2,X3))
| empty(X2)
| ~ in(X1,X2)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_3769,lemma,
( X1 = esk382_3(X2,X3,X1)
| in(esk379_2(X2,X3),X2)
| in(esk375_2(X2,X3),esk377_2(X2,X3))
| empty(X2)
| ~ in(X1,X2)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_3770,plain,
( in(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,X3)),X1)
| ~ relation(X1)
| ~ in(X3,X2)
| ~ is_reflexive_in(X1,X2) ),
inference(rw,[status(thm)],[i_0_1748,c_0_944]),
[final] ).
cnf(i_0_3771,lemma,
( in(X1,omega)
| in(X2,esk349_1(X3))
| X1 != X2
| ~ ordinal(X3)
| ~ ordinal(X1)
| ~ in(X2,set_union2(X3,unordered_pair(X3,X3))) ),
inference(rw,[status(thm)],[i_0_1749,c_0_1305]),
[final] ).
cnf(i_0_3772,plain,
( empty(X2)
| empty(X3)
| ~ empty(X1)
| ~ function(X1)
| ~ quasi_total(X1,X2,X3)
| ~ relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1692]),
[final] ).
cnf(i_0_3773,lemma,
( closed_subset(X1,X2)
| ~ in(X1,esk431_2(X2,X3))
| ~ element(X1,powerset(the_carrier(X2)))
| ~ element(X3,powerset(the_carrier(X2)))
| ~ topological_space(X2)
| ~ top_str(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1744]),
[final] ).
cnf(i_0_3774,lemma,
( subset(X1,X2)
| ~ in(X2,esk431_2(X3,X1))
| ~ element(X2,powerset(the_carrier(X3)))
| ~ element(X1,powerset(the_carrier(X3)))
| ~ topological_space(X3)
| ~ top_str(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1744]),
[final] ).
cnf(i_0_3775,lemma,
( subset(X1,X2)
| ~ in(X2,esk406_2(X3,X1))
| ~ element(X2,powerset(the_carrier(X3)))
| ~ topological_space(X3)
| ~ top_str(X3)
| ~ element(X1,powerset(the_carrier(X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1587]),
[final] ).
cnf(i_0_3776,plain,
( in(union_of_subsets(the_carrier(X2),X1),the_topology(X2))
| ~ element(X1,powerset(powerset(the_carrier(X2))))
| ~ subset(X1,the_topology(X2))
| ~ topological_space(X2)
| ~ top_str(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1520]),
[final] ).
cnf(i_0_3777,plain,
( interior(X1,X2) = subset_complement(the_carrier(X1),topstr_closure(X1,subset_complement(the_carrier(X1),X2)))
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1750]),
[final] ).
cnf(i_0_3778,lemma,
( X1 = esk204_2(X3,X2)
| X2 = empty_set
| in(esk200_0,omega)
| ~ in(X1,X2)
| ~ subset(esk204_2(X3,X2),X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X3,omega)
| ~ ordinal(X3)
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_1538]),
[final] ).
cnf(i_0_3779,lemma,
( closed_subsets(X2,X1)
| ~ open_subsets(complements_of_subsets(the_carrier(X1),X2),X1)
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1751]),
[final] ).
cnf(i_0_3780,lemma,
( open_subsets(X2,X1)
| ~ closed_subsets(complements_of_subsets(the_carrier(X1),X2),X1)
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1752]),
[final] ).
cnf(i_0_3781,lemma,
( X1 = esk404_2(X3,X2)
| X2 = empty_set
| in(esk400_0,omega)
| ~ in(X1,X2)
| ~ subset(esk404_2(X3,X2),X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X3,omega)
| ~ ordinal(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1541]),
[final] ).
cnf(i_0_3782,plain,
( in(esk244_3(X1,X2,X3),X1)
| esk235_1(X1) = esk237_1(X1)
| ~ in(X3,esk242_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_715]),
[final] ).
cnf(i_0_3783,plain,
( in(esk244_3(X1,X2,X3),X1)
| esk235_1(X1) = esk236_1(X1)
| ~ in(X3,esk242_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_715]),
[final] ).
cnf(i_0_3784,lemma,
( subset(set_difference(X1,set_difference(X1,X3)),set_difference(X2,set_difference(X2,X3)))
| ~ subset(X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1753,c_0_1442]),c_0_1442]),
[final] ).
cnf(i_0_3785,plain,
( empty_carrier(X1)
| join_commut(X1,X2,X3) = join(X1,X2,X3)
| ~ join_commutative(X1)
| ~ join_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1754]),
[final] ).
cnf(i_0_3786,plain,
( empty_carrier(X1)
| meet_commut(X1,X2,X3) = meet(X1,X2,X3)
| ~ meet_commutative(X1)
| ~ meet_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1755]),
[final] ).
cnf(i_0_3787,plain,
( empty_carrier(X1)
| meet_commut(X1,X2,X3) = meet_commut(X1,X3,X2)
| ~ meet_commutative(X1)
| ~ meet_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1756]),
[final] ).
cnf(i_0_3788,plain,
( empty_carrier(X1)
| join_commut(X1,X2,X3) = join_commut(X1,X3,X2)
| ~ join_commutative(X1)
| ~ join_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1757]),
[final] ).
cnf(i_0_3789,plain,
( element(subset_difference(X2,X1,X3),powerset(X2))
| ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1758]),
[final] ).
cnf(i_0_3790,plain,
( element(subset_intersection2(X2,X1,X3),powerset(X2))
| ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1759]),
[final] ).
cnf(i_0_3791,plain,
( element(subset_union2(X2,X1,X3),powerset(X2))
| ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1760]),
[final] ).
cnf(i_0_3792,lemma,
( in(esk412_3(X1,X2,X3),X2)
| ~ in(X1,relation_inverse_image(X3,X2))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_734]),
[final] ).
cnf(i_0_3793,lemma,
( in(esk411_3(X1,X2,X3),X2)
| ~ in(X1,relation_image(X3,X2))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_709]),
[final] ).
cnf(i_0_3794,lemma,
( in(esk373_3(X1,X2,X3),X1)
| ~ in(X3,esk372_2(X1,X2))
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_788]),
[final] ).
cnf(i_0_3795,plain,
( in(esk36_1(X1),the_topology(X1))
| topological_space(X1)
| ~ in(union_of_subsets(the_carrier(X1),esk34_1(X1)),the_topology(X1))
| ~ in(the_carrier(X1),the_topology(X1))
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1520]),
[final] ).
cnf(i_0_3796,plain,
( in(esk35_1(X1),the_topology(X1))
| topological_space(X1)
| ~ in(union_of_subsets(the_carrier(X1),esk34_1(X1)),the_topology(X1))
| ~ in(the_carrier(X1),the_topology(X1))
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1520]),
[final] ).
cnf(i_0_3797,lemma,
( in(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,X2)),X1)
| ~ relation(X1)
| ~ reflexive(X1)
| ~ in(X2,relation_field(X1)) ),
inference(rw,[status(thm)],[i_0_1761,c_0_944]),
[final] ).
cnf(i_0_3798,plain,
( subset(esk68_2(X1,X2),X2)
| ~ is_a_cover_of_carrier(X1,X2)
| ~ open_subsets(X2,X1)
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ compact_top_space(X1)
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1703]),
[final] ).
cnf(i_0_3799,plain,
( is_a_cover_of_carrier(X1,esk68_2(X1,X2))
| ~ is_a_cover_of_carrier(X1,X2)
| ~ open_subsets(X2,X1)
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ compact_top_space(X1)
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1703]),
[final] ).
cnf(i_0_3800,plain,
( in(X5,X6)
| X6 != cartesian_product2(X2,X4)
| X5 != unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1))
| ~ in(X3,X4)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_1762,c_0_944]),
[final] ).
cnf(i_0_3801,plain,
( is_well_founded_in(X2,X3)
| ~ in(X1,esk76_2(X2,X3))
| ~ disjoint(fiber(X2,X1),esk76_2(X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1596]),
[final] ).
cnf(i_0_3802,lemma,
( in(apply(X1,X2),relation_dom(X3))
| ~ in(X2,relation_dom(relation_composition(X1,X3)))
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1740]),
[final] ).
cnf(i_0_3803,plain,
( in(X3,a_2_3_lattice3(X2,X4))
| empty_carrier(X2)
| ~ element(X1,the_carrier(X2))
| X3 != X1
| ~ latt_set_smaller(X2,X1,X4)
| ~ lattice(X2)
| ~ complete_latt_str(X2)
| ~ latt_str(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1686]),
[final] ).
cnf(i_0_3804,plain,
( subset(X1,X2)
| ~ in(X2,esk260_2(X3,X1))
| esk256_2(X3,X1) != esk257_2(X3,X1)
| ~ topological_space(X3)
| ~ top_str(X3)
| ~ element(X1,powerset(the_carrier(X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3805,lemma,
( element(esk408_2(X1,X2),powerset(powerset(the_carrier(X1))))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1639]),
[final] ).
cnf(i_0_3806,lemma,
( below(boole_lattice(X3),X1,X2)
| ~ subset(X1,X2)
| ~ element(X2,the_carrier(boole_lattice(X3)))
| ~ element(X1,the_carrier(boole_lattice(X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1729]),
[final] ).
cnf(i_0_3807,lemma,
( X1 = esk204_2(X3,X2)
| X2 = empty_set
| being_limit_ordinal(esk200_0)
| ~ in(X1,X2)
| ~ subset(esk204_2(X3,X2),X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X3,omega)
| ~ ordinal(X3)
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_1538]),
[final] ).
cnf(i_0_3808,lemma,
( X1 = esk204_2(X3,X2)
| X2 = empty_set
| ordinal(esk200_0)
| ~ in(X1,X2)
| ~ subset(esk204_2(X3,X2),X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X3,omega)
| ~ ordinal(X3)
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_1538]),
[final] ).
cnf(i_0_3809,plain,
( in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),X4)
| X1 != X3
| X4 != identity_relation(X2)
| ~ relation(X4)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_1763,c_0_944]),
[final] ).
cnf(i_0_3810,lemma,
( X1 = esk404_2(X3,X2)
| X2 = empty_set
| ordinal(esk400_0)
| ~ in(X1,X2)
| ~ subset(esk404_2(X3,X2),X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X3,omega)
| ~ ordinal(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1541]),
[final] ).
cnf(i_0_3811,lemma,
( esk355_3(X1,X2,X3) = X3
| ~ in(X3,esk354_2(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1652]),
[final] ).
cnf(i_0_3812,lemma,
( in(esk347_3(X1,X2,X3),X1)
| ~ in(X3,esk346_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_722]),
[final] ).
cnf(i_0_3813,lemma,
( X1 = esk204_2(X3,X2)
| X2 = empty_set
| ~ in(X1,X2)
| ~ subset(esk204_2(X3,X2),X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X3,omega)
| ~ ordinal(X3)
| esk202_0 != empty_set
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_1538]),
[final] ).
cnf(i_0_3814,lemma,
( X1 = esk204_2(X3,X2)
| X2 = empty_set
| ~ in(X1,X2)
| ~ subset(esk204_2(X3,X2),X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X3,omega)
| ~ ordinal(X3)
| esk200_0 != empty_set
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_1538]),
[final] ).
cnf(i_0_3815,plain,
( subset(X1,X2)
| closed_subset(esk259_2(X3,X1),X3)
| ~ in(X2,esk260_2(X3,X1))
| ~ topological_space(X3)
| ~ top_str(X3)
| ~ element(X1,powerset(the_carrier(X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3816,plain,
( subset(X1,X2)
| closed_subset(esk258_2(X3,X1),X3)
| ~ in(X2,esk260_2(X3,X1))
| ~ topological_space(X3)
| ~ top_str(X3)
| ~ element(X1,powerset(the_carrier(X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3817,plain,
( subset(X1,X2)
| subset(X1,esk257_2(X3,X1))
| ~ in(X2,esk260_2(X3,X1))
| ~ topological_space(X3)
| ~ top_str(X3)
| ~ element(X1,powerset(the_carrier(X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3818,plain,
( subset(X1,X2)
| subset(X1,esk256_2(X3,X1))
| ~ in(X2,esk260_2(X3,X1))
| ~ topological_space(X3)
| ~ top_str(X3)
| ~ element(X1,powerset(the_carrier(X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3819,lemma,
( X1 = esk404_2(X3,X2)
| X2 = empty_set
| ~ in(X1,X2)
| ~ subset(esk404_2(X3,X2),X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X3,omega)
| ~ ordinal(X3)
| esk402_0 != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_1541]),
[final] ).
cnf(i_0_3820,lemma,
( apply(relation_dom_restriction(X1,X3),X2) = apply(X1,X2)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_dom(relation_dom_restriction(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1764]),
[final] ).
cnf(i_0_3821,lemma,
( ordinal(esk373_3(X1,X2,X3))
| ~ in(X3,esk372_2(X1,X2))
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_788]),
[final] ).
cnf(i_0_3822,plain,
( finite(esk68_2(X1,X2))
| ~ is_a_cover_of_carrier(X1,X2)
| ~ open_subsets(X2,X1)
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ compact_top_space(X1)
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1703]),
[final] ).
cnf(i_0_3823,lemma,
( empty_carrier(X1)
| ~ compact_top_space(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ centered(X2)
| ~ closed_subsets(X2,X1)
| meet_of_subsets(the_carrier(X1),X2) != empty_set
| ~ topological_space(X1)
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1765]),
[final] ).
cnf(i_0_3824,plain,
( X1 = empty_set
| X2 = empty_set
| ~ quasi_total(X1,X2,X3)
| X3 != empty_set
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1704]),
[final] ).
cnf(i_0_3825,lemma,
( join(boole_lattice(X1),X2,X3) = set_union2(X2,X3)
| ~ element(X3,the_carrier(boole_lattice(X1)))
| ~ element(X2,the_carrier(boole_lattice(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_798]),
[final] ).
cnf(i_0_3826,lemma,
( relation_isomorphism(X2,X1,function_inverse(X3))
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3)
| ~ function(X3)
| ~ relation_isomorphism(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1766]),
[final] ).
cnf(i_0_3827,plain,
( in(esk75_3(X1,X2,X3),X3)
| X3 = empty_set
| ~ subset(X3,X2)
| ~ is_well_founded_in(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1596]),
[final] ).
cnf(i_0_3828,plain,
( closed_subsets(X2,X1)
| ~ closed_subset(esk59_2(X1,X2),X1)
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1738]),
[final] ).
cnf(i_0_3829,plain,
( open_subsets(X2,X1)
| ~ open_subset(esk45_2(X1,X2),X1)
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1739]),
[final] ).
cnf(i_0_3830,lemma,
( X1 = esk382_3(X2,X3,X1)
| in(esk379_2(X2,X3),X2)
| empty(X2)
| ~ in(X1,X2)
| esk375_2(X2,X3) != esk376_2(X2,X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_3831,plain,
( X2 = set_meet(X1)
| X1 = empty_set
| ~ in(esk42_2(X1,X2),esk43_2(X1,X2))
| ~ in(esk42_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1724]),
[final] ).
cnf(i_0_3832,plain,
( in(X3,a_2_2_lattice3(X2,X4))
| empty_carrier(X2)
| ~ element(X1,the_carrier(X2))
| X3 != X1
| ~ latt_set_smaller(X2,X1,X4)
| ~ latt_str(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1701]),
[final] ).
cnf(i_0_3833,lemma,
( in(X1,X2)
| ~ ordinal(X2)
| ~ ordinal(X1)
| ~ ordinal_subset(set_union2(X1,unordered_pair(X1,X1)),X2) ),
inference(rw,[status(thm)],[i_0_1767,c_0_1305]),
[final] ).
cnf(i_0_3834,plain,
( subset_intersection2(X2,X1,X3) = subset_intersection2(X2,X3,X1)
| ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1768]),
[final] ).
cnf(i_0_3835,plain,
( subset_union2(X2,X1,X3) = subset_union2(X2,X3,X1)
| ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1769]),
[final] ).
cnf(i_0_3836,lemma,
( relation_of2_as_subset(X1,X2,X4)
| ~ relation_of2_as_subset(X1,X2,X3)
| ~ subset(relation_rng(X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1770]),
[final] ).
cnf(i_0_3837,lemma,
( X1 = empty_set
| subset_difference(X2,X2,union_of_subsets(X2,X1)) = meet_of_subsets(X2,complements_of_subsets(X2,X1))
| ~ element(X1,powerset(powerset(X2))) ),
inference(rw,[status(thm)],[i_0_1771,c_0_1772]),
[final] ).
cnf(i_0_3838,lemma,
( X1 = empty_set
| union_of_subsets(X2,complements_of_subsets(X2,X1)) = subset_difference(X2,X2,meet_of_subsets(X2,X1))
| ~ element(X1,powerset(powerset(X2))) ),
inference(rw,[status(thm)],[i_0_1773,c_0_1772]),
[final] ).
cnf(i_0_3839,plain,
( in(esk88_3(X1,X2,X3),relation_dom(X1))
| ~ in(X3,X2)
| X2 != relation_rng(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1774]),
[final] ).
cnf(i_0_3840,lemma,
( closed_subsets(complements_of_subsets(the_carrier(X2),X1),X2)
| ~ open_subsets(X1,X2)
| ~ element(X1,powerset(powerset(the_carrier(X2))))
| ~ top_str(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1752]),
[final] ).
cnf(i_0_3841,lemma,
( open_subsets(complements_of_subsets(the_carrier(X2),X1),X2)
| ~ closed_subsets(X1,X2)
| ~ element(X1,powerset(powerset(the_carrier(X2))))
| ~ top_str(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1751]),
[final] ).
cnf(i_0_3842,plain,
( subset(X1,X2)
| esk259_2(X3,X1) = esk257_2(X3,X1)
| ~ in(X2,esk260_2(X3,X1))
| ~ topological_space(X3)
| ~ top_str(X3)
| ~ element(X1,powerset(the_carrier(X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3843,plain,
( subset(X1,X2)
| esk258_2(X3,X1) = esk256_2(X3,X1)
| ~ in(X2,esk260_2(X3,X1))
| ~ topological_space(X3)
| ~ top_str(X3)
| ~ element(X1,powerset(the_carrier(X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3844,plain,
( subset(X1,X2)
| esk255_2(X3,X1) = esk257_2(X3,X1)
| ~ in(X2,esk260_2(X3,X1))
| ~ topological_space(X3)
| ~ top_str(X3)
| ~ element(X1,powerset(the_carrier(X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3845,plain,
( subset(X1,X2)
| esk255_2(X3,X1) = esk256_2(X3,X1)
| ~ in(X2,esk260_2(X3,X1))
| ~ topological_space(X3)
| ~ top_str(X3)
| ~ element(X1,powerset(the_carrier(X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_3846,lemma,
( relation(esk197_2(X1,X2))
| esk195_2(X1,X2) != esk196_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_712]),
[final] ).
cnf(i_0_3847,lemma,
( relation(esk192_2(X1,X2))
| esk190_2(X1,X2) != esk191_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_711]),
[final] ).
cnf(i_0_3848,lemma,
( function(esk197_2(X1,X2))
| esk195_2(X1,X2) != esk196_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_712]),
[final] ).
cnf(i_0_3849,lemma,
( function(esk192_2(X1,X2))
| esk190_2(X1,X2) != esk191_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_711]),
[final] ).
cnf(i_0_3850,lemma,
( X1 = esk382_3(X2,X3,X1)
| in(esk379_2(X2,X3),X2)
| in(esk374_2(X2,X3),X2)
| empty(X2)
| ~ in(X1,X2)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_3851,plain,
( in(esk250_2(X1,X2),set_union2(X1,unordered_pair(X1,X1)))
| esk248_1(X1) != esk247_1(X1)
| ~ ordinal(X1)
| ~ in(X2,esk249_1(X1)) ),
inference(rw,[status(thm)],[i_0_1775,c_0_1305]),
[final] ).
cnf(i_0_3852,plain,
( esk339_3(X1,X2,X3) = X3
| ~ in(X3,esk338_2(X1,X2))
| esk334_2(X1,X2) != esk335_2(X1,X2)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_762]),
[final] ).
cnf(i_0_3853,plain,
( X1 = esk340_3(X2,X3,X1)
| ~ in(X1,esk338_2(X2,X3))
| esk334_2(X2,X3) != esk335_2(X2,X3)
| ~ ordinal(X3) ),
inference(split_conjunct,[status(thm)],[i_0_762]),
[final] ).
cnf(i_0_3854,plain,
( empty_carrier(X1)
| element(X3,powerset(the_carrier(X1)))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ point_neighbourhood(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1776]),
[final] ).
cnf(i_0_3855,plain,
( element(esk59_2(X1,X2),powerset(the_carrier(X1)))
| closed_subsets(X2,X1)
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1738]),
[final] ).
cnf(i_0_3856,plain,
( element(esk45_2(X1,X2),powerset(the_carrier(X1)))
| open_subsets(X2,X1)
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1739]),
[final] ).
cnf(i_0_3857,lemma,
( finite(X2)
| ~ finite(complements_of_subsets(the_carrier(X1),X2))
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1777]),
[final] ).
cnf(i_0_3858,lemma,
( relation(esk197_2(X1,X2))
| in(esk194_2(X1,X2),X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_712]),
[final] ).
cnf(i_0_3859,lemma,
( relation(esk197_2(X1,X2))
| in(esk194_2(X1,X2),X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_712]),
[final] ).
cnf(i_0_3860,lemma,
( function(esk197_2(X1,X2))
| in(esk194_2(X1,X2),X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_712]),
[final] ).
cnf(i_0_3861,lemma,
( function(esk197_2(X1,X2))
| in(esk194_2(X1,X2),X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_712]),
[final] ).
cnf(i_0_3862,lemma,
( ~ disjoint(X2,X3)
| ~ in(X1,set_difference(X2,set_difference(X2,X3))) ),
inference(rw,[status(thm)],[i_0_1778,c_0_1442]),
[final] ).
cnf(i_0_3863,plain,
( X1 = apply(X2,esk88_3(X2,X3,X1))
| ~ in(X1,X3)
| X3 != relation_rng(X2)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1774]),
[final] ).
cnf(i_0_3864,plain,
( esk339_3(X1,X2,X3) = X3
| in(esk337_2(X1,X2),X1)
| ~ in(X3,esk338_2(X1,X2))
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_762]),
[final] ).
cnf(i_0_3865,plain,
( esk339_3(X1,X2,X3) = X3
| in(esk336_2(X1,X2),X1)
| ~ in(X3,esk338_2(X1,X2))
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_762]),
[final] ).
cnf(i_0_3866,plain,
( X1 = esk340_3(X2,X3,X1)
| in(esk337_2(X2,X3),X2)
| ~ in(X1,esk338_2(X2,X3))
| ~ ordinal(X3) ),
inference(split_conjunct,[status(thm)],[i_0_762]),
[final] ).
cnf(i_0_3867,plain,
( X1 = esk340_3(X2,X3,X1)
| in(esk336_2(X2,X3),X2)
| ~ in(X1,esk338_2(X2,X3))
| ~ ordinal(X3) ),
inference(split_conjunct,[status(thm)],[i_0_762]),
[final] ).
cnf(i_0_3868,plain,
( compact_top_space(X2)
| ~ element(X1,powerset(powerset(the_carrier(X2))))
| ~ subset(X1,esk69_1(X2))
| ~ is_a_cover_of_carrier(X2,X1)
| ~ finite(X1)
| ~ top_str(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1703]),
[final] ).
cnf(i_0_3869,lemma,
( relation_of2_as_subset(X1,X2,X4)
| ~ relation_of2_as_subset(X1,X2,X3)
| ~ subset(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1779]),
[final] ).
cnf(i_0_3870,plain,
( X1 = esk448_1(X2)
| X2 = empty_set
| subset(X3,esk446_1(X3))
| epred1_0
| ~ in(X1,X2)
| ~ subset(esk448_1(X2),X1)
| ~ element(X2,powerset(powerset(esk447_0)))
| ~ in(esk447_0,omega)
| ~ in(X3,esk445_0) ),
inference(split_conjunct,[status(thm)],[i_0_760]),
[final] ).
cnf(i_0_3871,lemma,
( in(esk204_2(X1,X2),X2)
| X2 = empty_set
| subset(X3,esk203_1(X3))
| ~ element(X2,powerset(powerset(X1)))
| ~ in(X1,omega)
| ~ ordinal(X1)
| ~ in(X3,esk202_0)
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_1538]),
[final] ).
cnf(i_0_3872,lemma,
( in(X1,relation_dom(X2))
| ~ in(X1,relation_dom(relation_composition(X2,X3)))
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1740]),
[final] ).
cnf(i_0_3873,lemma,
( open_subset(X2,X1)
| interior(X1,X2) != X2
| ~ element(X3,powerset(the_carrier(X4)))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X4)
| ~ topological_space(X1)
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1780]),
[final] ).
cnf(i_0_3874,lemma,
( in(X1,set_union2(X2,unordered_pair(X2,X2)))
| ~ ordinal(X2)
| ~ in(X1,esk372_2(X3,X2)) ),
inference(rw,[status(thm)],[i_0_1781,c_0_1305]),
[final] ).
cnf(i_0_3875,lemma,
( esk435_2(X1,X2) = apply(X1,esk436_2(X1,X2))
| esk434_2(X1,X2) = apply(X2,esk433_2(X1,X2))
| X2 = function_inverse(X1)
| relation_dom(X2) != relation_rng(X1)
| ~ relation(X2)
| ~ function(X2)
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1546]),
[final] ).
cnf(i_0_3876,lemma,
( in(X1,X2)
| in(X1,subset_complement(the_carrier(X3),X2))
| empty_carrier(X3)
| ~ element(X1,the_carrier(X3))
| ~ element(X2,powerset(the_carrier(X3)))
| ~ one_sorted_str(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1746]),
[final] ).
cnf(i_0_3877,lemma,
( interior(X2,X1) = X1
| ~ open_subset(X1,X2)
| ~ element(X1,powerset(the_carrier(X2)))
| ~ element(X3,powerset(the_carrier(X4)))
| ~ top_str(X2)
| ~ topological_space(X4)
| ~ top_str(X4) ),
inference(split_conjunct,[status(thm)],[i_0_1780]),
[final] ).
cnf(i_0_3878,lemma,
( in(X1,powerset(the_carrier(X2)))
| ~ in(X1,esk354_2(X2,X3))
| ~ topological_space(X2)
| ~ top_str(X2)
| ~ element(X3,powerset(the_carrier(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1652]),
[final] ).
cnf(i_0_3879,plain,
( X1 = esk448_1(X2)
| X2 = empty_set
| in(esk446_1(X3),esk445_0)
| epred1_0
| ~ in(X1,X2)
| ~ subset(esk448_1(X2),X1)
| ~ element(X2,powerset(powerset(esk447_0)))
| ~ in(esk447_0,omega)
| ~ in(X3,esk445_0) ),
inference(split_conjunct,[status(thm)],[i_0_760]),
[final] ).
cnf(i_0_3880,lemma,
( in(esk404_2(X1,X2),X2)
| X2 = empty_set
| subset(X3,esk403_1(X3))
| ~ element(X2,powerset(powerset(X1)))
| ~ in(X1,omega)
| ~ ordinal(X1)
| ~ in(X3,esk402_0) ),
inference(split_conjunct,[status(thm)],[i_0_1541]),
[final] ).
cnf(i_0_3881,lemma,
( X1 = esk413_2(X3,X2)
| X2 = empty_set
| ~ in(X1,X2)
| ~ subset(esk413_2(X3,X2),X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ finite(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1782]),
[final] ).
cnf(i_0_3882,lemma,
( in(esk204_2(X1,X2),X2)
| X2 = empty_set
| in(esk203_1(X3),esk202_0)
| ~ element(X2,powerset(powerset(X1)))
| ~ in(X1,omega)
| ~ ordinal(X1)
| ~ in(X3,esk202_0)
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_1538]),
[final] ).
cnf(i_0_3883,lemma,
( in(esk404_2(X1,X2),X2)
| X2 = empty_set
| in(esk403_1(X3),esk402_0)
| ~ element(X2,powerset(powerset(X1)))
| ~ in(X1,omega)
| ~ ordinal(X1)
| ~ in(X3,esk402_0) ),
inference(split_conjunct,[status(thm)],[i_0_1541]),
[final] ).
cnf(i_0_3884,plain,
( X2 = relation_rng(X1)
| ~ in(esk89_2(X1,X2),X2)
| ~ in(X3,relation_dom(X1))
| esk89_2(X1,X2) != apply(X1,X3)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1774]),
[final] ).
cnf(i_0_3885,plain,
( subset_intersection2(X2,X1,X3) = set_difference(X1,set_difference(X1,X3))
| ~ element(X3,powerset(X2))
| ~ element(X1,powerset(X2)) ),
inference(rw,[status(thm)],[i_0_1783,c_0_1442]),
[final] ).
cnf(i_0_3886,lemma,
( X1 = esk382_3(X2,X3,X1)
| in(esk379_2(X2,X3),X2)
| esk374_2(X2,X3) = esk378_2(X2,X3)
| empty(X2)
| ~ in(X1,X2)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_3887,lemma,
( X1 = esk382_3(X2,X3,X1)
| in(esk379_2(X2,X3),X2)
| esk374_2(X2,X3) = esk377_2(X2,X3)
| empty(X2)
| ~ in(X1,X2)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_3888,plain,
( element(X1,powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1784]),
[final] ).
cnf(i_0_3889,negated_conjecture,
( ~ relstr_set_smaller(esk440_0,empty_set,esk441_0)
| ~ relstr_element_smaller(esk440_0,empty_set,esk441_0) ),
inference(split_conjunct,[status(thm)],[i_0_1785]),
[final] ).
cnf(i_0_3890,plain,
( below_refl(X1,esk125_2(X2,X1),esk126_2(X2,X1))
| empty_carrier(X1)
| ~ in(X2,a_1_0_filter_1(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1455]),
[final] ).
cnf(i_0_3891,plain,
( esk339_3(X1,X2,X3) = X3
| ordinal(esk337_2(X1,X2))
| ~ in(X3,esk338_2(X1,X2))
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_762]),
[final] ).
cnf(i_0_3892,plain,
( esk339_3(X1,X2,X3) = X3
| ordinal(esk336_2(X1,X2))
| ~ in(X3,esk338_2(X1,X2))
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_762]),
[final] ).
cnf(i_0_3893,plain,
( X1 = esk340_3(X2,X3,X1)
| ordinal(esk337_2(X2,X3))
| ~ in(X1,esk338_2(X2,X3))
| ~ ordinal(X3) ),
inference(split_conjunct,[status(thm)],[i_0_762]),
[final] ).
cnf(i_0_3894,plain,
( X1 = esk340_3(X2,X3,X1)
| ordinal(esk336_2(X2,X3))
| ~ in(X1,esk338_2(X2,X3))
| ~ ordinal(X3) ),
inference(split_conjunct,[status(thm)],[i_0_762]),
[final] ).
cnf(i_0_3895,lemma,
( closed_subset(X2,X1)
| ~ open_subset(subset_complement(the_carrier(X1),X2),X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1786]),
[final] ).
cnf(i_0_3896,lemma,
( open_subset(X2,X1)
| ~ closed_subset(subset_complement(the_carrier(X1),X2),X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1787]),
[final] ).
cnf(i_0_3897,plain,
( element(esk36_1(X1),powerset(the_carrier(X1)))
| element(esk34_1(X1),powerset(powerset(the_carrier(X1))))
| topological_space(X1)
| ~ in(the_carrier(X1),the_topology(X1))
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1520]),
[final] ).
cnf(i_0_3898,plain,
( element(esk35_1(X1),powerset(the_carrier(X1)))
| element(esk34_1(X1),powerset(powerset(the_carrier(X1))))
| topological_space(X1)
| ~ in(the_carrier(X1),the_topology(X1))
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1520]),
[final] ).
cnf(i_0_3899,lemma,
( esk435_2(X1,X2) = apply(X1,esk436_2(X1,X2))
| in(esk433_2(X1,X2),relation_rng(X1))
| X2 = function_inverse(X1)
| relation_dom(X2) != relation_rng(X1)
| ~ relation(X2)
| ~ function(X2)
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1546]),
[final] ).
cnf(i_0_3900,lemma,
( in(esk436_2(X1,X2),relation_dom(X1))
| esk434_2(X1,X2) = apply(X2,esk433_2(X1,X2))
| X2 = function_inverse(X1)
| relation_dom(X2) != relation_rng(X1)
| ~ relation(X2)
| ~ function(X2)
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1546]),
[final] ).
cnf(i_0_3901,plain,
( X2 = union(X1)
| ~ in(esk84_2(X1,X2),X2)
| ~ in(esk84_2(X1,X2),X3)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1788]),
[final] ).
cnf(i_0_3902,plain,
( esk339_3(X1,X2,X3) = X3
| esk335_2(X1,X2) = esk337_2(X1,X2)
| ~ in(X3,esk338_2(X1,X2))
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_762]),
[final] ).
cnf(i_0_3903,plain,
( esk339_3(X1,X2,X3) = X3
| esk334_2(X1,X2) = esk336_2(X1,X2)
| ~ in(X3,esk338_2(X1,X2))
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_762]),
[final] ).
cnf(i_0_3904,plain,
( esk339_3(X1,X2,X3) = X3
| esk333_2(X1,X2) = esk335_2(X1,X2)
| ~ in(X3,esk338_2(X1,X2))
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_762]),
[final] ).
cnf(i_0_3905,plain,
( esk339_3(X1,X2,X3) = X3
| esk333_2(X1,X2) = esk334_2(X1,X2)
| ~ in(X3,esk338_2(X1,X2))
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_762]),
[final] ).
cnf(i_0_3906,plain,
( X1 = esk340_3(X2,X3,X1)
| esk335_2(X2,X3) = esk337_2(X2,X3)
| ~ in(X1,esk338_2(X2,X3))
| ~ ordinal(X3) ),
inference(split_conjunct,[status(thm)],[i_0_762]),
[final] ).
cnf(i_0_3907,plain,
( X1 = esk340_3(X2,X3,X1)
| esk334_2(X2,X3) = esk336_2(X2,X3)
| ~ in(X1,esk338_2(X2,X3))
| ~ ordinal(X3) ),
inference(split_conjunct,[status(thm)],[i_0_762]),
[final] ).
cnf(i_0_3908,plain,
( X1 = esk340_3(X2,X3,X1)
| esk333_2(X2,X3) = esk335_2(X2,X3)
| ~ in(X1,esk338_2(X2,X3))
| ~ ordinal(X3) ),
inference(split_conjunct,[status(thm)],[i_0_762]),
[final] ).
cnf(i_0_3909,plain,
( X1 = esk340_3(X2,X3,X1)
| esk333_2(X2,X3) = esk334_2(X2,X3)
| ~ in(X1,esk338_2(X2,X3))
| ~ ordinal(X3) ),
inference(split_conjunct,[status(thm)],[i_0_762]),
[final] ).
cnf(i_0_3910,plain,
( empty_carrier(X1)
| below_refl(X1,X2,X2)
| ~ meet_commutative(X1)
| ~ meet_absorbing(X1)
| ~ join_absorbing(X1)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1789]),
[final] ).
cnf(i_0_3911,plain,
( in(esk83_3(X1,X2,X3),X1)
| ~ in(X3,X2)
| X2 != union(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1788]),
[final] ).
cnf(i_0_3912,plain,
( in(X1,esk83_3(X2,X3,X1))
| ~ in(X1,X3)
| X3 != union(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1788]),
[final] ).
cnf(i_0_3913,plain,
( in(esk59_2(X1,X2),X2)
| closed_subsets(X2,X1)
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1738]),
[final] ).
cnf(i_0_3914,plain,
( in(esk45_2(X1,X2),X2)
| open_subsets(X2,X1)
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1739]),
[final] ).
cnf(i_0_3915,plain,
( X1 = esk448_1(X2)
| X2 = empty_set
| epred1_0
| ~ in(X1,X2)
| ~ subset(esk448_1(X2),X1)
| ~ element(X2,powerset(powerset(esk447_0)))
| ~ in(esk447_0,omega)
| esk446_1(X3) != X3
| ~ in(X3,esk445_0) ),
inference(split_conjunct,[status(thm)],[i_0_760]),
[final] ).
cnf(i_0_3916,lemma,
( in(esk204_2(X1,X2),X2)
| X2 = empty_set
| ~ element(X2,powerset(powerset(X1)))
| ~ in(X1,omega)
| ~ ordinal(X1)
| esk203_1(X3) != X3
| ~ in(X3,esk202_0)
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_1538]),
[final] ).
cnf(i_0_3917,plain,
( is_a_cover_of_carrier(X1,X2)
| cast_as_carrier_subset(X1) != union_of_subsets(the_carrier(X1),X2)
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1790]),
[final] ).
cnf(i_0_3918,lemma,
( in(esk404_2(X1,X2),X2)
| X2 = empty_set
| ~ element(X2,powerset(powerset(X1)))
| ~ in(X1,omega)
| ~ ordinal(X1)
| esk403_1(X3) != X3
| ~ in(X3,esk402_0) ),
inference(split_conjunct,[status(thm)],[i_0_1541]),
[final] ).
cnf(i_0_3919,lemma,
( relation_dom(esk381_2(X1,X2)) = X1
| in(esk379_2(X1,X2),X1)
| in(esk376_2(X1,X2),esk378_2(X1,X2))
| empty(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_3920,lemma,
( relation_dom(esk381_2(X1,X2)) = X1
| in(esk379_2(X1,X2),X1)
| in(esk375_2(X1,X2),esk377_2(X1,X2))
| empty(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_3921,lemma,
( relation_image(X1,X2) = relation_image(X1,set_difference(relation_dom(X1),set_difference(relation_dom(X1),X2)))
| ~ relation(X1) ),
inference(rw,[status(thm)],[i_0_1791,c_0_1442]),
[final] ).
cnf(i_0_3922,plain,
( esk243_3(X1,X2,X3) = X3
| esk241_1(X1) = unordered_pair(esk240_1(X1),esk240_1(X1))
| ~ in(X3,esk242_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1792,c_0_681]),
[final] ).
cnf(i_0_3923,plain,
( esk243_3(X1,X2,X3) = X3
| esk239_1(X1) = unordered_pair(esk238_1(X1),esk238_1(X1))
| ~ in(X3,esk242_2(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1793,c_0_681]),
[final] ).
cnf(i_0_3924,lemma,
( element(esk431_2(X1,X2),powerset(powerset(the_carrier(X1))))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ topological_space(X1)
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1744]),
[final] ).
cnf(i_0_3925,lemma,
( element(esk406_2(X1,X2),powerset(powerset(the_carrier(X1))))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1587]),
[final] ).
cnf(i_0_3926,lemma,
( relation(esk381_2(X1,X2))
| in(esk379_2(X1,X2),X1)
| in(esk376_2(X1,X2),esk378_2(X1,X2))
| empty(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_3927,lemma,
( relation(esk381_2(X1,X2))
| in(esk379_2(X1,X2),X1)
| in(esk375_2(X1,X2),esk377_2(X1,X2))
| empty(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_3928,lemma,
( function(esk381_2(X1,X2))
| in(esk379_2(X1,X2),X1)
| in(esk376_2(X1,X2),esk378_2(X1,X2))
| empty(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_3929,lemma,
( function(esk381_2(X1,X2))
| in(esk379_2(X1,X2),X1)
| in(esk375_2(X1,X2),esk377_2(X1,X2))
| empty(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_3930,lemma,
( in(X1,relation_dom(X2))
| ~ in(X1,relation_dom(relation_dom_restriction(X2,X3)))
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1794]),
[final] ).
cnf(i_0_3931,plain,
( in(X1,X4)
| ~ in(X1,relation_dom(X2))
| ~ in(apply(X2,X1),X3)
| X4 != relation_inverse_image(X2,X3)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1365]),
[final] ).
cnf(i_0_3932,plain,
( X1 = esk448_1(X2)
| X2 = empty_set
| element(esk445_0,powerset(powerset(empty_set)))
| epred1_0
| ~ in(X1,X2)
| ~ subset(esk448_1(X2),X1)
| ~ element(X2,powerset(powerset(esk447_0)))
| ~ in(esk447_0,omega) ),
inference(split_conjunct,[status(thm)],[i_0_760]),
[final] ).
cnf(i_0_3933,plain,
( meet(X1,X2,X3) = X2
| empty_carrier(X1)
| ~ element(X3,the_carrier(X1))
| X2 != bottom_of_semilattstr(X1)
| ~ element(X2,the_carrier(X1))
| ~ lower_bounded_semilattstr(X1)
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1590]),
[final] ).
cnf(i_0_3934,plain,
( meet(X1,X2,X3) = X3
| empty_carrier(X1)
| ~ element(X2,the_carrier(X1))
| X3 != bottom_of_semilattstr(X1)
| ~ element(X3,the_carrier(X1))
| ~ lower_bounded_semilattstr(X1)
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1590]),
[final] ).
cnf(i_0_3935,lemma,
( in(esk436_2(X1,X2),relation_dom(X1))
| in(esk433_2(X1,X2),relation_rng(X1))
| X2 = function_inverse(X1)
| relation_dom(X2) != relation_rng(X1)
| ~ relation(X2)
| ~ function(X2)
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1546]),
[final] ).
cnf(i_0_3936,plain,
( quasi_total(X1,X2,X3)
| X2 = empty_set
| X1 != empty_set
| X3 != empty_set
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1704]),
[final] ).
cnf(i_0_3937,lemma,
( in(esk204_2(X1,X2),X2)
| X2 = empty_set
| element(esk202_0,powerset(powerset(esk200_0)))
| ~ element(X2,powerset(powerset(X1)))
| ~ in(X1,omega)
| ~ ordinal(X1)
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_1538]),
[final] ).
cnf(i_0_3938,lemma,
( finite(complements_of_subsets(the_carrier(X2),X1))
| ~ finite(X1)
| ~ element(X1,powerset(powerset(the_carrier(X2))))
| ~ one_sorted_str(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1777]),
[final] ).
cnf(i_0_3939,lemma,
( in(esk404_2(X1,X2),X2)
| X2 = empty_set
| element(esk402_0,powerset(powerset(esk400_0)))
| ~ element(X2,powerset(powerset(X1)))
| ~ in(X1,omega)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1541]),
[final] ).
cnf(i_0_3940,lemma,
( subset_complement(the_carrier(X1),X2) = subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1795]),
[final] ).
cnf(i_0_3941,plain,
( in(esk41_3(X1,X2,X3),X1)
| in(X3,X2)
| X1 = empty_set
| X2 != set_meet(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1724]),
[final] ).
cnf(i_0_3942,plain,
( X1 = esk128_3(X1,X2,X3)
| empty_carrier(X2)
| ~ in(X1,a_2_3_lattice3(X2,X3))
| ~ lattice(X2)
| ~ complete_latt_str(X2)
| ~ latt_str(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1686]),
[final] ).
cnf(i_0_3943,plain,
( relation_rng_as_subset(X2,X3,X1) = relation_rng(X1)
| ~ relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1796]),
[final] ).
cnf(i_0_3944,plain,
( relation_dom_as_subset(X2,X3,X1) = relation_dom(X1)
| ~ relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1797]),
[final] ).
cnf(i_0_3945,plain,
( cast_as_carrier_subset(X1) = union_of_subsets(the_carrier(X1),X2)
| ~ is_a_cover_of_carrier(X1,X2)
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1790]),
[final] ).
cnf(i_0_3946,lemma,
( subset(X1,X2)
| ~ in(X2,esk354_2(X3,X1))
| ~ topological_space(X3)
| ~ top_str(X3)
| ~ element(X1,powerset(the_carrier(X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1652]),
[final] ).
cnf(i_0_3947,plain,
( ~ natural(X1)
| ~ ordinal(X1)
| ~ empty(set_union2(X1,unordered_pair(X1,X1))) ),
inference(rw,[status(thm)],[i_0_1798,c_0_1305]),
[final] ).
cnf(i_0_3948,plain,
( in(esk36_1(X1),the_topology(X1))
| element(esk34_1(X1),powerset(powerset(the_carrier(X1))))
| topological_space(X1)
| ~ in(the_carrier(X1),the_topology(X1))
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1520]),
[final] ).
cnf(i_0_3949,plain,
( in(esk35_1(X1),the_topology(X1))
| element(esk34_1(X1),powerset(powerset(the_carrier(X1))))
| topological_space(X1)
| ~ in(the_carrier(X1),the_topology(X1))
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1520]),
[final] ).
cnf(i_0_3950,plain,
( ordinal(esk251_2(X1,X2))
| epred2_3(esk248_1(X1),esk247_1(X1),esk246_1(X1))
| ~ in(X2,esk249_1(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_717]),
[final] ).
cnf(i_0_3951,lemma,
( disjoint(X1,X3)
| ~ subset(X1,subset_complement(X2,X3))
| ~ element(X3,powerset(X2))
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1799]),
[final] ).
cnf(i_0_3952,lemma,
( in(X1,X2)
| ~ in(X1,relation_dom(relation_dom_restriction(X3,X2)))
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1794]),
[final] ).
cnf(i_0_3953,lemma,
( in(X1,relation_dom(relation_dom_restriction(X2,X3)))
| ~ in(X1,relation_dom(X2))
| ~ in(X1,X3)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1794]),
[final] ).
cnf(i_0_3954,plain,
( X1 = esk453_3(X2,X3,X1)
| ~ epred2_3(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1208]),
[final] ).
cnf(i_0_3955,plain,
( X1 = esk451_3(X2,X1,X3)
| ~ epred2_3(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1208]),
[final] ).
cnf(i_0_3956,lemma,
( in(X1,relation_rng(X2))
| ~ in(X1,relation_rng(relation_rng_restriction(X3,X2)))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1800]),
[final] ).
cnf(i_0_3957,lemma,
( in(X1,relation_field(X2))
| ~ in(X1,relation_field(relation_restriction(X2,X3)))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1801]),
[final] ).
cnf(i_0_3958,lemma,
( in(X1,relation_dom(X2))
| ~ in(X1,relation_dom(relation_dom_restriction(X2,X3)))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1802]),
[final] ).
cnf(i_0_3959,plain,
( closed_subset(subset_complement(the_carrier(X1),X2),X1)
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ open_subset(X2,X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1803]),
[final] ).
cnf(i_0_3960,plain,
( open_subset(subset_complement(the_carrier(X1),X2),X1)
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ closed_subset(X2,X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1804]),
[final] ).
cnf(i_0_3961,lemma,
( apply(relation_composition(X1,X2),X3) = apply(X2,apply(X1,X3))
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X2)
| ~ function(X2)
| ~ in(X3,relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1805]),
[final] ).
cnf(i_0_3962,plain,
( relation_of2_as_subset(X1,X2,X3)
| ~ relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1806]),
[final] ).
cnf(i_0_3963,plain,
( relation_of2(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1806]),
[final] ).
cnf(i_0_3964,plain,
( disjoint(fiber(X1,esk60_2(X1,X2)),X2)
| X2 = empty_set
| ~ subset(X2,relation_field(X1))
| ~ well_founded_relation(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1807]),
[final] ).
cnf(i_0_3965,plain,
( esk243_3(X1,X2,X3) = X3
| in(esk240_1(X1),X1)
| ~ in(X3,esk242_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_715]),
[final] ).
cnf(i_0_3966,plain,
( esk243_3(X1,X2,X3) = X3
| in(esk238_1(X1),X1)
| ~ in(X3,esk242_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_715]),
[final] ).
cnf(i_0_3967,plain,
( empty(X1)
| ~ empty_carrier(rel_str_of(X1,X2))
| ~ relation_of2(X2,X1,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1808]),
[final] ).
cnf(i_0_3968,plain,
( empty_carrier(X1)
| related_reflexive(X1,X2,X2)
| ~ reflexive_relstr(X1)
| ~ rel_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1809]),
[final] ).
cnf(i_0_3969,lemma,
( subset(X1,set_difference(X2,set_difference(X2,X3)))
| ~ subset(X1,X3)
| ~ subset(X1,X2) ),
inference(rw,[status(thm)],[i_0_1810,c_0_1442]),
[final] ).
cnf(i_0_3970,plain,
( empty_carrier(X1)
| latt_element_smaller(X1,X2,X3)
| X2 != join_of_latt_set(X1,X3)
| ~ latt_str(X1)
| ~ lattice(X1)
| ~ complete_latt_str(X1)
| ~ element(X2,the_carrier(X1)) ),
inference(cn,[status(thm)],[i_0_1811]),
[final] ).
cnf(i_0_3971,lemma,
( latt_set_smaller(X1,X2,X3)
| empty_carrier(X1)
| X2 != meet_of_latt_set(X1,X3)
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ complete_latt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1524]),
[final] ).
cnf(i_0_3972,plain,
( ~ ordinal(X1)
| ~ empty(set_union2(X1,unordered_pair(X1,X1))) ),
inference(rw,[status(thm)],[i_0_1812,c_0_1305]),
[final] ).
cnf(i_0_3973,lemma,
( in(set_union2(X2,unordered_pair(X2,X2)),X1)
| ~ ordinal(X2)
| ~ ordinal(X1)
| ~ being_limit_ordinal(X1)
| ~ in(X2,X1) ),
inference(rw,[status(thm)],[i_0_1813,c_0_1305]),
[final] ).
cnf(i_0_3974,plain,
( quasi_total(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
| empty_carrier(X1)
| ~ meet_associative(X1)
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1814]),
[final] ).
cnf(i_0_3975,plain,
( quasi_total(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
| empty_carrier(X1)
| ~ meet_commutative(X1)
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1815]),
[final] ).
cnf(i_0_3976,plain,
( quasi_total(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
| empty_carrier(X1)
| ~ join_associative(X1)
| ~ join_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1816]),
[final] ).
cnf(i_0_3977,plain,
( quasi_total(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
| empty_carrier(X1)
| ~ join_commutative(X1)
| ~ join_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1817]),
[final] ).
cnf(i_0_3978,plain,
( v1_partfun1(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
| empty_carrier(X1)
| ~ meet_associative(X1)
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1814]),
[final] ).
cnf(i_0_3979,plain,
( v1_partfun1(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
| empty_carrier(X1)
| ~ meet_commutative(X1)
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1815]),
[final] ).
cnf(i_0_3980,plain,
( v1_partfun1(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
| empty_carrier(X1)
| ~ join_associative(X1)
| ~ join_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1816]),
[final] ).
cnf(i_0_3981,plain,
( v1_partfun1(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
| empty_carrier(X1)
| ~ join_commutative(X1)
| ~ join_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1817]),
[final] ).
cnf(i_0_3982,plain,
( 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)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1818]),
[final] ).
cnf(i_0_3983,lemma,
( in(X1,X2)
| ~ in(X1,relation_rng(relation_rng_restriction(X2,X3)))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1800]),
[final] ).
cnf(i_0_3984,lemma,
( in(X1,X2)
| ~ in(X1,relation_field(relation_restriction(X3,X2)))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1801]),
[final] ).
cnf(i_0_3985,lemma,
( in(X1,X2)
| ~ in(X1,relation_dom(relation_dom_restriction(X3,X2)))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1802]),
[final] ).
cnf(i_0_3986,lemma,
pair_second(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1))) = X2,
inference(rw,[status(thm)],[i_0_1819,c_0_944]),
[final] ).
cnf(i_0_3987,lemma,
pair_first(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1))) = X1,
inference(rw,[status(thm)],[i_0_1820,c_0_944]),
[final] ).
cnf(i_0_3988,lemma,
( in(X1,relation_rng(relation_rng_restriction(X2,X3)))
| ~ in(X1,X2)
| ~ in(X1,relation_rng(X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1800]),
[final] ).
cnf(i_0_3989,lemma,
( in(X1,relation_dom(relation_dom_restriction(X3,X2)))
| ~ in(X1,X2)
| ~ in(X1,relation_dom(X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1802]),
[final] ).
cnf(i_0_3990,plain,
( X1 = pair_second(X2)
| X1 != esk54_2(X2,X1)
| X2 != unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)) ),
inference(rw,[status(thm)],[i_0_1821,c_0_944]),
[final] ).
cnf(i_0_3991,plain,
( X1 = pair_first(X2)
| X1 != esk32_2(X2,X1)
| X2 != unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)) ),
inference(rw,[status(thm)],[i_0_1822,c_0_944]),
[final] ).
cnf(i_0_3992,plain,
( X1 = esk448_1(X2)
| X2 = empty_set
| in(empty_set,omega)
| epred1_0
| ~ in(X1,X2)
| ~ subset(esk448_1(X2),X1)
| ~ element(X2,powerset(powerset(esk447_0)))
| ~ in(esk447_0,omega) ),
inference(split_conjunct,[status(thm)],[i_0_760]),
[final] ).
cnf(i_0_3993,lemma,
( closed_subset(subset_complement(the_carrier(X2),X1),X2)
| ~ open_subset(X1,X2)
| ~ element(X1,powerset(the_carrier(X2)))
| ~ top_str(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1787]),
[final] ).
cnf(i_0_3994,lemma,
( open_subset(subset_complement(the_carrier(X2),X1),X2)
| ~ closed_subset(X1,X2)
| ~ element(X1,powerset(the_carrier(X2)))
| ~ top_str(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1786]),
[final] ).
cnf(i_0_3995,lemma,
( in(X1,relation_restriction(X2,X3))
| ~ in(X1,X2)
| ~ in(X1,cartesian_product2(X3,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1823]),
[final] ).
cnf(i_0_3996,lemma,
( in(esk204_2(X1,X2),X2)
| X2 = empty_set
| in(esk200_0,omega)
| ~ element(X2,powerset(powerset(X1)))
| ~ in(X1,omega)
| ~ ordinal(X1)
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_1538]),
[final] ).
cnf(i_0_3997,plain,
( subset_difference(X2,X1,X3) = set_difference(X1,X3)
| ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1824]),
[final] ).
cnf(i_0_3998,plain,
( subset_union2(X2,X1,X3) = set_union2(X1,X3)
| ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1825]),
[final] ).
cnf(i_0_3999,lemma,
( X1 = empty_set
| meet_of_subsets(X2,complements_of_subsets(X2,X1)) = subset_complement(X2,union_of_subsets(X2,X1))
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1826]),
[final] ).
cnf(i_0_4000,lemma,
( X1 = empty_set
| union_of_subsets(X2,complements_of_subsets(X2,X1)) = subset_complement(X2,meet_of_subsets(X2,X1))
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1827]),
[final] ).
cnf(i_0_4001,plain,
( X2 = X3
| ~ one_to_one(X1)
| ~ in(X2,relation_dom(X1))
| ~ in(X3,relation_dom(X1))
| apply(X1,X2) != apply(X1,X3)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1828]),
[final] ).
cnf(i_0_4002,lemma,
( relation(esk205_3(X1,X2,X3))
| ~ relation(X2)
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[i_0_713]),
[final] ).
cnf(i_0_4003,plain,
( X1 = X2
| rel_str_of(X1,X3) != rel_str_of(X2,X4)
| ~ relation_of2(X3,X1,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1829]),
[final] ).
cnf(i_0_4004,plain,
( X1 = X2
| rel_str_of(X3,X1) != rel_str_of(X4,X2)
| ~ relation_of2(X1,X3,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1829]),
[final] ).
cnf(i_0_4005,lemma,
( disjoint(X1,X2)
| in(esk432_2(X1,X2),set_difference(X1,set_difference(X1,X2))) ),
inference(rw,[status(thm)],[i_0_1830,c_0_1442]),
[final] ).
cnf(i_0_4006,lemma,
( in(esk404_2(X1,X2),X2)
| X2 = empty_set
| in(esk400_0,omega)
| ~ element(X2,powerset(powerset(X1)))
| ~ in(X1,omega)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1541]),
[final] ).
cnf(i_0_4007,plain,
( X2 = powerset(X1)
| ~ in(esk50_2(X1,X2),X2)
| ~ subset(esk50_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1831]),
[final] ).
cnf(i_0_4008,plain,
( esk243_3(X1,X2,X3) = X3
| ~ in(X3,esk242_2(X1,X2))
| esk236_1(X1) != esk237_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_715]),
[final] ).
cnf(i_0_4009,plain,
( empty_carrier(X1)
| point_neighbourhood(esk121_2(X1,X2),X1,X2)
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1832]),
[final] ).
cnf(i_0_4010,plain,
( in(X4,X5)
| ~ in(X1,relation_dom(X2))
| ~ in(X1,X3)
| X4 != apply(X2,X1)
| X5 != relation_image(X2,X3)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1468]),
[final] ).
cnf(i_0_4011,lemma,
( subset(X2,relation_inverse_image(X1,relation_image(X1,X2)))
| ~ relation(X1)
| ~ subset(X2,relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1833]),
[final] ).
cnf(i_0_4012,lemma,
( in(X1,set_union2(X2,unordered_pair(X2,X2)))
| ~ ordinal(X2)
| ~ in(X1,esk349_1(X2)) ),
inference(rw,[status(thm)],[i_0_1834,c_0_1305]),
[final] ).
cnf(i_0_4013,plain,
( X1 = esk127_3(X1,X2,X3)
| empty_carrier(X2)
| ~ in(X1,a_2_2_lattice3(X2,X3))
| ~ latt_str(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1701]),
[final] ).
cnf(i_0_4014,lemma,
( apply(esk387_1(X2),X1) = unordered_pair(X1,X1)
| esk385_1(X2) = unordered_pair(esk383_1(X2),esk383_1(X2))
| X3 != unordered_pair(esk386_1(X2),esk386_1(X2))
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1835,c_0_681]),c_0_681]),c_0_681]),
[final] ).
cnf(i_0_4015,lemma,
( apply(esk387_1(X2),X1) = unordered_pair(X1,X1)
| esk384_1(X2) = unordered_pair(esk383_1(X2),esk383_1(X2))
| X3 != unordered_pair(esk386_1(X2),esk386_1(X2))
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1836,c_0_681]),c_0_681]),c_0_681]),
[final] ).
cnf(i_0_4016,plain,
( X1 = unordered_pair(esk234_2(X2,X1),esk234_2(X2,X1))
| esk232_1(X2) = unordered_pair(esk230_1(X2),esk230_1(X2))
| ~ in(X1,esk233_1(X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1837,c_0_681]),c_0_681]),
[final] ).
cnf(i_0_4017,plain,
( X1 = unordered_pair(esk234_2(X2,X1),esk234_2(X2,X1))
| esk231_1(X2) = unordered_pair(esk230_1(X2),esk230_1(X2))
| ~ in(X1,esk233_1(X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1838,c_0_681]),c_0_681]),
[final] ).
cnf(i_0_4018,lemma,
( epred3_2(X2,X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3)
| ~ function(X3)
| ~ relation_isomorphism(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1839]),
[final] ).
cnf(i_0_4019,lemma,
( in(X3,X1)
| subset(X1,set_difference(X2,unordered_pair(X3,X3)))
| ~ subset(X1,X2) ),
inference(rw,[status(thm)],[i_0_1840,c_0_681]),
[final] ).
cnf(i_0_4020,plain,
~ empty(set_union2(X1,unordered_pair(X1,X1))),
inference(rw,[status(thm)],[i_0_1841,c_0_1305]),
[final] ).
cnf(i_0_4021,lemma,
( ordinal_subset(set_union2(X1,unordered_pair(X1,X1)),X2)
| ~ ordinal(X2)
| ~ ordinal(X1)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_1842,c_0_1305]),
[final] ).
cnf(i_0_4022,plain,
( X1 = X2
| ~ in(esk421_2(X1,X2),X1)
| ~ in(esk421_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1843]),
[final] ).
cnf(i_0_4023,plain,
( esk250_2(X1,X2) = X2
| epred2_3(esk248_1(X1),esk247_1(X1),esk246_1(X1))
| ~ in(X2,esk249_1(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_717]),
[final] ).
cnf(i_0_4024,plain,
( X1 = esk251_2(X2,X1)
| epred2_3(esk248_1(X2),esk247_1(X2),esk246_1(X2))
| ~ in(X1,esk249_1(X2))
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_717]),
[final] ).
cnf(i_0_4025,lemma,
( subset(X1,subset_complement(X3,X2))
| ~ disjoint(X1,X2)
| ~ element(X2,powerset(X3))
| ~ element(X1,powerset(X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1799]),
[final] ).
cnf(i_0_4026,lemma,
( relation_dom(esk381_2(X1,X2)) = X1
| in(esk379_2(X1,X2),X1)
| empty(X1)
| esk375_2(X1,X2) != esk376_2(X1,X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_4027,plain,
( esk243_3(X1,X2,X3) = X3
| esk235_1(X1) = esk237_1(X1)
| ~ in(X3,esk242_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_715]),
[final] ).
cnf(i_0_4028,plain,
( esk243_3(X1,X2,X3) = X3
| esk235_1(X1) = esk236_1(X1)
| ~ in(X3,esk242_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_715]),
[final] ).
cnf(i_0_4029,lemma,
( relation(esk381_2(X1,X2))
| in(esk379_2(X1,X2),X1)
| empty(X1)
| esk375_2(X1,X2) != esk376_2(X1,X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_4030,lemma,
( function(esk381_2(X1,X2))
| in(esk379_2(X1,X2),X1)
| empty(X1)
| esk375_2(X1,X2) != esk376_2(X1,X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_4031,lemma,
( well_ordering(X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3)
| ~ function(X3)
| ~ well_ordering(X1)
| ~ relation_isomorphism(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1844]),
[final] ).
cnf(i_0_4032,lemma,
( empty_carrier(X1)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ is_a_cover_of_carrier(X1,X2)
| X2 != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_1845]),
[final] ).
cnf(i_0_4033,plain,
( subset(X1,cartesian_product2(X2,X3))
| ~ relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1846]),
[final] ).
cnf(i_0_4034,lemma,
( subset_intersection2(the_carrier(X1),X2,cast_as_carrier_subset(X1)) = X2
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1847]),
[final] ).
cnf(i_0_4035,lemma,
( X1 = esk373_3(X2,X3,X1)
| ~ in(X1,esk372_2(X2,X3))
| ~ ordinal(X3) ),
inference(split_conjunct,[status(thm)],[i_0_788]),
[final] ).
cnf(i_0_4036,lemma,
( topstr_closure(X1,X2) = meet_of_subsets(the_carrier(X1),esk431_2(X1,X2))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ topological_space(X1)
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1744]),
[final] ).
cnf(i_0_4037,lemma,
( subset(fiber(relation_restriction(X1,X2),X3),fiber(X1,X3))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1848]),
[final] ).
cnf(i_0_4038,lemma,
( in(esk204_2(X1,X2),X2)
| X2 = empty_set
| being_limit_ordinal(esk200_0)
| ~ element(X2,powerset(powerset(X1)))
| ~ in(X1,omega)
| ~ ordinal(X1)
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_1538]),
[final] ).
cnf(i_0_4039,lemma,
( in(esk204_2(X1,X2),X2)
| X2 = empty_set
| ordinal(esk200_0)
| ~ element(X2,powerset(powerset(X1)))
| ~ in(X1,omega)
| ~ ordinal(X1)
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_1538]),
[final] ).
cnf(i_0_4040,plain,
( in(X1,X4)
| X4 != set_difference(X2,set_difference(X2,X3))
| ~ in(X1,X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_1849,c_0_1442]),
[final] ).
cnf(i_0_4041,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)],[i_0_1850]),
[final] ).
cnf(i_0_4042,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)],[i_0_1851]),
[final] ).
cnf(i_0_4043,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)],[i_0_1850]),
[final] ).
cnf(i_0_4044,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)],[i_0_1851]),
[final] ).
cnf(i_0_4045,lemma,
( in(esk404_2(X1,X2),X2)
| X2 = empty_set
| ordinal(esk400_0)
| ~ element(X2,powerset(powerset(X1)))
| ~ in(X1,omega)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1541]),
[final] ).
cnf(i_0_4046,plain,
( X1 = esk448_1(X2)
| X2 = empty_set
| epred1_0
| ~ in(X1,X2)
| ~ subset(esk448_1(X2),X1)
| ~ element(X2,powerset(powerset(esk447_0)))
| ~ in(esk447_0,omega)
| esk445_0 != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_760]),
[final] ).
cnf(i_0_4047,lemma,
( relation_dom(esk381_2(X1,X2)) = X1
| in(esk379_2(X1,X2),X1)
| in(esk374_2(X1,X2),X1)
| empty(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_4048,plain,
( in(esk448_1(X1),X1)
| X1 = empty_set
| subset(X2,esk446_1(X2))
| epred1_0
| ~ element(X1,powerset(powerset(esk447_0)))
| ~ in(esk447_0,omega)
| ~ in(X2,esk445_0) ),
inference(split_conjunct,[status(thm)],[i_0_760]),
[final] ).
cnf(i_0_4049,lemma,
( in(esk204_2(X1,X2),X2)
| X2 = empty_set
| ~ element(X2,powerset(powerset(X1)))
| ~ in(X1,omega)
| ~ ordinal(X1)
| esk202_0 != empty_set
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_1538]),
[final] ).
cnf(i_0_4050,lemma,
( in(esk204_2(X1,X2),X2)
| X2 = empty_set
| ~ element(X2,powerset(powerset(X1)))
| ~ in(X1,omega)
| ~ ordinal(X1)
| esk200_0 != empty_set
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_1538]),
[final] ).
cnf(i_0_4051,plain,
( relation_rng(X1) = relation_field(X2)
| ~ relation_isomorphism(X3,X2,X1)
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_693]),
[final] ).
cnf(i_0_4052,plain,
( relation_dom(X1) = relation_field(X2)
| ~ relation_isomorphism(X2,X3,X1)
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_693]),
[final] ).
cnf(i_0_4053,lemma,
( relation(esk381_2(X1,X2))
| in(esk379_2(X1,X2),X1)
| in(esk374_2(X1,X2),X1)
| empty(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_4054,lemma,
( function(esk381_2(X1,X2))
| in(esk379_2(X1,X2),X1)
| in(esk374_2(X1,X2),X1)
| empty(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_4055,lemma,
( in(esk404_2(X1,X2),X2)
| X2 = empty_set
| ~ element(X2,powerset(powerset(X1)))
| ~ in(X1,omega)
| ~ ordinal(X1)
| esk402_0 != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_1541]),
[final] ).
cnf(i_0_4056,plain,
( in(esk448_1(X1),X1)
| X1 = empty_set
| in(esk446_1(X2),esk445_0)
| epred1_0
| ~ element(X1,powerset(powerset(esk447_0)))
| ~ in(esk447_0,omega)
| ~ in(X2,esk445_0) ),
inference(split_conjunct,[status(thm)],[i_0_760]),
[final] ).
cnf(i_0_4057,plain,
( strict_rel_str(rel_str_of(X1,X2))
| empty(X1)
| ~ relation_of2(X2,X1,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1808]),
[final] ).
cnf(i_0_4058,lemma,
( in(X1,relation_rng(X2))
| ~ in(X3,relation_dom(X2))
| X1 != apply(X2,X3)
| X4 != function_inverse(X2)
| ~ relation(X4)
| ~ function(X4)
| ~ one_to_one(X2)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1546]),
[final] ).
cnf(i_0_4059,lemma,
( in(X1,relation_dom(X2))
| ~ in(X3,relation_rng(X2))
| X1 != apply(X4,X3)
| X4 != function_inverse(X2)
| ~ relation(X4)
| ~ function(X4)
| ~ one_to_one(X2)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1546]),
[final] ).
cnf(i_0_4060,lemma,
( apply(esk387_1(X2),X1) = unordered_pair(X1,X1)
| in(esk383_1(X2),X2)
| X3 != unordered_pair(esk386_1(X2),esk386_1(X2))
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1852,c_0_681]),c_0_681]),
[final] ).
cnf(i_0_4061,plain,
( subset_intersection2(X2,X1,X1) = X1
| ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1853]),
[final] ).
cnf(i_0_4062,plain,
( subset_union2(X2,X1,X1) = X1
| ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1854]),
[final] ).
cnf(i_0_4063,plain,
( X1 = unordered_pair(esk234_2(X2,X1),esk234_2(X2,X1))
| in(esk230_1(X2),X2)
| ~ in(X1,esk233_1(X2)) ),
inference(rw,[status(thm)],[i_0_1855,c_0_681]),
[final] ).
cnf(i_0_4064,plain,
( X1 = unordered_pair(esk234_2(X2,X1),esk234_2(X2,X1))
| in(esk230_1(X2),X2)
| ~ in(X1,esk233_1(X2)) ),
inference(rw,[status(thm)],[i_0_1856,c_0_681]),
[final] ).
cnf(i_0_4065,plain,
( one_to_one(X1)
| ~ relation_isomorphism(X2,X3,X1)
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_693]),
[final] ).
cnf(i_0_4066,plain,
( element(esk36_1(X1),powerset(the_carrier(X1)))
| subset(esk34_1(X1),the_topology(X1))
| topological_space(X1)
| ~ in(the_carrier(X1),the_topology(X1))
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1520]),
[final] ).
cnf(i_0_4067,plain,
( element(esk35_1(X1),powerset(the_carrier(X1)))
| subset(esk34_1(X1),the_topology(X1))
| topological_space(X1)
| ~ in(the_carrier(X1),the_topology(X1))
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1520]),
[final] ).
cnf(i_0_4068,lemma,
( ~ element(X1,powerset(X2))
| ~ in(X3,subset_complement(X2,X1))
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1857]),
[final] ).
cnf(i_0_4069,plain,
( relation_of2(X1,X2,X3)
| ~ subset(X1,cartesian_product2(X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1846]),
[final] ).
cnf(i_0_4070,plain,
( relation(X1)
| ~ element(X1,powerset(cartesian_product2(X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1858]),
[final] ).
cnf(i_0_4071,plain,
( element(interior(X1,X2),powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1859]),
[final] ).
cnf(i_0_4072,plain,
( element(topstr_closure(X1,X2),powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1860]),
[final] ).
cnf(i_0_4073,plain,
( well_founded_relation(X2)
| ~ in(X1,esk61_1(X2))
| ~ disjoint(fiber(X2,X1),esk61_1(X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1807]),
[final] ).
cnf(i_0_4074,plain,
( epred1_0
| subset(X1,esk446_1(X1))
| in(set_union2(esk447_0,unordered_pair(esk447_0,esk447_0)),omega)
| ~ in(X1,esk445_0) ),
inference(rw,[status(thm)],[i_0_1861,c_0_1305]),
[final] ).
cnf(i_0_4075,plain,
( X1 = X3
| X1 = X4
| X1 = X5
| ~ in(X1,X2)
| X2 != unordered_triple(X3,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_1243]),
[final] ).
cnf(i_0_4076,plain,
( empty_carrier(X1)
| element(cast_to_el_of_lattice(X1,X2),the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(poset_of_lattice(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1862]),
[final] ).
cnf(i_0_4077,plain,
( strict_rel_str(rel_str_of(X1,X2))
| ~ relation_of2(X2,X1,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1863]),
[final] ).
cnf(i_0_4078,plain,
( rel_str(rel_str_of(X1,X2))
| ~ relation_of2(X2,X1,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1863]),
[final] ).
cnf(i_0_4079,plain,
( meet(X1,esk11_1(X1),X2) = esk11_1(X1)
| empty_carrier(X1)
| ~ element(X2,the_carrier(X1))
| ~ lower_bounded_semilattstr(X1)
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1600]),
[final] ).
cnf(i_0_4080,plain,
( meet(X1,X2,esk11_1(X1)) = esk11_1(X1)
| empty_carrier(X1)
| ~ element(X2,the_carrier(X1))
| ~ lower_bounded_semilattstr(X1)
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1600]),
[final] ).
cnf(i_0_4081,lemma,
( X1 = apply(X2,X3)
| ~ in(X1,relation_dom(X4))
| X3 != apply(X4,X1)
| X2 != function_inverse(X4)
| ~ relation(X2)
| ~ function(X2)
| ~ one_to_one(X4)
| ~ relation(X4)
| ~ function(X4) ),
inference(split_conjunct,[status(thm)],[i_0_1546]),
[final] ).
cnf(i_0_4082,lemma,
( X1 = apply(X2,X3)
| ~ in(X1,relation_rng(X2))
| X3 != apply(X4,X1)
| X4 != function_inverse(X2)
| ~ relation(X4)
| ~ function(X4)
| ~ one_to_one(X2)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1546]),
[final] ).
cnf(i_0_4083,plain,
( epred1_0
| in(esk446_1(X1),esk445_0)
| in(set_union2(esk447_0,unordered_pair(esk447_0,esk447_0)),omega)
| ~ in(X1,esk445_0) ),
inference(rw,[status(thm)],[i_0_1864,c_0_1305]),
[final] ).
cnf(i_0_4084,lemma,
( relation_dom(X1) = set_difference(relation_dom(X2),set_difference(relation_dom(X2),X3))
| X1 != relation_dom_restriction(X2,X3)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1) ),
inference(rw,[status(thm)],[i_0_1865,c_0_1442]),
[final] ).
cnf(i_0_4085,plain,
( relation(X1)
| esk39_1(X1) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)) ),
inference(rw,[status(thm)],[i_0_1866,c_0_944]),
[final] ).
cnf(i_0_4086,plain,
( esk89_2(X1,X2) = apply(X1,esk90_2(X1,X2))
| in(esk89_2(X1,X2),X2)
| X2 = relation_rng(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1774]),
[final] ).
cnf(i_0_4087,lemma,
( apply(esk387_1(X2),X1) = unordered_pair(X1,X1)
| esk385_1(X2) != esk384_1(X2)
| X3 != unordered_pair(esk386_1(X2),esk386_1(X2))
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1867,c_0_681]),c_0_681]),
[final] ).
cnf(i_0_4088,lemma,
( apply(X2,X1) = apply(X3,X1)
| ~ in(X1,relation_dom(X2))
| X2 != relation_dom_restriction(X3,X4)
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_741]),
[final] ).
cnf(i_0_4089,lemma,
( X1 = identity_relation(X2)
| apply(X1,esk424_2(X2,X1)) != esk424_2(X2,X1)
| relation_dom(X1) != X2
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1868]),
[final] ).
cnf(i_0_4090,plain,
( relation_restriction(X1,X2) = set_difference(X1,set_difference(X1,cartesian_product2(X2,X2)))
| ~ relation(X1) ),
inference(rw,[status(thm)],[i_0_1869,c_0_1442]),
[final] ).
cnf(i_0_4091,plain,
( X1 = unordered_pair(esk234_2(X2,X1),esk234_2(X2,X1))
| esk232_1(X2) != esk231_1(X2)
| ~ in(X1,esk233_1(X2)) ),
inference(rw,[status(thm)],[i_0_1870,c_0_681]),
[final] ).
cnf(i_0_4092,plain,
( in(esk84_2(X1,X2),esk85_2(X1,X2))
| in(esk84_2(X1,X2),X2)
| X2 = union(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1788]),
[final] ).
cnf(i_0_4093,lemma,
( subset(cartesian_product2(X1,X3),cartesian_product2(X2,X4))
| ~ subset(X1,X2)
| ~ subset(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1871]),
[final] ).
cnf(i_0_4094,lemma,
( relation_dom(esk381_2(X1,X2)) = X1
| in(esk379_2(X1,X2),X1)
| esk374_2(X1,X2) = esk378_2(X1,X2)
| empty(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_4095,lemma,
( relation_dom(esk381_2(X1,X2)) = X1
| in(esk379_2(X1,X2),X1)
| esk374_2(X1,X2) = esk377_2(X1,X2)
| empty(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_4096,plain,
( in(esk448_1(X1),X1)
| X1 = empty_set
| epred1_0
| ~ element(X1,powerset(powerset(esk447_0)))
| ~ in(esk447_0,omega)
| esk446_1(X2) != X2
| ~ in(X2,esk445_0) ),
inference(split_conjunct,[status(thm)],[i_0_760]),
[final] ).
cnf(i_0_4097,lemma,
( X1 = empty_set
| in(X3,X2)
| in(X3,subset_complement(X1,X2))
| ~ element(X2,powerset(X1))
| ~ element(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1872]),
[final] ).
cnf(i_0_4098,lemma,
( in(X1,cartesian_product2(X2,X2))
| ~ in(X1,relation_restriction(X3,X2))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1823]),
[final] ).
cnf(i_0_4099,lemma,
( relation(esk381_2(X1,X2))
| in(esk379_2(X1,X2),X1)
| esk374_2(X1,X2) = esk378_2(X1,X2)
| empty(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_4100,lemma,
( function(esk381_2(X1,X2))
| in(esk379_2(X1,X2),X1)
| esk374_2(X1,X2) = esk378_2(X1,X2)
| empty(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_4101,lemma,
( relation(esk381_2(X1,X2))
| in(esk379_2(X1,X2),X1)
| esk374_2(X1,X2) = esk377_2(X1,X2)
| empty(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_4102,lemma,
( function(esk381_2(X1,X2))
| in(esk379_2(X1,X2),X1)
| esk374_2(X1,X2) = esk377_2(X1,X2)
| empty(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_4103,plain,
( in(esk43_2(X1,X2),X1)
| X2 = set_meet(X1)
| X1 = empty_set
| ~ in(esk42_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1724]),
[final] ).
cnf(i_0_4104,plain,
( in(esk42_2(X1,X2),X2)
| in(esk42_2(X1,X2),X3)
| X2 = set_meet(X1)
| X1 = empty_set
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1724]),
[final] ).
cnf(i_0_4105,plain,
( element(complements_of_subsets(X2,X1),powerset(powerset(X2)))
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1873]),
[final] ).
cnf(i_0_4106,plain,
( empty_carrier(X1)
| element(cast_to_el_of_LattPOSet(X1,X2),the_carrier(poset_of_lattice(X1)))
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1874]),
[final] ).
cnf(i_0_4107,plain,
( ~ in(X1,X2)
| ~ in(X1,esk442_2(X3,X2))
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1875]),
[final] ).
cnf(i_0_4108,lemma,
( relation(esk182_2(X1,X2))
| in(esk179_2(X1,X2),esk181_2(X1,X2))
| empty(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_690]),
[final] ).
cnf(i_0_4109,lemma,
( relation(esk182_2(X1,X2))
| in(esk178_2(X1,X2),esk180_2(X1,X2))
| empty(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_690]),
[final] ).
cnf(i_0_4110,lemma,
( function(esk182_2(X1,X2))
| in(esk179_2(X1,X2),esk181_2(X1,X2))
| empty(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_690]),
[final] ).
cnf(i_0_4111,lemma,
( function(esk182_2(X1,X2))
| in(esk178_2(X1,X2),esk180_2(X1,X2))
| empty(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_690]),
[final] ).
cnf(i_0_4112,lemma,
( apply(esk387_1(X2),X1) = unordered_pair(X1,X1)
| esk385_1(X2) = unordered_pair(esk383_1(X2),esk383_1(X2))
| in(esk386_1(X2),X2)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1876,c_0_681]),c_0_681]),
[final] ).
cnf(i_0_4113,lemma,
( apply(esk387_1(X2),X1) = unordered_pair(X1,X1)
| esk384_1(X2) = unordered_pair(esk383_1(X2),esk383_1(X2))
| in(esk386_1(X2),X2)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1877,c_0_681]),c_0_681]),
[final] ).
cnf(i_0_4114,plain,
( in(esk448_1(X1),X1)
| X1 = empty_set
| element(esk445_0,powerset(powerset(empty_set)))
| epred1_0
| ~ element(X1,powerset(powerset(esk447_0)))
| ~ in(esk447_0,omega) ),
inference(split_conjunct,[status(thm)],[i_0_760]),
[final] ).
cnf(i_0_4115,lemma,
( X1 = apply(relation_composition(function_inverse(X2),X2),X1)
| ~ one_to_one(X2)
| ~ in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1878]),
[final] ).
cnf(i_0_4116,lemma,
( X1 = apply(X2,apply(function_inverse(X2),X1))
| ~ one_to_one(X2)
| ~ in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1878]),
[final] ).
cnf(i_0_4117,plain,
( in(esk36_1(X1),the_topology(X1))
| subset(esk34_1(X1),the_topology(X1))
| topological_space(X1)
| ~ in(the_carrier(X1),the_topology(X1))
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1520]),
[final] ).
cnf(i_0_4118,plain,
( in(esk35_1(X1),the_topology(X1))
| subset(esk34_1(X1),the_topology(X1))
| topological_space(X1)
| ~ in(the_carrier(X1),the_topology(X1))
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1520]),
[final] ).
cnf(i_0_4119,lemma,
( subset(relation_rng(X1),X2)
| ~ relation_of2_as_subset(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1879]),
[final] ).
cnf(i_0_4120,lemma,
( subset(relation_dom(X1),X2)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1879]),
[final] ).
cnf(i_0_4121,plain,
( in(esk90_2(X1,X2),relation_dom(X1))
| in(esk89_2(X1,X2),X2)
| X2 = relation_rng(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1774]),
[final] ).
cnf(i_0_4122,lemma,
( subset(relation_image(X1,relation_inverse_image(X1,X2)),X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1880]),
[final] ).
cnf(i_0_4123,lemma,
( X1 = X2
| ~ subset(unordered_pair(X1,X1),unordered_pair(X2,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1881,c_0_681]),c_0_681]),
[final] ).
cnf(i_0_4124,plain,
( closed_subset(topstr_closure(X1,X2),X1)
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1882]),
[final] ).
cnf(i_0_4125,lemma,
( open_subset(interior(X1,X2),X1)
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1883]),
[final] ).
cnf(i_0_4126,plain,
( open_subset(interior(X1,X2),X1)
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1884]),
[final] ).
cnf(i_0_4127,plain,
( open_subset(X1,X2)
| ~ in(X1,the_topology(X2))
| ~ element(X1,powerset(the_carrier(X2)))
| ~ top_str(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1885]),
[final] ).
cnf(i_0_4128,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_triple(X2,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_1243]),
[final] ).
cnf(i_0_4129,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_triple(X4,X2,X5) ),
inference(split_conjunct,[status(thm)],[i_0_1243]),
[final] ).
cnf(i_0_4130,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_triple(X4,X5,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1243]),
[final] ).
cnf(i_0_4131,plain,
( epred1_0
| in(set_union2(esk447_0,unordered_pair(esk447_0,esk447_0)),omega)
| esk446_1(X1) != X1
| ~ in(X1,esk445_0) ),
inference(rw,[status(thm)],[i_0_1886,c_0_1305]),
[final] ).
cnf(i_0_4132,lemma,
( closed_subset(X2,X1)
| ~ topological_space(X1)
| topstr_closure(X1,X2) != X2
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1887]),
[final] ).
cnf(i_0_4133,lemma,
( in(X1,cartesian_product2(X2,X3))
| ~ in(X1,esk346_2(X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_722]),
[final] ).
cnf(i_0_4134,plain,
( esk232_1(X1) = unordered_pair(esk230_1(X1),esk230_1(X1))
| in(esk234_2(X1,X2),X1)
| ~ in(X2,esk233_1(X1)) ),
inference(rw,[status(thm)],[i_0_1888,c_0_681]),
[final] ).
cnf(i_0_4135,plain,
( esk231_1(X1) = unordered_pair(esk230_1(X1),esk230_1(X1))
| in(esk234_2(X1,X2),X1)
| ~ in(X2,esk233_1(X1)) ),
inference(rw,[status(thm)],[i_0_1889,c_0_681]),
[final] ).
cnf(i_0_4136,plain,
( element(esk23_2(X1,X2),the_carrier(X1))
| X2 = bottom_of_semilattstr(X1)
| empty_carrier(X1)
| ~ element(X2,the_carrier(X1))
| ~ lower_bounded_semilattstr(X1)
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1590]),
[final] ).
cnf(i_0_4137,plain,
( X2 = unordered_pair(X1,X1)
| esk44_2(X1,X2) != X1
| ~ in(esk44_2(X1,X2),X2) ),
inference(rw,[status(thm)],[i_0_1890,c_0_681]),
[final] ).
cnf(i_0_4138,plain,
( in(X1,the_topology(X2))
| ~ open_subset(X1,X2)
| ~ element(X1,powerset(the_carrier(X2)))
| ~ top_str(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1885]),
[final] ).
cnf(i_0_4139,plain,
( v1_partfun1(the_InternalRel(X1),the_carrier(X1),the_carrier(X1))
| ~ reflexive_relstr(X1)
| ~ transitive_relstr(X1)
| ~ antisymmetric_relstr(X1)
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1891]),
[final] ).
cnf(i_0_4140,plain,
( in(X1,X2)
| X3 != set_difference(X2,set_difference(X2,X4))
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[i_0_1892,c_0_1442]),
[final] ).
cnf(i_0_4141,plain,
( in(X1,X2)
| X3 != set_difference(X4,set_difference(X4,X2))
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[i_0_1893,c_0_1442]),
[final] ).
cnf(i_0_4142,lemma,
( ordinal_subset(esk423_2(X2,X3),X1)
| X2 = empty_set
| ~ ordinal(X1)
| ~ in(X1,X2)
| ~ subset(X2,X3)
| ~ ordinal(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1894]),
[final] ).
cnf(i_0_4143,plain,
( in(apply(X1,X2),X3)
| ~ in(X2,X4)
| X4 != relation_inverse_image(X1,X3)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1365]),
[final] ).
cnf(i_0_4144,plain,
( epred1_0
| element(esk445_0,powerset(powerset(empty_set)))
| in(set_union2(esk447_0,unordered_pair(esk447_0,esk447_0)),omega) ),
inference(rw,[status(thm)],[i_0_1895,c_0_1305]),
[final] ).
cnf(i_0_4145,lemma,
( in(esk413_2(X1,X2),X2)
| X2 = empty_set
| ~ element(X2,powerset(powerset(X1)))
| ~ finite(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1782]),
[final] ).
cnf(i_0_4146,lemma,
( in(apply(esk420_1(X2),X1),X1)
| in(esk419_1(X2),X2)
| empty(X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1896]),
[final] ).
cnf(i_0_4147,lemma,
( subset(interior(X1,X2),X2)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1897]),
[final] ).
cnf(i_0_4148,lemma,
( subset(X2,topstr_closure(X1,X2))
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1898]),
[final] ).
cnf(i_0_4149,lemma,
( apply(esk387_1(X2),X1) = unordered_pair(X1,X1)
| in(esk383_1(X2),X2)
| in(esk386_1(X2),X2)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_1899,c_0_681]),
[final] ).
cnf(i_0_4150,plain,
( element(meet_of_subsets(X2,X1),powerset(X2))
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1900]),
[final] ).
cnf(i_0_4151,plain,
( element(union_of_subsets(X2,X1),powerset(X2))
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1901]),
[final] ).
cnf(i_0_4152,plain,
( element(esk126_2(X1,X2),the_carrier(X2))
| empty_carrier(X2)
| ~ in(X1,a_1_0_filter_1(X2))
| ~ lattice(X2)
| ~ latt_str(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1455]),
[final] ).
cnf(i_0_4153,plain,
( element(esk125_2(X1,X2),the_carrier(X2))
| empty_carrier(X2)
| ~ in(X1,a_1_0_filter_1(X2))
| ~ lattice(X2)
| ~ latt_str(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1455]),
[final] ).
cnf(i_0_4154,plain,
( esk232_1(X2) = unordered_pair(esk230_1(X2),esk230_1(X2))
| in(X3,esk233_1(X2))
| X3 != unordered_pair(X1,X1)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1902,c_0_681]),c_0_681]),
[final] ).
cnf(i_0_4155,plain,
( esk231_1(X2) = unordered_pair(esk230_1(X2),esk230_1(X2))
| in(X3,esk233_1(X2))
| X3 != unordered_pair(X1,X1)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1903,c_0_681]),c_0_681]),
[final] ).
cnf(i_0_4156,lemma,
( topstr_closure(X2,X1) = X1
| ~ closed_subset(X1,X2)
| ~ element(X1,powerset(the_carrier(X2)))
| ~ top_str(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1887]),
[final] ).
cnf(i_0_4157,plain,
( relation(set_difference(X1,set_difference(X1,X2)))
| ~ relation(X2)
| ~ relation(X1) ),
inference(rw,[status(thm)],[i_0_1904,c_0_1442]),
[final] ).
cnf(i_0_4158,plain,
( epsilon_connected(set_union2(X1,unordered_pair(X1,X1)))
| ~ natural(X1)
| ~ ordinal(X1) ),
inference(rw,[status(thm)],[i_0_1905,c_0_1305]),
[final] ).
cnf(i_0_4159,plain,
( epsilon_transitive(set_union2(X1,unordered_pair(X1,X1)))
| ~ natural(X1)
| ~ ordinal(X1) ),
inference(rw,[status(thm)],[i_0_1906,c_0_1305]),
[final] ).
cnf(i_0_4160,plain,
( ordinal(set_union2(X1,unordered_pair(X1,X1)))
| ~ natural(X1)
| ~ ordinal(X1) ),
inference(rw,[status(thm)],[i_0_1907,c_0_1305]),
[final] ).
cnf(i_0_4161,plain,
( natural(set_union2(X1,unordered_pair(X1,X1)))
| ~ natural(X1)
| ~ ordinal(X1) ),
inference(rw,[status(thm)],[i_0_1908,c_0_1305]),
[final] ).
cnf(i_0_4162,lemma,
( subset(relation_inverse_image(X1,X2),relation_inverse_image(X1,X3))
| ~ relation(X1)
| ~ subset(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1909]),
[final] ).
cnf(i_0_4163,lemma,
( relation_rng(relation_rng_restriction(X2,X1)) = set_difference(relation_rng(X1),set_difference(relation_rng(X1),X2))
| ~ relation(X1) ),
inference(rw,[status(thm)],[i_0_1910,c_0_1442]),
[final] ).
cnf(i_0_4164,lemma,
( relation_dom(relation_dom_restriction(X1,X2)) = set_difference(relation_dom(X1),set_difference(relation_dom(X1),X2))
| ~ relation(X1) ),
inference(rw,[status(thm)],[i_0_1911,c_0_1442]),
[final] ).
cnf(i_0_4165,plain,
( in(X1,esk444_2(X3,X2))
| ~ subset(X1,X2)
| ~ in(X2,esk443_1(X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1912]),
[final] ).
cnf(i_0_4166,plain,
( element(esk12_2(X1,X2),the_carrier(X1))
| lower_bounded_semilattstr(X1)
| empty_carrier(X1)
| ~ element(X2,the_carrier(X1))
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1600]),
[final] ).
cnf(i_0_4167,plain,
( in(esk448_1(X1),X1)
| X1 = empty_set
| in(empty_set,omega)
| epred1_0
| ~ element(X1,powerset(powerset(esk447_0)))
| ~ in(esk447_0,omega) ),
inference(split_conjunct,[status(thm)],[i_0_760]),
[final] ).
cnf(i_0_4168,plain,
( in(X3,X4)
| ~ in(X1,relation_dom(X2))
| X3 != apply(X2,X1)
| X4 != relation_rng(X2)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1774]),
[final] ).
cnf(i_0_4169,plain,
( in(esk234_2(X1,X2),X1)
| in(esk230_1(X1),X1)
| ~ in(X2,esk233_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_829]),
[final] ).
cnf(i_0_4170,plain,
( in(esk234_2(X1,X2),X1)
| in(esk230_1(X1),X1)
| ~ in(X2,esk233_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_829]),
[final] ).
cnf(i_0_4171,lemma,
( subset(relation_rng(relation_composition(X1,X2)),relation_rng(X2))
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1913]),
[final] ).
cnf(i_0_4172,lemma,
( subset(relation_dom(relation_composition(X1,X2)),relation_dom(X1))
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1914]),
[final] ).
cnf(i_0_4173,plain,
( complements_of_subsets(X2,complements_of_subsets(X2,X1)) = X1
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1915]),
[final] ).
cnf(i_0_4174,lemma,
subset(set_difference(X1,set_difference(X1,X2)),X1),
inference(rw,[status(thm)],[i_0_1916,c_0_1442]),
[final] ).
cnf(i_0_4175,lemma,
in(X1,set_union2(X1,unordered_pair(X1,X1))),
inference(rw,[status(thm)],[i_0_1917,c_0_1305]),
[final] ).
cnf(i_0_4176,plain,
( relation_of2_as_subset(k2_lattice3(X1),the_carrier(X1),the_carrier(X1))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1918]),
[final] ).
cnf(i_0_4177,plain,
( v1_partfun1(k2_lattice3(X1),the_carrier(X1),the_carrier(X1))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1918]),
[final] ).
cnf(i_0_4178,lemma,
( apply(relation_dom_restriction(X1,X3),X2) = apply(X1,X2)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1919]),
[final] ).
cnf(i_0_4179,lemma,
( apply(esk387_1(X2),X1) = unordered_pair(X1,X1)
| in(esk386_1(X2),X2)
| esk385_1(X2) != esk384_1(X2)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_1920,c_0_681]),
[final] ).
cnf(i_0_4180,lemma,
( relation_rng(relation_composition(X2,X1)) = relation_rng(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ subset(relation_dom(X1),relation_rng(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1921]),
[final] ).
cnf(i_0_4181,lemma,
( relation_dom(relation_composition(X1,X2)) = relation_dom(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ subset(relation_rng(X1),relation_dom(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1922]),
[final] ).
cnf(i_0_4182,lemma,
( finite(set_difference(X1,set_difference(X1,X2)))
| ~ finite(X1) ),
inference(rw,[status(thm)],[i_0_1923,c_0_1442]),
[final] ).
cnf(i_0_4183,plain,
( finite(set_difference(X1,set_difference(X1,X2)))
| ~ finite(X1) ),
inference(rw,[status(thm)],[i_0_1924,c_0_1442]),
[final] ).
cnf(i_0_4184,plain,
( finite(set_difference(X2,set_difference(X2,X1)))
| ~ finite(X1) ),
inference(rw,[status(thm)],[i_0_1925,c_0_1442]),
[final] ).
cnf(i_0_4185,plain,
( epsilon_connected(set_union2(X1,unordered_pair(X1,X1)))
| ~ ordinal(X1) ),
inference(rw,[status(thm)],[i_0_1926,c_0_1305]),
[final] ).
cnf(i_0_4186,plain,
( epsilon_transitive(set_union2(X1,unordered_pair(X1,X1)))
| ~ ordinal(X1) ),
inference(rw,[status(thm)],[i_0_1927,c_0_1305]),
[final] ).
cnf(i_0_4187,plain,
( ordinal(set_union2(X1,unordered_pair(X1,X1)))
| ~ ordinal(X1) ),
inference(rw,[status(thm)],[i_0_1928,c_0_1305]),
[final] ).
cnf(i_0_4188,plain,
( v5_membered(set_difference(X1,set_difference(X1,X2)))
| ~ v5_membered(X1) ),
inference(rw,[status(thm)],[i_0_1929,c_0_1442]),
[final] ).
cnf(i_0_4189,plain,
( v5_membered(set_difference(X1,set_difference(X1,X2)))
| ~ v5_membered(X2) ),
inference(rw,[status(thm)],[i_0_1930,c_0_1442]),
[final] ).
cnf(i_0_4190,plain,
( v4_membered(set_difference(X1,set_difference(X1,X2)))
| ~ v5_membered(X1) ),
inference(rw,[status(thm)],[i_0_1931,c_0_1442]),
[final] ).
cnf(i_0_4191,plain,
( v4_membered(set_difference(X1,set_difference(X1,X2)))
| ~ v5_membered(X2) ),
inference(rw,[status(thm)],[i_0_1932,c_0_1442]),
[final] ).
cnf(i_0_4192,plain,
( v4_membered(set_difference(X1,set_difference(X1,X2)))
| ~ v4_membered(X1) ),
inference(rw,[status(thm)],[i_0_1933,c_0_1442]),
[final] ).
cnf(i_0_4193,plain,
( v4_membered(set_difference(X1,set_difference(X1,X2)))
| ~ v4_membered(X2) ),
inference(rw,[status(thm)],[i_0_1934,c_0_1442]),
[final] ).
cnf(i_0_4194,plain,
( v3_membered(set_difference(X1,set_difference(X1,X2)))
| ~ v5_membered(X1) ),
inference(rw,[status(thm)],[i_0_1935,c_0_1442]),
[final] ).
cnf(i_0_4195,plain,
( v3_membered(set_difference(X1,set_difference(X1,X2)))
| ~ v5_membered(X2) ),
inference(rw,[status(thm)],[i_0_1936,c_0_1442]),
[final] ).
cnf(i_0_4196,plain,
( v3_membered(set_difference(X1,set_difference(X1,X2)))
| ~ v4_membered(X1) ),
inference(rw,[status(thm)],[i_0_1937,c_0_1442]),
[final] ).
cnf(i_0_4197,plain,
( v3_membered(set_difference(X1,set_difference(X1,X2)))
| ~ v4_membered(X2) ),
inference(rw,[status(thm)],[i_0_1938,c_0_1442]),
[final] ).
cnf(i_0_4198,plain,
( v3_membered(set_difference(X1,set_difference(X1,X2)))
| ~ v3_membered(X1) ),
inference(rw,[status(thm)],[i_0_1939,c_0_1442]),
[final] ).
cnf(i_0_4199,plain,
( v3_membered(set_difference(X1,set_difference(X1,X2)))
| ~ v3_membered(X2) ),
inference(rw,[status(thm)],[i_0_1940,c_0_1442]),
[final] ).
cnf(i_0_4200,plain,
( v2_membered(set_difference(X1,set_difference(X1,X2)))
| ~ v5_membered(X1) ),
inference(rw,[status(thm)],[i_0_1941,c_0_1442]),
[final] ).
cnf(i_0_4201,plain,
( v2_membered(set_difference(X1,set_difference(X1,X2)))
| ~ v5_membered(X2) ),
inference(rw,[status(thm)],[i_0_1942,c_0_1442]),
[final] ).
cnf(i_0_4202,plain,
( v2_membered(set_difference(X1,set_difference(X1,X2)))
| ~ v4_membered(X1) ),
inference(rw,[status(thm)],[i_0_1943,c_0_1442]),
[final] ).
cnf(i_0_4203,plain,
( v2_membered(set_difference(X1,set_difference(X1,X2)))
| ~ v4_membered(X2) ),
inference(rw,[status(thm)],[i_0_1944,c_0_1442]),
[final] ).
cnf(i_0_4204,plain,
( v2_membered(set_difference(X1,set_difference(X1,X2)))
| ~ v3_membered(X1) ),
inference(rw,[status(thm)],[i_0_1945,c_0_1442]),
[final] ).
cnf(i_0_4205,plain,
( v2_membered(set_difference(X1,set_difference(X1,X2)))
| ~ v3_membered(X2) ),
inference(rw,[status(thm)],[i_0_1946,c_0_1442]),
[final] ).
cnf(i_0_4206,plain,
( v2_membered(set_difference(X1,set_difference(X1,X2)))
| ~ v2_membered(X1) ),
inference(rw,[status(thm)],[i_0_1947,c_0_1442]),
[final] ).
cnf(i_0_4207,plain,
( v2_membered(set_difference(X1,set_difference(X1,X2)))
| ~ v2_membered(X2) ),
inference(rw,[status(thm)],[i_0_1948,c_0_1442]),
[final] ).
cnf(i_0_4208,plain,
( v1_membered(set_difference(X1,set_difference(X1,X2)))
| ~ v5_membered(X1) ),
inference(rw,[status(thm)],[i_0_1949,c_0_1442]),
[final] ).
cnf(i_0_4209,plain,
( v1_membered(set_difference(X1,set_difference(X1,X2)))
| ~ v5_membered(X2) ),
inference(rw,[status(thm)],[i_0_1950,c_0_1442]),
[final] ).
cnf(i_0_4210,plain,
( v1_membered(set_difference(X1,set_difference(X1,X2)))
| ~ v4_membered(X1) ),
inference(rw,[status(thm)],[i_0_1951,c_0_1442]),
[final] ).
cnf(i_0_4211,plain,
( v1_membered(set_difference(X1,set_difference(X1,X2)))
| ~ v4_membered(X2) ),
inference(rw,[status(thm)],[i_0_1952,c_0_1442]),
[final] ).
cnf(i_0_4212,plain,
( v1_membered(set_difference(X1,set_difference(X1,X2)))
| ~ v3_membered(X1) ),
inference(rw,[status(thm)],[i_0_1953,c_0_1442]),
[final] ).
cnf(i_0_4213,plain,
( v1_membered(set_difference(X1,set_difference(X1,X2)))
| ~ v3_membered(X2) ),
inference(rw,[status(thm)],[i_0_1954,c_0_1442]),
[final] ).
cnf(i_0_4214,plain,
( v1_membered(set_difference(X1,set_difference(X1,X2)))
| ~ v2_membered(X1) ),
inference(rw,[status(thm)],[i_0_1955,c_0_1442]),
[final] ).
cnf(i_0_4215,plain,
( v1_membered(set_difference(X1,set_difference(X1,X2)))
| ~ v2_membered(X2) ),
inference(rw,[status(thm)],[i_0_1956,c_0_1442]),
[final] ).
cnf(i_0_4216,plain,
( v1_membered(set_difference(X1,set_difference(X1,X2)))
| ~ v1_membered(X1) ),
inference(rw,[status(thm)],[i_0_1957,c_0_1442]),
[final] ).
cnf(i_0_4217,plain,
( v1_membered(set_difference(X2,set_difference(X2,X1)))
| ~ v1_membered(X1) ),
inference(rw,[status(thm)],[i_0_1958,c_0_1442]),
[final] ).
cnf(i_0_4218,lemma,
( subset(set_difference(X1,X3),set_difference(X2,X3))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1959]),
[final] ).
cnf(i_0_4219,lemma,
( subset(cartesian_product2(X1,X2),cartesian_product2(X1,X3))
| ~ subset(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1960]),
[final] ).
cnf(i_0_4220,lemma,
( subset(cartesian_product2(X1,X2),cartesian_product2(X3,X2))
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1960]),
[final] ).
cnf(i_0_4221,plain,
( in(esk60_2(X1,X2),X2)
| X2 = empty_set
| ~ subset(X2,relation_field(X1))
| ~ well_founded_relation(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1807]),
[final] ).
cnf(i_0_4222,plain,
( X1 = X2
| ~ epred2_3(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1208]),
[final] ).
cnf(i_0_4223,plain,
( X1 = X2
| ~ epred2_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1208]),
[final] ).
cnf(i_0_4224,plain,
( X1 = latt_str_of(the_carrier(X1),the_L_join(X1),the_L_meet(X1))
| ~ latt_str(X1)
| ~ strict_latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1961]),
[final] ).
cnf(i_0_4225,lemma,
( relation_image(X1,relation_inverse_image(X1,X2)) = X2
| ~ relation(X1)
| ~ function(X1)
| ~ subset(X2,relation_rng(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1962]),
[final] ).
cnf(i_0_4226,plain,
( in(X3,esk233_1(X2))
| in(esk230_1(X2),X2)
| X3 != unordered_pair(X1,X1)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_1963,c_0_681]),
[final] ).
cnf(i_0_4227,plain,
( in(X3,esk233_1(X2))
| in(esk230_1(X2),X2)
| X3 != unordered_pair(X1,X1)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_1964,c_0_681]),
[final] ).
cnf(i_0_4228,plain,
( epred1_0
| in(empty_set,omega)
| in(set_union2(esk447_0,unordered_pair(esk447_0,esk447_0)),omega) ),
inference(rw,[status(thm)],[i_0_1965,c_0_1305]),
[final] ).
cnf(i_0_4229,lemma,
( set_difference(X1,unordered_pair(X2,X2)) != X1
| ~ in(X2,X1) ),
inference(rw,[status(thm)],[i_0_1966,c_0_681]),
[final] ).
cnf(i_0_4230,lemma,
( relation_dom_restriction(relation_rng_restriction(X2,X1),X3) = relation_rng_restriction(X2,relation_dom_restriction(X1,X3))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1967]),
[final] ).
cnf(i_0_4231,lemma,
( well_orders(esk133_2(X1,X2),X1)
| ~ well_ordering(X2)
| ~ equipotent(X1,relation_field(X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1968]),
[final] ).
cnf(i_0_4232,lemma,
( element(esk410_1(X1),powerset(powerset(the_carrier(X1))))
| compact_top_space(X1)
| empty_carrier(X1)
| ~ topological_space(X1)
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1765]),
[final] ).
cnf(i_0_4233,lemma,
( relation(esk182_2(X1,X2))
| empty(X1)
| esk178_2(X1,X2) != esk179_2(X1,X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_690]),
[final] ).
cnf(i_0_4234,lemma,
( function(esk182_2(X1,X2))
| empty(X1)
| esk178_2(X1,X2) != esk179_2(X1,X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_690]),
[final] ).
cnf(i_0_4235,lemma,
( X2 != set_union2(X1,unordered_pair(X1,X1))
| ~ ordinal(X2)
| ~ ordinal(X1)
| ~ being_limit_ordinal(X2) ),
inference(rw,[status(thm)],[i_0_1969,c_0_1305]),
[final] ).
cnf(i_0_4236,lemma,
( ~ in(X1,X2)
| ~ disjoint(unordered_pair(X1,X1),X2) ),
inference(rw,[status(thm)],[i_0_1970,c_0_681]),
[final] ).
cnf(i_0_4237,plain,
( in(esk85_2(X1,X2),X1)
| in(esk84_2(X1,X2),X2)
| X2 = union(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1788]),
[final] ).
cnf(i_0_4238,plain,
( in(esk50_2(X1,X2),X2)
| subset(esk50_2(X1,X2),X1)
| X2 = powerset(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1831]),
[final] ).
cnf(i_0_4239,plain,
( in(esk234_2(X1,X2),X1)
| ~ in(X2,esk233_1(X1))
| esk231_1(X1) != esk232_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_829]),
[final] ).
cnf(i_0_4240,lemma,
( subset(set_union2(X1,X3),X2)
| ~ subset(X1,X2)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1971]),
[final] ).
cnf(i_0_4241,lemma,
( subset(unordered_pair(X1,X3),X2)
| ~ in(X1,X2)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1972]),
[final] ).
cnf(i_0_4242,plain,
( empty_carrier(X1)
| cast_to_el_of_lattice(X1,X2) = X2
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(poset_of_lattice(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1973]),
[final] ).
cnf(i_0_4243,lemma,
( subset(relation_rng(relation_rng_restriction(X2,X1)),relation_rng(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1974]),
[final] ).
cnf(i_0_4244,lemma,
( subset(relation_rng(relation_dom_restriction(X1,X2)),relation_rng(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1975]),
[final] ).
cnf(i_0_4245,lemma,
( subset(relation_field(relation_restriction(X1,X2)),relation_field(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1976]),
[final] ).
cnf(i_0_4246,lemma,
( subset(relation_dom(relation_rng_restriction(X2,X1)),relation_dom(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1977]),
[final] ).
cnf(i_0_4247,lemma,
( in(X1,X2)
| ~ in(X1,relation_restriction(X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1823]),
[final] ).
cnf(i_0_4248,lemma,
( relation_dom(esk387_1(X1)) = X1
| esk385_1(X1) = unordered_pair(esk383_1(X1),esk383_1(X1))
| X2 != unordered_pair(esk386_1(X1),esk386_1(X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1978,c_0_681]),c_0_681]),
[final] ).
cnf(i_0_4249,lemma,
( relation_dom(esk387_1(X1)) = X1
| esk384_1(X1) = unordered_pair(esk383_1(X1),esk383_1(X1))
| X2 != unordered_pair(esk386_1(X1),esk386_1(X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1979,c_0_681]),c_0_681]),
[final] ).
cnf(i_0_4250,lemma,
( in(apply(esk420_1(X2),X1),X1)
| esk419_1(X2) = empty_set
| empty(X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1896]),
[final] ).
cnf(i_0_4251,lemma,
( esk385_1(X1) = unordered_pair(esk383_1(X1),esk383_1(X1))
| relation(esk387_1(X1))
| X2 != unordered_pair(esk386_1(X1),esk386_1(X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1980,c_0_681]),c_0_681]),
[final] ).
cnf(i_0_4252,lemma,
( esk385_1(X1) = unordered_pair(esk383_1(X1),esk383_1(X1))
| function(esk387_1(X1))
| X2 != unordered_pair(esk386_1(X1),esk386_1(X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1981,c_0_681]),c_0_681]),
[final] ).
cnf(i_0_4253,lemma,
( esk384_1(X1) = unordered_pair(esk383_1(X1),esk383_1(X1))
| relation(esk387_1(X1))
| X2 != unordered_pair(esk386_1(X1),esk386_1(X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1982,c_0_681]),c_0_681]),
[final] ).
cnf(i_0_4254,lemma,
( esk384_1(X1) = unordered_pair(esk383_1(X1),esk383_1(X1))
| function(esk387_1(X1))
| X2 != unordered_pair(esk386_1(X1),esk386_1(X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1983,c_0_681]),c_0_681]),
[final] ).
cnf(i_0_4255,lemma,
( element(X1,powerset(X2))
| ~ in(esk138_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1984]),
[final] ).
cnf(i_0_4256,plain,
( in(esk448_1(X1),X1)
| X1 = empty_set
| epred1_0
| ~ element(X1,powerset(powerset(esk447_0)))
| ~ in(esk447_0,omega)
| esk445_0 != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_760]),
[final] ).
cnf(i_0_4257,plain,
( in(X2,X3)
| X2 = X3
| in(X3,X2)
| ~ epsilon_connected(X1)
| ~ in(X2,X1)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1985]),
[final] ).
cnf(i_0_4258,lemma,
( X1 = set_union2(esk428_1(X1),unordered_pair(esk428_1(X1),esk428_1(X1)))
| being_limit_ordinal(X1)
| ~ ordinal(X1) ),
inference(rw,[status(thm)],[i_0_1986,c_0_1305]),
[final] ).
cnf(i_0_4259,plain,
( ordinal(esk251_2(X1,X2))
| ~ in(X2,esk249_1(X1))
| esk247_1(X1) != esk248_1(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_717]),
[final] ).
cnf(i_0_4260,plain,
( in(esk421_2(X1,X2),X1)
| in(esk421_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[i_0_1843]),
[final] ).
cnf(i_0_4261,plain,
( subset(X1,esk450_1(X1))
| subset(X2,esk446_1(X2))
| epred1_0
| ~ in(X1,esk449_0)
| ~ in(X2,esk445_0) ),
inference(split_conjunct,[status(thm)],[i_0_760]),
[final] ).
cnf(i_0_4262,lemma,
( relation(esk182_2(X1,X2))
| in(esk177_2(X1,X2),X1)
| empty(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_690]),
[final] ).
cnf(i_0_4263,lemma,
( relation(esk182_2(X1,X2))
| in(esk177_2(X1,X2),X1)
| empty(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_690]),
[final] ).
cnf(i_0_4264,lemma,
( function(esk182_2(X1,X2))
| in(esk177_2(X1,X2),X1)
| empty(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_690]),
[final] ).
cnf(i_0_4265,lemma,
( function(esk182_2(X1,X2))
| in(esk177_2(X1,X2),X1)
| empty(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_690]),
[final] ).
cnf(i_0_4266,plain,
( in(X1,relation_dom(X2))
| ~ in(X1,X3)
| X3 != relation_inverse_image(X2,X4)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1365]),
[final] ).
cnf(i_0_4267,plain,
( subset(X1,esk450_1(X1))
| in(esk446_1(X2),esk445_0)
| epred1_0
| ~ in(X1,esk449_0)
| ~ in(X2,esk445_0) ),
inference(split_conjunct,[status(thm)],[i_0_760]),
[final] ).
cnf(i_0_4268,plain,
( in(esk450_1(X1),esk449_0)
| subset(X2,esk446_1(X2))
| epred1_0
| ~ in(X1,esk449_0)
| ~ in(X2,esk445_0) ),
inference(split_conjunct,[status(thm)],[i_0_760]),
[final] ).
cnf(i_0_4269,plain,
relation_of2_as_subset(esk124_2(X1,X2),X1,X2),
inference(split_conjunct,[status(thm)],[i_0_1987]),
[final] ).
cnf(i_0_4270,plain,
quasi_total(esk142_2(X1,X2),X1,X2),
inference(split_conjunct,[status(thm)],[i_0_1988]),
[final] ).
cnf(i_0_4271,plain,
relation_of2(esk157_2(X1,X2),X1,X2),
inference(split_conjunct,[status(thm)],[i_0_1989]),
[final] ).
cnf(i_0_4272,plain,
relation_of2(esk142_2(X1,X2),X1,X2),
inference(split_conjunct,[status(thm)],[i_0_1988]),
[final] ).
cnf(i_0_4273,plain,
relation_of2(esk122_2(X1,X2),X1,X2),
inference(split_conjunct,[status(thm)],[i_0_1990]),
[final] ).
cnf(i_0_4274,lemma,
( ordinal_subset(esk199_1(X2),X1)
| ~ ordinal(X1)
| ~ in(X1,X2)
| ~ ordinal(X3)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1991]),
[final] ).
cnf(i_0_4275,plain,
( in(X3,esk233_1(X2))
| X3 != unordered_pair(X1,X1)
| esk232_1(X2) != esk231_1(X2)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_1992,c_0_681]),
[final] ).
cnf(i_0_4276,plain,
( relation_of2_as_subset(identity_on_carrier(X1),the_carrier(X1),the_carrier(X1))
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1993]),
[final] ).
cnf(i_0_4277,plain,
( relation_of2_as_subset(the_InternalRel(X1),the_carrier(X1),the_carrier(X1))
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1994]),
[final] ).
cnf(i_0_4278,plain,
( quasi_total(identity_on_carrier(X1),the_carrier(X1),the_carrier(X1))
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1993]),
[final] ).
cnf(i_0_4279,lemma,
( X1 = empty_set
| X1 = unordered_pair(X2,X2)
| ~ subset(X1,unordered_pair(X2,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1995,c_0_681]),c_0_681]),
[final] ).
cnf(i_0_4280,lemma,
( X1 = empty_set
| X1 = unordered_pair(X2,X2)
| ~ subset(X1,unordered_pair(X2,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1996,c_0_681]),c_0_681]),
[final] ).
cnf(i_0_4281,plain,
set_difference(X1,set_difference(X1,X2)) = set_difference(X2,set_difference(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1997,c_0_1442]),c_0_1442]),
[final] ).
cnf(i_0_4282,plain,
( in(esk450_1(X1),esk449_0)
| in(esk446_1(X2),esk445_0)
| epred1_0
| ~ in(X1,esk449_0)
| ~ in(X2,esk445_0) ),
inference(split_conjunct,[status(thm)],[i_0_760]),
[final] ).
cnf(i_0_4283,lemma,
( subset(relation_rng(relation_rng_restriction(X2,X1)),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1998]),
[final] ).
cnf(i_0_4284,lemma,
( subset(relation_field(relation_restriction(X1,X2)),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1976]),
[final] ).
cnf(i_0_4285,plain,
( element(esk31_2(X1,X2),powerset(X1))
| X2 = boole_lattice(X1)
| the_carrier(X2) != powerset(X1)
| ~ strict_latt_str(X2)
| ~ latt_str(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1407]),
[final] ).
cnf(i_0_4286,plain,
( element(esk30_2(X1,X2),powerset(X1))
| X2 = boole_lattice(X1)
| the_carrier(X2) != powerset(X1)
| ~ strict_latt_str(X2)
| ~ latt_str(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1407]),
[final] ).
cnf(i_0_4287,plain,
( element(subset_complement(X2,X1),powerset(X2))
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1999]),
[final] ).
cnf(i_0_4288,plain,
( in(esk444_2(X1,X2),esk443_1(X1))
| ~ in(X2,esk443_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1912]),
[final] ).
cnf(i_0_4289,lemma,
( relation_field(relation_restriction(X1,X2)) = X2
| ~ relation(X1)
| ~ well_ordering(X1)
| ~ subset(X2,relation_field(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2000]),
[final] ).
cnf(i_0_4290,plain,
( subset(X1,X2)
| ~ in(esk74_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2001]),
[final] ).
cnf(i_0_4291,lemma,
( in(X1,X2)
| ~ subset(unordered_pair(X1,X1),X2) ),
inference(rw,[status(thm)],[i_0_2002,c_0_681]),
[final] ).
cnf(i_0_4292,lemma,
( in(X1,X2)
| ~ subset(unordered_pair(X1,X1),X2) ),
inference(rw,[status(thm)],[i_0_2003,c_0_681]),
[final] ).
cnf(i_0_4293,lemma,
( in(X1,X2)
| ~ subset(unordered_pair(X1,X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1972]),
[final] ).
cnf(i_0_4294,lemma,
( in(X1,X2)
| ~ subset(unordered_pair(X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1972]),
[final] ).
cnf(i_0_4295,plain,
( disjoint(X1,X2)
| set_difference(X1,set_difference(X1,X2)) != empty_set ),
inference(rw,[status(thm)],[i_0_2004,c_0_1442]),
[final] ).
cnf(i_0_4296,plain,
( epred1_0
| in(set_union2(esk447_0,unordered_pair(esk447_0,esk447_0)),omega)
| esk445_0 != empty_set ),
inference(rw,[status(thm)],[i_0_2005,c_0_1305]),
[final] ).
cnf(i_0_4297,lemma,
( relation(esk133_2(X1,X2))
| ~ well_ordering(X2)
| ~ equipotent(X1,relation_field(X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1968]),
[final] ).
cnf(i_0_4298,lemma,
( X1 = empty_set
| ~ element(X1,powerset(powerset(X2)))
| complements_of_subsets(X2,X1) != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_2006]),
[final] ).
cnf(i_0_4299,lemma,
( X1 = empty_set
| complements_of_subsets(X2,X1) != empty_set
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_2007]),
[final] ).
cnf(i_0_4300,plain,
( in(esk327_2(X1,X2),X1)
| ordinal(esk325_0)
| ~ in(X2,esk326_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2008]),
[final] ).
cnf(i_0_4301,plain,
( in(esk327_2(X1,X2),X1)
| ordinal(esk324_0)
| ~ in(X2,esk326_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2008]),
[final] ).
cnf(i_0_4302,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X2 != set_union2(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_4303,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X4 != set_difference(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1489]),
[final] ).
cnf(i_0_4304,plain,
( in(X3,esk443_1(X2))
| ~ in(X1,esk443_1(X2))
| ~ subset(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1912]),
[final] ).
cnf(i_0_4305,lemma,
( in(X3,esk409_1(X2))
| ~ in(X1,esk409_1(X2))
| ~ subset(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2009]),
[final] ).
cnf(i_0_4306,lemma,
( relation_dom(esk387_1(X1)) = X1
| in(esk383_1(X1),X1)
| X2 != unordered_pair(esk386_1(X1),esk386_1(X1)) ),
inference(rw,[status(thm)],[i_0_2010,c_0_681]),
[final] ).
cnf(i_0_4307,plain,
( element(esk69_1(X1),powerset(powerset(the_carrier(X1))))
| compact_top_space(X1)
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1703]),
[final] ).
cnf(i_0_4308,lemma,
( relation(esk387_1(X1))
| in(esk383_1(X1),X1)
| X2 != unordered_pair(esk386_1(X1),esk386_1(X1)) ),
inference(rw,[status(thm)],[i_0_2011,c_0_681]),
[final] ).
cnf(i_0_4309,lemma,
( function(esk387_1(X1))
| in(esk383_1(X1),X1)
| X2 != unordered_pair(esk386_1(X1),esk386_1(X1)) ),
inference(rw,[status(thm)],[i_0_2012,c_0_681]),
[final] ).
cnf(i_0_4310,plain,
( in(esk327_2(X1,X2),X1)
| ~ in(X2,esk326_1(X1))
| esk324_0 != esk325_0 ),
inference(split_conjunct,[status(thm)],[i_0_2008]),
[final] ).
cnf(i_0_4311,plain,
( are_equipotent(X1,esk443_1(X2))
| in(X1,esk443_1(X2))
| ~ subset(X1,esk443_1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1912]),
[final] ).
cnf(i_0_4312,lemma,
( are_equipotent(X1,esk409_1(X2))
| in(X1,esk409_1(X2))
| ~ subset(X1,esk409_1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2009]),
[final] ).
cnf(i_0_4313,plain,
( in(esk327_2(X1,X2),X1)
| esk323_0 = esk325_0
| ~ in(X2,esk326_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2008]),
[final] ).
cnf(i_0_4314,plain,
( in(esk327_2(X1,X2),X1)
| esk323_0 = esk324_0
| ~ in(X2,esk326_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2008]),
[final] ).
cnf(i_0_4315,plain,
( subset_complement(X2,subset_complement(X2,X1)) = X1
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2013]),
[final] ).
cnf(i_0_4316,lemma,
( subset(X1,cartesian_product2(relation_dom(X1),relation_rng(X1)))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2014]),
[final] ).
cnf(i_0_4317,lemma,
( in(esk423_2(X1,X2),X1)
| X1 = empty_set
| ~ subset(X1,X2)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1894]),
[final] ).
cnf(i_0_4318,plain,
( X2 = unordered_pair(X1,X1)
| esk44_2(X1,X2) = X1
| in(esk44_2(X1,X2),X2) ),
inference(rw,[status(thm)],[i_0_2015,c_0_681]),
[final] ).
cnf(i_0_4319,plain,
( subset(X1,esk450_1(X1))
| epred1_0
| ~ in(X1,esk449_0)
| esk446_1(X2) != X2
| ~ in(X2,esk445_0) ),
inference(split_conjunct,[status(thm)],[i_0_760]),
[final] ).
cnf(i_0_4320,plain,
( subset(X2,esk446_1(X2))
| epred1_0
| esk450_1(X1) != X1
| ~ in(X1,esk449_0)
| ~ in(X2,esk445_0) ),
inference(split_conjunct,[status(thm)],[i_0_760]),
[final] ).
cnf(i_0_4321,lemma,
( relation(esk182_2(X1,X2))
| esk177_2(X1,X2) = esk181_2(X1,X2)
| empty(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_690]),
[final] ).
cnf(i_0_4322,lemma,
( function(esk182_2(X1,X2))
| esk177_2(X1,X2) = esk181_2(X1,X2)
| empty(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_690]),
[final] ).
cnf(i_0_4323,lemma,
( relation(esk182_2(X1,X2))
| esk177_2(X1,X2) = esk180_2(X1,X2)
| empty(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_690]),
[final] ).
cnf(i_0_4324,lemma,
( function(esk182_2(X1,X2))
| esk177_2(X1,X2) = esk180_2(X1,X2)
| empty(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_690]),
[final] ).
cnf(i_0_4325,plain,
( element(the_topology(X1),powerset(powerset(the_carrier(X1))))
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2016]),
[final] ).
cnf(i_0_4326,lemma,
( ordinal(esk350_2(X1,X2))
| ~ in(X2,esk349_1(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_721]),
[final] ).
cnf(i_0_4327,plain,
( in(X1,X3)
| X4 = empty_set
| ~ in(X1,X2)
| ~ in(X3,X4)
| X2 != set_meet(X4) ),
inference(split_conjunct,[status(thm)],[i_0_1724]),
[final] ).
cnf(i_0_4328,plain,
( meet_of_subsets(X2,X1) = set_meet(X1)
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_2017]),
[final] ).
cnf(i_0_4329,plain,
( union_of_subsets(X2,X1) = union(X1)
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_2018]),
[final] ).
cnf(i_0_4330,plain,
( element(X1,X3)
| ~ in(X1,X2)
| ~ element(X2,powerset(X3)) ),
inference(split_conjunct,[status(thm)],[i_0_2019]),
[final] ).
cnf(i_0_4331,lemma,
( in(X3,X2)
| ~ element(X1,powerset(X2))
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2020]),
[final] ).
cnf(i_0_4332,plain,
( ~ in(X1,X2)
| ~ in(X1,X3)
| X3 != set_difference(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1489]),
[final] ).
cnf(i_0_4333,plain,
( in(esk450_1(X1),esk449_0)
| epred1_0
| ~ in(X1,esk449_0)
| esk446_1(X2) != X2
| ~ in(X2,esk445_0) ),
inference(split_conjunct,[status(thm)],[i_0_760]),
[final] ).
cnf(i_0_4334,plain,
( in(esk446_1(X2),esk445_0)
| epred1_0
| esk450_1(X1) != X1
| ~ in(X1,esk449_0)
| ~ in(X2,esk445_0) ),
inference(split_conjunct,[status(thm)],[i_0_760]),
[final] ).
cnf(i_0_4335,plain,
( X1 = omega
| ~ subset(X1,esk91_1(X1))
| ~ in(empty_set,X1)
| ~ being_limit_ordinal(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2021]),
[final] ).
cnf(i_0_4336,lemma,
( in(esk424_2(X1,X2),X1)
| X2 = identity_relation(X1)
| relation_dom(X2) != X1
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1868]),
[final] ).
cnf(i_0_4337,plain,
( in(X1,X4)
| ~ in(X1,X2)
| ~ in(X2,X3)
| X4 != union(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1788]),
[final] ).
cnf(i_0_4338,lemma,
( complements_of_subsets(X1,X2) = empty_set
| X2 != empty_set
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2007]),
[final] ).
cnf(i_0_4339,lemma,
( ~ in(X1,X2)
| ~ in(X1,X3)
| ~ disjoint(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_2022]),
[final] ).
cnf(i_0_4340,lemma,
( ~ in(X1,X2)
| ~ in(X2,X3)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2023]),
[final] ).
cnf(i_0_4341,lemma,
( ~ proper_element(X1,powerset(X2))
| X1 != X2
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2024]),
[final] ).
cnf(i_0_4342,plain,
( esk250_2(X1,X2) = X2
| ~ in(X2,esk249_1(X1))
| esk247_1(X1) != esk248_1(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_717]),
[final] ).
cnf(i_0_4343,plain,
( X1 = esk251_2(X2,X1)
| ~ in(X1,esk249_1(X2))
| esk247_1(X2) != esk248_1(X2)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_717]),
[final] ).
cnf(i_0_4344,lemma,
( relation_dom(esk387_1(X1)) = X1
| esk385_1(X1) != esk384_1(X1)
| X2 != unordered_pair(esk386_1(X1),esk386_1(X1)) ),
inference(rw,[status(thm)],[i_0_2025,c_0_681]),
[final] ).
cnf(i_0_4345,lemma,
( relation(esk387_1(X1))
| esk385_1(X1) != esk384_1(X1)
| X2 != unordered_pair(esk386_1(X1),esk386_1(X1)) ),
inference(rw,[status(thm)],[i_0_2026,c_0_681]),
[final] ).
cnf(i_0_4346,lemma,
( function(esk387_1(X1))
| esk385_1(X1) != esk384_1(X1)
| X2 != unordered_pair(esk386_1(X1),esk386_1(X1)) ),
inference(rw,[status(thm)],[i_0_2027,c_0_681]),
[final] ).
cnf(i_0_4347,plain,
( subset(X1,esk450_1(X1))
| element(esk445_0,powerset(powerset(empty_set)))
| epred1_0
| ~ in(X1,esk449_0) ),
inference(split_conjunct,[status(thm)],[i_0_760]),
[final] ).
cnf(i_0_4348,plain,
( empty_carrier(X1)
| cast_to_el_of_LattPOSet(X1,X2) = X2
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2028]),
[final] ).
cnf(i_0_4349,plain,
( is_connected_in(X1,X2)
| esk95_2(X1,X2) != esk96_2(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_727]),
[final] ).
cnf(i_0_4350,plain,
( is_antisymmetric_in(X1,X2)
| esk81_2(X1,X2) != esk82_2(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_740]),
[final] ).
cnf(i_0_4351,plain,
( empty_carrier(X1)
| meet_of_latt_set(X1,X2) = join_of_latt_set(X1,a_2_2_lattice3(X1,X2))
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2029]),
[final] ).
cnf(i_0_4352,plain,
( in(esk450_1(X1),esk449_0)
| element(esk445_0,powerset(powerset(empty_set)))
| epred1_0
| ~ in(X1,esk449_0) ),
inference(split_conjunct,[status(thm)],[i_0_760]),
[final] ).
cnf(i_0_4353,lemma,
( relation_rng(relation_composition(X1,X2)) = relation_image(X2,relation_rng(X1))
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2030]),
[final] ).
cnf(i_0_4354,lemma,
( subset(X1,unordered_pair(X2,X2))
| X1 != unordered_pair(X2,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2031,c_0_681]),c_0_681]),
[final] ).
cnf(i_0_4355,lemma,
( subset(X1,unordered_pair(X2,X2))
| X1 != unordered_pair(X2,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2032,c_0_681]),c_0_681]),
[final] ).
cnf(i_0_4356,lemma,
( set_union2(unordered_pair(X1,X1),X2) = X2
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_2033,c_0_681]),
[final] ).
cnf(i_0_4357,lemma,
( set_union2(unordered_pair(X1,X1),X2) = X2
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_2034,c_0_681]),
[final] ).
cnf(i_0_4358,lemma,
( set_difference(X1,set_difference(X1,X2)) = X1
| ~ subset(X1,X2) ),
inference(rw,[status(thm)],[i_0_2035,c_0_1442]),
[final] ).
cnf(i_0_4359,lemma,
( X2 = set_union2(X1,set_difference(X2,X1))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2036]),
[final] ).
cnf(i_0_4360,lemma,
( subset(relation_rng(X1),relation_rng(X2))
| ~ subset(X1,X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2037]),
[final] ).
cnf(i_0_4361,lemma,
( subset(relation_dom(X1),relation_dom(X2))
| ~ subset(X1,X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2037]),
[final] ).
cnf(i_0_4362,lemma,
( X2 = empty_set
| ~ relation(X1)
| ~ subset(X2,relation_rng(X1))
| relation_inverse_image(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_2038]),
[final] ).
cnf(i_0_4363,lemma,
( subset(unordered_pair(X1,X1),X2)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_2039,c_0_681]),
[final] ).
cnf(i_0_4364,lemma,
( subset(unordered_pair(X1,X1),X2)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_2040,c_0_681]),
[final] ).
cnf(i_0_4365,plain,
( in(esk442_2(X1,X2),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1875]),
[final] ).
cnf(i_0_4366,plain,
( set_difference(X1,set_difference(X1,X2)) = empty_set
| ~ disjoint(X1,X2) ),
inference(rw,[status(thm)],[i_0_2041,c_0_1442]),
[final] ).
cnf(i_0_4367,lemma,
( relation_dom(esk387_1(X1)) = X1
| esk385_1(X1) = unordered_pair(esk383_1(X1),esk383_1(X1))
| in(esk386_1(X1),X1) ),
inference(rw,[status(thm)],[i_0_2042,c_0_681]),
[final] ).
cnf(i_0_4368,lemma,
( relation_dom(esk387_1(X1)) = X1
| esk384_1(X1) = unordered_pair(esk383_1(X1),esk383_1(X1))
| in(esk386_1(X1),X1) ),
inference(rw,[status(thm)],[i_0_2043,c_0_681]),
[final] ).
cnf(i_0_4369,plain,
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| ~ empty(X3) ),
inference(split_conjunct,[status(thm)],[i_0_2044]),
[final] ).
cnf(i_0_4370,plain,
( subset(esk76_2(X1,X2),X2)
| is_well_founded_in(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1596]),
[final] ).
cnf(i_0_4371,plain,
( in(esk40_2(X1,X2),X2)
| is_reflexive_in(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_725]),
[final] ).
cnf(i_0_4372,plain,
( in(esk112_2(X1,X2),X2)
| is_transitive_in(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_726]),
[final] ).
cnf(i_0_4373,plain,
( in(esk111_2(X1,X2),X2)
| is_transitive_in(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_726]),
[final] ).
cnf(i_0_4374,plain,
( in(esk110_2(X1,X2),X2)
| is_transitive_in(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_726]),
[final] ).
cnf(i_0_4375,plain,
( in(esk96_2(X1,X2),X2)
| is_connected_in(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_727]),
[final] ).
cnf(i_0_4376,plain,
( in(esk95_2(X1,X2),X2)
| is_connected_in(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_727]),
[final] ).
cnf(i_0_4377,plain,
( in(esk82_2(X1,X2),X2)
| is_antisymmetric_in(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_740]),
[final] ).
cnf(i_0_4378,plain,
( in(esk81_2(X1,X2),X2)
| is_antisymmetric_in(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_740]),
[final] ).
cnf(i_0_4379,lemma,
( ordinal(esk423_2(X1,X2))
| X1 = empty_set
| ~ subset(X1,X2)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1894]),
[final] ).
cnf(i_0_4380,lemma,
( esk385_1(X1) = unordered_pair(esk383_1(X1),esk383_1(X1))
| relation(esk387_1(X1))
| in(esk386_1(X1),X1) ),
inference(rw,[status(thm)],[i_0_2045,c_0_681]),
[final] ).
cnf(i_0_4381,lemma,
( esk385_1(X1) = unordered_pair(esk383_1(X1),esk383_1(X1))
| function(esk387_1(X1))
| in(esk386_1(X1),X1) ),
inference(rw,[status(thm)],[i_0_2046,c_0_681]),
[final] ).
cnf(i_0_4382,lemma,
( esk384_1(X1) = unordered_pair(esk383_1(X1),esk383_1(X1))
| relation(esk387_1(X1))
| in(esk386_1(X1),X1) ),
inference(rw,[status(thm)],[i_0_2047,c_0_681]),
[final] ).
cnf(i_0_4383,lemma,
( esk384_1(X1) = unordered_pair(esk383_1(X1),esk383_1(X1))
| function(esk387_1(X1))
| in(esk386_1(X1),X1) ),
inference(rw,[status(thm)],[i_0_2048,c_0_681]),
[final] ).
cnf(i_0_4384,plain,
( in(esk48_2(X1,X2),X1)
| X2 = inclusion_relation(X1)
| relation_field(X2) != X1
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_719]),
[final] ).
cnf(i_0_4385,plain,
( in(esk47_2(X1,X2),X1)
| X2 = inclusion_relation(X1)
| relation_field(X2) != X1
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_719]),
[final] ).
cnf(i_0_4386,lemma,
( relation_restriction(X1,X2) = relation_dom_restriction(relation_rng_restriction(X2,X1),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2049]),
[final] ).
cnf(i_0_4387,lemma,
( relation_restriction(X1,X2) = relation_rng_restriction(X2,relation_dom_restriction(X1,X2))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2050]),
[final] ).
cnf(i_0_4388,lemma,
( relation_field(relation_restriction(X1,X2)) = X2
| ~ well_orders(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2051]),
[final] ).
cnf(i_0_4389,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_difference(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1489]),
[final] ).
cnf(i_0_4390,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_4391,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_4392,lemma,
( in(esk138_2(X1,X2),X1)
| element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1984]),
[final] ).
cnf(i_0_4393,plain,
relation_of2_as_subset(identity_relation(X1),X1,X1),
inference(rw,[status(thm)],[i_0_2052,c_0_2053]),
[final] ).
cnf(i_0_4394,plain,
onto(esk154_1(X1),X1,X1),
inference(split_conjunct,[status(thm)],[i_0_2054]),
[final] ).
cnf(i_0_4395,plain,
bijective(esk154_1(X1),X1,X1),
inference(split_conjunct,[status(thm)],[i_0_2054]),
[final] ).
cnf(i_0_4396,plain,
quasi_total(esk154_1(X1),X1,X1),
inference(split_conjunct,[status(thm)],[i_0_2054]),
[final] ).
cnf(i_0_4397,plain,
v1_partfun1(esk167_1(X1),X1,X1),
inference(split_conjunct,[status(thm)],[i_0_2055]),
[final] ).
cnf(i_0_4398,plain,
v1_partfun1(identity_relation(X1),X1,X1),
inference(rw,[status(thm)],[i_0_2056,c_0_2053]),
[final] ).
cnf(i_0_4399,plain,
relation_of2(esk167_1(X1),X1,X1),
inference(split_conjunct,[status(thm)],[i_0_2055]),
[final] ).
cnf(i_0_4400,plain,
relation_of2(esk154_1(X1),X1,X1),
inference(split_conjunct,[status(thm)],[i_0_2054]),
[final] ).
cnf(i_0_4401,lemma,
( apply(X3,X1) = X1
| ~ in(X1,X2)
| X3 != identity_relation(X2)
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1868]),
[final] ).
cnf(i_0_4402,plain,
( subset_complement(X2,X1) = set_difference(X2,X1)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2057]),
[final] ).
cnf(i_0_4403,plain,
( X1 = empty_set
| in(X3,relation_dom(X2))
| X1 != apply(X2,X3)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_767]),
[final] ).
cnf(i_0_4404,lemma,
( well_ordering(relation_restriction(X1,X2))
| ~ well_orders(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2051]),
[final] ).
cnf(i_0_4405,lemma,
( disjoint(X1,X3)
| ~ subset(X1,X2)
| ~ disjoint(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_2058]),
[final] ).
cnf(i_0_4406,lemma,
( subset(X1,X3)
| ~ subset(X1,X2)
| ~ subset(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_2059]),
[final] ).
cnf(i_0_4407,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2001]),
[final] ).
cnf(i_0_4408,plain,
( lattice(X1)
| empty_carrier(X1)
| ~ join_commutative(X1)
| ~ join_associative(X1)
| ~ meet_commutative(X1)
| ~ meet_associative(X1)
| ~ meet_absorbing(X1)
| ~ join_absorbing(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2060]),
[final] ).
cnf(i_0_4409,plain,
( apply(X1,esk101_1(X1)) = apply(X1,esk102_1(X1))
| one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1828]),
[final] ).
cnf(i_0_4410,plain,
( relation(relation_composition(X1,X2))
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2061]),
[final] ).
cnf(i_0_4411,plain,
( function(relation_composition(X1,X2))
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2061]),
[final] ).
cnf(i_0_4412,lemma,
( in(powerset(X1),esk409_1(X2))
| ~ in(X1,esk409_1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2009]),
[final] ).
cnf(i_0_4413,plain,
( epred1_0
| esk450_1(X1) != X1
| ~ in(X1,esk449_0)
| esk446_1(X2) != X2
| ~ in(X2,esk445_0) ),
inference(split_conjunct,[status(thm)],[i_0_760]),
[final] ).
cnf(i_0_4414,plain,
( empty_carrier(X1)
| element(meet_of_latt_set(X1,X2),the_carrier(X1))
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2062]),
[final] ).
cnf(i_0_4415,plain,
( empty_carrier(X1)
| element(join_of_latt_set(X1,X2),the_carrier(X1))
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2063]),
[final] ).
cnf(i_0_4416,plain,
( element(esk175_1(X1),powerset(the_carrier(X1)))
| empty_carrier(X1)
| ~ topological_space(X1)
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2064]),
[final] ).
cnf(i_0_4417,plain,
( X1 != X2
| ~ in(X1,X3)
| X3 != fiber(X4,X2)
| ~ relation(X4) ),
inference(split_conjunct,[status(thm)],[i_0_703]),
[final] ).
cnf(i_0_4418,plain,
( finite(X2)
| ~ relation(X1)
| ~ function(X1)
| relation_rng(X1) != X2
| ~ in(relation_dom(X1),omega) ),
inference(split_conjunct,[status(thm)],[i_0_2065]),
[final] ).
cnf(i_0_4419,plain,
( in(X3,esk326_1(X2))
| ordinal(esk325_0)
| ~ in(X1,X2)
| X1 != X3
| ~ ordinal(X3) ),
inference(split_conjunct,[status(thm)],[i_0_2008]),
[final] ).
cnf(i_0_4420,plain,
( in(X3,esk326_1(X2))
| ordinal(esk324_0)
| ~ in(X1,X2)
| X1 != X3
| ~ ordinal(X3) ),
inference(split_conjunct,[status(thm)],[i_0_2008]),
[final] ).
cnf(i_0_4421,plain,
( empty(X1)
| empty(X2)
| ~ empty(cartesian_product2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2066]),
[final] ).
cnf(i_0_4422,lemma,
( apply(esk405_1(X2),X1) = unordered_pair(X1,X1)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_2067,c_0_681]),
[final] ).
cnf(i_0_4423,lemma,
( set_difference(X2,unordered_pair(X1,X1)) = X2
| in(X1,X2) ),
inference(rw,[status(thm)],[i_0_2068,c_0_681]),
[final] ).
cnf(i_0_4424,plain,
( in(X3,esk326_1(X2))
| ~ in(X1,X2)
| X1 != X3
| ~ ordinal(X3)
| esk324_0 != esk325_0 ),
inference(split_conjunct,[status(thm)],[i_0_2008]),
[final] ).
cnf(i_0_4425,plain,
( in(empty_set,esk91_1(X1))
| X1 = omega
| ~ in(empty_set,X1)
| ~ being_limit_ordinal(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2021]),
[final] ).
cnf(i_0_4426,lemma,
( X1 = X2
| proper_element(X1,powerset(X2))
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2024]),
[final] ).
cnf(i_0_4427,plain,
( in(X3,esk326_1(X2))
| esk323_0 = esk325_0
| ~ in(X1,X2)
| X1 != X3
| ~ ordinal(X3) ),
inference(split_conjunct,[status(thm)],[i_0_2008]),
[final] ).
cnf(i_0_4428,plain,
( in(X3,esk326_1(X2))
| esk323_0 = esk324_0
| ~ in(X1,X2)
| X1 != X3
| ~ ordinal(X3) ),
inference(split_conjunct,[status(thm)],[i_0_2008]),
[final] ).
cnf(i_0_4429,lemma,
( in(esk426_2(X1,X2),X1)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2022]),
[final] ).
cnf(i_0_4430,lemma,
( in(esk426_2(X1,X2),X2)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2022]),
[final] ).
cnf(i_0_4431,plain,
( in(esk74_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2001]),
[final] ).
cnf(i_0_4432,lemma,
( in(X1,X2)
| disjoint(unordered_pair(X1,X1),X2) ),
inference(rw,[status(thm)],[i_0_2069,c_0_681]),
[final] ).
cnf(i_0_4433,lemma,
( X1 = esk350_2(X2,X1)
| ~ in(X1,esk349_1(X2))
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_721]),
[final] ).
cnf(i_0_4434,plain,
( element(esk445_0,powerset(powerset(empty_set)))
| epred1_0
| esk450_1(X1) != X1
| ~ in(X1,esk449_0) ),
inference(split_conjunct,[status(thm)],[i_0_760]),
[final] ).
cnf(i_0_4435,lemma,
set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_2070]),
[final] ).
cnf(i_0_4436,lemma,
set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_2071]),
[final] ).
cnf(i_0_4437,plain,
( strict_latt_str(k8_filter_1(X1,X2))
| empty_carrier(X1)
| empty_carrier(X2)
| ~ latt_str(X1)
| ~ latt_str(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2072]),
[final] ).
cnf(i_0_4438,plain,
( latt_str(k8_filter_1(X1,X2))
| empty_carrier(X1)
| empty_carrier(X2)
| ~ latt_str(X1)
| ~ latt_str(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2072]),
[final] ).
cnf(i_0_4439,plain,
( relation_rng(esk86_2(X1,X2)) = X2
| ~ equipotent(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2073]),
[final] ).
cnf(i_0_4440,plain,
( relation_dom(esk86_2(X1,X2)) = X1
| ~ equipotent(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2073]),
[final] ).
cnf(i_0_4441,plain,
( ~ proper_element(X1,X2)
| X1 != union(X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2074]),
[final] ).
cnf(i_0_4442,lemma,
( ordinal(X1)
| ~ ordinal(esk422_1(X1))
| ~ subset(esk422_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[i_0_2075]),
[final] ).
cnf(i_0_4443,plain,
( antisymmetric_relstr(X1)
| ~ is_antisymmetric_in(the_InternalRel(X1),the_carrier(X1))
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2076]),
[final] ).
cnf(i_0_4444,plain,
( transitive_relstr(X1)
| ~ is_transitive_in(the_InternalRel(X1),the_carrier(X1))
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2077]),
[final] ).
cnf(i_0_4445,lemma,
( subset(relation_inverse_image(X1,X2),relation_dom(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2078]),
[final] ).
cnf(i_0_4446,lemma,
( subset(relation_image(X1,X2),relation_rng(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2079]),
[final] ).
cnf(i_0_4447,plain,
( element(esk174_1(X1),powerset(the_carrier(X1)))
| ~ topological_space(X1)
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2080]),
[final] ).
cnf(i_0_4448,plain,
( element(esk161_1(X1),powerset(the_carrier(X1)))
| ~ topological_space(X1)
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2081]),
[final] ).
cnf(i_0_4449,plain,
( element(esk150_1(X1),powerset(the_carrier(X1)))
| ~ topological_space(X1)
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2082]),
[final] ).
cnf(i_0_4450,plain,
( one_to_one(esk86_2(X1,X2))
| ~ equipotent(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2073]),
[final] ).
cnf(i_0_4451,plain,
( relation(esk86_2(X1,X2))
| ~ equipotent(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2073]),
[final] ).
cnf(i_0_4452,plain,
( function(esk86_2(X1,X2))
| ~ equipotent(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2073]),
[final] ).
cnf(i_0_4453,plain,
( subset(X1,esk450_1(X1))
| in(empty_set,omega)
| epred1_0
| ~ in(X1,esk449_0) ),
inference(split_conjunct,[status(thm)],[i_0_760]),
[final] ).
cnf(i_0_4454,plain,
( equipotent(X2,X3)
| ~ relation(X1)
| ~ function(X1)
| ~ one_to_one(X1)
| relation_dom(X1) != X2
| relation_rng(X1) != X3 ),
inference(split_conjunct,[status(thm)],[i_0_2073]),
[final] ).
cnf(i_0_4455,lemma,
( relation_dom(X1) = relation_rng(X2)
| X1 != function_inverse(X2)
| ~ relation(X1)
| ~ function(X1)
| ~ one_to_one(X2)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1546]),
[final] ).
cnf(i_0_4456,plain,
( X1 = apply(X2,X3)
| in(X3,relation_dom(X2))
| X1 != empty_set
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_767]),
[final] ).
cnf(i_0_4457,lemma,
( relation_dom(esk387_1(X1)) = X1
| in(esk386_1(X1),X1)
| in(esk383_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[i_0_828]),
[final] ).
cnf(i_0_4458,plain,
( empty(X1)
| ~ empty(set_union2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2083]),
[final] ).
cnf(i_0_4459,plain,
( empty(X1)
| ~ empty(set_union2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2084]),
[final] ).
cnf(i_0_4460,lemma,
( finite(relation_image(X1,X2))
| ~ relation(X1)
| ~ function(X1)
| ~ finite(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2085]),
[final] ).
cnf(i_0_4461,plain,
( finite(relation_image(X1,X2))
| ~ relation(X1)
| ~ function(X1)
| ~ finite(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2086]),
[final] ).
cnf(i_0_4462,lemma,
( relation(esk387_1(X1))
| in(esk386_1(X1),X1)
| in(esk383_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[i_0_828]),
[final] ).
cnf(i_0_4463,lemma,
( function(esk387_1(X1))
| in(esk386_1(X1),X1)
| in(esk383_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[i_0_828]),
[final] ).
cnf(i_0_4464,plain,
( subset(X2,X1)
| ~ ordinal(X1)
| ~ in(empty_set,X1)
| ~ being_limit_ordinal(X1)
| X2 != omega ),
inference(split_conjunct,[status(thm)],[i_0_2021]),
[final] ).
cnf(i_0_4465,plain,
( subset(X1,X2)
| ~ ordinal_subset(X1,X2)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2087]),
[final] ).
cnf(i_0_4466,plain,
( ordinal_subset(X1,X2)
| ~ subset(X1,X2)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2087]),
[final] ).
cnf(i_0_4467,lemma,
( in(X1,X2)
| ~ epsilon_transitive(X1)
| ~ ordinal(X2)
| ~ proper_subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2088]),
[final] ).
cnf(i_0_4468,plain,
( in(esk450_1(X1),esk449_0)
| in(empty_set,omega)
| epred1_0
| ~ in(X1,esk449_0) ),
inference(split_conjunct,[status(thm)],[i_0_760]),
[final] ).
cnf(i_0_4469,plain,
( X1 = X3
| X1 = X4
| ~ in(X1,X2)
| X2 != unordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1617]),
[final] ).
cnf(i_0_4470,plain,
( element(esk172_1(X1),powerset(the_carrier(X1)))
| empty_carrier(X1)
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2089]),
[final] ).
cnf(i_0_4471,plain,
( esk327_2(X1,X2) = X2
| ordinal(esk325_0)
| ~ in(X2,esk326_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2008]),
[final] ).
cnf(i_0_4472,plain,
( esk327_2(X1,X2) = X2
| ordinal(esk324_0)
| ~ in(X2,esk326_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2008]),
[final] ).
cnf(i_0_4473,lemma,
( in(esk199_1(X1),X1)
| ~ ordinal(X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1991]),
[final] ).
cnf(i_0_4474,lemma,
( in(X1,esk370_1(X2))
| ~ in(X1,X2)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2090]),
[final] ).
cnf(i_0_4475,lemma,
( meet_of_subsets(the_carrier(X1),esk410_1(X1)) = empty_set
| compact_top_space(X1)
| empty_carrier(X1)
| ~ topological_space(X1)
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1765]),
[final] ).
cnf(i_0_4476,plain,
( empty_carrier(X1)
| poset_of_lattice(X1) = rel_str_of(the_carrier(X1),k2_lattice3(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2091]),
[final] ).
cnf(i_0_4477,plain,
( X1 = X3
| X2 != unordered_pair(X3,X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_2092,c_0_681]),
[final] ).
cnf(i_0_4478,lemma,
( X1 = X3
| X1 = X4
| unordered_pair(X1,X2) != unordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_2093]),
[final] ).
cnf(i_0_4479,plain,
( esk327_2(X1,X2) = X2
| ~ in(X2,esk326_1(X1))
| esk324_0 != esk325_0 ),
inference(split_conjunct,[status(thm)],[i_0_2008]),
[final] ).
cnf(i_0_4480,plain,
( esk327_2(X1,X2) = X2
| esk323_0 = esk325_0
| ~ in(X2,esk326_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2008]),
[final] ).
cnf(i_0_4481,plain,
( esk327_2(X1,X2) = X2
| esk323_0 = esk324_0
| ~ in(X2,esk326_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2008]),
[final] ).
cnf(i_0_4482,plain,
~ empty(unordered_pair(X1,X1)),
inference(rw,[status(thm)],[i_0_2094,c_0_681]),
[final] ).
cnf(i_0_4483,plain,
~ empty(unordered_pair(X1,X1)),
inference(rw,[status(thm)],[i_0_2095,c_0_681]),
[final] ).
cnf(i_0_4484,plain,
~ empty(unordered_pair(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2096]),
[final] ).
cnf(i_0_4485,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2097]),
[final] ).
cnf(i_0_4486,plain,
( well_ordering(X1)
| ~ reflexive(X1)
| ~ transitive(X1)
| ~ antisymmetric(X1)
| ~ connected(X1)
| ~ well_founded_relation(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2098]),
[final] ).
cnf(i_0_4487,lemma,
( subset(relation_rng_restriction(X2,X1),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2099]),
[final] ).
cnf(i_0_4488,lemma,
( subset(relation_dom_restriction(X1,X2),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2100]),
[final] ).
cnf(i_0_4489,plain,
( being_limit_ordinal(esk91_1(X1))
| X1 = omega
| ~ in(empty_set,X1)
| ~ being_limit_ordinal(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2021]),
[final] ).
cnf(i_0_4490,plain,
( ordinal(esk91_1(X1))
| X1 = omega
| ~ in(empty_set,X1)
| ~ being_limit_ordinal(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2021]),
[final] ).
cnf(i_0_4491,plain,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2101]),
[final] ).
cnf(i_0_4492,lemma,
( in(X1,X2)
| ~ in(X1,esk370_1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2090]),
[final] ).
cnf(i_0_4493,lemma,
( X1 = X2
| unordered_pair(X1,X1) != unordered_pair(X2,X3) ),
inference(rw,[status(thm)],[i_0_2102,c_0_681]),
[final] ).
cnf(i_0_4494,lemma,
( X2 = X3
| unordered_pair(X1,X1) != unordered_pair(X2,X3) ),
inference(rw,[status(thm)],[i_0_2103,c_0_681]),
[final] ).
cnf(i_0_4495,plain,
( epsilon_connected(X1)
| ~ in(esk71_1(X1),esk70_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1985]),
[final] ).
cnf(i_0_4496,plain,
( epsilon_connected(X1)
| ~ in(esk70_1(X1),esk71_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1985]),
[final] ).
cnf(i_0_4497,plain,
( element(cast_as_carrier_subset(X1),powerset(the_carrier(X1)))
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2104]),
[final] ).
cnf(i_0_4498,plain,
( element(empty_carrier_subset(X1),powerset(the_carrier(X1)))
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2105]),
[final] ).
cnf(i_0_4499,plain,
( X1 = empty_set
| ~ subset(X1,X2)
| ~ finite(X1)
| set_meet(X1) != empty_set
| ~ centered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2106]),
[final] ).
cnf(i_0_4500,lemma,
( in(X1,X2)
| X1 = X2
| in(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2107]),
[final] ).
cnf(i_0_4501,plain,
( in(esk102_1(X1),relation_dom(X1))
| one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1828]),
[final] ).
cnf(i_0_4502,plain,
( in(esk101_1(X1),relation_dom(X1))
| one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1828]),
[final] ).
cnf(i_0_4503,plain,
( v2_binop_1(the_L_meet(X1),the_carrier(X1))
| empty_carrier(X1)
| ~ meet_associative(X1)
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1814]),
[final] ).
cnf(i_0_4504,plain,
( v2_binop_1(the_L_join(X1),the_carrier(X1))
| empty_carrier(X1)
| ~ join_associative(X1)
| ~ join_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1816]),
[final] ).
cnf(i_0_4505,plain,
( v1_binop_1(the_L_meet(X1),the_carrier(X1))
| empty_carrier(X1)
| ~ meet_commutative(X1)
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1815]),
[final] ).
cnf(i_0_4506,plain,
( v1_binop_1(the_L_join(X1),the_carrier(X1))
| empty_carrier(X1)
| ~ join_commutative(X1)
| ~ join_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1817]),
[final] ).
cnf(i_0_4507,plain,
( element(esk11_1(X1),the_carrier(X1))
| empty_carrier(X1)
| ~ lower_bounded_semilattstr(X1)
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1600]),
[final] ).
cnf(i_0_4508,plain,
( subset(X1,X3)
| ~ in(X1,X2)
| X2 != powerset(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1831]),
[final] ).
cnf(i_0_4509,plain,
( in(X1,X3)
| ~ subset(X1,X2)
| X3 != powerset(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1831]),
[final] ).
cnf(i_0_4510,lemma,
( ~ subset(X1,X2)
| ~ proper_subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2108]),
[final] ).
cnf(i_0_4511,plain,
( ~ proper_subset(X1,X2)
| ~ proper_subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2109]),
[final] ).
cnf(i_0_4512,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2110]),
[final] ).
cnf(i_0_4513,lemma,
( relation_dom(esk387_1(X1)) = X1
| in(esk386_1(X1),X1)
| esk384_1(X1) != esk385_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_828]),
[final] ).
cnf(i_0_4514,plain,
( relation_empty_yielding(relation_dom_restriction(X1,X2))
| ~ relation(X1)
| ~ relation_empty_yielding(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2111]),
[final] ).
cnf(i_0_4515,lemma,
( well_ordering(relation_restriction(X1,X2))
| ~ relation(X1)
| ~ well_ordering(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2112]),
[final] ).
cnf(i_0_4516,lemma,
( well_founded_relation(relation_restriction(X1,X2))
| ~ relation(X1)
| ~ well_founded_relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2113]),
[final] ).
cnf(i_0_4517,lemma,
( connected(relation_restriction(X1,X2))
| ~ relation(X1)
| ~ connected(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2114]),
[final] ).
cnf(i_0_4518,lemma,
( antisymmetric(relation_restriction(X1,X2))
| ~ relation(X1)
| ~ antisymmetric(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2115]),
[final] ).
cnf(i_0_4519,lemma,
( reflexive(relation_restriction(X1,X2))
| ~ relation(X1)
| ~ reflexive(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2116]),
[final] ).
cnf(i_0_4520,lemma,
( transitive(relation_restriction(X1,X2))
| ~ relation(X1)
| ~ transitive(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2117]),
[final] ).
cnf(i_0_4521,plain,
( relation(relation_composition(X1,X2))
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2118]),
[final] ).
cnf(i_0_4522,plain,
( relation(relation_composition(X1,X2))
| ~ empty(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2119]),
[final] ).
cnf(i_0_4523,plain,
( relation(relation_composition(X1,X2))
| ~ empty(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2120]),
[final] ).
cnf(i_0_4524,plain,
( relation(set_difference(X1,X2))
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2121]),
[final] ).
cnf(i_0_4525,plain,
( relation(relation_rng_restriction(X1,X2))
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2122]),
[final] ).
cnf(i_0_4526,plain,
( relation(relation_dom_restriction(X1,X2))
| ~ relation(X1)
| ~ relation_empty_yielding(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2111]),
[final] ).
cnf(i_0_4527,plain,
( relation(relation_dom_restriction(X1,X2))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2123]),
[final] ).
cnf(i_0_4528,plain,
( relation(set_union2(X1,X2))
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2124]),
[final] ).
cnf(i_0_4529,plain,
( function(relation_rng_restriction(X1,X2))
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2122]),
[final] ).
cnf(i_0_4530,plain,
( function(relation_dom_restriction(X1,X2))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2123]),
[final] ).
cnf(i_0_4531,plain,
( finite(set_union2(X1,X2))
| ~ finite(X1)
| ~ finite(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2125]),
[final] ).
cnf(i_0_4532,plain,
( empty(relation_composition(X1,X2))
| ~ empty(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2119]),
[final] ).
cnf(i_0_4533,plain,
( empty(relation_composition(X1,X2))
| ~ empty(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2120]),
[final] ).
cnf(i_0_4534,plain,
( ordinal(esk447_0)
| subset(X1,esk446_1(X1))
| epred1_0
| ~ in(X1,esk445_0) ),
inference(split_conjunct,[status(thm)],[i_0_760]),
[final] ).
cnf(i_0_4535,plain,
( is_well_founded_in(X1,X2)
| ~ well_orders(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1818]),
[final] ).
cnf(i_0_4536,plain,
( is_reflexive_in(X1,X2)
| ~ well_orders(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1818]),
[final] ).
cnf(i_0_4537,plain,
( is_transitive_in(X1,X2)
| ~ well_orders(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1818]),
[final] ).
cnf(i_0_4538,plain,
( is_connected_in(X1,X2)
| ~ well_orders(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1818]),
[final] ).
cnf(i_0_4539,plain,
( is_antisymmetric_in(X1,X2)
| ~ well_orders(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1818]),
[final] ).
cnf(i_0_4540,plain,
( subset(X2,X1)
| ~ epsilon_transitive(X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2126]),
[final] ).
cnf(i_0_4541,plain,
( is_well_founded_in(X1,X2)
| esk76_2(X1,X2) != empty_set
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1596]),
[final] ).
cnf(i_0_4542,lemma,
( relation(esk387_1(X1))
| in(esk386_1(X1),X1)
| esk384_1(X1) != esk385_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_828]),
[final] ).
cnf(i_0_4543,lemma,
( function(esk387_1(X1))
| in(esk386_1(X1),X1)
| esk384_1(X1) != esk385_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_828]),
[final] ).
cnf(i_0_4544,lemma,
( closed_subsets(esk410_1(X1),X1)
| compact_top_space(X1)
| empty_carrier(X1)
| ~ topological_space(X1)
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1765]),
[final] ).
cnf(i_0_4545,lemma,
( well_ordering(X1)
| ~ well_orders(X1,relation_field(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2127]),
[final] ).
cnf(i_0_4546,lemma,
( well_founded_relation(X1)
| ~ is_well_founded_in(X1,relation_field(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2128]),
[final] ).
cnf(i_0_4547,plain,
( connected(X1)
| ~ is_connected_in(X1,relation_field(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2129]),
[final] ).
cnf(i_0_4548,plain,
( antisymmetric(X1)
| ~ is_antisymmetric_in(X1,relation_field(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2130]),
[final] ).
cnf(i_0_4549,plain,
( reflexive(X1)
| ~ is_reflexive_in(X1,relation_field(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2131]),
[final] ).
cnf(i_0_4550,plain,
( transitive(X1)
| ~ is_transitive_in(X1,relation_field(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2132]),
[final] ).
cnf(i_0_4551,plain,
( finite(X2)
| ~ finite(X1)
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2133]),
[final] ).
cnf(i_0_4552,plain,
( v5_membered(X1)
| ~ element(X1,powerset(X2))
| ~ v5_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2134]),
[final] ).
cnf(i_0_4553,plain,
( v4_membered(X1)
| ~ element(X1,powerset(X2))
| ~ v5_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2134]),
[final] ).
cnf(i_0_4554,plain,
( v4_membered(X1)
| ~ element(X1,powerset(X2))
| ~ v4_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2135]),
[final] ).
cnf(i_0_4555,plain,
( v3_membered(X1)
| ~ element(X1,powerset(X2))
| ~ v5_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2134]),
[final] ).
cnf(i_0_4556,plain,
( v3_membered(X1)
| ~ element(X1,powerset(X2))
| ~ v4_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2135]),
[final] ).
cnf(i_0_4557,plain,
( v3_membered(X1)
| ~ element(X1,powerset(X2))
| ~ v3_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2136]),
[final] ).
cnf(i_0_4558,plain,
( v2_membered(X1)
| ~ element(X1,powerset(X2))
| ~ v5_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2134]),
[final] ).
cnf(i_0_4559,plain,
( v2_membered(X1)
| ~ element(X1,powerset(X2))
| ~ v4_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2135]),
[final] ).
cnf(i_0_4560,plain,
( v2_membered(X1)
| ~ element(X1,powerset(X2))
| ~ v3_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2136]),
[final] ).
cnf(i_0_4561,plain,
( v2_membered(X1)
| ~ element(X1,powerset(X2))
| ~ v2_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2137]),
[final] ).
cnf(i_0_4562,plain,
( v1_membered(X1)
| ~ element(X1,powerset(X2))
| ~ v5_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2134]),
[final] ).
cnf(i_0_4563,plain,
( v1_membered(X1)
| ~ element(X1,powerset(X2))
| ~ v4_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2135]),
[final] ).
cnf(i_0_4564,plain,
( v1_membered(X1)
| ~ element(X1,powerset(X2))
| ~ v3_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2136]),
[final] ).
cnf(i_0_4565,plain,
( v1_membered(X1)
| ~ element(X1,powerset(X2))
| ~ v2_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2137]),
[final] ).
cnf(i_0_4566,plain,
( v1_membered(X2)
| ~ v1_membered(X1)
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2138]),
[final] ).
cnf(i_0_4567,lemma,
( apply(identity_relation(X2),X1) = X1
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2139]),
[final] ).
cnf(i_0_4568,plain,
( ordinal_subset(X1,X2)
| ordinal_subset(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2140]),
[final] ).
cnf(i_0_4569,lemma,
( subset(X1,union(X2))
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2141]),
[final] ).
cnf(i_0_4570,lemma,
( subset(X1,union(X2))
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2142]),
[final] ).
cnf(i_0_4571,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2101]),
[final] ).
cnf(i_0_4572,plain,
( ordinal(esk447_0)
| in(esk446_1(X1),esk445_0)
| epred1_0
| ~ in(X1,esk445_0) ),
inference(split_conjunct,[status(thm)],[i_0_760]),
[final] ).
cnf(i_0_4573,plain,
( element(esk105_1(X1),the_carrier(X1))
| meet_absorbing(X1)
| empty_carrier(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1578]),
[final] ).
cnf(i_0_4574,plain,
( element(esk104_1(X1),the_carrier(X1))
| meet_absorbing(X1)
| empty_carrier(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1578]),
[final] ).
cnf(i_0_4575,lemma,
( bottom_of_semilattstr(X1) = join_of_latt_set(X1,empty_set)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ complete_latt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2143]),
[final] ).
cnf(i_0_4576,plain,
( subset(X1,esk450_1(X1))
| epred1_0
| ~ in(X1,esk449_0)
| esk445_0 != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_760]),
[final] ).
cnf(i_0_4577,plain,
( subset(X1,esk446_1(X1))
| epred1_0
| esk449_0 != empty_set
| ~ in(X1,esk445_0) ),
inference(split_conjunct,[status(thm)],[i_0_760]),
[final] ).
cnf(i_0_4578,lemma,
( subset(X1,unordered_pair(X2,X2))
| X1 != empty_set ),
inference(rw,[status(thm)],[i_0_2144,c_0_681]),
[final] ).
cnf(i_0_4579,lemma,
( subset(X1,unordered_pair(X2,X2))
| X1 != empty_set ),
inference(rw,[status(thm)],[i_0_2145,c_0_681]),
[final] ).
cnf(i_0_4580,plain,
( X1 = union(X2)
| proper_element(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2074]),
[final] ).
cnf(i_0_4581,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X2,X2) ),
inference(rw,[status(thm)],[i_0_2146,c_0_681]),
[final] ).
cnf(i_0_4582,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1617]),
[final] ).
cnf(i_0_4583,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1617]),
[final] ).
cnf(i_0_4584,plain,
~ proper_element(esk160_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_2147]),
[final] ).
cnf(i_0_4585,lemma,
( finite(relation_rng(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ finite(relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2148]),
[final] ).
cnf(i_0_4586,plain,
( X1 = rel_str_of(the_carrier(X1),the_InternalRel(X1))
| ~ rel_str(X1)
| ~ strict_rel_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2149]),
[final] ).
cnf(i_0_4587,plain,
( element(X1,X2)
| empty(X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2150]),
[final] ).
cnf(i_0_4588,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2151]),
[final] ).
cnf(i_0_4589,plain,
( in(X1,X2)
| empty(X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2150]),
[final] ).
cnf(i_0_4590,lemma,
( relation_dom_restriction(X1,X2) = relation_composition(identity_relation(X2),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2152]),
[final] ).
cnf(i_0_4591,plain,
( in(esk450_1(X1),esk449_0)
| epred1_0
| ~ in(X1,esk449_0)
| esk445_0 != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_760]),
[final] ).
cnf(i_0_4592,plain,
( in(esk446_1(X1),esk445_0)
| epred1_0
| esk449_0 != empty_set
| ~ in(X1,esk445_0) ),
inference(split_conjunct,[status(thm)],[i_0_760]),
[final] ).
cnf(i_0_4593,lemma,
( esk187_1(X1) = unordered_pair(esk185_1(X1),esk185_1(X1))
| relation(esk188_1(X1)) ),
inference(rw,[status(thm)],[i_0_2153,c_0_681]),
[final] ).
cnf(i_0_4594,lemma,
( esk187_1(X1) = unordered_pair(esk185_1(X1),esk185_1(X1))
| function(esk188_1(X1)) ),
inference(rw,[status(thm)],[i_0_2154,c_0_681]),
[final] ).
cnf(i_0_4595,lemma,
( esk186_1(X1) = unordered_pair(esk185_1(X1),esk185_1(X1))
| relation(esk188_1(X1)) ),
inference(rw,[status(thm)],[i_0_2155,c_0_681]),
[final] ).
cnf(i_0_4596,lemma,
( esk186_1(X1) = unordered_pair(esk185_1(X1),esk185_1(X1))
| function(esk188_1(X1)) ),
inference(rw,[status(thm)],[i_0_2156,c_0_681]),
[final] ).
cnf(i_0_4597,plain,
set_difference(X1,set_difference(X1,X1)) = X1,
inference(rw,[status(thm)],[i_0_2157,c_0_1442]),
[final] ).
cnf(i_0_4598,plain,
( is_transitive_in(the_InternalRel(X1),the_carrier(X1))
| ~ transitive_relstr(X1)
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2077]),
[final] ).
cnf(i_0_4599,plain,
( is_antisymmetric_in(the_InternalRel(X1),the_carrier(X1))
| ~ antisymmetric_relstr(X1)
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2076]),
[final] ).
cnf(i_0_4600,plain,
( in(the_carrier(X1),the_topology(X1))
| ~ topological_space(X1)
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1520]),
[final] ).
cnf(i_0_4601,plain,
( in(empty_set,omega)
| epred1_0
| esk450_1(X1) != X1
| ~ in(X1,esk449_0) ),
inference(split_conjunct,[status(thm)],[i_0_760]),
[final] ).
cnf(i_0_4602,lemma,
( ordinal(esk199_1(X1))
| ~ ordinal(X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1991]),
[final] ).
cnf(i_0_4603,lemma,
subset(set_difference(X1,X2),X1),
inference(split_conjunct,[status(thm)],[i_0_2158]),
[final] ).
cnf(i_0_4604,lemma,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2159]),
[final] ).
cnf(i_0_4605,plain,
( ordinal(X1)
| ordinal(esk325_0)
| ~ in(X1,esk326_1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2008]),
[final] ).
cnf(i_0_4606,plain,
( ordinal(X1)
| ordinal(esk324_0)
| ~ in(X1,esk326_1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2008]),
[final] ).
cnf(i_0_4607,plain,
( closed_subset(esk175_1(X1),X1)
| empty_carrier(X1)
| ~ topological_space(X1)
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2064]),
[final] ).
cnf(i_0_4608,plain,
( X1 = X2
| proper_subset(X1,X2)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2160]),
[final] ).
cnf(i_0_4609,plain,
( antisymmetric(the_InternalRel(X1))
| ~ reflexive_relstr(X1)
| ~ transitive_relstr(X1)
| ~ antisymmetric_relstr(X1)
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1891]),
[final] ).
cnf(i_0_4610,plain,
( reflexive(the_InternalRel(X1))
| ~ reflexive_relstr(X1)
| ~ transitive_relstr(X1)
| ~ antisymmetric_relstr(X1)
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1891]),
[final] ).
cnf(i_0_4611,plain,
( transitive(the_InternalRel(X1))
| ~ reflexive_relstr(X1)
| ~ transitive_relstr(X1)
| ~ antisymmetric_relstr(X1)
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1891]),
[final] ).
cnf(i_0_4612,plain,
( relation(the_InternalRel(X1))
| ~ reflexive_relstr(X1)
| ~ transitive_relstr(X1)
| ~ antisymmetric_relstr(X1)
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1891]),
[final] ).
cnf(i_0_4613,plain,
element(powerset(X1),powerset(powerset(X1))),
inference(rw,[status(thm)],[i_0_2161,c_0_2162]),
[final] ).
cnf(i_0_4614,plain,
( subset(esk61_1(X1),relation_field(X1))
| well_founded_relation(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1807]),
[final] ).
cnf(i_0_4615,lemma,
( in(esk137_1(X1),relation_field(X1))
| connected(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_750]),
[final] ).
cnf(i_0_4616,lemma,
( in(esk136_1(X1),relation_field(X1))
| connected(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_750]),
[final] ).
cnf(i_0_4617,lemma,
( in(esk129_1(X1),relation_field(X1))
| reflexive(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_751]),
[final] ).
cnf(i_0_4618,plain,
( empty_carrier(X1)
| element(bottom_of_semilattstr(X1),the_carrier(X1))
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2163]),
[final] ).
cnf(i_0_4619,plain,
( in(relation_dom(esk26_1(X1)),omega)
| ~ finite(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2065]),
[final] ).
cnf(i_0_4620,lemma,
( disjoint(X1,X2)
| set_difference(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[i_0_2164]),
[final] ).
cnf(i_0_4621,plain,
( ordinal(X1)
| ~ in(X1,esk326_1(X2))
| esk324_0 != esk325_0 ),
inference(split_conjunct,[status(thm)],[i_0_2008]),
[final] ).
cnf(i_0_4622,lemma,
( set_difference(X1,X2) = X1
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2164]),
[final] ).
cnf(i_0_4623,lemma,
( set_union2(X1,X2) = X2
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2165]),
[final] ).
cnf(i_0_4624,plain,
( ordinal(X1)
| esk323_0 = esk325_0
| ~ in(X1,esk326_1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2008]),
[final] ).
cnf(i_0_4625,plain,
( ordinal(X1)
| esk323_0 = esk324_0
| ~ in(X1,esk326_1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2008]),
[final] ).
cnf(i_0_4626,plain,
( relation_field(X1) = set_union2(relation_dom(X1),relation_rng(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2166]),
[final] ).
cnf(i_0_4627,plain,
( relation(relation_restriction(X1,X2))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2167]),
[final] ).
cnf(i_0_4628,plain,
( relation(relation_rng_restriction(X2,X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2168]),
[final] ).
cnf(i_0_4629,plain,
( relation(relation_dom_restriction(X1,X2))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2169]),
[final] ).
cnf(i_0_4630,plain,
( finite(set_difference(X1,X2))
| ~ finite(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2170]),
[final] ).
cnf(i_0_4631,plain,
( v5_membered(set_difference(X1,X2))
| ~ v5_membered(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2171]),
[final] ).
cnf(i_0_4632,plain,
( v4_membered(set_difference(X1,X2))
| ~ v5_membered(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2171]),
[final] ).
cnf(i_0_4633,plain,
( v4_membered(set_difference(X1,X2))
| ~ v4_membered(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2172]),
[final] ).
cnf(i_0_4634,plain,
( v3_membered(set_difference(X1,X2))
| ~ v5_membered(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2171]),
[final] ).
cnf(i_0_4635,plain,
( v3_membered(set_difference(X1,X2))
| ~ v4_membered(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2172]),
[final] ).
cnf(i_0_4636,plain,
( v3_membered(set_difference(X1,X2))
| ~ v3_membered(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2173]),
[final] ).
cnf(i_0_4637,plain,
( v2_membered(set_difference(X1,X2))
| ~ v5_membered(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2171]),
[final] ).
cnf(i_0_4638,plain,
( v2_membered(set_difference(X1,X2))
| ~ v4_membered(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2172]),
[final] ).
cnf(i_0_4639,plain,
( v2_membered(set_difference(X1,X2))
| ~ v3_membered(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2173]),
[final] ).
cnf(i_0_4640,plain,
( v2_membered(set_difference(X1,X2))
| ~ v2_membered(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2174]),
[final] ).
cnf(i_0_4641,plain,
( v1_membered(set_difference(X1,X2))
| ~ v5_membered(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2171]),
[final] ).
cnf(i_0_4642,plain,
( v1_membered(set_difference(X1,X2))
| ~ v4_membered(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2172]),
[final] ).
cnf(i_0_4643,plain,
( v1_membered(set_difference(X1,X2))
| ~ v3_membered(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2173]),
[final] ).
cnf(i_0_4644,plain,
( v1_membered(set_difference(X1,X2))
| ~ v2_membered(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2174]),
[final] ).
cnf(i_0_4645,plain,
( v1_membered(set_difference(X1,X2))
| ~ v1_membered(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2175]),
[final] ).
cnf(i_0_4646,plain,
set_difference(X1,set_difference(X1,empty_set)) = empty_set,
inference(rw,[status(thm)],[i_0_2176,c_0_1442]),
[final] ).
cnf(i_0_4647,plain,
( are_equipotent(X1,X2)
| ~ equipotent(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2177]),
[final] ).
cnf(i_0_4648,plain,
( equipotent(X1,X2)
| ~ are_equipotent(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2177]),
[final] ).
cnf(i_0_4649,plain,
( equipotent(X2,X1)
| ~ equipotent(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2178]),
[final] ).
cnf(i_0_4650,plain,
( disjoint(X2,X1)
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2179]),
[final] ).
cnf(i_0_4651,plain,
( subset(X1,X2)
| ~ proper_subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2160]),
[final] ).
cnf(i_0_4652,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2180]),
[final] ).
cnf(i_0_4653,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_2181]),
[final] ).
cnf(i_0_4654,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_2182]),
[final] ).
cnf(i_0_4655,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2181]),
[final] ).
cnf(i_0_4656,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2182]),
[final] ).
cnf(i_0_4657,plain,
( epsilon_transitive(X1)
| ~ subset(esk55_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[i_0_2126]),
[final] ).
cnf(i_0_4658,lemma,
( ordinal(X1)
| ~ in(X1,esk370_1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2090]),
[final] ).
cnf(i_0_4659,lemma,
( relation_dom(esk420_1(X1)) = X1
| in(esk419_1(X1),X1)
| empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1896]),
[final] ).
cnf(i_0_4660,lemma,
( relation_rng(X1) = relation_dom(function_inverse(X1))
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2183]),
[final] ).
cnf(i_0_4661,lemma,
( relation_dom(X1) = relation_rng(function_inverse(X1))
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2183]),
[final] ).
cnf(i_0_4662,lemma,
( relation(esk420_1(X1))
| in(esk419_1(X1),X1)
| empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1896]),
[final] ).
cnf(i_0_4663,lemma,
( function(esk420_1(X1))
| in(esk419_1(X1),X1)
| empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1896]),
[final] ).
cnf(i_0_4664,plain,
( empty_carrier(X1)
| ~ empty(esk175_1(X1))
| ~ topological_space(X1)
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2064]),
[final] ).
cnf(i_0_4665,plain,
( empty_carrier(X1)
| ~ empty_carrier(poset_of_lattice(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2184]),
[final] ).
cnf(i_0_4666,plain,
( closed_subset(esk174_1(X1),X1)
| ~ topological_space(X1)
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2080]),
[final] ).
cnf(i_0_4667,plain,
( closed_subset(esk161_1(X1),X1)
| ~ topological_space(X1)
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2081]),
[final] ).
cnf(i_0_4668,plain,
( closed_subset(cast_as_carrier_subset(X1),X1)
| ~ topological_space(X1)
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2185]),
[final] ).
cnf(i_0_4669,plain,
( open_subset(esk161_1(X1),X1)
| ~ topological_space(X1)
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2081]),
[final] ).
cnf(i_0_4670,plain,
( open_subset(esk150_1(X1),X1)
| ~ topological_space(X1)
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2082]),
[final] ).
cnf(i_0_4671,lemma,
( well_orders(X1,relation_field(X1))
| ~ well_ordering(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2127]),
[final] ).
cnf(i_0_4672,lemma,
( is_well_founded_in(X1,relation_field(X1))
| ~ well_founded_relation(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2128]),
[final] ).
cnf(i_0_4673,plain,
( is_reflexive_in(X1,relation_field(X1))
| ~ reflexive(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2131]),
[final] ).
cnf(i_0_4674,plain,
( is_transitive_in(X1,relation_field(X1))
| ~ transitive(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2132]),
[final] ).
cnf(i_0_4675,plain,
( is_connected_in(X1,relation_field(X1))
| ~ connected(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2129]),
[final] ).
cnf(i_0_4676,plain,
( is_antisymmetric_in(X1,relation_field(X1))
| ~ antisymmetric(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2130]),
[final] ).
cnf(i_0_4677,plain,
( well_founded_relation(X2)
| ~ well_founded_relation(X1)
| ~ epred3_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2186]),
[final] ).
cnf(i_0_4678,plain,
( connected(X2)
| ~ connected(X1)
| ~ epred3_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2186]),
[final] ).
cnf(i_0_4679,plain,
( antisymmetric(X2)
| ~ antisymmetric(X1)
| ~ epred3_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2186]),
[final] ).
cnf(i_0_4680,plain,
( reflexive(X2)
| ~ reflexive(X1)
| ~ epred3_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2186]),
[final] ).
cnf(i_0_4681,plain,
( transitive(X2)
| ~ transitive(X1)
| ~ epred3_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2186]),
[final] ).
cnf(i_0_4682,lemma,
( finite(X1)
| ~ subset(X1,X2)
| ~ finite(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2187]),
[final] ).
cnf(i_0_4683,plain,
( epsilon_connected(X1)
| ~ element(X1,X2)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2188]),
[final] ).
cnf(i_0_4684,plain,
( epsilon_transitive(X1)
| ~ element(X1,X2)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2188]),
[final] ).
cnf(i_0_4685,plain,
( ordinal(X1)
| ~ element(X1,X2)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2188]),
[final] ).
cnf(i_0_4686,lemma,
( ordinal(X2)
| ~ ordinal(X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2189]),
[final] ).
cnf(i_0_4687,plain,
( empty(X1)
| ~ element(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2150]),
[final] ).
cnf(i_0_4688,plain,
( natural(X1)
| ~ element(X1,X2)
| ~ v5_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2190]),
[final] ).
cnf(i_0_4689,plain,
( v1_int_1(X1)
| ~ element(X1,X2)
| ~ v5_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2190]),
[final] ).
cnf(i_0_4690,plain,
( v1_int_1(X1)
| ~ element(X1,X2)
| ~ v4_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2191]),
[final] ).
cnf(i_0_4691,plain,
( v1_rat_1(X1)
| ~ element(X1,X2)
| ~ v5_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2190]),
[final] ).
cnf(i_0_4692,plain,
( v1_rat_1(X1)
| ~ element(X1,X2)
| ~ v4_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2191]),
[final] ).
cnf(i_0_4693,plain,
( v1_rat_1(X1)
| ~ element(X1,X2)
| ~ v3_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2192]),
[final] ).
cnf(i_0_4694,plain,
( v1_xreal_0(X1)
| ~ element(X1,X2)
| ~ v5_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2190]),
[final] ).
cnf(i_0_4695,plain,
( v1_xreal_0(X1)
| ~ element(X1,X2)
| ~ v4_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2191]),
[final] ).
cnf(i_0_4696,plain,
( v1_xreal_0(X1)
| ~ element(X1,X2)
| ~ v3_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2192]),
[final] ).
cnf(i_0_4697,plain,
( v1_xreal_0(X1)
| ~ element(X1,X2)
| ~ v2_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2193]),
[final] ).
cnf(i_0_4698,plain,
( v1_xcmplx_0(X1)
| ~ element(X1,X2)
| ~ v5_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2190]),
[final] ).
cnf(i_0_4699,plain,
( v1_xcmplx_0(X1)
| ~ element(X1,X2)
| ~ v4_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2191]),
[final] ).
cnf(i_0_4700,plain,
( v1_xcmplx_0(X1)
| ~ element(X1,X2)
| ~ v3_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2192]),
[final] ).
cnf(i_0_4701,plain,
( v1_xcmplx_0(X1)
| ~ element(X1,X2)
| ~ v2_membered(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2193]),
[final] ).
cnf(i_0_4702,plain,
( v1_xcmplx_0(X2)
| ~ v1_membered(X1)
| ~ element(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2194]),
[final] ).
cnf(i_0_4703,lemma,
( centered(esk410_1(X1))
| compact_top_space(X1)
| empty_carrier(X1)
| ~ topological_space(X1)
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1765]),
[final] ).
cnf(i_0_4704,plain,
( ordinal(esk447_0)
| epred1_0
| esk446_1(X1) != X1
| ~ in(X1,esk445_0) ),
inference(split_conjunct,[status(thm)],[i_0_760]),
[final] ).
cnf(i_0_4705,lemma,
( in(esk427_1(X1),X1)
| being_limit_ordinal(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_777]),
[final] ).
cnf(i_0_4706,plain,
( open_subsets(esk69_1(X1),X1)
| compact_top_space(X1)
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1703]),
[final] ).
cnf(i_0_4707,plain,
( is_a_cover_of_carrier(X1,esk69_1(X1))
| compact_top_space(X1)
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1703]),
[final] ).
cnf(i_0_4708,lemma,
( one_to_one(function_inverse(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ one_to_one(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2195]),
[final] ).
cnf(i_0_4709,plain,
( relation(relation_inverse(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ one_to_one(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2196]),
[final] ).
cnf(i_0_4710,plain,
( function(relation_inverse(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ one_to_one(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2196]),
[final] ).
cnf(i_0_4711,plain,
( one_to_one(X1)
| esk101_1(X1) != esk102_1(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1828]),
[final] ).
cnf(i_0_4712,lemma,
( relation_image(X1,relation_dom(X1)) = relation_rng(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2197]),
[final] ).
cnf(i_0_4713,lemma,
( relation(esk188_1(X1))
| in(esk185_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[i_0_768]),
[final] ).
cnf(i_0_4714,lemma,
( relation(esk188_1(X1))
| in(esk185_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[i_0_768]),
[final] ).
cnf(i_0_4715,lemma,
( function(esk188_1(X1))
| in(esk185_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[i_0_768]),
[final] ).
cnf(i_0_4716,lemma,
( function(esk188_1(X1))
| in(esk185_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[i_0_768]),
[final] ).
cnf(i_0_4717,plain,
( element(esk170_1(X1),powerset(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2198]),
[final] ).
cnf(i_0_4718,plain,
( element(esk163_1(X1),powerset(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2199]),
[final] ).
cnf(i_0_4719,plain,
( element(esk149_1(X1),powerset(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2200]),
[final] ).
cnf(i_0_4720,plain,
( the_carrier(X1) = powerset(X2)
| X1 != boole_lattice(X2)
| ~ strict_latt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1407]),
[final] ).
cnf(i_0_4721,lemma,
( lower_bounded_semilattstr(X1)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ complete_latt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2143]),
[final] ).
cnf(i_0_4722,plain,
( epred1_0
| esk449_0 != empty_set
| esk446_1(X1) != X1
| ~ in(X1,esk445_0) ),
inference(split_conjunct,[status(thm)],[i_0_760]),
[final] ).
cnf(i_0_4723,plain,
( epred1_0
| esk450_1(X1) != X1
| ~ in(X1,esk449_0)
| esk445_0 != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_760]),
[final] ).
cnf(i_0_4724,plain,
relation(esk157_2(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1989]),
[final] ).
cnf(i_0_4725,plain,
relation(esk142_2(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1988]),
[final] ).
cnf(i_0_4726,plain,
function(esk157_2(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1989]),
[final] ).
cnf(i_0_4727,plain,
function(esk142_2(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1988]),
[final] ).
cnf(i_0_4728,plain,
finite(unordered_pair(X1,X1)),
inference(rw,[status(thm)],[i_0_2201,c_0_681]),
[final] ).
cnf(i_0_4729,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2202]),
[final] ).
cnf(i_0_4730,plain,
( function_inverse(X1) = relation_inverse(X1)
| ~ relation(X1)
| ~ function(X1)
| ~ one_to_one(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2203]),
[final] ).
cnf(i_0_4731,plain,
( reflexive_relstr(poset_of_lattice(X1))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2184]),
[final] ).
cnf(i_0_4732,plain,
( reflexive_relstr(poset_of_lattice(X1))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2204]),
[final] ).
cnf(i_0_4733,plain,
( antisymmetric_relstr(poset_of_lattice(X1))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2184]),
[final] ).
cnf(i_0_4734,plain,
( antisymmetric_relstr(poset_of_lattice(X1))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2204]),
[final] ).
cnf(i_0_4735,plain,
( transitive_relstr(poset_of_lattice(X1))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2184]),
[final] ).
cnf(i_0_4736,plain,
( transitive_relstr(poset_of_lattice(X1))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2204]),
[final] ).
cnf(i_0_4737,plain,
( antisymmetric(k2_lattice3(X1))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1918]),
[final] ).
cnf(i_0_4738,plain,
( reflexive(k2_lattice3(X1))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1918]),
[final] ).
cnf(i_0_4739,plain,
( transitive(k2_lattice3(X1))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1918]),
[final] ).
cnf(i_0_4740,plain,
( empty_carrier(X1)
| relation(relation_of_lattice(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2205]),
[final] ).
cnf(i_0_4741,plain,
( relation(the_L_meet(X1))
| empty_carrier(X1)
| ~ meet_associative(X1)
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1814]),
[final] ).
cnf(i_0_4742,plain,
( relation(the_L_meet(X1))
| empty_carrier(X1)
| ~ meet_commutative(X1)
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1815]),
[final] ).
cnf(i_0_4743,plain,
( relation(the_L_join(X1))
| empty_carrier(X1)
| ~ join_associative(X1)
| ~ join_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1816]),
[final] ).
cnf(i_0_4744,plain,
( relation(the_L_join(X1))
| empty_carrier(X1)
| ~ join_commutative(X1)
| ~ join_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1817]),
[final] ).
cnf(i_0_4745,plain,
( function(the_L_meet(X1))
| empty_carrier(X1)
| ~ meet_associative(X1)
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1814]),
[final] ).
cnf(i_0_4746,plain,
( function(the_L_meet(X1))
| empty_carrier(X1)
| ~ meet_commutative(X1)
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1815]),
[final] ).
cnf(i_0_4747,plain,
( function(the_L_join(X1))
| empty_carrier(X1)
| ~ join_associative(X1)
| ~ join_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1816]),
[final] ).
cnf(i_0_4748,plain,
( function(the_L_join(X1))
| empty_carrier(X1)
| ~ join_commutative(X1)
| ~ join_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1817]),
[final] ).
cnf(i_0_4749,plain,
( strict_rel_str(poset_of_lattice(X1))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2184]),
[final] ).
cnf(i_0_4750,plain,
( strict_rel_str(poset_of_lattice(X1))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2204]),
[final] ).
cnf(i_0_4751,plain,
( rel_str(poset_of_lattice(X1))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2204]),
[final] ).
cnf(i_0_4752,plain,
( ordinal(esk447_0)
| element(esk445_0,powerset(powerset(empty_set)))
| epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_760]),
[final] ).
cnf(i_0_4753,plain,
( ordinal_subset(X1,X1)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2206]),
[final] ).
cnf(i_0_4754,plain,
( element(X1,X2)
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2150]),
[final] ).
cnf(i_0_4755,plain,
( empty_carrier(X1)
| ~ empty(esk172_1(X1))
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2089]),
[final] ).
cnf(i_0_4756,plain,
( empty_carrier(X1)
| ~ one_sorted_str(X1)
| ~ empty(cast_as_carrier_subset(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2207]),
[final] ).
cnf(i_0_4757,plain,
( empty_carrier(X1)
| ~ one_sorted_str(X1)
| ~ empty(the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2208]),
[final] ).
cnf(i_0_4758,plain,
( empty_carrier(X1)
| ~ empty(the_carrier(X1))
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2209]),
[final] ).
cnf(i_0_4759,plain,
( empty(X1)
| ~ relation(X1)
| ~ empty(relation_rng(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2210]),
[final] ).
cnf(i_0_4760,plain,
( empty(X1)
| ~ relation(X1)
| ~ empty(relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2211]),
[final] ).
cnf(i_0_4761,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_2212]),
[final] ).
cnf(i_0_4762,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_2213]),
[final] ).
cnf(i_0_4763,lemma,
( relation_dom(X1) = X2
| X1 != identity_relation(X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1868]),
[final] ).
cnf(i_0_4764,plain,
( empty_carrier(X1)
| relation_of_lattice(X1) = a_1_0_filter_1(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2214]),
[final] ).
cnf(i_0_4765,plain,
( empty_carrier(X1)
| k2_lattice3(X1) = relation_of_lattice(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2215]),
[final] ).
cnf(i_0_4766,plain,
( element(esk445_0,powerset(powerset(empty_set)))
| epred1_0
| esk449_0 != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_760]),
[final] ).
cnf(i_0_4767,plain,
( subset(esk52_1(X1),X1)
| X1 = empty_set
| centered(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2106]),
[final] ).
cnf(i_0_4768,plain,
element(esk160_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_2147]),
[final] ).
cnf(i_0_4769,plain,
element(esk159_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_2216]),
[final] ).
cnf(i_0_4770,plain,
element(esk152_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_2217]),
[final] ).
cnf(i_0_4771,plain,
( X1 != X2
| ~ proper_subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2160]),
[final] ).
cnf(i_0_4772,plain,
( one_to_one(X1)
| ~ relation(X1)
| ~ empty(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2218]),
[final] ).
cnf(i_0_4773,plain,
( reflexive(X1)
| ~ relation(X1)
| ~ symmetric(X1)
| ~ transitive(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2219]),
[final] ).
cnf(i_0_4774,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2220]),
[final] ).
cnf(i_0_4775,plain,
( in(esk39_1(X1),X1)
| relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_766]),
[final] ).
cnf(i_0_4776,plain,
( in(esk71_1(X1),X1)
| epsilon_connected(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1985]),
[final] ).
cnf(i_0_4777,plain,
( in(esk70_1(X1),X1)
| epsilon_connected(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1985]),
[final] ).
cnf(i_0_4778,plain,
( in(esk55_1(X1),X1)
| epsilon_transitive(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2126]),
[final] ).
cnf(i_0_4779,lemma,
( in(esk422_1(X1),X1)
| ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2075]),
[final] ).
cnf(i_0_4780,plain,
( relation(function_inverse(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2221]),
[final] ).
cnf(i_0_4781,plain,
( function(function_inverse(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2221]),
[final] ).
cnf(i_0_4782,plain,
( empty(the_carrier(X1))
| ~ empty_carrier(X1)
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2209]),
[final] ).
cnf(i_0_4783,lemma,
( connected(X1)
| esk136_1(X1) != esk137_1(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_750]),
[final] ).
cnf(i_0_4784,lemma,
( antisymmetric(X1)
| esk134_1(X1) != esk135_1(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_743]),
[final] ).
cnf(i_0_4785,plain,
( epsilon_connected(X1)
| ~ element(X1,omega) ),
inference(split_conjunct,[status(thm)],[i_0_2222]),
[final] ).
cnf(i_0_4786,plain,
( epsilon_transitive(X1)
| ~ element(X1,omega) ),
inference(split_conjunct,[status(thm)],[i_0_2222]),
[final] ).
cnf(i_0_4787,plain,
( ordinal(X1)
| ~ element(X1,omega) ),
inference(split_conjunct,[status(thm)],[i_0_2222]),
[final] ).
cnf(i_0_4788,plain,
( natural(X1)
| ~ element(X1,omega) ),
inference(split_conjunct,[status(thm)],[i_0_2222]),
[final] ).
cnf(i_0_4789,lemma,
( relation(esk188_1(X1))
| esk186_1(X1) != esk187_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_768]),
[final] ).
cnf(i_0_4790,lemma,
( function(esk188_1(X1))
| esk186_1(X1) != esk187_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_768]),
[final] ).
cnf(i_0_4791,plain,
( join_absorbing(X1)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2223]),
[final] ).
cnf(i_0_4792,plain,
( meet_absorbing(X1)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2223]),
[final] ).
cnf(i_0_4793,plain,
( meet_associative(X1)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2223]),
[final] ).
cnf(i_0_4794,plain,
( meet_commutative(X1)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2223]),
[final] ).
cnf(i_0_4795,plain,
( join_associative(X1)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2223]),
[final] ).
cnf(i_0_4796,plain,
( join_commutative(X1)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2223]),
[final] ).
cnf(i_0_4797,plain,
~ proper_subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_2224]),
[final] ).
cnf(i_0_4798,lemma,
unordered_pair(X1,X1) != empty_set,
inference(rw,[status(thm)],[i_0_2225,c_0_681]),
[final] ).
cnf(i_0_4799,lemma,
( ordinal(esk428_1(X1))
| being_limit_ordinal(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_863]),
[final] ).
cnf(i_0_4800,lemma,
( ordinal(esk427_1(X1))
| being_limit_ordinal(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_777]),
[final] ).
cnf(i_0_4801,plain,
( in(esk49_1(X1),X1)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[i_0_2220]),
[final] ).
cnf(i_0_4802,lemma,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
inference(split_conjunct,[status(thm)],[i_0_2226]),
[final] ).
cnf(i_0_4803,lemma,
( relation_rng(X1) = relation_dom(relation_inverse(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2227]),
[final] ).
cnf(i_0_4804,lemma,
( relation_dom(X1) = relation_rng(relation_inverse(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2227]),
[final] ).
cnf(i_0_4805,plain,
( identity_on_carrier(X1) = identity_relation(the_carrier(X1))
| ~ one_sorted_str(X1) ),
inference(rw,[status(thm)],[i_0_2228,c_0_2053]),
[final] ).
cnf(i_0_4806,plain,
( empty(X1)
| ~ empty(esk170_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2198]),
[final] ).
cnf(i_0_4807,plain,
( empty(X1)
| ~ empty(esk163_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2199]),
[final] ).
cnf(i_0_4808,plain,
( empty(X1)
| ~ empty(esk149_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2200]),
[final] ).
cnf(i_0_4809,plain,
( relation_field(X1) = X2
| X1 != inclusion_relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_719]),
[final] ).
cnf(i_0_4810,lemma,
( relation_dom(esk420_1(X1)) = X1
| esk419_1(X1) = empty_set
| empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1896]),
[final] ).
cnf(i_0_4811,lemma,
well_orders(esk418_1(X1),X1),
inference(split_conjunct,[status(thm)],[i_0_2229]),
[final] ).
cnf(i_0_4812,plain,
element(esk123_1(X1),X1),
inference(split_conjunct,[status(thm)],[i_0_2230]),
[final] ).
cnf(i_0_4813,plain,
element(X1,powerset(X1)),
inference(rw,[status(thm)],[i_0_2231,c_0_1772]),
[final] ).
cnf(i_0_4814,plain,
in(X1,esk443_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_1912]),
[final] ).
cnf(i_0_4815,lemma,
in(X1,esk409_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_2009]),
[final] ).
cnf(i_0_4816,lemma,
( relation(esk420_1(X1))
| esk419_1(X1) = empty_set
| empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1896]),
[final] ).
cnf(i_0_4817,lemma,
( function(esk420_1(X1))
| esk419_1(X1) = empty_set
| empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1896]),
[final] ).
cnf(i_0_4818,plain,
( well_founded_relation(X1)
| ~ well_ordering(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2098]),
[final] ).
cnf(i_0_4819,plain,
( connected(X1)
| ~ well_ordering(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2098]),
[final] ).
cnf(i_0_4820,plain,
( antisymmetric(X1)
| ~ well_ordering(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2098]),
[final] ).
cnf(i_0_4821,plain,
( reflexive(X1)
| ~ well_ordering(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2098]),
[final] ).
cnf(i_0_4822,plain,
( transitive(X1)
| ~ well_ordering(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2098]),
[final] ).
cnf(i_0_4823,plain,
( preboolean(X1)
| ~ cup_closed(X1)
| ~ diff_closed(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2232]),
[final] ).
cnf(i_0_4824,plain,
( epsilon_connected(X1)
| ~ empty(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2233]),
[final] ).
cnf(i_0_4825,plain,
( epsilon_transitive(X1)
| ~ empty(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2233]),
[final] ).
cnf(i_0_4826,plain,
( ordinal(X1)
| ~ epsilon_transitive(X1)
| ~ epsilon_connected(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2234]),
[final] ).
cnf(i_0_4827,plain,
( ordinal(X1)
| ~ epsilon_transitive(X1)
| ~ epsilon_connected(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2235]),
[final] ).
cnf(i_0_4828,plain,
( natural(X1)
| ~ empty(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2233]),
[final] ).
cnf(i_0_4829,plain,
( well_founded_relation(X1)
| esk61_1(X1) != empty_set
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1807]),
[final] ).
cnf(i_0_4830,lemma,
( relation_rng(X1) = empty_set
| relation_dom(X1) != empty_set
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2236]),
[final] ).
cnf(i_0_4831,lemma,
( relation_dom(X1) = empty_set
| relation_rng(X1) != empty_set
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2236]),
[final] ).
cnf(i_0_4832,plain,
( relation_inverse(relation_inverse(X1)) = X1
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2237]),
[final] ).
cnf(i_0_4833,plain,
( relation_rng(esk26_1(X1)) = X1
| ~ finite(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2065]),
[final] ).
cnf(i_0_4834,plain,
( subset(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2097]),
[final] ).
cnf(i_0_4835,plain,
( subset(X1,X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_2097]),
[final] ).
cnf(i_0_4836,lemma,
( well_ordering(inclusion_relation(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2238]),
[final] ).
cnf(i_0_4837,lemma,
( well_founded_relation(inclusion_relation(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2239]),
[final] ).
cnf(i_0_4838,lemma,
( connected(inclusion_relation(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2240]),
[final] ).
cnf(i_0_4839,plain,
( relation(esk26_1(X1))
| ~ finite(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2065]),
[final] ).
cnf(i_0_4840,plain,
( relation(relation_inverse(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2241]),
[final] ).
cnf(i_0_4841,plain,
( relation(relation_inverse(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2242]),
[final] ).
cnf(i_0_4842,plain,
( relation(relation_rng(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2243]),
[final] ).
cnf(i_0_4843,plain,
( relation(relation_dom(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2244]),
[final] ).
cnf(i_0_4844,plain,
( function(esk26_1(X1))
| ~ finite(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2065]),
[final] ).
cnf(i_0_4845,plain,
( function(identity_on_carrier(X1))
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1993]),
[final] ).
cnf(i_0_4846,plain,
( function(the_L_meet(X1))
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1850]),
[final] ).
cnf(i_0_4847,plain,
( function(the_L_join(X1))
| ~ join_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1851]),
[final] ).
cnf(i_0_4848,plain,
( epsilon_connected(union(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2245]),
[final] ).
cnf(i_0_4849,plain,
( epsilon_transitive(union(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2245]),
[final] ).
cnf(i_0_4850,plain,
( ordinal(union(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2245]),
[final] ).
cnf(i_0_4851,plain,
( empty(relation_inverse(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2242]),
[final] ).
cnf(i_0_4852,plain,
( empty(empty_carrier_subset(X1))
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2246]),
[final] ).
cnf(i_0_4853,plain,
( empty(relation_rng(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2243]),
[final] ).
cnf(i_0_4854,plain,
( empty(relation_dom(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2244]),
[final] ).
cnf(i_0_4855,plain,
( v5_membered(empty_carrier_subset(X1))
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2246]),
[final] ).
cnf(i_0_4856,plain,
( v4_membered(empty_carrier_subset(X1))
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2246]),
[final] ).
cnf(i_0_4857,plain,
( v3_membered(empty_carrier_subset(X1))
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2246]),
[final] ).
cnf(i_0_4858,plain,
( v2_membered(empty_carrier_subset(X1))
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2246]),
[final] ).
cnf(i_0_4859,plain,
( v1_membered(empty_carrier_subset(X1))
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2246]),
[final] ).
cnf(i_0_4860,plain,
( function(X1)
| esk28_1(X1) != esk29_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_745]),
[final] ).
cnf(i_0_4861,plain,
( epsilon_connected(X1)
| esk70_1(X1) != esk71_1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1985]),
[final] ).
cnf(i_0_4862,plain,
~ empty_carrier(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[i_0_2247]),
[final] ).
cnf(i_0_4863,plain,
~ empty_carrier(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[i_0_2248]),
[final] ).
cnf(i_0_4864,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_2249]),
[final] ).
cnf(i_0_4865,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_2250]),
[final] ).
cnf(i_0_4866,plain,
( finite(esk52_1(X1))
| X1 = empty_set
| centered(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2106]),
[final] ).
cnf(i_0_4867,plain,
( set_meet(esk52_1(X1)) = empty_set
| X1 = empty_set
| centered(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2106]),
[final] ).
cnf(i_0_4868,plain,
( X1 = X2
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2251]),
[final] ).
cnf(i_0_4869,negated_conjecture,
element(esk441_0,the_carrier(esk440_0)),
inference(split_conjunct,[status(thm)],[i_0_1785]),
[final] ).
cnf(i_0_4870,lemma,
( X1 = empty_set
| relation_rng(X1) != empty_set
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2252]),
[final] ).
cnf(i_0_4871,lemma,
( X1 = empty_set
| relation_dom(X1) != empty_set
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2252]),
[final] ).
cnf(i_0_4872,lemma,
( cast_as_carrier_subset(X1) = the_carrier(X1)
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2253]),
[final] ).
cnf(i_0_4873,plain,
( cast_as_carrier_subset(X1) = the_carrier(X1)
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2254]),
[final] ).
cnf(i_0_4874,plain,
( in(empty_set,X1)
| X1 != omega ),
inference(split_conjunct,[status(thm)],[i_0_2021]),
[final] ).
cnf(i_0_4875,plain,
( ordinal(esk447_0)
| in(empty_set,omega)
| epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_760]),
[final] ).
cnf(i_0_4876,plain,
( finite(esk170_1(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2198]),
[final] ).
cnf(i_0_4877,plain,
( finite(esk163_1(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2199]),
[final] ).
cnf(i_0_4878,plain,
set_union2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_2255]),
[final] ).
cnf(i_0_4879,plain,
equipotent(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_2256]),
[final] ).
cnf(i_0_4880,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_2257]),
[final] ).
cnf(i_0_4881,lemma,
unordered_pair(empty_set,empty_set) = powerset(empty_set),
inference(rw,[status(thm)],[i_0_2258,c_0_681]),
[final] ).
cnf(i_0_4882,plain,
set_difference(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[i_0_2259]),
[final] ).
cnf(i_0_4883,plain,
set_union2(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[i_0_2260]),
[final] ).
cnf(i_0_4884,plain,
( in(empty_set,omega)
| epred1_0
| esk449_0 != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_760]),
[final] ).
cnf(i_0_4885,plain,
( X1 = empty_set
| centered(X1)
| esk52_1(X1) != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_2106]),
[final] ).
cnf(i_0_4886,plain,
( being_limit_ordinal(X1)
| X1 != union(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2261]),
[final] ).
cnf(i_0_4887,lemma,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[i_0_2262]),
[final] ).
cnf(i_0_4888,plain,
set_difference(empty_set,X1) = empty_set,
inference(split_conjunct,[status(thm)],[i_0_2263]),
[final] ).
cnf(i_0_4889,plain,
( X1 = union(X1)
| ~ being_limit_ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2261]),
[final] ).
cnf(i_0_4890,plain,
( X1 = empty_set
| X1 != set_meet(X2)
| X2 != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_1724]),
[final] ).
cnf(i_0_4891,plain,
( one_sorted_str(X1)
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2264]),
[final] ).
cnf(i_0_4892,plain,
( one_sorted_str(X1)
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2265]),
[final] ).
cnf(i_0_4893,plain,
( one_sorted_str(X1)
| ~ join_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2266]),
[final] ).
cnf(i_0_4894,plain,
( one_sorted_str(X1)
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2267]),
[final] ).
cnf(i_0_4895,plain,
( meet_semilatt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2268]),
[final] ).
cnf(i_0_4896,plain,
( join_semilatt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2268]),
[final] ).
cnf(i_0_4897,plain,
( relation(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2269]),
[final] ).
cnf(i_0_4898,plain,
( function(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2270]),
[final] ).
cnf(i_0_4899,plain,
( diff_closed(X1)
| ~ preboolean(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2271]),
[final] ).
cnf(i_0_4900,plain,
( cup_closed(X1)
| ~ preboolean(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2271]),
[final] ).
cnf(i_0_4901,plain,
( finite(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2272]),
[final] ).
cnf(i_0_4902,plain,
( epsilon_connected(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2234]),
[final] ).
cnf(i_0_4903,plain,
( epsilon_connected(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2273]),
[final] ).
cnf(i_0_4904,plain,
( epsilon_connected(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2274]),
[final] ).
cnf(i_0_4905,plain,
( epsilon_transitive(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2234]),
[final] ).
cnf(i_0_4906,plain,
( epsilon_transitive(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2273]),
[final] ).
cnf(i_0_4907,plain,
( epsilon_transitive(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2274]),
[final] ).
cnf(i_0_4908,plain,
( ordinal(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2274]),
[final] ).
cnf(i_0_4909,plain,
( v5_membered(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2275]),
[final] ).
cnf(i_0_4910,plain,
( v4_membered(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2275]),
[final] ).
cnf(i_0_4911,plain,
( v4_membered(X1)
| ~ v5_membered(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2276]),
[final] ).
cnf(i_0_4912,plain,
( v3_membered(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2275]),
[final] ).
cnf(i_0_4913,plain,
( v3_membered(X1)
| ~ v4_membered(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2277]),
[final] ).
cnf(i_0_4914,plain,
( v2_membered(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2275]),
[final] ).
cnf(i_0_4915,plain,
( v2_membered(X1)
| ~ v3_membered(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2278]),
[final] ).
cnf(i_0_4916,plain,
( v1_membered(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2275]),
[final] ).
cnf(i_0_4917,plain,
( v1_membered(X1)
| ~ v2_membered(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2279]),
[final] ).
cnf(i_0_4918,plain,
( empty_carrier_subset(X1) = empty_set
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2280]),
[final] ).
cnf(i_0_4919,lemma,
union(powerset(X1)) = X1,
inference(split_conjunct,[status(thm)],[i_0_2281]),
[final] ).
cnf(i_0_4920,lemma,
relation_rng(identity_relation(X1)) = X1,
inference(split_conjunct,[status(thm)],[i_0_2282]),
[final] ).
cnf(i_0_4921,lemma,
relation_dom(esk405_1(X1)) = X1,
inference(split_conjunct,[status(thm)],[i_0_887]),
[final] ).
cnf(i_0_4922,lemma,
relation_dom(identity_relation(X1)) = X1,
inference(split_conjunct,[status(thm)],[i_0_2282]),
[final] ).
cnf(i_0_4923,lemma,
lower_bounded_semilattstr(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[i_0_2283]),
[final] ).
cnf(i_0_4924,plain,
antisymmetric(esk167_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_2055]),
[final] ).
cnf(i_0_4925,lemma,
antisymmetric(inclusion_relation(X1)),
inference(split_conjunct,[status(thm)],[i_0_2284]),
[final] ).
cnf(i_0_4926,plain,
antisymmetric(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[i_0_2285]),
[final] ).
cnf(i_0_4927,plain,
one_to_one(esk154_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_2054]),
[final] ).
cnf(i_0_4928,plain,
one_to_one(esk152_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_2217]),
[final] ).
cnf(i_0_4929,plain,
reflexive(esk167_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_2055]),
[final] ).
cnf(i_0_4930,lemma,
reflexive(inclusion_relation(X1)),
inference(split_conjunct,[status(thm)],[i_0_2286]),
[final] ).
cnf(i_0_4931,plain,
reflexive(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[i_0_2285]),
[final] ).
cnf(i_0_4932,plain,
transitive(esk167_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_2055]),
[final] ).
cnf(i_0_4933,lemma,
transitive(inclusion_relation(X1)),
inference(split_conjunct,[status(thm)],[i_0_2287]),
[final] ).
cnf(i_0_4934,plain,
transitive(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[i_0_2285]),
[final] ).
cnf(i_0_4935,plain,
symmetric(esk167_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_2055]),
[final] ).
cnf(i_0_4936,plain,
symmetric(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[i_0_2285]),
[final] ).
cnf(i_0_4937,lemma,
relation(esk418_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_2229]),
[final] ).
cnf(i_0_4938,lemma,
relation(esk405_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_887]),
[final] ).
cnf(i_0_4939,plain,
relation(esk167_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_2055]),
[final] ).
cnf(i_0_4940,plain,
relation(esk154_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_2054]),
[final] ).
cnf(i_0_4941,plain,
relation(esk152_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_2217]),
[final] ).
cnf(i_0_4942,plain,
relation(inclusion_relation(X1)),
inference(split_conjunct,[status(thm)],[i_0_2288]),
[final] ).
cnf(i_0_4943,plain,
relation(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[i_0_2285]),
[final] ).
cnf(i_0_4944,plain,
relation(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[i_0_2289]),
[final] ).
cnf(i_0_4945,plain,
relation(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[i_0_2290]),
[final] ).
cnf(i_0_4946,plain,
join_absorbing(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[i_0_2247]),
[final] ).
cnf(i_0_4947,plain,
meet_absorbing(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[i_0_2247]),
[final] ).
cnf(i_0_4948,plain,
meet_associative(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[i_0_2247]),
[final] ).
cnf(i_0_4949,plain,
meet_commutative(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[i_0_2247]),
[final] ).
cnf(i_0_4950,plain,
join_associative(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[i_0_2247]),
[final] ).
cnf(i_0_4951,plain,
join_commutative(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[i_0_2247]),
[final] ).
cnf(i_0_4952,plain,
lattice(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[i_0_2247]),
[final] ).
cnf(i_0_4953,lemma,
function(esk405_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_887]),
[final] ).
cnf(i_0_4954,plain,
function(esk154_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_2054]),
[final] ).
cnf(i_0_4955,plain,
function(esk152_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_2217]),
[final] ).
cnf(i_0_4956,plain,
function(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[i_0_2285]),
[final] ).
cnf(i_0_4957,plain,
function(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[i_0_2289]),
[final] ).
cnf(i_0_4958,plain,
diff_closed(powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_2250]),
[final] ).
cnf(i_0_4959,plain,
cup_closed(powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_2250]),
[final] ).
cnf(i_0_4960,plain,
preboolean(powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_2250]),
[final] ).
cnf(i_0_4961,plain,
finite(esk152_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_2217]),
[final] ).
cnf(i_0_4962,plain,
epsilon_connected(esk152_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_2217]),
[final] ).
cnf(i_0_4963,plain,
epsilon_transitive(esk152_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_2217]),
[final] ).
cnf(i_0_4964,plain,
ordinal(esk152_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_2217]),
[final] ).
cnf(i_0_4965,plain,
empty(esk159_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_2216]),
[final] ).
cnf(i_0_4966,plain,
empty(esk152_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_2217]),
[final] ).
cnf(i_0_4967,plain,
natural(esk152_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_2217]),
[final] ).
cnf(i_0_4968,plain,
strict_latt_str(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[i_0_2247]),
[final] ).
cnf(i_0_4969,plain,
strict_latt_str(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[i_0_2248]),
[final] ).
cnf(i_0_4970,plain,
strict_latt_str(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[i_0_2291]),
[final] ).
cnf(i_0_4971,plain,
latt_str(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[i_0_2291]),
[final] ).
cnf(i_0_4972,lemma,
bottom_of_semilattstr(boole_lattice(X1)) = empty_set,
inference(split_conjunct,[status(thm)],[i_0_2283]),
[final] ).
cnf(i_0_4973,plain,
( X1 = set_meet(X2)
| X1 != empty_set
| X2 != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_1724]),
[final] ).
cnf(i_0_4974,plain,
( X1 != empty_set
| ~ centered(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2106]),
[final] ).
cnf(i_0_4975,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2292]),
[final] ).
cnf(i_0_4976,plain,
( being_limit_ordinal(X1)
| X1 != omega ),
inference(split_conjunct,[status(thm)],[i_0_2021]),
[final] ).
cnf(i_0_4977,plain,
( ordinal(X1)
| X1 != omega ),
inference(split_conjunct,[status(thm)],[i_0_2021]),
[final] ).
cnf(i_0_4978,plain,
( ordinal(esk447_0)
| epred1_0
| esk445_0 != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_760]),
[final] ).
cnf(i_0_4979,plain,
~ empty_carrier(esk176_0),
inference(split_conjunct,[status(thm)],[i_0_2293]),
[final] ).
cnf(i_0_4980,plain,
~ empty_carrier(esk173_0),
inference(split_conjunct,[status(thm)],[i_0_2294]),
[final] ).
cnf(i_0_4981,plain,
~ empty_carrier(esk169_0),
inference(split_conjunct,[status(thm)],[i_0_2295]),
[final] ).
cnf(i_0_4982,plain,
~ empty_carrier(esk155_0),
inference(split_conjunct,[status(thm)],[i_0_2296]),
[final] ).
cnf(i_0_4983,plain,
~ empty(esk166_0),
inference(split_conjunct,[status(thm)],[i_0_2297]),
[final] ).
cnf(i_0_4984,plain,
~ empty(esk162_0),
inference(split_conjunct,[status(thm)],[i_0_2298]),
[final] ).
cnf(i_0_4985,plain,
~ empty(esk158_0),
inference(split_conjunct,[status(thm)],[i_0_2299]),
[final] ).
cnf(i_0_4986,plain,
~ empty(esk143_0),
inference(split_conjunct,[status(thm)],[i_0_2300]),
[final] ).
cnf(i_0_4987,plain,
~ empty(esk140_0),
inference(split_conjunct,[status(thm)],[i_0_2301]),
[final] ).
cnf(i_0_4988,plain,
~ empty(esk139_0),
inference(split_conjunct,[status(thm)],[i_0_2302]),
[final] ).
cnf(i_0_4989,plain,
~ empty(omega),
inference(split_conjunct,[status(thm)],[i_0_2303]),
[final] ).
cnf(i_0_4990,plain,
( epred1_0
| esk449_0 != empty_set
| esk445_0 != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_760]),
[final] ).
cnf(i_0_4991,plain,
relation_empty_yielding(esk171_0),
inference(split_conjunct,[status(thm)],[i_0_2304]),
[final] ).
cnf(i_0_4992,plain,
relation_empty_yielding(esk168_0),
inference(split_conjunct,[status(thm)],[i_0_2305]),
[final] ).
cnf(i_0_4993,plain,
relation_empty_yielding(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]),
[final] ).
cnf(i_0_4994,plain,
relation_empty_yielding(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]),
[final] ).
cnf(i_0_4995,plain,
reflexive_relstr(esk155_0),
inference(split_conjunct,[status(thm)],[i_0_2296]),
[final] ).
cnf(i_0_4996,plain,
antisymmetric_relstr(esk155_0),
inference(split_conjunct,[status(thm)],[i_0_2296]),
[final] ).
cnf(i_0_4997,plain,
being_limit_ordinal(esk146_0),
inference(split_conjunct,[status(thm)],[i_0_2306]),
[final] ).
cnf(i_0_4998,plain,
transitive_relstr(esk155_0),
inference(split_conjunct,[status(thm)],[i_0_2296]),
[final] ).
cnf(i_0_4999,plain,
top_str(esk117_0),
inference(split_conjunct,[status(thm)],[i_0_2307]),
[final] ).
cnf(i_0_5000,plain,
one_sorted_str(esk169_0),
inference(split_conjunct,[status(thm)],[i_0_2295]),
[final] ).
cnf(i_0_5001,plain,
one_sorted_str(esk118_0),
inference(split_conjunct,[status(thm)],[i_0_2308]),
[final] ).
cnf(i_0_5002,plain,
meet_semilatt_str(esk115_0),
inference(split_conjunct,[status(thm)],[i_0_2309]),
[final] ).
cnf(i_0_5003,plain,
join_semilatt_str(esk119_0),
inference(split_conjunct,[status(thm)],[i_0_2310]),
[final] ).
cnf(i_0_5004,plain,
one_to_one(esk164_0),
inference(split_conjunct,[status(thm)],[i_0_2311]),
[final] ).
cnf(i_0_5005,plain,
one_to_one(esk156_0),
inference(split_conjunct,[status(thm)],[i_0_2312]),
[final] ).
cnf(i_0_5006,plain,
one_to_one(esk147_0),
inference(split_conjunct,[status(thm)],[i_0_2313]),
[final] ).
cnf(i_0_5007,plain,
one_to_one(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]),
[final] ).
cnf(i_0_5008,plain,
relation(esk171_0),
inference(split_conjunct,[status(thm)],[i_0_2304]),
[final] ).
cnf(i_0_5009,plain,
relation(esk168_0),
inference(split_conjunct,[status(thm)],[i_0_2305]),
[final] ).
cnf(i_0_5010,plain,
relation(esk164_0),
inference(split_conjunct,[status(thm)],[i_0_2311]),
[final] ).
cnf(i_0_5011,plain,
relation(esk158_0),
inference(split_conjunct,[status(thm)],[i_0_2299]),
[final] ).
cnf(i_0_5012,plain,
relation(esk156_0),
inference(split_conjunct,[status(thm)],[i_0_2312]),
[final] ).
cnf(i_0_5013,plain,
relation(esk153_0),
inference(split_conjunct,[status(thm)],[i_0_2314]),
[final] ).
cnf(i_0_5014,plain,
relation(esk148_0),
inference(split_conjunct,[status(thm)],[i_0_2315]),
[final] ).
cnf(i_0_5015,plain,
relation(esk147_0),
inference(split_conjunct,[status(thm)],[i_0_2313]),
[final] ).
cnf(i_0_5016,plain,
relation(esk141_0),
inference(split_conjunct,[status(thm)],[i_0_2316]),
[final] ).
cnf(i_0_5017,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[fc4_relat_1]),
[final] ).
cnf(i_0_5018,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]),
[final] ).
cnf(i_0_5019,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]),
[final] ).
cnf(i_0_5020,plain,
join_absorbing(esk176_0),
inference(split_conjunct,[status(thm)],[i_0_2293]),
[final] ).
cnf(i_0_5021,plain,
meet_absorbing(esk176_0),
inference(split_conjunct,[status(thm)],[i_0_2293]),
[final] ).
cnf(i_0_5022,plain,
meet_associative(esk176_0),
inference(split_conjunct,[status(thm)],[i_0_2293]),
[final] ).
cnf(i_0_5023,plain,
meet_commutative(esk176_0),
inference(split_conjunct,[status(thm)],[i_0_2293]),
[final] ).
cnf(i_0_5024,plain,
join_associative(esk176_0),
inference(split_conjunct,[status(thm)],[i_0_2293]),
[final] ).
cnf(i_0_5025,plain,
join_commutative(esk176_0),
inference(split_conjunct,[status(thm)],[i_0_2293]),
[final] ).
cnf(i_0_5026,plain,
lattice(esk176_0),
inference(split_conjunct,[status(thm)],[i_0_2293]),
[final] ).
cnf(i_0_5027,plain,
function(esk171_0),
inference(split_conjunct,[status(thm)],[i_0_2304]),
[final] ).
cnf(i_0_5028,plain,
function(esk164_0),
inference(split_conjunct,[status(thm)],[i_0_2311]),
[final] ).
cnf(i_0_5029,plain,
function(esk156_0),
inference(split_conjunct,[status(thm)],[i_0_2312]),
[final] ).
cnf(i_0_5030,plain,
function(esk153_0),
inference(split_conjunct,[status(thm)],[i_0_2314]),
[final] ).
cnf(i_0_5031,plain,
function(esk147_0),
inference(split_conjunct,[status(thm)],[i_0_2313]),
[final] ).
cnf(i_0_5032,plain,
function(esk141_0),
inference(split_conjunct,[status(thm)],[i_0_2316]),
[final] ).
cnf(i_0_5033,plain,
function(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]),
[final] ).
cnf(i_0_5034,plain,
finite(esk140_0),
inference(split_conjunct,[status(thm)],[i_0_2301]),
[final] ).
cnf(i_0_5035,plain,
epsilon_connected(esk166_0),
inference(split_conjunct,[status(thm)],[i_0_2297]),
[final] ).
cnf(i_0_5036,plain,
epsilon_connected(esk156_0),
inference(split_conjunct,[status(thm)],[i_0_2312]),
[final] ).
cnf(i_0_5037,plain,
epsilon_connected(esk146_0),
inference(split_conjunct,[status(thm)],[i_0_2306]),
[final] ).
cnf(i_0_5038,plain,
epsilon_connected(esk145_0),
inference(split_conjunct,[status(thm)],[i_0_2317]),
[final] ).
cnf(i_0_5039,plain,
epsilon_connected(esk139_0),
inference(split_conjunct,[status(thm)],[i_0_2302]),
[final] ).
cnf(i_0_5040,plain,
epsilon_connected(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]),
[final] ).
cnf(i_0_5041,plain,
epsilon_connected(omega),
inference(split_conjunct,[status(thm)],[i_0_2303]),
[final] ).
cnf(i_0_5042,plain,
epsilon_transitive(esk166_0),
inference(split_conjunct,[status(thm)],[i_0_2297]),
[final] ).
cnf(i_0_5043,plain,
epsilon_transitive(esk156_0),
inference(split_conjunct,[status(thm)],[i_0_2312]),
[final] ).
cnf(i_0_5044,plain,
epsilon_transitive(esk146_0),
inference(split_conjunct,[status(thm)],[i_0_2306]),
[final] ).
cnf(i_0_5045,plain,
epsilon_transitive(esk145_0),
inference(split_conjunct,[status(thm)],[i_0_2317]),
[final] ).
cnf(i_0_5046,plain,
epsilon_transitive(esk139_0),
inference(split_conjunct,[status(thm)],[i_0_2302]),
[final] ).
cnf(i_0_5047,plain,
epsilon_transitive(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]),
[final] ).
cnf(i_0_5048,plain,
epsilon_transitive(omega),
inference(split_conjunct,[status(thm)],[i_0_2303]),
[final] ).
cnf(i_0_5049,plain,
ordinal(esk166_0),
inference(split_conjunct,[status(thm)],[i_0_2297]),
[final] ).
cnf(i_0_5050,plain,
ordinal(esk156_0),
inference(split_conjunct,[status(thm)],[i_0_2312]),
[final] ).
cnf(i_0_5051,plain,
ordinal(esk146_0),
inference(split_conjunct,[status(thm)],[i_0_2306]),
[final] ).
cnf(i_0_5052,plain,
ordinal(esk145_0),
inference(split_conjunct,[status(thm)],[i_0_2317]),
[final] ).
cnf(i_0_5053,plain,
ordinal(esk139_0),
inference(split_conjunct,[status(thm)],[i_0_2302]),
[final] ).
cnf(i_0_5054,plain,
ordinal(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]),
[final] ).
cnf(i_0_5055,plain,
ordinal(omega),
inference(split_conjunct,[status(thm)],[i_0_2303]),
[final] ).
cnf(i_0_5056,plain,
empty(esk156_0),
inference(split_conjunct,[status(thm)],[i_0_2312]),
[final] ).
cnf(i_0_5057,plain,
empty(esk153_0),
inference(split_conjunct,[status(thm)],[i_0_2314]),
[final] ).
cnf(i_0_5058,plain,
empty(esk151_0),
inference(split_conjunct,[status(thm)],[i_0_2318]),
[final] ).
cnf(i_0_5059,plain,
empty(esk148_0),
inference(split_conjunct,[status(thm)],[i_0_2315]),
[final] ).
cnf(i_0_5060,plain,
empty(esk147_0),
inference(split_conjunct,[status(thm)],[i_0_2313]),
[final] ).
cnf(i_0_5061,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc6_membered]),
[final] ).
cnf(i_0_5062,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc4_relat_1]),
[final] ).
cnf(i_0_5063,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]),
[final] ).
cnf(i_0_5064,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]),
[final] ).
cnf(i_0_5065,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]),
[final] ).
cnf(i_0_5066,plain,
natural(esk139_0),
inference(split_conjunct,[status(thm)],[i_0_2302]),
[final] ).
cnf(i_0_5067,plain,
v5_membered(esk143_0),
inference(split_conjunct,[status(thm)],[i_0_2300]),
[final] ).
cnf(i_0_5068,plain,
v5_membered(empty_set),
inference(split_conjunct,[status(thm)],[fc6_membered]),
[final] ).
cnf(i_0_5069,plain,
v4_membered(esk143_0),
inference(split_conjunct,[status(thm)],[i_0_2300]),
[final] ).
cnf(i_0_5070,plain,
v4_membered(empty_set),
inference(split_conjunct,[status(thm)],[fc6_membered]),
[final] ).
cnf(i_0_5071,plain,
v3_membered(esk143_0),
inference(split_conjunct,[status(thm)],[i_0_2300]),
[final] ).
cnf(i_0_5072,plain,
v3_membered(empty_set),
inference(split_conjunct,[status(thm)],[fc6_membered]),
[final] ).
cnf(i_0_5073,plain,
v2_membered(esk143_0),
inference(split_conjunct,[status(thm)],[i_0_2300]),
[final] ).
cnf(i_0_5074,plain,
v2_membered(empty_set),
inference(split_conjunct,[status(thm)],[fc6_membered]),
[final] ).
cnf(i_0_5075,plain,
v1_membered(esk143_0),
inference(split_conjunct,[status(thm)],[i_0_2300]),
[final] ).
cnf(i_0_5076,plain,
v1_membered(empty_set),
inference(split_conjunct,[status(thm)],[fc6_membered]),
[final] ).
cnf(i_0_5077,plain,
strict_latt_str(esk176_0),
inference(split_conjunct,[status(thm)],[i_0_2293]),
[final] ).
cnf(i_0_5078,plain,
strict_latt_str(esk173_0),
inference(split_conjunct,[status(thm)],[i_0_2294]),
[final] ).
cnf(i_0_5079,plain,
strict_latt_str(esk165_0),
inference(split_conjunct,[status(thm)],[i_0_2319]),
[final] ).
cnf(i_0_5080,plain,
latt_str(esk176_0),
inference(split_conjunct,[status(thm)],[i_0_2293]),
[final] ).
cnf(i_0_5081,plain,
latt_str(esk173_0),
inference(split_conjunct,[status(thm)],[i_0_2294]),
[final] ).
cnf(i_0_5082,plain,
latt_str(esk165_0),
inference(split_conjunct,[status(thm)],[i_0_2319]),
[final] ).
cnf(i_0_5083,plain,
latt_str(esk120_0),
inference(split_conjunct,[status(thm)],[i_0_2320]),
[final] ).
cnf(i_0_5084,plain,
strict_rel_str(esk155_0),
inference(split_conjunct,[status(thm)],[i_0_2296]),
[final] ).
cnf(i_0_5085,plain,
strict_rel_str(esk144_0),
inference(split_conjunct,[status(thm)],[i_0_2321]),
[final] ).
cnf(i_0_5086,negated_conjecture,
rel_str(esk440_0),
inference(split_conjunct,[status(thm)],[i_0_1785]),
[final] ).
cnf(i_0_5087,plain,
rel_str(esk155_0),
inference(split_conjunct,[status(thm)],[i_0_2296]),
[final] ).
cnf(i_0_5088,plain,
rel_str(esk144_0),
inference(split_conjunct,[status(thm)],[i_0_2321]),
[final] ).
cnf(i_0_5089,plain,
rel_str(esk116_0),
inference(split_conjunct,[status(thm)],[i_0_2322]),
[final] ).
cnf(i_0_5090,lemma,
relation_rng(empty_set) = empty_set,
inference(split_conjunct,[status(thm)],[t60_relat_1]),
[final] ).
cnf(i_0_5091,lemma,
relation_dom(empty_set) = empty_set,
inference(split_conjunct,[status(thm)],[t60_relat_1]),
[final] ).
cnf(i_0_5092,axiom,
X1 = X1 ).
cnf(i_0_5093,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_5094,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_5095,axiom,
( X1 != X2
| esk217_2(X1,X3) = esk217_2(X2,X3) ) ).
cnf(i_0_5096,axiom,
( X1 != X2
| esk217_2(X3,X1) = esk217_2(X3,X2) ) ).
cnf(i_0_5097,axiom,
( X1 != X2
| esk379_2(X1,X3) = esk379_2(X2,X3) ) ).
cnf(i_0_5098,axiom,
( X1 != X2
| esk379_2(X3,X1) = esk379_2(X3,X2) ) ).
cnf(i_0_5099,axiom,
( X1 != X2
| esk378_2(X1,X3) = esk378_2(X2,X3) ) ).
cnf(i_0_5100,axiom,
( X1 != X2
| esk378_2(X3,X1) = esk378_2(X3,X2) ) ).
cnf(i_0_5101,axiom,
( X1 != X2
| esk382_3(X1,X3,X4) = esk382_3(X2,X3,X4) ) ).
cnf(i_0_5102,axiom,
( X1 != X2
| esk382_3(X3,X1,X4) = esk382_3(X3,X2,X4) ) ).
cnf(i_0_5103,axiom,
( X1 != X2
| esk382_3(X3,X4,X1) = esk382_3(X3,X4,X2) ) ).
cnf(i_0_5104,axiom,
( X1 != X2
| esk375_2(X1,X3) = esk375_2(X2,X3) ) ).
cnf(i_0_5105,axiom,
( X1 != X2
| esk375_2(X3,X1) = esk375_2(X3,X2) ) ).
cnf(i_0_5106,axiom,
( X1 != X2
| esk377_2(X1,X3) = esk377_2(X2,X3) ) ).
cnf(i_0_5107,axiom,
( X1 != X2
| esk377_2(X3,X1) = esk377_2(X3,X2) ) ).
cnf(i_0_5108,axiom,
( X1 != X2
| esk226_4(X1,X3,X4,X5) = esk226_4(X2,X3,X4,X5) ) ).
cnf(i_0_5109,axiom,
( X1 != X2
| esk226_4(X3,X1,X4,X5) = esk226_4(X3,X2,X4,X5) ) ).
cnf(i_0_5110,axiom,
( X1 != X2
| esk226_4(X3,X4,X1,X5) = esk226_4(X3,X4,X2,X5) ) ).
cnf(i_0_5111,axiom,
( X1 != X2
| esk226_4(X3,X4,X5,X1) = esk226_4(X3,X4,X5,X2) ) ).
cnf(i_0_5112,axiom,
( X1 != X2
| esk320_4(X1,X3,X4,X5) = esk320_4(X2,X3,X4,X5) ) ).
cnf(i_0_5113,axiom,
( X1 != X2
| esk320_4(X3,X1,X4,X5) = esk320_4(X3,X2,X4,X5) ) ).
cnf(i_0_5114,axiom,
( X1 != X2
| esk320_4(X3,X4,X1,X5) = esk320_4(X3,X4,X2,X5) ) ).
cnf(i_0_5115,axiom,
( X1 != X2
| esk320_4(X3,X4,X5,X1) = esk320_4(X3,X4,X5,X2) ) ).
cnf(i_0_5116,axiom,
( X1 != X2
| esk374_2(X1,X3) = esk374_2(X2,X3) ) ).
cnf(i_0_5117,axiom,
( X1 != X2
| esk374_2(X3,X1) = esk374_2(X3,X2) ) ).
cnf(i_0_5118,axiom,
( X1 != X2
| esk218_2(X1,X3) = esk218_2(X2,X3) ) ).
cnf(i_0_5119,axiom,
( X1 != X2
| esk218_2(X3,X1) = esk218_2(X3,X2) ) ).
cnf(i_0_5120,axiom,
( X1 != X2
| esk309_4(X1,X3,X4,X5) = esk309_4(X2,X3,X4,X5) ) ).
cnf(i_0_5121,axiom,
( X1 != X2
| esk309_4(X3,X1,X4,X5) = esk309_4(X3,X2,X4,X5) ) ).
cnf(i_0_5122,axiom,
( X1 != X2
| esk309_4(X3,X4,X1,X5) = esk309_4(X3,X4,X2,X5) ) ).
cnf(i_0_5123,axiom,
( X1 != X2
| esk309_4(X3,X4,X5,X1) = esk309_4(X3,X4,X5,X2) ) ).
cnf(i_0_5124,axiom,
( X1 != X2
| esk310_4(X1,X3,X4,X5) = esk310_4(X2,X3,X4,X5) ) ).
cnf(i_0_5125,axiom,
( X1 != X2
| esk310_4(X3,X1,X4,X5) = esk310_4(X3,X2,X4,X5) ) ).
cnf(i_0_5126,axiom,
( X1 != X2
| esk310_4(X3,X4,X1,X5) = esk310_4(X3,X4,X2,X5) ) ).
cnf(i_0_5127,axiom,
( X1 != X2
| esk310_4(X3,X4,X5,X1) = esk310_4(X3,X4,X5,X2) ) ).
cnf(i_0_5128,axiom,
( X1 != X2
| esk291_4(X1,X3,X4,X5) = esk291_4(X2,X3,X4,X5) ) ).
cnf(i_0_5129,axiom,
( X1 != X2
| esk291_4(X3,X1,X4,X5) = esk291_4(X3,X2,X4,X5) ) ).
cnf(i_0_5130,axiom,
( X1 != X2
| esk291_4(X3,X4,X1,X5) = esk291_4(X3,X4,X2,X5) ) ).
cnf(i_0_5131,axiom,
( X1 != X2
| esk291_4(X3,X4,X5,X1) = esk291_4(X3,X4,X5,X2) ) ).
cnf(i_0_5132,axiom,
( X1 != X2
| esk292_4(X1,X3,X4,X5) = esk292_4(X2,X3,X4,X5) ) ).
cnf(i_0_5133,axiom,
( X1 != X2
| esk292_4(X3,X1,X4,X5) = esk292_4(X3,X2,X4,X5) ) ).
cnf(i_0_5134,axiom,
( X1 != X2
| esk292_4(X3,X4,X1,X5) = esk292_4(X3,X4,X2,X5) ) ).
cnf(i_0_5135,axiom,
( X1 != X2
| esk292_4(X3,X4,X5,X1) = esk292_4(X3,X4,X5,X2) ) ).
cnf(i_0_5136,axiom,
( X1 != X2
| esk364_4(X1,X3,X4,X5) = esk364_4(X2,X3,X4,X5) ) ).
cnf(i_0_5137,axiom,
( X1 != X2
| esk364_4(X3,X1,X4,X5) = esk364_4(X3,X2,X4,X5) ) ).
cnf(i_0_5138,axiom,
( X1 != X2
| esk364_4(X3,X4,X1,X5) = esk364_4(X3,X4,X2,X5) ) ).
cnf(i_0_5139,axiom,
( X1 != X2
| esk364_4(X3,X4,X5,X1) = esk364_4(X3,X4,X5,X2) ) ).
cnf(i_0_5140,axiom,
( X1 != X2
| esk365_4(X1,X3,X4,X5) = esk365_4(X2,X3,X4,X5) ) ).
cnf(i_0_5141,axiom,
( X1 != X2
| esk365_4(X3,X1,X4,X5) = esk365_4(X3,X2,X4,X5) ) ).
cnf(i_0_5142,axiom,
( X1 != X2
| esk365_4(X3,X4,X1,X5) = esk365_4(X3,X4,X2,X5) ) ).
cnf(i_0_5143,axiom,
( X1 != X2
| esk365_4(X3,X4,X5,X1) = esk365_4(X3,X4,X5,X2) ) ).
cnf(i_0_5144,axiom,
( X1 != X2
| esk360_4(X1,X3,X4,X5) = esk360_4(X2,X3,X4,X5) ) ).
cnf(i_0_5145,axiom,
( X1 != X2
| esk360_4(X3,X1,X4,X5) = esk360_4(X3,X2,X4,X5) ) ).
cnf(i_0_5146,axiom,
( X1 != X2
| esk360_4(X3,X4,X1,X5) = esk360_4(X3,X4,X2,X5) ) ).
cnf(i_0_5147,axiom,
( X1 != X2
| esk360_4(X3,X4,X5,X1) = esk360_4(X3,X4,X5,X2) ) ).
cnf(i_0_5148,axiom,
( X1 != X2
| esk361_4(X1,X3,X4,X5) = esk361_4(X2,X3,X4,X5) ) ).
cnf(i_0_5149,axiom,
( X1 != X2
| esk361_4(X3,X1,X4,X5) = esk361_4(X3,X2,X4,X5) ) ).
cnf(i_0_5150,axiom,
( X1 != X2
| esk361_4(X3,X4,X1,X5) = esk361_4(X3,X4,X2,X5) ) ).
cnf(i_0_5151,axiom,
( X1 != X2
| esk361_4(X3,X4,X5,X1) = esk361_4(X3,X4,X5,X2) ) ).
cnf(i_0_5152,axiom,
( X1 != X2
| esk342_4(X1,X3,X4,X5) = esk342_4(X2,X3,X4,X5) ) ).
cnf(i_0_5153,axiom,
( X1 != X2
| esk342_4(X3,X1,X4,X5) = esk342_4(X3,X2,X4,X5) ) ).
cnf(i_0_5154,axiom,
( X1 != X2
| esk342_4(X3,X4,X1,X5) = esk342_4(X3,X4,X2,X5) ) ).
cnf(i_0_5155,axiom,
( X1 != X2
| esk342_4(X3,X4,X5,X1) = esk342_4(X3,X4,X5,X2) ) ).
cnf(i_0_5156,axiom,
( X1 != X2
| esk216_2(X1,X3) = esk216_2(X2,X3) ) ).
cnf(i_0_5157,axiom,
( X1 != X2
| esk216_2(X3,X1) = esk216_2(X3,X2) ) ).
cnf(i_0_5158,axiom,
( X1 != X2
| fiber(X1,X3) = fiber(X2,X3) ) ).
cnf(i_0_5159,axiom,
( X1 != X2
| fiber(X3,X1) = fiber(X3,X2) ) ).
cnf(i_0_5160,axiom,
( X1 != X2
| esk46_3(X1,X3,X4) = esk46_3(X2,X3,X4) ) ).
cnf(i_0_5161,axiom,
( X1 != X2
| esk46_3(X3,X1,X4) = esk46_3(X3,X2,X4) ) ).
cnf(i_0_5162,axiom,
( X1 != X2
| esk46_3(X3,X4,X1) = esk46_3(X3,X4,X2) ) ).
cnf(i_0_5163,axiom,
( X1 != X2
| relation_inverse_image(X1,X3) = relation_inverse_image(X2,X3) ) ).
cnf(i_0_5164,axiom,
( X1 != X2
| relation_inverse_image(X3,X1) = relation_inverse_image(X3,X2) ) ).
cnf(i_0_5165,axiom,
( X1 != X2
| relation_dom_as_subset(X1,X3,X4) = relation_dom_as_subset(X2,X3,X4) ) ).
cnf(i_0_5166,axiom,
( X1 != X2
| relation_dom_as_subset(X3,X1,X4) = relation_dom_as_subset(X3,X2,X4) ) ).
cnf(i_0_5167,axiom,
( X1 != X2
| relation_dom_as_subset(X3,X4,X1) = relation_dom_as_subset(X3,X4,X2) ) ).
cnf(i_0_5168,axiom,
( X1 != X2
| esk215_2(X1,X3) = esk215_2(X2,X3) ) ).
cnf(i_0_5169,axiom,
( X1 != X2
| esk215_2(X3,X1) = esk215_2(X3,X2) ) ).
cnf(i_0_5170,axiom,
( X1 != X2
| esk454_4(X1,X3,X4,X5) = esk454_4(X2,X3,X4,X5) ) ).
cnf(i_0_5171,axiom,
( X1 != X2
| esk454_4(X3,X1,X4,X5) = esk454_4(X3,X2,X4,X5) ) ).
cnf(i_0_5172,axiom,
( X1 != X2
| esk454_4(X3,X4,X1,X5) = esk454_4(X3,X4,X2,X5) ) ).
cnf(i_0_5173,axiom,
( X1 != X2
| esk454_4(X3,X4,X5,X1) = esk454_4(X3,X4,X5,X2) ) ).
cnf(i_0_5174,axiom,
( X1 != X2
| esk453_3(X1,X3,X4) = esk453_3(X2,X3,X4) ) ).
cnf(i_0_5175,axiom,
( X1 != X2
| esk453_3(X3,X1,X4) = esk453_3(X3,X2,X4) ) ).
cnf(i_0_5176,axiom,
( X1 != X2
| esk453_3(X3,X4,X1) = esk453_3(X3,X4,X2) ) ).
cnf(i_0_5177,axiom,
( X1 != X2
| esk452_4(X1,X3,X4,X5) = esk452_4(X2,X3,X4,X5) ) ).
cnf(i_0_5178,axiom,
( X1 != X2
| esk452_4(X3,X1,X4,X5) = esk452_4(X3,X2,X4,X5) ) ).
cnf(i_0_5179,axiom,
( X1 != X2
| esk452_4(X3,X4,X1,X5) = esk452_4(X3,X4,X2,X5) ) ).
cnf(i_0_5180,axiom,
( X1 != X2
| esk452_4(X3,X4,X5,X1) = esk452_4(X3,X4,X5,X2) ) ).
cnf(i_0_5181,axiom,
( X1 != X2
| esk451_3(X1,X3,X4) = esk451_3(X2,X3,X4) ) ).
cnf(i_0_5182,axiom,
( X1 != X2
| esk451_3(X3,X1,X4) = esk451_3(X3,X2,X4) ) ).
cnf(i_0_5183,axiom,
( X1 != X2
| esk451_3(X3,X4,X1) = esk451_3(X3,X4,X2) ) ).
cnf(i_0_5184,axiom,
( X1 != X2
| relation_inverse(X1) = relation_inverse(X2) ) ).
cnf(i_0_5185,axiom,
( X1 != X2
| esk183_4(X1,X3,X4,X5) = esk183_4(X2,X3,X4,X5) ) ).
cnf(i_0_5186,axiom,
( X1 != X2
| esk183_4(X3,X1,X4,X5) = esk183_4(X3,X2,X4,X5) ) ).
cnf(i_0_5187,axiom,
( X1 != X2
| esk183_4(X3,X4,X1,X5) = esk183_4(X3,X4,X2,X5) ) ).
cnf(i_0_5188,axiom,
( X1 != X2
| esk183_4(X3,X4,X5,X1) = esk183_4(X3,X4,X5,X2) ) ).
cnf(i_0_5189,axiom,
( X1 != X2
| esk25_4(X1,X3,X4,X5) = esk25_4(X2,X3,X4,X5) ) ).
cnf(i_0_5190,axiom,
( X1 != X2
| esk25_4(X3,X1,X4,X5) = esk25_4(X3,X2,X4,X5) ) ).
cnf(i_0_5191,axiom,
( X1 != X2
| esk25_4(X3,X4,X1,X5) = esk25_4(X3,X4,X2,X5) ) ).
cnf(i_0_5192,axiom,
( X1 != X2
| esk25_4(X3,X4,X5,X1) = esk25_4(X3,X4,X5,X2) ) ).
cnf(i_0_5193,axiom,
( X1 != X2
| unordered_triple(X1,X3,X4) = unordered_triple(X2,X3,X4) ) ).
cnf(i_0_5194,axiom,
( X1 != X2
| unordered_triple(X3,X1,X4) = unordered_triple(X3,X2,X4) ) ).
cnf(i_0_5195,axiom,
( X1 != X2
| unordered_triple(X3,X4,X1) = unordered_triple(X3,X4,X2) ) ).
cnf(i_0_5196,axiom,
( X1 != X2
| esk191_2(X1,X3) = esk191_2(X2,X3) ) ).
cnf(i_0_5197,axiom,
( X1 != X2
| esk191_2(X3,X1) = esk191_2(X3,X2) ) ).
cnf(i_0_5198,axiom,
( X1 != X2
| esk189_2(X1,X3) = esk189_2(X2,X3) ) ).
cnf(i_0_5199,axiom,
( X1 != X2
| esk189_2(X3,X1) = esk189_2(X3,X2) ) ).
cnf(i_0_5200,axiom,
( X1 != X2
| esk193_4(X1,X3,X4,X5) = esk193_4(X2,X3,X4,X5) ) ).
cnf(i_0_5201,axiom,
( X1 != X2
| esk193_4(X3,X1,X4,X5) = esk193_4(X3,X2,X4,X5) ) ).
cnf(i_0_5202,axiom,
( X1 != X2
| esk193_4(X3,X4,X1,X5) = esk193_4(X3,X4,X2,X5) ) ).
cnf(i_0_5203,axiom,
( X1 != X2
| esk193_4(X3,X4,X5,X1) = esk193_4(X3,X4,X5,X2) ) ).
cnf(i_0_5204,axiom,
( X1 != X2
| esk190_2(X1,X3) = esk190_2(X2,X3) ) ).
cnf(i_0_5205,axiom,
( X1 != X2
| esk190_2(X3,X1) = esk190_2(X3,X2) ) ).
cnf(i_0_5206,axiom,
( X1 != X2
| esk225_4(X1,X3,X4,X5) = esk225_4(X2,X3,X4,X5) ) ).
cnf(i_0_5207,axiom,
( X1 != X2
| esk225_4(X3,X1,X4,X5) = esk225_4(X3,X2,X4,X5) ) ).
cnf(i_0_5208,axiom,
( X1 != X2
| esk225_4(X3,X4,X1,X5) = esk225_4(X3,X4,X2,X5) ) ).
cnf(i_0_5209,axiom,
( X1 != X2
| esk225_4(X3,X4,X5,X1) = esk225_4(X3,X4,X5,X2) ) ).
cnf(i_0_5210,axiom,
( X1 != X2
| esk196_2(X1,X3) = esk196_2(X2,X3) ) ).
cnf(i_0_5211,axiom,
( X1 != X2
| esk196_2(X3,X1) = esk196_2(X3,X2) ) ).
cnf(i_0_5212,axiom,
( X1 != X2
| esk194_2(X1,X3) = esk194_2(X2,X3) ) ).
cnf(i_0_5213,axiom,
( X1 != X2
| esk194_2(X3,X1) = esk194_2(X3,X2) ) ).
cnf(i_0_5214,axiom,
( X1 != X2
| esk198_4(X1,X3,X4,X5) = esk198_4(X2,X3,X4,X5) ) ).
cnf(i_0_5215,axiom,
( X1 != X2
| esk198_4(X3,X1,X4,X5) = esk198_4(X3,X2,X4,X5) ) ).
cnf(i_0_5216,axiom,
( X1 != X2
| esk198_4(X3,X4,X1,X5) = esk198_4(X3,X4,X2,X5) ) ).
cnf(i_0_5217,axiom,
( X1 != X2
| esk198_4(X3,X4,X5,X1) = esk198_4(X3,X4,X5,X2) ) ).
cnf(i_0_5218,axiom,
( X1 != X2
| esk195_2(X1,X3) = esk195_2(X2,X3) ) ).
cnf(i_0_5219,axiom,
( X1 != X2
| esk195_2(X3,X1) = esk195_2(X3,X2) ) ).
cnf(i_0_5220,axiom,
( X1 != X2
| esk290_4(X1,X3,X4,X5) = esk290_4(X2,X3,X4,X5) ) ).
cnf(i_0_5221,axiom,
( X1 != X2
| esk290_4(X3,X1,X4,X5) = esk290_4(X3,X2,X4,X5) ) ).
cnf(i_0_5222,axiom,
( X1 != X2
| esk290_4(X3,X4,X1,X5) = esk290_4(X3,X4,X2,X5) ) ).
cnf(i_0_5223,axiom,
( X1 != X2
| esk290_4(X3,X4,X5,X1) = esk290_4(X3,X4,X5,X2) ) ).
cnf(i_0_5224,axiom,
( X1 != X2
| esk278_2(X1,X3) = esk278_2(X2,X3) ) ).
cnf(i_0_5225,axiom,
( X1 != X2
| esk278_2(X3,X1) = esk278_2(X3,X2) ) ).
cnf(i_0_5226,axiom,
( X1 != X2
| esk281_4(X1,X3,X4,X5) = esk281_4(X2,X3,X4,X5) ) ).
cnf(i_0_5227,axiom,
( X1 != X2
| esk281_4(X3,X1,X4,X5) = esk281_4(X3,X2,X4,X5) ) ).
cnf(i_0_5228,axiom,
( X1 != X2
| esk281_4(X3,X4,X1,X5) = esk281_4(X3,X4,X2,X5) ) ).
cnf(i_0_5229,axiom,
( X1 != X2
| esk281_4(X3,X4,X5,X1) = esk281_4(X3,X4,X5,X2) ) ).
cnf(i_0_5230,axiom,
( X1 != X2
| esk276_2(X1,X3) = esk276_2(X2,X3) ) ).
cnf(i_0_5231,axiom,
( X1 != X2
| esk276_2(X3,X1) = esk276_2(X3,X2) ) ).
cnf(i_0_5232,axiom,
( X1 != X2
| esk277_2(X1,X3) = esk277_2(X2,X3) ) ).
cnf(i_0_5233,axiom,
( X1 != X2
| esk277_2(X3,X1) = esk277_2(X3,X2) ) ).
cnf(i_0_5234,axiom,
( X1 != X2
| esk65_3(X1,X3,X4) = esk65_3(X2,X3,X4) ) ).
cnf(i_0_5235,axiom,
( X1 != X2
| esk65_3(X3,X1,X4) = esk65_3(X3,X2,X4) ) ).
cnf(i_0_5236,axiom,
( X1 != X2
| esk65_3(X3,X4,X1) = esk65_3(X3,X4,X2) ) ).
cnf(i_0_5237,axiom,
( X1 != X2
| esk308_4(X1,X3,X4,X5) = esk308_4(X2,X3,X4,X5) ) ).
cnf(i_0_5238,axiom,
( X1 != X2
| esk308_4(X3,X1,X4,X5) = esk308_4(X3,X2,X4,X5) ) ).
cnf(i_0_5239,axiom,
( X1 != X2
| esk308_4(X3,X4,X1,X5) = esk308_4(X3,X4,X2,X5) ) ).
cnf(i_0_5240,axiom,
( X1 != X2
| esk308_4(X3,X4,X5,X1) = esk308_4(X3,X4,X5,X2) ) ).
cnf(i_0_5241,axiom,
( X1 != X2
| relation_composition(X1,X3) = relation_composition(X2,X3) ) ).
cnf(i_0_5242,axiom,
( X1 != X2
| relation_composition(X3,X1) = relation_composition(X3,X2) ) ).
cnf(i_0_5243,axiom,
( X1 != X2
| esk241_1(X1) = esk241_1(X2) ) ).
cnf(i_0_5244,axiom,
( X1 != X2
| esk237_1(X1) = esk237_1(X2) ) ).
cnf(i_0_5245,axiom,
( X1 != X2
| esk245_3(X1,X3,X4) = esk245_3(X2,X3,X4) ) ).
cnf(i_0_5246,axiom,
( X1 != X2
| esk245_3(X3,X1,X4) = esk245_3(X3,X2,X4) ) ).
cnf(i_0_5247,axiom,
( X1 != X2
| esk245_3(X3,X4,X1) = esk245_3(X3,X4,X2) ) ).
cnf(i_0_5248,axiom,
( X1 != X2
| esk239_1(X1) = esk239_1(X2) ) ).
cnf(i_0_5249,axiom,
( X1 != X2
| esk236_1(X1) = esk236_1(X2) ) ).
cnf(i_0_5250,axiom,
( X1 != X2
| esk296_2(X1,X3) = esk296_2(X2,X3) ) ).
cnf(i_0_5251,axiom,
( X1 != X2
| esk296_2(X3,X1) = esk296_2(X3,X2) ) ).
cnf(i_0_5252,axiom,
( X1 != X2
| apply(X1,X3) = apply(X2,X3) ) ).
cnf(i_0_5253,axiom,
( X1 != X2
| apply(X3,X1) = apply(X3,X2) ) ).
cnf(i_0_5254,axiom,
( X1 != X2
| esk299_4(X1,X3,X4,X5) = esk299_4(X2,X3,X4,X5) ) ).
cnf(i_0_5255,axiom,
( X1 != X2
| esk299_4(X3,X1,X4,X5) = esk299_4(X3,X2,X4,X5) ) ).
cnf(i_0_5256,axiom,
( X1 != X2
| esk299_4(X3,X4,X1,X5) = esk299_4(X3,X4,X2,X5) ) ).
cnf(i_0_5257,axiom,
( X1 != X2
| esk299_4(X3,X4,X5,X1) = esk299_4(X3,X4,X5,X2) ) ).
cnf(i_0_5258,axiom,
( X1 != X2
| esk294_2(X1,X3) = esk294_2(X2,X3) ) ).
cnf(i_0_5259,axiom,
( X1 != X2
| esk294_2(X3,X1) = esk294_2(X3,X2) ) ).
cnf(i_0_5260,axiom,
( X1 != X2
| esk295_2(X1,X3) = esk295_2(X2,X3) ) ).
cnf(i_0_5261,axiom,
( X1 != X2
| esk295_2(X3,X1) = esk295_2(X3,X2) ) ).
cnf(i_0_5262,axiom,
( X1 != X2
| esk248_1(X1) = esk248_1(X2) ) ).
cnf(i_0_5263,axiom,
( X1 != X2
| esk247_1(X1) = esk247_1(X2) ) ).
cnf(i_0_5264,axiom,
( X1 != X2
| esk254_4(X1,X3,X4,X5) = esk254_4(X2,X3,X4,X5) ) ).
cnf(i_0_5265,axiom,
( X1 != X2
| esk254_4(X3,X1,X4,X5) = esk254_4(X3,X2,X4,X5) ) ).
cnf(i_0_5266,axiom,
( X1 != X2
| esk254_4(X3,X4,X1,X5) = esk254_4(X3,X4,X2,X5) ) ).
cnf(i_0_5267,axiom,
( X1 != X2
| esk254_4(X3,X4,X5,X1) = esk254_4(X3,X4,X5,X2) ) ).
cnf(i_0_5268,axiom,
( X1 != X2
| esk253_3(X1,X3,X4) = esk253_3(X2,X3,X4) ) ).
cnf(i_0_5269,axiom,
( X1 != X2
| esk253_3(X3,X1,X4) = esk253_3(X3,X2,X4) ) ).
cnf(i_0_5270,axiom,
( X1 != X2
| esk253_3(X3,X4,X1) = esk253_3(X3,X4,X2) ) ).
cnf(i_0_5271,axiom,
( X1 != X2
| set_union2(X1,X3) = set_union2(X2,X3) ) ).
cnf(i_0_5272,axiom,
( X1 != X2
| set_union2(X3,X1) = set_union2(X3,X2) ) ).
cnf(i_0_5273,axiom,
( X1 != X2
| esk332_4(X1,X3,X4,X5) = esk332_4(X2,X3,X4,X5) ) ).
cnf(i_0_5274,axiom,
( X1 != X2
| esk332_4(X3,X1,X4,X5) = esk332_4(X3,X2,X4,X5) ) ).
cnf(i_0_5275,axiom,
( X1 != X2
| esk332_4(X3,X4,X1,X5) = esk332_4(X3,X4,X2,X5) ) ).
cnf(i_0_5276,axiom,
( X1 != X2
| esk332_4(X3,X4,X5,X1) = esk332_4(X3,X4,X5,X2) ) ).
cnf(i_0_5277,axiom,
( X1 != X2
| esk330_3(X1,X3,X4) = esk330_3(X2,X3,X4) ) ).
cnf(i_0_5278,axiom,
( X1 != X2
| esk330_3(X3,X1,X4) = esk330_3(X3,X2,X4) ) ).
cnf(i_0_5279,axiom,
( X1 != X2
| esk330_3(X3,X4,X1) = esk330_3(X3,X4,X2) ) ).
cnf(i_0_5280,axiom,
( X1 != X2
| esk329_3(X1,X3,X4) = esk329_3(X2,X3,X4) ) ).
cnf(i_0_5281,axiom,
( X1 != X2
| esk329_3(X3,X1,X4) = esk329_3(X3,X2,X4) ) ).
cnf(i_0_5282,axiom,
( X1 != X2
| esk329_3(X3,X4,X1) = esk329_3(X3,X4,X2) ) ).
cnf(i_0_5283,axiom,
( X1 != X2
| inclusion_relation(X1) = inclusion_relation(X2) ) ).
cnf(i_0_5284,axiom,
( X1 != X2
| identity_relation(X1) = identity_relation(X2) ) ).
cnf(i_0_5285,axiom,
( X1 != X2
| esk2_2(X1,X3) = esk2_2(X2,X3) ) ).
cnf(i_0_5286,axiom,
( X1 != X2
| esk2_2(X3,X1) = esk2_2(X3,X2) ) ).
cnf(i_0_5287,axiom,
( X1 != X2
| unordered_pair(X1,X3) = unordered_pair(X2,X3) ) ).
cnf(i_0_5288,axiom,
( X1 != X2
| unordered_pair(X3,X1) = unordered_pair(X3,X2) ) ).
cnf(i_0_5289,axiom,
( X1 != X2
| esk1_2(X1,X3) = esk1_2(X2,X3) ) ).
cnf(i_0_5290,axiom,
( X1 != X2
| esk1_2(X3,X1) = esk1_2(X3,X2) ) ).
cnf(i_0_5291,axiom,
( X1 != X2
| esk235_1(X1) = esk235_1(X2) ) ).
cnf(i_0_5292,axiom,
( X1 != X2
| esk353_4(X1,X3,X4,X5) = esk353_4(X2,X3,X4,X5) ) ).
cnf(i_0_5293,axiom,
( X1 != X2
| esk353_4(X3,X1,X4,X5) = esk353_4(X3,X2,X4,X5) ) ).
cnf(i_0_5294,axiom,
( X1 != X2
| esk353_4(X3,X4,X1,X5) = esk353_4(X3,X4,X2,X5) ) ).
cnf(i_0_5295,axiom,
( X1 != X2
| esk353_4(X3,X4,X5,X1) = esk353_4(X3,X4,X5,X2) ) ).
cnf(i_0_5296,axiom,
( X1 != X2
| esk352_3(X1,X3,X4) = esk352_3(X2,X3,X4) ) ).
cnf(i_0_5297,axiom,
( X1 != X2
| esk352_3(X3,X1,X4) = esk352_3(X3,X2,X4) ) ).
cnf(i_0_5298,axiom,
( X1 != X2
| esk352_3(X3,X4,X1) = esk352_3(X3,X4,X2) ) ).
cnf(i_0_5299,axiom,
( X1 != X2
| esk348_3(X1,X3,X4) = esk348_3(X2,X3,X4) ) ).
cnf(i_0_5300,axiom,
( X1 != X2
| esk348_3(X3,X1,X4) = esk348_3(X3,X2,X4) ) ).
cnf(i_0_5301,axiom,
( X1 != X2
| esk348_3(X3,X4,X1) = esk348_3(X3,X4,X2) ) ).
cnf(i_0_5302,axiom,
( X1 != X2
| ordered_pair_as_product_element(X1,X3,X4,X5) = ordered_pair_as_product_element(X2,X3,X4,X5) ) ).
cnf(i_0_5303,axiom,
( X1 != X2
| ordered_pair_as_product_element(X3,X1,X4,X5) = ordered_pair_as_product_element(X3,X2,X4,X5) ) ).
cnf(i_0_5304,axiom,
( X1 != X2
| ordered_pair_as_product_element(X3,X4,X1,X5) = ordered_pair_as_product_element(X3,X4,X2,X5) ) ).
cnf(i_0_5305,axiom,
( X1 != X2
| ordered_pair_as_product_element(X3,X4,X5,X1) = ordered_pair_as_product_element(X3,X4,X5,X2) ) ).
cnf(i_0_5306,axiom,
( X1 != X2
| relation_of_lattice(X1) = relation_of_lattice(X2) ) ).
cnf(i_0_5307,axiom,
( X1 != X2
| esk213_3(X1,X3,X4) = esk213_3(X2,X3,X4) ) ).
cnf(i_0_5308,axiom,
( X1 != X2
| esk213_3(X3,X1,X4) = esk213_3(X3,X2,X4) ) ).
cnf(i_0_5309,axiom,
( X1 != X2
| esk213_3(X3,X4,X1) = esk213_3(X3,X4,X2) ) ).
cnf(i_0_5310,axiom,
( X1 != X2
| esk96_2(X1,X3) = esk96_2(X2,X3) ) ).
cnf(i_0_5311,axiom,
( X1 != X2
| esk96_2(X3,X1) = esk96_2(X3,X2) ) ).
cnf(i_0_5312,axiom,
( X1 != X2
| esk95_2(X1,X3) = esk95_2(X2,X3) ) ).
cnf(i_0_5313,axiom,
( X1 != X2
| esk95_2(X3,X1) = esk95_2(X3,X2) ) ).
cnf(i_0_5314,axiom,
( X1 != X2
| esk328_3(X1,X3,X4) = esk328_3(X2,X3,X4) ) ).
cnf(i_0_5315,axiom,
( X1 != X2
| esk328_3(X3,X1,X4) = esk328_3(X3,X2,X4) ) ).
cnf(i_0_5316,axiom,
( X1 != X2
| esk328_3(X3,X4,X1) = esk328_3(X3,X4,X2) ) ).
cnf(i_0_5317,axiom,
( X1 != X2
| set_difference(X1,X3) = set_difference(X2,X3) ) ).
cnf(i_0_5318,axiom,
( X1 != X2
| set_difference(X3,X1) = set_difference(X3,X2) ) ).
cnf(i_0_5319,axiom,
( X1 != X2
| esk270_2(X1,X3) = esk270_2(X2,X3) ) ).
cnf(i_0_5320,axiom,
( X1 != X2
| esk270_2(X3,X1) = esk270_2(X3,X2) ) ).
cnf(i_0_5321,axiom,
( X1 != X2
| esk269_2(X1,X3) = esk269_2(X2,X3) ) ).
cnf(i_0_5322,axiom,
( X1 != X2
| esk269_2(X3,X1) = esk269_2(X3,X2) ) ).
cnf(i_0_5323,axiom,
( X1 != X2
| esk274_3(X1,X3,X4) = esk274_3(X2,X3,X4) ) ).
cnf(i_0_5324,axiom,
( X1 != X2
| esk274_3(X3,X1,X4) = esk274_3(X3,X2,X4) ) ).
cnf(i_0_5325,axiom,
( X1 != X2
| esk274_3(X3,X4,X1) = esk274_3(X3,X4,X2) ) ).
cnf(i_0_5326,axiom,
( X1 != X2
| esk268_2(X1,X3) = esk268_2(X2,X3) ) ).
cnf(i_0_5327,axiom,
( X1 != X2
| esk268_2(X3,X1) = esk268_2(X3,X2) ) ).
cnf(i_0_5328,axiom,
( X1 != X2
| boole_lattice(X1) = boole_lattice(X2) ) ).
cnf(i_0_5329,axiom,
( X1 != X2
| subset_union2(X1,X3,X4) = subset_union2(X2,X3,X4) ) ).
cnf(i_0_5330,axiom,
( X1 != X2
| subset_union2(X3,X1,X4) = subset_union2(X3,X2,X4) ) ).
cnf(i_0_5331,axiom,
( X1 != X2
| subset_union2(X3,X4,X1) = subset_union2(X3,X4,X2) ) ).
cnf(i_0_5332,axiom,
( X1 != X2
| subset_intersection2(X1,X3,X4) = subset_intersection2(X2,X3,X4) ) ).
cnf(i_0_5333,axiom,
( X1 != X2
| subset_intersection2(X3,X1,X4) = subset_intersection2(X3,X2,X4) ) ).
cnf(i_0_5334,axiom,
( X1 != X2
| subset_intersection2(X3,X4,X1) = subset_intersection2(X3,X4,X2) ) ).
cnf(i_0_5335,axiom,
( X1 != X2
| esk212_3(X1,X3,X4) = esk212_3(X2,X3,X4) ) ).
cnf(i_0_5336,axiom,
( X1 != X2
| esk212_3(X3,X1,X4) = esk212_3(X3,X2,X4) ) ).
cnf(i_0_5337,axiom,
( X1 != X2
| esk212_3(X3,X4,X1) = esk212_3(X3,X4,X2) ) ).
cnf(i_0_5338,axiom,
( X1 != X2
| apply_as_element(X1,X3,X4,X5) = apply_as_element(X2,X3,X4,X5) ) ).
cnf(i_0_5339,axiom,
( X1 != X2
| apply_as_element(X3,X1,X4,X5) = apply_as_element(X3,X2,X4,X5) ) ).
cnf(i_0_5340,axiom,
( X1 != X2
| apply_as_element(X3,X4,X1,X5) = apply_as_element(X3,X4,X2,X5) ) ).
cnf(i_0_5341,axiom,
( X1 != X2
| apply_as_element(X3,X4,X5,X1) = apply_as_element(X3,X4,X5,X2) ) ).
cnf(i_0_5342,axiom,
( X1 != X2
| topstr_closure(X1,X3) = topstr_closure(X2,X3) ) ).
cnf(i_0_5343,axiom,
( X1 != X2
| topstr_closure(X3,X1) = topstr_closure(X3,X2) ) ).
cnf(i_0_5344,axiom,
( X1 != X2
| latt_str_of(X1,X3,X4) = latt_str_of(X2,X3,X4) ) ).
cnf(i_0_5345,axiom,
( X1 != X2
| latt_str_of(X3,X1,X4) = latt_str_of(X3,X2,X4) ) ).
cnf(i_0_5346,axiom,
( X1 != X2
| latt_str_of(X3,X4,X1) = latt_str_of(X3,X4,X2) ) ).
cnf(i_0_5347,axiom,
( X1 != X2
| k10_filter_1(X1,X3,X4,X5) = k10_filter_1(X2,X3,X4,X5) ) ).
cnf(i_0_5348,axiom,
( X1 != X2
| k10_filter_1(X3,X1,X4,X5) = k10_filter_1(X3,X2,X4,X5) ) ).
cnf(i_0_5349,axiom,
( X1 != X2
| k10_filter_1(X3,X4,X1,X5) = k10_filter_1(X3,X4,X2,X5) ) ).
cnf(i_0_5350,axiom,
( X1 != X2
| k10_filter_1(X3,X4,X5,X1) = k10_filter_1(X3,X4,X5,X2) ) ).
cnf(i_0_5351,axiom,
( X1 != X2
| esk252_3(X1,X3,X4) = esk252_3(X2,X3,X4) ) ).
cnf(i_0_5352,axiom,
( X1 != X2
| esk252_3(X3,X1,X4) = esk252_3(X3,X2,X4) ) ).
cnf(i_0_5353,axiom,
( X1 != X2
| esk252_3(X3,X4,X1) = esk252_3(X3,X4,X2) ) ).
cnf(i_0_5354,axiom,
( X1 != X2
| esk251_2(X1,X3) = esk251_2(X2,X3) ) ).
cnf(i_0_5355,axiom,
( X1 != X2
| esk251_2(X3,X1) = esk251_2(X3,X2) ) ).
cnf(i_0_5356,axiom,
( X1 != X2
| esk390_2(X1,X3) = esk390_2(X2,X3) ) ).
cnf(i_0_5357,axiom,
( X1 != X2
| esk390_2(X3,X1) = esk390_2(X3,X2) ) ).
cnf(i_0_5358,axiom,
( X1 != X2
| esk392_3(X1,X3,X4) = esk392_3(X2,X3,X4) ) ).
cnf(i_0_5359,axiom,
( X1 != X2
| esk392_3(X3,X1,X4) = esk392_3(X3,X2,X4) ) ).
cnf(i_0_5360,axiom,
( X1 != X2
| esk392_3(X3,X4,X1) = esk392_3(X3,X4,X2) ) ).
cnf(i_0_5361,axiom,
( X1 != X2
| esk388_2(X1,X3) = esk388_2(X2,X3) ) ).
cnf(i_0_5362,axiom,
( X1 != X2
| esk388_2(X3,X1) = esk388_2(X3,X2) ) ).
cnf(i_0_5363,axiom,
( X1 != X2
| esk389_2(X1,X3) = esk389_2(X2,X3) ) ).
cnf(i_0_5364,axiom,
( X1 != X2
| esk389_2(X3,X1) = esk389_2(X3,X2) ) ).
cnf(i_0_5365,axiom,
( X1 != X2
| a_1_0_filter_1(X1) = a_1_0_filter_1(X2) ) ).
cnf(i_0_5366,axiom,
( X1 != X2
| esk351_3(X1,X3,X4) = esk351_3(X2,X3,X4) ) ).
cnf(i_0_5367,axiom,
( X1 != X2
| esk351_3(X3,X1,X4) = esk351_3(X3,X2,X4) ) ).
cnf(i_0_5368,axiom,
( X1 != X2
| esk351_3(X3,X4,X1) = esk351_3(X3,X4,X2) ) ).
cnf(i_0_5369,axiom,
( X1 != X2
| esk287_2(X1,X3) = esk287_2(X2,X3) ) ).
cnf(i_0_5370,axiom,
( X1 != X2
| esk287_2(X3,X1) = esk287_2(X3,X2) ) ).
cnf(i_0_5371,axiom,
( X1 != X2
| esk350_2(X1,X3) = esk350_2(X2,X3) ) ).
cnf(i_0_5372,axiom,
( X1 != X2
| esk350_2(X3,X1) = esk350_2(X3,X2) ) ).
cnf(i_0_5373,axiom,
( X1 != X2
| esk82_2(X1,X3) = esk82_2(X2,X3) ) ).
cnf(i_0_5374,axiom,
( X1 != X2
| esk82_2(X3,X1) = esk82_2(X3,X2) ) ).
cnf(i_0_5375,axiom,
( X1 != X2
| esk81_2(X1,X3) = esk81_2(X2,X3) ) ).
cnf(i_0_5376,axiom,
( X1 != X2
| esk81_2(X3,X1) = esk81_2(X3,X2) ) ).
cnf(i_0_5377,axiom,
( X1 != X2
| esk396_2(X1,X3) = esk396_2(X2,X3) ) ).
cnf(i_0_5378,axiom,
( X1 != X2
| esk396_2(X3,X1) = esk396_2(X3,X2) ) ).
cnf(i_0_5379,axiom,
( X1 != X2
| esk398_3(X1,X3,X4) = esk398_3(X2,X3,X4) ) ).
cnf(i_0_5380,axiom,
( X1 != X2
| esk398_3(X3,X1,X4) = esk398_3(X3,X2,X4) ) ).
cnf(i_0_5381,axiom,
( X1 != X2
| esk398_3(X3,X4,X1) = esk398_3(X3,X4,X2) ) ).
cnf(i_0_5382,axiom,
( X1 != X2
| esk394_2(X1,X3) = esk394_2(X2,X3) ) ).
cnf(i_0_5383,axiom,
( X1 != X2
| esk394_2(X3,X1) = esk394_2(X3,X2) ) ).
cnf(i_0_5384,axiom,
( X1 != X2
| esk395_2(X1,X3) = esk395_2(X2,X3) ) ).
cnf(i_0_5385,axiom,
( X1 != X2
| esk395_2(X3,X1) = esk395_2(X3,X2) ) ).
cnf(i_0_5386,axiom,
( X1 != X2
| esk288_2(X1,X3) = esk288_2(X2,X3) ) ).
cnf(i_0_5387,axiom,
( X1 != X2
| esk288_2(X3,X1) = esk288_2(X3,X2) ) ).
cnf(i_0_5388,axiom,
( X1 != X2
| esk391_2(X1,X3) = esk391_2(X2,X3) ) ).
cnf(i_0_5389,axiom,
( X1 != X2
| esk391_2(X3,X1) = esk391_2(X3,X2) ) ).
cnf(i_0_5390,axiom,
( X1 != X2
| esk298_3(X1,X3,X4) = esk298_3(X2,X3,X4) ) ).
cnf(i_0_5391,axiom,
( X1 != X2
| esk298_3(X3,X1,X4) = esk298_3(X3,X2,X4) ) ).
cnf(i_0_5392,axiom,
( X1 != X2
| esk298_3(X3,X4,X1) = esk298_3(X3,X4,X2) ) ).
cnf(i_0_5393,axiom,
( X1 != X2
| esk280_3(X1,X3,X4) = esk280_3(X2,X3,X4) ) ).
cnf(i_0_5394,axiom,
( X1 != X2
| esk280_3(X3,X1,X4) = esk280_3(X3,X2,X4) ) ).
cnf(i_0_5395,axiom,
( X1 != X2
| esk280_3(X3,X4,X1) = esk280_3(X3,X4,X2) ) ).
cnf(i_0_5396,axiom,
( X1 != X2
| esk284_2(X1,X3) = esk284_2(X2,X3) ) ).
cnf(i_0_5397,axiom,
( X1 != X2
| esk284_2(X3,X1) = esk284_2(X3,X2) ) ).
cnf(i_0_5398,axiom,
( X1 != X2
| union_of_subsets(X1,X3) = union_of_subsets(X2,X3) ) ).
cnf(i_0_5399,axiom,
( X1 != X2
| union_of_subsets(X3,X1) = union_of_subsets(X3,X2) ) ).
cnf(i_0_5400,axiom,
( X1 != X2
| meet_of_latt_set(X1,X3) = meet_of_latt_set(X2,X3) ) ).
cnf(i_0_5401,axiom,
( X1 != X2
| meet_of_latt_set(X3,X1) = meet_of_latt_set(X3,X2) ) ).
cnf(i_0_5402,axiom,
( X1 != X2
| join_of_latt_set(X1,X3) = join_of_latt_set(X2,X3) ) ).
cnf(i_0_5403,axiom,
( X1 != X2
| join_of_latt_set(X3,X1) = join_of_latt_set(X3,X2) ) ).
cnf(i_0_5404,axiom,
( X1 != X2
| esk397_2(X1,X3) = esk397_2(X2,X3) ) ).
cnf(i_0_5405,axiom,
( X1 != X2
| esk397_2(X3,X1) = esk397_2(X3,X2) ) ).
cnf(i_0_5406,axiom,
( X1 != X2
| esk267_3(X1,X3,X4) = esk267_3(X2,X3,X4) ) ).
cnf(i_0_5407,axiom,
( X1 != X2
| esk267_3(X3,X1,X4) = esk267_3(X3,X2,X4) ) ).
cnf(i_0_5408,axiom,
( X1 != X2
| esk267_3(X3,X4,X1) = esk267_3(X3,X4,X2) ) ).
cnf(i_0_5409,axiom,
( X1 != X2
| cast_as_carrier_subset(X1) = cast_as_carrier_subset(X2) ) ).
cnf(i_0_5410,axiom,
( X1 != X2
| esk265_2(X1,X3) = esk265_2(X2,X3) ) ).
cnf(i_0_5411,axiom,
( X1 != X2
| esk265_2(X3,X1) = esk265_2(X3,X2) ) ).
cnf(i_0_5412,axiom,
( X1 != X2
| esk264_2(X1,X3) = esk264_2(X2,X3) ) ).
cnf(i_0_5413,axiom,
( X1 != X2
| esk264_2(X3,X1) = esk264_2(X3,X2) ) ).
cnf(i_0_5414,axiom,
( X1 != X2
| esk137_1(X1) = esk137_1(X2) ) ).
cnf(i_0_5415,axiom,
( X1 != X2
| esk136_1(X1) = esk136_1(X2) ) ).
cnf(i_0_5416,axiom,
( X1 != X2
| esk204_2(X1,X3) = esk204_2(X2,X3) ) ).
cnf(i_0_5417,axiom,
( X1 != X2
| esk204_2(X3,X1) = esk204_2(X3,X2) ) ).
cnf(i_0_5418,axiom,
( X1 != X2
| esk201_2(X1,X3) = esk201_2(X2,X3) ) ).
cnf(i_0_5419,axiom,
( X1 != X2
| esk201_2(X3,X1) = esk201_2(X3,X2) ) ).
cnf(i_0_5420,axiom,
( X1 != X2
| subset_complement(X1,X3) = subset_complement(X2,X3) ) ).
cnf(i_0_5421,axiom,
( X1 != X2
| subset_complement(X3,X1) = subset_complement(X3,X2) ) ).
cnf(i_0_5422,axiom,
( X1 != X2
| pair_second(X1) = pair_second(X2) ) ).
cnf(i_0_5423,axiom,
( X1 != X2
| esk54_2(X1,X3) = esk54_2(X2,X3) ) ).
cnf(i_0_5424,axiom,
( X1 != X2
| esk54_2(X3,X1) = esk54_2(X3,X2) ) ).
cnf(i_0_5425,axiom,
( X1 != X2
| pair_first(X1) = pair_first(X2) ) ).
cnf(i_0_5426,axiom,
( X1 != X2
| esk32_2(X1,X3) = esk32_2(X2,X3) ) ).
cnf(i_0_5427,axiom,
( X1 != X2
| esk32_2(X3,X1) = esk32_2(X3,X2) ) ).
cnf(i_0_5428,axiom,
( X1 != X2
| esk404_2(X1,X3) = esk404_2(X2,X3) ) ).
cnf(i_0_5429,axiom,
( X1 != X2
| esk404_2(X3,X1) = esk404_2(X3,X2) ) ).
cnf(i_0_5430,axiom,
( X1 != X2
| esk401_2(X1,X3) = esk401_2(X2,X3) ) ).
cnf(i_0_5431,axiom,
( X1 != X2
| esk401_2(X3,X1) = esk401_2(X3,X2) ) ).
cnf(i_0_5432,axiom,
( X1 != X2
| esk6_3(X1,X3,X4) = esk6_3(X2,X3,X4) ) ).
cnf(i_0_5433,axiom,
( X1 != X2
| esk6_3(X3,X1,X4) = esk6_3(X3,X2,X4) ) ).
cnf(i_0_5434,axiom,
( X1 != X2
| esk6_3(X3,X4,X1) = esk6_3(X3,X4,X2) ) ).
cnf(i_0_5435,axiom,
( X1 != X2
| function_inverse(X1) = function_inverse(X2) ) ).
cnf(i_0_5436,axiom,
( X1 != X2
| the_carrier(X1) = the_carrier(X2) ) ).
cnf(i_0_5437,axiom,
( X1 != X2
| esk435_2(X1,X3) = esk435_2(X2,X3) ) ).
cnf(i_0_5438,axiom,
( X1 != X2
| esk435_2(X3,X1) = esk435_2(X3,X2) ) ).
cnf(i_0_5439,axiom,
( X1 != X2
| esk436_2(X1,X3) = esk436_2(X2,X3) ) ).
cnf(i_0_5440,axiom,
( X1 != X2
| esk436_2(X3,X1) = esk436_2(X3,X2) ) ).
cnf(i_0_5441,axiom,
( X1 != X2
| esk434_2(X1,X3) = esk434_2(X2,X3) ) ).
cnf(i_0_5442,axiom,
( X1 != X2
| esk434_2(X3,X1) = esk434_2(X3,X2) ) ).
cnf(i_0_5443,axiom,
( X1 != X2
| esk433_2(X1,X3) = esk433_2(X2,X3) ) ).
cnf(i_0_5444,axiom,
( X1 != X2
| esk433_2(X3,X1) = esk433_2(X3,X2) ) ).
cnf(i_0_5445,axiom,
( X1 != X2
| esk293_6(X1,X3,X4,X5,X6,X7) = esk293_6(X2,X3,X4,X5,X6,X7) ) ).
cnf(i_0_5446,axiom,
( X1 != X2
| esk293_6(X3,X1,X4,X5,X6,X7) = esk293_6(X3,X2,X4,X5,X6,X7) ) ).
cnf(i_0_5447,axiom,
( X1 != X2
| esk293_6(X3,X4,X1,X5,X6,X7) = esk293_6(X3,X4,X2,X5,X6,X7) ) ).
cnf(i_0_5448,axiom,
( X1 != X2
| esk293_6(X3,X4,X5,X1,X6,X7) = esk293_6(X3,X4,X5,X2,X6,X7) ) ).
cnf(i_0_5449,axiom,
( X1 != X2
| esk293_6(X3,X4,X5,X6,X1,X7) = esk293_6(X3,X4,X5,X6,X2,X7) ) ).
cnf(i_0_5450,axiom,
( X1 != X2
| esk293_6(X3,X4,X5,X6,X7,X1) = esk293_6(X3,X4,X5,X6,X7,X2) ) ).
cnf(i_0_5451,axiom,
( X1 != X2
| esk263_2(X1,X3) = esk263_2(X2,X3) ) ).
cnf(i_0_5452,axiom,
( X1 != X2
| esk263_2(X3,X1) = esk263_2(X3,X2) ) ).
cnf(i_0_5453,axiom,
( X1 != X2
| esk243_3(X1,X3,X4) = esk243_3(X2,X3,X4) ) ).
cnf(i_0_5454,axiom,
( X1 != X2
| esk243_3(X3,X1,X4) = esk243_3(X3,X2,X4) ) ).
cnf(i_0_5455,axiom,
( X1 != X2
| esk243_3(X3,X4,X1) = esk243_3(X3,X4,X2) ) ).
cnf(i_0_5456,axiom,
( X1 != X2
| esk262_3(X1,X3,X4) = esk262_3(X2,X3,X4) ) ).
cnf(i_0_5457,axiom,
( X1 != X2
| esk262_3(X3,X1,X4) = esk262_3(X3,X2,X4) ) ).
cnf(i_0_5458,axiom,
( X1 != X2
| esk262_3(X3,X4,X1) = esk262_3(X3,X4,X2) ) ).
cnf(i_0_5459,axiom,
( X1 != X2
| esk259_2(X1,X3) = esk259_2(X2,X3) ) ).
cnf(i_0_5460,axiom,
( X1 != X2
| esk259_2(X3,X1) = esk259_2(X3,X2) ) ).
cnf(i_0_5461,axiom,
( X1 != X2
| esk261_3(X1,X3,X4) = esk261_3(X2,X3,X4) ) ).
cnf(i_0_5462,axiom,
( X1 != X2
| esk261_3(X3,X1,X4) = esk261_3(X3,X2,X4) ) ).
cnf(i_0_5463,axiom,
( X1 != X2
| esk261_3(X3,X4,X1) = esk261_3(X3,X4,X2) ) ).
cnf(i_0_5464,axiom,
( X1 != X2
| esk258_2(X1,X3) = esk258_2(X2,X3) ) ).
cnf(i_0_5465,axiom,
( X1 != X2
| esk258_2(X3,X1) = esk258_2(X3,X2) ) ).
cnf(i_0_5466,axiom,
( X1 != X2
| complements_of_subsets(X1,X3) = complements_of_subsets(X2,X3) ) ).
cnf(i_0_5467,axiom,
( X1 != X2
| complements_of_subsets(X3,X1) = complements_of_subsets(X3,X2) ) ).
cnf(i_0_5468,axiom,
( X1 != X2
| esk105_1(X1) = esk105_1(X2) ) ).
cnf(i_0_5469,axiom,
( X1 != X2
| esk446_1(X1) = esk446_1(X2) ) ).
cnf(i_0_5470,axiom,
( X1 != X2
| esk407_3(X1,X3,X4) = esk407_3(X2,X3,X4) ) ).
cnf(i_0_5471,axiom,
( X1 != X2
| esk407_3(X3,X1,X4) = esk407_3(X3,X2,X4) ) ).
cnf(i_0_5472,axiom,
( X1 != X2
| esk407_3(X3,X4,X1) = esk407_3(X3,X4,X2) ) ).
cnf(i_0_5473,axiom,
( X1 != X2
| poset_of_lattice(X1) = poset_of_lattice(X2) ) ).
cnf(i_0_5474,axiom,
( X1 != X2
| cast_to_el_of_LattPOSet(X1,X3) = cast_to_el_of_LattPOSet(X2,X3) ) ).
cnf(i_0_5475,axiom,
( X1 != X2
| cast_to_el_of_LattPOSet(X3,X1) = cast_to_el_of_LattPOSet(X3,X2) ) ).
cnf(i_0_5476,axiom,
( X1 != X2
| esk339_3(X1,X3,X4) = esk339_3(X2,X3,X4) ) ).
cnf(i_0_5477,axiom,
( X1 != X2
| esk339_3(X3,X1,X4) = esk339_3(X3,X2,X4) ) ).
cnf(i_0_5478,axiom,
( X1 != X2
| esk339_3(X3,X4,X1) = esk339_3(X3,X4,X2) ) ).
cnf(i_0_5479,axiom,
( X1 != X2
| esk335_2(X1,X3) = esk335_2(X2,X3) ) ).
cnf(i_0_5480,axiom,
( X1 != X2
| esk335_2(X3,X1) = esk335_2(X3,X2) ) ).
cnf(i_0_5481,axiom,
( X1 != X2
| esk334_2(X1,X3) = esk334_2(X2,X3) ) ).
cnf(i_0_5482,axiom,
( X1 != X2
| esk334_2(X3,X1) = esk334_2(X3,X2) ) ).
cnf(i_0_5483,axiom,
( X1 != X2
| powerset(X1) = powerset(X2) ) ).
cnf(i_0_5484,axiom,
( X1 != X2
| esk256_2(X1,X3) = esk256_2(X2,X3) ) ).
cnf(i_0_5485,axiom,
( X1 != X2
| esk256_2(X3,X1) = esk256_2(X3,X2) ) ).
cnf(i_0_5486,axiom,
( X1 != X2
| esk257_2(X1,X3) = esk257_2(X2,X3) ) ).
cnf(i_0_5487,axiom,
( X1 != X2
| esk257_2(X3,X1) = esk257_2(X3,X2) ) ).
cnf(i_0_5488,axiom,
( X1 != X2
| bottom_of_semilattstr(X1) = bottom_of_semilattstr(X2) ) ).
cnf(i_0_5489,axiom,
( X1 != X2
| identity_on_carrier(X1) = identity_on_carrier(X2) ) ).
cnf(i_0_5490,axiom,
( X1 != X2
| esk337_2(X1,X3) = esk337_2(X2,X3) ) ).
cnf(i_0_5491,axiom,
( X1 != X2
| esk337_2(X3,X1) = esk337_2(X3,X2) ) ).
cnf(i_0_5492,axiom,
( X1 != X2
| esk336_2(X1,X3) = esk336_2(X2,X3) ) ).
cnf(i_0_5493,axiom,
( X1 != X2
| esk336_2(X3,X1) = esk336_2(X3,X2) ) ).
cnf(i_0_5494,axiom,
( X1 != X2
| esk285_2(X1,X3) = esk285_2(X2,X3) ) ).
cnf(i_0_5495,axiom,
( X1 != X2
| esk285_2(X3,X1) = esk285_2(X3,X2) ) ).
cnf(i_0_5496,axiom,
( X1 != X2
| subset_difference(X1,X3,X4) = subset_difference(X2,X3,X4) ) ).
cnf(i_0_5497,axiom,
( X1 != X2
| subset_difference(X3,X1,X4) = subset_difference(X3,X2,X4) ) ).
cnf(i_0_5498,axiom,
( X1 != X2
| subset_difference(X3,X4,X1) = subset_difference(X3,X4,X2) ) ).
cnf(i_0_5499,axiom,
( X1 != X2
| esk333_2(X1,X3) = esk333_2(X2,X3) ) ).
cnf(i_0_5500,axiom,
( X1 != X2
| esk333_2(X3,X1) = esk333_2(X3,X2) ) ).
cnf(i_0_5501,axiom,
( X1 != X2
| esk255_2(X1,X3) = esk255_2(X2,X3) ) ).
cnf(i_0_5502,axiom,
( X1 != X2
| esk255_2(X3,X1) = esk255_2(X3,X2) ) ).
cnf(i_0_5503,axiom,
( X1 != X2
| esk58_3(X1,X3,X4) = esk58_3(X2,X3,X4) ) ).
cnf(i_0_5504,axiom,
( X1 != X2
| esk58_3(X3,X1,X4) = esk58_3(X3,X2,X4) ) ).
cnf(i_0_5505,axiom,
( X1 != X2
| esk58_3(X3,X4,X1) = esk58_3(X3,X4,X2) ) ).
cnf(i_0_5506,axiom,
( X1 != X2
| esk187_1(X1) = esk187_1(X2) ) ).
cnf(i_0_5507,axiom,
( X1 != X2
| esk286_2(X1,X3) = esk286_2(X2,X3) ) ).
cnf(i_0_5508,axiom,
( X1 != X2
| esk286_2(X3,X1) = esk286_2(X3,X2) ) ).
cnf(i_0_5509,axiom,
( X1 != X2
| esk186_1(X1) = esk186_1(X2) ) ).
cnf(i_0_5510,axiom,
( X1 != X2
| esk355_3(X1,X3,X4) = esk355_3(X2,X3,X4) ) ).
cnf(i_0_5511,axiom,
( X1 != X2
| esk355_3(X3,X1,X4) = esk355_3(X3,X2,X4) ) ).
cnf(i_0_5512,axiom,
( X1 != X2
| esk355_3(X3,X4,X1) = esk355_3(X3,X4,X2) ) ).
cnf(i_0_5513,axiom,
( X1 != X2
| cast_to_el_of_lattice(X1,X3) = cast_to_el_of_lattice(X2,X3) ) ).
cnf(i_0_5514,axiom,
( X1 != X2
| cast_to_el_of_lattice(X3,X1) = cast_to_el_of_lattice(X3,X2) ) ).
cnf(i_0_5515,axiom,
( X1 != X2
| esk135_1(X1) = esk135_1(X2) ) ).
cnf(i_0_5516,axiom,
( X1 != X2
| esk134_1(X1) = esk134_1(X2) ) ).
cnf(i_0_5517,axiom,
( X1 != X2
| esk283_2(X1,X3) = esk283_2(X2,X3) ) ).
cnf(i_0_5518,axiom,
( X1 != X2
| esk283_2(X3,X1) = esk283_2(X3,X2) ) ).
cnf(i_0_5519,axiom,
( X1 != X2
| meet_commut(X1,X3,X4) = meet_commut(X2,X3,X4) ) ).
cnf(i_0_5520,axiom,
( X1 != X2
| meet_commut(X3,X1,X4) = meet_commut(X3,X2,X4) ) ).
cnf(i_0_5521,axiom,
( X1 != X2
| meet_commut(X3,X4,X1) = meet_commut(X3,X4,X2) ) ).
cnf(i_0_5522,axiom,
( X1 != X2
| esk128_3(X1,X3,X4) = esk128_3(X2,X3,X4) ) ).
cnf(i_0_5523,axiom,
( X1 != X2
| esk128_3(X3,X1,X4) = esk128_3(X3,X2,X4) ) ).
cnf(i_0_5524,axiom,
( X1 != X2
| esk128_3(X3,X4,X1) = esk128_3(X3,X4,X2) ) ).
cnf(i_0_5525,axiom,
( X1 != X2
| esk29_1(X1) = esk29_1(X2) ) ).
cnf(i_0_5526,axiom,
( X1 != X2
| esk28_1(X1) = esk28_1(X2) ) ).
cnf(i_0_5527,axiom,
( X1 != X2
| esk127_3(X1,X3,X4) = esk127_3(X2,X3,X4) ) ).
cnf(i_0_5528,axiom,
( X1 != X2
| esk127_3(X3,X1,X4) = esk127_3(X3,X2,X4) ) ).
cnf(i_0_5529,axiom,
( X1 != X2
| esk127_3(X3,X4,X1) = esk127_3(X3,X4,X2) ) ).
cnf(i_0_5530,axiom,
( X1 != X2
| esk305_2(X1,X3) = esk305_2(X2,X3) ) ).
cnf(i_0_5531,axiom,
( X1 != X2
| esk305_2(X3,X1) = esk305_2(X3,X2) ) ).
cnf(i_0_5532,axiom,
( X1 != X2
| esk340_3(X1,X3,X4) = esk340_3(X2,X3,X4) ) ).
cnf(i_0_5533,axiom,
( X1 != X2
| esk340_3(X3,X1,X4) = esk340_3(X3,X2,X4) ) ).
cnf(i_0_5534,axiom,
( X1 != X2
| esk340_3(X3,X4,X1) = esk340_3(X3,X4,X2) ) ).
cnf(i_0_5535,axiom,
( X1 != X2
| esk250_2(X1,X3) = esk250_2(X2,X3) ) ).
cnf(i_0_5536,axiom,
( X1 != X2
| esk250_2(X3,X1) = esk250_2(X3,X2) ) ).
cnf(i_0_5537,axiom,
( X1 != X2
| interior(X1,X3) = interior(X2,X3) ) ).
cnf(i_0_5538,axiom,
( X1 != X2
| interior(X3,X1) = interior(X3,X2) ) ).
cnf(i_0_5539,axiom,
( X1 != X2
| rel_str_of(X1,X3) = rel_str_of(X2,X3) ) ).
cnf(i_0_5540,axiom,
( X1 != X2
| rel_str_of(X3,X1) = rel_str_of(X3,X2) ) ).
cnf(i_0_5541,axiom,
( X1 != X2
| esk203_1(X1) = esk203_1(X2) ) ).
cnf(i_0_5542,axiom,
( X1 != X2
| esk403_1(X1) = esk403_1(X2) ) ).
cnf(i_0_5543,axiom,
( X1 != X2
| meet_of_subsets(X1,X3) = meet_of_subsets(X2,X3) ) ).
cnf(i_0_5544,axiom,
( X1 != X2
| meet_of_subsets(X3,X1) = meet_of_subsets(X3,X2) ) ).
cnf(i_0_5545,axiom,
( X1 != X2
| esk306_2(X1,X3) = esk306_2(X2,X3) ) ).
cnf(i_0_5546,axiom,
( X1 != X2
| esk306_2(X3,X1) = esk306_2(X3,X2) ) ).
cnf(i_0_5547,axiom,
( X1 != X2
| set_meet(X1) = set_meet(X2) ) ).
cnf(i_0_5548,axiom,
( X1 != X2
| join_commut(X1,X3,X4) = join_commut(X2,X3,X4) ) ).
cnf(i_0_5549,axiom,
( X1 != X2
| join_commut(X3,X1,X4) = join_commut(X3,X2,X4) ) ).
cnf(i_0_5550,axiom,
( X1 != X2
| join_commut(X3,X4,X1) = join_commut(X3,X4,X2) ) ).
cnf(i_0_5551,axiom,
( X1 != X2
| esk373_3(X1,X3,X4) = esk373_3(X2,X3,X4) ) ).
cnf(i_0_5552,axiom,
( X1 != X2
| esk373_3(X3,X1,X4) = esk373_3(X3,X2,X4) ) ).
cnf(i_0_5553,axiom,
( X1 != X2
| esk373_3(X3,X4,X1) = esk373_3(X3,X4,X2) ) ).
cnf(i_0_5554,axiom,
( X1 != X2
| esk76_2(X1,X3) = esk76_2(X2,X3) ) ).
cnf(i_0_5555,axiom,
( X1 != X2
| esk76_2(X3,X1) = esk76_2(X3,X2) ) ).
cnf(i_0_5556,axiom,
( X1 != X2
| esk223_2(X1,X3) = esk223_2(X2,X3) ) ).
cnf(i_0_5557,axiom,
( X1 != X2
| esk223_2(X3,X1) = esk223_2(X3,X2) ) ).
cnf(i_0_5558,axiom,
( X1 != X2
| esk302_2(X1,X3) = esk302_2(X2,X3) ) ).
cnf(i_0_5559,axiom,
( X1 != X2
| esk302_2(X3,X1) = esk302_2(X3,X2) ) ).
cnf(i_0_5560,axiom,
( X1 != X2
| esk448_1(X1) = esk448_1(X2) ) ).
cnf(i_0_5561,axiom,
( X1 != X2
| esk413_2(X1,X3) = esk413_2(X2,X3) ) ).
cnf(i_0_5562,axiom,
( X1 != X2
| esk413_2(X3,X1) = esk413_2(X3,X2) ) ).
cnf(i_0_5563,axiom,
( X1 != X2
| esk89_2(X1,X3) = esk89_2(X2,X3) ) ).
cnf(i_0_5564,axiom,
( X1 != X2
| esk89_2(X3,X1) = esk89_2(X3,X2) ) ).
cnf(i_0_5565,axiom,
( X1 != X2
| union(X1) = union(X2) ) ).
cnf(i_0_5566,axiom,
( X1 != X2
| relation_restriction(X1,X3) = relation_restriction(X2,X3) ) ).
cnf(i_0_5567,axiom,
( X1 != X2
| relation_restriction(X3,X1) = relation_restriction(X3,X2) ) ).
cnf(i_0_5568,axiom,
( X1 != X2
| esk385_1(X1) = esk385_1(X2) ) ).
cnf(i_0_5569,axiom,
( X1 != X2
| esk384_1(X1) = esk384_1(X2) ) ).
cnf(i_0_5570,axiom,
( X1 != X2
| esk232_1(X1) = esk232_1(X2) ) ).
cnf(i_0_5571,axiom,
( X1 != X2
| esk311_6(X1,X3,X4,X5,X6,X7) = esk311_6(X2,X3,X4,X5,X6,X7) ) ).
cnf(i_0_5572,axiom,
( X1 != X2
| esk311_6(X3,X1,X4,X5,X6,X7) = esk311_6(X3,X2,X4,X5,X6,X7) ) ).
cnf(i_0_5573,axiom,
( X1 != X2
| esk311_6(X3,X4,X1,X5,X6,X7) = esk311_6(X3,X4,X2,X5,X6,X7) ) ).
cnf(i_0_5574,axiom,
( X1 != X2
| esk311_6(X3,X4,X5,X1,X6,X7) = esk311_6(X3,X4,X5,X2,X6,X7) ) ).
cnf(i_0_5575,axiom,
( X1 != X2
| esk311_6(X3,X4,X5,X6,X1,X7) = esk311_6(X3,X4,X5,X6,X2,X7) ) ).
cnf(i_0_5576,axiom,
( X1 != X2
| esk311_6(X3,X4,X5,X6,X7,X1) = esk311_6(X3,X4,X5,X6,X7,X2) ) ).
cnf(i_0_5577,axiom,
( X1 != X2
| esk231_1(X1) = esk231_1(X2) ) ).
cnf(i_0_5578,axiom,
( X1 != X2
| esk61_1(X1) = esk61_1(X2) ) ).
cnf(i_0_5579,axiom,
( X1 != X2
| esk11_1(X1) = esk11_1(X2) ) ).
cnf(i_0_5580,axiom,
( X1 != X2
| esk39_1(X1) = esk39_1(X2) ) ).
cnf(i_0_5581,axiom,
( X1 != X2
| esk424_2(X1,X3) = esk424_2(X2,X3) ) ).
cnf(i_0_5582,axiom,
( X1 != X2
| esk424_2(X3,X1) = esk424_2(X3,X2) ) ).
cnf(i_0_5583,axiom,
( X1 != X2
| esk303_2(X1,X3) = esk303_2(X2,X3) ) ).
cnf(i_0_5584,axiom,
( X1 != X2
| esk303_2(X3,X1) = esk303_2(X3,X2) ) ).
cnf(i_0_5585,axiom,
( X1 != X2
| esk44_2(X1,X3) = esk44_2(X2,X3) ) ).
cnf(i_0_5586,axiom,
( X1 != X2
| esk44_2(X3,X1) = esk44_2(X3,X2) ) ).
cnf(i_0_5587,axiom,
( X1 != X2
| esk419_1(X1) = esk419_1(X2) ) ).
cnf(i_0_5588,axiom,
( X1 != X2
| k2_lattice3(X1) = k2_lattice3(X2) ) ).
cnf(i_0_5589,axiom,
( X1 != X2
| esk304_2(X1,X3) = esk304_2(X2,X3) ) ).
cnf(i_0_5590,axiom,
( X1 != X2
| esk304_2(X3,X1) = esk304_2(X3,X2) ) ).
cnf(i_0_5591,axiom,
( X1 != X2
| esk450_1(X1) = esk450_1(X2) ) ).
cnf(i_0_5592,axiom,
( X1 != X2
| esk327_2(X1,X3) = esk327_2(X2,X3) ) ).
cnf(i_0_5593,axiom,
( X1 != X2
| esk327_2(X3,X1) = esk327_2(X3,X2) ) ).
cnf(i_0_5594,axiom,
( X1 != X2
| esk301_2(X1,X3) = esk301_2(X2,X3) ) ).
cnf(i_0_5595,axiom,
( X1 != X2
| esk301_2(X3,X1) = esk301_2(X3,X2) ) ).
cnf(i_0_5596,axiom,
( X1 != X2
| esk101_1(X1) = esk101_1(X2) ) ).
cnf(i_0_5597,axiom,
( X1 != X2
| esk102_1(X1) = esk102_1(X2) ) ).
cnf(i_0_5598,axiom,
( X1 != X2
| esk282_2(X1,X3) = esk282_2(X2,X3) ) ).
cnf(i_0_5599,axiom,
( X1 != X2
| esk282_2(X3,X1) = esk282_2(X3,X2) ) ).
cnf(i_0_5600,axiom,
( X1 != X2
| esk71_1(X1) = esk71_1(X2) ) ).
cnf(i_0_5601,axiom,
( X1 != X2
| esk70_1(X1) = esk70_1(X2) ) ).
cnf(i_0_5602,axiom,
( X1 != X2
| empty_carrier_subset(X1) = empty_carrier_subset(X2) ) ).
cnf(i_0_5603,axiom,
( X1 != X2
| esk52_1(X1) = esk52_1(X2) ) ).
cnf(i_0_5604,axiom,
( X1 != X2
| esk362_6(X1,X3,X4,X5,X6,X7) = esk362_6(X2,X3,X4,X5,X6,X7) ) ).
cnf(i_0_5605,axiom,
( X1 != X2
| esk362_6(X3,X1,X4,X5,X6,X7) = esk362_6(X3,X2,X4,X5,X6,X7) ) ).
cnf(i_0_5606,axiom,
( X1 != X2
| esk362_6(X3,X4,X1,X5,X6,X7) = esk362_6(X3,X4,X2,X5,X6,X7) ) ).
cnf(i_0_5607,axiom,
( X1 != X2
| esk362_6(X3,X4,X5,X1,X6,X7) = esk362_6(X3,X4,X5,X2,X6,X7) ) ).
cnf(i_0_5608,axiom,
( X1 != X2
| esk362_6(X3,X4,X5,X6,X1,X7) = esk362_6(X3,X4,X5,X6,X2,X7) ) ).
cnf(i_0_5609,axiom,
( X1 != X2
| esk362_6(X3,X4,X5,X6,X7,X1) = esk362_6(X3,X4,X5,X6,X7,X2) ) ).
cnf(i_0_5610,axiom,
( X1 != X2
| esk300_2(X1,X3) = esk300_2(X2,X3) ) ).
cnf(i_0_5611,axiom,
( X1 != X2
| esk300_2(X3,X1) = esk300_2(X3,X2) ) ).
cnf(i_0_5612,axiom,
( X1 != X2
| cartesian_product2(X1,X3) = cartesian_product2(X2,X3) ) ).
cnf(i_0_5613,axiom,
( X1 != X2
| cartesian_product2(X3,X1) = cartesian_product2(X3,X2) ) ).
cnf(i_0_5614,axiom,
( X1 != X2
| esk366_6(X1,X3,X4,X5,X6,X7) = esk366_6(X2,X3,X4,X5,X6,X7) ) ).
cnf(i_0_5615,axiom,
( X1 != X2
| esk366_6(X3,X1,X4,X5,X6,X7) = esk366_6(X3,X2,X4,X5,X6,X7) ) ).
cnf(i_0_5616,axiom,
( X1 != X2
| esk366_6(X3,X4,X1,X5,X6,X7) = esk366_6(X3,X4,X2,X5,X6,X7) ) ).
cnf(i_0_5617,axiom,
( X1 != X2
| esk366_6(X3,X4,X5,X1,X6,X7) = esk366_6(X3,X4,X5,X2,X6,X7) ) ).
cnf(i_0_5618,axiom,
( X1 != X2
| esk366_6(X3,X4,X5,X6,X1,X7) = esk366_6(X3,X4,X5,X6,X2,X7) ) ).
cnf(i_0_5619,axiom,
( X1 != X2
| esk366_6(X3,X4,X5,X6,X7,X1) = esk366_6(X3,X4,X5,X6,X7,X2) ) ).
cnf(i_0_5620,axiom,
( X1 != X2
| esk314_3(X1,X3,X4) = esk314_3(X2,X3,X4) ) ).
cnf(i_0_5621,axiom,
( X1 != X2
| esk314_3(X3,X1,X4) = esk314_3(X3,X2,X4) ) ).
cnf(i_0_5622,axiom,
( X1 != X2
| esk314_3(X3,X4,X1) = esk314_3(X3,X4,X2) ) ).
cnf(i_0_5623,axiom,
( X1 != X2
| esk313_3(X1,X3,X4) = esk313_3(X2,X3,X4) ) ).
cnf(i_0_5624,axiom,
( X1 != X2
| esk313_3(X3,X1,X4) = esk313_3(X3,X2,X4) ) ).
cnf(i_0_5625,axiom,
( X1 != X2
| esk313_3(X3,X4,X1) = esk313_3(X3,X4,X2) ) ).
cnf(i_0_5626,axiom,
( X1 != X2
| esk312_3(X1,X3,X4) = esk312_3(X2,X3,X4) ) ).
cnf(i_0_5627,axiom,
( X1 != X2
| esk312_3(X3,X1,X4) = esk312_3(X3,X2,X4) ) ).
cnf(i_0_5628,axiom,
( X1 != X2
| esk312_3(X3,X4,X1) = esk312_3(X3,X4,X2) ) ).
cnf(i_0_5629,axiom,
( X1 != X2
| esk179_2(X1,X3) = esk179_2(X2,X3) ) ).
cnf(i_0_5630,axiom,
( X1 != X2
| esk179_2(X3,X1) = esk179_2(X3,X2) ) ).
cnf(i_0_5631,axiom,
( X1 != X2
| esk181_2(X1,X3) = esk181_2(X2,X3) ) ).
cnf(i_0_5632,axiom,
( X1 != X2
| esk181_2(X3,X1) = esk181_2(X3,X2) ) ).
cnf(i_0_5633,axiom,
( X1 != X2
| esk178_2(X1,X3) = esk178_2(X2,X3) ) ).
cnf(i_0_5634,axiom,
( X1 != X2
| esk178_2(X3,X1) = esk178_2(X3,X2) ) ).
cnf(i_0_5635,axiom,
( X1 != X2
| esk180_2(X1,X3) = esk180_2(X2,X3) ) ).
cnf(i_0_5636,axiom,
( X1 != X2
| esk180_2(X3,X1) = esk180_2(X3,X2) ) ).
cnf(i_0_5637,axiom,
( X1 != X2
| esk208_2(X1,X3) = esk208_2(X2,X3) ) ).
cnf(i_0_5638,axiom,
( X1 != X2
| esk208_2(X3,X1) = esk208_2(X3,X2) ) ).
cnf(i_0_5639,axiom,
( X1 != X2
| esk210_2(X1,X3) = esk210_2(X2,X3) ) ).
cnf(i_0_5640,axiom,
( X1 != X2
| esk210_2(X3,X1) = esk210_2(X3,X2) ) ).
cnf(i_0_5641,axiom,
( X1 != X2
| esk207_2(X1,X3) = esk207_2(X2,X3) ) ).
cnf(i_0_5642,axiom,
( X1 != X2
| esk207_2(X3,X1) = esk207_2(X3,X2) ) ).
cnf(i_0_5643,axiom,
( X1 != X2
| esk209_2(X1,X3) = esk209_2(X2,X3) ) ).
cnf(i_0_5644,axiom,
( X1 != X2
| esk209_2(X3,X1) = esk209_2(X3,X2) ) ).
cnf(i_0_5645,axiom,
( X1 != X2
| esk177_2(X1,X3) = esk177_2(X2,X3) ) ).
cnf(i_0_5646,axiom,
( X1 != X2
| esk177_2(X3,X1) = esk177_2(X3,X2) ) ).
cnf(i_0_5647,axiom,
( X1 != X2
| esk206_2(X1,X3) = esk206_2(X2,X3) ) ).
cnf(i_0_5648,axiom,
( X1 != X2
| esk206_2(X3,X1) = esk206_2(X3,X2) ) ).
cnf(i_0_5649,axiom,
( X1 != X2
| apply_binary_as_element(X1,X3,X4,X5,X6,X7) = apply_binary_as_element(X2,X3,X4,X5,X6,X7) ) ).
cnf(i_0_5650,axiom,
( X1 != X2
| apply_binary_as_element(X3,X1,X4,X5,X6,X7) = apply_binary_as_element(X3,X2,X4,X5,X6,X7) ) ).
cnf(i_0_5651,axiom,
( X1 != X2
| apply_binary_as_element(X3,X4,X1,X5,X6,X7) = apply_binary_as_element(X3,X4,X2,X5,X6,X7) ) ).
cnf(i_0_5652,axiom,
( X1 != X2
| apply_binary_as_element(X3,X4,X5,X1,X6,X7) = apply_binary_as_element(X3,X4,X5,X2,X6,X7) ) ).
cnf(i_0_5653,axiom,
( X1 != X2
| apply_binary_as_element(X3,X4,X5,X6,X1,X7) = apply_binary_as_element(X3,X4,X5,X6,X2,X7) ) ).
cnf(i_0_5654,axiom,
( X1 != X2
| apply_binary_as_element(X3,X4,X5,X6,X7,X1) = apply_binary_as_element(X3,X4,X5,X6,X7,X2) ) ).
cnf(i_0_5655,axiom,
( X1 != X2
| relation_field(X1) = relation_field(X2) ) ).
cnf(i_0_5656,axiom,
( X1 != X2
| relation_dom(X1) = relation_dom(X2) ) ).
cnf(i_0_5657,axiom,
( X1 != X2
| relation_rng(X1) = relation_rng(X2) ) ).
cnf(i_0_5658,axiom,
( X1 != X2
| esk228_4(X1,X3,X4,X5) = esk228_4(X2,X3,X4,X5) ) ).
cnf(i_0_5659,axiom,
( X1 != X2
| esk228_4(X3,X1,X4,X5) = esk228_4(X3,X2,X4,X5) ) ).
cnf(i_0_5660,axiom,
( X1 != X2
| esk228_4(X3,X4,X1,X5) = esk228_4(X3,X4,X2,X5) ) ).
cnf(i_0_5661,axiom,
( X1 != X2
| esk228_4(X3,X4,X5,X1) = esk228_4(X3,X4,X5,X2) ) ).
cnf(i_0_5662,axiom,
( X1 != X2
| esk220_2(X1,X3) = esk220_2(X2,X3) ) ).
cnf(i_0_5663,axiom,
( X1 != X2
| esk220_2(X3,X1) = esk220_2(X3,X2) ) ).
cnf(i_0_5664,axiom,
( X1 != X2
| esk344_4(X1,X3,X4,X5) = esk344_4(X2,X3,X4,X5) ) ).
cnf(i_0_5665,axiom,
( X1 != X2
| esk344_4(X3,X1,X4,X5) = esk344_4(X3,X2,X4,X5) ) ).
cnf(i_0_5666,axiom,
( X1 != X2
| esk344_4(X3,X4,X1,X5) = esk344_4(X3,X4,X2,X5) ) ).
cnf(i_0_5667,axiom,
( X1 != X2
| esk344_4(X3,X4,X5,X1) = esk344_4(X3,X4,X5,X2) ) ).
cnf(i_0_5668,axiom,
( X1 != X2
| apply_binary(X1,X3,X4) = apply_binary(X2,X3,X4) ) ).
cnf(i_0_5669,axiom,
( X1 != X2
| apply_binary(X3,X1,X4) = apply_binary(X3,X2,X4) ) ).
cnf(i_0_5670,axiom,
( X1 != X2
| apply_binary(X3,X4,X1) = apply_binary(X3,X4,X2) ) ).
cnf(i_0_5671,axiom,
( X1 != X2
| relation_rng_as_subset(X1,X3,X4) = relation_rng_as_subset(X2,X3,X4) ) ).
cnf(i_0_5672,axiom,
( X1 != X2
| relation_rng_as_subset(X3,X1,X4) = relation_rng_as_subset(X3,X2,X4) ) ).
cnf(i_0_5673,axiom,
( X1 != X2
| relation_rng_as_subset(X3,X4,X1) = relation_rng_as_subset(X3,X4,X2) ) ).
cnf(i_0_5674,axiom,
( X1 != X2
| join(X1,X3,X4) = join(X2,X3,X4) ) ).
cnf(i_0_5675,axiom,
( X1 != X2
| join(X3,X1,X4) = join(X3,X2,X4) ) ).
cnf(i_0_5676,axiom,
( X1 != X2
| join(X3,X4,X1) = join(X3,X4,X2) ) ).
cnf(i_0_5677,axiom,
( X1 != X2
| meet(X1,X3,X4) = meet(X2,X3,X4) ) ).
cnf(i_0_5678,axiom,
( X1 != X2
| meet(X3,X1,X4) = meet(X3,X2,X4) ) ).
cnf(i_0_5679,axiom,
( X1 != X2
| meet(X3,X4,X1) = meet(X3,X4,X2) ) ).
cnf(i_0_5680,axiom,
( X1 != X2
| esk221_2(X1,X3) = esk221_2(X2,X3) ) ).
cnf(i_0_5681,axiom,
( X1 != X2
| esk221_2(X3,X1) = esk221_2(X3,X2) ) ).
cnf(i_0_5682,axiom,
( X1 != X2
| relation_image(X1,X3) = relation_image(X2,X3) ) ).
cnf(i_0_5683,axiom,
( X1 != X2
| relation_image(X3,X1) = relation_image(X3,X2) ) ).
cnf(i_0_5684,axiom,
( X1 != X2
| relation_rng_restriction(X1,X3) = relation_rng_restriction(X2,X3) ) ).
cnf(i_0_5685,axiom,
( X1 != X2
| relation_rng_restriction(X3,X1) = relation_rng_restriction(X3,X2) ) ).
cnf(i_0_5686,axiom,
( X1 != X2
| relation_dom_restriction(X1,X3) = relation_dom_restriction(X2,X3) ) ).
cnf(i_0_5687,axiom,
( X1 != X2
| relation_dom_restriction(X3,X1) = relation_dom_restriction(X3,X2) ) ).
cnf(i_0_5688,axiom,
( X1 != X2
| esk376_2(X1,X3) = esk376_2(X2,X3) ) ).
cnf(i_0_5689,axiom,
( X1 != X2
| esk376_2(X3,X1) = esk376_2(X3,X2) ) ).
cnf(i_0_5690,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_5691,axiom,
( X1 != X2
| ~ one_to_one(X1)
| one_to_one(X2) ) ).
cnf(i_0_5692,axiom,
( X1 != X2
| ~ relation_of2_as_subset(X1,X3,X4)
| relation_of2_as_subset(X2,X3,X4) ) ).
cnf(i_0_5693,axiom,
( X1 != X2
| ~ relation_of2_as_subset(X3,X1,X4)
| relation_of2_as_subset(X3,X2,X4) ) ).
cnf(i_0_5694,axiom,
( X1 != X2
| ~ relation_of2_as_subset(X3,X4,X1)
| relation_of2_as_subset(X3,X4,X2) ) ).
cnf(i_0_5695,axiom,
( X1 != X2
| ~ empty_carrier(X1)
| empty_carrier(X2) ) ).
cnf(i_0_5696,axiom,
( X1 != X2
| ~ join_semilatt_str(X1)
| join_semilatt_str(X2) ) ).
cnf(i_0_5697,axiom,
( X1 != X2
| ~ meet_semilatt_str(X1)
| meet_semilatt_str(X2) ) ).
cnf(i_0_5698,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_5699,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_5700,axiom,
( X1 != X2
| ~ epred2_3(X1,X3,X4)
| epred2_3(X2,X3,X4) ) ).
cnf(i_0_5701,axiom,
( X1 != X2
| ~ epred2_3(X3,X1,X4)
| epred2_3(X3,X2,X4) ) ).
cnf(i_0_5702,axiom,
( X1 != X2
| ~ epred2_3(X3,X4,X1)
| epred2_3(X3,X4,X2) ) ).
cnf(i_0_5703,axiom,
( X1 != X2
| ~ ordinal(X1)
| ordinal(X2) ) ).
cnf(i_0_5704,axiom,
( X1 != X2
| ~ below_refl(X1,X3,X4)
| below_refl(X2,X3,X4) ) ).
cnf(i_0_5705,axiom,
( X1 != X2
| ~ below_refl(X3,X1,X4)
| below_refl(X3,X2,X4) ) ).
cnf(i_0_5706,axiom,
( X1 != X2
| ~ below_refl(X3,X4,X1)
| below_refl(X3,X4,X2) ) ).
cnf(i_0_5707,axiom,
( X1 != X2
| ~ lattice(X1)
| lattice(X2) ) ).
cnf(i_0_5708,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_5709,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_5710,axiom,
( X1 != X2
| ~ latt_str(X1)
| latt_str(X2) ) ).
cnf(i_0_5711,axiom,
( X1 != X2
| ~ is_reflexive_in(X1,X3)
| is_reflexive_in(X2,X3) ) ).
cnf(i_0_5712,axiom,
( X1 != X2
| ~ is_reflexive_in(X3,X1)
| is_reflexive_in(X3,X2) ) ).
cnf(i_0_5713,axiom,
( X1 != X2
| ~ is_transitive_in(X1,X3)
| is_transitive_in(X2,X3) ) ).
cnf(i_0_5714,axiom,
( X1 != X2
| ~ is_transitive_in(X3,X1)
| is_transitive_in(X3,X2) ) ).
cnf(i_0_5715,axiom,
( X1 != X2
| ~ is_connected_in(X1,X3)
| is_connected_in(X2,X3) ) ).
cnf(i_0_5716,axiom,
( X1 != X2
| ~ is_connected_in(X3,X1)
| is_connected_in(X3,X2) ) ).
cnf(i_0_5717,axiom,
( X1 != X2
| ~ strict_latt_str(X1)
| strict_latt_str(X2) ) ).
cnf(i_0_5718,axiom,
( X1 != X2
| ~ top_str(X1)
| top_str(X2) ) ).
cnf(i_0_5719,axiom,
( X1 != X2
| ~ open_subset(X1,X3)
| open_subset(X2,X3) ) ).
cnf(i_0_5720,axiom,
( X1 != X2
| ~ open_subset(X3,X1)
| open_subset(X3,X2) ) ).
cnf(i_0_5721,axiom,
( X1 != X2
| ~ disjoint(X1,X3)
| disjoint(X2,X3) ) ).
cnf(i_0_5722,axiom,
( X1 != X2
| ~ disjoint(X3,X1)
| disjoint(X3,X2) ) ).
cnf(i_0_5723,axiom,
( X1 != X2
| ~ transitive(X1)
| transitive(X2) ) ).
cnf(i_0_5724,axiom,
( X1 != X2
| ~ is_antisymmetric_in(X1,X3)
| is_antisymmetric_in(X2,X3) ) ).
cnf(i_0_5725,axiom,
( X1 != X2
| ~ is_antisymmetric_in(X3,X1)
| is_antisymmetric_in(X3,X2) ) ).
cnf(i_0_5726,axiom,
( X1 != X2
| ~ relation(X1)
| relation(X2) ) ).
cnf(i_0_5727,axiom,
( X1 != X2
| ~ antisymmetric(X1)
| antisymmetric(X2) ) ).
cnf(i_0_5728,axiom,
( X1 != X2
| ~ topological_space(X1)
| topological_space(X2) ) ).
cnf(i_0_5729,axiom,
( X1 != X2
| ~ latt_set_smaller(X1,X3,X4)
| latt_set_smaller(X2,X3,X4) ) ).
cnf(i_0_5730,axiom,
( X1 != X2
| ~ latt_set_smaller(X3,X1,X4)
| latt_set_smaller(X3,X2,X4) ) ).
cnf(i_0_5731,axiom,
( X1 != X2
| ~ latt_set_smaller(X3,X4,X1)
| latt_set_smaller(X3,X4,X2) ) ).
cnf(i_0_5732,axiom,
( X1 != X2
| ~ complete_latt_str(X1)
| complete_latt_str(X2) ) ).
cnf(i_0_5733,axiom,
( X1 != X2
| ~ latt_element_smaller(X1,X3,X4)
| latt_element_smaller(X2,X3,X4) ) ).
cnf(i_0_5734,axiom,
( X1 != X2
| ~ latt_element_smaller(X3,X1,X4)
| latt_element_smaller(X3,X2,X4) ) ).
cnf(i_0_5735,axiom,
( X1 != X2
| ~ latt_element_smaller(X3,X4,X1)
| latt_element_smaller(X3,X4,X2) ) ).
cnf(i_0_5736,axiom,
( X1 != X2
| ~ below(X1,X3,X4)
| below(X2,X3,X4) ) ).
cnf(i_0_5737,axiom,
( X1 != X2
| ~ below(X3,X1,X4)
| below(X3,X2,X4) ) ).
cnf(i_0_5738,axiom,
( X1 != X2
| ~ below(X3,X4,X1)
| below(X3,X4,X2) ) ).
cnf(i_0_5739,axiom,
( X1 != X2
| ~ connected(X1)
| connected(X2) ) ).
cnf(i_0_5740,axiom,
( X1 != X2
| ~ reflexive(X1)
| reflexive(X2) ) ).
cnf(i_0_5741,axiom,
( X1 != X2
| ~ related(X1,X3,X4)
| related(X2,X3,X4) ) ).
cnf(i_0_5742,axiom,
( X1 != X2
| ~ related(X3,X1,X4)
| related(X3,X2,X4) ) ).
cnf(i_0_5743,axiom,
( X1 != X2
| ~ related(X3,X4,X1)
| related(X3,X4,X2) ) ).
cnf(i_0_5744,axiom,
( X1 != X2
| ~ function(X1)
| function(X2) ) ).
cnf(i_0_5745,axiom,
( X1 != X2
| ~ rel_str(X1)
| rel_str(X2) ) ).
cnf(i_0_5746,axiom,
( X1 != X2
| ~ relstr_set_smaller(X1,X3,X4)
| relstr_set_smaller(X2,X3,X4) ) ).
cnf(i_0_5747,axiom,
( X1 != X2
| ~ relstr_set_smaller(X3,X1,X4)
| relstr_set_smaller(X3,X2,X4) ) ).
cnf(i_0_5748,axiom,
( X1 != X2
| ~ relstr_set_smaller(X3,X4,X1)
| relstr_set_smaller(X3,X4,X2) ) ).
cnf(i_0_5749,axiom,
( X1 != X2
| ~ relstr_element_smaller(X1,X3,X4)
| relstr_element_smaller(X2,X3,X4) ) ).
cnf(i_0_5750,axiom,
( X1 != X2
| ~ relstr_element_smaller(X3,X1,X4)
| relstr_element_smaller(X3,X2,X4) ) ).
cnf(i_0_5751,axiom,
( X1 != X2
| ~ relstr_element_smaller(X3,X4,X1)
| relstr_element_smaller(X3,X4,X2) ) ).
cnf(i_0_5752,axiom,
( X1 != X2
| ~ transitive_relstr(X1)
| transitive_relstr(X2) ) ).
cnf(i_0_5753,axiom,
( X1 != X2
| ~ onto(X1,X3,X4)
| onto(X2,X3,X4) ) ).
cnf(i_0_5754,axiom,
( X1 != X2
| ~ onto(X3,X1,X4)
| onto(X3,X2,X4) ) ).
cnf(i_0_5755,axiom,
( X1 != X2
| ~ onto(X3,X4,X1)
| onto(X3,X4,X2) ) ).
cnf(i_0_5756,axiom,
( X1 != X2
| ~ v1_partfun1(X1,X3,X4)
| v1_partfun1(X2,X3,X4) ) ).
cnf(i_0_5757,axiom,
( X1 != X2
| ~ v1_partfun1(X3,X1,X4)
| v1_partfun1(X3,X2,X4) ) ).
cnf(i_0_5758,axiom,
( X1 != X2
| ~ v1_partfun1(X3,X4,X1)
| v1_partfun1(X3,X4,X2) ) ).
cnf(i_0_5759,axiom,
( X1 != X2
| ~ bijective(X1,X3,X4)
| bijective(X2,X3,X4) ) ).
cnf(i_0_5760,axiom,
( X1 != X2
| ~ bijective(X3,X1,X4)
| bijective(X3,X2,X4) ) ).
cnf(i_0_5761,axiom,
( X1 != X2
| ~ bijective(X3,X4,X1)
| bijective(X3,X4,X2) ) ).
cnf(i_0_5762,axiom,
( X1 != X2
| ~ meet_absorbing(X1)
| meet_absorbing(X2) ) ).
cnf(i_0_5763,axiom,
( X1 != X2
| ~ closed_subset(X1,X3)
| closed_subset(X2,X3) ) ).
cnf(i_0_5764,axiom,
( X1 != X2
| ~ closed_subset(X3,X1)
| closed_subset(X3,X2) ) ).
cnf(i_0_5765,axiom,
( X1 != X2
| ~ related_reflexive(X1,X3,X4)
| related_reflexive(X2,X3,X4) ) ).
cnf(i_0_5766,axiom,
( X1 != X2
| ~ related_reflexive(X3,X1,X4)
| related_reflexive(X3,X2,X4) ) ).
cnf(i_0_5767,axiom,
( X1 != X2
| ~ related_reflexive(X3,X4,X1)
| related_reflexive(X3,X4,X2) ) ).
cnf(i_0_5768,axiom,
( X1 != X2
| ~ one_sorted_str(X1)
| one_sorted_str(X2) ) ).
cnf(i_0_5769,axiom,
( X1 != X2
| ~ lower_bounded_semilattstr(X1)
| lower_bounded_semilattstr(X2) ) ).
cnf(i_0_5770,axiom,
( X1 != X2
| ~ is_well_founded_in(X1,X3)
| is_well_founded_in(X2,X3) ) ).
cnf(i_0_5771,axiom,
( X1 != X2
| ~ is_well_founded_in(X3,X1)
| is_well_founded_in(X3,X2) ) ).
cnf(i_0_5772,axiom,
( X1 != X2
| ~ join_commutative(X1)
| join_commutative(X2) ) ).
cnf(i_0_5773,axiom,
( X1 != X2
| ~ antisymmetric_relstr(X1)
| antisymmetric_relstr(X2) ) ).
cnf(i_0_5774,axiom,
( X1 != X2
| ~ being_limit_ordinal(X1)
| being_limit_ordinal(X2) ) ).
cnf(i_0_5775,axiom,
( X1 != X2
| ~ meet_commutative(X1)
| meet_commutative(X2) ) ).
cnf(i_0_5776,axiom,
( X1 != X2
| ~ join_absorbing(X1)
| join_absorbing(X2) ) ).
cnf(i_0_5777,axiom,
( X1 != X2
| ~ is_a_cover_of_carrier(X1,X3)
| is_a_cover_of_carrier(X2,X3) ) ).
cnf(i_0_5778,axiom,
( X1 != X2
| ~ is_a_cover_of_carrier(X3,X1)
| is_a_cover_of_carrier(X3,X2) ) ).
cnf(i_0_5779,axiom,
( X1 != X2
| ~ open_subsets(X1,X3)
| open_subsets(X2,X3) ) ).
cnf(i_0_5780,axiom,
( X1 != X2
| ~ open_subsets(X3,X1)
| open_subsets(X3,X2) ) ).
cnf(i_0_5781,axiom,
( X1 != X2
| ~ compact_top_space(X1)
| compact_top_space(X2) ) ).
cnf(i_0_5782,axiom,
( X1 != X2
| ~ element(X1,X3)
| element(X2,X3) ) ).
cnf(i_0_5783,axiom,
( X1 != X2
| ~ element(X3,X1)
| element(X3,X2) ) ).
cnf(i_0_5784,axiom,
( X1 != X2
| ~ point_neighbourhood(X1,X3,X4)
| point_neighbourhood(X2,X3,X4) ) ).
cnf(i_0_5785,axiom,
( X1 != X2
| ~ point_neighbourhood(X3,X1,X4)
| point_neighbourhood(X3,X2,X4) ) ).
cnf(i_0_5786,axiom,
( X1 != X2
| ~ point_neighbourhood(X3,X4,X1)
| point_neighbourhood(X3,X4,X2) ) ).
cnf(i_0_5787,axiom,
( X1 != X2
| ~ reflexive_relstr(X1)
| reflexive_relstr(X2) ) ).
cnf(i_0_5788,axiom,
( X1 != X2
| ~ strict_rel_str(X1)
| strict_rel_str(X2) ) ).
cnf(i_0_5789,axiom,
( X1 != X2
| ~ closed_subsets(X1,X3)
| closed_subsets(X2,X3) ) ).
cnf(i_0_5790,axiom,
( X1 != X2
| ~ closed_subsets(X3,X1)
| closed_subsets(X3,X2) ) ).
cnf(i_0_5791,axiom,
( X1 != X2
| ~ finite(X1)
| finite(X2) ) ).
cnf(i_0_5792,axiom,
( X1 != X2
| ~ centered(X1)
| centered(X2) ) ).
cnf(i_0_5793,axiom,
( X1 != X2
| ~ ordinal_subset(X1,X3)
| ordinal_subset(X2,X3) ) ).
cnf(i_0_5794,axiom,
( X1 != X2
| ~ ordinal_subset(X3,X1)
| ordinal_subset(X3,X2) ) ).
cnf(i_0_5795,axiom,
( X1 != X2
| ~ natural(X1)
| natural(X2) ) ).
cnf(i_0_5796,axiom,
( X1 != X2
| ~ well_founded_relation(X1)
| well_founded_relation(X2) ) ).
cnf(i_0_5797,axiom,
( X1 != X2
| ~ meet_associative(X1)
| meet_associative(X2) ) ).
cnf(i_0_5798,axiom,
( X1 != X2
| ~ quasi_total(X1,X3,X4)
| quasi_total(X2,X3,X4) ) ).
cnf(i_0_5799,axiom,
( X1 != X2
| ~ quasi_total(X3,X1,X4)
| quasi_total(X3,X2,X4) ) ).
cnf(i_0_5800,axiom,
( X1 != X2
| ~ quasi_total(X3,X4,X1)
| quasi_total(X3,X4,X2) ) ).
cnf(i_0_5801,axiom,
( X1 != X2
| ~ join_associative(X1)
| join_associative(X2) ) ).
cnf(i_0_5802,axiom,
( X1 != X2
| ~ well_orders(X1,X3)
| well_orders(X2,X3) ) ).
cnf(i_0_5803,axiom,
( X1 != X2
| ~ well_orders(X3,X1)
| well_orders(X3,X2) ) ).
cnf(i_0_5804,axiom,
( X1 != X2
| ~ epred3_2(X1,X3)
| epred3_2(X2,X3) ) ).
cnf(i_0_5805,axiom,
( X1 != X2
| ~ epred3_2(X3,X1)
| epred3_2(X3,X2) ) ).
cnf(i_0_5806,axiom,
( X1 != X2
| ~ well_ordering(X1)
| well_ordering(X2) ) ).
cnf(i_0_5807,axiom,
( X1 != X2
| ~ epsilon_connected(X1)
| epsilon_connected(X2) ) ).
cnf(i_0_5808,axiom,
( X1 != X2
| ~ epsilon_transitive(X1)
| epsilon_transitive(X2) ) ).
cnf(i_0_5809,axiom,
( X1 != X2
| ~ v5_membered(X1)
| v5_membered(X2) ) ).
cnf(i_0_5810,axiom,
( X1 != X2
| ~ v4_membered(X1)
| v4_membered(X2) ) ).
cnf(i_0_5811,axiom,
( X1 != X2
| ~ v3_membered(X1)
| v3_membered(X2) ) ).
cnf(i_0_5812,axiom,
( X1 != X2
| ~ v2_membered(X1)
| v2_membered(X2) ) ).
cnf(i_0_5813,axiom,
( X1 != X2
| ~ relation_of2(X1,X3,X4)
| relation_of2(X2,X3,X4) ) ).
cnf(i_0_5814,axiom,
( X1 != X2
| ~ relation_of2(X3,X1,X4)
| relation_of2(X3,X2,X4) ) ).
cnf(i_0_5815,axiom,
( X1 != X2
| ~ relation_of2(X3,X4,X1)
| relation_of2(X3,X4,X2) ) ).
cnf(i_0_5816,axiom,
( X1 != X2
| ~ v1_membered(X1)
| v1_membered(X2) ) ).
cnf(i_0_5817,axiom,
( X1 != X2
| ~ equipotent(X1,X3)
| equipotent(X2,X3) ) ).
cnf(i_0_5818,axiom,
( X1 != X2
| ~ equipotent(X3,X1)
| equipotent(X3,X2) ) ).
cnf(i_0_5819,axiom,
( X1 != X2
| ~ are_equipotent(X1,X3)
| are_equipotent(X2,X3) ) ).
cnf(i_0_5820,axiom,
( X1 != X2
| ~ are_equipotent(X3,X1)
| are_equipotent(X3,X2) ) ).
cnf(i_0_5821,axiom,
( X1 != X2
| ~ proper_element(X1,X3)
| proper_element(X2,X3) ) ).
cnf(i_0_5822,axiom,
( X1 != X2
| ~ proper_element(X3,X1)
| proper_element(X3,X2) ) ).
cnf(i_0_5823,axiom,
( X1 != X2
| ~ proper_subset(X1,X3)
| proper_subset(X2,X3) ) ).
cnf(i_0_5824,axiom,
( X1 != X2
| ~ proper_subset(X3,X1)
| proper_subset(X3,X2) ) ).
cnf(i_0_5825,axiom,
( X1 != X2
| ~ v2_binop_1(X1,X3)
| v2_binop_1(X2,X3) ) ).
cnf(i_0_5826,axiom,
( X1 != X2
| ~ v2_binop_1(X3,X1)
| v2_binop_1(X3,X2) ) ).
cnf(i_0_5827,axiom,
( X1 != X2
| ~ v1_binop_1(X1,X3)
| v1_binop_1(X2,X3) ) ).
cnf(i_0_5828,axiom,
( X1 != X2
| ~ v1_binop_1(X3,X1)
| v1_binop_1(X3,X2) ) ).
cnf(i_0_5829,axiom,
( X1 != X2
| ~ relation_empty_yielding(X1)
| relation_empty_yielding(X2) ) ).
cnf(i_0_5830,axiom,
( X1 != X2
| ~ v1_int_1(X1)
| v1_int_1(X2) ) ).
cnf(i_0_5831,axiom,
( X1 != X2
| ~ v1_rat_1(X1)
| v1_rat_1(X2) ) ).
cnf(i_0_5832,axiom,
( X1 != X2
| ~ relation_isomorphism(X1,X3,X4)
| relation_isomorphism(X2,X3,X4) ) ).
cnf(i_0_5833,axiom,
( X1 != X2
| ~ relation_isomorphism(X3,X1,X4)
| relation_isomorphism(X3,X2,X4) ) ).
cnf(i_0_5834,axiom,
( X1 != X2
| ~ relation_isomorphism(X3,X4,X1)
| relation_isomorphism(X3,X4,X2) ) ).
cnf(i_0_5835,axiom,
( X1 != X2
| ~ v1_xreal_0(X1)
| v1_xreal_0(X2) ) ).
cnf(i_0_5836,axiom,
( X1 != X2
| ~ v1_xcmplx_0(X1)
| v1_xcmplx_0(X2) ) ).
cnf(i_0_5837,axiom,
( X1 != X2
| ~ symmetric(X1)
| symmetric(X2) ) ).
cnf(i_0_5838,axiom,
( X1 != X2
| ~ preboolean(X1)
| preboolean(X2) ) ).
cnf(i_0_5839,axiom,
( X1 != X2
| ~ cup_closed(X1)
| cup_closed(X2) ) ).
cnf(i_0_5840,axiom,
( X1 != X2
| ~ diff_closed(X1)
| diff_closed(X2) ) ).
cnf(i_0_5092_001,axiom,
X1 = X1 ).
cnf(i_0_5093_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_5094_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_5095_004,axiom,
( X1 != X2
| esk217_2(X1,X3) = esk217_2(X2,X3) ) ).
cnf(i_0_5096_005,axiom,
( X1 != X2
| esk217_2(X3,X1) = esk217_2(X3,X2) ) ).
cnf(i_0_5097_006,axiom,
( X1 != X2
| esk379_2(X1,X3) = esk379_2(X2,X3) ) ).
cnf(i_0_5098_007,axiom,
( X1 != X2
| esk379_2(X3,X1) = esk379_2(X3,X2) ) ).
cnf(i_0_5099_008,axiom,
( X1 != X2
| esk378_2(X1,X3) = esk378_2(X2,X3) ) ).
cnf(i_0_5100_009,axiom,
( X1 != X2
| esk378_2(X3,X1) = esk378_2(X3,X2) ) ).
cnf(i_0_5101_010,axiom,
( X1 != X2
| esk382_3(X1,X3,X4) = esk382_3(X2,X3,X4) ) ).
cnf(i_0_5102_011,axiom,
( X1 != X2
| esk382_3(X3,X1,X4) = esk382_3(X3,X2,X4) ) ).
cnf(i_0_5103_012,axiom,
( X1 != X2
| esk382_3(X3,X4,X1) = esk382_3(X3,X4,X2) ) ).
cnf(i_0_5104_013,axiom,
( X1 != X2
| esk375_2(X1,X3) = esk375_2(X2,X3) ) ).
cnf(i_0_5105_014,axiom,
( X1 != X2
| esk375_2(X3,X1) = esk375_2(X3,X2) ) ).
cnf(i_0_5106_015,axiom,
( X1 != X2
| esk377_2(X1,X3) = esk377_2(X2,X3) ) ).
cnf(i_0_5107_016,axiom,
( X1 != X2
| esk377_2(X3,X1) = esk377_2(X3,X2) ) ).
cnf(i_0_5108_017,axiom,
( X1 != X2
| esk226_4(X1,X3,X4,X5) = esk226_4(X2,X3,X4,X5) ) ).
cnf(i_0_5109_018,axiom,
( X1 != X2
| esk226_4(X3,X1,X4,X5) = esk226_4(X3,X2,X4,X5) ) ).
cnf(i_0_5110_019,axiom,
( X1 != X2
| esk226_4(X3,X4,X1,X5) = esk226_4(X3,X4,X2,X5) ) ).
cnf(i_0_5111_020,axiom,
( X1 != X2
| esk226_4(X3,X4,X5,X1) = esk226_4(X3,X4,X5,X2) ) ).
cnf(i_0_5112_021,axiom,
( X1 != X2
| esk320_4(X1,X3,X4,X5) = esk320_4(X2,X3,X4,X5) ) ).
cnf(i_0_5113_022,axiom,
( X1 != X2
| esk320_4(X3,X1,X4,X5) = esk320_4(X3,X2,X4,X5) ) ).
cnf(i_0_5114_023,axiom,
( X1 != X2
| esk320_4(X3,X4,X1,X5) = esk320_4(X3,X4,X2,X5) ) ).
cnf(i_0_5115_024,axiom,
( X1 != X2
| esk320_4(X3,X4,X5,X1) = esk320_4(X3,X4,X5,X2) ) ).
cnf(i_0_5116_025,axiom,
( X1 != X2
| esk374_2(X1,X3) = esk374_2(X2,X3) ) ).
cnf(i_0_5117_026,axiom,
( X1 != X2
| esk374_2(X3,X1) = esk374_2(X3,X2) ) ).
cnf(i_0_5118_027,axiom,
( X1 != X2
| esk218_2(X1,X3) = esk218_2(X2,X3) ) ).
cnf(i_0_5119_028,axiom,
( X1 != X2
| esk218_2(X3,X1) = esk218_2(X3,X2) ) ).
cnf(i_0_5120_029,axiom,
( X1 != X2
| esk309_4(X1,X3,X4,X5) = esk309_4(X2,X3,X4,X5) ) ).
cnf(i_0_5121_030,axiom,
( X1 != X2
| esk309_4(X3,X1,X4,X5) = esk309_4(X3,X2,X4,X5) ) ).
cnf(i_0_5122_031,axiom,
( X1 != X2
| esk309_4(X3,X4,X1,X5) = esk309_4(X3,X4,X2,X5) ) ).
cnf(i_0_5123_032,axiom,
( X1 != X2
| esk309_4(X3,X4,X5,X1) = esk309_4(X3,X4,X5,X2) ) ).
cnf(i_0_5124_033,axiom,
( X1 != X2
| esk310_4(X1,X3,X4,X5) = esk310_4(X2,X3,X4,X5) ) ).
cnf(i_0_5125_034,axiom,
( X1 != X2
| esk310_4(X3,X1,X4,X5) = esk310_4(X3,X2,X4,X5) ) ).
cnf(i_0_5126_035,axiom,
( X1 != X2
| esk310_4(X3,X4,X1,X5) = esk310_4(X3,X4,X2,X5) ) ).
cnf(i_0_5127_036,axiom,
( X1 != X2
| esk310_4(X3,X4,X5,X1) = esk310_4(X3,X4,X5,X2) ) ).
cnf(i_0_5128_037,axiom,
( X1 != X2
| esk291_4(X1,X3,X4,X5) = esk291_4(X2,X3,X4,X5) ) ).
cnf(i_0_5129_038,axiom,
( X1 != X2
| esk291_4(X3,X1,X4,X5) = esk291_4(X3,X2,X4,X5) ) ).
cnf(i_0_5130_039,axiom,
( X1 != X2
| esk291_4(X3,X4,X1,X5) = esk291_4(X3,X4,X2,X5) ) ).
cnf(i_0_5131_040,axiom,
( X1 != X2
| esk291_4(X3,X4,X5,X1) = esk291_4(X3,X4,X5,X2) ) ).
cnf(i_0_5132_041,axiom,
( X1 != X2
| esk292_4(X1,X3,X4,X5) = esk292_4(X2,X3,X4,X5) ) ).
cnf(i_0_5133_042,axiom,
( X1 != X2
| esk292_4(X3,X1,X4,X5) = esk292_4(X3,X2,X4,X5) ) ).
cnf(i_0_5134_043,axiom,
( X1 != X2
| esk292_4(X3,X4,X1,X5) = esk292_4(X3,X4,X2,X5) ) ).
cnf(i_0_5135_044,axiom,
( X1 != X2
| esk292_4(X3,X4,X5,X1) = esk292_4(X3,X4,X5,X2) ) ).
cnf(i_0_5136_045,axiom,
( X1 != X2
| esk364_4(X1,X3,X4,X5) = esk364_4(X2,X3,X4,X5) ) ).
cnf(i_0_5137_046,axiom,
( X1 != X2
| esk364_4(X3,X1,X4,X5) = esk364_4(X3,X2,X4,X5) ) ).
cnf(i_0_5138_047,axiom,
( X1 != X2
| esk364_4(X3,X4,X1,X5) = esk364_4(X3,X4,X2,X5) ) ).
cnf(i_0_5139_048,axiom,
( X1 != X2
| esk364_4(X3,X4,X5,X1) = esk364_4(X3,X4,X5,X2) ) ).
cnf(i_0_5140_049,axiom,
( X1 != X2
| esk365_4(X1,X3,X4,X5) = esk365_4(X2,X3,X4,X5) ) ).
cnf(i_0_5141_050,axiom,
( X1 != X2
| esk365_4(X3,X1,X4,X5) = esk365_4(X3,X2,X4,X5) ) ).
cnf(i_0_5142_051,axiom,
( X1 != X2
| esk365_4(X3,X4,X1,X5) = esk365_4(X3,X4,X2,X5) ) ).
cnf(i_0_5143_052,axiom,
( X1 != X2
| esk365_4(X3,X4,X5,X1) = esk365_4(X3,X4,X5,X2) ) ).
cnf(i_0_5144_053,axiom,
( X1 != X2
| esk360_4(X1,X3,X4,X5) = esk360_4(X2,X3,X4,X5) ) ).
cnf(i_0_5145_054,axiom,
( X1 != X2
| esk360_4(X3,X1,X4,X5) = esk360_4(X3,X2,X4,X5) ) ).
cnf(i_0_5146_055,axiom,
( X1 != X2
| esk360_4(X3,X4,X1,X5) = esk360_4(X3,X4,X2,X5) ) ).
cnf(i_0_5147_056,axiom,
( X1 != X2
| esk360_4(X3,X4,X5,X1) = esk360_4(X3,X4,X5,X2) ) ).
cnf(i_0_5148_057,axiom,
( X1 != X2
| esk361_4(X1,X3,X4,X5) = esk361_4(X2,X3,X4,X5) ) ).
cnf(i_0_5149_058,axiom,
( X1 != X2
| esk361_4(X3,X1,X4,X5) = esk361_4(X3,X2,X4,X5) ) ).
cnf(i_0_5150_059,axiom,
( X1 != X2
| esk361_4(X3,X4,X1,X5) = esk361_4(X3,X4,X2,X5) ) ).
cnf(i_0_5151_060,axiom,
( X1 != X2
| esk361_4(X3,X4,X5,X1) = esk361_4(X3,X4,X5,X2) ) ).
cnf(i_0_5152_061,axiom,
( X1 != X2
| esk342_4(X1,X3,X4,X5) = esk342_4(X2,X3,X4,X5) ) ).
cnf(i_0_5153_062,axiom,
( X1 != X2
| esk342_4(X3,X1,X4,X5) = esk342_4(X3,X2,X4,X5) ) ).
cnf(i_0_5154_063,axiom,
( X1 != X2
| esk342_4(X3,X4,X1,X5) = esk342_4(X3,X4,X2,X5) ) ).
cnf(i_0_5155_064,axiom,
( X1 != X2
| esk342_4(X3,X4,X5,X1) = esk342_4(X3,X4,X5,X2) ) ).
cnf(i_0_5156_065,axiom,
( X1 != X2
| esk216_2(X1,X3) = esk216_2(X2,X3) ) ).
cnf(i_0_5157_066,axiom,
( X1 != X2
| esk216_2(X3,X1) = esk216_2(X3,X2) ) ).
cnf(i_0_5158_067,axiom,
( X1 != X2
| fiber(X1,X3) = fiber(X2,X3) ) ).
cnf(i_0_5159_068,axiom,
( X1 != X2
| fiber(X3,X1) = fiber(X3,X2) ) ).
cnf(i_0_5160_069,axiom,
( X1 != X2
| esk46_3(X1,X3,X4) = esk46_3(X2,X3,X4) ) ).
cnf(i_0_5161_070,axiom,
( X1 != X2
| esk46_3(X3,X1,X4) = esk46_3(X3,X2,X4) ) ).
cnf(i_0_5162_071,axiom,
( X1 != X2
| esk46_3(X3,X4,X1) = esk46_3(X3,X4,X2) ) ).
cnf(i_0_5163_072,axiom,
( X1 != X2
| relation_inverse_image(X1,X3) = relation_inverse_image(X2,X3) ) ).
cnf(i_0_5164_073,axiom,
( X1 != X2
| relation_inverse_image(X3,X1) = relation_inverse_image(X3,X2) ) ).
cnf(i_0_5165_074,axiom,
( X1 != X2
| relation_dom_as_subset(X1,X3,X4) = relation_dom_as_subset(X2,X3,X4) ) ).
cnf(i_0_5166_075,axiom,
( X1 != X2
| relation_dom_as_subset(X3,X1,X4) = relation_dom_as_subset(X3,X2,X4) ) ).
cnf(i_0_5167_076,axiom,
( X1 != X2
| relation_dom_as_subset(X3,X4,X1) = relation_dom_as_subset(X3,X4,X2) ) ).
cnf(i_0_5168_077,axiom,
( X1 != X2
| esk215_2(X1,X3) = esk215_2(X2,X3) ) ).
cnf(i_0_5169_078,axiom,
( X1 != X2
| esk215_2(X3,X1) = esk215_2(X3,X2) ) ).
cnf(i_0_5170_079,axiom,
( X1 != X2
| esk454_4(X1,X3,X4,X5) = esk454_4(X2,X3,X4,X5) ) ).
cnf(i_0_5171_080,axiom,
( X1 != X2
| esk454_4(X3,X1,X4,X5) = esk454_4(X3,X2,X4,X5) ) ).
cnf(i_0_5172_081,axiom,
( X1 != X2
| esk454_4(X3,X4,X1,X5) = esk454_4(X3,X4,X2,X5) ) ).
cnf(i_0_5173_082,axiom,
( X1 != X2
| esk454_4(X3,X4,X5,X1) = esk454_4(X3,X4,X5,X2) ) ).
cnf(i_0_5174_083,axiom,
( X1 != X2
| esk453_3(X1,X3,X4) = esk453_3(X2,X3,X4) ) ).
cnf(i_0_5175_084,axiom,
( X1 != X2
| esk453_3(X3,X1,X4) = esk453_3(X3,X2,X4) ) ).
cnf(i_0_5176_085,axiom,
( X1 != X2
| esk453_3(X3,X4,X1) = esk453_3(X3,X4,X2) ) ).
cnf(i_0_5177_086,axiom,
( X1 != X2
| esk452_4(X1,X3,X4,X5) = esk452_4(X2,X3,X4,X5) ) ).
cnf(i_0_5178_087,axiom,
( X1 != X2
| esk452_4(X3,X1,X4,X5) = esk452_4(X3,X2,X4,X5) ) ).
cnf(i_0_5179_088,axiom,
( X1 != X2
| esk452_4(X3,X4,X1,X5) = esk452_4(X3,X4,X2,X5) ) ).
cnf(i_0_5180_089,axiom,
( X1 != X2
| esk452_4(X3,X4,X5,X1) = esk452_4(X3,X4,X5,X2) ) ).
cnf(i_0_5181_090,axiom,
( X1 != X2
| esk451_3(X1,X3,X4) = esk451_3(X2,X3,X4) ) ).
cnf(i_0_5182_091,axiom,
( X1 != X2
| esk451_3(X3,X1,X4) = esk451_3(X3,X2,X4) ) ).
cnf(i_0_5183_092,axiom,
( X1 != X2
| esk451_3(X3,X4,X1) = esk451_3(X3,X4,X2) ) ).
cnf(i_0_5184_093,axiom,
( X1 != X2
| relation_inverse(X1) = relation_inverse(X2) ) ).
cnf(i_0_5185_094,axiom,
( X1 != X2
| esk183_4(X1,X3,X4,X5) = esk183_4(X2,X3,X4,X5) ) ).
cnf(i_0_5186_095,axiom,
( X1 != X2
| esk183_4(X3,X1,X4,X5) = esk183_4(X3,X2,X4,X5) ) ).
cnf(i_0_5187_096,axiom,
( X1 != X2
| esk183_4(X3,X4,X1,X5) = esk183_4(X3,X4,X2,X5) ) ).
cnf(i_0_5188_097,axiom,
( X1 != X2
| esk183_4(X3,X4,X5,X1) = esk183_4(X3,X4,X5,X2) ) ).
cnf(i_0_5189_098,axiom,
( X1 != X2
| esk25_4(X1,X3,X4,X5) = esk25_4(X2,X3,X4,X5) ) ).
cnf(i_0_5190_099,axiom,
( X1 != X2
| esk25_4(X3,X1,X4,X5) = esk25_4(X3,X2,X4,X5) ) ).
cnf(i_0_5191_100,axiom,
( X1 != X2
| esk25_4(X3,X4,X1,X5) = esk25_4(X3,X4,X2,X5) ) ).
cnf(i_0_5192_101,axiom,
( X1 != X2
| esk25_4(X3,X4,X5,X1) = esk25_4(X3,X4,X5,X2) ) ).
cnf(i_0_5193_102,axiom,
( X1 != X2
| unordered_triple(X1,X3,X4) = unordered_triple(X2,X3,X4) ) ).
cnf(i_0_5194_103,axiom,
( X1 != X2
| unordered_triple(X3,X1,X4) = unordered_triple(X3,X2,X4) ) ).
cnf(i_0_5195_104,axiom,
( X1 != X2
| unordered_triple(X3,X4,X1) = unordered_triple(X3,X4,X2) ) ).
cnf(i_0_5196_105,axiom,
( X1 != X2
| esk191_2(X1,X3) = esk191_2(X2,X3) ) ).
cnf(i_0_5197_106,axiom,
( X1 != X2
| esk191_2(X3,X1) = esk191_2(X3,X2) ) ).
cnf(i_0_5198_107,axiom,
( X1 != X2
| esk189_2(X1,X3) = esk189_2(X2,X3) ) ).
cnf(i_0_5199_108,axiom,
( X1 != X2
| esk189_2(X3,X1) = esk189_2(X3,X2) ) ).
cnf(i_0_5200_109,axiom,
( X1 != X2
| esk193_4(X1,X3,X4,X5) = esk193_4(X2,X3,X4,X5) ) ).
cnf(i_0_5201_110,axiom,
( X1 != X2
| esk193_4(X3,X1,X4,X5) = esk193_4(X3,X2,X4,X5) ) ).
cnf(i_0_5202_111,axiom,
( X1 != X2
| esk193_4(X3,X4,X1,X5) = esk193_4(X3,X4,X2,X5) ) ).
cnf(i_0_5203_112,axiom,
( X1 != X2
| esk193_4(X3,X4,X5,X1) = esk193_4(X3,X4,X5,X2) ) ).
cnf(i_0_5204_113,axiom,
( X1 != X2
| esk190_2(X1,X3) = esk190_2(X2,X3) ) ).
cnf(i_0_5205_114,axiom,
( X1 != X2
| esk190_2(X3,X1) = esk190_2(X3,X2) ) ).
cnf(i_0_5206_115,axiom,
( X1 != X2
| esk225_4(X1,X3,X4,X5) = esk225_4(X2,X3,X4,X5) ) ).
cnf(i_0_5207_116,axiom,
( X1 != X2
| esk225_4(X3,X1,X4,X5) = esk225_4(X3,X2,X4,X5) ) ).
cnf(i_0_5208_117,axiom,
( X1 != X2
| esk225_4(X3,X4,X1,X5) = esk225_4(X3,X4,X2,X5) ) ).
cnf(i_0_5209_118,axiom,
( X1 != X2
| esk225_4(X3,X4,X5,X1) = esk225_4(X3,X4,X5,X2) ) ).
cnf(i_0_5210_119,axiom,
( X1 != X2
| esk196_2(X1,X3) = esk196_2(X2,X3) ) ).
cnf(i_0_5211_120,axiom,
( X1 != X2
| esk196_2(X3,X1) = esk196_2(X3,X2) ) ).
cnf(i_0_5212_121,axiom,
( X1 != X2
| esk194_2(X1,X3) = esk194_2(X2,X3) ) ).
cnf(i_0_5213_122,axiom,
( X1 != X2
| esk194_2(X3,X1) = esk194_2(X3,X2) ) ).
cnf(i_0_5214_123,axiom,
( X1 != X2
| esk198_4(X1,X3,X4,X5) = esk198_4(X2,X3,X4,X5) ) ).
cnf(i_0_5215_124,axiom,
( X1 != X2
| esk198_4(X3,X1,X4,X5) = esk198_4(X3,X2,X4,X5) ) ).
cnf(i_0_5216_125,axiom,
( X1 != X2
| esk198_4(X3,X4,X1,X5) = esk198_4(X3,X4,X2,X5) ) ).
cnf(i_0_5217_126,axiom,
( X1 != X2
| esk198_4(X3,X4,X5,X1) = esk198_4(X3,X4,X5,X2) ) ).
cnf(i_0_5218_127,axiom,
( X1 != X2
| esk195_2(X1,X3) = esk195_2(X2,X3) ) ).
cnf(i_0_5219_128,axiom,
( X1 != X2
| esk195_2(X3,X1) = esk195_2(X3,X2) ) ).
cnf(i_0_5220_129,axiom,
( X1 != X2
| esk290_4(X1,X3,X4,X5) = esk290_4(X2,X3,X4,X5) ) ).
cnf(i_0_5221_130,axiom,
( X1 != X2
| esk290_4(X3,X1,X4,X5) = esk290_4(X3,X2,X4,X5) ) ).
cnf(i_0_5222_131,axiom,
( X1 != X2
| esk290_4(X3,X4,X1,X5) = esk290_4(X3,X4,X2,X5) ) ).
cnf(i_0_5223_132,axiom,
( X1 != X2
| esk290_4(X3,X4,X5,X1) = esk290_4(X3,X4,X5,X2) ) ).
cnf(i_0_5224_133,axiom,
( X1 != X2
| esk278_2(X1,X3) = esk278_2(X2,X3) ) ).
cnf(i_0_5225_134,axiom,
( X1 != X2
| esk278_2(X3,X1) = esk278_2(X3,X2) ) ).
cnf(i_0_5226_135,axiom,
( X1 != X2
| esk281_4(X1,X3,X4,X5) = esk281_4(X2,X3,X4,X5) ) ).
cnf(i_0_5227_136,axiom,
( X1 != X2
| esk281_4(X3,X1,X4,X5) = esk281_4(X3,X2,X4,X5) ) ).
cnf(i_0_5228_137,axiom,
( X1 != X2
| esk281_4(X3,X4,X1,X5) = esk281_4(X3,X4,X2,X5) ) ).
cnf(i_0_5229_138,axiom,
( X1 != X2
| esk281_4(X3,X4,X5,X1) = esk281_4(X3,X4,X5,X2) ) ).
cnf(i_0_5230_139,axiom,
( X1 != X2
| esk276_2(X1,X3) = esk276_2(X2,X3) ) ).
cnf(i_0_5231_140,axiom,
( X1 != X2
| esk276_2(X3,X1) = esk276_2(X3,X2) ) ).
cnf(i_0_5232_141,axiom,
( X1 != X2
| esk277_2(X1,X3) = esk277_2(X2,X3) ) ).
cnf(i_0_5233_142,axiom,
( X1 != X2
| esk277_2(X3,X1) = esk277_2(X3,X2) ) ).
cnf(i_0_5234_143,axiom,
( X1 != X2
| esk65_3(X1,X3,X4) = esk65_3(X2,X3,X4) ) ).
cnf(i_0_5235_144,axiom,
( X1 != X2
| esk65_3(X3,X1,X4) = esk65_3(X3,X2,X4) ) ).
cnf(i_0_5236_145,axiom,
( X1 != X2
| esk65_3(X3,X4,X1) = esk65_3(X3,X4,X2) ) ).
cnf(i_0_5237_146,axiom,
( X1 != X2
| esk308_4(X1,X3,X4,X5) = esk308_4(X2,X3,X4,X5) ) ).
cnf(i_0_5238_147,axiom,
( X1 != X2
| esk308_4(X3,X1,X4,X5) = esk308_4(X3,X2,X4,X5) ) ).
cnf(i_0_5239_148,axiom,
( X1 != X2
| esk308_4(X3,X4,X1,X5) = esk308_4(X3,X4,X2,X5) ) ).
cnf(i_0_5240_149,axiom,
( X1 != X2
| esk308_4(X3,X4,X5,X1) = esk308_4(X3,X4,X5,X2) ) ).
cnf(i_0_5241_150,axiom,
( X1 != X2
| relation_composition(X1,X3) = relation_composition(X2,X3) ) ).
cnf(i_0_5242_151,axiom,
( X1 != X2
| relation_composition(X3,X1) = relation_composition(X3,X2) ) ).
cnf(i_0_5243_152,axiom,
( X1 != X2
| esk241_1(X1) = esk241_1(X2) ) ).
cnf(i_0_5244_153,axiom,
( X1 != X2
| esk237_1(X1) = esk237_1(X2) ) ).
cnf(i_0_5245_154,axiom,
( X1 != X2
| esk245_3(X1,X3,X4) = esk245_3(X2,X3,X4) ) ).
cnf(i_0_5246_155,axiom,
( X1 != X2
| esk245_3(X3,X1,X4) = esk245_3(X3,X2,X4) ) ).
cnf(i_0_5247_156,axiom,
( X1 != X2
| esk245_3(X3,X4,X1) = esk245_3(X3,X4,X2) ) ).
cnf(i_0_5248_157,axiom,
( X1 != X2
| esk239_1(X1) = esk239_1(X2) ) ).
cnf(i_0_5249_158,axiom,
( X1 != X2
| esk236_1(X1) = esk236_1(X2) ) ).
cnf(i_0_5250_159,axiom,
( X1 != X2
| esk296_2(X1,X3) = esk296_2(X2,X3) ) ).
cnf(i_0_5251_160,axiom,
( X1 != X2
| esk296_2(X3,X1) = esk296_2(X3,X2) ) ).
cnf(i_0_5252_161,axiom,
( X1 != X2
| apply(X1,X3) = apply(X2,X3) ) ).
cnf(i_0_5253_162,axiom,
( X1 != X2
| apply(X3,X1) = apply(X3,X2) ) ).
cnf(i_0_5254_163,axiom,
( X1 != X2
| esk299_4(X1,X3,X4,X5) = esk299_4(X2,X3,X4,X5) ) ).
cnf(i_0_5255_164,axiom,
( X1 != X2
| esk299_4(X3,X1,X4,X5) = esk299_4(X3,X2,X4,X5) ) ).
cnf(i_0_5256_165,axiom,
( X1 != X2
| esk299_4(X3,X4,X1,X5) = esk299_4(X3,X4,X2,X5) ) ).
cnf(i_0_5257_166,axiom,
( X1 != X2
| esk299_4(X3,X4,X5,X1) = esk299_4(X3,X4,X5,X2) ) ).
cnf(i_0_5258_167,axiom,
( X1 != X2
| esk294_2(X1,X3) = esk294_2(X2,X3) ) ).
cnf(i_0_5259_168,axiom,
( X1 != X2
| esk294_2(X3,X1) = esk294_2(X3,X2) ) ).
cnf(i_0_5260_169,axiom,
( X1 != X2
| esk295_2(X1,X3) = esk295_2(X2,X3) ) ).
cnf(i_0_5261_170,axiom,
( X1 != X2
| esk295_2(X3,X1) = esk295_2(X3,X2) ) ).
cnf(i_0_5262_171,axiom,
( X1 != X2
| esk248_1(X1) = esk248_1(X2) ) ).
cnf(i_0_5263_172,axiom,
( X1 != X2
| esk247_1(X1) = esk247_1(X2) ) ).
cnf(i_0_5264_173,axiom,
( X1 != X2
| esk254_4(X1,X3,X4,X5) = esk254_4(X2,X3,X4,X5) ) ).
cnf(i_0_5265_174,axiom,
( X1 != X2
| esk254_4(X3,X1,X4,X5) = esk254_4(X3,X2,X4,X5) ) ).
cnf(i_0_5266_175,axiom,
( X1 != X2
| esk254_4(X3,X4,X1,X5) = esk254_4(X3,X4,X2,X5) ) ).
cnf(i_0_5267_176,axiom,
( X1 != X2
| esk254_4(X3,X4,X5,X1) = esk254_4(X3,X4,X5,X2) ) ).
cnf(i_0_5268_177,axiom,
( X1 != X2
| esk253_3(X1,X3,X4) = esk253_3(X2,X3,X4) ) ).
cnf(i_0_5269_178,axiom,
( X1 != X2
| esk253_3(X3,X1,X4) = esk253_3(X3,X2,X4) ) ).
cnf(i_0_5270_179,axiom,
( X1 != X2
| esk253_3(X3,X4,X1) = esk253_3(X3,X4,X2) ) ).
cnf(i_0_5271_180,axiom,
( X1 != X2
| set_union2(X1,X3) = set_union2(X2,X3) ) ).
cnf(i_0_5272_181,axiom,
( X1 != X2
| set_union2(X3,X1) = set_union2(X3,X2) ) ).
cnf(i_0_5273_182,axiom,
( X1 != X2
| esk332_4(X1,X3,X4,X5) = esk332_4(X2,X3,X4,X5) ) ).
cnf(i_0_5274_183,axiom,
( X1 != X2
| esk332_4(X3,X1,X4,X5) = esk332_4(X3,X2,X4,X5) ) ).
cnf(i_0_5275_184,axiom,
( X1 != X2
| esk332_4(X3,X4,X1,X5) = esk332_4(X3,X4,X2,X5) ) ).
cnf(i_0_5276_185,axiom,
( X1 != X2
| esk332_4(X3,X4,X5,X1) = esk332_4(X3,X4,X5,X2) ) ).
cnf(i_0_5277_186,axiom,
( X1 != X2
| esk330_3(X1,X3,X4) = esk330_3(X2,X3,X4) ) ).
cnf(i_0_5278_187,axiom,
( X1 != X2
| esk330_3(X3,X1,X4) = esk330_3(X3,X2,X4) ) ).
cnf(i_0_5279_188,axiom,
( X1 != X2
| esk330_3(X3,X4,X1) = esk330_3(X3,X4,X2) ) ).
cnf(i_0_5280_189,axiom,
( X1 != X2
| esk329_3(X1,X3,X4) = esk329_3(X2,X3,X4) ) ).
cnf(i_0_5281_190,axiom,
( X1 != X2
| esk329_3(X3,X1,X4) = esk329_3(X3,X2,X4) ) ).
cnf(i_0_5282_191,axiom,
( X1 != X2
| esk329_3(X3,X4,X1) = esk329_3(X3,X4,X2) ) ).
cnf(i_0_5283_192,axiom,
( X1 != X2
| inclusion_relation(X1) = inclusion_relation(X2) ) ).
cnf(i_0_5284_193,axiom,
( X1 != X2
| identity_relation(X1) = identity_relation(X2) ) ).
cnf(i_0_5285_194,axiom,
( X1 != X2
| esk2_2(X1,X3) = esk2_2(X2,X3) ) ).
cnf(i_0_5286_195,axiom,
( X1 != X2
| esk2_2(X3,X1) = esk2_2(X3,X2) ) ).
cnf(i_0_5287_196,axiom,
( X1 != X2
| unordered_pair(X1,X3) = unordered_pair(X2,X3) ) ).
cnf(i_0_5288_197,axiom,
( X1 != X2
| unordered_pair(X3,X1) = unordered_pair(X3,X2) ) ).
cnf(i_0_5289_198,axiom,
( X1 != X2
| esk1_2(X1,X3) = esk1_2(X2,X3) ) ).
cnf(i_0_5290_199,axiom,
( X1 != X2
| esk1_2(X3,X1) = esk1_2(X3,X2) ) ).
cnf(i_0_5291_200,axiom,
( X1 != X2
| esk235_1(X1) = esk235_1(X2) ) ).
cnf(i_0_5292_201,axiom,
( X1 != X2
| esk353_4(X1,X3,X4,X5) = esk353_4(X2,X3,X4,X5) ) ).
cnf(i_0_5293_202,axiom,
( X1 != X2
| esk353_4(X3,X1,X4,X5) = esk353_4(X3,X2,X4,X5) ) ).
cnf(i_0_5294_203,axiom,
( X1 != X2
| esk353_4(X3,X4,X1,X5) = esk353_4(X3,X4,X2,X5) ) ).
cnf(i_0_5295_204,axiom,
( X1 != X2
| esk353_4(X3,X4,X5,X1) = esk353_4(X3,X4,X5,X2) ) ).
cnf(i_0_5296_205,axiom,
( X1 != X2
| esk352_3(X1,X3,X4) = esk352_3(X2,X3,X4) ) ).
cnf(i_0_5297_206,axiom,
( X1 != X2
| esk352_3(X3,X1,X4) = esk352_3(X3,X2,X4) ) ).
cnf(i_0_5298_207,axiom,
( X1 != X2
| esk352_3(X3,X4,X1) = esk352_3(X3,X4,X2) ) ).
cnf(i_0_5299_208,axiom,
( X1 != X2
| esk348_3(X1,X3,X4) = esk348_3(X2,X3,X4) ) ).
cnf(i_0_5300_209,axiom,
( X1 != X2
| esk348_3(X3,X1,X4) = esk348_3(X3,X2,X4) ) ).
cnf(i_0_5301_210,axiom,
( X1 != X2
| esk348_3(X3,X4,X1) = esk348_3(X3,X4,X2) ) ).
cnf(i_0_5302_211,axiom,
( X1 != X2
| ordered_pair_as_product_element(X1,X3,X4,X5) = ordered_pair_as_product_element(X2,X3,X4,X5) ) ).
cnf(i_0_5303_212,axiom,
( X1 != X2
| ordered_pair_as_product_element(X3,X1,X4,X5) = ordered_pair_as_product_element(X3,X2,X4,X5) ) ).
cnf(i_0_5304_213,axiom,
( X1 != X2
| ordered_pair_as_product_element(X3,X4,X1,X5) = ordered_pair_as_product_element(X3,X4,X2,X5) ) ).
cnf(i_0_5305_214,axiom,
( X1 != X2
| ordered_pair_as_product_element(X3,X4,X5,X1) = ordered_pair_as_product_element(X3,X4,X5,X2) ) ).
cnf(i_0_5306_215,axiom,
( X1 != X2
| relation_of_lattice(X1) = relation_of_lattice(X2) ) ).
cnf(i_0_5307_216,axiom,
( X1 != X2
| esk213_3(X1,X3,X4) = esk213_3(X2,X3,X4) ) ).
cnf(i_0_5308_217,axiom,
( X1 != X2
| esk213_3(X3,X1,X4) = esk213_3(X3,X2,X4) ) ).
cnf(i_0_5309_218,axiom,
( X1 != X2
| esk213_3(X3,X4,X1) = esk213_3(X3,X4,X2) ) ).
cnf(i_0_5310_219,axiom,
( X1 != X2
| esk96_2(X1,X3) = esk96_2(X2,X3) ) ).
cnf(i_0_5311_220,axiom,
( X1 != X2
| esk96_2(X3,X1) = esk96_2(X3,X2) ) ).
cnf(i_0_5312_221,axiom,
( X1 != X2
| esk95_2(X1,X3) = esk95_2(X2,X3) ) ).
cnf(i_0_5313_222,axiom,
( X1 != X2
| esk95_2(X3,X1) = esk95_2(X3,X2) ) ).
cnf(i_0_5314_223,axiom,
( X1 != X2
| esk328_3(X1,X3,X4) = esk328_3(X2,X3,X4) ) ).
cnf(i_0_5315_224,axiom,
( X1 != X2
| esk328_3(X3,X1,X4) = esk328_3(X3,X2,X4) ) ).
cnf(i_0_5316_225,axiom,
( X1 != X2
| esk328_3(X3,X4,X1) = esk328_3(X3,X4,X2) ) ).
cnf(i_0_5317_226,axiom,
( X1 != X2
| set_difference(X1,X3) = set_difference(X2,X3) ) ).
cnf(i_0_5318_227,axiom,
( X1 != X2
| set_difference(X3,X1) = set_difference(X3,X2) ) ).
cnf(i_0_5319_228,axiom,
( X1 != X2
| esk270_2(X1,X3) = esk270_2(X2,X3) ) ).
cnf(i_0_5320_229,axiom,
( X1 != X2
| esk270_2(X3,X1) = esk270_2(X3,X2) ) ).
cnf(i_0_5321_230,axiom,
( X1 != X2
| esk269_2(X1,X3) = esk269_2(X2,X3) ) ).
cnf(i_0_5322_231,axiom,
( X1 != X2
| esk269_2(X3,X1) = esk269_2(X3,X2) ) ).
cnf(i_0_5323_232,axiom,
( X1 != X2
| esk274_3(X1,X3,X4) = esk274_3(X2,X3,X4) ) ).
cnf(i_0_5324_233,axiom,
( X1 != X2
| esk274_3(X3,X1,X4) = esk274_3(X3,X2,X4) ) ).
cnf(i_0_5325_234,axiom,
( X1 != X2
| esk274_3(X3,X4,X1) = esk274_3(X3,X4,X2) ) ).
cnf(i_0_5326_235,axiom,
( X1 != X2
| esk268_2(X1,X3) = esk268_2(X2,X3) ) ).
cnf(i_0_5327_236,axiom,
( X1 != X2
| esk268_2(X3,X1) = esk268_2(X3,X2) ) ).
cnf(i_0_5328_237,axiom,
( X1 != X2
| boole_lattice(X1) = boole_lattice(X2) ) ).
cnf(i_0_5329_238,axiom,
( X1 != X2
| subset_union2(X1,X3,X4) = subset_union2(X2,X3,X4) ) ).
cnf(i_0_5330_239,axiom,
( X1 != X2
| subset_union2(X3,X1,X4) = subset_union2(X3,X2,X4) ) ).
cnf(i_0_5331_240,axiom,
( X1 != X2
| subset_union2(X3,X4,X1) = subset_union2(X3,X4,X2) ) ).
cnf(i_0_5332_241,axiom,
( X1 != X2
| subset_intersection2(X1,X3,X4) = subset_intersection2(X2,X3,X4) ) ).
cnf(i_0_5333_242,axiom,
( X1 != X2
| subset_intersection2(X3,X1,X4) = subset_intersection2(X3,X2,X4) ) ).
cnf(i_0_5334_243,axiom,
( X1 != X2
| subset_intersection2(X3,X4,X1) = subset_intersection2(X3,X4,X2) ) ).
cnf(i_0_5335_244,axiom,
( X1 != X2
| esk212_3(X1,X3,X4) = esk212_3(X2,X3,X4) ) ).
cnf(i_0_5336_245,axiom,
( X1 != X2
| esk212_3(X3,X1,X4) = esk212_3(X3,X2,X4) ) ).
cnf(i_0_5337_246,axiom,
( X1 != X2
| esk212_3(X3,X4,X1) = esk212_3(X3,X4,X2) ) ).
cnf(i_0_5338_247,axiom,
( X1 != X2
| apply_as_element(X1,X3,X4,X5) = apply_as_element(X2,X3,X4,X5) ) ).
cnf(i_0_5339_248,axiom,
( X1 != X2
| apply_as_element(X3,X1,X4,X5) = apply_as_element(X3,X2,X4,X5) ) ).
cnf(i_0_5340_249,axiom,
( X1 != X2
| apply_as_element(X3,X4,X1,X5) = apply_as_element(X3,X4,X2,X5) ) ).
cnf(i_0_5341_250,axiom,
( X1 != X2
| apply_as_element(X3,X4,X5,X1) = apply_as_element(X3,X4,X5,X2) ) ).
cnf(i_0_5342_251,axiom,
( X1 != X2
| topstr_closure(X1,X3) = topstr_closure(X2,X3) ) ).
cnf(i_0_5343_252,axiom,
( X1 != X2
| topstr_closure(X3,X1) = topstr_closure(X3,X2) ) ).
cnf(i_0_5344_253,axiom,
( X1 != X2
| latt_str_of(X1,X3,X4) = latt_str_of(X2,X3,X4) ) ).
cnf(i_0_5345_254,axiom,
( X1 != X2
| latt_str_of(X3,X1,X4) = latt_str_of(X3,X2,X4) ) ).
cnf(i_0_5346_255,axiom,
( X1 != X2
| latt_str_of(X3,X4,X1) = latt_str_of(X3,X4,X2) ) ).
cnf(i_0_5347_256,axiom,
( X1 != X2
| k10_filter_1(X1,X3,X4,X5) = k10_filter_1(X2,X3,X4,X5) ) ).
cnf(i_0_5348_257,axiom,
( X1 != X2
| k10_filter_1(X3,X1,X4,X5) = k10_filter_1(X3,X2,X4,X5) ) ).
cnf(i_0_5349_258,axiom,
( X1 != X2
| k10_filter_1(X3,X4,X1,X5) = k10_filter_1(X3,X4,X2,X5) ) ).
cnf(i_0_5350_259,axiom,
( X1 != X2
| k10_filter_1(X3,X4,X5,X1) = k10_filter_1(X3,X4,X5,X2) ) ).
cnf(i_0_5351_260,axiom,
( X1 != X2
| esk252_3(X1,X3,X4) = esk252_3(X2,X3,X4) ) ).
cnf(i_0_5352_261,axiom,
( X1 != X2
| esk252_3(X3,X1,X4) = esk252_3(X3,X2,X4) ) ).
cnf(i_0_5353_262,axiom,
( X1 != X2
| esk252_3(X3,X4,X1) = esk252_3(X3,X4,X2) ) ).
cnf(i_0_5354_263,axiom,
( X1 != X2
| esk251_2(X1,X3) = esk251_2(X2,X3) ) ).
cnf(i_0_5355_264,axiom,
( X1 != X2
| esk251_2(X3,X1) = esk251_2(X3,X2) ) ).
cnf(i_0_5356_265,axiom,
( X1 != X2
| esk390_2(X1,X3) = esk390_2(X2,X3) ) ).
cnf(i_0_5357_266,axiom,
( X1 != X2
| esk390_2(X3,X1) = esk390_2(X3,X2) ) ).
cnf(i_0_5358_267,axiom,
( X1 != X2
| esk392_3(X1,X3,X4) = esk392_3(X2,X3,X4) ) ).
cnf(i_0_5359_268,axiom,
( X1 != X2
| esk392_3(X3,X1,X4) = esk392_3(X3,X2,X4) ) ).
cnf(i_0_5360_269,axiom,
( X1 != X2
| esk392_3(X3,X4,X1) = esk392_3(X3,X4,X2) ) ).
cnf(i_0_5361_270,axiom,
( X1 != X2
| esk388_2(X1,X3) = esk388_2(X2,X3) ) ).
cnf(i_0_5362_271,axiom,
( X1 != X2
| esk388_2(X3,X1) = esk388_2(X3,X2) ) ).
cnf(i_0_5363_272,axiom,
( X1 != X2
| esk389_2(X1,X3) = esk389_2(X2,X3) ) ).
cnf(i_0_5364_273,axiom,
( X1 != X2
| esk389_2(X3,X1) = esk389_2(X3,X2) ) ).
cnf(i_0_5365_274,axiom,
( X1 != X2
| a_1_0_filter_1(X1) = a_1_0_filter_1(X2) ) ).
cnf(i_0_5366_275,axiom,
( X1 != X2
| esk351_3(X1,X3,X4) = esk351_3(X2,X3,X4) ) ).
cnf(i_0_5367_276,axiom,
( X1 != X2
| esk351_3(X3,X1,X4) = esk351_3(X3,X2,X4) ) ).
cnf(i_0_5368_277,axiom,
( X1 != X2
| esk351_3(X3,X4,X1) = esk351_3(X3,X4,X2) ) ).
cnf(i_0_5369_278,axiom,
( X1 != X2
| esk287_2(X1,X3) = esk287_2(X2,X3) ) ).
cnf(i_0_5370_279,axiom,
( X1 != X2
| esk287_2(X3,X1) = esk287_2(X3,X2) ) ).
cnf(i_0_5371_280,axiom,
( X1 != X2
| esk350_2(X1,X3) = esk350_2(X2,X3) ) ).
cnf(i_0_5372_281,axiom,
( X1 != X2
| esk350_2(X3,X1) = esk350_2(X3,X2) ) ).
cnf(i_0_5373_282,axiom,
( X1 != X2
| esk82_2(X1,X3) = esk82_2(X2,X3) ) ).
cnf(i_0_5374_283,axiom,
( X1 != X2
| esk82_2(X3,X1) = esk82_2(X3,X2) ) ).
cnf(i_0_5375_284,axiom,
( X1 != X2
| esk81_2(X1,X3) = esk81_2(X2,X3) ) ).
cnf(i_0_5376_285,axiom,
( X1 != X2
| esk81_2(X3,X1) = esk81_2(X3,X2) ) ).
cnf(i_0_5377_286,axiom,
( X1 != X2
| esk396_2(X1,X3) = esk396_2(X2,X3) ) ).
cnf(i_0_5378_287,axiom,
( X1 != X2
| esk396_2(X3,X1) = esk396_2(X3,X2) ) ).
cnf(i_0_5379_288,axiom,
( X1 != X2
| esk398_3(X1,X3,X4) = esk398_3(X2,X3,X4) ) ).
cnf(i_0_5380_289,axiom,
( X1 != X2
| esk398_3(X3,X1,X4) = esk398_3(X3,X2,X4) ) ).
cnf(i_0_5381_290,axiom,
( X1 != X2
| esk398_3(X3,X4,X1) = esk398_3(X3,X4,X2) ) ).
cnf(i_0_5382_291,axiom,
( X1 != X2
| esk394_2(X1,X3) = esk394_2(X2,X3) ) ).
cnf(i_0_5383_292,axiom,
( X1 != X2
| esk394_2(X3,X1) = esk394_2(X3,X2) ) ).
cnf(i_0_5384_293,axiom,
( X1 != X2
| esk395_2(X1,X3) = esk395_2(X2,X3) ) ).
cnf(i_0_5385_294,axiom,
( X1 != X2
| esk395_2(X3,X1) = esk395_2(X3,X2) ) ).
cnf(i_0_5386_295,axiom,
( X1 != X2
| esk288_2(X1,X3) = esk288_2(X2,X3) ) ).
cnf(i_0_5387_296,axiom,
( X1 != X2
| esk288_2(X3,X1) = esk288_2(X3,X2) ) ).
cnf(i_0_5388_297,axiom,
( X1 != X2
| esk391_2(X1,X3) = esk391_2(X2,X3) ) ).
cnf(i_0_5389_298,axiom,
( X1 != X2
| esk391_2(X3,X1) = esk391_2(X3,X2) ) ).
cnf(i_0_5390_299,axiom,
( X1 != X2
| esk298_3(X1,X3,X4) = esk298_3(X2,X3,X4) ) ).
cnf(i_0_5391_300,axiom,
( X1 != X2
| esk298_3(X3,X1,X4) = esk298_3(X3,X2,X4) ) ).
cnf(i_0_5392_301,axiom,
( X1 != X2
| esk298_3(X3,X4,X1) = esk298_3(X3,X4,X2) ) ).
cnf(i_0_5393_302,axiom,
( X1 != X2
| esk280_3(X1,X3,X4) = esk280_3(X2,X3,X4) ) ).
cnf(i_0_5394_303,axiom,
( X1 != X2
| esk280_3(X3,X1,X4) = esk280_3(X3,X2,X4) ) ).
cnf(i_0_5395_304,axiom,
( X1 != X2
| esk280_3(X3,X4,X1) = esk280_3(X3,X4,X2) ) ).
cnf(i_0_5396_305,axiom,
( X1 != X2
| esk284_2(X1,X3) = esk284_2(X2,X3) ) ).
cnf(i_0_5397_306,axiom,
( X1 != X2
| esk284_2(X3,X1) = esk284_2(X3,X2) ) ).
cnf(i_0_5398_307,axiom,
( X1 != X2
| union_of_subsets(X1,X3) = union_of_subsets(X2,X3) ) ).
cnf(i_0_5399_308,axiom,
( X1 != X2
| union_of_subsets(X3,X1) = union_of_subsets(X3,X2) ) ).
cnf(i_0_5400_309,axiom,
( X1 != X2
| meet_of_latt_set(X1,X3) = meet_of_latt_set(X2,X3) ) ).
cnf(i_0_5401_310,axiom,
( X1 != X2
| meet_of_latt_set(X3,X1) = meet_of_latt_set(X3,X2) ) ).
cnf(i_0_5402_311,axiom,
( X1 != X2
| join_of_latt_set(X1,X3) = join_of_latt_set(X2,X3) ) ).
cnf(i_0_5403_312,axiom,
( X1 != X2
| join_of_latt_set(X3,X1) = join_of_latt_set(X3,X2) ) ).
cnf(i_0_5404_313,axiom,
( X1 != X2
| esk397_2(X1,X3) = esk397_2(X2,X3) ) ).
cnf(i_0_5405_314,axiom,
( X1 != X2
| esk397_2(X3,X1) = esk397_2(X3,X2) ) ).
cnf(i_0_5406_315,axiom,
( X1 != X2
| esk267_3(X1,X3,X4) = esk267_3(X2,X3,X4) ) ).
cnf(i_0_5407_316,axiom,
( X1 != X2
| esk267_3(X3,X1,X4) = esk267_3(X3,X2,X4) ) ).
cnf(i_0_5408_317,axiom,
( X1 != X2
| esk267_3(X3,X4,X1) = esk267_3(X3,X4,X2) ) ).
cnf(i_0_5409_318,axiom,
( X1 != X2
| cast_as_carrier_subset(X1) = cast_as_carrier_subset(X2) ) ).
cnf(i_0_5410_319,axiom,
( X1 != X2
| esk265_2(X1,X3) = esk265_2(X2,X3) ) ).
cnf(i_0_5411_320,axiom,
( X1 != X2
| esk265_2(X3,X1) = esk265_2(X3,X2) ) ).
cnf(i_0_5412_321,axiom,
( X1 != X2
| esk264_2(X1,X3) = esk264_2(X2,X3) ) ).
cnf(i_0_5413_322,axiom,
( X1 != X2
| esk264_2(X3,X1) = esk264_2(X3,X2) ) ).
cnf(i_0_5414_323,axiom,
( X1 != X2
| esk137_1(X1) = esk137_1(X2) ) ).
cnf(i_0_5415_324,axiom,
( X1 != X2
| esk136_1(X1) = esk136_1(X2) ) ).
cnf(i_0_5416_325,axiom,
( X1 != X2
| esk204_2(X1,X3) = esk204_2(X2,X3) ) ).
cnf(i_0_5417_326,axiom,
( X1 != X2
| esk204_2(X3,X1) = esk204_2(X3,X2) ) ).
cnf(i_0_5418_327,axiom,
( X1 != X2
| esk201_2(X1,X3) = esk201_2(X2,X3) ) ).
cnf(i_0_5419_328,axiom,
( X1 != X2
| esk201_2(X3,X1) = esk201_2(X3,X2) ) ).
cnf(i_0_5420_329,axiom,
( X1 != X2
| subset_complement(X1,X3) = subset_complement(X2,X3) ) ).
cnf(i_0_5421_330,axiom,
( X1 != X2
| subset_complement(X3,X1) = subset_complement(X3,X2) ) ).
cnf(i_0_5422_331,axiom,
( X1 != X2
| pair_second(X1) = pair_second(X2) ) ).
cnf(i_0_5423_332,axiom,
( X1 != X2
| esk54_2(X1,X3) = esk54_2(X2,X3) ) ).
cnf(i_0_5424_333,axiom,
( X1 != X2
| esk54_2(X3,X1) = esk54_2(X3,X2) ) ).
cnf(i_0_5425_334,axiom,
( X1 != X2
| pair_first(X1) = pair_first(X2) ) ).
cnf(i_0_5426_335,axiom,
( X1 != X2
| esk32_2(X1,X3) = esk32_2(X2,X3) ) ).
cnf(i_0_5427_336,axiom,
( X1 != X2
| esk32_2(X3,X1) = esk32_2(X3,X2) ) ).
cnf(i_0_5428_337,axiom,
( X1 != X2
| esk404_2(X1,X3) = esk404_2(X2,X3) ) ).
cnf(i_0_5429_338,axiom,
( X1 != X2
| esk404_2(X3,X1) = esk404_2(X3,X2) ) ).
cnf(i_0_5430_339,axiom,
( X1 != X2
| esk401_2(X1,X3) = esk401_2(X2,X3) ) ).
cnf(i_0_5431_340,axiom,
( X1 != X2
| esk401_2(X3,X1) = esk401_2(X3,X2) ) ).
cnf(i_0_5432_341,axiom,
( X1 != X2
| esk6_3(X1,X3,X4) = esk6_3(X2,X3,X4) ) ).
cnf(i_0_5433_342,axiom,
( X1 != X2
| esk6_3(X3,X1,X4) = esk6_3(X3,X2,X4) ) ).
cnf(i_0_5434_343,axiom,
( X1 != X2
| esk6_3(X3,X4,X1) = esk6_3(X3,X4,X2) ) ).
cnf(i_0_5435_344,axiom,
( X1 != X2
| function_inverse(X1) = function_inverse(X2) ) ).
cnf(i_0_5436_345,axiom,
( X1 != X2
| the_carrier(X1) = the_carrier(X2) ) ).
cnf(i_0_5437_346,axiom,
( X1 != X2
| esk435_2(X1,X3) = esk435_2(X2,X3) ) ).
cnf(i_0_5438_347,axiom,
( X1 != X2
| esk435_2(X3,X1) = esk435_2(X3,X2) ) ).
cnf(i_0_5439_348,axiom,
( X1 != X2
| esk436_2(X1,X3) = esk436_2(X2,X3) ) ).
cnf(i_0_5440_349,axiom,
( X1 != X2
| esk436_2(X3,X1) = esk436_2(X3,X2) ) ).
cnf(i_0_5441_350,axiom,
( X1 != X2
| esk434_2(X1,X3) = esk434_2(X2,X3) ) ).
cnf(i_0_5442_351,axiom,
( X1 != X2
| esk434_2(X3,X1) = esk434_2(X3,X2) ) ).
cnf(i_0_5443_352,axiom,
( X1 != X2
| esk433_2(X1,X3) = esk433_2(X2,X3) ) ).
cnf(i_0_5444_353,axiom,
( X1 != X2
| esk433_2(X3,X1) = esk433_2(X3,X2) ) ).
cnf(i_0_5445_354,axiom,
( X1 != X2
| esk293_6(X1,X3,X4,X5,X6,X7) = esk293_6(X2,X3,X4,X5,X6,X7) ) ).
cnf(i_0_5446_355,axiom,
( X1 != X2
| esk293_6(X3,X1,X4,X5,X6,X7) = esk293_6(X3,X2,X4,X5,X6,X7) ) ).
cnf(i_0_5447_356,axiom,
( X1 != X2
| esk293_6(X3,X4,X1,X5,X6,X7) = esk293_6(X3,X4,X2,X5,X6,X7) ) ).
cnf(i_0_5448_357,axiom,
( X1 != X2
| esk293_6(X3,X4,X5,X1,X6,X7) = esk293_6(X3,X4,X5,X2,X6,X7) ) ).
cnf(i_0_5449_358,axiom,
( X1 != X2
| esk293_6(X3,X4,X5,X6,X1,X7) = esk293_6(X3,X4,X5,X6,X2,X7) ) ).
cnf(i_0_5450_359,axiom,
( X1 != X2
| esk293_6(X3,X4,X5,X6,X7,X1) = esk293_6(X3,X4,X5,X6,X7,X2) ) ).
cnf(i_0_5451_360,axiom,
( X1 != X2
| esk263_2(X1,X3) = esk263_2(X2,X3) ) ).
cnf(i_0_5452_361,axiom,
( X1 != X2
| esk263_2(X3,X1) = esk263_2(X3,X2) ) ).
cnf(i_0_5453_362,axiom,
( X1 != X2
| esk243_3(X1,X3,X4) = esk243_3(X2,X3,X4) ) ).
cnf(i_0_5454_363,axiom,
( X1 != X2
| esk243_3(X3,X1,X4) = esk243_3(X3,X2,X4) ) ).
cnf(i_0_5455_364,axiom,
( X1 != X2
| esk243_3(X3,X4,X1) = esk243_3(X3,X4,X2) ) ).
cnf(i_0_5456_365,axiom,
( X1 != X2
| esk262_3(X1,X3,X4) = esk262_3(X2,X3,X4) ) ).
cnf(i_0_5457_366,axiom,
( X1 != X2
| esk262_3(X3,X1,X4) = esk262_3(X3,X2,X4) ) ).
cnf(i_0_5458_367,axiom,
( X1 != X2
| esk262_3(X3,X4,X1) = esk262_3(X3,X4,X2) ) ).
cnf(i_0_5459_368,axiom,
( X1 != X2
| esk259_2(X1,X3) = esk259_2(X2,X3) ) ).
cnf(i_0_5460_369,axiom,
( X1 != X2
| esk259_2(X3,X1) = esk259_2(X3,X2) ) ).
cnf(i_0_5461_370,axiom,
( X1 != X2
| esk261_3(X1,X3,X4) = esk261_3(X2,X3,X4) ) ).
cnf(i_0_5462_371,axiom,
( X1 != X2
| esk261_3(X3,X1,X4) = esk261_3(X3,X2,X4) ) ).
cnf(i_0_5463_372,axiom,
( X1 != X2
| esk261_3(X3,X4,X1) = esk261_3(X3,X4,X2) ) ).
cnf(i_0_5464_373,axiom,
( X1 != X2
| esk258_2(X1,X3) = esk258_2(X2,X3) ) ).
cnf(i_0_5465_374,axiom,
( X1 != X2
| esk258_2(X3,X1) = esk258_2(X3,X2) ) ).
cnf(i_0_5466_375,axiom,
( X1 != X2
| complements_of_subsets(X1,X3) = complements_of_subsets(X2,X3) ) ).
cnf(i_0_5467_376,axiom,
( X1 != X2
| complements_of_subsets(X3,X1) = complements_of_subsets(X3,X2) ) ).
cnf(i_0_5468_377,axiom,
( X1 != X2
| esk105_1(X1) = esk105_1(X2) ) ).
cnf(i_0_5469_378,axiom,
( X1 != X2
| esk446_1(X1) = esk446_1(X2) ) ).
cnf(i_0_5470_379,axiom,
( X1 != X2
| esk407_3(X1,X3,X4) = esk407_3(X2,X3,X4) ) ).
cnf(i_0_5471_380,axiom,
( X1 != X2
| esk407_3(X3,X1,X4) = esk407_3(X3,X2,X4) ) ).
cnf(i_0_5472_381,axiom,
( X1 != X2
| esk407_3(X3,X4,X1) = esk407_3(X3,X4,X2) ) ).
cnf(i_0_5473_382,axiom,
( X1 != X2
| poset_of_lattice(X1) = poset_of_lattice(X2) ) ).
cnf(i_0_5474_383,axiom,
( X1 != X2
| cast_to_el_of_LattPOSet(X1,X3) = cast_to_el_of_LattPOSet(X2,X3) ) ).
cnf(i_0_5475_384,axiom,
( X1 != X2
| cast_to_el_of_LattPOSet(X3,X1) = cast_to_el_of_LattPOSet(X3,X2) ) ).
cnf(i_0_5476_385,axiom,
( X1 != X2
| esk339_3(X1,X3,X4) = esk339_3(X2,X3,X4) ) ).
cnf(i_0_5477_386,axiom,
( X1 != X2
| esk339_3(X3,X1,X4) = esk339_3(X3,X2,X4) ) ).
cnf(i_0_5478_387,axiom,
( X1 != X2
| esk339_3(X3,X4,X1) = esk339_3(X3,X4,X2) ) ).
cnf(i_0_5479_388,axiom,
( X1 != X2
| esk335_2(X1,X3) = esk335_2(X2,X3) ) ).
cnf(i_0_5480_389,axiom,
( X1 != X2
| esk335_2(X3,X1) = esk335_2(X3,X2) ) ).
cnf(i_0_5481_390,axiom,
( X1 != X2
| esk334_2(X1,X3) = esk334_2(X2,X3) ) ).
cnf(i_0_5482_391,axiom,
( X1 != X2
| esk334_2(X3,X1) = esk334_2(X3,X2) ) ).
cnf(i_0_5483_392,axiom,
( X1 != X2
| powerset(X1) = powerset(X2) ) ).
cnf(i_0_5484_393,axiom,
( X1 != X2
| esk256_2(X1,X3) = esk256_2(X2,X3) ) ).
cnf(i_0_5485_394,axiom,
( X1 != X2
| esk256_2(X3,X1) = esk256_2(X3,X2) ) ).
cnf(i_0_5486_395,axiom,
( X1 != X2
| esk257_2(X1,X3) = esk257_2(X2,X3) ) ).
cnf(i_0_5487_396,axiom,
( X1 != X2
| esk257_2(X3,X1) = esk257_2(X3,X2) ) ).
cnf(i_0_5488_397,axiom,
( X1 != X2
| bottom_of_semilattstr(X1) = bottom_of_semilattstr(X2) ) ).
cnf(i_0_5489_398,axiom,
( X1 != X2
| identity_on_carrier(X1) = identity_on_carrier(X2) ) ).
cnf(i_0_5490_399,axiom,
( X1 != X2
| esk337_2(X1,X3) = esk337_2(X2,X3) ) ).
cnf(i_0_5491_400,axiom,
( X1 != X2
| esk337_2(X3,X1) = esk337_2(X3,X2) ) ).
cnf(i_0_5492_401,axiom,
( X1 != X2
| esk336_2(X1,X3) = esk336_2(X2,X3) ) ).
cnf(i_0_5493_402,axiom,
( X1 != X2
| esk336_2(X3,X1) = esk336_2(X3,X2) ) ).
cnf(i_0_5494_403,axiom,
( X1 != X2
| esk285_2(X1,X3) = esk285_2(X2,X3) ) ).
cnf(i_0_5495_404,axiom,
( X1 != X2
| esk285_2(X3,X1) = esk285_2(X3,X2) ) ).
cnf(i_0_5496_405,axiom,
( X1 != X2
| subset_difference(X1,X3,X4) = subset_difference(X2,X3,X4) ) ).
cnf(i_0_5497_406,axiom,
( X1 != X2
| subset_difference(X3,X1,X4) = subset_difference(X3,X2,X4) ) ).
cnf(i_0_5498_407,axiom,
( X1 != X2
| subset_difference(X3,X4,X1) = subset_difference(X3,X4,X2) ) ).
cnf(i_0_5499_408,axiom,
( X1 != X2
| esk333_2(X1,X3) = esk333_2(X2,X3) ) ).
cnf(i_0_5500_409,axiom,
( X1 != X2
| esk333_2(X3,X1) = esk333_2(X3,X2) ) ).
cnf(i_0_5501_410,axiom,
( X1 != X2
| esk255_2(X1,X3) = esk255_2(X2,X3) ) ).
cnf(i_0_5502_411,axiom,
( X1 != X2
| esk255_2(X3,X1) = esk255_2(X3,X2) ) ).
cnf(i_0_5503_412,axiom,
( X1 != X2
| esk58_3(X1,X3,X4) = esk58_3(X2,X3,X4) ) ).
cnf(i_0_5504_413,axiom,
( X1 != X2
| esk58_3(X3,X1,X4) = esk58_3(X3,X2,X4) ) ).
cnf(i_0_5505_414,axiom,
( X1 != X2
| esk58_3(X3,X4,X1) = esk58_3(X3,X4,X2) ) ).
cnf(i_0_5506_415,axiom,
( X1 != X2
| esk187_1(X1) = esk187_1(X2) ) ).
cnf(i_0_5507_416,axiom,
( X1 != X2
| esk286_2(X1,X3) = esk286_2(X2,X3) ) ).
cnf(i_0_5508_417,axiom,
( X1 != X2
| esk286_2(X3,X1) = esk286_2(X3,X2) ) ).
cnf(i_0_5509_418,axiom,
( X1 != X2
| esk186_1(X1) = esk186_1(X2) ) ).
cnf(i_0_5510_419,axiom,
( X1 != X2
| esk355_3(X1,X3,X4) = esk355_3(X2,X3,X4) ) ).
cnf(i_0_5511_420,axiom,
( X1 != X2
| esk355_3(X3,X1,X4) = esk355_3(X3,X2,X4) ) ).
cnf(i_0_5512_421,axiom,
( X1 != X2
| esk355_3(X3,X4,X1) = esk355_3(X3,X4,X2) ) ).
cnf(i_0_5513_422,axiom,
( X1 != X2
| cast_to_el_of_lattice(X1,X3) = cast_to_el_of_lattice(X2,X3) ) ).
cnf(i_0_5514_423,axiom,
( X1 != X2
| cast_to_el_of_lattice(X3,X1) = cast_to_el_of_lattice(X3,X2) ) ).
cnf(i_0_5515_424,axiom,
( X1 != X2
| esk135_1(X1) = esk135_1(X2) ) ).
cnf(i_0_5516_425,axiom,
( X1 != X2
| esk134_1(X1) = esk134_1(X2) ) ).
cnf(i_0_5517_426,axiom,
( X1 != X2
| esk283_2(X1,X3) = esk283_2(X2,X3) ) ).
cnf(i_0_5518_427,axiom,
( X1 != X2
| esk283_2(X3,X1) = esk283_2(X3,X2) ) ).
cnf(i_0_5519_428,axiom,
( X1 != X2
| meet_commut(X1,X3,X4) = meet_commut(X2,X3,X4) ) ).
cnf(i_0_5520_429,axiom,
( X1 != X2
| meet_commut(X3,X1,X4) = meet_commut(X3,X2,X4) ) ).
cnf(i_0_5521_430,axiom,
( X1 != X2
| meet_commut(X3,X4,X1) = meet_commut(X3,X4,X2) ) ).
cnf(i_0_5522_431,axiom,
( X1 != X2
| esk128_3(X1,X3,X4) = esk128_3(X2,X3,X4) ) ).
cnf(i_0_5523_432,axiom,
( X1 != X2
| esk128_3(X3,X1,X4) = esk128_3(X3,X2,X4) ) ).
cnf(i_0_5524_433,axiom,
( X1 != X2
| esk128_3(X3,X4,X1) = esk128_3(X3,X4,X2) ) ).
cnf(i_0_5525_434,axiom,
( X1 != X2
| esk29_1(X1) = esk29_1(X2) ) ).
cnf(i_0_5526_435,axiom,
( X1 != X2
| esk28_1(X1) = esk28_1(X2) ) ).
cnf(i_0_5527_436,axiom,
( X1 != X2
| esk127_3(X1,X3,X4) = esk127_3(X2,X3,X4) ) ).
cnf(i_0_5528_437,axiom,
( X1 != X2
| esk127_3(X3,X1,X4) = esk127_3(X3,X2,X4) ) ).
cnf(i_0_5529_438,axiom,
( X1 != X2
| esk127_3(X3,X4,X1) = esk127_3(X3,X4,X2) ) ).
cnf(i_0_5530_439,axiom,
( X1 != X2
| esk305_2(X1,X3) = esk305_2(X2,X3) ) ).
cnf(i_0_5531_440,axiom,
( X1 != X2
| esk305_2(X3,X1) = esk305_2(X3,X2) ) ).
cnf(i_0_5532_441,axiom,
( X1 != X2
| esk340_3(X1,X3,X4) = esk340_3(X2,X3,X4) ) ).
cnf(i_0_5533_442,axiom,
( X1 != X2
| esk340_3(X3,X1,X4) = esk340_3(X3,X2,X4) ) ).
cnf(i_0_5534_443,axiom,
( X1 != X2
| esk340_3(X3,X4,X1) = esk340_3(X3,X4,X2) ) ).
cnf(i_0_5535_444,axiom,
( X1 != X2
| esk250_2(X1,X3) = esk250_2(X2,X3) ) ).
cnf(i_0_5536_445,axiom,
( X1 != X2
| esk250_2(X3,X1) = esk250_2(X3,X2) ) ).
cnf(i_0_5537_446,axiom,
( X1 != X2
| interior(X1,X3) = interior(X2,X3) ) ).
cnf(i_0_5538_447,axiom,
( X1 != X2
| interior(X3,X1) = interior(X3,X2) ) ).
cnf(i_0_5539_448,axiom,
( X1 != X2
| rel_str_of(X1,X3) = rel_str_of(X2,X3) ) ).
cnf(i_0_5540_449,axiom,
( X1 != X2
| rel_str_of(X3,X1) = rel_str_of(X3,X2) ) ).
cnf(i_0_5541_450,axiom,
( X1 != X2
| esk203_1(X1) = esk203_1(X2) ) ).
cnf(i_0_5542_451,axiom,
( X1 != X2
| esk403_1(X1) = esk403_1(X2) ) ).
cnf(i_0_5543_452,axiom,
( X1 != X2
| meet_of_subsets(X1,X3) = meet_of_subsets(X2,X3) ) ).
cnf(i_0_5544_453,axiom,
( X1 != X2
| meet_of_subsets(X3,X1) = meet_of_subsets(X3,X2) ) ).
cnf(i_0_5545_454,axiom,
( X1 != X2
| esk306_2(X1,X3) = esk306_2(X2,X3) ) ).
cnf(i_0_5546_455,axiom,
( X1 != X2
| esk306_2(X3,X1) = esk306_2(X3,X2) ) ).
cnf(i_0_5547_456,axiom,
( X1 != X2
| set_meet(X1) = set_meet(X2) ) ).
cnf(i_0_5548_457,axiom,
( X1 != X2
| join_commut(X1,X3,X4) = join_commut(X2,X3,X4) ) ).
cnf(i_0_5549_458,axiom,
( X1 != X2
| join_commut(X3,X1,X4) = join_commut(X3,X2,X4) ) ).
cnf(i_0_5550_459,axiom,
( X1 != X2
| join_commut(X3,X4,X1) = join_commut(X3,X4,X2) ) ).
cnf(i_0_5551_460,axiom,
( X1 != X2
| esk373_3(X1,X3,X4) = esk373_3(X2,X3,X4) ) ).
cnf(i_0_5552_461,axiom,
( X1 != X2
| esk373_3(X3,X1,X4) = esk373_3(X3,X2,X4) ) ).
cnf(i_0_5553_462,axiom,
( X1 != X2
| esk373_3(X3,X4,X1) = esk373_3(X3,X4,X2) ) ).
cnf(i_0_5554_463,axiom,
( X1 != X2
| esk76_2(X1,X3) = esk76_2(X2,X3) ) ).
cnf(i_0_5555_464,axiom,
( X1 != X2
| esk76_2(X3,X1) = esk76_2(X3,X2) ) ).
cnf(i_0_5556_465,axiom,
( X1 != X2
| esk223_2(X1,X3) = esk223_2(X2,X3) ) ).
cnf(i_0_5557_466,axiom,
( X1 != X2
| esk223_2(X3,X1) = esk223_2(X3,X2) ) ).
cnf(i_0_5558_467,axiom,
( X1 != X2
| esk302_2(X1,X3) = esk302_2(X2,X3) ) ).
cnf(i_0_5559_468,axiom,
( X1 != X2
| esk302_2(X3,X1) = esk302_2(X3,X2) ) ).
cnf(i_0_5560_469,axiom,
( X1 != X2
| esk448_1(X1) = esk448_1(X2) ) ).
cnf(i_0_5561_470,axiom,
( X1 != X2
| esk413_2(X1,X3) = esk413_2(X2,X3) ) ).
cnf(i_0_5562_471,axiom,
( X1 != X2
| esk413_2(X3,X1) = esk413_2(X3,X2) ) ).
cnf(i_0_5563_472,axiom,
( X1 != X2
| esk89_2(X1,X3) = esk89_2(X2,X3) ) ).
cnf(i_0_5564_473,axiom,
( X1 != X2
| esk89_2(X3,X1) = esk89_2(X3,X2) ) ).
cnf(i_0_5565_474,axiom,
( X1 != X2
| union(X1) = union(X2) ) ).
cnf(i_0_5566_475,axiom,
( X1 != X2
| relation_restriction(X1,X3) = relation_restriction(X2,X3) ) ).
cnf(i_0_5567_476,axiom,
( X1 != X2
| relation_restriction(X3,X1) = relation_restriction(X3,X2) ) ).
cnf(i_0_5568_477,axiom,
( X1 != X2
| esk385_1(X1) = esk385_1(X2) ) ).
cnf(i_0_5569_478,axiom,
( X1 != X2
| esk384_1(X1) = esk384_1(X2) ) ).
cnf(i_0_5570_479,axiom,
( X1 != X2
| esk232_1(X1) = esk232_1(X2) ) ).
cnf(i_0_5571_480,axiom,
( X1 != X2
| esk311_6(X1,X3,X4,X5,X6,X7) = esk311_6(X2,X3,X4,X5,X6,X7) ) ).
cnf(i_0_5572_481,axiom,
( X1 != X2
| esk311_6(X3,X1,X4,X5,X6,X7) = esk311_6(X3,X2,X4,X5,X6,X7) ) ).
cnf(i_0_5573_482,axiom,
( X1 != X2
| esk311_6(X3,X4,X1,X5,X6,X7) = esk311_6(X3,X4,X2,X5,X6,X7) ) ).
cnf(i_0_5574_483,axiom,
( X1 != X2
| esk311_6(X3,X4,X5,X1,X6,X7) = esk311_6(X3,X4,X5,X2,X6,X7) ) ).
cnf(i_0_5575_484,axiom,
( X1 != X2
| esk311_6(X3,X4,X5,X6,X1,X7) = esk311_6(X3,X4,X5,X6,X2,X7) ) ).
cnf(i_0_5576_485,axiom,
( X1 != X2
| esk311_6(X3,X4,X5,X6,X7,X1) = esk311_6(X3,X4,X5,X6,X7,X2) ) ).
cnf(i_0_5577_486,axiom,
( X1 != X2
| esk231_1(X1) = esk231_1(X2) ) ).
cnf(i_0_5578_487,axiom,
( X1 != X2
| esk61_1(X1) = esk61_1(X2) ) ).
cnf(i_0_5579_488,axiom,
( X1 != X2
| esk11_1(X1) = esk11_1(X2) ) ).
cnf(i_0_5580_489,axiom,
( X1 != X2
| esk39_1(X1) = esk39_1(X2) ) ).
cnf(i_0_5581_490,axiom,
( X1 != X2
| esk424_2(X1,X3) = esk424_2(X2,X3) ) ).
cnf(i_0_5582_491,axiom,
( X1 != X2
| esk424_2(X3,X1) = esk424_2(X3,X2) ) ).
cnf(i_0_5583_492,axiom,
( X1 != X2
| esk303_2(X1,X3) = esk303_2(X2,X3) ) ).
cnf(i_0_5584_493,axiom,
( X1 != X2
| esk303_2(X3,X1) = esk303_2(X3,X2) ) ).
cnf(i_0_5585_494,axiom,
( X1 != X2
| esk44_2(X1,X3) = esk44_2(X2,X3) ) ).
cnf(i_0_5586_495,axiom,
( X1 != X2
| esk44_2(X3,X1) = esk44_2(X3,X2) ) ).
cnf(i_0_5587_496,axiom,
( X1 != X2
| esk419_1(X1) = esk419_1(X2) ) ).
cnf(i_0_5588_497,axiom,
( X1 != X2
| k2_lattice3(X1) = k2_lattice3(X2) ) ).
cnf(i_0_5589_498,axiom,
( X1 != X2
| esk304_2(X1,X3) = esk304_2(X2,X3) ) ).
cnf(i_0_5590_499,axiom,
( X1 != X2
| esk304_2(X3,X1) = esk304_2(X3,X2) ) ).
cnf(i_0_5591_500,axiom,
( X1 != X2
| esk450_1(X1) = esk450_1(X2) ) ).
cnf(i_0_5592_501,axiom,
( X1 != X2
| esk327_2(X1,X3) = esk327_2(X2,X3) ) ).
cnf(i_0_5593_502,axiom,
( X1 != X2
| esk327_2(X3,X1) = esk327_2(X3,X2) ) ).
cnf(i_0_5594_503,axiom,
( X1 != X2
| esk301_2(X1,X3) = esk301_2(X2,X3) ) ).
cnf(i_0_5595_504,axiom,
( X1 != X2
| esk301_2(X3,X1) = esk301_2(X3,X2) ) ).
cnf(i_0_5596_505,axiom,
( X1 != X2
| esk101_1(X1) = esk101_1(X2) ) ).
cnf(i_0_5597_506,axiom,
( X1 != X2
| esk102_1(X1) = esk102_1(X2) ) ).
cnf(i_0_5598_507,axiom,
( X1 != X2
| esk282_2(X1,X3) = esk282_2(X2,X3) ) ).
cnf(i_0_5599_508,axiom,
( X1 != X2
| esk282_2(X3,X1) = esk282_2(X3,X2) ) ).
cnf(i_0_5600_509,axiom,
( X1 != X2
| esk71_1(X1) = esk71_1(X2) ) ).
cnf(i_0_5601_510,axiom,
( X1 != X2
| esk70_1(X1) = esk70_1(X2) ) ).
cnf(i_0_5602_511,axiom,
( X1 != X2
| empty_carrier_subset(X1) = empty_carrier_subset(X2) ) ).
cnf(i_0_5603_512,axiom,
( X1 != X2
| esk52_1(X1) = esk52_1(X2) ) ).
cnf(i_0_5604_513,axiom,
( X1 != X2
| esk362_6(X1,X3,X4,X5,X6,X7) = esk362_6(X2,X3,X4,X5,X6,X7) ) ).
cnf(i_0_5605_514,axiom,
( X1 != X2
| esk362_6(X3,X1,X4,X5,X6,X7) = esk362_6(X3,X2,X4,X5,X6,X7) ) ).
cnf(i_0_5606_515,axiom,
( X1 != X2
| esk362_6(X3,X4,X1,X5,X6,X7) = esk362_6(X3,X4,X2,X5,X6,X7) ) ).
cnf(i_0_5607_516,axiom,
( X1 != X2
| esk362_6(X3,X4,X5,X1,X6,X7) = esk362_6(X3,X4,X5,X2,X6,X7) ) ).
cnf(i_0_5608_517,axiom,
( X1 != X2
| esk362_6(X3,X4,X5,X6,X1,X7) = esk362_6(X3,X4,X5,X6,X2,X7) ) ).
cnf(i_0_5609_518,axiom,
( X1 != X2
| esk362_6(X3,X4,X5,X6,X7,X1) = esk362_6(X3,X4,X5,X6,X7,X2) ) ).
cnf(i_0_5610_519,axiom,
( X1 != X2
| esk300_2(X1,X3) = esk300_2(X2,X3) ) ).
cnf(i_0_5611_520,axiom,
( X1 != X2
| esk300_2(X3,X1) = esk300_2(X3,X2) ) ).
cnf(i_0_5612_521,axiom,
( X1 != X2
| cartesian_product2(X1,X3) = cartesian_product2(X2,X3) ) ).
cnf(i_0_5613_522,axiom,
( X1 != X2
| cartesian_product2(X3,X1) = cartesian_product2(X3,X2) ) ).
cnf(i_0_5614_523,axiom,
( X1 != X2
| esk366_6(X1,X3,X4,X5,X6,X7) = esk366_6(X2,X3,X4,X5,X6,X7) ) ).
cnf(i_0_5615_524,axiom,
( X1 != X2
| esk366_6(X3,X1,X4,X5,X6,X7) = esk366_6(X3,X2,X4,X5,X6,X7) ) ).
cnf(i_0_5616_525,axiom,
( X1 != X2
| esk366_6(X3,X4,X1,X5,X6,X7) = esk366_6(X3,X4,X2,X5,X6,X7) ) ).
cnf(i_0_5617_526,axiom,
( X1 != X2
| esk366_6(X3,X4,X5,X1,X6,X7) = esk366_6(X3,X4,X5,X2,X6,X7) ) ).
cnf(i_0_5618_527,axiom,
( X1 != X2
| esk366_6(X3,X4,X5,X6,X1,X7) = esk366_6(X3,X4,X5,X6,X2,X7) ) ).
cnf(i_0_5619_528,axiom,
( X1 != X2
| esk366_6(X3,X4,X5,X6,X7,X1) = esk366_6(X3,X4,X5,X6,X7,X2) ) ).
cnf(i_0_5620_529,axiom,
( X1 != X2
| esk314_3(X1,X3,X4) = esk314_3(X2,X3,X4) ) ).
cnf(i_0_5621_530,axiom,
( X1 != X2
| esk314_3(X3,X1,X4) = esk314_3(X3,X2,X4) ) ).
cnf(i_0_5622_531,axiom,
( X1 != X2
| esk314_3(X3,X4,X1) = esk314_3(X3,X4,X2) ) ).
cnf(i_0_5623_532,axiom,
( X1 != X2
| esk313_3(X1,X3,X4) = esk313_3(X2,X3,X4) ) ).
cnf(i_0_5624_533,axiom,
( X1 != X2
| esk313_3(X3,X1,X4) = esk313_3(X3,X2,X4) ) ).
cnf(i_0_5625_534,axiom,
( X1 != X2
| esk313_3(X3,X4,X1) = esk313_3(X3,X4,X2) ) ).
cnf(i_0_5626_535,axiom,
( X1 != X2
| esk312_3(X1,X3,X4) = esk312_3(X2,X3,X4) ) ).
cnf(i_0_5627_536,axiom,
( X1 != X2
| esk312_3(X3,X1,X4) = esk312_3(X3,X2,X4) ) ).
cnf(i_0_5628_537,axiom,
( X1 != X2
| esk312_3(X3,X4,X1) = esk312_3(X3,X4,X2) ) ).
cnf(i_0_5629_538,axiom,
( X1 != X2
| esk179_2(X1,X3) = esk179_2(X2,X3) ) ).
cnf(i_0_5630_539,axiom,
( X1 != X2
| esk179_2(X3,X1) = esk179_2(X3,X2) ) ).
cnf(i_0_5631_540,axiom,
( X1 != X2
| esk181_2(X1,X3) = esk181_2(X2,X3) ) ).
cnf(i_0_5632_541,axiom,
( X1 != X2
| esk181_2(X3,X1) = esk181_2(X3,X2) ) ).
cnf(i_0_5633_542,axiom,
( X1 != X2
| esk178_2(X1,X3) = esk178_2(X2,X3) ) ).
cnf(i_0_5634_543,axiom,
( X1 != X2
| esk178_2(X3,X1) = esk178_2(X3,X2) ) ).
cnf(i_0_5635_544,axiom,
( X1 != X2
| esk180_2(X1,X3) = esk180_2(X2,X3) ) ).
cnf(i_0_5636_545,axiom,
( X1 != X2
| esk180_2(X3,X1) = esk180_2(X3,X2) ) ).
cnf(i_0_5637_546,axiom,
( X1 != X2
| esk208_2(X1,X3) = esk208_2(X2,X3) ) ).
cnf(i_0_5638_547,axiom,
( X1 != X2
| esk208_2(X3,X1) = esk208_2(X3,X2) ) ).
cnf(i_0_5639_548,axiom,
( X1 != X2
| esk210_2(X1,X3) = esk210_2(X2,X3) ) ).
cnf(i_0_5640_549,axiom,
( X1 != X2
| esk210_2(X3,X1) = esk210_2(X3,X2) ) ).
cnf(i_0_5641_550,axiom,
( X1 != X2
| esk207_2(X1,X3) = esk207_2(X2,X3) ) ).
cnf(i_0_5642_551,axiom,
( X1 != X2
| esk207_2(X3,X1) = esk207_2(X3,X2) ) ).
cnf(i_0_5643_552,axiom,
( X1 != X2
| esk209_2(X1,X3) = esk209_2(X2,X3) ) ).
cnf(i_0_5644_553,axiom,
( X1 != X2
| esk209_2(X3,X1) = esk209_2(X3,X2) ) ).
cnf(i_0_5645_554,axiom,
( X1 != X2
| esk177_2(X1,X3) = esk177_2(X2,X3) ) ).
cnf(i_0_5646_555,axiom,
( X1 != X2
| esk177_2(X3,X1) = esk177_2(X3,X2) ) ).
cnf(i_0_5647_556,axiom,
( X1 != X2
| esk206_2(X1,X3) = esk206_2(X2,X3) ) ).
cnf(i_0_5648_557,axiom,
( X1 != X2
| esk206_2(X3,X1) = esk206_2(X3,X2) ) ).
cnf(i_0_5649_558,axiom,
( X1 != X2
| apply_binary_as_element(X1,X3,X4,X5,X6,X7) = apply_binary_as_element(X2,X3,X4,X5,X6,X7) ) ).
cnf(i_0_5650_559,axiom,
( X1 != X2
| apply_binary_as_element(X3,X1,X4,X5,X6,X7) = apply_binary_as_element(X3,X2,X4,X5,X6,X7) ) ).
cnf(i_0_5651_560,axiom,
( X1 != X2
| apply_binary_as_element(X3,X4,X1,X5,X6,X7) = apply_binary_as_element(X3,X4,X2,X5,X6,X7) ) ).
cnf(i_0_5652_561,axiom,
( X1 != X2
| apply_binary_as_element(X3,X4,X5,X1,X6,X7) = apply_binary_as_element(X3,X4,X5,X2,X6,X7) ) ).
cnf(i_0_5653_562,axiom,
( X1 != X2
| apply_binary_as_element(X3,X4,X5,X6,X1,X7) = apply_binary_as_element(X3,X4,X5,X6,X2,X7) ) ).
cnf(i_0_5654_563,axiom,
( X1 != X2
| apply_binary_as_element(X3,X4,X5,X6,X7,X1) = apply_binary_as_element(X3,X4,X5,X6,X7,X2) ) ).
cnf(i_0_5655_564,axiom,
( X1 != X2
| relation_field(X1) = relation_field(X2) ) ).
cnf(i_0_5656_565,axiom,
( X1 != X2
| relation_dom(X1) = relation_dom(X2) ) ).
cnf(i_0_5657_566,axiom,
( X1 != X2
| relation_rng(X1) = relation_rng(X2) ) ).
cnf(i_0_5658_567,axiom,
( X1 != X2
| esk228_4(X1,X3,X4,X5) = esk228_4(X2,X3,X4,X5) ) ).
cnf(i_0_5659_568,axiom,
( X1 != X2
| esk228_4(X3,X1,X4,X5) = esk228_4(X3,X2,X4,X5) ) ).
cnf(i_0_5660_569,axiom,
( X1 != X2
| esk228_4(X3,X4,X1,X5) = esk228_4(X3,X4,X2,X5) ) ).
cnf(i_0_5661_570,axiom,
( X1 != X2
| esk228_4(X3,X4,X5,X1) = esk228_4(X3,X4,X5,X2) ) ).
cnf(i_0_5662_571,axiom,
( X1 != X2
| esk220_2(X1,X3) = esk220_2(X2,X3) ) ).
cnf(i_0_5663_572,axiom,
( X1 != X2
| esk220_2(X3,X1) = esk220_2(X3,X2) ) ).
cnf(i_0_5664_573,axiom,
( X1 != X2
| esk344_4(X1,X3,X4,X5) = esk344_4(X2,X3,X4,X5) ) ).
cnf(i_0_5665_574,axiom,
( X1 != X2
| esk344_4(X3,X1,X4,X5) = esk344_4(X3,X2,X4,X5) ) ).
cnf(i_0_5666_575,axiom,
( X1 != X2
| esk344_4(X3,X4,X1,X5) = esk344_4(X3,X4,X2,X5) ) ).
cnf(i_0_5667_576,axiom,
( X1 != X2
| esk344_4(X3,X4,X5,X1) = esk344_4(X3,X4,X5,X2) ) ).
cnf(i_0_5668_577,axiom,
( X1 != X2
| apply_binary(X1,X3,X4) = apply_binary(X2,X3,X4) ) ).
cnf(i_0_5669_578,axiom,
( X1 != X2
| apply_binary(X3,X1,X4) = apply_binary(X3,X2,X4) ) ).
cnf(i_0_5670_579,axiom,
( X1 != X2
| apply_binary(X3,X4,X1) = apply_binary(X3,X4,X2) ) ).
cnf(i_0_5671_580,axiom,
( X1 != X2
| relation_rng_as_subset(X1,X3,X4) = relation_rng_as_subset(X2,X3,X4) ) ).
cnf(i_0_5672_581,axiom,
( X1 != X2
| relation_rng_as_subset(X3,X1,X4) = relation_rng_as_subset(X3,X2,X4) ) ).
cnf(i_0_5673_582,axiom,
( X1 != X2
| relation_rng_as_subset(X3,X4,X1) = relation_rng_as_subset(X3,X4,X2) ) ).
cnf(i_0_5674_583,axiom,
( X1 != X2
| join(X1,X3,X4) = join(X2,X3,X4) ) ).
cnf(i_0_5675_584,axiom,
( X1 != X2
| join(X3,X1,X4) = join(X3,X2,X4) ) ).
cnf(i_0_5676_585,axiom,
( X1 != X2
| join(X3,X4,X1) = join(X3,X4,X2) ) ).
cnf(i_0_5677_586,axiom,
( X1 != X2
| meet(X1,X3,X4) = meet(X2,X3,X4) ) ).
cnf(i_0_5678_587,axiom,
( X1 != X2
| meet(X3,X1,X4) = meet(X3,X2,X4) ) ).
cnf(i_0_5679_588,axiom,
( X1 != X2
| meet(X3,X4,X1) = meet(X3,X4,X2) ) ).
cnf(i_0_5680_589,axiom,
( X1 != X2
| esk221_2(X1,X3) = esk221_2(X2,X3) ) ).
cnf(i_0_5681_590,axiom,
( X1 != X2
| esk221_2(X3,X1) = esk221_2(X3,X2) ) ).
cnf(i_0_5682_591,axiom,
( X1 != X2
| relation_image(X1,X3) = relation_image(X2,X3) ) ).
cnf(i_0_5683_592,axiom,
( X1 != X2
| relation_image(X3,X1) = relation_image(X3,X2) ) ).
cnf(i_0_5684_593,axiom,
( X1 != X2
| relation_rng_restriction(X1,X3) = relation_rng_restriction(X2,X3) ) ).
cnf(i_0_5685_594,axiom,
( X1 != X2
| relation_rng_restriction(X3,X1) = relation_rng_restriction(X3,X2) ) ).
cnf(i_0_5686_595,axiom,
( X1 != X2
| relation_dom_restriction(X1,X3) = relation_dom_restriction(X2,X3) ) ).
cnf(i_0_5687_596,axiom,
( X1 != X2
| relation_dom_restriction(X3,X1) = relation_dom_restriction(X3,X2) ) ).
cnf(i_0_5688_597,axiom,
( X1 != X2
| esk376_2(X1,X3) = esk376_2(X2,X3) ) ).
cnf(i_0_5689_598,axiom,
( X1 != X2
| esk376_2(X3,X1) = esk376_2(X3,X2) ) ).
cnf(i_0_5690_599,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_5691_600,axiom,
( X1 != X2
| ~ one_to_one(X1)
| one_to_one(X2) ) ).
cnf(i_0_5692_601,axiom,
( X1 != X2
| ~ relation_of2_as_subset(X1,X3,X4)
| relation_of2_as_subset(X2,X3,X4) ) ).
cnf(i_0_5693_602,axiom,
( X1 != X2
| ~ relation_of2_as_subset(X3,X1,X4)
| relation_of2_as_subset(X3,X2,X4) ) ).
cnf(i_0_5694_603,axiom,
( X1 != X2
| ~ relation_of2_as_subset(X3,X4,X1)
| relation_of2_as_subset(X3,X4,X2) ) ).
cnf(i_0_5695_604,axiom,
( X1 != X2
| ~ empty_carrier(X1)
| empty_carrier(X2) ) ).
cnf(i_0_5696_605,axiom,
( X1 != X2
| ~ join_semilatt_str(X1)
| join_semilatt_str(X2) ) ).
cnf(i_0_5697_606,axiom,
( X1 != X2
| ~ meet_semilatt_str(X1)
| meet_semilatt_str(X2) ) ).
cnf(i_0_5698_607,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_5699_608,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_5700_609,axiom,
( X1 != X2
| ~ epred2_3(X1,X3,X4)
| epred2_3(X2,X3,X4) ) ).
cnf(i_0_5701_610,axiom,
( X1 != X2
| ~ epred2_3(X3,X1,X4)
| epred2_3(X3,X2,X4) ) ).
cnf(i_0_5702_611,axiom,
( X1 != X2
| ~ epred2_3(X3,X4,X1)
| epred2_3(X3,X4,X2) ) ).
cnf(i_0_5703_612,axiom,
( X1 != X2
| ~ ordinal(X1)
| ordinal(X2) ) ).
cnf(i_0_5704_613,axiom,
( X1 != X2
| ~ below_refl(X1,X3,X4)
| below_refl(X2,X3,X4) ) ).
cnf(i_0_5705_614,axiom,
( X1 != X2
| ~ below_refl(X3,X1,X4)
| below_refl(X3,X2,X4) ) ).
cnf(i_0_5706_615,axiom,
( X1 != X2
| ~ below_refl(X3,X4,X1)
| below_refl(X3,X4,X2) ) ).
cnf(i_0_5707_616,axiom,
( X1 != X2
| ~ lattice(X1)
| lattice(X2) ) ).
cnf(i_0_5708_617,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_5709_618,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_5710_619,axiom,
( X1 != X2
| ~ latt_str(X1)
| latt_str(X2) ) ).
cnf(i_0_5711_620,axiom,
( X1 != X2
| ~ is_reflexive_in(X1,X3)
| is_reflexive_in(X2,X3) ) ).
cnf(i_0_5712_621,axiom,
( X1 != X2
| ~ is_reflexive_in(X3,X1)
| is_reflexive_in(X3,X2) ) ).
cnf(i_0_5713_622,axiom,
( X1 != X2
| ~ is_transitive_in(X1,X3)
| is_transitive_in(X2,X3) ) ).
cnf(i_0_5714_623,axiom,
( X1 != X2
| ~ is_transitive_in(X3,X1)
| is_transitive_in(X3,X2) ) ).
cnf(i_0_5715_624,axiom,
( X1 != X2
| ~ is_connected_in(X1,X3)
| is_connected_in(X2,X3) ) ).
cnf(i_0_5716_625,axiom,
( X1 != X2
| ~ is_connected_in(X3,X1)
| is_connected_in(X3,X2) ) ).
cnf(i_0_5717_626,axiom,
( X1 != X2
| ~ strict_latt_str(X1)
| strict_latt_str(X2) ) ).
cnf(i_0_5718_627,axiom,
( X1 != X2
| ~ top_str(X1)
| top_str(X2) ) ).
cnf(i_0_5719_628,axiom,
( X1 != X2
| ~ open_subset(X1,X3)
| open_subset(X2,X3) ) ).
cnf(i_0_5720_629,axiom,
( X1 != X2
| ~ open_subset(X3,X1)
| open_subset(X3,X2) ) ).
cnf(i_0_5721_630,axiom,
( X1 != X2
| ~ disjoint(X1,X3)
| disjoint(X2,X3) ) ).
cnf(i_0_5722_631,axiom,
( X1 != X2
| ~ disjoint(X3,X1)
| disjoint(X3,X2) ) ).
cnf(i_0_5723_632,axiom,
( X1 != X2
| ~ transitive(X1)
| transitive(X2) ) ).
cnf(i_0_5724_633,axiom,
( X1 != X2
| ~ is_antisymmetric_in(X1,X3)
| is_antisymmetric_in(X2,X3) ) ).
cnf(i_0_5725_634,axiom,
( X1 != X2
| ~ is_antisymmetric_in(X3,X1)
| is_antisymmetric_in(X3,X2) ) ).
cnf(i_0_5726_635,axiom,
( X1 != X2
| ~ relation(X1)
| relation(X2) ) ).
cnf(i_0_5727_636,axiom,
( X1 != X2
| ~ antisymmetric(X1)
| antisymmetric(X2) ) ).
cnf(i_0_5728_637,axiom,
( X1 != X2
| ~ topological_space(X1)
| topological_space(X2) ) ).
cnf(i_0_5729_638,axiom,
( X1 != X2
| ~ latt_set_smaller(X1,X3,X4)
| latt_set_smaller(X2,X3,X4) ) ).
cnf(i_0_5730_639,axiom,
( X1 != X2
| ~ latt_set_smaller(X3,X1,X4)
| latt_set_smaller(X3,X2,X4) ) ).
cnf(i_0_5731_640,axiom,
( X1 != X2
| ~ latt_set_smaller(X3,X4,X1)
| latt_set_smaller(X3,X4,X2) ) ).
cnf(i_0_5732_641,axiom,
( X1 != X2
| ~ complete_latt_str(X1)
| complete_latt_str(X2) ) ).
cnf(i_0_5733_642,axiom,
( X1 != X2
| ~ latt_element_smaller(X1,X3,X4)
| latt_element_smaller(X2,X3,X4) ) ).
cnf(i_0_5734_643,axiom,
( X1 != X2
| ~ latt_element_smaller(X3,X1,X4)
| latt_element_smaller(X3,X2,X4) ) ).
cnf(i_0_5735_644,axiom,
( X1 != X2
| ~ latt_element_smaller(X3,X4,X1)
| latt_element_smaller(X3,X4,X2) ) ).
cnf(i_0_5736_645,axiom,
( X1 != X2
| ~ below(X1,X3,X4)
| below(X2,X3,X4) ) ).
cnf(i_0_5737_646,axiom,
( X1 != X2
| ~ below(X3,X1,X4)
| below(X3,X2,X4) ) ).
cnf(i_0_5738_647,axiom,
( X1 != X2
| ~ below(X3,X4,X1)
| below(X3,X4,X2) ) ).
cnf(i_0_5739_648,axiom,
( X1 != X2
| ~ connected(X1)
| connected(X2) ) ).
cnf(i_0_5740_649,axiom,
( X1 != X2
| ~ reflexive(X1)
| reflexive(X2) ) ).
cnf(i_0_5741_650,axiom,
( X1 != X2
| ~ related(X1,X3,X4)
| related(X2,X3,X4) ) ).
cnf(i_0_5742_651,axiom,
( X1 != X2
| ~ related(X3,X1,X4)
| related(X3,X2,X4) ) ).
cnf(i_0_5743_652,axiom,
( X1 != X2
| ~ related(X3,X4,X1)
| related(X3,X4,X2) ) ).
cnf(i_0_5744_653,axiom,
( X1 != X2
| ~ function(X1)
| function(X2) ) ).
cnf(i_0_5745_654,axiom,
( X1 != X2
| ~ rel_str(X1)
| rel_str(X2) ) ).
cnf(i_0_5746_655,axiom,
( X1 != X2
| ~ relstr_set_smaller(X1,X3,X4)
| relstr_set_smaller(X2,X3,X4) ) ).
cnf(i_0_5747_656,axiom,
( X1 != X2
| ~ relstr_set_smaller(X3,X1,X4)
| relstr_set_smaller(X3,X2,X4) ) ).
cnf(i_0_5748_657,axiom,
( X1 != X2
| ~ relstr_set_smaller(X3,X4,X1)
| relstr_set_smaller(X3,X4,X2) ) ).
cnf(i_0_5749_658,axiom,
( X1 != X2
| ~ relstr_element_smaller(X1,X3,X4)
| relstr_element_smaller(X2,X3,X4) ) ).
cnf(i_0_5750_659,axiom,
( X1 != X2
| ~ relstr_element_smaller(X3,X1,X4)
| relstr_element_smaller(X3,X2,X4) ) ).
cnf(i_0_5751_660,axiom,
( X1 != X2
| ~ relstr_element_smaller(X3,X4,X1)
| relstr_element_smaller(X3,X4,X2) ) ).
cnf(i_0_5752_661,axiom,
( X1 != X2
| ~ transitive_relstr(X1)
| transitive_relstr(X2) ) ).
cnf(i_0_5753_662,axiom,
( X1 != X2
| ~ onto(X1,X3,X4)
| onto(X2,X3,X4) ) ).
cnf(i_0_5754_663,axiom,
( X1 != X2
| ~ onto(X3,X1,X4)
| onto(X3,X2,X4) ) ).
cnf(i_0_5755_664,axiom,
( X1 != X2
| ~ onto(X3,X4,X1)
| onto(X3,X4,X2) ) ).
cnf(i_0_5756_665,axiom,
( X1 != X2
| ~ v1_partfun1(X1,X3,X4)
| v1_partfun1(X2,X3,X4) ) ).
cnf(i_0_5757_666,axiom,
( X1 != X2
| ~ v1_partfun1(X3,X1,X4)
| v1_partfun1(X3,X2,X4) ) ).
cnf(i_0_5758_667,axiom,
( X1 != X2
| ~ v1_partfun1(X3,X4,X1)
| v1_partfun1(X3,X4,X2) ) ).
cnf(i_0_5759_668,axiom,
( X1 != X2
| ~ bijective(X1,X3,X4)
| bijective(X2,X3,X4) ) ).
cnf(i_0_5760_669,axiom,
( X1 != X2
| ~ bijective(X3,X1,X4)
| bijective(X3,X2,X4) ) ).
cnf(i_0_5761_670,axiom,
( X1 != X2
| ~ bijective(X3,X4,X1)
| bijective(X3,X4,X2) ) ).
cnf(i_0_5762_671,axiom,
( X1 != X2
| ~ meet_absorbing(X1)
| meet_absorbing(X2) ) ).
cnf(i_0_5763_672,axiom,
( X1 != X2
| ~ closed_subset(X1,X3)
| closed_subset(X2,X3) ) ).
cnf(i_0_5764_673,axiom,
( X1 != X2
| ~ closed_subset(X3,X1)
| closed_subset(X3,X2) ) ).
cnf(i_0_5765_674,axiom,
( X1 != X2
| ~ related_reflexive(X1,X3,X4)
| related_reflexive(X2,X3,X4) ) ).
cnf(i_0_5766_675,axiom,
( X1 != X2
| ~ related_reflexive(X3,X1,X4)
| related_reflexive(X3,X2,X4) ) ).
cnf(i_0_5767_676,axiom,
( X1 != X2
| ~ related_reflexive(X3,X4,X1)
| related_reflexive(X3,X4,X2) ) ).
cnf(i_0_5768_677,axiom,
( X1 != X2
| ~ one_sorted_str(X1)
| one_sorted_str(X2) ) ).
cnf(i_0_5769_678,axiom,
( X1 != X2
| ~ lower_bounded_semilattstr(X1)
| lower_bounded_semilattstr(X2) ) ).
cnf(i_0_5770_679,axiom,
( X1 != X2
| ~ is_well_founded_in(X1,X3)
| is_well_founded_in(X2,X3) ) ).
cnf(i_0_5771_680,axiom,
( X1 != X2
| ~ is_well_founded_in(X3,X1)
| is_well_founded_in(X3,X2) ) ).
cnf(i_0_5772_681,axiom,
( X1 != X2
| ~ join_commutative(X1)
| join_commutative(X2) ) ).
cnf(i_0_5773_682,axiom,
( X1 != X2
| ~ antisymmetric_relstr(X1)
| antisymmetric_relstr(X2) ) ).
cnf(i_0_5774_683,axiom,
( X1 != X2
| ~ being_limit_ordinal(X1)
| being_limit_ordinal(X2) ) ).
cnf(i_0_5775_684,axiom,
( X1 != X2
| ~ meet_commutative(X1)
| meet_commutative(X2) ) ).
cnf(i_0_5776_685,axiom,
( X1 != X2
| ~ join_absorbing(X1)
| join_absorbing(X2) ) ).
cnf(i_0_5777_686,axiom,
( X1 != X2
| ~ is_a_cover_of_carrier(X1,X3)
| is_a_cover_of_carrier(X2,X3) ) ).
cnf(i_0_5778_687,axiom,
( X1 != X2
| ~ is_a_cover_of_carrier(X3,X1)
| is_a_cover_of_carrier(X3,X2) ) ).
cnf(i_0_5779_688,axiom,
( X1 != X2
| ~ open_subsets(X1,X3)
| open_subsets(X2,X3) ) ).
cnf(i_0_5780_689,axiom,
( X1 != X2
| ~ open_subsets(X3,X1)
| open_subsets(X3,X2) ) ).
cnf(i_0_5781_690,axiom,
( X1 != X2
| ~ compact_top_space(X1)
| compact_top_space(X2) ) ).
cnf(i_0_5782_691,axiom,
( X1 != X2
| ~ element(X1,X3)
| element(X2,X3) ) ).
cnf(i_0_5783_692,axiom,
( X1 != X2
| ~ element(X3,X1)
| element(X3,X2) ) ).
cnf(i_0_5784_693,axiom,
( X1 != X2
| ~ point_neighbourhood(X1,X3,X4)
| point_neighbourhood(X2,X3,X4) ) ).
cnf(i_0_5785_694,axiom,
( X1 != X2
| ~ point_neighbourhood(X3,X1,X4)
| point_neighbourhood(X3,X2,X4) ) ).
cnf(i_0_5786_695,axiom,
( X1 != X2
| ~ point_neighbourhood(X3,X4,X1)
| point_neighbourhood(X3,X4,X2) ) ).
cnf(i_0_5787_696,axiom,
( X1 != X2
| ~ reflexive_relstr(X1)
| reflexive_relstr(X2) ) ).
cnf(i_0_5788_697,axiom,
( X1 != X2
| ~ strict_rel_str(X1)
| strict_rel_str(X2) ) ).
cnf(i_0_5789_698,axiom,
( X1 != X2
| ~ closed_subsets(X1,X3)
| closed_subsets(X2,X3) ) ).
cnf(i_0_5790_699,axiom,
( X1 != X2
| ~ closed_subsets(X3,X1)
| closed_subsets(X3,X2) ) ).
cnf(i_0_5791_700,axiom,
( X1 != X2
| ~ finite(X1)
| finite(X2) ) ).
cnf(i_0_5792_701,axiom,
( X1 != X2
| ~ centered(X1)
| centered(X2) ) ).
cnf(i_0_5793_702,axiom,
( X1 != X2
| ~ ordinal_subset(X1,X3)
| ordinal_subset(X2,X3) ) ).
cnf(i_0_5794_703,axiom,
( X1 != X2
| ~ ordinal_subset(X3,X1)
| ordinal_subset(X3,X2) ) ).
cnf(i_0_5795_704,axiom,
( X1 != X2
| ~ natural(X1)
| natural(X2) ) ).
cnf(i_0_5796_705,axiom,
( X1 != X2
| ~ well_founded_relation(X1)
| well_founded_relation(X2) ) ).
cnf(i_0_5797_706,axiom,
( X1 != X2
| ~ meet_associative(X1)
| meet_associative(X2) ) ).
cnf(i_0_5798_707,axiom,
( X1 != X2
| ~ quasi_total(X1,X3,X4)
| quasi_total(X2,X3,X4) ) ).
cnf(i_0_5799_708,axiom,
( X1 != X2
| ~ quasi_total(X3,X1,X4)
| quasi_total(X3,X2,X4) ) ).
cnf(i_0_5800_709,axiom,
( X1 != X2
| ~ quasi_total(X3,X4,X1)
| quasi_total(X3,X4,X2) ) ).
cnf(i_0_5801_710,axiom,
( X1 != X2
| ~ join_associative(X1)
| join_associative(X2) ) ).
cnf(i_0_5802_711,axiom,
( X1 != X2
| ~ well_orders(X1,X3)
| well_orders(X2,X3) ) ).
cnf(i_0_5803_712,axiom,
( X1 != X2
| ~ well_orders(X3,X1)
| well_orders(X3,X2) ) ).
cnf(i_0_5804_713,axiom,
( X1 != X2
| ~ epred3_2(X1,X3)
| epred3_2(X2,X3) ) ).
cnf(i_0_5805_714,axiom,
( X1 != X2
| ~ epred3_2(X3,X1)
| epred3_2(X3,X2) ) ).
cnf(i_0_5806_715,axiom,
( X1 != X2
| ~ well_ordering(X1)
| well_ordering(X2) ) ).
cnf(i_0_5807_716,axiom,
( X1 != X2
| ~ epsilon_connected(X1)
| epsilon_connected(X2) ) ).
cnf(i_0_5808_717,axiom,
( X1 != X2
| ~ epsilon_transitive(X1)
| epsilon_transitive(X2) ) ).
cnf(i_0_5809_718,axiom,
( X1 != X2
| ~ v5_membered(X1)
| v5_membered(X2) ) ).
cnf(i_0_5810_719,axiom,
( X1 != X2
| ~ v4_membered(X1)
| v4_membered(X2) ) ).
cnf(i_0_5811_720,axiom,
( X1 != X2
| ~ v3_membered(X1)
| v3_membered(X2) ) ).
cnf(i_0_5812_721,axiom,
( X1 != X2
| ~ v2_membered(X1)
| v2_membered(X2) ) ).
cnf(i_0_5813_722,axiom,
( X1 != X2
| ~ relation_of2(X1,X3,X4)
| relation_of2(X2,X3,X4) ) ).
cnf(i_0_5814_723,axiom,
( X1 != X2
| ~ relation_of2(X3,X1,X4)
| relation_of2(X3,X2,X4) ) ).
cnf(i_0_5815_724,axiom,
( X1 != X2
| ~ relation_of2(X3,X4,X1)
| relation_of2(X3,X4,X2) ) ).
cnf(i_0_5816_725,axiom,
( X1 != X2
| ~ v1_membered(X1)
| v1_membered(X2) ) ).
cnf(i_0_5817_726,axiom,
( X1 != X2
| ~ equipotent(X1,X3)
| equipotent(X2,X3) ) ).
cnf(i_0_5818_727,axiom,
( X1 != X2
| ~ equipotent(X3,X1)
| equipotent(X3,X2) ) ).
cnf(i_0_5819_728,axiom,
( X1 != X2
| ~ are_equipotent(X1,X3)
| are_equipotent(X2,X3) ) ).
cnf(i_0_5820_729,axiom,
( X1 != X2
| ~ are_equipotent(X3,X1)
| are_equipotent(X3,X2) ) ).
cnf(i_0_5821_730,axiom,
( X1 != X2
| ~ proper_element(X1,X3)
| proper_element(X2,X3) ) ).
cnf(i_0_5822_731,axiom,
( X1 != X2
| ~ proper_element(X3,X1)
| proper_element(X3,X2) ) ).
cnf(i_0_5823_732,axiom,
( X1 != X2
| ~ proper_subset(X1,X3)
| proper_subset(X2,X3) ) ).
cnf(i_0_5824_733,axiom,
( X1 != X2
| ~ proper_subset(X3,X1)
| proper_subset(X3,X2) ) ).
cnf(i_0_5825_734,axiom,
( X1 != X2
| ~ v2_binop_1(X1,X3)
| v2_binop_1(X2,X3) ) ).
cnf(i_0_5826_735,axiom,
( X1 != X2
| ~ v2_binop_1(X3,X1)
| v2_binop_1(X3,X2) ) ).
cnf(i_0_5827_736,axiom,
( X1 != X2
| ~ v1_binop_1(X1,X3)
| v1_binop_1(X2,X3) ) ).
cnf(i_0_5828_737,axiom,
( X1 != X2
| ~ v1_binop_1(X3,X1)
| v1_binop_1(X3,X2) ) ).
cnf(i_0_5829_738,axiom,
( X1 != X2
| ~ relation_empty_yielding(X1)
| relation_empty_yielding(X2) ) ).
cnf(i_0_5830_739,axiom,
( X1 != X2
| ~ v1_int_1(X1)
| v1_int_1(X2) ) ).
cnf(i_0_5831_740,axiom,
( X1 != X2
| ~ v1_rat_1(X1)
| v1_rat_1(X2) ) ).
cnf(i_0_5832_741,axiom,
( X1 != X2
| ~ relation_isomorphism(X1,X3,X4)
| relation_isomorphism(X2,X3,X4) ) ).
cnf(i_0_5833_742,axiom,
( X1 != X2
| ~ relation_isomorphism(X3,X1,X4)
| relation_isomorphism(X3,X2,X4) ) ).
cnf(i_0_5834_743,axiom,
( X1 != X2
| ~ relation_isomorphism(X3,X4,X1)
| relation_isomorphism(X3,X4,X2) ) ).
cnf(i_0_5835_744,axiom,
( X1 != X2
| ~ v1_xreal_0(X1)
| v1_xreal_0(X2) ) ).
cnf(i_0_5836_745,axiom,
( X1 != X2
| ~ v1_xcmplx_0(X1)
| v1_xcmplx_0(X2) ) ).
cnf(i_0_5837_746,axiom,
( X1 != X2
| ~ symmetric(X1)
| symmetric(X2) ) ).
cnf(i_0_5838_747,axiom,
( X1 != X2
| ~ preboolean(X1)
| preboolean(X2) ) ).
cnf(i_0_5839_748,axiom,
( X1 != X2
| ~ cup_closed(X1)
| cup_closed(X2) ) ).
cnf(i_0_5840_749,axiom,
( X1 != X2
| ~ diff_closed(X1)
| diff_closed(X2) ) ).
cnf(i_0_5841,plain,
( ~ relation(relation_composition(X1,X2))
| ~ relation(X2)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),relation_composition(X1,X2))
| in(unordered_pair(unordered_pair(esk106_5(X1,X2,relation_composition(X1,X2),X3,X4),X4),unordered_pair(esk106_5(X1,X2,relation_composition(X1,X2),X3,X4),esk106_5(X1,X2,relation_composition(X1,X2),X3,X4))),X2) ),
inference(equality_inference,[],[2351]) ).
cnf(i_0_5842,plain,
( ~ relation(X1)
| ~ in(X2,X3)
| ~ in(X4,X2)
| empty(X3)
| ~ in(X5,esk181_2(X3,X1))
| ~ in(unordered_pair(unordered_pair(X4,esk184_5(X3,X1,X2,X4,X2)),unordered_pair(X4,X4)),X1)
| in(unordered_pair(unordered_pair(X2,X4),unordered_pair(X2,X2)),esk182_2(X3,X1))
| in(unordered_pair(unordered_pair(esk179_2(X3,X1),X5),unordered_pair(esk179_2(X3,X1),esk179_2(X3,X1))),X1) ),
inference(equality_inference,[],[2380]) ).
cnf(i_0_5843,plain,
( ~ relation(X1)
| ~ in(X2,X3)
| ~ in(X4,X2)
| empty(X3)
| ~ in(X5,esk180_2(X3,X1))
| ~ in(unordered_pair(unordered_pair(X4,esk184_5(X3,X1,X2,X4,X2)),unordered_pair(X4,X4)),X1)
| in(unordered_pair(unordered_pair(X2,X4),unordered_pair(X2,X2)),esk182_2(X3,X1))
| in(unordered_pair(unordered_pair(esk178_2(X3,X1),X5),unordered_pair(esk178_2(X3,X1),esk178_2(X3,X1))),X1) ),
inference(equality_inference,[],[2381]) ).
cnf(i_0_5844,plain,
( ~ relation(X1)
| ~ in(X2,X3)
| ~ in(X4,X2)
| empty(X3)
| ~ in(X5,esk210_2(X3,X1))
| in(X4,esk211_2(X3,X1))
| ~ in(unordered_pair(unordered_pair(X4,esk214_5(X3,X1,X4,X2,X2)),unordered_pair(X4,X4)),X1)
| in(unordered_pair(unordered_pair(esk208_2(X3,X1),X5),unordered_pair(esk208_2(X3,X1),esk208_2(X3,X1))),X1) ),
inference(equality_inference,[],[2382]) ).
cnf(i_0_5845,plain,
( ~ relation(X1)
| ~ in(X2,X3)
| ~ in(X4,X2)
| empty(X3)
| ~ in(X5,esk209_2(X3,X1))
| in(X4,esk211_2(X3,X1))
| ~ in(unordered_pair(unordered_pair(X4,esk214_5(X3,X1,X4,X2,X2)),unordered_pair(X4,X4)),X1)
| in(unordered_pair(unordered_pair(esk207_2(X3,X1),X5),unordered_pair(esk207_2(X3,X1),esk207_2(X3,X1))),X1) ),
inference(equality_inference,[],[2383]) ).
cnf(i_0_5846,plain,
( ~ relation(X1)
| ~ in(X2,X3)
| ~ in(X4,X2)
| empty(X3)
| in(esk179_2(X3,X1),esk181_2(X3,X1))
| ~ in(unordered_pair(unordered_pair(X4,esk184_5(X3,X1,X2,X4,X2)),unordered_pair(X4,X4)),X1)
| in(unordered_pair(unordered_pair(X2,X4),unordered_pair(X2,X2)),esk182_2(X3,X1)) ),
inference(equality_inference,[],[2384]) ).
cnf(i_0_5847,plain,
( ~ relation(X1)
| ~ in(X2,X3)
| ~ in(X4,X2)
| empty(X3)
| in(esk178_2(X3,X1),esk180_2(X3,X1))
| ~ in(unordered_pair(unordered_pair(X4,esk184_5(X3,X1,X2,X4,X2)),unordered_pair(X4,X4)),X1)
| in(unordered_pair(unordered_pair(X2,X4),unordered_pair(X2,X2)),esk182_2(X3,X1)) ),
inference(equality_inference,[],[2385]) ).
cnf(i_0_5848,plain,
( ~ relation(X1)
| ~ in(X2,X3)
| ~ in(X4,X2)
| empty(X3)
| in(esk177_2(X3,X1),X3)
| ~ in(unordered_pair(unordered_pair(X4,esk184_5(X3,X1,X2,X4,X2)),unordered_pair(X4,X4)),X1)
| in(unordered_pair(unordered_pair(X2,X4),unordered_pair(X2,X2)),esk182_2(X3,X1)) ),
inference(equality_inference,[],[2388]) ).
cnf(i_0_5849,plain,
( empty(X1)
| ~ relation(X2)
| ~ in(X3,X1)
| ~ in(X4,X3)
| esk181_2(X1,X2) = esk177_2(X1,X2)
| ~ in(unordered_pair(unordered_pair(X4,esk184_5(X1,X2,X3,X4,X3)),unordered_pair(X4,X4)),X2)
| in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),esk182_2(X1,X2)) ),
inference(equality_inference,[],[2389]) ).
cnf(i_0_5850,plain,
( empty(X1)
| ~ relation(X2)
| ~ in(X3,X1)
| ~ in(X4,X3)
| esk180_2(X1,X2) = esk177_2(X1,X2)
| ~ in(unordered_pair(unordered_pair(X4,esk184_5(X1,X2,X3,X4,X3)),unordered_pair(X4,X4)),X2)
| in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),esk182_2(X1,X2)) ),
inference(equality_inference,[],[2390]) ).
cnf(i_0_5851,plain,
( ~ relation(X1)
| ~ in(X2,X3)
| ~ in(X4,X2)
| empty(X3)
| in(esk208_2(X3,X1),esk210_2(X3,X1))
| in(X4,esk211_2(X3,X1))
| ~ in(unordered_pair(unordered_pair(X4,esk214_5(X3,X1,X4,X2,X2)),unordered_pair(X4,X4)),X1) ),
inference(equality_inference,[],[2391]) ).
cnf(i_0_5852,plain,
( ~ relation(X1)
| ~ in(X2,X3)
| ~ in(X4,X2)
| empty(X3)
| in(esk207_2(X3,X1),esk209_2(X3,X1))
| in(X4,esk211_2(X3,X1))
| ~ in(unordered_pair(unordered_pair(X4,esk214_5(X3,X1,X4,X2,X2)),unordered_pair(X4,X4)),X1) ),
inference(equality_inference,[],[2392]) ).
cnf(i_0_5853,plain,
( ~ relation(X1)
| ~ in(X2,X3)
| ~ in(X4,X2)
| empty(X3)
| in(esk206_2(X3,X1),X3)
| in(X4,esk211_2(X3,X1))
| ~ in(unordered_pair(unordered_pair(X4,esk214_5(X3,X1,X4,X2,X2)),unordered_pair(X4,X4)),X1) ),
inference(equality_inference,[],[2395]) ).
cnf(i_0_5854,plain,
( empty(X1)
| ~ relation(X2)
| ~ in(X3,X1)
| ~ in(X4,X3)
| esk210_2(X1,X2) = esk206_2(X1,X2)
| in(X4,esk211_2(X1,X2))
| ~ in(unordered_pair(unordered_pair(X4,esk214_5(X1,X2,X4,X3,X3)),unordered_pair(X4,X4)),X2) ),
inference(equality_inference,[],[2396]) ).
cnf(i_0_5855,plain,
( empty(X1)
| ~ relation(X2)
| ~ in(X3,X1)
| ~ in(X4,X3)
| esk209_2(X1,X2) = esk206_2(X1,X2)
| in(X4,esk211_2(X1,X2))
| ~ in(unordered_pair(unordered_pair(X4,esk214_5(X1,X2,X4,X3,X3)),unordered_pair(X4,X4)),X2) ),
inference(equality_inference,[],[2397]) ).
cnf(i_0_5856,plain,
( ~ one_sorted_str(X1)
| in(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),esk359_3(X1,X4,X5))
| ~ in(X2,complements_of_subsets(the_carrier(X1),X4))
| element(esk362_6(X1,X4,X5,unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),X2,X3),powerset(the_carrier(X1)))
| ~ element(X4,powerset(powerset(the_carrier(X1))))
| ~ in(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),cartesian_product2(complements_of_subsets(the_carrier(X1),X4),X5)) ),
inference(equality_inference,[],[2409]) ).
cnf(i_0_5857,plain,
( ~ one_sorted_str(X1)
| ~ in(X2,X3)
| ~ in(unordered_pair(unordered_pair(X2,X4),unordered_pair(X2,X2)),cartesian_product2(X3,X5))
| in(unordered_pair(unordered_pair(X2,X4),unordered_pair(X2,X2)),esk363_3(X1,X3,X5))
| element(esk366_6(X1,X3,X5,unordered_pair(unordered_pair(X2,X4),unordered_pair(X2,X2)),X2,X4),powerset(the_carrier(X1)))
| ~ element(X3,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[2417]) ).
cnf(i_0_5858,plain,
( ~ relation(relation_composition(X1,X2))
| ~ relation(X2)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),relation_composition(X1,X2))
| in(unordered_pair(unordered_pair(X3,esk106_5(X1,X2,relation_composition(X1,X2),X3,X4)),unordered_pair(X3,X3)),X1) ),
inference(equality_inference,[],[2419]) ).
cnf(i_0_5859,plain,
( ~ one_sorted_str(X1)
| in(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),esk359_3(X1,X4,X5))
| esk362_6(X1,X4,X5,unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),X2,X3) = X2
| ~ in(X2,complements_of_subsets(the_carrier(X1),X4))
| ~ element(X4,powerset(powerset(the_carrier(X1))))
| ~ in(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),cartesian_product2(complements_of_subsets(the_carrier(X1),X4),X5)) ),
inference(equality_inference,[],[2448]) ).
cnf(i_0_5860,plain,
( ~ one_sorted_str(X1)
| ~ in(X2,X3)
| in(unordered_pair(unordered_pair(X2,X4),unordered_pair(X2,X2)),esk363_3(X1,X3,X5))
| ~ in(unordered_pair(unordered_pair(X2,X4),unordered_pair(X2,X2)),cartesian_product2(X3,X5))
| esk366_6(X1,X3,X5,unordered_pair(unordered_pair(X2,X4),unordered_pair(X2,X2)),X2,X4) = X2
| ~ element(X3,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[2456]) ).
cnf(i_0_5861,plain,
( ~ relation(X1)
| ~ in(X2,relation_image(X1,X3))
| in(unordered_pair(unordered_pair(esk16_4(X1,X3,relation_image(X1,X3),X2),X2),unordered_pair(esk16_4(X1,X3,relation_image(X1,X3),X2),esk16_4(X1,X3,relation_image(X1,X3),X2))),X1) ),
inference(equality_inference,[],[2461]) ).
cnf(i_0_5862,plain,
( ~ relation(X1)
| ~ in(X2,X3)
| empty(X3)
| ~ in(X4,esk379_2(X3,X1))
| ~ in(X5,esk378_2(X3,X1))
| ~ in(X6,esk382_3(X3,X1,X2))
| ~ in(unordered_pair(unordered_pair(X4,esk380_4(X3,X1,X4,esk379_2(X3,X1))),unordered_pair(X4,X4)),X1)
| in(unordered_pair(unordered_pair(esk376_2(X3,X1),X5),unordered_pair(esk376_2(X3,X1),esk376_2(X3,X1))),X1)
| in(unordered_pair(unordered_pair(apply(esk381_2(X3,X1),X2),X6),unordered_pair(apply(esk381_2(X3,X1),X2),apply(esk381_2(X3,X1),X2))),X1) ),
inference(equality_inference,[],[2468]) ).
cnf(i_0_5863,plain,
( ~ relation(X1)
| ~ in(X2,X3)
| empty(X3)
| ~ in(X4,esk379_2(X3,X1))
| ~ in(X5,esk377_2(X3,X1))
| ~ in(X6,esk382_3(X3,X1,X2))
| ~ in(unordered_pair(unordered_pair(X4,esk380_4(X3,X1,X4,esk379_2(X3,X1))),unordered_pair(X4,X4)),X1)
| in(unordered_pair(unordered_pair(esk375_2(X3,X1),X5),unordered_pair(esk375_2(X3,X1),esk375_2(X3,X1))),X1)
| in(unordered_pair(unordered_pair(apply(esk381_2(X3,X1),X2),X6),unordered_pair(apply(esk381_2(X3,X1),X2),apply(esk381_2(X3,X1),X2))),X1) ),
inference(equality_inference,[],[2469]) ).
cnf(i_0_5864,plain,
( ~ relation(X1)
| ~ in(X2,X3)
| empty(X3)
| ~ in(X4,esk379_2(X3,X1))
| ~ in(X5,esk382_3(X3,X1,X2))
| in(esk376_2(X3,X1),esk378_2(X3,X1))
| ~ in(unordered_pair(unordered_pair(X4,esk380_4(X3,X1,X4,esk379_2(X3,X1))),unordered_pair(X4,X4)),X1)
| in(unordered_pair(unordered_pair(apply(esk381_2(X3,X1),X2),X5),unordered_pair(apply(esk381_2(X3,X1),X2),apply(esk381_2(X3,X1),X2))),X1) ),
inference(equality_inference,[],[2472]) ).
cnf(i_0_5865,plain,
( ~ relation(X1)
| ~ in(X2,X3)
| empty(X3)
| ~ in(X4,esk379_2(X3,X1))
| ~ in(X5,esk382_3(X3,X1,X2))
| in(esk375_2(X3,X1),esk377_2(X3,X1))
| ~ in(unordered_pair(unordered_pair(X4,esk380_4(X3,X1,X4,esk379_2(X3,X1))),unordered_pair(X4,X4)),X1)
| in(unordered_pair(unordered_pair(apply(esk381_2(X3,X1),X2),X5),unordered_pair(apply(esk381_2(X3,X1),X2),apply(esk381_2(X3,X1),X2))),X1) ),
inference(equality_inference,[],[2473]) ).
cnf(i_0_5866,plain,
( ~ relation(X1)
| ~ in(X2,X3)
| empty(X3)
| ~ in(X4,esk379_2(X3,X1))
| ~ in(X5,esk382_3(X3,X1,X2))
| in(esk374_2(X3,X1),X3)
| ~ in(unordered_pair(unordered_pair(X4,esk380_4(X3,X1,X4,esk379_2(X3,X1))),unordered_pair(X4,X4)),X1)
| in(unordered_pair(unordered_pair(apply(esk381_2(X3,X1),X2),X5),unordered_pair(apply(esk381_2(X3,X1),X2),apply(esk381_2(X3,X1),X2))),X1) ),
inference(equality_inference,[],[2479]) ).
cnf(i_0_5867,plain,
( empty(X1)
| ~ relation(X2)
| ~ in(X3,X1)
| ~ in(X4,esk379_2(X1,X2))
| ~ in(X5,esk382_3(X1,X2,X3))
| esk378_2(X1,X2) = esk374_2(X1,X2)
| ~ in(unordered_pair(unordered_pair(X4,esk380_4(X1,X2,X4,esk379_2(X1,X2))),unordered_pair(X4,X4)),X2)
| in(unordered_pair(unordered_pair(apply(esk381_2(X1,X2),X3),X5),unordered_pair(apply(esk381_2(X1,X2),X3),apply(esk381_2(X1,X2),X3))),X2) ),
inference(equality_inference,[],[2480]) ).
cnf(i_0_5868,plain,
( empty(X1)
| ~ relation(X2)
| ~ in(X3,X1)
| ~ in(X4,esk379_2(X1,X2))
| ~ in(X5,esk382_3(X1,X2,X3))
| esk377_2(X1,X2) = esk374_2(X1,X2)
| ~ in(unordered_pair(unordered_pair(X4,esk380_4(X1,X2,X4,esk379_2(X1,X2))),unordered_pair(X4,X4)),X2)
| in(unordered_pair(unordered_pair(apply(esk381_2(X1,X2),X3),X5),unordered_pair(apply(esk381_2(X1,X2),X3),apply(esk381_2(X1,X2),X3))),X2) ),
inference(equality_inference,[],[2481]) ).
cnf(i_0_5869,plain,
( ~ one_sorted_str(X1)
| ~ in(X2,esk307_3(X1,X3,X4))
| ~ element(esk305_2(X1,X3),powerset(the_carrier(X1)))
| esk306_2(X1,X3) = subset_complement(the_carrier(X1),esk305_2(X1,X3))
| ~ element(X3,powerset(powerset(the_carrier(X1))))
| unordered_pair(unordered_pair(esk309_4(X1,X3,X4,X2),esk310_4(X1,X3,X4,X2)),unordered_pair(esk309_4(X1,X3,X4,X2),esk309_4(X1,X3,X4,X2))) = X2 ),
inference(equality_inference,[],[2490]) ).
cnf(i_0_5870,plain,
( ~ one_sorted_str(X1)
| ~ in(X2,esk307_3(X1,X3,X4))
| ~ element(esk303_2(X1,X3),powerset(the_carrier(X1)))
| esk304_2(X1,X3) = subset_complement(the_carrier(X1),esk303_2(X1,X3))
| ~ element(X3,powerset(powerset(the_carrier(X1))))
| unordered_pair(unordered_pair(esk309_4(X1,X3,X4,X2),esk310_4(X1,X3,X4,X2)),unordered_pair(esk309_4(X1,X3,X4,X2),esk309_4(X1,X3,X4,X2))) = X2 ),
inference(equality_inference,[],[2491]) ).
cnf(i_0_5871,plain,
( ~ one_sorted_str(X1)
| ~ in(X2,esk289_3(X1,X3,X4))
| ~ element(esk287_2(X1,X3),powerset(the_carrier(X1)))
| esk288_2(X1,X3) = subset_complement(the_carrier(X1),esk287_2(X1,X3))
| ~ element(X3,powerset(powerset(the_carrier(X1))))
| unordered_pair(unordered_pair(esk291_4(X1,X3,X4,X2),esk292_4(X1,X3,X4,X2)),unordered_pair(esk291_4(X1,X3,X4,X2),esk291_4(X1,X3,X4,X2))) = X2 ),
inference(equality_inference,[],[2492]) ).
cnf(i_0_5872,plain,
( ~ one_sorted_str(X1)
| ~ in(X2,esk289_3(X1,X3,X4))
| ~ element(esk285_2(X1,X3),powerset(the_carrier(X1)))
| esk286_2(X1,X3) = subset_complement(the_carrier(X1),esk285_2(X1,X3))
| ~ element(X3,powerset(powerset(the_carrier(X1))))
| unordered_pair(unordered_pair(esk291_4(X1,X3,X4,X2),esk292_4(X1,X3,X4,X2)),unordered_pair(esk291_4(X1,X3,X4,X2),esk291_4(X1,X3,X4,X2))) = X2 ),
inference(equality_inference,[],[2493]) ).
cnf(i_0_5873,plain,
( ~ relation(X1)
| ~ in(X2,X3)
| empty(X3)
| ~ in(X4,esk379_2(X3,X1))
| ~ in(X5,esk378_2(X3,X1))
| ~ in(unordered_pair(unordered_pair(X4,esk380_4(X3,X1,X4,esk379_2(X3,X1))),unordered_pair(X4,X4)),X1)
| in(apply(esk381_2(X3,X1),X2),esk382_3(X3,X1,X2))
| in(unordered_pair(unordered_pair(esk376_2(X3,X1),X5),unordered_pair(esk376_2(X3,X1),esk376_2(X3,X1))),X1) ),
inference(equality_inference,[],[2520]) ).
cnf(i_0_5874,plain,
( ~ relation(X1)
| ~ in(X2,X3)
| empty(X3)
| ~ in(X4,esk379_2(X3,X1))
| ~ in(X5,esk377_2(X3,X1))
| ~ in(unordered_pair(unordered_pair(X4,esk380_4(X3,X1,X4,esk379_2(X3,X1))),unordered_pair(X4,X4)),X1)
| in(apply(esk381_2(X3,X1),X2),esk382_3(X3,X1,X2))
| in(unordered_pair(unordered_pair(esk375_2(X3,X1),X5),unordered_pair(esk375_2(X3,X1),esk375_2(X3,X1))),X1) ),
inference(equality_inference,[],[2521]) ).
cnf(i_0_5875,plain,
( ~ in(X1,cartesian_product2(X2,X3))
| X1 = unordered_pair(unordered_pair(esk63_4(X2,X3,cartesian_product2(X2,X3),X1),esk64_4(X2,X3,cartesian_product2(X2,X3),X1)),unordered_pair(esk63_4(X2,X3,cartesian_product2(X2,X3),X1),esk63_4(X2,X3,cartesian_product2(X2,X3),X1))) ),
inference(equality_inference,[],[2522]) ).
cnf(i_0_5876,plain,
( empty(X1)
| ~ relation(X2)
| ~ in(X3,X1)
| ~ in(X4,esk379_2(X1,X2))
| ~ in(X5,esk378_2(X1,X2))
| X3 = esk382_3(X1,X2,X3)
| ~ in(unordered_pair(unordered_pair(X4,esk380_4(X1,X2,X4,esk379_2(X1,X2))),unordered_pair(X4,X4)),X2)
| in(unordered_pair(unordered_pair(esk376_2(X1,X2),X5),unordered_pair(esk376_2(X1,X2),esk376_2(X1,X2))),X2) ),
inference(equality_inference,[],[2523]) ).
cnf(i_0_5877,plain,
( empty(X1)
| ~ relation(X2)
| ~ in(X3,X1)
| ~ in(X4,esk379_2(X1,X2))
| ~ in(X5,esk377_2(X1,X2))
| X3 = esk382_3(X1,X2,X3)
| ~ in(unordered_pair(unordered_pair(X4,esk380_4(X1,X2,X4,esk379_2(X1,X2))),unordered_pair(X4,X4)),X2)
| in(unordered_pair(unordered_pair(esk375_2(X1,X2),X5),unordered_pair(esk375_2(X1,X2),esk375_2(X1,X2))),X2) ),
inference(equality_inference,[],[2524]) ).
cnf(i_0_5878,plain,
( empty(X1)
| ~ relation(X2)
| ~ in(X3,esk379_2(X1,X2))
| ~ in(X4,esk378_2(X1,X2))
| ~ in(unordered_pair(unordered_pair(X3,esk380_4(X1,X2,X3,esk379_2(X1,X2))),unordered_pair(X3,X3)),X2)
| relation_dom(esk381_2(X1,X2)) = X1
| in(unordered_pair(unordered_pair(esk376_2(X1,X2),X4),unordered_pair(esk376_2(X1,X2),esk376_2(X1,X2))),X2) ),
inference(equality_inference,[],[2525]) ).
cnf(i_0_5879,plain,
( empty(X1)
| ~ relation(X2)
| ~ in(X3,esk379_2(X1,X2))
| ~ in(X4,esk377_2(X1,X2))
| ~ in(unordered_pair(unordered_pair(X3,esk380_4(X1,X2,X3,esk379_2(X1,X2))),unordered_pair(X3,X3)),X2)
| relation_dom(esk381_2(X1,X2)) = X1
| in(unordered_pair(unordered_pair(esk375_2(X1,X2),X4),unordered_pair(esk375_2(X1,X2),esk375_2(X1,X2))),X2) ),
inference(equality_inference,[],[2526]) ).
cnf(i_0_5880,plain,
( ~ relation(X1)
| empty(X2)
| ~ in(X3,esk379_2(X2,X1))
| ~ in(X4,esk378_2(X2,X1))
| ~ in(unordered_pair(unordered_pair(X3,esk380_4(X2,X1,X3,esk379_2(X2,X1))),unordered_pair(X3,X3)),X1)
| relation(esk381_2(X2,X1))
| in(unordered_pair(unordered_pair(esk376_2(X2,X1),X4),unordered_pair(esk376_2(X2,X1),esk376_2(X2,X1))),X1) ),
inference(equality_inference,[],[2527]) ).
cnf(i_0_5881,plain,
( ~ relation(X1)
| empty(X2)
| ~ in(X3,esk379_2(X2,X1))
| ~ in(X4,esk377_2(X2,X1))
| ~ in(unordered_pair(unordered_pair(X3,esk380_4(X2,X1,X3,esk379_2(X2,X1))),unordered_pair(X3,X3)),X1)
| relation(esk381_2(X2,X1))
| in(unordered_pair(unordered_pair(esk375_2(X2,X1),X4),unordered_pair(esk375_2(X2,X1),esk375_2(X2,X1))),X1) ),
inference(equality_inference,[],[2528]) ).
cnf(i_0_5882,plain,
( ~ relation(X1)
| empty(X2)
| ~ in(X3,esk379_2(X2,X1))
| ~ in(X4,esk378_2(X2,X1))
| ~ in(unordered_pair(unordered_pair(X3,esk380_4(X2,X1,X3,esk379_2(X2,X1))),unordered_pair(X3,X3)),X1)
| function(esk381_2(X2,X1))
| in(unordered_pair(unordered_pair(esk376_2(X2,X1),X4),unordered_pair(esk376_2(X2,X1),esk376_2(X2,X1))),X1) ),
inference(equality_inference,[],[2529]) ).
cnf(i_0_5883,plain,
( ~ relation(X1)
| empty(X2)
| ~ in(X3,esk379_2(X2,X1))
| ~ in(X4,esk377_2(X2,X1))
| ~ in(unordered_pair(unordered_pair(X3,esk380_4(X2,X1,X3,esk379_2(X2,X1))),unordered_pair(X3,X3)),X1)
| function(esk381_2(X2,X1))
| in(unordered_pair(unordered_pair(esk375_2(X2,X1),X4),unordered_pair(esk375_2(X2,X1),esk375_2(X2,X1))),X1) ),
inference(equality_inference,[],[2530]) ).
cnf(i_0_5884,plain,
( ~ relation(X1)
| ~ in(X2,X3)
| empty(X3)
| ~ in(X4,esk379_2(X3,X1))
| in(esk376_2(X3,X1),esk378_2(X3,X1))
| ~ in(unordered_pair(unordered_pair(X4,esk380_4(X3,X1,X4,esk379_2(X3,X1))),unordered_pair(X4,X4)),X1)
| in(apply(esk381_2(X3,X1),X2),esk382_3(X3,X1,X2)) ),
inference(equality_inference,[],[2535]) ).
cnf(i_0_5885,plain,
( ~ relation(X1)
| ~ in(X2,X3)
| empty(X3)
| ~ in(X4,esk379_2(X3,X1))
| in(esk375_2(X3,X1),esk377_2(X3,X1))
| ~ in(unordered_pair(unordered_pair(X4,esk380_4(X3,X1,X4,esk379_2(X3,X1))),unordered_pair(X4,X4)),X1)
| in(apply(esk381_2(X3,X1),X2),esk382_3(X3,X1,X2)) ),
inference(equality_inference,[],[2536]) ).
cnf(i_0_5886,plain,
( ~ relation(X1)
| ~ in(X2,X3)
| empty(X3)
| ~ in(X4,esk379_2(X3,X1))
| in(esk374_2(X3,X1),X3)
| ~ in(unordered_pair(unordered_pair(X4,esk380_4(X3,X1,X4,esk379_2(X3,X1))),unordered_pair(X4,X4)),X1)
| in(apply(esk381_2(X3,X1),X2),esk382_3(X3,X1,X2)) ),
inference(equality_inference,[],[2538]) ).
cnf(i_0_5887,plain,
( empty(X1)
| ~ relation(X2)
| ~ in(X3,X1)
| ~ in(X4,esk379_2(X1,X2))
| esk378_2(X1,X2) = esk374_2(X1,X2)
| ~ in(unordered_pair(unordered_pair(X4,esk380_4(X1,X2,X4,esk379_2(X1,X2))),unordered_pair(X4,X4)),X2)
| in(apply(esk381_2(X1,X2),X3),esk382_3(X1,X2,X3)) ),
inference(equality_inference,[],[2539]) ).
cnf(i_0_5888,plain,
( empty(X1)
| ~ relation(X2)
| ~ in(X3,X1)
| ~ in(X4,esk379_2(X1,X2))
| esk377_2(X1,X2) = esk374_2(X1,X2)
| ~ in(unordered_pair(unordered_pair(X4,esk380_4(X1,X2,X4,esk379_2(X1,X2))),unordered_pair(X4,X4)),X2)
| in(apply(esk381_2(X1,X2),X3),esk382_3(X1,X2,X3)) ),
inference(equality_inference,[],[2540]) ).
cnf(i_0_5889,plain,
( empty(X1)
| ~ relation(X2)
| ~ in(X3,X1)
| ~ in(X4,esk379_2(X1,X2))
| in(esk376_2(X1,X2),esk378_2(X1,X2))
| X3 = esk382_3(X1,X2,X3)
| ~ in(unordered_pair(unordered_pair(X4,esk380_4(X1,X2,X4,esk379_2(X1,X2))),unordered_pair(X4,X4)),X2) ),
inference(equality_inference,[],[2541]) ).
cnf(i_0_5890,plain,
( empty(X1)
| ~ relation(X2)
| ~ in(X3,X1)
| ~ in(X4,esk379_2(X1,X2))
| in(esk375_2(X1,X2),esk377_2(X1,X2))
| X3 = esk382_3(X1,X2,X3)
| ~ in(unordered_pair(unordered_pair(X4,esk380_4(X1,X2,X4,esk379_2(X1,X2))),unordered_pair(X4,X4)),X2) ),
inference(equality_inference,[],[2542]) ).
cnf(i_0_5891,plain,
( empty(X1)
| ~ relation(X2)
| ~ in(X3,X1)
| ~ in(X4,esk379_2(X1,X2))
| in(esk374_2(X1,X2),X1)
| X3 = esk382_3(X1,X2,X3)
| ~ in(unordered_pair(unordered_pair(X4,esk380_4(X1,X2,X4,esk379_2(X1,X2))),unordered_pair(X4,X4)),X2) ),
inference(equality_inference,[],[2544]) ).
cnf(i_0_5892,plain,
( empty(X1)
| ~ relation(X2)
| ~ in(X3,X1)
| ~ in(X4,esk379_2(X1,X2))
| esk378_2(X1,X2) = esk374_2(X1,X2)
| X3 = esk382_3(X1,X2,X3)
| ~ in(unordered_pair(unordered_pair(X4,esk380_4(X1,X2,X4,esk379_2(X1,X2))),unordered_pair(X4,X4)),X2) ),
inference(equality_inference,[],[2545]) ).
cnf(i_0_5893,plain,
( empty(X1)
| ~ relation(X2)
| ~ in(X3,X1)
| ~ in(X4,esk379_2(X1,X2))
| esk377_2(X1,X2) = esk374_2(X1,X2)
| X3 = esk382_3(X1,X2,X3)
| ~ in(unordered_pair(unordered_pair(X4,esk380_4(X1,X2,X4,esk379_2(X1,X2))),unordered_pair(X4,X4)),X2) ),
inference(equality_inference,[],[2546]) ).
cnf(i_0_5894,plain,
( empty(X1)
| ~ relation(X2)
| ~ in(X3,esk379_2(X1,X2))
| in(esk376_2(X1,X2),esk378_2(X1,X2))
| ~ in(unordered_pair(unordered_pair(X3,esk380_4(X1,X2,X3,esk379_2(X1,X2))),unordered_pair(X3,X3)),X2)
| relation_dom(esk381_2(X1,X2)) = X1 ),
inference(equality_inference,[],[2547]) ).
cnf(i_0_5895,plain,
( empty(X1)
| ~ relation(X2)
| ~ in(X3,esk379_2(X1,X2))
| in(esk375_2(X1,X2),esk377_2(X1,X2))
| ~ in(unordered_pair(unordered_pair(X3,esk380_4(X1,X2,X3,esk379_2(X1,X2))),unordered_pair(X3,X3)),X2)
| relation_dom(esk381_2(X1,X2)) = X1 ),
inference(equality_inference,[],[2548]) ).
cnf(i_0_5896,plain,
( ~ relation(X1)
| empty(X2)
| ~ in(X3,esk379_2(X2,X1))
| in(esk376_2(X2,X1),esk378_2(X2,X1))
| ~ in(unordered_pair(unordered_pair(X3,esk380_4(X2,X1,X3,esk379_2(X2,X1))),unordered_pair(X3,X3)),X1)
| relation(esk381_2(X2,X1)) ),
inference(equality_inference,[],[2549]) ).
cnf(i_0_5897,plain,
( ~ relation(X1)
| empty(X2)
| ~ in(X3,esk379_2(X2,X1))
| in(esk375_2(X2,X1),esk377_2(X2,X1))
| ~ in(unordered_pair(unordered_pair(X3,esk380_4(X2,X1,X3,esk379_2(X2,X1))),unordered_pair(X3,X3)),X1)
| relation(esk381_2(X2,X1)) ),
inference(equality_inference,[],[2550]) ).
cnf(i_0_5898,plain,
( ~ relation(X1)
| empty(X2)
| ~ in(X3,esk379_2(X2,X1))
| in(esk376_2(X2,X1),esk378_2(X2,X1))
| ~ in(unordered_pair(unordered_pair(X3,esk380_4(X2,X1,X3,esk379_2(X2,X1))),unordered_pair(X3,X3)),X1)
| function(esk381_2(X2,X1)) ),
inference(equality_inference,[],[2551]) ).
cnf(i_0_5899,plain,
( ~ relation(X1)
| empty(X2)
| ~ in(X3,esk379_2(X2,X1))
| in(esk375_2(X2,X1),esk377_2(X2,X1))
| ~ in(unordered_pair(unordered_pair(X3,esk380_4(X2,X1,X3,esk379_2(X2,X1))),unordered_pair(X3,X3)),X1)
| function(esk381_2(X2,X1)) ),
inference(equality_inference,[],[2552]) ).
cnf(i_0_5900,plain,
( empty(X1)
| ~ relation(X2)
| ~ in(X3,esk379_2(X1,X2))
| in(esk374_2(X1,X2),X1)
| ~ in(unordered_pair(unordered_pair(X3,esk380_4(X1,X2,X3,esk379_2(X1,X2))),unordered_pair(X3,X3)),X2)
| relation_dom(esk381_2(X1,X2)) = X1 ),
inference(equality_inference,[],[2556]) ).
cnf(i_0_5901,plain,
( ~ relation(X1)
| empty(X2)
| ~ in(X3,esk379_2(X2,X1))
| in(esk374_2(X2,X1),X2)
| ~ in(unordered_pair(unordered_pair(X3,esk380_4(X2,X1,X3,esk379_2(X2,X1))),unordered_pair(X3,X3)),X1)
| relation(esk381_2(X2,X1)) ),
inference(equality_inference,[],[2557]) ).
cnf(i_0_5902,plain,
( ~ relation(X1)
| empty(X2)
| ~ in(X3,esk379_2(X2,X1))
| in(esk374_2(X2,X1),X2)
| ~ in(unordered_pair(unordered_pair(X3,esk380_4(X2,X1,X3,esk379_2(X2,X1))),unordered_pair(X3,X3)),X1)
| function(esk381_2(X2,X1)) ),
inference(equality_inference,[],[2558]) ).
cnf(i_0_5903,plain,
( empty(X1)
| ~ relation(X2)
| ~ in(X3,esk379_2(X1,X2))
| esk378_2(X1,X2) = esk374_2(X1,X2)
| ~ in(unordered_pair(unordered_pair(X3,esk380_4(X1,X2,X3,esk379_2(X1,X2))),unordered_pair(X3,X3)),X2)
| relation_dom(esk381_2(X1,X2)) = X1 ),
inference(equality_inference,[],[2559]) ).
cnf(i_0_5904,plain,
( empty(X1)
| ~ relation(X2)
| ~ in(X3,esk379_2(X1,X2))
| esk377_2(X1,X2) = esk374_2(X1,X2)
| ~ in(unordered_pair(unordered_pair(X3,esk380_4(X1,X2,X3,esk379_2(X1,X2))),unordered_pair(X3,X3)),X2)
| relation_dom(esk381_2(X1,X2)) = X1 ),
inference(equality_inference,[],[2560]) ).
cnf(i_0_5905,plain,
( empty(X1)
| ~ relation(X2)
| ~ in(X3,esk379_2(X1,X2))
| esk378_2(X1,X2) = esk374_2(X1,X2)
| relation(esk381_2(X1,X2))
| ~ in(unordered_pair(unordered_pair(X3,esk380_4(X1,X2,X3,esk379_2(X1,X2))),unordered_pair(X3,X3)),X2) ),
inference(equality_inference,[],[2561]) ).
cnf(i_0_5906,plain,
( empty(X1)
| ~ relation(X2)
| ~ in(X3,esk379_2(X1,X2))
| esk378_2(X1,X2) = esk374_2(X1,X2)
| function(esk381_2(X1,X2))
| ~ in(unordered_pair(unordered_pair(X3,esk380_4(X1,X2,X3,esk379_2(X1,X2))),unordered_pair(X3,X3)),X2) ),
inference(equality_inference,[],[2562]) ).
cnf(i_0_5907,plain,
( empty(X1)
| ~ relation(X2)
| ~ in(X3,esk379_2(X1,X2))
| esk377_2(X1,X2) = esk374_2(X1,X2)
| relation(esk381_2(X1,X2))
| ~ in(unordered_pair(unordered_pair(X3,esk380_4(X1,X2,X3,esk379_2(X1,X2))),unordered_pair(X3,X3)),X2) ),
inference(equality_inference,[],[2563]) ).
cnf(i_0_5908,plain,
( empty(X1)
| ~ relation(X2)
| ~ in(X3,esk379_2(X1,X2))
| esk377_2(X1,X2) = esk374_2(X1,X2)
| function(esk381_2(X1,X2))
| ~ in(unordered_pair(unordered_pair(X3,esk380_4(X1,X2,X3,esk379_2(X1,X2))),unordered_pair(X3,X3)),X2) ),
inference(equality_inference,[],[2564]) ).
cnf(i_0_5909,plain,
( ~ relation(X1)
| ~ in(X2,X3)
| ~ in(X3,X4)
| empty(X4)
| ~ in(X5,esk181_2(X4,X1))
| in(esk184_5(X4,X1,X3,X2,X3),X3)
| in(unordered_pair(unordered_pair(X3,X2),unordered_pair(X3,X3)),esk182_2(X4,X1))
| in(unordered_pair(unordered_pair(esk179_2(X4,X1),X5),unordered_pair(esk179_2(X4,X1),esk179_2(X4,X1))),X1) ),
inference(equality_inference,[],[2565]) ).
cnf(i_0_5910,plain,
( ~ relation(X1)
| ~ in(X2,X3)
| ~ in(X3,X4)
| empty(X4)
| ~ in(X5,esk180_2(X4,X1))
| in(esk184_5(X4,X1,X3,X2,X3),X3)
| in(unordered_pair(unordered_pair(X3,X2),unordered_pair(X3,X3)),esk182_2(X4,X1))
| in(unordered_pair(unordered_pair(esk178_2(X4,X1),X5),unordered_pair(esk178_2(X4,X1),esk178_2(X4,X1))),X1) ),
inference(equality_inference,[],[2566]) ).
cnf(i_0_5911,plain,
( ~ relation(X1)
| ~ in(X2,X3)
| ~ in(X4,X2)
| empty(X3)
| ~ in(X5,esk210_2(X3,X1))
| in(esk214_5(X3,X1,X4,X2,X2),X2)
| in(X4,esk211_2(X3,X1))
| in(unordered_pair(unordered_pair(esk208_2(X3,X1),X5),unordered_pair(esk208_2(X3,X1),esk208_2(X3,X1))),X1) ),
inference(equality_inference,[],[2567]) ).
cnf(i_0_5912,plain,
( ~ relation(X1)
| ~ in(X2,X3)
| ~ in(X4,X2)
| empty(X3)
| ~ in(X5,esk209_2(X3,X1))
| in(esk214_5(X3,X1,X4,X2,X2),X2)
| in(X4,esk211_2(X3,X1))
| in(unordered_pair(unordered_pair(esk207_2(X3,X1),X5),unordered_pair(esk207_2(X3,X1),esk207_2(X3,X1))),X1) ),
inference(equality_inference,[],[2568]) ).
cnf(i_0_5913,plain,
( ~ relation(X1)
| ~ in(X2,X3)
| ~ in(X3,X4)
| empty(X4)
| in(esk179_2(X4,X1),esk181_2(X4,X1))
| in(esk184_5(X4,X1,X3,X2,X3),X3)
| in(unordered_pair(unordered_pair(X3,X2),unordered_pair(X3,X3)),esk182_2(X4,X1)) ),
inference(equality_inference,[],[2569]) ).
cnf(i_0_5914,plain,
( ~ relation(X1)
| ~ in(X2,X3)
| ~ in(X3,X4)
| empty(X4)
| in(esk178_2(X4,X1),esk180_2(X4,X1))
| in(esk184_5(X4,X1,X3,X2,X3),X3)
| in(unordered_pair(unordered_pair(X3,X2),unordered_pair(X3,X3)),esk182_2(X4,X1)) ),
inference(equality_inference,[],[2570]) ).
cnf(i_0_5915,plain,
( ~ relation(X1)
| ~ in(X2,X3)
| ~ in(X3,X4)
| empty(X4)
| in(esk177_2(X4,X1),X4)
| in(esk184_5(X4,X1,X3,X2,X3),X3)
| in(unordered_pair(unordered_pair(X3,X2),unordered_pair(X3,X3)),esk182_2(X4,X1)) ),
inference(equality_inference,[],[2573]) ).
cnf(i_0_5916,plain,
( empty(X1)
| ~ relation(X2)
| ~ in(X3,X4)
| ~ in(X4,X1)
| esk181_2(X1,X2) = esk177_2(X1,X2)
| in(esk184_5(X1,X2,X4,X3,X4),X4)
| in(unordered_pair(unordered_pair(X4,X3),unordered_pair(X4,X4)),esk182_2(X1,X2)) ),
inference(equality_inference,[],[2574]) ).
cnf(i_0_5917,plain,
( empty(X1)
| ~ relation(X2)
| ~ in(X3,X4)
| ~ in(X4,X1)
| esk180_2(X1,X2) = esk177_2(X1,X2)
| in(esk184_5(X1,X2,X4,X3,X4),X4)
| in(unordered_pair(unordered_pair(X4,X3),unordered_pair(X4,X4)),esk182_2(X1,X2)) ),
inference(equality_inference,[],[2575]) ).
cnf(i_0_5918,plain,
( empty(X1)
| ~ in(X2,X3)
| ~ in(X3,X1)
| ~ relation(X4)
| in(X2,esk211_2(X1,X4))
| in(esk208_2(X1,X4),esk210_2(X1,X4))
| in(esk214_5(X1,X4,X2,X3,X3),X3) ),
inference(equality_inference,[],[2576]) ).
cnf(i_0_5919,plain,
( empty(X1)
| ~ in(X2,X3)
| ~ in(X3,X1)
| ~ relation(X4)
| in(X2,esk211_2(X1,X4))
| in(esk207_2(X1,X4),esk209_2(X1,X4))
| in(esk214_5(X1,X4,X2,X3,X3),X3) ),
inference(equality_inference,[],[2577]) ).
cnf(i_0_5920,plain,
( empty(X1)
| ~ in(X2,X3)
| ~ in(X3,X1)
| ~ relation(X4)
| in(X2,esk211_2(X1,X4))
| in(esk206_2(X1,X4),X1)
| in(esk214_5(X1,X4,X2,X3,X3),X3) ),
inference(equality_inference,[],[2580]) ).
cnf(i_0_5921,plain,
( empty(X1)
| ~ in(X2,X3)
| ~ in(X3,X1)
| ~ relation(X4)
| in(X2,esk211_2(X1,X4))
| esk206_2(X1,X4) = esk210_2(X1,X4)
| in(esk214_5(X1,X4,X2,X3,X3),X3) ),
inference(equality_inference,[],[2581]) ).
cnf(i_0_5922,plain,
( empty(X1)
| ~ in(X2,X3)
| ~ in(X3,X1)
| ~ relation(X4)
| in(X2,esk211_2(X1,X4))
| esk206_2(X1,X4) = esk209_2(X1,X4)
| in(esk214_5(X1,X4,X2,X3,X3),X3) ),
inference(equality_inference,[],[2582]) ).
cnf(i_0_5923,plain,
( ~ relation(X1)
| ~ in(X2,esk379_2(X3,X1))
| ~ in(X4,X3)
| empty(X3)
| ~ in(X5,esk378_2(X3,X1))
| ~ in(X6,esk382_3(X3,X1,X4))
| in(esk380_4(X3,X1,X2,esk379_2(X3,X1)),esk379_2(X3,X1))
| in(unordered_pair(unordered_pair(esk376_2(X3,X1),X5),unordered_pair(esk376_2(X3,X1),esk376_2(X3,X1))),X1)
| in(unordered_pair(unordered_pair(apply(esk381_2(X3,X1),X4),X6),unordered_pair(apply(esk381_2(X3,X1),X4),apply(esk381_2(X3,X1),X4))),X1) ),
inference(equality_inference,[],[2586]) ).
cnf(i_0_5924,plain,
( ~ relation(X1)
| ~ in(X2,esk379_2(X3,X1))
| ~ in(X4,X3)
| empty(X3)
| ~ in(X5,esk377_2(X3,X1))
| ~ in(X6,esk382_3(X3,X1,X4))
| in(esk380_4(X3,X1,X2,esk379_2(X3,X1)),esk379_2(X3,X1))
| in(unordered_pair(unordered_pair(esk375_2(X3,X1),X5),unordered_pair(esk375_2(X3,X1),esk375_2(X3,X1))),X1)
| in(unordered_pair(unordered_pair(apply(esk381_2(X3,X1),X4),X6),unordered_pair(apply(esk381_2(X3,X1),X4),apply(esk381_2(X3,X1),X4))),X1) ),
inference(equality_inference,[],[2587]) ).
cnf(i_0_5925,plain,
( ~ relation(X1)
| ~ in(X2,relation_inverse_image(X1,X3))
| in(unordered_pair(unordered_pair(X2,esk19_4(X1,X3,relation_inverse_image(X1,X3),X2)),unordered_pair(X2,X2)),X1) ),
inference(equality_inference,[],[2589]) ).
cnf(i_0_5926,plain,
( ~ relation(X1)
| ~ in(X2,esk379_2(X3,X1))
| ~ in(X4,X3)
| empty(X3)
| in(esk376_2(X3,X1),esk378_2(X3,X1))
| ~ in(X5,esk382_3(X3,X1,X4))
| in(esk380_4(X3,X1,X2,esk379_2(X3,X1)),esk379_2(X3,X1))
| in(unordered_pair(unordered_pair(apply(esk381_2(X3,X1),X4),X5),unordered_pair(apply(esk381_2(X3,X1),X4),apply(esk381_2(X3,X1),X4))),X1) ),
inference(equality_inference,[],[2600]) ).
cnf(i_0_5927,plain,
( ~ relation(X1)
| ~ in(X2,esk379_2(X3,X1))
| ~ in(X4,X3)
| empty(X3)
| in(esk375_2(X3,X1),esk377_2(X3,X1))
| ~ in(X5,esk382_3(X3,X1,X4))
| in(esk380_4(X3,X1,X2,esk379_2(X3,X1)),esk379_2(X3,X1))
| in(unordered_pair(unordered_pair(apply(esk381_2(X3,X1),X4),X5),unordered_pair(apply(esk381_2(X3,X1),X4),apply(esk381_2(X3,X1),X4))),X1) ),
inference(equality_inference,[],[2601]) ).
cnf(i_0_5928,plain,
( ~ relation(X1)
| ~ in(X2,esk379_2(X3,X1))
| ~ in(X4,X3)
| empty(X3)
| ~ in(X5,esk382_3(X3,X1,X4))
| in(esk374_2(X3,X1),X3)
| in(esk380_4(X3,X1,X2,esk379_2(X3,X1)),esk379_2(X3,X1))
| in(unordered_pair(unordered_pair(apply(esk381_2(X3,X1),X4),X5),unordered_pair(apply(esk381_2(X3,X1),X4),apply(esk381_2(X3,X1),X4))),X1) ),
inference(equality_inference,[],[2603]) ).
cnf(i_0_5929,plain,
( empty(X1)
| ~ relation(X2)
| ~ in(X3,esk379_2(X1,X2))
| ~ in(X4,X1)
| ~ in(X5,esk382_3(X1,X2,X4))
| esk378_2(X1,X2) = esk374_2(X1,X2)
| in(esk380_4(X1,X2,X3,esk379_2(X1,X2)),esk379_2(X1,X2))
| in(unordered_pair(unordered_pair(apply(esk381_2(X1,X2),X4),X5),unordered_pair(apply(esk381_2(X1,X2),X4),apply(esk381_2(X1,X2),X4))),X2) ),
inference(equality_inference,[],[2604]) ).
cnf(i_0_5930,plain,
( empty(X1)
| ~ relation(X2)
| ~ in(X3,esk379_2(X1,X2))
| ~ in(X4,X1)
| ~ in(X5,esk382_3(X1,X2,X4))
| esk377_2(X1,X2) = esk374_2(X1,X2)
| in(esk380_4(X1,X2,X3,esk379_2(X1,X2)),esk379_2(X1,X2))
| in(unordered_pair(unordered_pair(apply(esk381_2(X1,X2),X4),X5),unordered_pair(apply(esk381_2(X1,X2),X4),apply(esk381_2(X1,X2),X4))),X2) ),
inference(equality_inference,[],[2605]) ).
cnf(i_0_5931,plain,
( ~ relation(X1)
| ~ in(X2,relation_rng(X1))
| in(unordered_pair(unordered_pair(esk92_3(X1,relation_rng(X1),X2),X2),unordered_pair(esk92_3(X1,relation_rng(X1),X2),esk92_3(X1,relation_rng(X1),X2))),X1) ),
inference(equality_inference,[],[2622]) ).
cnf(i_0_5932,plain,
( ~ relation(X1)
| ~ in(X2,esk379_2(X3,X1))
| ~ in(X4,X3)
| empty(X3)
| ~ in(X5,esk378_2(X3,X1))
| in(esk380_4(X3,X1,X2,esk379_2(X3,X1)),esk379_2(X3,X1))
| in(apply(esk381_2(X3,X1),X4),esk382_3(X3,X1,X4))
| in(unordered_pair(unordered_pair(esk376_2(X3,X1),X5),unordered_pair(esk376_2(X3,X1),esk376_2(X3,X1))),X1) ),
inference(equality_inference,[],[2633]) ).
cnf(i_0_5933,plain,
( ~ relation(X1)
| ~ in(X2,esk379_2(X3,X1))
| ~ in(X4,X3)
| empty(X3)
| ~ in(X5,esk377_2(X3,X1))
| in(esk380_4(X3,X1,X2,esk379_2(X3,X1)),esk379_2(X3,X1))
| in(apply(esk381_2(X3,X1),X4),esk382_3(X3,X1,X4))
| in(unordered_pair(unordered_pair(esk375_2(X3,X1),X5),unordered_pair(esk375_2(X3,X1),esk375_2(X3,X1))),X1) ),
inference(equality_inference,[],[2634]) ).
cnf(i_0_5934,plain,
( ~ one_sorted_str(X1)
| ~ in(X2,esk307_3(X1,X3,X4))
| ~ element(esk309_4(X1,X3,X4,X2),powerset(the_carrier(X1)))
| esk310_4(X1,X3,X4,X2) = subset_complement(the_carrier(X1),esk309_4(X1,X3,X4,X2))
| unordered_pair(unordered_pair(esk305_2(X1,X3),esk306_2(X1,X3)),unordered_pair(esk305_2(X1,X3),esk305_2(X1,X3))) = esk302_2(X1,X3)
| ~ element(X3,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[2641]) ).
cnf(i_0_5935,plain,
( ~ one_sorted_str(X1)
| ~ in(X2,esk307_3(X1,X3,X4))
| ~ element(esk309_4(X1,X3,X4,X2),powerset(the_carrier(X1)))
| esk310_4(X1,X3,X4,X2) = subset_complement(the_carrier(X1),esk309_4(X1,X3,X4,X2))
| unordered_pair(unordered_pair(esk303_2(X1,X3),esk304_2(X1,X3)),unordered_pair(esk303_2(X1,X3),esk303_2(X1,X3))) = esk301_2(X1,X3)
| ~ element(X3,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[2642]) ).
cnf(i_0_5936,plain,
( ~ one_sorted_str(X1)
| ~ in(X2,esk289_3(X1,X3,X4))
| ~ element(esk291_4(X1,X3,X4,X2),powerset(the_carrier(X1)))
| esk292_4(X1,X3,X4,X2) = subset_complement(the_carrier(X1),esk291_4(X1,X3,X4,X2))
| unordered_pair(unordered_pair(esk287_2(X1,X3),esk288_2(X1,X3)),unordered_pair(esk287_2(X1,X3),esk287_2(X1,X3))) = esk284_2(X1,X3)
| ~ element(X3,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[2643]) ).
cnf(i_0_5937,plain,
( ~ one_sorted_str(X1)
| ~ in(X2,esk289_3(X1,X3,X4))
| ~ element(esk291_4(X1,X3,X4,X2),powerset(the_carrier(X1)))
| esk292_4(X1,X3,X4,X2) = subset_complement(the_carrier(X1),esk291_4(X1,X3,X4,X2))
| unordered_pair(unordered_pair(esk285_2(X1,X3),esk286_2(X1,X3)),unordered_pair(esk285_2(X1,X3),esk285_2(X1,X3))) = esk283_2(X1,X3)
| ~ element(X3,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[2644]) ).
cnf(i_0_5938,plain,
( ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),cartesian_product2(X5,X5))
| in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),esk367_3(X5,X2,X1))
| ~ in(unordered_pair(unordered_pair(apply(X1,X3),apply(X1,X4)),unordered_pair(apply(X1,X3),apply(X1,X3))),X2) ),
inference(equality_inference,[],[2678]) ).
cnf(i_0_5939,plain,
( empty(X1)
| ~ relation(X2)
| ~ in(X3,esk379_2(X1,X2))
| ~ in(X4,X1)
| ~ in(X5,esk378_2(X1,X2))
| X4 = esk382_3(X1,X2,X4)
| in(esk380_4(X1,X2,X3,esk379_2(X1,X2)),esk379_2(X1,X2))
| in(unordered_pair(unordered_pair(esk376_2(X1,X2),X5),unordered_pair(esk376_2(X1,X2),esk376_2(X1,X2))),X2) ),
inference(equality_inference,[],[2681]) ).
cnf(i_0_5940,plain,
( empty(X1)
| ~ relation(X2)
| ~ in(X3,esk379_2(X1,X2))
| ~ in(X4,X1)
| ~ in(X5,esk377_2(X1,X2))
| X4 = esk382_3(X1,X2,X4)
| in(esk380_4(X1,X2,X3,esk379_2(X1,X2)),esk379_2(X1,X2))
| in(unordered_pair(unordered_pair(esk375_2(X1,X2),X5),unordered_pair(esk375_2(X1,X2),esk375_2(X1,X2))),X2) ),
inference(equality_inference,[],[2682]) ).
cnf(i_0_5941,plain,
( empty(X1)
| ~ relation(X2)
| ~ in(X3,esk379_2(X1,X2))
| ~ in(X4,esk378_2(X1,X2))
| in(esk380_4(X1,X2,X3,esk379_2(X1,X2)),esk379_2(X1,X2))
| relation_dom(esk381_2(X1,X2)) = X1
| in(unordered_pair(unordered_pair(esk376_2(X1,X2),X4),unordered_pair(esk376_2(X1,X2),esk376_2(X1,X2))),X2) ),
inference(equality_inference,[],[2693]) ).
cnf(i_0_5942,plain,
( empty(X1)
| ~ relation(X2)
| ~ in(X3,esk379_2(X1,X2))
| ~ in(X4,esk377_2(X1,X2))
| in(esk380_4(X1,X2,X3,esk379_2(X1,X2)),esk379_2(X1,X2))
| relation_dom(esk381_2(X1,X2)) = X1
| in(unordered_pair(unordered_pair(esk375_2(X1,X2),X4),unordered_pair(esk375_2(X1,X2),esk375_2(X1,X2))),X2) ),
inference(equality_inference,[],[2694]) ).
cnf(i_0_5943,plain,
( ~ relation(X1)
| ~ in(X2,esk379_2(X3,X1))
| empty(X3)
| ~ in(X4,esk378_2(X3,X1))
| in(esk380_4(X3,X1,X2,esk379_2(X3,X1)),esk379_2(X3,X1))
| relation(esk381_2(X3,X1))
| in(unordered_pair(unordered_pair(esk376_2(X3,X1),X4),unordered_pair(esk376_2(X3,X1),esk376_2(X3,X1))),X1) ),
inference(equality_inference,[],[2695]) ).
cnf(i_0_5944,plain,
( ~ relation(X1)
| ~ in(X2,esk379_2(X3,X1))
| empty(X3)
| ~ in(X4,esk377_2(X3,X1))
| in(esk380_4(X3,X1,X2,esk379_2(X3,X1)),esk379_2(X3,X1))
| relation(esk381_2(X3,X1))
| in(unordered_pair(unordered_pair(esk375_2(X3,X1),X4),unordered_pair(esk375_2(X3,X1),esk375_2(X3,X1))),X1) ),
inference(equality_inference,[],[2696]) ).
cnf(i_0_5945,plain,
( ~ relation(X1)
| ~ in(X2,esk379_2(X3,X1))
| empty(X3)
| ~ in(X4,esk378_2(X3,X1))
| in(esk380_4(X3,X1,X2,esk379_2(X3,X1)),esk379_2(X3,X1))
| function(esk381_2(X3,X1))
| in(unordered_pair(unordered_pair(esk376_2(X3,X1),X4),unordered_pair(esk376_2(X3,X1),esk376_2(X3,X1))),X1) ),
inference(equality_inference,[],[2697]) ).
cnf(i_0_5946,plain,
( ~ relation(X1)
| ~ in(X2,esk379_2(X3,X1))
| empty(X3)
| ~ in(X4,esk377_2(X3,X1))
| in(esk380_4(X3,X1,X2,esk379_2(X3,X1)),esk379_2(X3,X1))
| function(esk381_2(X3,X1))
| in(unordered_pair(unordered_pair(esk375_2(X3,X1),X4),unordered_pair(esk375_2(X3,X1),esk375_2(X3,X1))),X1) ),
inference(equality_inference,[],[2698]) ).
cnf(i_0_5947,plain,
( ~ one_sorted_str(X1)
| ~ in(X2,esk289_3(X1,X3,X4))
| in(esk287_2(X1,X3),complements_of_subsets(the_carrier(X1),X3))
| ~ element(esk291_4(X1,X3,X4,X2),powerset(the_carrier(X1)))
| esk292_4(X1,X3,X4,X2) = subset_complement(the_carrier(X1),esk291_4(X1,X3,X4,X2))
| ~ element(X3,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[2714]) ).
cnf(i_0_5948,plain,
( ~ one_sorted_str(X1)
| ~ in(X2,esk289_3(X1,X3,X4))
| in(esk285_2(X1,X3),complements_of_subsets(the_carrier(X1),X3))
| ~ element(esk291_4(X1,X3,X4,X2),powerset(the_carrier(X1)))
| esk292_4(X1,X3,X4,X2) = subset_complement(the_carrier(X1),esk291_4(X1,X3,X4,X2))
| ~ element(X3,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[2715]) ).
cnf(i_0_5949,plain,
( ~ one_sorted_str(X1)
| in(esk305_2(X1,X2),X2)
| ~ in(X3,esk307_3(X1,X2,X4))
| ~ element(esk309_4(X1,X2,X4,X3),powerset(the_carrier(X1)))
| esk310_4(X1,X2,X4,X3) = subset_complement(the_carrier(X1),esk309_4(X1,X2,X4,X3))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[2723]) ).
cnf(i_0_5950,plain,
( ~ one_sorted_str(X1)
| in(esk303_2(X1,X2),X2)
| ~ in(X3,esk307_3(X1,X2,X4))
| ~ element(esk309_4(X1,X2,X4,X3),powerset(the_carrier(X1)))
| esk310_4(X1,X2,X4,X3) = subset_complement(the_carrier(X1),esk309_4(X1,X2,X4,X3))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[2724]) ).
cnf(i_0_5951,plain,
( ~ one_sorted_str(X1)
| esk300_2(X1,X2) = esk302_2(X1,X2)
| ~ in(X3,esk307_3(X1,X2,X4))
| ~ element(esk309_4(X1,X2,X4,X3),powerset(the_carrier(X1)))
| esk310_4(X1,X2,X4,X3) = subset_complement(the_carrier(X1),esk309_4(X1,X2,X4,X3))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[2727]) ).
cnf(i_0_5952,plain,
( ~ one_sorted_str(X1)
| esk300_2(X1,X2) = esk301_2(X1,X2)
| ~ in(X3,esk307_3(X1,X2,X4))
| ~ element(esk309_4(X1,X2,X4,X3),powerset(the_carrier(X1)))
| esk310_4(X1,X2,X4,X3) = subset_complement(the_carrier(X1),esk309_4(X1,X2,X4,X3))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[2728]) ).
cnf(i_0_5953,plain,
( ~ one_sorted_str(X1)
| esk282_2(X1,X2) = esk284_2(X1,X2)
| ~ in(X3,esk289_3(X1,X2,X4))
| ~ element(esk291_4(X1,X2,X4,X3),powerset(the_carrier(X1)))
| esk292_4(X1,X2,X4,X3) = subset_complement(the_carrier(X1),esk291_4(X1,X2,X4,X3))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[2729]) ).
cnf(i_0_5954,plain,
( ~ one_sorted_str(X1)
| esk282_2(X1,X2) = esk283_2(X1,X2)
| ~ in(X3,esk289_3(X1,X2,X4))
| ~ element(esk291_4(X1,X2,X4,X3),powerset(the_carrier(X1)))
| esk292_4(X1,X2,X4,X3) = subset_complement(the_carrier(X1),esk291_4(X1,X2,X4,X3))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[2730]) ).
cnf(i_0_5955,plain,
( ~ one_sorted_str(X1)
| ~ in(X2,esk289_3(X1,X3,X4))
| ~ element(esk287_2(X1,X3),powerset(the_carrier(X1)))
| esk288_2(X1,X3) = subset_complement(the_carrier(X1),esk287_2(X1,X3))
| ~ element(X3,powerset(powerset(the_carrier(X1))))
| in(esk290_4(X1,X3,X4,X2),cartesian_product2(complements_of_subsets(the_carrier(X1),X3),X4)) ),
inference(equality_inference,[],[2738]) ).
cnf(i_0_5956,plain,
( ~ one_sorted_str(X1)
| ~ in(X2,esk289_3(X1,X3,X4))
| ~ element(esk285_2(X1,X3),powerset(the_carrier(X1)))
| esk286_2(X1,X3) = subset_complement(the_carrier(X1),esk285_2(X1,X3))
| ~ element(X3,powerset(powerset(the_carrier(X1))))
| in(esk290_4(X1,X3,X4,X2),cartesian_product2(complements_of_subsets(the_carrier(X1),X3),X4)) ),
inference(equality_inference,[],[2739]) ).
cnf(i_0_5957,plain,
( ~ relation(X1)
| ~ subset(esk47_2(relation_field(X1),X1),esk48_2(relation_field(X1),X1))
| X1 = inclusion_relation(relation_field(X1))
| ~ in(unordered_pair(unordered_pair(esk47_2(relation_field(X1),X1),esk48_2(relation_field(X1),X1)),unordered_pair(esk47_2(relation_field(X1),X1),esk47_2(relation_field(X1),X1))),X1) ),
inference(equality_inference,[],[2743]) ).
cnf(i_0_5958,plain,
( ~ one_sorted_str(X1)
| ~ in(X2,esk363_3(X1,X3,X4))
| ~ element(esk364_4(X1,X3,X4,X2),powerset(the_carrier(X1)))
| esk365_4(X1,X3,X4,X2) = subset_complement(the_carrier(X1),esk364_4(X1,X3,X4,X2))
| ~ element(X3,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[2746]) ).
cnf(i_0_5959,plain,
( ~ one_sorted_str(X1)
| ~ in(X2,esk359_3(X1,X3,X4))
| ~ element(esk360_4(X1,X3,X4,X2),powerset(the_carrier(X1)))
| esk361_4(X1,X3,X4,X2) = subset_complement(the_carrier(X1),esk360_4(X1,X3,X4,X2))
| ~ element(X3,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[2747]) ).
cnf(i_0_5960,plain,
( ~ ordinal(X1)
| ~ ordinal(X2)
| ~ in(X3,esk352_3(X2,X1,X1))
| in(esk353_4(X2,X1,X1,X3),esk352_3(X2,X1,X1))
| in(X1,esk349_1(X2))
| ~ in(X1,set_union2(X2,unordered_pair(X2,X2))) ),
inference(equality_inference,[],[2752]) ).
cnf(i_0_5961,plain,
( ~ one_sorted_str(X1)
| in(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),esk192_2(X1,X4))
| ~ element(esk189_2(X1,X4),powerset(the_carrier(X1)))
| ~ in(X2,complements_of_subsets(the_carrier(X1),X4))
| esk191_2(X1,X4) = subset_complement(the_carrier(X1),esk189_2(X1,X4))
| element(esk193_4(X1,X4,X2,X3),powerset(the_carrier(X1)))
| ~ element(X4,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[2753]) ).
cnf(i_0_5962,plain,
( ~ one_sorted_str(X1)
| in(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),esk192_2(X1,X4))
| ~ element(esk189_2(X1,X4),powerset(the_carrier(X1)))
| ~ in(X2,complements_of_subsets(the_carrier(X1),X4))
| esk190_2(X1,X4) = subset_complement(the_carrier(X1),esk189_2(X1,X4))
| element(esk193_4(X1,X4,X2,X3),powerset(the_carrier(X1)))
| ~ element(X4,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[2754]) ).
cnf(i_0_5963,plain,
( ~ one_sorted_str(X1)
| ~ in(X2,esk289_3(X1,X3,X4))
| ~ element(esk287_2(X1,X3),powerset(the_carrier(X1)))
| in(esk291_4(X1,X3,X4,X2),complements_of_subsets(the_carrier(X1),X3))
| esk288_2(X1,X3) = subset_complement(the_carrier(X1),esk287_2(X1,X3))
| ~ element(X3,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[2768]) ).
cnf(i_0_5964,plain,
( ~ one_sorted_str(X1)
| ~ in(X2,esk289_3(X1,X3,X4))
| ~ element(esk285_2(X1,X3),powerset(the_carrier(X1)))
| in(esk291_4(X1,X3,X4,X2),complements_of_subsets(the_carrier(X1),X3))
| esk286_2(X1,X3) = subset_complement(the_carrier(X1),esk285_2(X1,X3))
| ~ element(X3,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[2769]) ).
cnf(i_0_5965,plain,
( ~ one_sorted_str(X1)
| ~ in(X2,esk307_3(X1,X3,X4))
| in(esk308_4(X1,X3,X4,X2),cartesian_product2(X3,X4))
| ~ element(esk305_2(X1,X3),powerset(the_carrier(X1)))
| esk306_2(X1,X3) = subset_complement(the_carrier(X1),esk305_2(X1,X3))
| ~ element(X3,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[2771]) ).
cnf(i_0_5966,plain,
( ~ one_sorted_str(X1)
| ~ in(X2,esk307_3(X1,X3,X4))
| in(esk308_4(X1,X3,X4,X2),cartesian_product2(X3,X4))
| ~ element(esk303_2(X1,X3),powerset(the_carrier(X1)))
| esk304_2(X1,X3) = subset_complement(the_carrier(X1),esk303_2(X1,X3))
| ~ element(X3,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[2772]) ).
cnf(i_0_5967,plain,
( ~ one_sorted_str(X1)
| ~ in(X2,X3)
| in(unordered_pair(unordered_pair(X2,X4),unordered_pair(X2,X2)),esk197_2(X1,X3))
| ~ element(esk194_2(X1,X3),powerset(the_carrier(X1)))
| esk196_2(X1,X3) = subset_complement(the_carrier(X1),esk194_2(X1,X3))
| element(esk198_4(X1,X3,X2,X4),powerset(the_carrier(X1)))
| ~ element(X3,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[2775]) ).
cnf(i_0_5968,plain,
( ~ one_sorted_str(X1)
| ~ in(X2,X3)
| in(unordered_pair(unordered_pair(X2,X4),unordered_pair(X2,X2)),esk197_2(X1,X3))
| ~ element(esk194_2(X1,X3),powerset(the_carrier(X1)))
| esk195_2(X1,X3) = subset_complement(the_carrier(X1),esk194_2(X1,X3))
| element(esk198_4(X1,X3,X2,X4),powerset(the_carrier(X1)))
| ~ element(X3,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[2776]) ).
cnf(i_0_5969,plain,
( ~ one_sorted_str(X1)
| ~ in(X2,esk307_3(X1,X3,X4))
| in(esk309_4(X1,X3,X4,X2),X3)
| ~ element(esk305_2(X1,X3),powerset(the_carrier(X1)))
| esk306_2(X1,X3) = subset_complement(the_carrier(X1),esk305_2(X1,X3))
| ~ element(X3,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[2784]) ).
cnf(i_0_5970,plain,
( ~ one_sorted_str(X1)
| ~ in(X2,esk307_3(X1,X3,X4))
| in(esk309_4(X1,X3,X4,X2),X3)
| ~ element(esk303_2(X1,X3),powerset(the_carrier(X1)))
| esk304_2(X1,X3) = subset_complement(the_carrier(X1),esk303_2(X1,X3))
| ~ element(X3,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[2785]) ).
cnf(i_0_5971,plain,
( ~ ordinal(X1)
| ~ ordinal(X2)
| ~ in(X3,esk352_3(X2,X1,X1))
| subset(X3,esk353_4(X2,X1,X1,X3))
| in(X1,esk349_1(X2))
| ~ in(X1,set_union2(X2,unordered_pair(X2,X2))) ),
inference(equality_inference,[],[2794]) ).
cnf(i_0_5972,plain,
( ~ one_sorted_str(X1)
| in(X2,esk279_2(X1,X3))
| ~ in(X4,complements_of_subsets(the_carrier(X1),X3))
| ~ element(esk276_2(X1,X3),powerset(the_carrier(X1)))
| element(esk281_4(X1,X3,X2,X4),powerset(the_carrier(X1)))
| esk278_2(X1,X3) = subset_complement(the_carrier(X1),esk276_2(X1,X3))
| ~ element(X3,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[2804]) ).
cnf(i_0_5973,plain,
( ~ one_sorted_str(X1)
| in(X2,esk279_2(X1,X3))
| ~ in(X4,complements_of_subsets(the_carrier(X1),X3))
| ~ element(esk276_2(X1,X3),powerset(the_carrier(X1)))
| element(esk281_4(X1,X3,X2,X4),powerset(the_carrier(X1)))
| esk277_2(X1,X3) = subset_complement(the_carrier(X1),esk276_2(X1,X3))
| ~ element(X3,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[2805]) ).
cnf(i_0_5974,plain,
( empty(X1)
| ~ in(X2,X1)
| ~ in(X3,esk379_2(X1,X4))
| ~ relation(X4)
| in(esk376_2(X1,X4),esk378_2(X1,X4))
| in(esk380_4(X1,X4,X3,esk379_2(X1,X4)),esk379_2(X1,X4))
| in(apply(esk381_2(X1,X4),X2),esk382_3(X1,X4,X2)) ),
inference(equality_inference,[],[2808]) ).
cnf(i_0_5975,plain,
( empty(X1)
| ~ in(X2,X1)
| ~ in(X3,esk379_2(X1,X4))
| ~ relation(X4)
| in(esk375_2(X1,X4),esk377_2(X1,X4))
| in(esk380_4(X1,X4,X3,esk379_2(X1,X4)),esk379_2(X1,X4))
| in(apply(esk381_2(X1,X4),X2),esk382_3(X1,X4,X2)) ),
inference(equality_inference,[],[2809]) ).
cnf(i_0_5976,plain,
( empty(X1)
| ~ in(X2,X1)
| ~ in(X3,esk379_2(X1,X4))
| ~ relation(X4)
| in(esk374_2(X1,X4),X1)
| in(esk380_4(X1,X4,X3,esk379_2(X1,X4)),esk379_2(X1,X4))
| in(apply(esk381_2(X1,X4),X2),esk382_3(X1,X4,X2)) ),
inference(equality_inference,[],[2823]) ).
cnf(i_0_5977,plain,
( empty(X1)
| ~ in(X2,X1)
| ~ in(X3,esk379_2(X1,X4))
| ~ relation(X4)
| esk374_2(X1,X4) = esk378_2(X1,X4)
| in(esk380_4(X1,X4,X3,esk379_2(X1,X4)),esk379_2(X1,X4))
| in(apply(esk381_2(X1,X4),X2),esk382_3(X1,X4,X2)) ),
inference(equality_inference,[],[2837]) ).
cnf(i_0_5978,plain,
( empty(X1)
| ~ in(X2,X1)
| ~ in(X3,esk379_2(X1,X4))
| ~ relation(X4)
| esk374_2(X1,X4) = esk377_2(X1,X4)
| in(esk380_4(X1,X4,X3,esk379_2(X1,X4)),esk379_2(X1,X4))
| in(apply(esk381_2(X1,X4),X2),esk382_3(X1,X4,X2)) ),
inference(equality_inference,[],[2838]) ).
cnf(i_0_5979,plain,
( ~ in(X1,X2)
| ~ one_sorted_str(X3)
| in(X4,esk297_2(X3,X2))
| ~ element(esk294_2(X3,X2),powerset(the_carrier(X3)))
| element(esk299_4(X3,X2,X4,X1),powerset(the_carrier(X3)))
| esk296_2(X3,X2) = subset_complement(the_carrier(X3),esk294_2(X3,X2))
| ~ element(X2,powerset(powerset(the_carrier(X3)))) ),
inference(equality_inference,[],[2850]) ).
cnf(i_0_5980,plain,
( ~ in(X1,X2)
| ~ one_sorted_str(X3)
| in(X4,esk297_2(X3,X2))
| ~ element(esk294_2(X3,X2),powerset(the_carrier(X3)))
| element(esk299_4(X3,X2,X4,X1),powerset(the_carrier(X3)))
| esk295_2(X3,X2) = subset_complement(the_carrier(X3),esk294_2(X3,X2))
| ~ element(X2,powerset(powerset(the_carrier(X3)))) ),
inference(equality_inference,[],[2851]) ).
cnf(i_0_5981,plain,
( empty(X1)
| ~ in(X2,X1)
| ~ in(X3,esk379_2(X1,X4))
| ~ relation(X4)
| in(esk376_2(X1,X4),esk378_2(X1,X4))
| X2 = esk382_3(X1,X4,X2)
| in(esk380_4(X1,X4,X3,esk379_2(X1,X4)),esk379_2(X1,X4)) ),
inference(equality_inference,[],[2921]) ).
cnf(i_0_5982,plain,
( empty(X1)
| ~ in(X2,X1)
| ~ in(X3,esk379_2(X1,X4))
| ~ relation(X4)
| in(esk375_2(X1,X4),esk377_2(X1,X4))
| X2 = esk382_3(X1,X4,X2)
| in(esk380_4(X1,X4,X3,esk379_2(X1,X4)),esk379_2(X1,X4)) ),
inference(equality_inference,[],[2922]) ).
cnf(i_0_5983,plain,
( ~ one_sorted_str(X1)
| esk193_4(X1,X2,X3,X4) = X3
| in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),esk192_2(X1,X2))
| ~ element(esk189_2(X1,X2),powerset(the_carrier(X1)))
| ~ in(X3,complements_of_subsets(the_carrier(X1),X2))
| esk191_2(X1,X2) = subset_complement(the_carrier(X1),esk189_2(X1,X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[2924]) ).
cnf(i_0_5984,plain,
( ~ one_sorted_str(X1)
| esk193_4(X1,X2,X3,X4) = X3
| in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),esk192_2(X1,X2))
| ~ element(esk189_2(X1,X2),powerset(the_carrier(X1)))
| ~ in(X3,complements_of_subsets(the_carrier(X1),X2))
| esk190_2(X1,X2) = subset_complement(the_carrier(X1),esk189_2(X1,X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[2925]) ).
cnf(i_0_5985,plain,
( ~ ordinal(X1)
| ~ in(X2,X3)
| ~ in(set_difference(X2,unordered_pair(X1,X1)),powerset(X1))
| in(set_difference(X2,unordered_pair(X1,X1)),esk357_2(X1,X3))
| ~ element(X3,powerset(powerset(set_union2(X1,unordered_pair(X1,X1))))) ),
inference(equality_inference,[],[2926]) ).
cnf(i_0_5986,plain,
( in(X1,topstr_closure(X2,X3))
| ~ top_str(X2)
| ~ in(X1,the_carrier(X2))
| ~ element(topstr_closure(X2,X3),powerset(the_carrier(X2)))
| ~ element(X3,powerset(the_carrier(X2)))
| element(esk13_4(X2,X3,topstr_closure(X2,X3),X1),powerset(the_carrier(X2))) ),
inference(equality_inference,[],[2931]) ).
cnf(i_0_5987,plain,
( ~ function(X1)
| ~ function(X2)
| X3 = X3
| ~ quasi_total(X1,cartesian_product2(X3,X3),X3)
| ~ relation_of2(X1,cartesian_product2(X3,X3),X3)
| ~ quasi_total(X2,cartesian_product2(X3,X3),X3)
| ~ relation_of2(X2,cartesian_product2(X3,X3),X3) ),
inference(equality_inference,[],[2936]) ).
cnf(i_0_5988,plain,
( ~ function(X1)
| ~ function(X2)
| X1 = X1
| ~ quasi_total(X1,cartesian_product2(X3,X3),X3)
| ~ relation_of2(X1,cartesian_product2(X3,X3),X3)
| ~ quasi_total(X2,cartesian_product2(X3,X3),X3)
| ~ relation_of2(X2,cartesian_product2(X3,X3),X3) ),
inference(equality_inference,[],[2937]) ).
cnf(i_0_5989,plain,
( ~ function(X1)
| ~ function(X2)
| X2 = X2
| ~ quasi_total(X1,cartesian_product2(X3,X3),X3)
| ~ relation_of2(X1,cartesian_product2(X3,X3),X3)
| ~ quasi_total(X2,cartesian_product2(X3,X3),X3)
| ~ relation_of2(X2,cartesian_product2(X3,X3),X3) ),
inference(equality_inference,[],[2938]) ).
cnf(i_0_5990,plain,
( in(X1,topstr_closure(X2,X3))
| ~ top_str(X2)
| ~ in(X1,the_carrier(X2))
| open_subset(esk13_4(X2,X3,topstr_closure(X2,X3),X1),X2)
| ~ element(topstr_closure(X2,X3),powerset(the_carrier(X2)))
| ~ element(X3,powerset(the_carrier(X2))) ),
inference(equality_inference,[],[2943]) ).
cnf(i_0_5991,plain,
( in(X1,topstr_closure(X2,X3))
| ~ top_str(X2)
| ~ in(X1,the_carrier(X2))
| in(X1,esk13_4(X2,X3,topstr_closure(X2,X3),X1))
| ~ element(topstr_closure(X2,X3),powerset(the_carrier(X2)))
| ~ element(X3,powerset(the_carrier(X2))) ),
inference(equality_inference,[],[2944]) ).
cnf(i_0_5992,plain,
( in(X1,topstr_closure(X2,X3))
| ~ top_str(X2)
| ~ in(X1,the_carrier(X2))
| disjoint(X3,esk13_4(X2,X3,topstr_closure(X2,X3),X1))
| ~ element(topstr_closure(X2,X3),powerset(the_carrier(X2)))
| ~ element(X3,powerset(the_carrier(X2))) ),
inference(equality_inference,[],[2945]) ).
cnf(i_0_5993,plain,
( empty(X1)
| ~ in(X2,X1)
| ~ in(X3,esk379_2(X1,X4))
| ~ relation(X4)
| in(esk374_2(X1,X4),X1)
| X2 = esk382_3(X1,X4,X2)
| in(esk380_4(X1,X4,X3,esk379_2(X1,X4)),esk379_2(X1,X4)) ),
inference(equality_inference,[],[2946]) ).
cnf(i_0_5994,plain,
( empty(X1)
| ~ in(X2,X1)
| ~ in(X3,esk379_2(X1,X4))
| ~ relation(X4)
| esk374_2(X1,X4) = esk378_2(X1,X4)
| X2 = esk382_3(X1,X4,X2)
| in(esk380_4(X1,X4,X3,esk379_2(X1,X4)),esk379_2(X1,X4)) ),
inference(equality_inference,[],[2950]) ).
cnf(i_0_5995,plain,
( empty(X1)
| ~ in(X2,X1)
| ~ in(X3,esk379_2(X1,X4))
| ~ relation(X4)
| esk374_2(X1,X4) = esk377_2(X1,X4)
| X2 = esk382_3(X1,X4,X2)
| in(esk380_4(X1,X4,X3,esk379_2(X1,X4)),esk379_2(X1,X4)) ),
inference(equality_inference,[],[2951]) ).
cnf(i_0_5996,plain,
( empty(X1)
| ~ in(X2,esk379_2(X1,X3))
| ~ relation(X3)
| in(esk376_2(X1,X3),esk378_2(X1,X3))
| in(esk380_4(X1,X3,X2,esk379_2(X1,X3)),esk379_2(X1,X3))
| relation_dom(esk381_2(X1,X3)) = X1 ),
inference(equality_inference,[],[2953]) ).
cnf(i_0_5997,plain,
( empty(X1)
| ~ in(X2,esk379_2(X1,X3))
| ~ relation(X3)
| in(esk375_2(X1,X3),esk377_2(X1,X3))
| in(esk380_4(X1,X3,X2,esk379_2(X1,X3)),esk379_2(X1,X3))
| relation_dom(esk381_2(X1,X3)) = X1 ),
inference(equality_inference,[],[2954]) ).
cnf(i_0_5998,plain,
( empty(X1)
| ~ in(X2,esk379_2(X1,X3))
| ~ relation(X3)
| in(esk376_2(X1,X3),esk378_2(X1,X3))
| in(esk380_4(X1,X3,X2,esk379_2(X1,X3)),esk379_2(X1,X3))
| relation(esk381_2(X1,X3)) ),
inference(equality_inference,[],[2955]) ).
cnf(i_0_5999,plain,
( empty(X1)
| ~ in(X2,esk379_2(X1,X3))
| ~ relation(X3)
| in(esk375_2(X1,X3),esk377_2(X1,X3))
| in(esk380_4(X1,X3,X2,esk379_2(X1,X3)),esk379_2(X1,X3))
| relation(esk381_2(X1,X3)) ),
inference(equality_inference,[],[2956]) ).
cnf(i_0_6000,plain,
( empty(X1)
| ~ in(X2,esk379_2(X1,X3))
| ~ relation(X3)
| in(esk376_2(X1,X3),esk378_2(X1,X3))
| in(esk380_4(X1,X3,X2,esk379_2(X1,X3)),esk379_2(X1,X3))
| function(esk381_2(X1,X3)) ),
inference(equality_inference,[],[2957]) ).
cnf(i_0_6001,plain,
( empty(X1)
| ~ in(X2,esk379_2(X1,X3))
| ~ relation(X3)
| in(esk375_2(X1,X3),esk377_2(X1,X3))
| in(esk380_4(X1,X3,X2,esk379_2(X1,X3)),esk379_2(X1,X3))
| function(esk381_2(X1,X3)) ),
inference(equality_inference,[],[2958]) ).
cnf(i_0_6002,plain,
( ~ one_sorted_str(X1)
| ~ in(X2,X3)
| esk198_4(X1,X3,X2,X4) = X2
| in(unordered_pair(unordered_pair(X2,X4),unordered_pair(X2,X2)),esk197_2(X1,X3))
| ~ element(esk194_2(X1,X3),powerset(the_carrier(X1)))
| esk196_2(X1,X3) = subset_complement(the_carrier(X1),esk194_2(X1,X3))
| ~ element(X3,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[2962]) ).
cnf(i_0_6003,plain,
( ~ one_sorted_str(X1)
| ~ in(X2,X3)
| esk198_4(X1,X3,X2,X4) = X2
| in(unordered_pair(unordered_pair(X2,X4),unordered_pair(X2,X2)),esk197_2(X1,X3))
| ~ element(esk194_2(X1,X3),powerset(the_carrier(X1)))
| esk195_2(X1,X3) = subset_complement(the_carrier(X1),esk194_2(X1,X3))
| ~ element(X3,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[2963]) ).
cnf(i_0_6004,plain,
( ~ relation(X1)
| subset(esk47_2(relation_field(X1),X1),esk48_2(relation_field(X1),X1))
| X1 = inclusion_relation(relation_field(X1))
| in(unordered_pair(unordered_pair(esk47_2(relation_field(X1),X1),esk48_2(relation_field(X1),X1)),unordered_pair(esk47_2(relation_field(X1),X1),esk47_2(relation_field(X1),X1))),X1) ),
inference(equality_inference,[],[2964]) ).
cnf(i_0_6005,plain,
( ~ one_sorted_str(X1)
| ~ in(X2,esk307_3(X1,X3,X4))
| esk308_4(X1,X3,X4,X2) = X2
| ~ element(esk305_2(X1,X3),powerset(the_carrier(X1)))
| esk306_2(X1,X3) = subset_complement(the_carrier(X1),esk305_2(X1,X3))
| ~ element(X3,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[2965]) ).
cnf(i_0_6006,plain,
( ~ one_sorted_str(X1)
| ~ in(X2,esk307_3(X1,X3,X4))
| esk308_4(X1,X3,X4,X2) = X2
| ~ element(esk303_2(X1,X3),powerset(the_carrier(X1)))
| esk304_2(X1,X3) = subset_complement(the_carrier(X1),esk303_2(X1,X3))
| ~ element(X3,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[2966]) ).
cnf(i_0_6007,plain,
( ~ one_sorted_str(X1)
| ~ in(X2,esk289_3(X1,X3,X4))
| esk290_4(X1,X3,X4,X2) = X2
| ~ element(esk287_2(X1,X3),powerset(the_carrier(X1)))
| esk288_2(X1,X3) = subset_complement(the_carrier(X1),esk287_2(X1,X3))
| ~ element(X3,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[2967]) ).
cnf(i_0_6008,plain,
( ~ one_sorted_str(X1)
| ~ in(X2,esk289_3(X1,X3,X4))
| esk290_4(X1,X3,X4,X2) = X2
| ~ element(esk285_2(X1,X3),powerset(the_carrier(X1)))
| esk286_2(X1,X3) = subset_complement(the_carrier(X1),esk285_2(X1,X3))
| ~ element(X3,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[2968]) ).
cnf(i_0_6009,plain,
( ~ relation(relation_composition(X1,X2))
| ~ relation(X2)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),X1)
| in(unordered_pair(unordered_pair(X3,X5),unordered_pair(X3,X3)),relation_composition(X1,X2))
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X2) ),
inference(equality_inference,[],[2970]) ).
cnf(i_0_6010,plain,
( empty(X1)
| ~ in(X2,esk379_2(X1,X3))
| ~ relation(X3)
| in(esk374_2(X1,X3),X1)
| in(esk380_4(X1,X3,X2,esk379_2(X1,X3)),esk379_2(X1,X3))
| relation_dom(esk381_2(X1,X3)) = X1 ),
inference(equality_inference,[],[2976]) ).
cnf(i_0_6011,plain,
( empty(X1)
| ~ in(X2,esk379_2(X1,X3))
| ~ relation(X3)
| in(esk374_2(X1,X3),X1)
| in(esk380_4(X1,X3,X2,esk379_2(X1,X3)),esk379_2(X1,X3))
| relation(esk381_2(X1,X3)) ),
inference(equality_inference,[],[2977]) ).
cnf(i_0_6012,plain,
( empty(X1)
| ~ in(X2,esk379_2(X1,X3))
| ~ relation(X3)
| in(esk374_2(X1,X3),X1)
| in(esk380_4(X1,X3,X2,esk379_2(X1,X3)),esk379_2(X1,X3))
| function(esk381_2(X1,X3)) ),
inference(equality_inference,[],[2978]) ).
cnf(i_0_6013,plain,
( empty(X1)
| ~ in(X2,esk379_2(X1,X3))
| ~ relation(X3)
| esk374_2(X1,X3) = esk378_2(X1,X3)
| in(esk380_4(X1,X3,X2,esk379_2(X1,X3)),esk379_2(X1,X3))
| relation_dom(esk381_2(X1,X3)) = X1 ),
inference(equality_inference,[],[2983]) ).
cnf(i_0_6014,plain,
( empty(X1)
| ~ in(X2,esk379_2(X1,X3))
| ~ relation(X3)
| esk374_2(X1,X3) = esk377_2(X1,X3)
| in(esk380_4(X1,X3,X2,esk379_2(X1,X3)),esk379_2(X1,X3))
| relation_dom(esk381_2(X1,X3)) = X1 ),
inference(equality_inference,[],[2984]) ).
cnf(i_0_6015,plain,
( empty(X1)
| ~ in(X2,esk379_2(X1,X3))
| ~ relation(X3)
| esk374_2(X1,X3) = esk378_2(X1,X3)
| in(esk380_4(X1,X3,X2,esk379_2(X1,X3)),esk379_2(X1,X3))
| relation(esk381_2(X1,X3)) ),
inference(equality_inference,[],[2985]) ).
cnf(i_0_6016,plain,
( empty(X1)
| ~ in(X2,esk379_2(X1,X3))
| ~ relation(X3)
| esk374_2(X1,X3) = esk378_2(X1,X3)
| in(esk380_4(X1,X3,X2,esk379_2(X1,X3)),esk379_2(X1,X3))
| function(esk381_2(X1,X3)) ),
inference(equality_inference,[],[2986]) ).
cnf(i_0_6017,plain,
( empty(X1)
| ~ in(X2,esk379_2(X1,X3))
| ~ relation(X3)
| esk374_2(X1,X3) = esk377_2(X1,X3)
| in(esk380_4(X1,X3,X2,esk379_2(X1,X3)),esk379_2(X1,X3))
| relation(esk381_2(X1,X3)) ),
inference(equality_inference,[],[2987]) ).
cnf(i_0_6018,plain,
( empty(X1)
| ~ in(X2,esk379_2(X1,X3))
| ~ relation(X3)
| esk374_2(X1,X3) = esk377_2(X1,X3)
| in(esk380_4(X1,X3,X2,esk379_2(X1,X3)),esk379_2(X1,X3))
| function(esk381_2(X1,X3)) ),
inference(equality_inference,[],[2988]) ).
cnf(i_0_6019,plain,
( ~ relation(X1)
| ~ in(X2,relation_dom(X1))
| in(unordered_pair(unordered_pair(X2,esk78_3(X1,relation_dom(X1),X2)),unordered_pair(X2,X2)),X1) ),
inference(equality_inference,[],[2998]) ).
cnf(i_0_6020,plain,
( empty_carrier(X1)
| ~ below_refl(X1,X2,X3)
| ~ lattice(X1)
| ~ latt_str(X1)
| in(ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3),a_1_0_filter_1(X1))
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1)) ),
inference(equality_inference,[],[3007]) ).
cnf(i_0_6021,plain,
( ~ one_sorted_str(X1)
| in(X2,esk279_2(X1,X3))
| esk281_4(X1,X3,X2,X4) = X4
| ~ in(X4,complements_of_subsets(the_carrier(X1),X3))
| ~ element(esk276_2(X1,X3),powerset(the_carrier(X1)))
| esk278_2(X1,X3) = subset_complement(the_carrier(X1),esk276_2(X1,X3))
| ~ element(X3,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3024]) ).
cnf(i_0_6022,plain,
( ~ one_sorted_str(X1)
| in(X2,esk279_2(X1,X3))
| esk281_4(X1,X3,X2,X4) = X4
| ~ in(X4,complements_of_subsets(the_carrier(X1),X3))
| ~ element(esk276_2(X1,X3),powerset(the_carrier(X1)))
| esk277_2(X1,X3) = subset_complement(the_carrier(X1),esk276_2(X1,X3))
| ~ element(X3,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3025]) ).
cnf(i_0_6023,plain,
( ~ in(X1,relation_image(X2,X3))
| ~ relation(X2)
| ~ function(X2)
| in(esk5_4(X2,X3,relation_image(X2,X3),X1),relation_dom(X2)) ),
inference(equality_inference,[],[3029]) ).
cnf(i_0_6024,plain,
( ~ in(X1,relation_image(X2,X3))
| ~ relation(X2)
| ~ function(X2)
| X1 = apply(X2,esk5_4(X2,X3,relation_image(X2,X3),X1)) ),
inference(equality_inference,[],[3033]) ).
cnf(i_0_6025,plain,
( ~ in(X1,relation_image(X2,X3))
| ~ relation(X2)
| ~ function(X2)
| in(esk5_4(X2,X3,relation_image(X2,X3),X1),X3) ),
inference(equality_inference,[],[3034]) ).
cnf(i_0_6026,plain,
( ~ in(X1,relation_inverse_image(X2,X3))
| ~ relation(X2)
| in(esk19_4(X2,X3,relation_inverse_image(X2,X3),X1),X3) ),
inference(equality_inference,[],[3041]) ).
cnf(i_0_6027,plain,
( ~ in(X1,relation_image(X2,X3))
| ~ relation(X2)
| in(esk16_4(X2,X3,relation_image(X2,X3),X1),X3) ),
inference(equality_inference,[],[3042]) ).
cnf(i_0_6028,plain,
( ~ relation(X1)
| ~ function(X1)
| ~ in(relation_image(X1,X2),X3)
| in(X2,esk331_3(X4,X3,X1))
| in(relation_image(X1,esk330_3(X4,X3,X1)),X3)
| ~ element(X3,powerset(powerset(X4)))
| ~ in(X2,powerset(relation_dom(X1))) ),
inference(equality_inference,[],[3047]) ).
cnf(i_0_6029,plain,
( ~ relation(X1)
| ~ function(X1)
| ~ in(relation_image(X1,X2),X3)
| in(X2,esk331_3(X4,X3,X1))
| in(relation_image(X1,esk329_3(X4,X3,X1)),X3)
| ~ element(X3,powerset(powerset(X4)))
| ~ in(X2,powerset(relation_dom(X1))) ),
inference(equality_inference,[],[3048]) ).
cnf(i_0_6030,plain,
( ~ in(X1,cartesian_product2(X2,X3))
| in(esk64_4(X2,X3,cartesian_product2(X2,X3),X1),X3) ),
inference(equality_inference,[],[3051]) ).
cnf(i_0_6031,plain,
( ~ in(X1,cartesian_product2(X2,X3))
| in(esk63_4(X2,X3,cartesian_product2(X2,X3),X1),X2) ),
inference(equality_inference,[],[3052]) ).
cnf(i_0_6032,plain,
( ~ one_sorted_str(X1)
| ~ element(esk189_2(X1,X2),powerset(the_carrier(X1)))
| esk191_2(X1,X2) = subset_complement(the_carrier(X1),esk189_2(X1,X2))
| ~ in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),esk192_2(X1,X2))
| in(X3,complements_of_subsets(the_carrier(X1),X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3069]) ).
cnf(i_0_6033,plain,
( ~ one_sorted_str(X1)
| ~ element(esk189_2(X1,X2),powerset(the_carrier(X1)))
| esk190_2(X1,X2) = subset_complement(the_carrier(X1),esk189_2(X1,X2))
| ~ in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),esk192_2(X1,X2))
| in(X3,complements_of_subsets(the_carrier(X1),X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3070]) ).
cnf(i_0_6034,plain,
( ~ one_sorted_str(X1)
| ~ in(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),esk192_2(X1,X4))
| X3 = subset_complement(the_carrier(X1),X2)
| in(esk189_2(X1,X4),complements_of_subsets(the_carrier(X1),X4))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ element(X4,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3073]) ).
cnf(i_0_6035,plain,
( ~ in(X1,X2)
| ~ one_sorted_str(X3)
| in(X4,esk297_2(X3,X2))
| esk299_4(X3,X2,X4,X1) = X1
| ~ element(esk294_2(X3,X2),powerset(the_carrier(X3)))
| esk296_2(X3,X2) = subset_complement(the_carrier(X3),esk294_2(X3,X2))
| ~ element(X2,powerset(powerset(the_carrier(X3)))) ),
inference(equality_inference,[],[3074]) ).
cnf(i_0_6036,plain,
( ~ in(X1,X2)
| ~ one_sorted_str(X3)
| in(X4,esk297_2(X3,X2))
| esk299_4(X3,X2,X4,X1) = X1
| ~ element(esk294_2(X3,X2),powerset(the_carrier(X3)))
| esk295_2(X3,X2) = subset_complement(the_carrier(X3),esk294_2(X3,X2))
| ~ element(X2,powerset(powerset(the_carrier(X3)))) ),
inference(equality_inference,[],[3075]) ).
cnf(i_0_6037,plain,
( ~ one_sorted_str(X1)
| in(esk388_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| ~ in(X3,complements_of_subsets(the_carrier(X1),X2))
| ~ element(X3,powerset(the_carrier(X1)))
| apply(esk393_2(X1,X2),X3) = subset_complement(the_carrier(X1),X3)
| element(esk392_3(X1,X2,X4),powerset(the_carrier(X1)))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3079]) ).
cnf(i_0_6038,plain,
( ~ one_sorted_str(X1)
| in(X2,X3)
| ~ element(esk194_2(X1,X3),powerset(the_carrier(X1)))
| esk196_2(X1,X3) = subset_complement(the_carrier(X1),esk194_2(X1,X3))
| ~ in(unordered_pair(unordered_pair(X2,X4),unordered_pair(X2,X2)),esk197_2(X1,X3))
| ~ element(X3,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3088]) ).
cnf(i_0_6039,plain,
( ~ one_sorted_str(X1)
| in(X2,X3)
| ~ element(esk194_2(X1,X3),powerset(the_carrier(X1)))
| esk195_2(X1,X3) = subset_complement(the_carrier(X1),esk194_2(X1,X3))
| ~ in(unordered_pair(unordered_pair(X2,X4),unordered_pair(X2,X2)),esk197_2(X1,X3))
| ~ element(X3,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3089]) ).
cnf(i_0_6040,plain,
( ~ one_sorted_str(X1)
| in(esk194_2(X1,X2),X2)
| ~ in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),esk197_2(X1,X2))
| X4 = subset_complement(the_carrier(X1),X3)
| ~ element(X3,powerset(the_carrier(X1)))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3097]) ).
cnf(i_0_6041,plain,
( ~ one_sorted_str(X1)
| in(esk391_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| in(esk388_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| ~ in(X3,complements_of_subsets(the_carrier(X1),X2))
| ~ element(X3,powerset(the_carrier(X1)))
| apply(esk393_2(X1,X2),X3) = subset_complement(the_carrier(X1),X3)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3123]) ).
cnf(i_0_6042,plain,
( ~ one_sorted_str(X1)
| esk392_3(X1,X2,X3) = esk391_2(X1,X2)
| in(esk388_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| ~ in(X4,complements_of_subsets(the_carrier(X1),X2))
| ~ element(X4,powerset(the_carrier(X1)))
| apply(esk393_2(X1,X2),X4) = subset_complement(the_carrier(X1),X4)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3129]) ).
cnf(i_0_6043,plain,
( ~ relation(relation_dom_restriction(X1,X2))
| ~ relation(X1)
| ~ in(X3,X2)
| ~ in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),X1)
| in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),relation_dom_restriction(X1,X2)) ),
inference(equality_inference,[],[3148]) ).
cnf(i_0_6044,plain,
( ~ relation(relation_rng_restriction(X1,X2))
| ~ relation(X2)
| ~ in(X3,X1)
| ~ in(unordered_pair(unordered_pair(X4,X3),unordered_pair(X4,X4)),X2)
| in(unordered_pair(unordered_pair(X4,X3),unordered_pair(X4,X4)),relation_rng_restriction(X1,X2)) ),
inference(equality_inference,[],[3149]) ).
cnf(i_0_6045,plain,
( ~ one_sorted_str(X1)
| ~ in(X2,esk279_2(X1,X3))
| ~ element(esk276_2(X1,X3),powerset(the_carrier(X1)))
| in(esk280_3(X1,X3,X2),complements_of_subsets(the_carrier(X1),X3))
| esk278_2(X1,X3) = subset_complement(the_carrier(X1),esk276_2(X1,X3))
| ~ element(X3,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3156]) ).
cnf(i_0_6046,plain,
( ~ one_sorted_str(X1)
| ~ in(X2,esk279_2(X1,X3))
| ~ element(esk276_2(X1,X3),powerset(the_carrier(X1)))
| in(esk280_3(X1,X3,X2),complements_of_subsets(the_carrier(X1),X3))
| esk277_2(X1,X3) = subset_complement(the_carrier(X1),esk276_2(X1,X3))
| ~ element(X3,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3157]) ).
cnf(i_0_6047,plain,
( ~ in(X1,X2)
| ~ one_sorted_str(X3)
| in(esk394_2(X3,X2),X2)
| ~ element(X1,powerset(the_carrier(X3)))
| apply(esk399_2(X3,X2),X1) = subset_complement(the_carrier(X3),X1)
| element(esk398_3(X3,X2,X4),powerset(the_carrier(X3)))
| ~ element(X2,powerset(powerset(the_carrier(X3)))) ),
inference(equality_inference,[],[3166]) ).
cnf(i_0_6048,plain,
( ~ relation(X1)
| ~ function(X1)
| esk328_3(X2,X3,X1) = esk330_3(X2,X3,X1)
| ~ in(relation_image(X1,X4),X3)
| in(X4,esk331_3(X2,X3,X1))
| ~ element(X3,powerset(powerset(X2)))
| ~ in(X4,powerset(relation_dom(X1))) ),
inference(equality_inference,[],[3167]) ).
cnf(i_0_6049,plain,
( ~ relation(X1)
| ~ function(X1)
| esk328_3(X2,X3,X1) = esk329_3(X2,X3,X1)
| ~ in(relation_image(X1,X4),X3)
| in(X4,esk331_3(X2,X3,X1))
| ~ element(X3,powerset(powerset(X2)))
| ~ in(X4,powerset(relation_dom(X1))) ),
inference(equality_inference,[],[3168]) ).
cnf(i_0_6050,plain,
( ~ relation(relation_rng_restriction(X1,X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),relation_rng_restriction(X1,X2))
| in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),X2) ),
inference(equality_inference,[],[3175]) ).
cnf(i_0_6051,plain,
( ~ relation(relation_dom_restriction(X1,X2))
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),relation_dom_restriction(X1,X2))
| in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),X1) ),
inference(equality_inference,[],[3176]) ).
cnf(i_0_6052,plain,
( ~ one_sorted_str(X1)
| ~ in(X2,esk279_2(X1,X3))
| X2 = subset_complement(the_carrier(X1),esk280_3(X1,X3,X2))
| in(esk276_2(X1,X3),complements_of_subsets(the_carrier(X1),X3))
| ~ element(esk280_3(X1,X3,X2),powerset(the_carrier(X1)))
| ~ element(X3,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3187]) ).
cnf(i_0_6053,plain,
( ~ one_sorted_str(X1)
| ~ element(esk388_2(X1,X2),powerset(the_carrier(X1)))
| relation_dom(esk393_2(X1,X2)) = complements_of_subsets(the_carrier(X1),X2)
| element(esk392_3(X1,X2,X3),powerset(the_carrier(X1)))
| esk390_2(X1,X2) = subset_complement(the_carrier(X1),esk388_2(X1,X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3190]) ).
cnf(i_0_6054,plain,
( ~ one_sorted_str(X1)
| ~ element(esk388_2(X1,X2),powerset(the_carrier(X1)))
| relation_dom(esk393_2(X1,X2)) = complements_of_subsets(the_carrier(X1),X2)
| element(esk392_3(X1,X2,X3),powerset(the_carrier(X1)))
| esk389_2(X1,X2) = subset_complement(the_carrier(X1),esk388_2(X1,X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3191]) ).
cnf(i_0_6055,plain,
( ~ relation(X1)
| ~ relation(relation_inverse(X1))
| ~ in(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),relation_inverse(X1))
| in(unordered_pair(unordered_pair(X3,X2),unordered_pair(X3,X3)),X1) ),
inference(equality_inference,[],[3194]) ).
cnf(i_0_6056,plain,
( ~ relation(relation_inverse(X1))
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),X1)
| in(unordered_pair(unordered_pair(X3,X2),unordered_pair(X3,X3)),relation_inverse(X1)) ),
inference(equality_inference,[],[3195]) ).
cnf(i_0_6057,plain,
( ~ one_sorted_str(X1)
| ~ in(X2,esk297_2(X1,X3))
| in(esk298_3(X1,X3,X2),X3)
| ~ element(esk294_2(X1,X3),powerset(the_carrier(X1)))
| esk296_2(X1,X3) = subset_complement(the_carrier(X1),esk294_2(X1,X3))
| ~ element(X3,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3197]) ).
cnf(i_0_6058,plain,
( ~ one_sorted_str(X1)
| ~ in(X2,esk297_2(X1,X3))
| in(esk298_3(X1,X3,X2),X3)
| ~ element(esk294_2(X1,X3),powerset(the_carrier(X1)))
| esk295_2(X1,X3) = subset_complement(the_carrier(X1),esk294_2(X1,X3))
| ~ element(X3,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3198]) ).
cnf(i_0_6059,plain,
( ~ topological_space(X1)
| ~ top_str(X1)
| in(X2,esk266_2(X1,X3))
| in(set_difference(cast_as_carrier_subset(X1),esk265_2(X1,X3)),X3)
| ~ in(set_difference(cast_as_carrier_subset(X1),X2),X3)
| ~ in(X2,powerset(the_carrier(X1)))
| ~ element(X3,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3203]) ).
cnf(i_0_6060,plain,
( ~ topological_space(X1)
| ~ top_str(X1)
| in(X2,esk266_2(X1,X3))
| in(set_difference(cast_as_carrier_subset(X1),esk264_2(X1,X3)),X3)
| ~ in(set_difference(cast_as_carrier_subset(X1),X2),X3)
| ~ in(X2,powerset(the_carrier(X1)))
| ~ element(X3,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3204]) ).
cnf(i_0_6061,plain,
( X1 = pair_second(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)))
| unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)) = unordered_pair(unordered_pair(esk53_2(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),X1),esk54_2(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),X1)),unordered_pair(esk53_2(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),X1),esk53_2(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),X1))) ),
inference(equality_inference,[],[3208]) ).
cnf(i_0_6062,plain,
( X1 = pair_first(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)))
| unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)) = unordered_pair(unordered_pair(esk32_2(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),X1),esk33_2(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),X1)),unordered_pair(esk32_2(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),X1),esk32_2(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),X1))) ),
inference(equality_inference,[],[3209]) ).
cnf(i_0_6063,plain,
( ~ one_sorted_str(X1)
| ~ element(esk394_2(X1,X2),powerset(the_carrier(X1)))
| relation_dom(esk399_2(X1,X2)) = X2
| element(esk398_3(X1,X2,X3),powerset(the_carrier(X1)))
| esk396_2(X1,X2) = subset_complement(the_carrier(X1),esk394_2(X1,X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3215]) ).
cnf(i_0_6064,plain,
( ~ one_sorted_str(X1)
| ~ element(esk394_2(X1,X2),powerset(the_carrier(X1)))
| relation_dom(esk399_2(X1,X2)) = X2
| element(esk398_3(X1,X2,X3),powerset(the_carrier(X1)))
| esk395_2(X1,X2) = subset_complement(the_carrier(X1),esk394_2(X1,X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3216]) ).
cnf(i_0_6065,plain,
( ~ one_sorted_str(X1)
| ~ element(esk394_2(X1,X2),powerset(the_carrier(X1)))
| element(esk398_3(X1,X2,X3),powerset(the_carrier(X1)))
| relation(esk399_2(X1,X2))
| esk396_2(X1,X2) = subset_complement(the_carrier(X1),esk394_2(X1,X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3217]) ).
cnf(i_0_6066,plain,
( ~ one_sorted_str(X1)
| ~ element(esk394_2(X1,X2),powerset(the_carrier(X1)))
| element(esk398_3(X1,X2,X3),powerset(the_carrier(X1)))
| function(esk399_2(X1,X2))
| esk396_2(X1,X2) = subset_complement(the_carrier(X1),esk394_2(X1,X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3218]) ).
cnf(i_0_6067,plain,
( ~ one_sorted_str(X1)
| ~ element(esk394_2(X1,X2),powerset(the_carrier(X1)))
| element(esk398_3(X1,X2,X3),powerset(the_carrier(X1)))
| relation(esk399_2(X1,X2))
| esk395_2(X1,X2) = subset_complement(the_carrier(X1),esk394_2(X1,X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3219]) ).
cnf(i_0_6068,plain,
( ~ one_sorted_str(X1)
| ~ element(esk394_2(X1,X2),powerset(the_carrier(X1)))
| element(esk398_3(X1,X2,X3),powerset(the_carrier(X1)))
| function(esk399_2(X1,X2))
| esk395_2(X1,X2) = subset_complement(the_carrier(X1),esk394_2(X1,X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3220]) ).
cnf(i_0_6069,plain,
( ~ one_sorted_str(X1)
| ~ element(esk388_2(X1,X2),powerset(the_carrier(X1)))
| element(esk392_3(X1,X2,X3),powerset(the_carrier(X1)))
| relation(esk393_2(X1,X2))
| esk390_2(X1,X2) = subset_complement(the_carrier(X1),esk388_2(X1,X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3221]) ).
cnf(i_0_6070,plain,
( ~ one_sorted_str(X1)
| ~ element(esk388_2(X1,X2),powerset(the_carrier(X1)))
| element(esk392_3(X1,X2,X3),powerset(the_carrier(X1)))
| function(esk393_2(X1,X2))
| esk390_2(X1,X2) = subset_complement(the_carrier(X1),esk388_2(X1,X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3222]) ).
cnf(i_0_6071,plain,
( ~ one_sorted_str(X1)
| ~ element(esk388_2(X1,X2),powerset(the_carrier(X1)))
| element(esk392_3(X1,X2,X3),powerset(the_carrier(X1)))
| relation(esk393_2(X1,X2))
| esk389_2(X1,X2) = subset_complement(the_carrier(X1),esk388_2(X1,X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3223]) ).
cnf(i_0_6072,plain,
( ~ one_sorted_str(X1)
| ~ element(esk388_2(X1,X2),powerset(the_carrier(X1)))
| element(esk392_3(X1,X2,X3),powerset(the_carrier(X1)))
| function(esk393_2(X1,X2))
| esk389_2(X1,X2) = subset_complement(the_carrier(X1),esk388_2(X1,X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3224]) ).
cnf(i_0_6073,plain,
( ~ one_sorted_str(X1)
| ~ in(X2,esk297_2(X1,X3))
| in(esk294_2(X1,X3),X3)
| X2 = subset_complement(the_carrier(X1),esk298_3(X1,X3,X2))
| ~ element(esk298_3(X1,X3,X2),powerset(the_carrier(X1)))
| ~ element(X3,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3251]) ).
cnf(i_0_6074,plain,
( ~ in(X1,X2)
| ~ one_sorted_str(X3)
| in(esk394_2(X3,X2),X2)
| esk398_3(X3,X2,X4) = esk397_2(X3,X2)
| ~ element(X1,powerset(the_carrier(X3)))
| apply(esk399_2(X3,X2),X1) = subset_complement(the_carrier(X3),X1)
| ~ element(X2,powerset(powerset(the_carrier(X3)))) ),
inference(equality_inference,[],[3267]) ).
cnf(i_0_6075,plain,
( ~ one_sorted_str(X1)
| in(esk391_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| ~ element(esk388_2(X1,X2),powerset(the_carrier(X1)))
| relation_dom(esk393_2(X1,X2)) = complements_of_subsets(the_carrier(X1),X2)
| esk390_2(X1,X2) = subset_complement(the_carrier(X1),esk388_2(X1,X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3274]) ).
cnf(i_0_6076,plain,
( ~ one_sorted_str(X1)
| in(esk391_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| ~ element(esk388_2(X1,X2),powerset(the_carrier(X1)))
| relation_dom(esk393_2(X1,X2)) = complements_of_subsets(the_carrier(X1),X2)
| esk389_2(X1,X2) = subset_complement(the_carrier(X1),esk388_2(X1,X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3275]) ).
cnf(i_0_6077,plain,
( ~ one_sorted_str(X1)
| esk392_3(X1,X2,X3) = esk391_2(X1,X2)
| ~ element(esk388_2(X1,X2),powerset(the_carrier(X1)))
| relation_dom(esk393_2(X1,X2)) = complements_of_subsets(the_carrier(X1),X2)
| esk390_2(X1,X2) = subset_complement(the_carrier(X1),esk388_2(X1,X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3299]) ).
cnf(i_0_6078,plain,
( ~ one_sorted_str(X1)
| esk392_3(X1,X2,X3) = esk391_2(X1,X2)
| ~ element(esk388_2(X1,X2),powerset(the_carrier(X1)))
| relation_dom(esk393_2(X1,X2)) = complements_of_subsets(the_carrier(X1),X2)
| esk389_2(X1,X2) = subset_complement(the_carrier(X1),esk388_2(X1,X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3300]) ).
cnf(i_0_6079,plain,
( ~ ordinal(X1)
| ~ ordinal(X2)
| in(X1,esk349_1(X2))
| ~ in(X1,set_union2(X2,unordered_pair(X2,X2)))
| element(esk352_3(X2,X1,X1),powerset(powerset(X1))) ),
inference(equality_inference,[],[3308]) ).
cnf(i_0_6080,plain,
( ~ in(X1,X2)
| ~ one_sorted_str(X3)
| in(esk397_2(X3,X2),X2)
| in(esk394_2(X3,X2),X2)
| ~ element(X1,powerset(the_carrier(X3)))
| apply(esk399_2(X3,X2),X1) = subset_complement(the_carrier(X3),X1)
| ~ element(X2,powerset(powerset(the_carrier(X3)))) ),
inference(equality_inference,[],[3325]) ).
cnf(i_0_6081,plain,
( ~ one_sorted_str(X1)
| in(esk391_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| ~ element(esk388_2(X1,X2),powerset(the_carrier(X1)))
| esk390_2(X1,X2) = subset_complement(the_carrier(X1),esk388_2(X1,X2))
| relation(esk393_2(X1,X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3327]) ).
cnf(i_0_6082,plain,
( ~ one_sorted_str(X1)
| in(esk391_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| ~ element(esk388_2(X1,X2),powerset(the_carrier(X1)))
| esk390_2(X1,X2) = subset_complement(the_carrier(X1),esk388_2(X1,X2))
| function(esk393_2(X1,X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3328]) ).
cnf(i_0_6083,plain,
( ~ one_sorted_str(X1)
| in(esk391_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| ~ element(esk388_2(X1,X2),powerset(the_carrier(X1)))
| esk389_2(X1,X2) = subset_complement(the_carrier(X1),esk388_2(X1,X2))
| relation(esk393_2(X1,X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3329]) ).
cnf(i_0_6084,plain,
( ~ one_sorted_str(X1)
| in(esk391_2(X1,X2),complements_of_subsets(the_carrier(X1),X2))
| ~ element(esk388_2(X1,X2),powerset(the_carrier(X1)))
| esk389_2(X1,X2) = subset_complement(the_carrier(X1),esk388_2(X1,X2))
| function(esk393_2(X1,X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3330]) ).
cnf(i_0_6085,plain,
( ~ topological_space(X1)
| ~ top_str(X1)
| esk263_2(X1,X2) = esk265_2(X1,X2)
| in(X3,esk266_2(X1,X2))
| ~ in(set_difference(cast_as_carrier_subset(X1),X3),X2)
| ~ in(X3,powerset(the_carrier(X1)))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3343]) ).
cnf(i_0_6086,plain,
( ~ topological_space(X1)
| ~ top_str(X1)
| esk263_2(X1,X2) = esk264_2(X1,X2)
| in(X3,esk266_2(X1,X2))
| ~ in(set_difference(cast_as_carrier_subset(X1),X3),X2)
| ~ in(X3,powerset(the_carrier(X1)))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3344]) ).
cnf(i_0_6087,plain,
( ~ open_subset(X1,X2)
| ~ in(X3,X1)
| ~ top_str(X2)
| ~ in(X3,topstr_closure(X2,X4))
| ~ disjoint(X4,X1)
| ~ in(X3,the_carrier(X2))
| ~ element(X1,powerset(the_carrier(X2)))
| ~ element(topstr_closure(X2,X4),powerset(the_carrier(X2)))
| ~ element(X4,powerset(the_carrier(X2))) ),
inference(equality_inference,[],[3357]) ).
cnf(i_0_6088,plain,
( ~ one_sorted_str(X1)
| esk398_3(X1,X2,X3) = esk397_2(X1,X2)
| ~ element(esk394_2(X1,X2),powerset(the_carrier(X1)))
| relation_dom(esk399_2(X1,X2)) = X2
| esk396_2(X1,X2) = subset_complement(the_carrier(X1),esk394_2(X1,X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3366]) ).
cnf(i_0_6089,plain,
( ~ one_sorted_str(X1)
| esk398_3(X1,X2,X3) = esk397_2(X1,X2)
| ~ element(esk394_2(X1,X2),powerset(the_carrier(X1)))
| relation_dom(esk399_2(X1,X2)) = X2
| esk395_2(X1,X2) = subset_complement(the_carrier(X1),esk394_2(X1,X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3367]) ).
cnf(i_0_6090,plain,
( ~ one_sorted_str(X1)
| esk398_3(X1,X2,X3) = esk397_2(X1,X2)
| ~ element(esk394_2(X1,X2),powerset(the_carrier(X1)))
| relation(esk399_2(X1,X2))
| esk396_2(X1,X2) = subset_complement(the_carrier(X1),esk394_2(X1,X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3369]) ).
cnf(i_0_6091,plain,
( ~ one_sorted_str(X1)
| esk398_3(X1,X2,X3) = esk397_2(X1,X2)
| ~ element(esk394_2(X1,X2),powerset(the_carrier(X1)))
| function(esk399_2(X1,X2))
| esk396_2(X1,X2) = subset_complement(the_carrier(X1),esk394_2(X1,X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3370]) ).
cnf(i_0_6092,plain,
( ~ one_sorted_str(X1)
| esk398_3(X1,X2,X3) = esk397_2(X1,X2)
| ~ element(esk394_2(X1,X2),powerset(the_carrier(X1)))
| relation(esk399_2(X1,X2))
| esk395_2(X1,X2) = subset_complement(the_carrier(X1),esk394_2(X1,X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3371]) ).
cnf(i_0_6093,plain,
( ~ one_sorted_str(X1)
| esk398_3(X1,X2,X3) = esk397_2(X1,X2)
| ~ element(esk394_2(X1,X2),powerset(the_carrier(X1)))
| function(esk399_2(X1,X2))
| esk395_2(X1,X2) = subset_complement(the_carrier(X1),esk394_2(X1,X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3372]) ).
cnf(i_0_6094,plain,
( ~ one_sorted_str(X1)
| esk392_3(X1,X2,X3) = esk391_2(X1,X2)
| ~ element(esk388_2(X1,X2),powerset(the_carrier(X1)))
| relation(esk393_2(X1,X2))
| esk390_2(X1,X2) = subset_complement(the_carrier(X1),esk388_2(X1,X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3373]) ).
cnf(i_0_6095,plain,
( ~ one_sorted_str(X1)
| esk392_3(X1,X2,X3) = esk391_2(X1,X2)
| ~ element(esk388_2(X1,X2),powerset(the_carrier(X1)))
| function(esk393_2(X1,X2))
| esk390_2(X1,X2) = subset_complement(the_carrier(X1),esk388_2(X1,X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3374]) ).
cnf(i_0_6096,plain,
( ~ one_sorted_str(X1)
| esk392_3(X1,X2,X3) = esk391_2(X1,X2)
| ~ element(esk388_2(X1,X2),powerset(the_carrier(X1)))
| relation(esk393_2(X1,X2))
| esk389_2(X1,X2) = subset_complement(the_carrier(X1),esk388_2(X1,X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3375]) ).
cnf(i_0_6097,plain,
( ~ one_sorted_str(X1)
| esk392_3(X1,X2,X3) = esk391_2(X1,X2)
| ~ element(esk388_2(X1,X2),powerset(the_carrier(X1)))
| function(esk393_2(X1,X2))
| esk389_2(X1,X2) = subset_complement(the_carrier(X1),esk388_2(X1,X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3376]) ).
cnf(i_0_6098,plain,
( ~ relation(inclusion_relation(X1))
| ~ in(X2,X1)
| ~ in(X3,X1)
| subset(X3,X2)
| ~ in(unordered_pair(unordered_pair(X3,X2),unordered_pair(X3,X3)),inclusion_relation(X1)) ),
inference(equality_inference,[],[3390]) ).
cnf(i_0_6099,plain,
( ~ relation(X1)
| in(X2,relation_inverse_image(X1,X3))
| ~ in(X4,X3)
| ~ in(unordered_pair(unordered_pair(X2,X4),unordered_pair(X2,X2)),X1) ),
inference(equality_inference,[],[3409]) ).
cnf(i_0_6100,plain,
( ~ relation(X1)
| in(X2,relation_image(X1,X3))
| ~ in(X4,X3)
| ~ in(unordered_pair(unordered_pair(X4,X2),unordered_pair(X4,X4)),X1) ),
inference(equality_inference,[],[3410]) ).
cnf(i_0_6101,plain,
( ~ relation(X1)
| ~ relation(relation_rng_restriction(X2,X1))
| in(X3,X2)
| ~ in(unordered_pair(unordered_pair(X4,X3),unordered_pair(X4,X4)),relation_rng_restriction(X2,X1)) ),
inference(equality_inference,[],[3447]) ).
cnf(i_0_6102,plain,
( ~ relation(X1)
| ~ relation(relation_dom_restriction(X1,X2))
| in(X3,X2)
| ~ in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),relation_dom_restriction(X1,X2)) ),
inference(equality_inference,[],[3448]) ).
cnf(i_0_6103,plain,
( ~ one_sorted_str(X1)
| in(esk397_2(X1,X2),X2)
| ~ element(esk394_2(X1,X2),powerset(the_carrier(X1)))
| relation_dom(esk399_2(X1,X2)) = X2
| esk396_2(X1,X2) = subset_complement(the_carrier(X1),esk394_2(X1,X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3455]) ).
cnf(i_0_6104,plain,
( ~ one_sorted_str(X1)
| in(esk397_2(X1,X2),X2)
| ~ element(esk394_2(X1,X2),powerset(the_carrier(X1)))
| relation_dom(esk399_2(X1,X2)) = X2
| esk395_2(X1,X2) = subset_complement(the_carrier(X1),esk394_2(X1,X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3456]) ).
cnf(i_0_6105,plain,
( ~ one_sorted_str(X1)
| in(esk397_2(X1,X2),X2)
| ~ element(esk394_2(X1,X2),powerset(the_carrier(X1)))
| esk396_2(X1,X2) = subset_complement(the_carrier(X1),esk394_2(X1,X2))
| relation(esk399_2(X1,X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3460]) ).
cnf(i_0_6106,plain,
( ~ one_sorted_str(X1)
| in(esk397_2(X1,X2),X2)
| ~ element(esk394_2(X1,X2),powerset(the_carrier(X1)))
| esk396_2(X1,X2) = subset_complement(the_carrier(X1),esk394_2(X1,X2))
| function(esk399_2(X1,X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3461]) ).
cnf(i_0_6107,plain,
( ~ one_sorted_str(X1)
| in(esk397_2(X1,X2),X2)
| ~ element(esk394_2(X1,X2),powerset(the_carrier(X1)))
| esk395_2(X1,X2) = subset_complement(the_carrier(X1),esk394_2(X1,X2))
| relation(esk399_2(X1,X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3462]) ).
cnf(i_0_6108,plain,
( ~ one_sorted_str(X1)
| in(esk397_2(X1,X2),X2)
| ~ element(esk394_2(X1,X2),powerset(the_carrier(X1)))
| esk395_2(X1,X2) = subset_complement(the_carrier(X1),esk394_2(X1,X2))
| function(esk399_2(X1,X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3463]) ).
cnf(i_0_6109,plain,
( ~ relation(X1)
| X2 = X3
| in(X2,fiber(X1,X3))
| ~ in(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),X1) ),
inference(equality_inference,[],[3466]) ).
cnf(i_0_6110,plain,
( ~ function(X1)
| ~ quasi_total(X1,empty_set,X2)
| ~ relation_of2_as_subset(X1,empty_set,X2)
| quasi_total(X1,empty_set,X3)
| ~ subset(X2,X3) ),
inference(equality_inference,[],[3508]) ).
cnf(i_0_6111,plain,
( ~ closed_subset(X1,X2)
| ~ subset(X3,X1)
| ~ topological_space(X2)
| ~ top_str(X2)
| in(X1,esk354_2(X2,X3))
| ~ in(X1,powerset(the_carrier(X2)))
| ~ element(X3,powerset(the_carrier(X2)))
| ~ element(X1,powerset(the_carrier(X2))) ),
inference(equality_inference,[],[3514]) ).
cnf(i_0_6112,plain,
( ~ closed_subset(X1,X2)
| ~ subset(X3,X1)
| ~ topological_space(X2)
| ~ top_str(X2)
| in(X1,esk406_2(X2,X3))
| ~ element(X1,powerset(the_carrier(X2)))
| ~ element(X3,powerset(the_carrier(X2)))
| ~ element(X1,powerset(the_carrier(X2))) ),
inference(equality_inference,[],[3515]) ).
cnf(i_0_6113,plain,
( ~ relation(identity_relation(X1))
| in(X2,X1)
| ~ in(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),identity_relation(X1)) ),
inference(equality_inference,[],[3527]) ).
cnf(i_0_6114,plain,
( ~ relation(X1)
| in(X2,relation_dom(X1))
| ~ in(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),X1) ),
inference(equality_inference,[],[3528]) ).
cnf(i_0_6115,plain,
( ~ relation(X1)
| in(X2,relation_rng(X1))
| ~ in(unordered_pair(unordered_pair(X3,X2),unordered_pair(X3,X3)),X1) ),
inference(equality_inference,[],[3529]) ).
cnf(i_0_6116,plain,
( empty_carrier(X1)
| ~ lattice(X1)
| ~ complete_latt_str(X1)
| ~ latt_str(X1)
| below_refl(X1,X2,meet_of_latt_set(X1,X3))
| ~ latt_set_smaller(X1,X2,X3)
| ~ element(X2,the_carrier(X1))
| ~ element(meet_of_latt_set(X1,X3),the_carrier(X1)) ),
inference(equality_inference,[],[3532]) ).
cnf(i_0_6117,plain,
( ~ latt_str(X1)
| ~ lattice(X1)
| ~ complete_latt_str(X1)
| ~ latt_element_smaller(X1,X2,X3)
| empty_carrier(X1)
| below(X1,join_of_latt_set(X1,X3),X2)
| ~ element(join_of_latt_set(X1,X3),the_carrier(X1))
| ~ element(X2,the_carrier(X1)) ),
inference(equality_inference,[],[3533]) ).
cnf(i_0_6118,plain,
( ~ relation(identity_relation(X1))
| X2 = X3
| ~ in(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),identity_relation(X1)) ),
inference(equality_inference,[],[3568]) ).
cnf(i_0_6119,plain,
( in(X1,complements_of_subsets(X2,X3))
| ~ element(X1,powerset(X2))
| ~ in(subset_complement(X2,X1),X3)
| ~ element(complements_of_subsets(X2,X3),powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2))) ),
inference(equality_inference,[],[3593]) ).
cnf(i_0_6120,plain,
( ~ one_sorted_str(X1)
| ~ element(esk194_2(X1,X2),powerset(the_carrier(X1)))
| esk196_2(X1,X2) = subset_complement(the_carrier(X1),esk194_2(X1,X2))
| relation(esk197_2(X1,X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3594]) ).
cnf(i_0_6121,plain,
( ~ one_sorted_str(X1)
| ~ element(esk194_2(X1,X2),powerset(the_carrier(X1)))
| esk196_2(X1,X2) = subset_complement(the_carrier(X1),esk194_2(X1,X2))
| function(esk197_2(X1,X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3595]) ).
cnf(i_0_6122,plain,
( ~ one_sorted_str(X1)
| ~ element(esk194_2(X1,X2),powerset(the_carrier(X1)))
| esk195_2(X1,X2) = subset_complement(the_carrier(X1),esk194_2(X1,X2))
| relation(esk197_2(X1,X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3596]) ).
cnf(i_0_6123,plain,
( ~ one_sorted_str(X1)
| ~ element(esk194_2(X1,X2),powerset(the_carrier(X1)))
| esk195_2(X1,X2) = subset_complement(the_carrier(X1),esk194_2(X1,X2))
| function(esk197_2(X1,X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3597]) ).
cnf(i_0_6124,plain,
( ~ one_sorted_str(X1)
| ~ element(esk189_2(X1,X2),powerset(the_carrier(X1)))
| esk191_2(X1,X2) = subset_complement(the_carrier(X1),esk189_2(X1,X2))
| relation(esk192_2(X1,X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3598]) ).
cnf(i_0_6125,plain,
( ~ one_sorted_str(X1)
| ~ element(esk189_2(X1,X2),powerset(the_carrier(X1)))
| esk191_2(X1,X2) = subset_complement(the_carrier(X1),esk189_2(X1,X2))
| function(esk192_2(X1,X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3599]) ).
cnf(i_0_6126,plain,
( ~ one_sorted_str(X1)
| ~ element(esk189_2(X1,X2),powerset(the_carrier(X1)))
| esk190_2(X1,X2) = subset_complement(the_carrier(X1),esk189_2(X1,X2))
| relation(esk192_2(X1,X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3600]) ).
cnf(i_0_6127,plain,
( ~ one_sorted_str(X1)
| ~ element(esk189_2(X1,X2),powerset(the_carrier(X1)))
| esk190_2(X1,X2) = subset_complement(the_carrier(X1),esk189_2(X1,X2))
| function(esk192_2(X1,X2))
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[3601]) ).
cnf(i_0_6128,plain,
( ~ quasi_total(X1,empty_set,X2)
| ~ relation_of2_as_subset(X1,empty_set,X2)
| empty_set = relation_dom_as_subset(empty_set,X2,X1) ),
inference(equality_inference,[],[3623]) ).
cnf(i_0_6129,plain,
( ~ relation(inclusion_relation(X1))
| ~ in(X2,X1)
| ~ in(X3,X1)
| ~ subset(X3,X2)
| in(unordered_pair(unordered_pair(X3,X2),unordered_pair(X3,X3)),inclusion_relation(X1)) ),
inference(equality_inference,[],[3630]) ).
cnf(i_0_6130,plain,
( ~ in(X1,X2)
| esk187_1(X2) = unordered_pair(esk185_1(X2),esk185_1(X2))
| in(unordered_pair(unordered_pair(X1,unordered_pair(X1,X1)),unordered_pair(X1,X1)),esk188_1(X2)) ),
inference(equality_inference,[],[3631]) ).
cnf(i_0_6131,plain,
( ~ in(X1,X2)
| esk186_1(X2) = unordered_pair(esk185_1(X2),esk185_1(X2))
| in(unordered_pair(unordered_pair(X1,unordered_pair(X1,X1)),unordered_pair(X1,X1)),esk188_1(X2)) ),
inference(equality_inference,[],[3632]) ).
cnf(i_0_6132,plain,
( ~ ordinal(X1)
| ~ ordinal(X2)
| ~ in(X1,X3)
| in(X1,esk372_2(X3,X2))
| ~ in(X1,set_union2(X2,unordered_pair(X2,X2))) ),
inference(equality_inference,[],[3637]) ).
cnf(i_0_6133,plain,
( ~ in(X1,complements_of_subsets(X2,X3))
| ~ element(X1,powerset(X2))
| in(subset_complement(X2,X1),X3)
| ~ element(complements_of_subsets(X2,X3),powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2))) ),
inference(equality_inference,[],[3665]) ).
cnf(i_0_6134,plain,
( ~ in(X1,X2)
| in(esk185_1(X2),X2)
| in(unordered_pair(unordered_pair(X1,unordered_pair(X1,X1)),unordered_pair(X1,X1)),esk188_1(X2)) ),
inference(equality_inference,[],[3689]) ).
cnf(i_0_6135,plain,
( in(X1,set_meet(X2))
| ~ in(X1,esk41_3(X2,set_meet(X2),X1))
| X2 = empty_set ),
inference(equality_inference,[],[3698]) ).
cnf(i_0_6136,plain,
( ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_dom(X1))
| in(unordered_pair(unordered_pair(X2,apply(X1,X2)),unordered_pair(X2,X2)),X1) ),
inference(equality_inference,[],[3700]) ).
cnf(i_0_6137,plain,
X1 = X1,
inference(equality_inference,[],[3731]) ).
cnf(i_0_6138,plain,
X1 = X1,
inference(equality_inference,[],[3732]) ).
cnf(i_0_6139,plain,
( ~ strict_latt_str(boole_lattice(X1))
| ~ latt_str(boole_lattice(X1))
| ~ element(X2,powerset(X1))
| ~ element(X3,powerset(X1))
| apply_binary(the_L_meet(boole_lattice(X1)),X3,X2) = subset_intersection2(X1,X3,X2) ),
inference(equality_inference,[],[3754]) ).
cnf(i_0_6140,plain,
( ~ strict_latt_str(boole_lattice(X1))
| ~ latt_str(boole_lattice(X1))
| ~ element(X2,powerset(X1))
| ~ element(X3,powerset(X1))
| apply_binary(the_L_join(boole_lattice(X1)),X3,X2) = subset_union2(X1,X3,X2) ),
inference(equality_inference,[],[3755]) ).
cnf(i_0_6141,plain,
( ~ relation(X1)
| ~ in(X2,fiber(X1,X3))
| in(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),X1) ),
inference(equality_inference,[],[3761]) ).
cnf(i_0_6142,plain,
( ~ ordinal(X1)
| ~ ordinal(X2)
| in(X2,omega)
| in(X2,esk349_1(X1))
| ~ in(X2,set_union2(X1,unordered_pair(X1,X1))) ),
inference(equality_inference,[],[3771]) ).
cnf(i_0_6143,plain,
( empty_carrier(X1)
| ~ latt_set_smaller(X1,X2,X3)
| ~ lattice(X1)
| ~ complete_latt_str(X1)
| ~ latt_str(X1)
| in(X2,a_2_3_lattice3(X1,X3))
| ~ element(X2,the_carrier(X1)) ),
inference(equality_inference,[],[3803]) ).
cnf(i_0_6144,plain,
( ~ relation_of2_as_subset(X1,X2,empty_set)
| ~ quasi_total(X1,X2,empty_set)
| X1 = empty_set
| X2 = empty_set ),
inference(equality_inference,[],[3824]) ).
cnf(i_0_6145,plain,
( empty_carrier(X1)
| ~ latt_set_smaller(X1,X2,X3)
| ~ latt_str(X1)
| in(X2,a_2_2_lattice3(X1,X3))
| ~ element(X2,the_carrier(X1)) ),
inference(equality_inference,[],[3832]) ).
cnf(i_0_6146,plain,
( ~ in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ function(X2)
| in(esk88_3(X2,relation_rng(X2),X1),relation_dom(X2)) ),
inference(equality_inference,[],[3839]) ).
cnf(i_0_6147,plain,
( ~ in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ function(X2)
| X1 = apply(X2,esk88_3(X2,relation_rng(X2),X1)) ),
inference(equality_inference,[],[3863]) ).
cnf(i_0_6148,plain,
( ~ in(X1,union(X2))
| in(esk83_3(X2,union(X2),X1),X2) ),
inference(equality_inference,[],[3911]) ).
cnf(i_0_6149,plain,
( ~ in(X1,union(X2))
| in(X1,esk83_3(X2,union(X2),X1)) ),
inference(equality_inference,[],[3912]) ).
cnf(i_0_6150,plain,
( ~ relation(X1)
| ~ function(X1)
| in(X2,relation_inverse_image(X1,X3))
| ~ in(apply(X1,X2),X3)
| ~ in(X2,relation_dom(X1)) ),
inference(equality_inference,[],[3931]) ).
cnf(i_0_6151,plain,
( empty_carrier(X1)
| ~ lower_bounded_semilattstr(X1)
| ~ meet_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(bottom_of_semilattstr(X1),the_carrier(X1))
| meet(X1,bottom_of_semilattstr(X1),X2) = bottom_of_semilattstr(X1) ),
inference(equality_inference,[],[3933]) ).
cnf(i_0_6152,plain,
( empty_carrier(X1)
| ~ lower_bounded_semilattstr(X1)
| ~ meet_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(bottom_of_semilattstr(X1),the_carrier(X1))
| meet(X1,X2,bottom_of_semilattstr(X1)) = bottom_of_semilattstr(X1) ),
inference(equality_inference,[],[3934]) ).
cnf(i_0_6153,plain,
( in(X1,set_meet(X2))
| X2 = empty_set
| in(esk41_3(X2,set_meet(X2),X1),X2) ),
inference(equality_inference,[],[3941]) ).
cnf(i_0_6154,plain,
( ~ latt_str(X1)
| ~ lattice(X1)
| ~ complete_latt_str(X1)
| empty_carrier(X1)
| latt_element_smaller(X1,join_of_latt_set(X1,X2),X2)
| ~ element(join_of_latt_set(X1,X2),the_carrier(X1)) ),
inference(equality_inference,[],[3970]) ).
cnf(i_0_6155,plain,
( empty_carrier(X1)
| ~ lattice(X1)
| ~ complete_latt_str(X1)
| ~ latt_str(X1)
| latt_set_smaller(X1,meet_of_latt_set(X1,X2),X2)
| ~ element(meet_of_latt_set(X1,X2),the_carrier(X1)) ),
inference(equality_inference,[],[3971]) ).
cnf(i_0_6156,plain,
( ~ relation(X1)
| ~ function(X1)
| X2 = X2
| ~ one_to_one(X1)
| ~ in(X2,relation_dom(X1))
| ~ in(X2,relation_dom(X1)) ),
inference(equality_inference,[],[4001]) ).
cnf(i_0_6157,plain,
( ~ relation_of2(X1,X2,X2)
| X2 = X2 ),
inference(equality_inference,[],[4003]) ).
cnf(i_0_6158,plain,
( ~ relation_of2(X1,X2,X2)
| X1 = X1 ),
inference(equality_inference,[],[4004]) ).
cnf(i_0_6159,plain,
( ~ in(X1,X2)
| esk385_1(X2) = unordered_pair(esk383_1(X2),esk383_1(X2))
| apply(esk387_1(X2),X1) = unordered_pair(X1,X1) ),
inference(equality_inference,[],[4014]) ).
cnf(i_0_6160,plain,
( ~ in(X1,X2)
| esk384_1(X2) = unordered_pair(esk383_1(X2),esk383_1(X2))
| apply(esk387_1(X2),X1) = unordered_pair(X1,X1) ),
inference(equality_inference,[],[4015]) ).
cnf(i_0_6161,plain,
( ~ one_sorted_str(X1)
| ~ is_a_cover_of_carrier(X1,empty_set)
| empty_carrier(X1)
| ~ element(empty_set,powerset(powerset(the_carrier(X1)))) ),
inference(equality_inference,[],[4032]) ).
cnf(i_0_6162,plain,
( ~ in(X1,X2)
| ~ in(X1,X3)
| in(X1,set_difference(X3,set_difference(X3,X2))) ),
inference(equality_inference,[],[4040]) ).
cnf(i_0_6163,plain,
( ~ in(X1,X2)
| in(esk383_1(X2),X2)
| apply(esk387_1(X2),X1) = unordered_pair(X1,X1) ),
inference(equality_inference,[],[4060]) ).
cnf(i_0_6164,plain,
( X1 = X2
| X1 = X3
| X1 = X4
| ~ in(X1,unordered_triple(X2,X3,X4)) ),
inference(equality_inference,[],[4075]) ).
cnf(i_0_6165,plain,
( ~ function(X1)
| ~ function(relation_dom_restriction(X1,X2))
| ~ relation(X1)
| ~ relation(relation_dom_restriction(X1,X2))
| relation_dom(relation_dom_restriction(X1,X2)) = set_difference(relation_dom(X1),set_difference(relation_dom(X1),X2)) ),
inference(equality_inference,[],[4084]) ).
cnf(i_0_6166,plain,
( ~ relation(X1)
| ~ function(X1)
| ~ relation(relation_dom_restriction(X1,X2))
| ~ function(relation_dom_restriction(X1,X2))
| ~ in(X3,relation_dom(relation_dom_restriction(X1,X2)))
| apply(relation_dom_restriction(X1,X2),X3) = apply(X1,X3) ),
inference(equality_inference,[],[4088]) ).
cnf(i_0_6167,plain,
( ~ in(X1,set_difference(X2,set_difference(X2,X3)))
| in(X1,X3) ),
inference(equality_inference,[],[4141]) ).
cnf(i_0_6168,plain,
( ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_inverse_image(X1,X3))
| in(apply(X1,X2),X3) ),
inference(equality_inference,[],[4143]) ).
cnf(i_0_6169,plain,
( ~ in(X1,X2)
| in(unordered_pair(X1,X1),esk233_1(X2))
| esk232_1(X2) = unordered_pair(esk230_1(X2),esk230_1(X2)) ),
inference(equality_inference,[],[4154]) ).
cnf(i_0_6170,plain,
( ~ in(X1,X2)
| in(unordered_pair(X1,X1),esk233_1(X2))
| esk231_1(X2) = unordered_pair(esk230_1(X2),esk230_1(X2)) ),
inference(equality_inference,[],[4155]) ).
cnf(i_0_6171,plain,
( ~ in(X1,X2)
| in(esk230_1(X2),X2)
| in(unordered_pair(X1,X1),esk233_1(X2)) ),
inference(equality_inference,[],[4227]) ).
cnf(i_0_6172,plain,
( ~ ordinal(set_union2(X1,unordered_pair(X1,X1)))
| ~ ordinal(X1)
| ~ being_limit_ordinal(set_union2(X1,unordered_pair(X1,X1))) ),
inference(equality_inference,[],[4235]) ).
cnf(i_0_6173,plain,
( esk385_1(X1) = unordered_pair(esk383_1(X1),esk383_1(X1))
| relation_dom(esk387_1(X1)) = X1 ),
inference(equality_inference,[],[4248]) ).
cnf(i_0_6174,plain,
( esk384_1(X1) = unordered_pair(esk383_1(X1),esk383_1(X1))
| relation_dom(esk387_1(X1)) = X1 ),
inference(equality_inference,[],[4249]) ).
cnf(i_0_6175,plain,
( relation(esk387_1(X1))
| esk385_1(X1) = unordered_pair(esk383_1(X1),esk383_1(X1)) ),
inference(equality_inference,[],[4251]) ).
cnf(i_0_6176,plain,
( function(esk387_1(X1))
| esk385_1(X1) = unordered_pair(esk383_1(X1),esk383_1(X1)) ),
inference(equality_inference,[],[4252]) ).
cnf(i_0_6177,plain,
( relation(esk387_1(X1))
| esk384_1(X1) = unordered_pair(esk383_1(X1),esk383_1(X1)) ),
inference(equality_inference,[],[4253]) ).
cnf(i_0_6178,plain,
( function(esk387_1(X1))
| esk384_1(X1) = unordered_pair(esk383_1(X1),esk383_1(X1)) ),
inference(equality_inference,[],[4254]) ).
cnf(i_0_6179,plain,
( ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_inverse_image(X1,X3))
| in(X2,relation_dom(X1)) ),
inference(equality_inference,[],[4266]) ).
cnf(i_0_6180,plain,
( in(X1,X2)
| in(X1,X3)
| ~ in(X1,set_union2(X2,X3)) ),
inference(equality_inference,[],[4302]) ).
cnf(i_0_6181,plain,
( in(X1,X2)
| in(X1,set_difference(X3,X2))
| ~ in(X1,X3) ),
inference(equality_inference,[],[4303]) ).
cnf(i_0_6182,plain,
( in(esk383_1(X1),X1)
| relation_dom(esk387_1(X1)) = X1 ),
inference(equality_inference,[],[4306]) ).
cnf(i_0_6183,plain,
( in(esk383_1(X1),X1)
| relation(esk387_1(X1)) ),
inference(equality_inference,[],[4308]) ).
cnf(i_0_6184,plain,
( in(esk383_1(X1),X1)
| function(esk387_1(X1)) ),
inference(equality_inference,[],[4309]) ).
cnf(i_0_6185,plain,
( ~ in(X1,X2)
| in(X3,X1)
| ~ in(X3,set_meet(X2))
| X2 = empty_set ),
inference(equality_inference,[],[4327]) ).
cnf(i_0_6186,plain,
( ~ in(X1,X2)
| ~ in(X1,set_difference(X3,X2)) ),
inference(equality_inference,[],[4332]) ).
cnf(i_0_6187,plain,
( ~ relation(X1)
| ~ function(X1)
| X1 = identity_relation(relation_dom(X1))
| in(esk424_2(relation_dom(X1),X1),relation_dom(X1)) ),
inference(equality_inference,[],[4336]) ).
cnf(i_0_6188,plain,
( in(X1,union(X2))
| ~ in(X1,X3)
| ~ in(X3,X2) ),
inference(equality_inference,[],[4337]) ).
cnf(i_0_6189,plain,
( ~ element(empty_set,powerset(powerset(X1)))
| complements_of_subsets(X1,empty_set) = empty_set ),
inference(equality_inference,[],[4338]) ).
cnf(i_0_6190,plain,
( ~ proper_element(X1,powerset(X1))
| ~ element(X1,powerset(X1)) ),
inference(equality_inference,[],[4341]) ).
cnf(i_0_6191,plain,
( ~ relation(X1)
| X1 = inclusion_relation(relation_field(X1))
| in(esk48_2(relation_field(X1),X1),relation_field(X1)) ),
inference(equality_inference,[],[4384]) ).
cnf(i_0_6192,plain,
( ~ relation(X1)
| X1 = inclusion_relation(relation_field(X1))
| in(esk47_2(relation_field(X1),X1),relation_field(X1)) ),
inference(equality_inference,[],[4385]) ).
cnf(i_0_6193,plain,
( in(X1,X2)
| ~ in(X1,set_difference(X2,X3)) ),
inference(equality_inference,[],[4389]) ).
cnf(i_0_6194,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X2) ),
inference(equality_inference,[],[4390]) ).
cnf(i_0_6195,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X3) ),
inference(equality_inference,[],[4391]) ).
cnf(i_0_6196,plain,
( ~ relation(identity_relation(X1))
| ~ function(identity_relation(X1))
| ~ in(X2,X1)
| apply(identity_relation(X1),X2) = X2 ),
inference(equality_inference,[],[4401]) ).
cnf(i_0_6197,plain,
( ~ relation(X1)
| ~ function(X1)
| apply(X1,X2) = empty_set
| in(X2,relation_dom(X1)) ),
inference(equality_inference,[],[4403]) ).
cnf(i_0_6198,plain,
( ~ function(X1)
| finite(relation_rng(X1))
| ~ relation(X1)
| ~ in(relation_dom(X1),omega) ),
inference(equality_inference,[],[4418]) ).
cnf(i_0_6199,plain,
( ~ ordinal(X1)
| ~ in(X1,X2)
| in(X1,esk326_1(X2))
| ordinal(esk325_0) ),
inference(equality_inference,[],[4419]) ).
cnf(i_0_6200,plain,
( ~ ordinal(X1)
| ~ in(X1,X2)
| in(X1,esk326_1(X2))
| ordinal(esk324_0) ),
inference(equality_inference,[],[4420]) ).
cnf(i_0_6201,plain,
( ~ ordinal(X1)
| ~ in(X1,X2)
| esk323_0 = esk325_0
| in(X1,esk326_1(X2)) ),
inference(equality_inference,[],[4427]) ).
cnf(i_0_6202,plain,
( ~ ordinal(X1)
| ~ in(X1,X2)
| esk323_0 = esk324_0
| in(X1,esk326_1(X2)) ),
inference(equality_inference,[],[4428]) ).
cnf(i_0_6203,plain,
( ~ element(union(X1),X1)
| ~ proper_element(union(X1),X1) ),
inference(equality_inference,[],[4441]) ).
cnf(i_0_6204,plain,
( ~ relation(function_inverse(X1))
| ~ function(function_inverse(X1))
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1)
| relation_dom(function_inverse(X1)) = relation_rng(X1) ),
inference(equality_inference,[],[4455]) ).
cnf(i_0_6205,plain,
( ~ relation(X1)
| ~ function(X1)
| in(X2,relation_dom(X1))
| empty_set = apply(X1,X2) ),
inference(equality_inference,[],[4456]) ).
cnf(i_0_6206,plain,
( ~ ordinal(X1)
| ~ being_limit_ordinal(X1)
| subset(omega,X1)
| ~ in(empty_set,X1) ),
inference(equality_inference,[],[4464]) ).
cnf(i_0_6207,plain,
( X1 = X2
| X1 = X3
| ~ in(X1,unordered_pair(X2,X3)) ),
inference(equality_inference,[],[4469]) ).
cnf(i_0_6208,plain,
( ~ in(X1,unordered_pair(X2,X2))
| X1 = X2 ),
inference(equality_inference,[],[4477]) ).
cnf(i_0_6209,plain,
( X1 = X1
| X1 = X2 ),
inference(equality_inference,[],[4478]) ).
cnf(i_0_6210,plain,
X1 = X1,
inference(equality_inference,[],[4493]) ).
cnf(i_0_6211,plain,
X1 = X1,
inference(equality_inference,[],[4494]) ).
cnf(i_0_6212,plain,
( subset(X1,X2)
| ~ in(X1,powerset(X2)) ),
inference(equality_inference,[],[4508]) ).
cnf(i_0_6213,plain,
( in(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(equality_inference,[],[4509]) ).
cnf(i_0_6214,plain,
subset(empty_set,unordered_pair(X1,X1)),
inference(equality_inference,[],[4579]) ).
cnf(i_0_6215,plain,
( ~ strict_latt_str(boole_lattice(X1))
| ~ latt_str(boole_lattice(X1))
| the_carrier(boole_lattice(X1)) = powerset(X1) ),
inference(equality_inference,[],[4720]) ).
cnf(i_0_6216,plain,
( ~ relation(identity_relation(X1))
| ~ function(identity_relation(X1))
| relation_dom(identity_relation(X1)) = X1 ),
inference(equality_inference,[],[4763]) ).
cnf(i_0_6217,plain,
~ proper_subset(X1,X1),
inference(equality_inference,[],[4771]) ).
cnf(i_0_6218,plain,
~ in(X1,empty_set),
inference(equality_inference,[],[4774]) ).
cnf(i_0_6219,plain,
( ~ relation(inclusion_relation(X1))
| relation_field(inclusion_relation(X1)) = X1 ),
inference(equality_inference,[],[4809]) ).
cnf(i_0_6220,plain,
subset(X1,X1),
inference(equality_inference,[],[4834]) ).
cnf(i_0_6221,plain,
subset(X1,X1),
inference(equality_inference,[],[4835]) ).
cnf(i_0_6222,plain,
in(empty_set,omega),
inference(equality_inference,[],[4874]) ).
cnf(i_0_6223,plain,
~ centered(empty_set),
inference(equality_inference,[],[4974]) ).
cnf(i_0_6224,plain,
being_limit_ordinal(omega),
inference(equality_inference,[],[4976]) ).
cnf(i_0_6225,plain,
ordinal(omega),
inference(equality_inference,[],[4977]) ).
cnf(i_0_6226,plain,
( ~ ordinal(X1)
| ordinal_subset(X1,X1) ),
inference(scs_inference,[],[i_0_5049,i_0_4753]) ).
cnf(i_0_6227,plain,
one_sorted_str(esk440_0),
inference(scs_inference,[],[i_0_5086,i_0_4894]) ).
cnf(i_0_6228,plain,
( ~ rel_str(X1)
| one_sorted_str(X1) ),
inference(rename_variables,[],[i_0_4894]) ).
cnf(i_0_6229,plain,
relation_of2(identity_relation(X1),X1,X1),
inference(scs_inference,[],[i_0_5086,i_0_4393,i_0_4894,i_0_3963]) ).
cnf(i_0_6230,plain,
( ~ relation_of2_as_subset(X1,X2,X3)
| relation_of2(X1,X2,X3) ),
inference(rename_variables,[],[i_0_3963]) ).
cnf(i_0_6231,plain,
relation_of2(cartesian_product2(X1,X2),X1,X2),
inference(scs_inference,[],[i_0_5086,i_0_4880,i_0_4393,i_0_4894,i_0_3963,i_0_4069]) ).
cnf(i_0_6232,plain,
subset(X1,X1),
inference(rename_variables,[],[i_0_4880]) ).
cnf(i_0_6233,plain,
( ~ subset(X1,cartesian_product2(X2,X3))
| relation_of2(X1,X2,X3) ),
inference(rename_variables,[],[i_0_4069]) ).
cnf(i_0_6234,plain,
relation(esk160_1(cartesian_product2(X1,X2))),
inference(scs_inference,[],[i_0_5086,i_0_4768,i_0_4880,i_0_4393,i_0_4894,i_0_3963,i_0_4069,i_0_4070]) ).
cnf(i_0_6235,plain,
element(esk160_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_4768]) ).
cnf(i_0_6236,plain,
( ~ element(X1,powerset(cartesian_product2(X2,X3)))
| relation(X1) ),
inference(rename_variables,[],[i_0_4070]) ).
cnf(i_0_6237,plain,
element(complements_of_subsets(X1,esk160_1(powerset(X1))),powerset(powerset(X1))),
inference(scs_inference,[],[i_0_5086,i_0_4768,i_0_6235,i_0_4880,i_0_4393,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105]) ).
cnf(i_0_6238,plain,
element(esk160_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_4768]) ).
cnf(i_0_6239,plain,
( ~ element(X1,powerset(powerset(X2)))
| element(complements_of_subsets(X2,X1),powerset(powerset(X2))) ),
inference(rename_variables,[],[i_0_4105]) ).
cnf(i_0_6240,plain,
element(meet_of_subsets(X1,esk160_1(powerset(X1))),powerset(X1)),
inference(scs_inference,[],[i_0_5086,i_0_4768,i_0_6235,i_0_6238,i_0_4880,i_0_4393,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150]) ).
cnf(i_0_6241,plain,
element(esk160_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_4768]) ).
cnf(i_0_6242,plain,
( ~ element(X1,powerset(powerset(X2)))
| element(meet_of_subsets(X2,X1),powerset(X2)) ),
inference(rename_variables,[],[i_0_4150]) ).
cnf(i_0_6243,plain,
element(union_of_subsets(X1,esk160_1(powerset(X1))),powerset(X1)),
inference(scs_inference,[],[i_0_5086,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_4880,i_0_4393,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151]) ).
cnf(i_0_6244,plain,
element(esk160_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_4768]) ).
cnf(i_0_6245,plain,
( ~ element(X1,powerset(powerset(X2)))
| element(union_of_subsets(X2,X1),powerset(X2)) ),
inference(rename_variables,[],[i_0_4151]) ).
cnf(i_0_6246,plain,
complements_of_subsets(X1,complements_of_subsets(X1,esk160_1(powerset(X1)))) = esk160_1(powerset(X1)),
inference(scs_inference,[],[i_0_5086,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_4880,i_0_4393,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173]) ).
cnf(i_0_6247,plain,
element(esk160_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_4768]) ).
cnf(i_0_6248,plain,
( ~ element(X1,powerset(powerset(X2)))
| complements_of_subsets(X2,complements_of_subsets(X2,X1)) = X1 ),
inference(rename_variables,[],[i_0_4173]) ).
cnf(i_0_6249,plain,
~ epred2_3(empty_set,X1,unordered_pair(X2,X2)),
inference(scs_inference,[],[i_0_5086,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_4880,i_0_4393,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222]) ).
cnf(i_0_6250,plain,
( X1 = X2
| ~ epred2_3(X2,X3,X1) ),
inference(rename_variables,[],[i_0_4222]) ).
cnf(i_0_6251,plain,
~ epred2_3(X1,empty_set,unordered_pair(X2,X2)),
inference(scs_inference,[],[i_0_5086,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_4880,i_0_4393,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223]) ).
cnf(i_0_6252,plain,
( X1 = X2
| ~ epred2_3(X3,X2,X1) ),
inference(rename_variables,[],[i_0_4223]) ).
cnf(i_0_6253,plain,
element(subset_complement(X1,esk160_1(X1)),powerset(X1)),
inference(scs_inference,[],[i_0_5086,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_4880,i_0_4393,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287]) ).
cnf(i_0_6254,plain,
( ~ element(X1,powerset(X2))
| element(subset_complement(X2,X1),powerset(X2)) ),
inference(rename_variables,[],[i_0_4287]) ).
cnf(i_0_6255,plain,
in(esk444_2(X1,X1),esk443_1(X1)),
inference(scs_inference,[],[i_0_5086,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_4880,i_0_4393,i_0_4814,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288]) ).
cnf(i_0_6256,plain,
( ~ in(X1,esk443_1(X2))
| in(esk444_2(X2,X1),esk443_1(X2)) ),
inference(rename_variables,[],[i_0_4288]) ).
cnf(i_0_6257,plain,
meet_of_subsets(X1,esk160_1(powerset(X1))) = set_meet(esk160_1(powerset(X1))),
inference(scs_inference,[],[i_0_5086,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_4880,i_0_4393,i_0_4814,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328]) ).
cnf(i_0_6258,plain,
element(esk160_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_4768]) ).
cnf(i_0_6259,plain,
( ~ element(X1,powerset(powerset(X2)))
| meet_of_subsets(X2,X1) = set_meet(X1) ),
inference(rename_variables,[],[i_0_4328]) ).
cnf(i_0_6260,plain,
union_of_subsets(X1,esk160_1(powerset(X1))) = union(esk160_1(powerset(X1))),
inference(scs_inference,[],[i_0_5086,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_4880,i_0_4393,i_0_4814,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329]) ).
cnf(i_0_6261,plain,
element(esk160_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_4768]) ).
cnf(i_0_6262,plain,
( ~ element(X1,powerset(powerset(X2)))
| union_of_subsets(X2,X1) = union(X1) ),
inference(rename_variables,[],[i_0_4329]) ).
cnf(i_0_6263,plain,
subset_complement(X1,esk160_1(X1)) = set_difference(X1,esk160_1(X1)),
inference(scs_inference,[],[i_0_5086,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4880,i_0_4393,i_0_4814,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402]) ).
cnf(i_0_6264,plain,
( ~ element(X1,powerset(X2))
| subset_complement(X2,X1) = set_difference(X2,X1) ),
inference(rename_variables,[],[i_0_4402]) ).
cnf(i_0_6265,plain,
subset(esk160_1(X1),X1),
inference(scs_inference,[],[i_0_5086,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4880,i_0_4393,i_0_4814,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491]) ).
cnf(i_0_6266,plain,
( ~ element(X1,powerset(X2))
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_4491]) ).
cnf(i_0_6267,plain,
~ in(esk443_1(X1),X1),
inference(scs_inference,[],[i_0_5086,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4880,i_0_4393,i_0_4814,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512]) ).
cnf(i_0_6268,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_4512]) ).
cnf(i_0_6269,plain,
element(empty_set,omega),
inference(scs_inference,[],[i_0_5086,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4880,i_0_6222,i_0_4393,i_0_4814,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652]) ).
cnf(i_0_6270,plain,
( ~ in(X1,X2)
| element(X1,X2) ),
inference(rename_variables,[],[i_0_4652]) ).
cnf(i_0_6271,plain,
~ in(X1,esk156_0),
inference(scs_inference,[],[i_0_5086,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4880,i_0_6222,i_0_4393,i_0_4814,i_0_5056,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729]) ).
cnf(i_0_6272,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_4729]) ).
cnf(i_0_6273,plain,
~ in(X1,set_union2(empty_set,empty_set)),
inference(scs_inference,[],[i_0_5086,i_0_4878,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4880,i_0_6222,i_0_4393,i_0_4814,i_0_5056,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774]) ).
cnf(i_0_6274,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_4878]) ).
cnf(i_0_6275,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_4774]) ).
cnf(i_0_6276,plain,
epsilon_connected(esk123_1(omega)),
inference(scs_inference,[],[i_0_5086,i_0_4878,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_4880,i_0_6222,i_0_4393,i_0_4814,i_0_5056,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785]) ).
cnf(i_0_6277,plain,
element(esk123_1(X1),X1),
inference(rename_variables,[],[i_0_4812]) ).
cnf(i_0_6278,plain,
( ~ element(X1,omega)
| epsilon_connected(X1) ),
inference(rename_variables,[],[i_0_4785]) ).
cnf(i_0_6279,plain,
epsilon_transitive(esk123_1(omega)),
inference(scs_inference,[],[i_0_5086,i_0_4878,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_4880,i_0_6222,i_0_4393,i_0_4814,i_0_5056,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786]) ).
cnf(i_0_6280,plain,
element(esk123_1(X1),X1),
inference(rename_variables,[],[i_0_4812]) ).
cnf(i_0_6281,plain,
( ~ element(X1,omega)
| epsilon_transitive(X1) ),
inference(rename_variables,[],[i_0_4786]) ).
cnf(i_0_6282,plain,
ordinal(esk123_1(omega)),
inference(scs_inference,[],[i_0_5086,i_0_4878,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_4880,i_0_6222,i_0_4393,i_0_4814,i_0_5056,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787]) ).
cnf(i_0_6283,plain,
element(esk123_1(X1),X1),
inference(rename_variables,[],[i_0_4812]) ).
cnf(i_0_6284,plain,
( ~ element(X1,omega)
| ordinal(X1) ),
inference(rename_variables,[],[i_0_4787]) ).
cnf(i_0_6285,plain,
natural(esk123_1(omega)),
inference(scs_inference,[],[i_0_5086,i_0_4878,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_4880,i_0_6222,i_0_4393,i_0_4814,i_0_5056,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788]) ).
cnf(i_0_6286,plain,
element(esk123_1(X1),X1),
inference(rename_variables,[],[i_0_4812]) ).
cnf(i_0_6287,plain,
( ~ element(X1,omega)
| natural(X1) ),
inference(rename_variables,[],[i_0_4788]) ).
cnf(i_0_6288,plain,
in(esk49_1(unordered_pair(X1,X1)),unordered_pair(X1,X1)),
inference(scs_inference,[],[i_0_5086,i_0_4878,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_4880,i_0_6222,i_0_4393,i_0_4814,i_0_5056,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801]) ).
cnf(i_0_6289,plain,
( X1 = empty_set
| in(esk49_1(X1),X1) ),
inference(rename_variables,[],[i_0_4801]) ).
cnf(i_0_6290,plain,
esk160_1(empty_set) = empty_set,
inference(scs_inference,[],[i_0_5086,i_0_4878,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_4880,i_0_6222,i_0_4393,i_0_4814,i_0_5056,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802]) ).
cnf(i_0_6291,plain,
( ~ subset(X1,empty_set)
| X1 = empty_set ),
inference(rename_variables,[],[i_0_4802]) ).
cnf(i_0_6292,plain,
subset(set_union2(X1,X1),X1),
inference(scs_inference,[],[i_0_5086,i_0_4878,i_0_6274,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_4880,i_0_6222,i_0_4393,i_0_4814,i_0_5056,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834]) ).
cnf(i_0_6293,plain,
( X1 != X2
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_4834]) ).
cnf(i_0_6294,plain,
subset(set_union2(X1,X2),set_union2(X2,X1)),
inference(scs_inference,[],[i_0_5086,i_0_4878,i_0_6274,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_4880,i_0_6222,i_0_4393,i_0_4814,i_0_5056,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835]) ).
cnf(i_0_6295,plain,
( X1 != X2
| subset(X2,X1) ),
inference(rename_variables,[],[i_0_4835]) ).
cnf(i_0_6296,plain,
relation(esk151_0),
inference(scs_inference,[],[i_0_5086,i_0_4878,i_0_6274,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_4880,i_0_6222,i_0_4393,i_0_4814,i_0_5056,i_0_5058,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897]) ).
cnf(i_0_6297,plain,
( ~ empty(X1)
| relation(X1) ),
inference(rename_variables,[],[i_0_4897]) ).
cnf(i_0_6298,plain,
function(esk151_0),
inference(scs_inference,[],[i_0_5086,i_0_4878,i_0_6274,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_4880,i_0_6222,i_0_4393,i_0_4814,i_0_5056,i_0_5058,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898]) ).
cnf(i_0_6299,plain,
( ~ empty(X1)
| function(X1) ),
inference(rename_variables,[],[i_0_4898]) ).
cnf(i_0_6300,plain,
finite(esk156_0),
inference(scs_inference,[],[i_0_5086,i_0_4878,i_0_6274,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_4880,i_0_6222,i_0_4393,i_0_4814,i_0_5056,i_0_5058,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901]) ).
cnf(i_0_6301,plain,
( ~ empty(X1)
| finite(X1) ),
inference(rename_variables,[],[i_0_4901]) ).
cnf(i_0_6302,plain,
epsilon_connected(esk153_0),
inference(scs_inference,[],[i_0_5086,i_0_4878,i_0_6274,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_4880,i_0_6222,i_0_4393,i_0_4814,i_0_5056,i_0_5057,i_0_5058,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904]) ).
cnf(i_0_6303,plain,
( ~ empty(X1)
| epsilon_connected(X1) ),
inference(rename_variables,[],[i_0_4904]) ).
cnf(i_0_6304,plain,
epsilon_transitive(esk153_0),
inference(scs_inference,[],[i_0_5086,i_0_4878,i_0_6274,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_4880,i_0_6222,i_0_4393,i_0_4814,i_0_5056,i_0_5057,i_0_5058,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907]) ).
cnf(i_0_6305,plain,
( ~ empty(X1)
| epsilon_transitive(X1) ),
inference(rename_variables,[],[i_0_4907]) ).
cnf(i_0_6306,plain,
ordinal(esk153_0),
inference(scs_inference,[],[i_0_5086,i_0_4878,i_0_6274,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_4880,i_0_6222,i_0_4393,i_0_4814,i_0_5056,i_0_5057,i_0_5058,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908]) ).
cnf(i_0_6307,plain,
( ~ empty(X1)
| ordinal(X1) ),
inference(rename_variables,[],[i_0_4908]) ).
cnf(i_0_6308,plain,
v5_membered(esk156_0),
inference(scs_inference,[],[i_0_5086,i_0_4878,i_0_6274,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_4880,i_0_6222,i_0_4393,i_0_4814,i_0_5056,i_0_5057,i_0_5058,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909]) ).
cnf(i_0_6309,plain,
( ~ empty(X1)
| v5_membered(X1) ),
inference(rename_variables,[],[i_0_4909]) ).
cnf(i_0_6310,plain,
v4_membered(esk156_0),
inference(scs_inference,[],[i_0_5086,i_0_4878,i_0_6274,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_4880,i_0_6222,i_0_4393,i_0_4814,i_0_5056,i_0_5057,i_0_5058,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910]) ).
cnf(i_0_6311,plain,
( ~ empty(X1)
| v4_membered(X1) ),
inference(rename_variables,[],[i_0_4910]) ).
cnf(i_0_6312,plain,
v3_membered(esk156_0),
inference(scs_inference,[],[i_0_5086,i_0_4878,i_0_6274,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_4880,i_0_6222,i_0_4393,i_0_4814,i_0_5056,i_0_5057,i_0_5058,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912]) ).
cnf(i_0_6313,plain,
( ~ empty(X1)
| v3_membered(X1) ),
inference(rename_variables,[],[i_0_4912]) ).
cnf(i_0_6314,plain,
v2_membered(esk156_0),
inference(scs_inference,[],[i_0_5086,i_0_4878,i_0_6274,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_4880,i_0_6222,i_0_4393,i_0_4814,i_0_5056,i_0_5057,i_0_5058,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914]) ).
cnf(i_0_6315,plain,
( ~ empty(X1)
| v2_membered(X1) ),
inference(rename_variables,[],[i_0_4914]) ).
cnf(i_0_6316,plain,
v1_membered(esk156_0),
inference(scs_inference,[],[i_0_5086,i_0_4878,i_0_6274,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_4880,i_0_6222,i_0_4393,i_0_4814,i_0_5056,i_0_5057,i_0_5058,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916]) ).
cnf(i_0_6317,plain,
( ~ empty(X1)
| v1_membered(X1) ),
inference(rename_variables,[],[i_0_4916]) ).
cnf(i_0_6318,plain,
~ in(X1,cartesian_product2(X2,empty_set)),
inference(scs_inference,[],[i_0_5086,i_0_6218,i_0_4878,i_0_6274,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_4880,i_0_6222,i_0_4393,i_0_4814,i_0_5056,i_0_5057,i_0_5058,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030]) ).
cnf(i_0_6319,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6320,plain,
( in(esk64_4(X1,X2,cartesian_product2(X1,X2),X3),X2)
| ~ in(X3,cartesian_product2(X1,X2)) ),
inference(rename_variables,[],[i_0_6030]) ).
cnf(i_0_6321,plain,
~ in(X1,cartesian_product2(empty_set,X2)),
inference(scs_inference,[],[i_0_5086,i_0_6218,i_0_6319,i_0_4878,i_0_6274,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_4880,i_0_6222,i_0_4393,i_0_4814,i_0_5056,i_0_5057,i_0_5058,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031]) ).
cnf(i_0_6322,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6323,plain,
( in(esk63_4(X1,X2,cartesian_product2(X1,X2),X3),X1)
| ~ in(X3,cartesian_product2(X1,X2)) ),
inference(rename_variables,[],[i_0_6031]) ).
cnf(i_0_6324,plain,
~ in(X1,union(empty_set)),
inference(scs_inference,[],[i_0_5086,i_0_6218,i_0_6319,i_0_6322,i_0_4878,i_0_6274,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_4880,i_0_6222,i_0_4393,i_0_4814,i_0_5056,i_0_5057,i_0_5058,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148]) ).
cnf(i_0_6325,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6326,plain,
( in(esk83_3(X1,union(X1),X2),X1)
| ~ in(X2,union(X1)) ),
inference(rename_variables,[],[i_0_6148]) ).
cnf(i_0_6327,plain,
~ in(X1,set_difference(X2,set_difference(X2,empty_set))),
inference(scs_inference,[],[i_0_5086,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_4880,i_0_6222,i_0_4393,i_0_4814,i_0_5056,i_0_5057,i_0_5058,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167]) ).
cnf(i_0_6328,plain,
( in(X1,X2)
| ~ in(X1,set_difference(X3,set_difference(X3,X2))) ),
inference(rename_variables,[],[i_0_6167]) ).
cnf(i_0_6329,plain,
~ in(empty_set,set_difference(X1,omega)),
inference(scs_inference,[],[i_0_5086,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_4880,i_0_6222,i_0_4393,i_0_4814,i_0_5056,i_0_5057,i_0_5058,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186]) ).
cnf(i_0_6330,plain,
( ~ in(X1,X2)
| ~ in(X1,set_difference(X3,X2)) ),
inference(rename_variables,[],[i_0_6186]) ).
cnf(i_0_6331,plain,
~ in(X1,set_difference(empty_set,X2)),
inference(scs_inference,[],[i_0_5086,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_4880,i_0_6222,i_0_4393,i_0_4814,i_0_5056,i_0_5057,i_0_5058,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193]) ).
cnf(i_0_6332,plain,
( in(X1,X2)
| ~ in(X1,set_difference(X2,X3)) ),
inference(rename_variables,[],[i_0_6193]) ).
cnf(i_0_6333,plain,
in(empty_set,set_union2(omega,X1)),
inference(scs_inference,[],[i_0_5086,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_4880,i_0_6222,i_0_4393,i_0_4814,i_0_5056,i_0_5057,i_0_5058,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194]) ).
cnf(i_0_6334,plain,
( ~ in(X1,X2)
| in(X1,set_union2(X2,X3)) ),
inference(rename_variables,[],[i_0_6194]) ).
cnf(i_0_6335,plain,
in(empty_set,set_union2(X1,omega)),
inference(scs_inference,[],[i_0_5086,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_4880,i_0_6222,i_0_4393,i_0_4814,i_0_5056,i_0_5057,i_0_5058,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195]) ).
cnf(i_0_6336,plain,
( ~ in(X1,X2)
| in(X1,set_union2(X3,X2)) ),
inference(rename_variables,[],[i_0_6195]) ).
cnf(i_0_6337,plain,
~ in(unordered_pair(X1,X1),unordered_pair(empty_set,empty_set)),
inference(scs_inference,[],[i_0_5086,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_4880,i_0_6222,i_0_4393,i_0_4814,i_0_5056,i_0_5057,i_0_5058,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208]) ).
cnf(i_0_6338,plain,
( X1 = X2
| ~ in(X1,unordered_pair(X2,X2)) ),
inference(rename_variables,[],[i_0_6208]) ).
cnf(i_0_6339,plain,
X1 = set_union2(X1,X1),
inference(scs_inference,[],[i_0_5086,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_4880,i_0_6222,i_0_4393,i_0_4814,i_0_5056,i_0_5057,i_0_5058,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093]) ).
cnf(i_0_6340,plain,
relation_of2_as_subset(esk167_1(X1),X1,X1),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_4880,i_0_6222,i_0_4393,i_0_4814,i_0_5056,i_0_5057,i_0_5058,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962]) ).
cnf(i_0_6341,plain,
( ~ relation_of2(X1,X2,X3)
| relation_of2_as_subset(X1,X2,X3) ),
inference(rename_variables,[],[i_0_3962]) ).
cnf(i_0_6342,plain,
disjoint(X1,empty_set),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_4880,i_0_6222,i_0_4393,i_0_4814,i_0_5056,i_0_5057,i_0_5058,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005]) ).
cnf(i_0_6343,plain,
( in(esk432_2(X1,X2),set_difference(X1,set_difference(X1,X2)))
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_4005]) ).
cnf(i_0_6344,plain,
in(X1,unordered_pair(X1,X2)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_4880,i_0_6232,i_0_6222,i_0_4393,i_0_4814,i_0_5056,i_0_5057,i_0_5058,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293]) ).
cnf(i_0_6345,plain,
subset(X1,X1),
inference(rename_variables,[],[i_0_4880]) ).
cnf(i_0_6346,plain,
( ~ subset(unordered_pair(X1,X2),X3)
| in(X1,X3) ),
inference(rename_variables,[],[i_0_4293]) ).
cnf(i_0_6347,plain,
in(X1,unordered_pair(X2,X1)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_4880,i_0_6232,i_0_6345,i_0_6222,i_0_4393,i_0_4814,i_0_5056,i_0_5057,i_0_5058,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294]) ).
cnf(i_0_6348,plain,
subset(X1,X1),
inference(rename_variables,[],[i_0_4880]) ).
cnf(i_0_6349,plain,
( ~ subset(unordered_pair(X1,X2),X3)
| in(X2,X3) ),
inference(rename_variables,[],[i_0_4294]) ).
cnf(i_0_6350,plain,
disjoint(empty_set,X1),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_4888,i_0_4880,i_0_6232,i_0_6345,i_0_6222,i_0_4393,i_0_4814,i_0_5056,i_0_5057,i_0_5058,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295]) ).
cnf(i_0_6351,plain,
set_difference(empty_set,X1) = empty_set,
inference(rename_variables,[],[i_0_4888]) ).
cnf(i_0_6352,plain,
( set_difference(X1,set_difference(X1,X2)) != empty_set
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_4295]) ).
cnf(i_0_6353,plain,
disjoint(esk156_0,X1),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_4888,i_0_4880,i_0_6232,i_0_6345,i_0_6222,i_0_4393,i_0_4814,i_0_5056,i_0_5057,i_0_5058,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429]) ).
cnf(i_0_6354,plain,
( in(esk426_2(X1,X2),X1)
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_4429]) ).
cnf(i_0_6355,plain,
disjoint(X1,set_union2(empty_set,empty_set)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_4888,i_0_4880,i_0_6232,i_0_6345,i_0_6222,i_0_4393,i_0_4814,i_0_5056,i_0_5057,i_0_5058,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430]) ).
cnf(i_0_6356,plain,
( in(esk426_2(X1,X2),X2)
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_4430]) ).
cnf(i_0_6357,plain,
subset(cartesian_product2(X1,empty_set),X2),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_4888,i_0_4880,i_0_6232,i_0_6345,i_0_6222,i_0_4393,i_0_4814,i_0_5056,i_0_5057,i_0_5058,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431]) ).
cnf(i_0_6358,plain,
( in(esk74_2(X1,X2),X1)
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_4431]) ).
cnf(i_0_6359,plain,
subset(set_union2(empty_set,empty_set),unordered_pair(X1,X1)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_4888,i_0_4880,i_0_6232,i_0_6345,i_0_6222,i_0_4393,i_0_4814,i_0_5056,i_0_5057,i_0_5058,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579]) ).
cnf(i_0_6360,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_4878]) ).
cnf(i_0_6361,plain,
( X1 != empty_set
| subset(X1,unordered_pair(X2,X2)) ),
inference(rename_variables,[],[i_0_4579]) ).
cnf(i_0_6362,plain,
disjoint(X1,set_difference(X1,X1)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_4597,i_0_4888,i_0_4880,i_0_6232,i_0_6345,i_0_6222,i_0_4393,i_0_4814,i_0_5056,i_0_5057,i_0_5058,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620]) ).
cnf(i_0_6363,plain,
( set_difference(X1,X2) != X1
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_4620]) ).
cnf(i_0_6364,plain,
are_equipotent(X1,X1),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_4597,i_0_4888,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6222,i_0_4393,i_0_4814,i_0_5056,i_0_5057,i_0_5058,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647]) ).
cnf(i_0_6365,plain,
( ~ equipotent(X1,X2)
| are_equipotent(X1,X2) ),
inference(rename_variables,[],[i_0_4647]) ).
cnf(i_0_6366,plain,
disjoint(X1,esk156_0),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_4597,i_0_4888,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6222,i_0_4393,i_0_4814,i_0_5056,i_0_5057,i_0_5058,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650]) ).
cnf(i_0_6367,plain,
( ~ disjoint(X1,X2)
| disjoint(X2,X1) ),
inference(rename_variables,[],[i_0_4650]) ).
cnf(i_0_6368,plain,
subset(X1,set_difference(X1,empty_set)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6222,i_0_4393,i_0_4814,i_0_5056,i_0_5057,i_0_5058,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654]) ).
cnf(i_0_6369,plain,
( set_difference(X1,X2) != empty_set
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_4654]) ).
cnf(i_0_6370,plain,
relation(cartesian_product2(empty_set,X1)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6222,i_0_4393,i_0_4814,i_0_5056,i_0_5057,i_0_5058,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775]) ).
cnf(i_0_6371,plain,
( in(esk39_1(X1),X1)
| relation(X1) ),
inference(rename_variables,[],[i_0_4775]) ).
cnf(i_0_6372,plain,
epsilon_connected(union(empty_set)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6222,i_0_4393,i_0_4814,i_0_5056,i_0_5057,i_0_5058,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776]) ).
cnf(i_0_6373,plain,
( in(esk71_1(X1),X1)
| epsilon_connected(X1) ),
inference(rename_variables,[],[i_0_4776]) ).
cnf(i_0_6374,plain,
in(empty_set,set_difference(omega,empty_set)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_4882,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6222,i_0_4393,i_0_4814,i_0_5056,i_0_5057,i_0_5058,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874]) ).
cnf(i_0_6375,plain,
set_difference(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_4882]) ).
cnf(i_0_6376,plain,
( X1 != omega
| in(empty_set,X1) ),
inference(rename_variables,[],[i_0_4874]) ).
cnf(i_0_6377,plain,
one_sorted_str(esk117_0),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_4882,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6222,i_0_4393,i_0_4814,i_0_4999,i_0_5056,i_0_5057,i_0_5058,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891]) ).
cnf(i_0_6378,plain,
( ~ top_str(X1)
| one_sorted_str(X1) ),
inference(rename_variables,[],[i_0_4891]) ).
cnf(i_0_6379,plain,
one_sorted_str(esk115_0),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_4882,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6222,i_0_4393,i_0_4814,i_0_4999,i_0_5002,i_0_5056,i_0_5057,i_0_5058,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892]) ).
cnf(i_0_6380,plain,
( ~ meet_semilatt_str(X1)
| one_sorted_str(X1) ),
inference(rename_variables,[],[i_0_4892]) ).
cnf(i_0_6381,plain,
one_sorted_str(esk119_0),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_4882,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6222,i_0_4393,i_0_4814,i_0_4999,i_0_5002,i_0_5003,i_0_5056,i_0_5057,i_0_5058,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893]) ).
cnf(i_0_6382,plain,
( ~ join_semilatt_str(X1)
| one_sorted_str(X1) ),
inference(rename_variables,[],[i_0_4893]) ).
cnf(i_0_6383,plain,
meet_semilatt_str(esk176_0),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_4882,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6222,i_0_4393,i_0_4814,i_0_4999,i_0_5002,i_0_5003,i_0_5056,i_0_5057,i_0_5058,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895]) ).
cnf(i_0_6384,plain,
( ~ latt_str(X1)
| meet_semilatt_str(X1) ),
inference(rename_variables,[],[i_0_4895]) ).
cnf(i_0_6385,plain,
join_semilatt_str(esk176_0),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_4882,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6222,i_0_4393,i_0_4814,i_0_4999,i_0_5002,i_0_5003,i_0_5056,i_0_5057,i_0_5058,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896]) ).
cnf(i_0_6386,plain,
( ~ latt_str(X1)
| join_semilatt_str(X1) ),
inference(rename_variables,[],[i_0_4896]) ).
cnf(i_0_6387,plain,
~ centered(set_union2(empty_set,empty_set)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_6360,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_4882,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6222,i_0_4393,i_0_4814,i_0_4999,i_0_5002,i_0_5003,i_0_5056,i_0_5057,i_0_5058,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974]) ).
cnf(i_0_6388,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_4878]) ).
cnf(i_0_6389,plain,
( X1 != empty_set
| ~ centered(X1) ),
inference(rename_variables,[],[i_0_4974]) ).
cnf(i_0_6390,plain,
being_limit_ordinal(set_union2(omega,omega)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_4882,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6222,i_0_4393,i_0_4814,i_0_4999,i_0_5002,i_0_5003,i_0_5056,i_0_5057,i_0_5058,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976]) ).
cnf(i_0_6391,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_4878]) ).
cnf(i_0_6392,plain,
( X1 != omega
| being_limit_ordinal(X1) ),
inference(rename_variables,[],[i_0_4976]) ).
cnf(i_0_6393,plain,
ordinal(set_union2(omega,omega)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_4882,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6222,i_0_4393,i_0_4814,i_0_4999,i_0_5002,i_0_5003,i_0_5056,i_0_5057,i_0_5058,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977]) ).
cnf(i_0_6394,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_4878]) ).
cnf(i_0_6395,plain,
( X1 != omega
| ordinal(X1) ),
inference(rename_variables,[],[i_0_4977]) ).
cnf(i_0_6396,plain,
in(X1,powerset(X1)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_4882,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4814,i_0_4999,i_0_5002,i_0_5003,i_0_5056,i_0_5057,i_0_5058,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213]) ).
cnf(i_0_6397,plain,
( ~ subset(X1,X2)
| in(X1,powerset(X2)) ),
inference(rename_variables,[],[i_0_6213]) ).
cnf(i_0_6398,plain,
in(esk123_1(esk166_0),esk166_0),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4814,i_0_4999,i_0_5002,i_0_5003,i_0_5056,i_0_5057,i_0_5058,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589]) ).
cnf(i_0_6399,plain,
element(esk123_1(X1),X1),
inference(rename_variables,[],[i_0_4812]) ).
cnf(i_0_6400,plain,
( empty(X1)
| ~ element(X2,X1)
| in(X2,X1) ),
inference(rename_variables,[],[i_0_4589]) ).
cnf(i_0_6401,plain,
epsilon_connected(esk123_1(esk166_0)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4814,i_0_4999,i_0_5002,i_0_5003,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683]) ).
cnf(i_0_6402,plain,
element(esk123_1(X1),X1),
inference(rename_variables,[],[i_0_4812]) ).
cnf(i_0_6403,plain,
( ~ ordinal(X1)
| epsilon_connected(X2)
| ~ element(X2,X1) ),
inference(rename_variables,[],[i_0_4683]) ).
cnf(i_0_6404,plain,
epsilon_transitive(esk123_1(esk166_0)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4814,i_0_4999,i_0_5002,i_0_5003,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684]) ).
cnf(i_0_6405,plain,
element(esk123_1(X1),X1),
inference(rename_variables,[],[i_0_4812]) ).
cnf(i_0_6406,plain,
( ~ ordinal(X1)
| epsilon_transitive(X2)
| ~ element(X2,X1) ),
inference(rename_variables,[],[i_0_4684]) ).
cnf(i_0_6407,plain,
ordinal(esk123_1(esk166_0)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4814,i_0_4999,i_0_5002,i_0_5003,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685]) ).
cnf(i_0_6408,plain,
element(esk123_1(X1),X1),
inference(rename_variables,[],[i_0_4812]) ).
cnf(i_0_6409,plain,
( ~ ordinal(X1)
| ordinal(X2)
| ~ element(X2,X1) ),
inference(rename_variables,[],[i_0_4685]) ).
cnf(i_0_6410,plain,
~ element(esk166_0,esk156_0),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4814,i_0_4999,i_0_5002,i_0_5003,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687]) ).
cnf(i_0_6411,plain,
( ~ empty(X1)
| empty(X2)
| ~ element(X2,X1) ),
inference(rename_variables,[],[i_0_4687]) ).
cnf(i_0_6412,plain,
natural(esk123_1(esk143_0)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4814,i_0_4999,i_0_5002,i_0_5003,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688]) ).
cnf(i_0_6413,plain,
element(esk123_1(X1),X1),
inference(rename_variables,[],[i_0_4812]) ).
cnf(i_0_6414,plain,
( ~ v5_membered(X1)
| natural(X2)
| ~ element(X2,X1) ),
inference(rename_variables,[],[i_0_4688]) ).
cnf(i_0_6415,plain,
v1_int_1(esk123_1(esk143_0)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4814,i_0_4999,i_0_5002,i_0_5003,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689]) ).
cnf(i_0_6416,plain,
element(esk123_1(X1),X1),
inference(rename_variables,[],[i_0_4812]) ).
cnf(i_0_6417,plain,
( ~ v5_membered(X1)
| v1_int_1(X2)
| ~ element(X2,X1) ),
inference(rename_variables,[],[i_0_4689]) ).
cnf(i_0_6418,plain,
v1_int_1(esk123_1(empty_set)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4814,i_0_4999,i_0_5002,i_0_5003,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5070,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690]) ).
cnf(i_0_6419,plain,
element(esk123_1(X1),X1),
inference(rename_variables,[],[i_0_4812]) ).
cnf(i_0_6420,plain,
( ~ v4_membered(X1)
| v1_int_1(X2)
| ~ element(X2,X1) ),
inference(rename_variables,[],[i_0_4690]) ).
cnf(i_0_6421,plain,
v1_rat_1(esk123_1(esk143_0)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4814,i_0_4999,i_0_5002,i_0_5003,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5070,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691]) ).
cnf(i_0_6422,plain,
element(esk123_1(X1),X1),
inference(rename_variables,[],[i_0_4812]) ).
cnf(i_0_6423,plain,
( ~ v5_membered(X1)
| v1_rat_1(X2)
| ~ element(X2,X1) ),
inference(rename_variables,[],[i_0_4691]) ).
cnf(i_0_6424,plain,
v1_rat_1(esk123_1(empty_set)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4814,i_0_4999,i_0_5002,i_0_5003,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5070,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692]) ).
cnf(i_0_6425,plain,
element(esk123_1(X1),X1),
inference(rename_variables,[],[i_0_4812]) ).
cnf(i_0_6426,plain,
( ~ v4_membered(X1)
| v1_rat_1(X2)
| ~ element(X2,X1) ),
inference(rename_variables,[],[i_0_4692]) ).
cnf(i_0_6427,plain,
v1_rat_1(esk123_1(esk156_0)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4814,i_0_4999,i_0_5002,i_0_5003,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5070,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693]) ).
cnf(i_0_6428,plain,
element(esk123_1(X1),X1),
inference(rename_variables,[],[i_0_4812]) ).
cnf(i_0_6429,plain,
( ~ v3_membered(X1)
| v1_rat_1(X2)
| ~ element(X2,X1) ),
inference(rename_variables,[],[i_0_4693]) ).
cnf(i_0_6430,plain,
v1_xreal_0(esk123_1(esk143_0)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4814,i_0_4999,i_0_5002,i_0_5003,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5070,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694]) ).
cnf(i_0_6431,plain,
element(esk123_1(X1),X1),
inference(rename_variables,[],[i_0_4812]) ).
cnf(i_0_6432,plain,
( ~ v5_membered(X1)
| v1_xreal_0(X2)
| ~ element(X2,X1) ),
inference(rename_variables,[],[i_0_4694]) ).
cnf(i_0_6433,plain,
v1_xreal_0(esk123_1(empty_set)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4814,i_0_4999,i_0_5002,i_0_5003,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5070,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695]) ).
cnf(i_0_6434,plain,
element(esk123_1(X1),X1),
inference(rename_variables,[],[i_0_4812]) ).
cnf(i_0_6435,plain,
( ~ v4_membered(X1)
| v1_xreal_0(X2)
| ~ element(X2,X1) ),
inference(rename_variables,[],[i_0_4695]) ).
cnf(i_0_6436,plain,
v1_xreal_0(esk123_1(esk156_0)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4814,i_0_4999,i_0_5002,i_0_5003,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5070,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696]) ).
cnf(i_0_6437,plain,
element(esk123_1(X1),X1),
inference(rename_variables,[],[i_0_4812]) ).
cnf(i_0_6438,plain,
( ~ v3_membered(X1)
| v1_xreal_0(X2)
| ~ element(X2,X1) ),
inference(rename_variables,[],[i_0_4696]) ).
cnf(i_0_6439,plain,
v1_xcmplx_0(esk123_1(esk143_0)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4814,i_0_4999,i_0_5002,i_0_5003,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5070,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698]) ).
cnf(i_0_6440,plain,
element(esk123_1(X1),X1),
inference(rename_variables,[],[i_0_4812]) ).
cnf(i_0_6441,plain,
( ~ v5_membered(X1)
| v1_xcmplx_0(X2)
| ~ element(X2,X1) ),
inference(rename_variables,[],[i_0_4698]) ).
cnf(i_0_6442,plain,
v1_xcmplx_0(esk123_1(empty_set)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4814,i_0_4999,i_0_5002,i_0_5003,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5070,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699]) ).
cnf(i_0_6443,plain,
element(esk123_1(X1),X1),
inference(rename_variables,[],[i_0_4812]) ).
cnf(i_0_6444,plain,
( ~ v4_membered(X1)
| v1_xcmplx_0(X2)
| ~ element(X2,X1) ),
inference(rename_variables,[],[i_0_4699]) ).
cnf(i_0_6445,plain,
v1_xcmplx_0(esk123_1(esk156_0)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4814,i_0_4999,i_0_5002,i_0_5003,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5070,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700]) ).
cnf(i_0_6446,plain,
element(esk123_1(X1),X1),
inference(rename_variables,[],[i_0_4812]) ).
cnf(i_0_6447,plain,
( ~ v3_membered(X1)
| v1_xcmplx_0(X2)
| ~ element(X2,X1) ),
inference(rename_variables,[],[i_0_4700]) ).
cnf(i_0_6448,plain,
~ element(set_union2(esk166_0,esk166_0),esk156_0),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4814,i_0_4999,i_0_5002,i_0_5003,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5070,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782]) ).
cnf(i_0_6449,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_4878]) ).
cnf(i_0_6450,plain,
~ element(esk166_0,set_union2(esk156_0,esk156_0)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4814,i_0_4999,i_0_5002,i_0_5003,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5070,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783]) ).
cnf(i_0_6451,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_4878]) ).
cnf(i_0_6452,plain,
element(subset_difference(empty_set,esk160_1(empty_set),esk160_1(empty_set)),powerset(empty_set)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4814,i_0_4999,i_0_5002,i_0_5003,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5070,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789]) ).
cnf(i_0_6453,plain,
element(esk160_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_4768]) ).
cnf(i_0_6454,plain,
( ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2))
| element(subset_difference(X2,X1,X3),powerset(X2)) ),
inference(rename_variables,[],[i_0_3789]) ).
cnf(i_0_6455,plain,
element(subset_intersection2(X1,esk160_1(X1),esk160_1(X1)),powerset(X1)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4814,i_0_4999,i_0_5002,i_0_5003,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5070,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790]) ).
cnf(i_0_6456,plain,
( ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2))
| element(subset_intersection2(X2,X1,X3),powerset(X2)) ),
inference(rename_variables,[],[i_0_3790]) ).
cnf(i_0_6457,plain,
element(subset_union2(X1,esk160_1(X1),esk160_1(X1)),powerset(X1)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4814,i_0_4999,i_0_5002,i_0_5003,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5070,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791]) ).
cnf(i_0_6458,plain,
( ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2))
| element(subset_union2(X2,X1,X3),powerset(X2)) ),
inference(rename_variables,[],[i_0_3791]) ).
cnf(i_0_6459,plain,
subset_intersection2(X1,esk159_1(X1),esk160_1(X1)) = subset_intersection2(X1,esk160_1(X1),esk159_1(X1)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_4769,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4814,i_0_4999,i_0_5002,i_0_5003,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5070,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834]) ).
cnf(i_0_6460,plain,
element(esk159_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_4769]) ).
cnf(i_0_6461,plain,
( ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2))
| subset_intersection2(X2,X1,X3) = subset_intersection2(X2,X3,X1) ),
inference(rename_variables,[],[i_0_3834]) ).
cnf(i_0_6462,plain,
subset_union2(X1,esk159_1(X1),esk160_1(X1)) = subset_union2(X1,esk160_1(X1),esk159_1(X1)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_4769,i_0_6460,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4814,i_0_4999,i_0_5002,i_0_5003,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5070,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835]) ).
cnf(i_0_6463,plain,
element(esk159_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_4769]) ).
cnf(i_0_6464,plain,
( ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2))
| subset_union2(X2,X1,X3) = subset_union2(X2,X3,X1) ),
inference(rename_variables,[],[i_0_3835]) ).
cnf(i_0_6465,plain,
~ in(esk443_1(set_union2(esk166_0,unordered_pair(esk166_0,esk166_0))),esk372_2(X1,esk166_0)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_4769,i_0_6460,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4814,i_0_4999,i_0_5002,i_0_5003,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5070,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874]) ).
cnf(i_0_6466,plain,
( in(X1,set_union2(X2,unordered_pair(X2,X2)))
| ~ in(X1,esk372_2(X3,X2))
| ~ ordinal(X2) ),
inference(rename_variables,[],[i_0_3874]) ).
cnf(i_0_6467,plain,
subset_difference(X1,esk160_1(X1),esk160_1(X1)) = set_difference(esk160_1(X1),esk160_1(X1)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_4769,i_0_6460,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4814,i_0_4999,i_0_5002,i_0_5003,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5070,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997]) ).
cnf(i_0_6468,plain,
( ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2))
| subset_difference(X2,X1,X3) = set_difference(X1,X3) ),
inference(rename_variables,[],[i_0_3997]) ).
cnf(i_0_6469,plain,
subset_union2(X1,esk160_1(X1),esk160_1(X1)) = set_union2(esk160_1(X1),esk160_1(X1)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_4769,i_0_6460,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4814,i_0_4999,i_0_5002,i_0_5003,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5070,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998]) ).
cnf(i_0_6470,plain,
( ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2))
| subset_union2(X2,X1,X3) = set_union2(X1,X3) ),
inference(rename_variables,[],[i_0_3998]) ).
cnf(i_0_6471,plain,
~ in(esk443_1(set_union2(esk166_0,unordered_pair(esk166_0,esk166_0))),esk349_1(esk166_0)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_4769,i_0_6460,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4814,i_0_4999,i_0_5002,i_0_5003,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5070,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012]) ).
cnf(i_0_6472,plain,
( in(X1,set_union2(X2,unordered_pair(X2,X2)))
| ~ in(X1,esk349_1(X2))
| ~ ordinal(X2) ),
inference(rename_variables,[],[i_0_4012]) ).
cnf(i_0_6473,plain,
subset_intersection2(X1,esk160_1(X1),esk160_1(X1)) = esk160_1(X1),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_4769,i_0_6460,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4814,i_0_4999,i_0_5002,i_0_5003,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5070,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061]) ).
cnf(i_0_6474,plain,
( ~ element(X1,powerset(X2))
| subset_intersection2(X2,X1,X1) = X1
| ~ element(X3,powerset(X2)) ),
inference(rename_variables,[],[i_0_4061]) ).
cnf(i_0_6475,plain,
subset_union2(X1,esk160_1(X1),esk160_1(X1)) = esk160_1(X1),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_4769,i_0_6460,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4814,i_0_4999,i_0_5002,i_0_5003,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5070,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062]) ).
cnf(i_0_6476,plain,
( ~ element(X1,powerset(X2))
| subset_union2(X2,X1,X1) = X1
| ~ element(X3,powerset(X2)) ),
inference(rename_variables,[],[i_0_4062]) ).
cnf(i_0_6477,plain,
~ in(empty_set,subset_complement(omega,omega)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_4769,i_0_6460,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4814,i_0_4999,i_0_5002,i_0_5003,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5070,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068]) ).
cnf(i_0_6478,plain,
element(X1,powerset(X1)),
inference(rename_variables,[],[i_0_4813]) ).
cnf(i_0_6479,plain,
( ~ element(X1,powerset(X2))
| ~ in(X3,subset_complement(X2,X1))
| ~ in(X3,X1) ),
inference(rename_variables,[],[i_0_4068]) ).
cnf(i_0_6480,plain,
element(interior(esk117_0,esk160_1(the_carrier(esk117_0))),powerset(the_carrier(esk117_0))),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_4769,i_0_6460,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4814,i_0_4999,i_0_5002,i_0_5003,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5070,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071]) ).
cnf(i_0_6481,plain,
element(esk160_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_4768]) ).
cnf(i_0_6482,plain,
( ~ element(X1,powerset(the_carrier(X2)))
| element(interior(X2,X1),powerset(the_carrier(X2)))
| ~ top_str(X2) ),
inference(rename_variables,[],[i_0_4071]) ).
cnf(i_0_6483,plain,
element(topstr_closure(esk117_0,esk160_1(the_carrier(esk117_0))),powerset(the_carrier(esk117_0))),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_4769,i_0_6460,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4814,i_0_4999,i_0_5002,i_0_5003,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5070,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072]) ).
cnf(i_0_6484,plain,
element(esk160_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_4768]) ).
cnf(i_0_6485,plain,
( ~ element(X1,powerset(the_carrier(X2)))
| element(topstr_closure(X2,X1),powerset(the_carrier(X2)))
| ~ top_str(X2) ),
inference(rename_variables,[],[i_0_4072]) ).
cnf(i_0_6486,plain,
~ in(esk74_2(cartesian_product2(empty_set,empty_set),X1),relation_restriction(esk171_0,empty_set)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_4769,i_0_6460,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4814,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5070,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098]) ).
cnf(i_0_6487,plain,
( in(X1,cartesian_product2(X2,X2))
| ~ in(X1,relation_restriction(X3,X2))
| ~ relation(X3) ),
inference(rename_variables,[],[i_0_4098]) ).
cnf(i_0_6488,plain,
in(set_union2(X1,X2),set_union2(unordered_triple(set_union2(X2,X1),X3,X4),unordered_triple(set_union2(X2,X1),X3,X4))),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_4769,i_0_6460,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4814,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5070,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128]) ).
cnf(i_0_6489,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_4878]) ).
cnf(i_0_6490,plain,
( X1 != unordered_triple(X2,X3,X4)
| in(X5,X1)
| X5 != X2 ),
inference(rename_variables,[],[i_0_4128]) ).
cnf(i_0_6491,plain,
in(set_union2(X1,X2),set_union2(unordered_triple(X3,set_union2(X2,X1),X4),unordered_triple(X3,set_union2(X2,X1),X4))),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_4769,i_0_6460,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4814,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5070,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129]) ).
cnf(i_0_6492,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_4878]) ).
cnf(i_0_6493,plain,
( X1 != unordered_triple(X2,X3,X4)
| in(X5,X1)
| X5 != X3 ),
inference(rename_variables,[],[i_0_4129]) ).
cnf(i_0_6494,plain,
in(set_union2(X1,X2),set_union2(unordered_triple(X3,X4,set_union2(X2,X1)),unordered_triple(X3,X4,set_union2(X2,X1)))),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_4769,i_0_6460,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4814,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5070,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130]) ).
cnf(i_0_6495,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_4878]) ).
cnf(i_0_6496,plain,
( X1 != unordered_triple(X2,X3,X4)
| in(X5,X1)
| X5 != X4 ),
inference(rename_variables,[],[i_0_4130]) ).
cnf(i_0_6497,plain,
~ in(esk432_2(X1,empty_set),set_union2(set_difference(X2,set_difference(X2,empty_set)),set_difference(X2,set_difference(X2,empty_set)))),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_4769,i_0_6460,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4814,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5070,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141]) ).
cnf(i_0_6498,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_4878]) ).
cnf(i_0_6499,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6500,plain,
( X1 != set_difference(X2,set_difference(X2,X3))
| ~ in(X4,X1)
| in(X4,X3) ),
inference(rename_variables,[],[i_0_4141]) ).
cnf(i_0_6501,plain,
subset(interior(esk117_0,esk160_1(the_carrier(esk117_0))),esk160_1(the_carrier(esk117_0))),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_4769,i_0_6460,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4814,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5070,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147]) ).
cnf(i_0_6502,plain,
element(esk160_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_4768]) ).
cnf(i_0_6503,plain,
( ~ element(X1,powerset(the_carrier(X2)))
| subset(interior(X2,X1),X1)
| ~ top_str(X2) ),
inference(rename_variables,[],[i_0_4147]) ).
cnf(i_0_6504,plain,
subset(esk160_1(the_carrier(esk117_0)),topstr_closure(esk117_0,esk160_1(the_carrier(esk117_0)))),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_4769,i_0_6460,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4814,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5070,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148]) ).
cnf(i_0_6505,plain,
element(esk160_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_4768]) ).
cnf(i_0_6506,plain,
( ~ element(X1,powerset(the_carrier(X2)))
| subset(X1,topstr_closure(X2,X1))
| ~ top_str(X2) ),
inference(rename_variables,[],[i_0_4148]) ).
cnf(i_0_6507,plain,
in(set_union2(esk166_0,unordered_pair(esk166_0,esk166_0)),esk444_2(set_union2(esk166_0,unordered_pair(esk166_0,esk166_0)),set_union2(esk166_0,unordered_pair(esk166_0,esk166_0)))),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_4769,i_0_6460,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4814,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5070,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165]) ).
cnf(i_0_6508,plain,
in(X1,esk443_1(X1)),
inference(rename_variables,[],[i_0_4814]) ).
cnf(i_0_6509,plain,
subset(X1,X1),
inference(rename_variables,[],[i_0_4880]) ).
cnf(i_0_6510,plain,
( ~ in(X1,esk443_1(X2))
| in(X3,esk444_2(X2,X1))
| ~ subset(X3,X1) ),
inference(rename_variables,[],[i_0_4165]) ).
cnf(i_0_6511,plain,
~ in(esk166_0,esk160_1(esk156_0)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_4769,i_0_6460,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4814,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5070,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330]) ).
cnf(i_0_6512,plain,
element(esk160_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_4768]) ).
cnf(i_0_6513,plain,
( ~ element(X1,powerset(X2))
| element(X3,X2)
| ~ in(X3,X1) ),
inference(rename_variables,[],[i_0_4330]) ).
cnf(i_0_6514,plain,
~ in(X1,esk160_1(empty_set)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_4769,i_0_6460,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4814,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5070,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331]) ).
cnf(i_0_6515,plain,
element(esk160_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_4768]) ).
cnf(i_0_6516,plain,
( ~ element(X1,powerset(X2))
| ~ in(X3,X1)
| in(X3,X2) ),
inference(rename_variables,[],[i_0_4331]) ).
cnf(i_0_6517,plain,
~ in(empty_set,set_union2(set_difference(X1,omega),set_difference(X1,omega))),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_4769,i_0_6460,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4814,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5070,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332]) ).
cnf(i_0_6518,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_4878]) ).
cnf(i_0_6519,plain,
( X1 != set_difference(X2,X3)
| ~ in(X4,X3)
| ~ in(X4,X1) ),
inference(rename_variables,[],[i_0_4332]) ).
cnf(i_0_6520,plain,
~ in(esk409_1(esk443_1(X1)),X1),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_4769,i_0_6460,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4814,i_0_6508,i_0_4815,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5070,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340]) ).
cnf(i_0_6521,plain,
in(X1,esk409_1(X1)),
inference(rename_variables,[],[i_0_4815]) ).
cnf(i_0_6522,plain,
( ~ in(X1,X2)
| ~ in(X2,X3)
| ~ in(X3,X1) ),
inference(rename_variables,[],[i_0_4340]) ).
cnf(i_0_6523,plain,
~ in(X1,esk160_1(esk156_0)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_4769,i_0_6460,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4814,i_0_6508,i_0_4815,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5070,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369]) ).
cnf(i_0_6524,plain,
element(esk160_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_4768]) ).
cnf(i_0_6525,plain,
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X3,X1) ),
inference(rename_variables,[],[i_0_4369]) ).
cnf(i_0_6526,plain,
~ in(X1,set_union2(set_difference(empty_set,X2),set_difference(empty_set,X2))),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_4769,i_0_6460,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4814,i_0_6508,i_0_4815,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5070,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389]) ).
cnf(i_0_6527,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_4878]) ).
cnf(i_0_6528,plain,
( X1 != set_difference(X2,X3)
| in(X4,X2)
| ~ in(X4,X1) ),
inference(rename_variables,[],[i_0_4389]) ).
cnf(i_0_6529,plain,
~ in(esk409_1(esk443_1(set_union2(set_union2(X1,X2),set_union2(X1,X2)))),X1),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_4769,i_0_6460,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4814,i_0_6508,i_0_4815,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5070,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390]) ).
cnf(i_0_6530,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_4878]) ).
cnf(i_0_6531,plain,
( X1 != set_union2(X2,X3)
| in(X4,X1)
| ~ in(X4,X2) ),
inference(rename_variables,[],[i_0_4390]) ).
cnf(i_0_6532,plain,
~ in(esk409_1(esk443_1(set_union2(set_union2(X1,X2),set_union2(X1,X2)))),X2),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_4769,i_0_6460,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4814,i_0_6508,i_0_4815,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5070,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391]) ).
cnf(i_0_6533,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_4878]) ).
cnf(i_0_6534,plain,
( X1 != set_union2(X2,X3)
| in(X4,X1)
| ~ in(X4,X3) ),
inference(rename_variables,[],[i_0_4391]) ).
cnf(i_0_6535,plain,
~ subset(omega,empty_set),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_4769,i_0_6460,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4814,i_0_6508,i_0_4815,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5070,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407]) ).
cnf(i_0_6536,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6537,plain,
( ~ in(X1,X2)
| in(X1,X3)
| ~ subset(X2,X3) ),
inference(rename_variables,[],[i_0_4407]) ).
cnf(i_0_6538,plain,
esk160_1(X1) = X1,
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_4769,i_0_6460,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5070,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426]) ).
cnf(i_0_6539,plain,
~ proper_element(esk160_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_4584]) ).
cnf(i_0_6540,plain,
( proper_element(X1,powerset(X2))
| ~ element(X1,powerset(X2))
| X1 = X2 ),
inference(rename_variables,[],[i_0_4426]) ).
cnf(i_0_6541,plain,
~ in(unordered_pair(X1,X1),set_union2(unordered_pair(empty_set,empty_set),unordered_pair(empty_set,empty_set))),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_4769,i_0_6460,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5070,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477]) ).
cnf(i_0_6542,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_4878]) ).
cnf(i_0_6543,plain,
( X1 != unordered_pair(X2,X2)
| ~ in(X3,X1)
| X3 = X2 ),
inference(rename_variables,[],[i_0_4477]) ).
cnf(i_0_6544,plain,
X1 = set_difference(X1,empty_set),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_4769,i_0_6460,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5070,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485]) ).
cnf(i_0_6545,plain,
subset(set_difference(X1,X2),X1),
inference(rename_variables,[],[i_0_4603]) ).
cnf(i_0_6546,plain,
( ~ subset(X1,X2)
| ~ subset(X2,X1)
| X1 = X2 ),
inference(rename_variables,[],[i_0_4485]) ).
cnf(i_0_6547,plain,
~ in(omega,set_union2(powerset(empty_set),powerset(empty_set))),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_4769,i_0_6460,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5070,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508]) ).
cnf(i_0_6548,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_4878]) ).
cnf(i_0_6549,plain,
( X1 != powerset(X2)
| subset(X3,X2)
| ~ in(X3,X1) ),
inference(rename_variables,[],[i_0_4508]) ).
cnf(i_0_6550,plain,
subset(esk123_1(esk166_0),esk166_0),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_4769,i_0_6460,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5042,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5070,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540]) ).
cnf(i_0_6551,plain,
( ~ epsilon_transitive(X1)
| ~ in(X2,X1)
| subset(X2,X1) ),
inference(rename_variables,[],[i_0_4540]) ).
cnf(i_0_6552,plain,
finite(esk160_1(esk140_0)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_4769,i_0_6460,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5034,i_0_5042,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5070,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551]) ).
cnf(i_0_6553,plain,
element(esk160_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_4768]) ).
cnf(i_0_6554,plain,
( ~ element(X1,powerset(X2))
| finite(X1)
| ~ finite(X2) ),
inference(rename_variables,[],[i_0_4551]) ).
cnf(i_0_6555,plain,
v5_membered(esk160_1(esk143_0)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_4769,i_0_6460,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5034,i_0_5042,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5070,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552]) ).
cnf(i_0_6556,plain,
element(esk160_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_4768]) ).
cnf(i_0_6557,plain,
( ~ element(X1,powerset(X2))
| ~ v5_membered(X2)
| v5_membered(X1) ),
inference(rename_variables,[],[i_0_4552]) ).
cnf(i_0_6558,plain,
v4_membered(esk160_1(esk143_0)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_4769,i_0_6460,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5034,i_0_5042,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5070,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553]) ).
cnf(i_0_6559,plain,
element(esk160_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_4768]) ).
cnf(i_0_6560,plain,
( ~ element(X1,powerset(X2))
| ~ v5_membered(X2)
| v4_membered(X1) ),
inference(rename_variables,[],[i_0_4553]) ).
cnf(i_0_6561,plain,
v4_membered(esk159_1(esk143_0)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_4769,i_0_6460,i_0_6463,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5034,i_0_5042,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554]) ).
cnf(i_0_6562,plain,
element(esk159_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_4769]) ).
cnf(i_0_6563,plain,
( ~ element(X1,powerset(X2))
| ~ v4_membered(X2)
| v4_membered(X1) ),
inference(rename_variables,[],[i_0_4554]) ).
cnf(i_0_6564,plain,
v3_membered(esk160_1(esk143_0)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_4769,i_0_6460,i_0_6463,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5034,i_0_5042,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555]) ).
cnf(i_0_6565,plain,
element(esk160_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_4768]) ).
cnf(i_0_6566,plain,
( ~ element(X1,powerset(X2))
| ~ v5_membered(X2)
| v3_membered(X1) ),
inference(rename_variables,[],[i_0_4555]) ).
cnf(i_0_6567,plain,
v3_membered(esk159_1(esk143_0)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5034,i_0_5042,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556]) ).
cnf(i_0_6568,plain,
element(esk159_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_4769]) ).
cnf(i_0_6569,plain,
( ~ element(X1,powerset(X2))
| ~ v4_membered(X2)
| v3_membered(X1) ),
inference(rename_variables,[],[i_0_4556]) ).
cnf(i_0_6570,plain,
v3_membered(esk152_1(esk143_0)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_4770,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5034,i_0_5042,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557]) ).
cnf(i_0_6571,plain,
element(esk152_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_4770]) ).
cnf(i_0_6572,plain,
( ~ element(X1,powerset(X2))
| ~ v3_membered(X2)
| v3_membered(X1) ),
inference(rename_variables,[],[i_0_4557]) ).
cnf(i_0_6573,plain,
v2_membered(esk160_1(esk143_0)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_4770,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5034,i_0_5042,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558]) ).
cnf(i_0_6574,plain,
element(esk160_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_4768]) ).
cnf(i_0_6575,plain,
( ~ element(X1,powerset(X2))
| ~ v5_membered(X2)
| v2_membered(X1) ),
inference(rename_variables,[],[i_0_4558]) ).
cnf(i_0_6576,plain,
v2_membered(esk159_1(esk143_0)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_4770,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5034,i_0_5042,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559]) ).
cnf(i_0_6577,plain,
element(esk159_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_4769]) ).
cnf(i_0_6578,plain,
( ~ element(X1,powerset(X2))
| ~ v4_membered(X2)
| v2_membered(X1) ),
inference(rename_variables,[],[i_0_4559]) ).
cnf(i_0_6579,plain,
v2_membered(esk152_1(esk143_0)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_4770,i_0_6571,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5034,i_0_5042,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560]) ).
cnf(i_0_6580,plain,
element(esk152_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_4770]) ).
cnf(i_0_6581,plain,
( ~ element(X1,powerset(X2))
| ~ v3_membered(X2)
| v2_membered(X1) ),
inference(rename_variables,[],[i_0_4560]) ).
cnf(i_0_6582,plain,
v2_membered(esk123_1(powerset(esk143_0))),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_4770,i_0_6571,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5034,i_0_5042,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561]) ).
cnf(i_0_6583,plain,
element(esk123_1(X1),X1),
inference(rename_variables,[],[i_0_4812]) ).
cnf(i_0_6584,plain,
( ~ element(X1,powerset(X2))
| ~ v2_membered(X2)
| v2_membered(X1) ),
inference(rename_variables,[],[i_0_4561]) ).
cnf(i_0_6585,plain,
v1_membered(esk160_1(esk143_0)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_4770,i_0_6571,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5034,i_0_5042,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562]) ).
cnf(i_0_6586,plain,
element(esk160_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_4768]) ).
cnf(i_0_6587,plain,
( ~ element(X1,powerset(X2))
| ~ v5_membered(X2)
| v1_membered(X1) ),
inference(rename_variables,[],[i_0_4562]) ).
cnf(i_0_6588,plain,
v1_membered(esk159_1(esk143_0)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5034,i_0_5042,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563]) ).
cnf(i_0_6589,plain,
element(esk159_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_4769]) ).
cnf(i_0_6590,plain,
( ~ element(X1,powerset(X2))
| ~ v4_membered(X2)
| v1_membered(X1) ),
inference(rename_variables,[],[i_0_4563]) ).
cnf(i_0_6591,plain,
v1_membered(esk152_1(esk143_0)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5034,i_0_5042,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564]) ).
cnf(i_0_6592,plain,
element(esk152_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_4770]) ).
cnf(i_0_6593,plain,
( ~ element(X1,powerset(X2))
| ~ v3_membered(X2)
| v1_membered(X1) ),
inference(rename_variables,[],[i_0_4564]) ).
cnf(i_0_6594,plain,
v1_membered(esk123_1(powerset(esk143_0))),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5034,i_0_5042,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565]) ).
cnf(i_0_6595,plain,
element(esk123_1(X1),X1),
inference(rename_variables,[],[i_0_4812]) ).
cnf(i_0_6596,plain,
( ~ element(X1,powerset(X2))
| ~ v2_membered(X2)
| v1_membered(X1) ),
inference(rename_variables,[],[i_0_4565]) ).
cnf(i_0_6597,plain,
v1_membered(meet_of_subsets(esk143_0,esk160_1(powerset(esk143_0)))),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5034,i_0_5042,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566]) ).
cnf(i_0_6598,plain,
( ~ element(X1,powerset(X2))
| v1_membered(X1)
| ~ v1_membered(X2) ),
inference(rename_variables,[],[i_0_4566]) ).
cnf(i_0_6599,plain,
element(esk156_0,esk156_0),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5034,i_0_5042,i_0_5049,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754]) ).
cnf(i_0_6600,plain,
( ~ empty(X1)
| ~ empty(X2)
| element(X1,X2) ),
inference(rename_variables,[],[i_0_4754]) ).
cnf(i_0_6601,plain,
natural(esk156_0),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828]) ).
cnf(i_0_6602,plain,
( ~ empty(X1)
| ~ ordinal(X1)
| natural(X1) ),
inference(rename_variables,[],[i_0_4828]) ).
cnf(i_0_6603,plain,
relation_rng(esk405_1(empty_set)) = empty_set,
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4921,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4938,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830]) ).
cnf(i_0_6604,plain,
relation_dom(esk405_1(X1)) = X1,
inference(rename_variables,[],[i_0_4921]) ).
cnf(i_0_6605,plain,
relation(esk405_1(X1)),
inference(rename_variables,[],[i_0_4938]) ).
cnf(i_0_6606,plain,
( relation_dom(X1) != empty_set
| relation_rng(X1) = empty_set
| ~ relation(X1) ),
inference(rename_variables,[],[i_0_4830]) ).
cnf(i_0_6607,plain,
identity_relation(empty_set) = empty_set,
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4920,i_0_4921,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4938,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870]) ).
cnf(i_0_6608,plain,
relation_rng(identity_relation(X1)) = X1,
inference(rename_variables,[],[i_0_4920]) ).
cnf(i_0_6609,plain,
relation(identity_relation(X1)),
inference(rename_variables,[],[i_0_4945]) ).
cnf(i_0_6610,plain,
( relation_rng(X1) != empty_set
| X1 = empty_set
| ~ relation(X1) ),
inference(rename_variables,[],[i_0_4870]) ).
cnf(i_0_6611,plain,
esk405_1(empty_set) = empty_set,
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871]) ).
cnf(i_0_6612,plain,
relation_dom(esk405_1(X1)) = X1,
inference(rename_variables,[],[i_0_4921]) ).
cnf(i_0_6613,plain,
relation(esk405_1(X1)),
inference(rename_variables,[],[i_0_4938]) ).
cnf(i_0_6614,plain,
( relation_dom(X1) != empty_set
| X1 = empty_set
| ~ relation(X1) ),
inference(rename_variables,[],[i_0_4871]) ).
cnf(i_0_6615,plain,
unordered_pair(X1,X1) != set_meet(set_union2(empty_set,empty_set)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890]) ).
cnf(i_0_6616,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_4878]) ).
cnf(i_0_6617,plain,
( X1 != empty_set
| X2 = empty_set
| X2 != set_meet(X1) ),
inference(rename_variables,[],[i_0_4890]) ).
cnf(i_0_6618,plain,
set_union2(empty_set,empty_set) = set_meet(set_union2(empty_set,empty_set)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973]) ).
cnf(i_0_6619,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_4878]) ).
cnf(i_0_6620,plain,
( X1 != empty_set
| X2 != empty_set
| X1 = set_meet(X2) ),
inference(rename_variables,[],[i_0_4973]) ).
cnf(i_0_6621,plain,
~ in(X1,relation_image(empty_set,X2)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5019,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861]) ).
cnf(i_0_6622,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6623,plain,
( in(unordered_pair(unordered_pair(esk16_4(X1,X2,relation_image(X1,X2),X3),X3),unordered_pair(esk16_4(X1,X2,relation_image(X1,X2),X3),esk16_4(X1,X2,relation_image(X1,X2),X3))),X1)
| ~ relation(X1)
| ~ in(X3,relation_image(X1,X2)) ),
inference(rename_variables,[],[i_0_5861]) ).
cnf(i_0_6624,plain,
~ in(X1,relation_inverse_image(empty_set,X2)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5019,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925]) ).
cnf(i_0_6625,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6626,plain,
( in(unordered_pair(unordered_pair(X1,esk19_4(X2,X3,relation_inverse_image(X2,X3),X1)),unordered_pair(X1,X1)),X2)
| ~ relation(X2)
| ~ in(X1,relation_inverse_image(X2,X3)) ),
inference(rename_variables,[],[i_0_5925]) ).
cnf(i_0_6627,plain,
~ in(X1,relation_rng(empty_set)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5019,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931]) ).
cnf(i_0_6628,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6629,plain,
( in(unordered_pair(unordered_pair(esk92_3(X1,relation_rng(X1),X2),X2),unordered_pair(esk92_3(X1,relation_rng(X1),X2),esk92_3(X1,relation_rng(X1),X2))),X1)
| ~ relation(X1)
| ~ in(X2,relation_rng(X1)) ),
inference(rename_variables,[],[i_0_5931]) ).
cnf(i_0_6630,plain,
~ in(X1,relation_dom(empty_set)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5019,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019]) ).
cnf(i_0_6631,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6632,plain,
( in(unordered_pair(unordered_pair(X1,esk78_3(X2,relation_dom(X2),X1)),unordered_pair(X1,X1)),X2)
| ~ relation(X2)
| ~ in(X1,relation_dom(X2)) ),
inference(rename_variables,[],[i_0_6019]) ).
cnf(i_0_6633,plain,
~ in(X1,relation_inverse_image(esk171_0,empty_set)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5019,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026]) ).
cnf(i_0_6634,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6635,plain,
( ~ relation(X1)
| in(esk19_4(X1,X2,relation_inverse_image(X1,X2),X3),X2)
| ~ in(X3,relation_inverse_image(X1,X2)) ),
inference(rename_variables,[],[i_0_6026]) ).
cnf(i_0_6636,plain,
~ in(X1,relation_image(esk171_0,empty_set)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5019,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027]) ).
cnf(i_0_6637,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6638,plain,
( ~ relation(X1)
| in(esk16_4(X1,X2,relation_image(X1,X2),X3),X2)
| ~ in(X3,relation_image(X1,X2)) ),
inference(rename_variables,[],[i_0_6027]) ).
cnf(i_0_6639,plain,
~ in(X1,fiber(empty_set,X2)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5019,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141]) ).
cnf(i_0_6640,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6641,plain,
( in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3)
| ~ relation(X3)
| ~ in(X1,fiber(X3,X2)) ),
inference(rename_variables,[],[i_0_6141]) ).
cnf(i_0_6642,plain,
in(set_union2(X1,X2),unordered_triple(set_union2(X2,X1),X3,X4)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5019,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180]) ).
cnf(i_0_6643,plain,
( ~ in(X1,set_union2(X2,X3))
| in(X1,X2)
| in(X1,X3) ),
inference(rename_variables,[],[i_0_6180]) ).
cnf(i_0_6644,plain,
in(set_union2(set_union2(X1,X2),set_union2(X1,X2)),set_difference(esk443_1(set_union2(set_union2(X1,X2),set_union2(X1,X2))),empty_set)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5019,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181]) ).
cnf(i_0_6645,plain,
in(X1,esk443_1(X1)),
inference(rename_variables,[],[i_0_4814]) ).
cnf(i_0_6646,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6647,plain,
( ~ in(X1,X2)
| in(X1,X3)
| in(X1,set_difference(X2,X3)) ),
inference(rename_variables,[],[i_0_6181]) ).
cnf(i_0_6648,plain,
~ in(esk409_1(esk443_1(set_union2(set_union2(union(esk166_0),X1),set_union2(union(esk166_0),X1)))),esk123_1(esk166_0)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5019,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188]) ).
cnf(i_0_6649,plain,
( ~ in(X1,X2)
| in(X3,union(X2))
| ~ in(X3,X1) ),
inference(rename_variables,[],[i_0_6188]) ).
cnf(i_0_6650,plain,
esk49_1(unordered_pair(X1,X1)) = X1,
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5019,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207]) ).
cnf(i_0_6651,plain,
( ~ in(X1,unordered_pair(X2,X3))
| X1 = X2
| X1 = X3 ),
inference(rename_variables,[],[i_0_6207]) ).
cnf(i_0_6652,plain,
unordered_pair(X1,X1) != set_union2(empty_set,empty_set),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5019,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094]) ).
cnf(i_0_6653,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_4878]) ).
cnf(i_0_6654,plain,
esk156_0 != esk166_0,
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5008,i_0_5019,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690]) ).
cnf(i_0_6655,plain,
one_to_one(set_difference(esk164_0,empty_set)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5019,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691]) ).
cnf(i_0_6656,plain,
~ subset(set_union2(omega,omega),empty_set),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5019,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698]) ).
cnf(i_0_6657,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_4878]) ).
cnf(i_0_6658,plain,
~ subset(omega,set_union2(empty_set,empty_set)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5019,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699]) ).
cnf(i_0_6659,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_4878]) ).
cnf(i_0_6660,plain,
~ epred2_3(set_union2(empty_set,empty_set),X1,unordered_pair(X2,X2)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5019,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700]) ).
cnf(i_0_6661,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_4878]) ).
cnf(i_0_6662,plain,
~ epred2_3(X1,set_union2(empty_set,empty_set),unordered_pair(X2,X2)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5019,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701]) ).
cnf(i_0_6663,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_4878]) ).
cnf(i_0_6664,plain,
~ epred2_3(empty_set,X1,set_union2(unordered_pair(X2,X2),unordered_pair(X2,X2))),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5019,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702]) ).
cnf(i_0_6665,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_4878]) ).
cnf(i_0_6666,plain,
ordinal(set_union2(empty_set,empty_set)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5019,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703]) ).
cnf(i_0_6667,plain,
~ in(set_union2(esk443_1(set_union2(esk166_0,unordered_pair(esk166_0,esk166_0))),esk443_1(set_union2(esk166_0,unordered_pair(esk166_0,esk166_0)))),set_union2(esk166_0,unordered_pair(esk166_0,esk166_0))),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5019,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708]) ).
cnf(i_0_6668,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_4878]) ).
cnf(i_0_6669,plain,
~ in(esk443_1(set_union2(esk166_0,unordered_pair(esk166_0,esk166_0))),set_union2(set_union2(esk166_0,unordered_pair(esk166_0,esk166_0)),set_union2(esk166_0,unordered_pair(esk166_0,esk166_0)))),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5019,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709]) ).
cnf(i_0_6670,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_4878]) ).
cnf(i_0_6671,plain,
transitive(empty_set),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5019,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4934,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723]) ).
cnf(i_0_6672,plain,
transitive(identity_relation(X1)),
inference(rename_variables,[],[i_0_4934]) ).
cnf(i_0_6673,plain,
relation(set_difference(esk164_0,empty_set)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4934,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726]) ).
cnf(i_0_6674,plain,
antisymmetric(empty_set),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4926,i_0_4934,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727]) ).
cnf(i_0_6675,plain,
antisymmetric(identity_relation(X1)),
inference(rename_variables,[],[i_0_4926]) ).
cnf(i_0_6676,plain,
reflexive(empty_set),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740]) ).
cnf(i_0_6677,plain,
reflexive(identity_relation(X1)),
inference(rename_variables,[],[i_0_4931]) ).
cnf(i_0_6678,plain,
function(set_difference(esk164_0,empty_set)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744]) ).
cnf(i_0_6679,plain,
~ proper_element(set_union2(esk160_1(X1),esk160_1(X1)),powerset(X1)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_6539,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821]) ).
cnf(i_0_6680,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_4878]) ).
cnf(i_0_6681,plain,
~ proper_element(esk160_1(X1),set_union2(powerset(X1),powerset(X1))),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_6539,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822]) ).
cnf(i_0_6682,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_4878]) ).
cnf(i_0_6683,plain,
~ proper_subset(set_union2(X1,X1),X1),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_6539,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823]) ).
cnf(i_0_6684,plain,
~ proper_subset(X1,X1),
inference(rename_variables,[],[i_0_4797]) ).
cnf(i_0_6685,plain,
~ proper_subset(X1,set_union2(X1,X1)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_6539,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824]) ).
cnf(i_0_6686,plain,
~ proper_subset(X1,X1),
inference(rename_variables,[],[i_0_4797]) ).
cnf(i_0_6687,plain,
relation_empty_yielding(set_union2(empty_set,empty_set)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_6539,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829]) ).
cnf(i_0_6688,plain,
symmetric(empty_set),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_6539,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837]) ).
cnf(i_0_6689,plain,
symmetric(identity_relation(X1)),
inference(rename_variables,[],[i_0_4936]) ).
cnf(i_0_6690,plain,
is_transitive_in(empty_set,X1),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_6539,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016]) ).
cnf(i_0_6691,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6692,plain,
( in(unordered_pair(unordered_pair(esk111_2(X1,X2),esk112_2(X1,X2)),unordered_pair(esk111_2(X1,X2),esk111_2(X1,X2))),X1)
| ~ relation(X1)
| is_transitive_in(X1,X2) ),
inference(rename_variables,[],[i_0_3016]) ).
cnf(i_0_6693,plain,
is_antisymmetric_in(empty_set,X1),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_6539,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018]) ).
cnf(i_0_6694,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6695,plain,
( in(unordered_pair(unordered_pair(esk82_2(X1,X2),esk81_2(X1,X2)),unordered_pair(esk82_2(X1,X2),esk82_2(X1,X2))),X1)
| ~ relation(X1)
| is_antisymmetric_in(X1,X2) ),
inference(rename_variables,[],[i_0_3018]) ).
cnf(i_0_6696,plain,
~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),relation_composition(identity_relation(X3),empty_set)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6222,i_0_4393,i_0_4584,i_0_6539,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145]) ).
cnf(i_0_6697,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6698,plain,
( in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),relation_composition(identity_relation(X4),X3))
| ~ relation(X3) ),
inference(rename_variables,[],[i_0_3145]) ).
cnf(i_0_6699,plain,
relation_of2_as_subset(identity_relation(X1),X1,relation_rng(identity_relation(X1))),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6222,i_0_4393,i_0_4584,i_0_6539,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836]) ).
cnf(i_0_6700,plain,
subset(X1,X1),
inference(rename_variables,[],[i_0_4880]) ).
cnf(i_0_6701,plain,
( ~ subset(relation_rng(X1),X2)
| relation_of2_as_subset(X1,X3,X2)
| ~ relation_of2_as_subset(X1,X3,X4) ),
inference(rename_variables,[],[i_0_3836]) ).
cnf(i_0_6702,plain,
relation_of2_as_subset(identity_relation(empty_set),empty_set,X1),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6222,i_0_4393,i_0_4887,i_0_4584,i_0_6539,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869]) ).
cnf(i_0_6703,plain,
relation_of2_as_subset(identity_relation(X1),X1,X1),
inference(rename_variables,[],[i_0_4393]) ).
cnf(i_0_6704,plain,
( ~ subset(X1,X2)
| relation_of2_as_subset(X3,X4,X2)
| ~ relation_of2_as_subset(X3,X4,X1) ),
inference(rename_variables,[],[i_0_3869]) ).
cnf(i_0_6705,plain,
is_reflexive_in(esk171_0,empty_set),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6222,i_0_4393,i_0_4887,i_0_4584,i_0_6539,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371]) ).
cnf(i_0_6706,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6707,plain,
( in(esk40_2(X1,X2),X2)
| is_reflexive_in(X1,X2)
| ~ relation(X1) ),
inference(rename_variables,[],[i_0_4371]) ).
cnf(i_0_6708,plain,
is_transitive_in(esk171_0,empty_set),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6222,i_0_4393,i_0_4887,i_0_4584,i_0_6539,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372]) ).
cnf(i_0_6709,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6710,plain,
( in(esk112_2(X1,X2),X2)
| is_transitive_in(X1,X2)
| ~ relation(X1) ),
inference(rename_variables,[],[i_0_4372]) ).
cnf(i_0_6711,plain,
is_transitive_in(esk171_0,esk160_1(esk156_0)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6222,i_0_4393,i_0_4887,i_0_4584,i_0_6539,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373]) ).
cnf(i_0_6712,plain,
( in(esk111_2(X1,X2),X2)
| is_transitive_in(X1,X2)
| ~ relation(X1) ),
inference(rename_variables,[],[i_0_4373]) ).
cnf(i_0_6713,plain,
is_transitive_in(esk171_0,relation_image(empty_set,X1)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6222,i_0_4393,i_0_4887,i_0_4584,i_0_6539,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374]) ).
cnf(i_0_6714,plain,
( in(esk110_2(X1,X2),X2)
| is_transitive_in(X1,X2)
| ~ relation(X1) ),
inference(rename_variables,[],[i_0_4374]) ).
cnf(i_0_6715,plain,
is_connected_in(esk171_0,empty_set),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6222,i_0_4393,i_0_4887,i_0_4584,i_0_6539,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375]) ).
cnf(i_0_6716,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6717,plain,
( in(esk96_2(X1,X2),X2)
| is_connected_in(X1,X2)
| ~ relation(X1) ),
inference(rename_variables,[],[i_0_4375]) ).
cnf(i_0_6718,plain,
is_connected_in(esk171_0,relation_inverse_image(empty_set,X1)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6222,i_0_4393,i_0_4887,i_0_4584,i_0_6539,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376]) ).
cnf(i_0_6719,plain,
( in(esk95_2(X1,X2),X2)
| is_connected_in(X1,X2)
| ~ relation(X1) ),
inference(rename_variables,[],[i_0_4376]) ).
cnf(i_0_6720,plain,
is_antisymmetric_in(esk171_0,empty_set),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6222,i_0_4393,i_0_4887,i_0_4584,i_0_6539,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377]) ).
cnf(i_0_6721,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6722,plain,
( in(esk82_2(X1,X2),X2)
| is_antisymmetric_in(X1,X2)
| ~ relation(X1) ),
inference(rename_variables,[],[i_0_4377]) ).
cnf(i_0_6723,plain,
is_antisymmetric_in(esk171_0,relation_rng(empty_set)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6222,i_0_4393,i_0_4887,i_0_4584,i_0_6539,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378]) ).
cnf(i_0_6724,plain,
( in(esk81_2(X1,X2),X2)
| is_antisymmetric_in(X1,X2)
| ~ relation(X1) ),
inference(rename_variables,[],[i_0_4378]) ).
cnf(i_0_6725,plain,
~ subset(omega,set_difference(empty_set,X1)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6222,i_0_4393,i_0_4887,i_0_4584,i_0_6539,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_6545,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406]) ).
cnf(i_0_6726,plain,
subset(set_difference(X1,X2),X1),
inference(rename_variables,[],[i_0_4603]) ).
cnf(i_0_6727,plain,
( ~ subset(X1,X2)
| subset(X3,X2)
| ~ subset(X3,X1) ),
inference(rename_variables,[],[i_0_4406]) ).
cnf(i_0_6728,plain,
~ subset(unordered_pair(X1,X1),empty_set),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4881,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6222,i_0_4393,i_0_4887,i_0_4584,i_0_6539,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_6545,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509]) ).
cnf(i_0_6729,plain,
( X1 != powerset(X2)
| in(X3,X1)
| ~ subset(X3,X2) ),
inference(rename_variables,[],[i_0_4509]) ).
cnf(i_0_6730,plain,
is_well_founded_in(esk418_1(X1),X1),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4881,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6222,i_0_4393,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_6545,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535]) ).
cnf(i_0_6731,plain,
well_orders(esk418_1(X1),X1),
inference(rename_variables,[],[i_0_4811]) ).
cnf(i_0_6732,plain,
( ~ well_orders(X1,X2)
| ~ relation(X1)
| is_well_founded_in(X1,X2) ),
inference(rename_variables,[],[i_0_4535]) ).
cnf(i_0_6733,plain,
is_reflexive_in(esk418_1(X1),X1),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4881,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6222,i_0_4393,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_6545,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536]) ).
cnf(i_0_6734,plain,
well_orders(esk418_1(X1),X1),
inference(rename_variables,[],[i_0_4811]) ).
cnf(i_0_6735,plain,
( ~ well_orders(X1,X2)
| ~ relation(X1)
| is_reflexive_in(X1,X2) ),
inference(rename_variables,[],[i_0_4536]) ).
cnf(i_0_6736,plain,
is_transitive_in(esk418_1(X1),X1),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4881,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6222,i_0_4393,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_6545,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537]) ).
cnf(i_0_6737,plain,
well_orders(esk418_1(X1),X1),
inference(rename_variables,[],[i_0_4811]) ).
cnf(i_0_6738,plain,
( ~ well_orders(X1,X2)
| ~ relation(X1)
| is_transitive_in(X1,X2) ),
inference(rename_variables,[],[i_0_4537]) ).
cnf(i_0_6739,plain,
is_connected_in(esk418_1(X1),X1),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4881,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6222,i_0_4393,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_6545,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538]) ).
cnf(i_0_6740,plain,
well_orders(esk418_1(X1),X1),
inference(rename_variables,[],[i_0_4811]) ).
cnf(i_0_6741,plain,
( ~ well_orders(X1,X2)
| ~ relation(X1)
| is_connected_in(X1,X2) ),
inference(rename_variables,[],[i_0_4538]) ).
cnf(i_0_6742,plain,
is_antisymmetric_in(esk418_1(X1),X1),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4881,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6222,i_0_4393,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_6545,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539]) ).
cnf(i_0_6743,plain,
well_orders(esk418_1(X1),X1),
inference(rename_variables,[],[i_0_4811]) ).
cnf(i_0_6744,plain,
( ~ well_orders(X1,X2)
| ~ relation(X1)
| is_antisymmetric_in(X1,X2) ),
inference(rename_variables,[],[i_0_4539]) ).
cnf(i_0_6745,plain,
being_limit_ordinal(empty_set),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4881,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6222,i_0_4393,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_6545,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5042,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705]) ).
cnf(i_0_6746,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6747,plain,
( in(esk427_1(X1),X1)
| being_limit_ordinal(X1)
| ~ ordinal(X1) ),
inference(rename_variables,[],[i_0_4705]) ).
cnf(i_0_6748,plain,
epsilon_connected(set_union2(empty_set,empty_set)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4881,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6222,i_0_4393,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_6545,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5040,i_0_5042,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807]) ).
cnf(i_0_6749,plain,
epsilon_transitive(set_union2(empty_set,empty_set)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4881,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6222,i_0_4393,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_6545,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808]) ).
cnf(i_0_6750,plain,
v5_membered(set_union2(empty_set,empty_set)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4881,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6222,i_0_4393,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_6545,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809]) ).
cnf(i_0_6751,plain,
v4_membered(set_union2(empty_set,empty_set)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4881,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6222,i_0_4393,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_6545,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810]) ).
cnf(i_0_6752,plain,
v3_membered(set_union2(empty_set,empty_set)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4881,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6222,i_0_4393,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_6545,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5075,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811]) ).
cnf(i_0_6753,plain,
v2_membered(set_union2(empty_set,empty_set)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4881,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6222,i_0_4393,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_6545,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812]) ).
cnf(i_0_6754,plain,
v1_membered(set_union2(empty_set,empty_set)),
inference(scs_inference,[],[i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4881,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6222,i_0_4393,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_6545,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816]) ).
cnf(i_0_6755,plain,
relstr_set_smaller(esk440_0,empty_set,esk441_0),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4881,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6222,i_0_4393,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_6545,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691]) ).
cnf(i_0_6756,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6757,plain,
( ~ element(X1,the_carrier(X2))
| in(esk114_3(X2,X3,X1),X3)
| relstr_set_smaller(X2,X3,X1)
| ~ rel_str(X2) ),
inference(rename_variables,[],[i_0_3691]) ).
cnf(i_0_6758,plain,
relstr_element_smaller(esk440_0,empty_set,esk441_0),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4881,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6222,i_0_4393,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_6545,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692]) ).
cnf(i_0_6759,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6760,plain,
( ~ element(X1,the_carrier(X2))
| in(esk103_3(X2,X3,X1),X3)
| relstr_element_smaller(X2,X3,X1)
| ~ rel_str(X2) ),
inference(rename_variables,[],[i_0_3692]) ).
cnf(i_0_6761,plain,
~ in(X1,set_union2(relation_image(empty_set,X2),relation_image(empty_set,X2))),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4881,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6222,i_0_4393,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_6545,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461]) ).
cnf(i_0_6762,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6763,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_4878]) ).
cnf(i_0_6764,plain,
( in(unordered_pair(unordered_pair(esk16_4(X1,X2,X3,X4),X4),unordered_pair(esk16_4(X1,X2,X3,X4),esk16_4(X1,X2,X3,X4))),X1)
| X3 != relation_image(X1,X2)
| ~ relation(X1)
| ~ in(X4,X3) ),
inference(rename_variables,[],[i_0_2461]) ).
cnf(i_0_6765,plain,
~ in(X1,set_union2(relation_inverse_image(empty_set,X2),relation_inverse_image(empty_set,X2))),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4881,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6222,i_0_4393,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_6545,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589]) ).
cnf(i_0_6766,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6767,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_4878]) ).
cnf(i_0_6768,plain,
( in(unordered_pair(unordered_pair(X1,esk19_4(X2,X3,X4,X1)),unordered_pair(X1,X1)),X2)
| X4 != relation_inverse_image(X2,X3)
| ~ relation(X2)
| ~ in(X1,X4) ),
inference(rename_variables,[],[i_0_2589]) ).
cnf(i_0_6769,plain,
relation_dom(empty_set) = relation_inverse_image(empty_set,X1),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4881,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6222,i_0_4393,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_6545,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598]) ).
cnf(i_0_6770,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6771,plain,
( in(unordered_pair(unordered_pair(esk20_3(X1,X2,X3),esk21_3(X1,X2,X3)),unordered_pair(esk20_3(X1,X2,X3),esk20_3(X1,X2,X3))),X1)
| in(esk20_3(X1,X2,X3),X3)
| X3 = relation_inverse_image(X1,X2)
| ~ relation(X1) ),
inference(rename_variables,[],[i_0_2598]) ).
cnf(i_0_6772,plain,
relation_inverse_image(esk171_0,empty_set) = relation_image(empty_set,X1),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4881,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6222,i_0_4393,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_6545,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599]) ).
cnf(i_0_6773,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6774,plain,
( in(unordered_pair(unordered_pair(esk18_3(X1,X2,X3),esk17_3(X1,X2,X3)),unordered_pair(esk18_3(X1,X2,X3),esk18_3(X1,X2,X3))),X1)
| in(esk17_3(X1,X2,X3),X3)
| X3 = relation_image(X1,X2)
| ~ relation(X1) ),
inference(rename_variables,[],[i_0_2599]) ).
cnf(i_0_6775,plain,
relation_image(esk171_0,empty_set) = fiber(empty_set,X1),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4881,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6222,i_0_4393,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_6545,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616]) ).
cnf(i_0_6776,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6777,plain,
( in(unordered_pair(unordered_pair(esk46_3(X1,X2,X3),X2),unordered_pair(esk46_3(X1,X2,X3),esk46_3(X1,X2,X3))),X1)
| in(esk46_3(X1,X2,X3),X3)
| X3 = fiber(X1,X2)
| ~ relation(X1) ),
inference(rename_variables,[],[i_0_2616]) ).
cnf(i_0_6778,plain,
~ in(X1,set_union2(relation_rng(empty_set),relation_rng(empty_set))),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4881,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6222,i_0_4393,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_6545,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622]) ).
cnf(i_0_6779,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6780,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_4878]) ).
cnf(i_0_6781,plain,
( in(unordered_pair(unordered_pair(esk92_3(X1,X2,X3),X3),unordered_pair(esk92_3(X1,X2,X3),esk92_3(X1,X2,X3))),X1)
| X2 != relation_rng(X1)
| ~ relation(X1)
| ~ in(X3,X2) ),
inference(rename_variables,[],[i_0_2622]) ).
cnf(i_0_6782,plain,
fiber(empty_set,X1) = relation_rng(empty_set),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4881,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6222,i_0_4393,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_6545,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994]) ).
cnf(i_0_6783,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6784,plain,
( in(unordered_pair(unordered_pair(esk94_2(X1,X2),esk93_2(X1,X2)),unordered_pair(esk94_2(X1,X2),esk94_2(X1,X2))),X1)
| in(esk93_2(X1,X2),X2)
| X2 = relation_rng(X1)
| ~ relation(X1) ),
inference(rename_variables,[],[i_0_2994]) ).
cnf(i_0_6785,plain,
set_union2(relation_image(empty_set,X1),relation_image(empty_set,X1)) = relation_dom(empty_set),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4881,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6222,i_0_4393,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_6545,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995]) ).
cnf(i_0_6786,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6787,plain,
( in(unordered_pair(unordered_pair(esk79_2(X1,X2),esk80_2(X1,X2)),unordered_pair(esk79_2(X1,X2),esk79_2(X1,X2))),X1)
| in(esk79_2(X1,X2),X2)
| X2 = relation_dom(X1)
| ~ relation(X1) ),
inference(rename_variables,[],[i_0_2995]) ).
cnf(i_0_6788,plain,
empty_set = identity_relation(set_union2(relation_inverse_image(empty_set,X1),relation_inverse_image(empty_set,X1))),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4881,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6222,i_0_4393,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_6545,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996]) ).
cnf(i_0_6789,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6790,plain,
( in(unordered_pair(unordered_pair(esk1_2(X1,X2),esk2_2(X1,X2)),unordered_pair(esk1_2(X1,X2),esk1_2(X1,X2))),X2)
| in(esk1_2(X1,X2),X1)
| X2 = identity_relation(X1)
| ~ relation(X2) ),
inference(rename_variables,[],[i_0_2996]) ).
cnf(i_0_6791,plain,
~ in(X1,set_union2(relation_dom(empty_set),relation_dom(empty_set))),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4881,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6222,i_0_4393,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_6545,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998]) ).
cnf(i_0_6792,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6793,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_4878]) ).
cnf(i_0_6794,plain,
( in(unordered_pair(unordered_pair(X1,esk78_3(X2,X3,X1)),unordered_pair(X1,X1)),X2)
| X3 != relation_dom(X2)
| ~ relation(X2)
| ~ in(X1,X3) ),
inference(rename_variables,[],[i_0_2998]) ).
cnf(i_0_6795,plain,
~ in(X1,set_union2(relation_inverse_image(esk171_0,empty_set),relation_inverse_image(esk171_0,empty_set))),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4881,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6222,i_0_4393,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_6545,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041]) ).
cnf(i_0_6796,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_4878]) ).
cnf(i_0_6797,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6798,plain,
( X1 != relation_inverse_image(X2,X3)
| in(esk19_4(X2,X3,X1,X4),X3)
| ~ in(X4,X1)
| ~ relation(X2) ),
inference(rename_variables,[],[i_0_3041]) ).
cnf(i_0_6799,plain,
~ in(X1,set_union2(relation_image(esk171_0,empty_set),relation_image(esk171_0,empty_set))),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4881,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6222,i_0_4393,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_6545,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042]) ).
cnf(i_0_6800,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_4878]) ).
cnf(i_0_6801,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6802,plain,
( X1 != relation_image(X2,X3)
| in(esk16_4(X2,X3,X1,X4),X3)
| ~ in(X4,X1)
| ~ relation(X2) ),
inference(rename_variables,[],[i_0_3042]) ).
cnf(i_0_6803,plain,
~ function(unordered_pair(unordered_pair(unordered_pair(X1,empty_set),unordered_pair(X1,X1)),unordered_pair(unordered_pair(X1,unordered_pair(X2,X2)),unordered_pair(X1,X1)))),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4881,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6222,i_0_4393,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_6545,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116]) ).
cnf(i_0_6804,plain,
( ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3)
| ~ in(unordered_pair(unordered_pair(X1,X4),unordered_pair(X1,X1)),X3)
| X2 = X4
| ~ function(X3) ),
inference(rename_variables,[],[i_0_3116]) ).
cnf(i_0_6805,plain,
in(esk62_3(empty_set,empty_set,unordered_pair(X1,X1)),unordered_pair(X1,X1)),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4881,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6222,i_0_4393,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_6545,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212]) ).
cnf(i_0_6806,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6807,plain,
( X1 = set_union2(X2,X3)
| in(esk62_3(X2,X3,X1),X1)
| in(esk62_3(X2,X3,X1),X2)
| in(esk62_3(X2,X3,X1),X3) ),
inference(rename_variables,[],[i_0_3212]) ).
cnf(i_0_6808,plain,
empty_set = relation_inverse_image(esk171_0,set_union2(relation_rng(empty_set),relation_rng(empty_set))),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4881,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6222,i_0_4393,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_6545,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490]) ).
cnf(i_0_6809,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6810,plain,
( in(esk20_3(X1,X2,X3),X3)
| X3 = relation_inverse_image(X1,X2)
| in(esk21_3(X1,X2,X3),X2)
| ~ relation(X1) ),
inference(rename_variables,[],[i_0_3490]) ).
cnf(i_0_6811,plain,
empty_set = relation_image(esk171_0,set_union2(relation_dom(empty_set),relation_dom(empty_set))),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4881,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6222,i_0_4393,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_6545,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491]) ).
cnf(i_0_6812,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6813,plain,
( in(esk17_3(X1,X2,X3),X3)
| X3 = relation_image(X1,X2)
| in(esk18_3(X1,X2,X3),X2)
| ~ relation(X1) ),
inference(rename_variables,[],[i_0_3491]) ).
cnf(i_0_6814,plain,
~ in(esk409_1(esk443_1(set_union2(set_union2(union(esk166_0),cartesian_product2(esk166_0,X1)),set_union2(union(esk166_0),cartesian_product2(esk166_0,X1))))),esk341_3(esk166_0,esk171_0,X1)),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4881,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6222,i_0_4393,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_6545,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576]) ).
cnf(i_0_6815,plain,
( in(X1,cartesian_product2(X2,X3))
| ~ in(X1,esk341_3(X2,X4,X3))
| empty(X2)
| ~ relation(X4) ),
inference(rename_variables,[],[i_0_3576]) ).
cnf(i_0_6816,plain,
quasi_total(identity_relation(empty_set),empty_set,empty_set),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_4983,i_0_5028,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_6545,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614]) ).
cnf(i_0_6817,plain,
function(identity_relation(X1)),
inference(rename_variables,[],[i_0_4957]) ).
cnf(i_0_6818,plain,
v1_partfun1(identity_relation(X1),X1,X1),
inference(rename_variables,[],[i_0_4398]) ).
cnf(i_0_6819,plain,
( ~ function(X1)
| ~ v1_partfun1(X1,X2,X3)
| ~ relation_of2(X1,X2,X3)
| quasi_total(X1,X2,X3) ),
inference(rename_variables,[],[i_0_3614]) ).
cnf(i_0_6820,plain,
set_difference(pair_first(set_union2(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)))),empty_set) = X1,
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_6375,i_0_4983,i_0_5028,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_6545,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673]) ).
cnf(i_0_6821,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_4878]) ).
cnf(i_0_6822,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_4878]) ).
cnf(i_0_6823,plain,
set_difference(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_4882]) ).
cnf(i_0_6824,plain,
( X1 != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2))
| X1 != unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4))
| X6 != pair_first(X1)
| X6 = X4 ),
inference(rename_variables,[],[i_0_3673]) ).
cnf(i_0_6825,plain,
set_difference(pair_second(set_union2(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)))),empty_set) = X2,
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6821,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_6375,i_0_6823,i_0_4983,i_0_5028,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_6545,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674]) ).
cnf(i_0_6826,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_4878]) ).
cnf(i_0_6827,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_4878]) ).
cnf(i_0_6828,plain,
set_difference(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_4882]) ).
cnf(i_0_6829,plain,
( X1 != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2))
| X1 != unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4))
| X6 != pair_second(X1)
| X6 = X5 ),
inference(rename_variables,[],[i_0_3674]) ).
cnf(i_0_6830,plain,
~ in(X1,set_union2(fiber(empty_set,X2),fiber(empty_set,X2))),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6821,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_6375,i_0_6823,i_0_4983,i_0_5028,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_6545,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761]) ).
cnf(i_0_6831,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6832,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_4878]) ).
cnf(i_0_6833,plain,
( in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3)
| X4 != fiber(X3,X2)
| ~ relation(X3)
| ~ in(X1,X4) ),
inference(rename_variables,[],[i_0_3761]) ).
cnf(i_0_6834,plain,
~ is_reflexive_in(empty_set,omega),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6821,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_6375,i_0_6823,i_0_4983,i_0_5028,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_6545,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770]) ).
cnf(i_0_6835,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6836,plain,
( in(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,X1)),X2)
| ~ relation(X2)
| ~ is_reflexive_in(X2,X3)
| ~ in(X1,X3) ),
inference(rename_variables,[],[i_0_3770]) ).
cnf(i_0_6837,plain,
~ in(X1,relation_field(empty_set)),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6821,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_4813,i_0_4882,i_0_6375,i_0_6823,i_0_4983,i_0_5028,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_6545,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797]) ).
cnf(i_0_6838,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6839,plain,
( in(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,X1)),X2)
| ~ in(X1,relation_field(X2))
| ~ relation(X2)
| ~ reflexive(X2) ),
inference(rename_variables,[],[i_0_3797]) ).
cnf(i_0_6840,plain,
below(boole_lattice(X1),esk123_1(the_carrier(boole_lattice(X1))),esk123_1(the_carrier(boole_lattice(X1)))),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6821,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_4813,i_0_4882,i_0_6375,i_0_6823,i_0_4983,i_0_5028,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_6545,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806]) ).
cnf(i_0_6841,plain,
element(esk123_1(X1),X1),
inference(rename_variables,[],[i_0_4812]) ).
cnf(i_0_6842,plain,
element(esk123_1(X1),X1),
inference(rename_variables,[],[i_0_4812]) ).
cnf(i_0_6843,plain,
subset(X1,X1),
inference(rename_variables,[],[i_0_4880]) ).
cnf(i_0_6844,plain,
( ~ element(X1,the_carrier(boole_lattice(X2)))
| ~ element(X3,the_carrier(boole_lattice(X2)))
| below(boole_lattice(X2),X3,X1)
| ~ subset(X3,X1) ),
inference(rename_variables,[],[i_0_3806]) ).
cnf(i_0_6845,plain,
subset(esk160_1(empty_set),subset_complement(empty_set,empty_set)),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6821,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_4983,i_0_5028,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_6545,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025]) ).
cnf(i_0_6846,plain,
element(X1,powerset(X1)),
inference(rename_variables,[],[i_0_4813]) ).
cnf(i_0_6847,plain,
element(esk160_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_4768]) ).
cnf(i_0_6848,plain,
( ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2))
| subset(X3,subset_complement(X2,X1))
| ~ disjoint(X3,X1) ),
inference(rename_variables,[],[i_0_4025]) ).
cnf(i_0_6849,plain,
in(empty_set,set_union2(set_difference(omega,set_difference(omega,omega)),set_difference(omega,set_difference(omega,omega)))),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6821,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_4983,i_0_5028,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_6545,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040]) ).
cnf(i_0_6850,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_4878]) ).
cnf(i_0_6851,plain,
( X1 != set_difference(X2,set_difference(X2,X3))
| ~ in(X4,X3)
| ~ in(X4,X2)
| in(X4,X1) ),
inference(rename_variables,[],[i_0_4040]) ).
cnf(i_0_6852,plain,
~ in(X1,set_union2(set_union2(empty_set,empty_set),set_union2(empty_set,empty_set))),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6821,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_4983,i_0_5028,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_6545,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302]) ).
cnf(i_0_6853,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_4878]) ).
cnf(i_0_6854,plain,
( X1 != set_union2(X2,X3)
| in(X4,X2)
| in(X4,X3)
| ~ in(X4,X1) ),
inference(rename_variables,[],[i_0_4302]) ).
cnf(i_0_6855,plain,
in(empty_set,set_difference(set_difference(omega,empty_set),empty_set)),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6821,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_4983,i_0_5028,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_4815,i_0_4603,i_0_6545,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303]) ).
cnf(i_0_6856,plain,
set_difference(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_4882]) ).
cnf(i_0_6857,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6858,plain,
( X1 != set_difference(X2,X3)
| in(X4,X3)
| in(X4,X1)
| ~ in(X4,X2) ),
inference(rename_variables,[],[i_0_4303]) ).
cnf(i_0_6859,plain,
in(empty_set,set_union2(union(esk443_1(omega)),union(esk443_1(omega)))),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6821,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_4983,i_0_5028,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337]) ).
cnf(i_0_6860,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_4878]) ).
cnf(i_0_6861,plain,
in(X1,esk443_1(X1)),
inference(rename_variables,[],[i_0_4814]) ).
cnf(i_0_6862,plain,
( X1 != union(X2)
| in(X3,X1)
| ~ in(X3,X4)
| ~ in(X4,X2) ),
inference(rename_variables,[],[i_0_4337]) ).
cnf(i_0_6863,plain,
~ in(set_union2(X1,X1),set_union2(fiber(esk171_0,X1),fiber(esk171_0,X1))),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_4983,i_0_5028,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337,i_0_4417]) ).
cnf(i_0_6864,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_4878]) ).
cnf(i_0_6865,plain,
( X1 != fiber(X2,X3)
| ~ relation(X2)
| X4 != X3
| ~ in(X4,X1) ),
inference(rename_variables,[],[i_0_4417]) ).
cnf(i_0_6866,plain,
~ in(unordered_pair(X1,X1),set_difference(unordered_pair(empty_set,empty_set),empty_set)),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_6856,i_0_4983,i_0_5028,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337,i_0_4417,i_0_4469]) ).
cnf(i_0_6867,plain,
set_difference(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_4882]) ).
cnf(i_0_6868,plain,
( X1 != unordered_pair(X2,X3)
| X4 = X2
| X4 = X3
| ~ in(X4,X1) ),
inference(rename_variables,[],[i_0_4469]) ).
cnf(i_0_6869,plain,
relation_dom(empty_set) = set_union2(relation_inverse_image(empty_set,X1),relation_inverse_image(empty_set,X1)),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_6856,i_0_4983,i_0_5028,i_0_5033,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5019,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337,i_0_4417,i_0_4469,i_0_4763]) ).
cnf(i_0_6870,plain,
( X1 != identity_relation(X2)
| relation_dom(X1) = X2
| ~ relation(X1)
| ~ function(X1) ),
inference(rename_variables,[],[i_0_4763]) ).
cnf(i_0_6871,plain,
one_to_one(esk153_0),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_6856,i_0_4983,i_0_5028,i_0_5030,i_0_5033,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5013,i_0_5019,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337,i_0_4417,i_0_4469,i_0_4763,i_0_4772]) ).
cnf(i_0_6872,plain,
( ~ relation(X1)
| ~ empty(X1)
| ~ function(X1)
| one_to_one(X1) ),
inference(rename_variables,[],[i_0_4772]) ).
cnf(i_0_6873,plain,
~ in(X1,relation_image(esk164_0,empty_set)),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_6857,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_6856,i_0_4983,i_0_5028,i_0_5030,i_0_5033,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5013,i_0_5019,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337,i_0_4417,i_0_4469,i_0_4763,i_0_4772,i_0_6025]) ).
cnf(i_0_6874,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6875,plain,
( ~ relation(X1)
| ~ function(X1)
| in(esk5_4(X1,X2,relation_image(X1,X2),X3),X2)
| ~ in(X3,relation_image(X1,X2)) ),
inference(rename_variables,[],[i_0_6025]) ).
cnf(i_0_6876,plain,
~ in(X1,relation_inverse_image(esk164_0,empty_set)),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_6857,i_0_6874,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_6856,i_0_4983,i_0_5028,i_0_5030,i_0_5033,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5013,i_0_5019,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337,i_0_4417,i_0_4469,i_0_4763,i_0_4772,i_0_6025,i_0_6168]) ).
cnf(i_0_6877,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6878,plain,
( ~ function(X1)
| in(apply(X1,X2),X3)
| ~ relation(X1)
| ~ in(X2,relation_inverse_image(X1,X3)) ),
inference(rename_variables,[],[i_0_6168]) ).
cnf(i_0_6879,plain,
ordinal_subset(esk166_0,esk166_0),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_6857,i_0_6874,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_6856,i_0_4983,i_0_5028,i_0_5030,i_0_5033,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6843,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5013,i_0_5019,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337,i_0_4417,i_0_4469,i_0_4763,i_0_4772,i_0_6025,i_0_6168,i_0_4466]) ).
cnf(i_0_6880,plain,
subset(X1,X1),
inference(rename_variables,[],[i_0_4880]) ).
cnf(i_0_6881,plain,
( ~ subset(X1,X2)
| ~ ordinal(X1)
| ~ ordinal(X2)
| ordinal_subset(X1,X2) ),
inference(rename_variables,[],[i_0_4466]) ).
cnf(i_0_6882,plain,
latt_element_smaller(esk176_0,esk123_1(the_carrier(esk176_0)),empty_set),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_6857,i_0_6874,i_0_6877,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_6842,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_6856,i_0_4983,i_0_5028,i_0_5030,i_0_5033,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6843,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4979,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5013,i_0_5019,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337,i_0_4417,i_0_4469,i_0_4763,i_0_4772,i_0_6025,i_0_6168,i_0_4466,i_0_3678]) ).
cnf(i_0_6883,plain,
element(esk123_1(X1),X1),
inference(rename_variables,[],[i_0_4812]) ).
cnf(i_0_6884,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6885,plain,
( ~ element(X1,the_carrier(X2))
| in(esk24_3(X2,X1,X3),X3)
| latt_element_smaller(X2,X1,X3)
| empty_carrier(X2)
| ~ latt_str(X2) ),
inference(rename_variables,[],[i_0_3678]) ).
cnf(i_0_6886,plain,
latt_set_smaller(esk176_0,esk123_1(the_carrier(esk176_0)),empty_set),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_6857,i_0_6874,i_0_6877,i_0_6884,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_6842,i_0_6883,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_6856,i_0_4983,i_0_5028,i_0_5030,i_0_5033,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6843,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4979,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5013,i_0_5019,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337,i_0_4417,i_0_4469,i_0_4763,i_0_4772,i_0_6025,i_0_6168,i_0_4466,i_0_3678,i_0_3679]) ).
cnf(i_0_6887,plain,
element(esk123_1(X1),X1),
inference(rename_variables,[],[i_0_4812]) ).
cnf(i_0_6888,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6889,plain,
( ~ element(X1,the_carrier(X2))
| in(esk22_3(X2,X1,X3),X3)
| latt_set_smaller(X2,X1,X3)
| empty_carrier(X2)
| ~ latt_str(X2) ),
inference(rename_variables,[],[i_0_3679]) ).
cnf(i_0_6890,plain,
cast_to_el_of_LattPOSet(esk176_0,esk123_1(the_carrier(esk176_0))) = esk123_1(the_carrier(esk176_0)),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_6857,i_0_6874,i_0_6877,i_0_6884,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_6842,i_0_6883,i_0_6887,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_6856,i_0_4983,i_0_5028,i_0_5030,i_0_5033,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6843,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4979,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5013,i_0_5019,i_0_5026,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337,i_0_4417,i_0_4469,i_0_4763,i_0_4772,i_0_6025,i_0_6168,i_0_4466,i_0_3678,i_0_3679,i_0_4348]) ).
cnf(i_0_6891,plain,
element(esk123_1(X1),X1),
inference(rename_variables,[],[i_0_4812]) ).
cnf(i_0_6892,plain,
( ~ element(X1,the_carrier(X2))
| cast_to_el_of_LattPOSet(X2,X1) = X1
| ~ lattice(X2)
| ~ latt_str(X2)
| empty_carrier(X2) ),
inference(rename_variables,[],[i_0_4348]) ).
cnf(i_0_6893,plain,
in(esk123_1(the_carrier(esk176_0)),a_2_2_lattice3(esk176_0,empty_set)),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_6857,i_0_6874,i_0_6877,i_0_6884,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_6842,i_0_6883,i_0_6887,i_0_6891,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_6856,i_0_4983,i_0_5028,i_0_5030,i_0_5033,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6843,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4979,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5013,i_0_5019,i_0_5026,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337,i_0_4417,i_0_4469,i_0_4763,i_0_4772,i_0_6025,i_0_6168,i_0_4466,i_0_3678,i_0_3679,i_0_4348,i_0_6145]) ).
cnf(i_0_6894,plain,
element(esk123_1(X1),X1),
inference(rename_variables,[],[i_0_4812]) ).
cnf(i_0_6895,plain,
( ~ latt_str(X1)
| in(X2,a_2_2_lattice3(X1,X3))
| ~ element(X2,the_carrier(X1))
| empty_carrier(X1)
| ~ latt_set_smaller(X1,X2,X3) ),
inference(rename_variables,[],[i_0_6145]) ).
cnf(i_0_6896,plain,
~ in(X1,esk367_3(X2,empty_set,esk171_0)),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_6857,i_0_6874,i_0_6877,i_0_6884,i_0_6888,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_6842,i_0_6883,i_0_6887,i_0_6891,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_6856,i_0_4983,i_0_5027,i_0_5028,i_0_5030,i_0_5033,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6843,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4979,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5013,i_0_5019,i_0_5026,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337,i_0_4417,i_0_4469,i_0_4763,i_0_4772,i_0_6025,i_0_6168,i_0_4466,i_0_3678,i_0_3679,i_0_4348,i_0_6145,i_0_2379]) ).
cnf(i_0_6897,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6898,plain,
( in(unordered_pair(unordered_pair(apply(X1,esk368_4(X2,X3,X1,X4)),apply(X1,esk369_4(X2,X3,X1,X4))),unordered_pair(apply(X1,esk368_4(X2,X3,X1,X4)),apply(X1,esk368_4(X2,X3,X1,X4)))),X3)
| ~ in(X4,esk367_3(X2,X3,X1))
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1) ),
inference(rename_variables,[],[i_0_2379]) ).
cnf(i_0_6899,plain,
empty_set = relation_rng_restriction(X1,empty_set),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_6857,i_0_6874,i_0_6877,i_0_6884,i_0_6888,i_0_6897,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_6842,i_0_6883,i_0_6887,i_0_6891,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_6856,i_0_4983,i_0_5027,i_0_5028,i_0_5030,i_0_5033,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6843,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4979,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5013,i_0_5019,i_0_5026,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337,i_0_4417,i_0_4469,i_0_4763,i_0_4772,i_0_6025,i_0_6168,i_0_4466,i_0_3678,i_0_3679,i_0_4348,i_0_6145,i_0_2379,i_0_2533]) ).
cnf(i_0_6900,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6901,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6902,plain,
( in(unordered_pair(unordered_pair(esk8_3(X1,X2,X3),esk9_3(X1,X2,X3)),unordered_pair(esk8_3(X1,X2,X3),esk8_3(X1,X2,X3))),X3)
| in(unordered_pair(unordered_pair(esk8_3(X1,X2,X3),esk9_3(X1,X2,X3)),unordered_pair(esk8_3(X1,X2,X3),esk8_3(X1,X2,X3))),X2)
| X3 = relation_rng_restriction(X1,X2)
| ~ relation(X3)
| ~ relation(X2) ),
inference(rename_variables,[],[i_0_2533]) ).
cnf(i_0_6903,plain,
empty_set = relation_dom_restriction(empty_set,X1),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_6857,i_0_6874,i_0_6877,i_0_6884,i_0_6888,i_0_6897,i_0_6901,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_6842,i_0_6883,i_0_6887,i_0_6891,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_6856,i_0_4983,i_0_5027,i_0_5028,i_0_5030,i_0_5033,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6843,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4979,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5013,i_0_5019,i_0_5026,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337,i_0_4417,i_0_4469,i_0_4763,i_0_4772,i_0_6025,i_0_6168,i_0_4466,i_0_3678,i_0_3679,i_0_4348,i_0_6145,i_0_2379,i_0_2533,i_0_2534]) ).
cnf(i_0_6904,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6905,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6906,plain,
( in(unordered_pair(unordered_pair(esk3_3(X1,X2,X3),esk4_3(X1,X2,X3)),unordered_pair(esk3_3(X1,X2,X3),esk3_3(X1,X2,X3))),X3)
| in(unordered_pair(unordered_pair(esk3_3(X1,X2,X3),esk4_3(X1,X2,X3)),unordered_pair(esk3_3(X1,X2,X3),esk3_3(X1,X2,X3))),X1)
| X3 = relation_dom_restriction(X1,X2)
| ~ relation(X3)
| ~ relation(X1) ),
inference(rename_variables,[],[i_0_2534]) ).
cnf(i_0_6907,plain,
empty_set = relation_rng_restriction(empty_set,esk171_0),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_6857,i_0_6874,i_0_6877,i_0_6884,i_0_6888,i_0_6897,i_0_6901,i_0_6905,i_0_6904,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_6842,i_0_6883,i_0_6887,i_0_6891,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_6856,i_0_4983,i_0_5027,i_0_5028,i_0_5030,i_0_5033,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6843,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4979,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5013,i_0_5019,i_0_5026,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337,i_0_4417,i_0_4469,i_0_4763,i_0_4772,i_0_6025,i_0_6168,i_0_4466,i_0_3678,i_0_3679,i_0_4348,i_0_6145,i_0_2379,i_0_2533,i_0_2534,i_0_2596]) ).
cnf(i_0_6908,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6909,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6910,plain,
( in(unordered_pair(unordered_pair(esk8_3(X1,X2,X3),esk9_3(X1,X2,X3)),unordered_pair(esk8_3(X1,X2,X3),esk8_3(X1,X2,X3))),X3)
| in(esk9_3(X1,X2,X3),X1)
| X3 = relation_rng_restriction(X1,X2)
| ~ relation(X3)
| ~ relation(X2) ),
inference(rename_variables,[],[i_0_2596]) ).
cnf(i_0_6911,plain,
empty_set = relation_dom_restriction(esk171_0,empty_set),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_6857,i_0_6874,i_0_6877,i_0_6884,i_0_6888,i_0_6897,i_0_6901,i_0_6905,i_0_6908,i_0_6904,i_0_6909,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_6842,i_0_6883,i_0_6887,i_0_6891,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_6856,i_0_4983,i_0_5027,i_0_5028,i_0_5030,i_0_5033,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6843,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4979,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5013,i_0_5019,i_0_5026,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337,i_0_4417,i_0_4469,i_0_4763,i_0_4772,i_0_6025,i_0_6168,i_0_4466,i_0_3678,i_0_3679,i_0_4348,i_0_6145,i_0_2379,i_0_2533,i_0_2534,i_0_2596,i_0_2597]) ).
cnf(i_0_6912,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6913,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6914,plain,
( in(unordered_pair(unordered_pair(esk3_3(X1,X2,X3),esk4_3(X1,X2,X3)),unordered_pair(esk3_3(X1,X2,X3),esk3_3(X1,X2,X3))),X3)
| in(esk3_3(X1,X2,X3),X2)
| X3 = relation_dom_restriction(X1,X2)
| ~ relation(X3)
| ~ relation(X1) ),
inference(rename_variables,[],[i_0_2597]) ).
cnf(i_0_6915,plain,
empty_set = relation_inverse(empty_set),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_6857,i_0_6874,i_0_6877,i_0_6884,i_0_6888,i_0_6897,i_0_6901,i_0_6905,i_0_6908,i_0_6912,i_0_6904,i_0_6909,i_0_6913,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_6842,i_0_6883,i_0_6887,i_0_6891,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_6856,i_0_4983,i_0_5027,i_0_5028,i_0_5030,i_0_5033,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6843,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4979,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5013,i_0_5019,i_0_5026,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337,i_0_4417,i_0_4469,i_0_4763,i_0_4772,i_0_6025,i_0_6168,i_0_4466,i_0_3678,i_0_3679,i_0_4348,i_0_6145,i_0_2379,i_0_2533,i_0_2534,i_0_2596,i_0_2597,i_0_2688]) ).
cnf(i_0_6916,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6917,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6918,plain,
( in(unordered_pair(unordered_pair(esk97_2(X1,X2),esk98_2(X1,X2)),unordered_pair(esk97_2(X1,X2),esk97_2(X1,X2))),X2)
| in(unordered_pair(unordered_pair(esk98_2(X1,X2),esk97_2(X1,X2)),unordered_pair(esk98_2(X1,X2),esk98_2(X1,X2))),X1)
| X2 = relation_inverse(X1)
| ~ relation(X2)
| ~ relation(X1) ),
inference(rename_variables,[],[i_0_2688]) ).
cnf(i_0_6919,plain,
~ in(X1,set_difference(relation_image(esk171_0,empty_set),empty_set)),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_6857,i_0_6874,i_0_6877,i_0_6884,i_0_6888,i_0_6897,i_0_6901,i_0_6905,i_0_6908,i_0_6912,i_0_6916,i_0_6904,i_0_6909,i_0_6913,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_6842,i_0_6883,i_0_6887,i_0_6891,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_6856,i_0_6867,i_0_4983,i_0_5027,i_0_5028,i_0_5030,i_0_5033,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6843,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4979,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5013,i_0_5019,i_0_5026,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337,i_0_4417,i_0_4469,i_0_4763,i_0_4772,i_0_6025,i_0_6168,i_0_4466,i_0_3678,i_0_3679,i_0_4348,i_0_6145,i_0_2379,i_0_2533,i_0_2534,i_0_2596,i_0_2597,i_0_2688,i_0_3034]) ).
cnf(i_0_6920,plain,
set_difference(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_4882]) ).
cnf(i_0_6921,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6922,plain,
( X1 != relation_image(X2,X3)
| in(esk5_4(X2,X3,X1,X4),X3)
| ~ in(X4,X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(rename_variables,[],[i_0_3034]) ).
cnf(i_0_6923,plain,
empty_set = relation_inverse_image(esk171_0,empty_set),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_6857,i_0_6874,i_0_6877,i_0_6884,i_0_6888,i_0_6897,i_0_6901,i_0_6905,i_0_6908,i_0_6912,i_0_6916,i_0_6921,i_0_6904,i_0_6909,i_0_6913,i_0_6917,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_6842,i_0_6883,i_0_6887,i_0_6891,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_6856,i_0_6867,i_0_4983,i_0_5027,i_0_5028,i_0_5030,i_0_5033,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6843,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4979,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5013,i_0_5019,i_0_5026,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337,i_0_4417,i_0_4469,i_0_4763,i_0_4772,i_0_6025,i_0_6168,i_0_4466,i_0_3678,i_0_3679,i_0_4348,i_0_6145,i_0_2379,i_0_2533,i_0_2534,i_0_2596,i_0_2597,i_0_2688,i_0_3034,i_0_3183]) ).
cnf(i_0_6924,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6925,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6926,plain,
( in(apply(X1,esk10_3(X1,X2,X3)),X2)
| X3 = relation_inverse_image(X1,X2)
| in(esk10_3(X1,X2,X3),X3)
| ~ relation(X1)
| ~ function(X1) ),
inference(rename_variables,[],[i_0_3183]) ).
cnf(i_0_6927,plain,
empty_set = relation_image(esk171_0,empty_set),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_6857,i_0_6874,i_0_6877,i_0_6884,i_0_6888,i_0_6897,i_0_6901,i_0_6905,i_0_6908,i_0_6912,i_0_6916,i_0_6921,i_0_6924,i_0_6904,i_0_6909,i_0_6913,i_0_6917,i_0_6925,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_6842,i_0_6883,i_0_6887,i_0_6891,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_6856,i_0_6867,i_0_4983,i_0_5027,i_0_5028,i_0_5030,i_0_5033,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6843,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4979,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5013,i_0_5019,i_0_5026,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337,i_0_4417,i_0_4469,i_0_4763,i_0_4772,i_0_6025,i_0_6168,i_0_4466,i_0_3678,i_0_3679,i_0_4348,i_0_6145,i_0_2379,i_0_2533,i_0_2534,i_0_2596,i_0_2597,i_0_2688,i_0_3034,i_0_3183,i_0_3470]) ).
cnf(i_0_6928,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6929,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6930,plain,
( in(esk6_3(X1,X2,X3),X3)
| X3 = relation_image(X1,X2)
| in(esk7_3(X1,X2,X3),X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(rename_variables,[],[i_0_3470]) ).
cnf(i_0_6931,plain,
~ in(esk74_2(cartesian_product2(empty_set,empty_set),X1),esk367_3(empty_set,esk171_0,esk171_0)),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_6857,i_0_6874,i_0_6877,i_0_6884,i_0_6888,i_0_6897,i_0_6901,i_0_6905,i_0_6908,i_0_6912,i_0_6916,i_0_6921,i_0_6924,i_0_6904,i_0_6909,i_0_6913,i_0_6917,i_0_6925,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_6842,i_0_6883,i_0_6887,i_0_6891,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_6856,i_0_6867,i_0_4983,i_0_5027,i_0_5028,i_0_5030,i_0_5033,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6843,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4979,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5013,i_0_5019,i_0_5026,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337,i_0_4417,i_0_4469,i_0_4763,i_0_4772,i_0_6025,i_0_6168,i_0_4466,i_0_3678,i_0_3679,i_0_4348,i_0_6145,i_0_2379,i_0_2533,i_0_2534,i_0_2596,i_0_2597,i_0_2688,i_0_3034,i_0_3183,i_0_3470,i_0_3548]) ).
cnf(i_0_6932,plain,
( in(X1,cartesian_product2(X2,X2))
| ~ in(X1,esk367_3(X2,X3,X4))
| ~ relation(X3)
| ~ relation(X4)
| ~ function(X4) ),
inference(rename_variables,[],[i_0_3548]) ).
cnf(i_0_6933,plain,
in(set_union2(unordered_pair(unordered_pair(empty_set,empty_set),unordered_pair(empty_set,empty_set)),unordered_pair(unordered_pair(empty_set,empty_set),unordered_pair(empty_set,empty_set))),set_union2(cartesian_product2(omega,omega),cartesian_product2(omega,omega))),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_6857,i_0_6874,i_0_6877,i_0_6884,i_0_6888,i_0_6897,i_0_6901,i_0_6905,i_0_6908,i_0_6912,i_0_6916,i_0_6921,i_0_6924,i_0_6904,i_0_6909,i_0_6913,i_0_6917,i_0_6925,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6864,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_6842,i_0_6883,i_0_6887,i_0_6891,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_6856,i_0_6867,i_0_4983,i_0_5027,i_0_5028,i_0_5030,i_0_5033,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6843,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4979,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5013,i_0_5019,i_0_5026,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337,i_0_4417,i_0_4469,i_0_4763,i_0_4772,i_0_6025,i_0_6168,i_0_4466,i_0_3678,i_0_3679,i_0_4348,i_0_6145,i_0_2379,i_0_2533,i_0_2534,i_0_2596,i_0_2597,i_0_2688,i_0_3034,i_0_3183,i_0_3470,i_0_3548,i_0_3800]) ).
cnf(i_0_6934,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_4878]) ).
cnf(i_0_6935,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_4878]) ).
cnf(i_0_6936,plain,
( X1 != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2))
| X4 != cartesian_product2(X5,X6)
| ~ in(X3,X6)
| ~ in(X2,X5)
| in(X1,X4) ),
inference(rename_variables,[],[i_0_3800]) ).
cnf(i_0_6937,plain,
in(esk75_3(esk418_1(unordered_pair(X1,X1)),unordered_pair(X1,X1),unordered_pair(X1,X1)),unordered_pair(X1,X1)),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_6857,i_0_6874,i_0_6877,i_0_6884,i_0_6888,i_0_6897,i_0_6901,i_0_6905,i_0_6908,i_0_6912,i_0_6916,i_0_6921,i_0_6924,i_0_6904,i_0_6909,i_0_6913,i_0_6917,i_0_6925,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6864,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_6842,i_0_6883,i_0_6887,i_0_6891,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_6856,i_0_6867,i_0_4983,i_0_5027,i_0_5028,i_0_5030,i_0_5033,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6843,i_0_6880,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4979,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5013,i_0_5019,i_0_5026,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337,i_0_4417,i_0_4469,i_0_4763,i_0_4772,i_0_6025,i_0_6168,i_0_4466,i_0_3678,i_0_3679,i_0_4348,i_0_6145,i_0_2379,i_0_2533,i_0_2534,i_0_2596,i_0_2597,i_0_2688,i_0_3034,i_0_3183,i_0_3470,i_0_3548,i_0_3800,i_0_3827]) ).
cnf(i_0_6938,plain,
subset(X1,X1),
inference(rename_variables,[],[i_0_4880]) ).
cnf(i_0_6939,plain,
relation(esk418_1(X1)),
inference(rename_variables,[],[i_0_4937]) ).
cnf(i_0_6940,plain,
( X1 = empty_set
| in(esk75_3(X2,X3,X1),X1)
| ~ subset(X1,X3)
| ~ is_well_founded_in(X2,X3)
| ~ relation(X2) ),
inference(rename_variables,[],[i_0_3827]) ).
cnf(i_0_6941,plain,
~ in(unordered_pair(X1,X1),set_union2(unordered_triple(empty_set,empty_set,empty_set),unordered_triple(empty_set,empty_set,empty_set))),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_6857,i_0_6874,i_0_6877,i_0_6884,i_0_6888,i_0_6897,i_0_6901,i_0_6905,i_0_6908,i_0_6912,i_0_6916,i_0_6921,i_0_6924,i_0_6904,i_0_6909,i_0_6913,i_0_6917,i_0_6925,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6864,i_0_6934,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_6842,i_0_6883,i_0_6887,i_0_6891,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_6856,i_0_6867,i_0_4983,i_0_5027,i_0_5028,i_0_5030,i_0_5033,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6843,i_0_6880,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4979,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5013,i_0_5019,i_0_5026,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337,i_0_4417,i_0_4469,i_0_4763,i_0_4772,i_0_6025,i_0_6168,i_0_4466,i_0_3678,i_0_3679,i_0_4348,i_0_6145,i_0_2379,i_0_2533,i_0_2534,i_0_2596,i_0_2597,i_0_2688,i_0_3034,i_0_3183,i_0_3470,i_0_3548,i_0_3800,i_0_3827,i_0_4075]) ).
cnf(i_0_6942,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_4878]) ).
cnf(i_0_6943,plain,
( X1 != unordered_triple(X2,X3,X4)
| X5 = X2
| X5 = X3
| X5 = X4
| ~ in(X5,X1) ),
inference(rename_variables,[],[i_0_4075]) ).
cnf(i_0_6944,plain,
element(cast_to_el_of_lattice(esk176_0,esk123_1(the_carrier(poset_of_lattice(esk176_0)))),the_carrier(esk176_0)),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_6857,i_0_6874,i_0_6877,i_0_6884,i_0_6888,i_0_6897,i_0_6901,i_0_6905,i_0_6908,i_0_6912,i_0_6916,i_0_6921,i_0_6924,i_0_6904,i_0_6909,i_0_6913,i_0_6917,i_0_6925,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6864,i_0_6934,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_6842,i_0_6883,i_0_6887,i_0_6891,i_0_6894,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_6856,i_0_6867,i_0_4983,i_0_5027,i_0_5028,i_0_5030,i_0_5033,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6843,i_0_6880,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4979,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5013,i_0_5019,i_0_5026,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337,i_0_4417,i_0_4469,i_0_4763,i_0_4772,i_0_6025,i_0_6168,i_0_4466,i_0_3678,i_0_3679,i_0_4348,i_0_6145,i_0_2379,i_0_2533,i_0_2534,i_0_2596,i_0_2597,i_0_2688,i_0_3034,i_0_3183,i_0_3470,i_0_3548,i_0_3800,i_0_3827,i_0_4075,i_0_4076]) ).
cnf(i_0_6945,plain,
element(esk123_1(X1),X1),
inference(rename_variables,[],[i_0_4812]) ).
cnf(i_0_6946,plain,
( ~ element(X1,the_carrier(poset_of_lattice(X2)))
| element(cast_to_el_of_lattice(X2,X1),the_carrier(X2))
| ~ lattice(X2)
| ~ latt_str(X2)
| empty_carrier(X2) ),
inference(rename_variables,[],[i_0_4076]) ).
cnf(i_0_6947,plain,
~ in(X1,set_difference(relation_inverse_image(esk171_0,empty_set),empty_set)),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_6857,i_0_6874,i_0_6877,i_0_6884,i_0_6888,i_0_6897,i_0_6901,i_0_6905,i_0_6908,i_0_6912,i_0_6916,i_0_6921,i_0_6924,i_0_6928,i_0_6904,i_0_6909,i_0_6913,i_0_6917,i_0_6925,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6864,i_0_6934,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_6842,i_0_6883,i_0_6887,i_0_6891,i_0_6894,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_6856,i_0_6867,i_0_6920,i_0_4983,i_0_5027,i_0_5028,i_0_5030,i_0_5033,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6843,i_0_6880,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4979,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5013,i_0_5019,i_0_5026,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337,i_0_4417,i_0_4469,i_0_4763,i_0_4772,i_0_6025,i_0_6168,i_0_4466,i_0_3678,i_0_3679,i_0_4348,i_0_6145,i_0_2379,i_0_2533,i_0_2534,i_0_2596,i_0_2597,i_0_2688,i_0_3034,i_0_3183,i_0_3470,i_0_3548,i_0_3800,i_0_3827,i_0_4075,i_0_4076,i_0_4143]) ).
cnf(i_0_6948,plain,
set_difference(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_4882]) ).
cnf(i_0_6949,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6950,plain,
( X1 != relation_inverse_image(X2,X3)
| in(apply(X2,X4),X3)
| ~ relation(X2)
| ~ function(X2)
| ~ in(X4,X1) ),
inference(rename_variables,[],[i_0_4143]) ).
cnf(i_0_6951,plain,
cast_to_el_of_lattice(esk176_0,esk123_1(the_carrier(poset_of_lattice(esk176_0)))) = esk123_1(the_carrier(poset_of_lattice(esk176_0))),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_6857,i_0_6874,i_0_6877,i_0_6884,i_0_6888,i_0_6897,i_0_6901,i_0_6905,i_0_6908,i_0_6912,i_0_6916,i_0_6921,i_0_6924,i_0_6928,i_0_6904,i_0_6909,i_0_6913,i_0_6917,i_0_6925,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6864,i_0_6934,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_6842,i_0_6883,i_0_6887,i_0_6891,i_0_6894,i_0_6945,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_6856,i_0_6867,i_0_6920,i_0_4983,i_0_5027,i_0_5028,i_0_5030,i_0_5033,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6843,i_0_6880,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4979,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5013,i_0_5019,i_0_5026,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337,i_0_4417,i_0_4469,i_0_4763,i_0_4772,i_0_6025,i_0_6168,i_0_4466,i_0_3678,i_0_3679,i_0_4348,i_0_6145,i_0_2379,i_0_2533,i_0_2534,i_0_2596,i_0_2597,i_0_2688,i_0_3034,i_0_3183,i_0_3470,i_0_3548,i_0_3800,i_0_3827,i_0_4075,i_0_4076,i_0_4143,i_0_4242]) ).
cnf(i_0_6952,plain,
element(esk123_1(X1),X1),
inference(rename_variables,[],[i_0_4812]) ).
cnf(i_0_6953,plain,
( ~ element(X1,the_carrier(poset_of_lattice(X2)))
| cast_to_el_of_lattice(X2,X1) = X1
| ~ lattice(X2)
| ~ latt_str(X2)
| empty_carrier(X2) ),
inference(rename_variables,[],[i_0_4242]) ).
cnf(i_0_6954,plain,
set_union2(apply(empty_set,esk20_3(empty_set,X1,relation_dom(empty_set))),apply(empty_set,esk20_3(empty_set,X1,relation_dom(empty_set)))) = empty_set,
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_6857,i_0_6874,i_0_6877,i_0_6884,i_0_6888,i_0_6897,i_0_6901,i_0_6905,i_0_6908,i_0_6912,i_0_6916,i_0_6921,i_0_6924,i_0_6928,i_0_6904,i_0_6909,i_0_6913,i_0_6917,i_0_6925,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6864,i_0_6934,i_0_6942,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_6842,i_0_6883,i_0_6887,i_0_6891,i_0_6894,i_0_6945,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_6856,i_0_6867,i_0_6920,i_0_4983,i_0_5027,i_0_5028,i_0_5030,i_0_5033,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6843,i_0_6880,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4979,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5013,i_0_5019,i_0_5026,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337,i_0_4417,i_0_4469,i_0_4763,i_0_4772,i_0_6025,i_0_6168,i_0_4466,i_0_3678,i_0_3679,i_0_4348,i_0_6145,i_0_2379,i_0_2533,i_0_2534,i_0_2596,i_0_2597,i_0_2688,i_0_3034,i_0_3183,i_0_3470,i_0_3548,i_0_3800,i_0_3827,i_0_4075,i_0_4076,i_0_4143,i_0_4242,i_0_4403]) ).
cnf(i_0_6955,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_4878]) ).
cnf(i_0_6956,plain,
( X1 != apply(X2,X3)
| X1 = empty_set
| in(X3,relation_dom(X2))
| ~ relation(X2)
| ~ function(X2) ),
inference(rename_variables,[],[i_0_4403]) ).
cnf(i_0_6957,plain,
set_union2(empty_set,empty_set) = apply(empty_set,esk20_3(empty_set,X1,relation_dom(empty_set))),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_6857,i_0_6874,i_0_6877,i_0_6884,i_0_6888,i_0_6897,i_0_6901,i_0_6905,i_0_6908,i_0_6912,i_0_6916,i_0_6921,i_0_6924,i_0_6928,i_0_6904,i_0_6909,i_0_6913,i_0_6917,i_0_6925,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6864,i_0_6934,i_0_6942,i_0_6955,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_6842,i_0_6883,i_0_6887,i_0_6891,i_0_6894,i_0_6945,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_6856,i_0_6867,i_0_6920,i_0_4983,i_0_5027,i_0_5028,i_0_5030,i_0_5033,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6843,i_0_6880,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4979,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5013,i_0_5019,i_0_5026,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337,i_0_4417,i_0_4469,i_0_4763,i_0_4772,i_0_6025,i_0_6168,i_0_4466,i_0_3678,i_0_3679,i_0_4348,i_0_6145,i_0_2379,i_0_2533,i_0_2534,i_0_2596,i_0_2597,i_0_2688,i_0_3034,i_0_3183,i_0_3470,i_0_3548,i_0_3800,i_0_3827,i_0_4075,i_0_4076,i_0_4143,i_0_4242,i_0_4403,i_0_4456]) ).
cnf(i_0_6958,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_4878]) ).
cnf(i_0_6959,plain,
( in(X1,relation_dom(X2))
| X3 != empty_set
| X3 = apply(X2,X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(rename_variables,[],[i_0_4456]) ).
cnf(i_0_6960,plain,
in(unordered_pair(unordered_pair(empty_set,empty_set),unordered_pair(empty_set,empty_set)),inclusion_relation(omega)),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_6857,i_0_6874,i_0_6877,i_0_6884,i_0_6888,i_0_6897,i_0_6901,i_0_6905,i_0_6908,i_0_6912,i_0_6916,i_0_6921,i_0_6924,i_0_6928,i_0_6904,i_0_6909,i_0_6913,i_0_6917,i_0_6925,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6864,i_0_6934,i_0_6942,i_0_6955,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_6842,i_0_6883,i_0_6887,i_0_6891,i_0_6894,i_0_6945,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_6856,i_0_6867,i_0_6920,i_0_4983,i_0_5027,i_0_5028,i_0_5030,i_0_5033,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6843,i_0_6880,i_0_6938,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4979,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5013,i_0_5019,i_0_5026,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4942,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337,i_0_4417,i_0_4469,i_0_4763,i_0_4772,i_0_6025,i_0_6168,i_0_4466,i_0_3678,i_0_3679,i_0_4348,i_0_6145,i_0_2379,i_0_2533,i_0_2534,i_0_2596,i_0_2597,i_0_2688,i_0_3034,i_0_3183,i_0_3470,i_0_3548,i_0_3800,i_0_3827,i_0_4075,i_0_4076,i_0_4143,i_0_4242,i_0_4403,i_0_4456,i_0_6129]) ).
cnf(i_0_6961,plain,
subset(X1,X1),
inference(rename_variables,[],[i_0_4880]) ).
cnf(i_0_6962,plain,
relation(inclusion_relation(X1)),
inference(rename_variables,[],[i_0_4942]) ).
cnf(i_0_6963,plain,
( ~ subset(X1,X2)
| in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),inclusion_relation(X3))
| ~ relation(inclusion_relation(X3))
| ~ in(X2,X3)
| ~ in(X1,X3) ),
inference(rename_variables,[],[i_0_6129]) ).
cnf(i_0_6964,plain,
~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),esk205_3(X3,empty_set,esk171_0)),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_6857,i_0_6874,i_0_6877,i_0_6884,i_0_6888,i_0_6897,i_0_6901,i_0_6905,i_0_6908,i_0_6912,i_0_6916,i_0_6921,i_0_6924,i_0_6928,i_0_6949,i_0_6904,i_0_6909,i_0_6913,i_0_6917,i_0_6925,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6864,i_0_6934,i_0_6942,i_0_6955,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_6842,i_0_6883,i_0_6887,i_0_6891,i_0_6894,i_0_6945,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_6856,i_0_6867,i_0_6920,i_0_4983,i_0_5027,i_0_5028,i_0_5030,i_0_5033,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6843,i_0_6880,i_0_6938,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4979,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5013,i_0_5019,i_0_5026,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4942,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337,i_0_4417,i_0_4469,i_0_4763,i_0_4772,i_0_6025,i_0_6168,i_0_4466,i_0_3678,i_0_3679,i_0_4348,i_0_6145,i_0_2379,i_0_2533,i_0_2534,i_0_2596,i_0_2597,i_0_2688,i_0_3034,i_0_3183,i_0_3470,i_0_3548,i_0_3800,i_0_3827,i_0_4075,i_0_4076,i_0_4143,i_0_4242,i_0_4403,i_0_4456,i_0_6129,i_0_2761]) ).
cnf(i_0_6965,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6966,plain,
( in(unordered_pair(unordered_pair(apply(X1,X2),apply(X1,X3)),unordered_pair(apply(X1,X2),apply(X1,X2))),X4)
| ~ in(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),esk205_3(X5,X4,X1))
| ~ function(X1)
| ~ relation(X4)
| ~ relation(X1) ),
inference(rename_variables,[],[i_0_2761]) ).
cnf(i_0_6967,plain,
inclusion_relation(omega) != relation_rng_restriction(X1,empty_set),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_6857,i_0_6874,i_0_6877,i_0_6884,i_0_6888,i_0_6897,i_0_6901,i_0_6905,i_0_6908,i_0_6912,i_0_6916,i_0_6921,i_0_6924,i_0_6928,i_0_6949,i_0_6965,i_0_6904,i_0_6909,i_0_6913,i_0_6917,i_0_6925,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6864,i_0_6934,i_0_6942,i_0_6955,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_6842,i_0_6883,i_0_6887,i_0_6891,i_0_6894,i_0_6945,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_6856,i_0_6867,i_0_6920,i_0_4983,i_0_5027,i_0_5028,i_0_5030,i_0_5033,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6843,i_0_6880,i_0_6938,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4979,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5013,i_0_5019,i_0_5026,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4942,i_0_6962,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337,i_0_4417,i_0_4469,i_0_4763,i_0_4772,i_0_6025,i_0_6168,i_0_4466,i_0_3678,i_0_3679,i_0_4348,i_0_6145,i_0_2379,i_0_2533,i_0_2534,i_0_2596,i_0_2597,i_0_2688,i_0_3034,i_0_3183,i_0_3470,i_0_3548,i_0_3800,i_0_3827,i_0_4075,i_0_4076,i_0_4143,i_0_4242,i_0_4403,i_0_4456,i_0_6129,i_0_2761,i_0_3175]) ).
cnf(i_0_6968,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6969,plain,
relation(inclusion_relation(X1)),
inference(rename_variables,[],[i_0_4942]) ).
cnf(i_0_6970,plain,
( ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3)
| in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X4)
| X3 != relation_rng_restriction(X5,X4)
| ~ relation(X3)
| ~ relation(X4) ),
inference(rename_variables,[],[i_0_3175]) ).
cnf(i_0_6971,plain,
inclusion_relation(omega) != relation_dom_restriction(empty_set,X1),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_6857,i_0_6874,i_0_6877,i_0_6884,i_0_6888,i_0_6897,i_0_6901,i_0_6905,i_0_6908,i_0_6912,i_0_6916,i_0_6921,i_0_6924,i_0_6928,i_0_6949,i_0_6965,i_0_6968,i_0_6904,i_0_6909,i_0_6913,i_0_6917,i_0_6925,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6864,i_0_6934,i_0_6942,i_0_6955,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_6842,i_0_6883,i_0_6887,i_0_6891,i_0_6894,i_0_6945,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_6856,i_0_6867,i_0_6920,i_0_4983,i_0_5027,i_0_5028,i_0_5030,i_0_5033,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6843,i_0_6880,i_0_6938,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4979,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5013,i_0_5019,i_0_5026,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4942,i_0_6962,i_0_6969,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337,i_0_4417,i_0_4469,i_0_4763,i_0_4772,i_0_6025,i_0_6168,i_0_4466,i_0_3678,i_0_3679,i_0_4348,i_0_6145,i_0_2379,i_0_2533,i_0_2534,i_0_2596,i_0_2597,i_0_2688,i_0_3034,i_0_3183,i_0_3470,i_0_3548,i_0_3800,i_0_3827,i_0_4075,i_0_4076,i_0_4143,i_0_4242,i_0_4403,i_0_4456,i_0_6129,i_0_2761,i_0_3175,i_0_3176]) ).
cnf(i_0_6972,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6973,plain,
relation(inclusion_relation(X1)),
inference(rename_variables,[],[i_0_4942]) ).
cnf(i_0_6974,plain,
( ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3)
| in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X4)
| X3 != relation_dom_restriction(X4,X5)
| ~ relation(X3)
| ~ relation(X4) ),
inference(rename_variables,[],[i_0_3176]) ).
cnf(i_0_6975,plain,
inclusion_relation(omega) != relation_inverse(empty_set),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_6857,i_0_6874,i_0_6877,i_0_6884,i_0_6888,i_0_6897,i_0_6901,i_0_6905,i_0_6908,i_0_6912,i_0_6916,i_0_6921,i_0_6924,i_0_6928,i_0_6949,i_0_6965,i_0_6968,i_0_6972,i_0_6904,i_0_6909,i_0_6913,i_0_6917,i_0_6925,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6864,i_0_6934,i_0_6942,i_0_6955,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_6842,i_0_6883,i_0_6887,i_0_6891,i_0_6894,i_0_6945,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_6856,i_0_6867,i_0_6920,i_0_4983,i_0_5027,i_0_5028,i_0_5030,i_0_5033,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6843,i_0_6880,i_0_6938,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4979,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5013,i_0_5019,i_0_5026,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4942,i_0_6962,i_0_6969,i_0_6973,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337,i_0_4417,i_0_4469,i_0_4763,i_0_4772,i_0_6025,i_0_6168,i_0_4466,i_0_3678,i_0_3679,i_0_4348,i_0_6145,i_0_2379,i_0_2533,i_0_2534,i_0_2596,i_0_2597,i_0_2688,i_0_3034,i_0_3183,i_0_3470,i_0_3548,i_0_3800,i_0_3827,i_0_4075,i_0_4076,i_0_4143,i_0_4242,i_0_4403,i_0_4456,i_0_6129,i_0_2761,i_0_3175,i_0_3176,i_0_3194]) ).
cnf(i_0_6976,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6977,plain,
relation(inclusion_relation(X1)),
inference(rename_variables,[],[i_0_4942]) ).
cnf(i_0_6978,plain,
( ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3)
| in(unordered_pair(unordered_pair(X2,X1),unordered_pair(X2,X2)),X4)
| X3 != relation_inverse(X4)
| ~ relation(X4)
| ~ relation(X3) ),
inference(rename_variables,[],[i_0_3194]) ).
cnf(i_0_6979,plain,
empty_set != relation_inverse(inclusion_relation(omega)),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_6857,i_0_6874,i_0_6877,i_0_6884,i_0_6888,i_0_6897,i_0_6901,i_0_6905,i_0_6908,i_0_6912,i_0_6916,i_0_6921,i_0_6924,i_0_6928,i_0_6949,i_0_6965,i_0_6968,i_0_6972,i_0_6976,i_0_6904,i_0_6909,i_0_6913,i_0_6917,i_0_6925,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6864,i_0_6934,i_0_6942,i_0_6955,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_6842,i_0_6883,i_0_6887,i_0_6891,i_0_6894,i_0_6945,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_6856,i_0_6867,i_0_6920,i_0_4983,i_0_5027,i_0_5028,i_0_5030,i_0_5033,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6843,i_0_6880,i_0_6938,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4979,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5013,i_0_5019,i_0_5026,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4942,i_0_6962,i_0_6969,i_0_6973,i_0_6977,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337,i_0_4417,i_0_4469,i_0_4763,i_0_4772,i_0_6025,i_0_6168,i_0_4466,i_0_3678,i_0_3679,i_0_4348,i_0_6145,i_0_2379,i_0_2533,i_0_2534,i_0_2596,i_0_2597,i_0_2688,i_0_3034,i_0_3183,i_0_3470,i_0_3548,i_0_3800,i_0_3827,i_0_4075,i_0_4076,i_0_4143,i_0_4242,i_0_4403,i_0_4456,i_0_6129,i_0_2761,i_0_3175,i_0_3176,i_0_3194,i_0_3195]) ).
cnf(i_0_6980,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6981,plain,
relation(inclusion_relation(X1)),
inference(rename_variables,[],[i_0_4942]) ).
cnf(i_0_6982,plain,
( ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3)
| in(unordered_pair(unordered_pair(X2,X1),unordered_pair(X2,X2)),X4)
| X4 != relation_inverse(X3)
| ~ relation(X4)
| ~ relation(X3) ),
inference(rename_variables,[],[i_0_3195]) ).
cnf(i_0_6983,plain,
inclusion_relation(omega) != relation_rng_restriction(empty_set,esk171_0),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_6857,i_0_6874,i_0_6877,i_0_6884,i_0_6888,i_0_6897,i_0_6901,i_0_6905,i_0_6908,i_0_6912,i_0_6916,i_0_6921,i_0_6924,i_0_6928,i_0_6949,i_0_6965,i_0_6968,i_0_6972,i_0_6976,i_0_6980,i_0_6904,i_0_6909,i_0_6913,i_0_6917,i_0_6925,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6864,i_0_6934,i_0_6942,i_0_6955,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_6842,i_0_6883,i_0_6887,i_0_6891,i_0_6894,i_0_6945,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_6856,i_0_6867,i_0_6920,i_0_4983,i_0_5027,i_0_5028,i_0_5030,i_0_5033,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6843,i_0_6880,i_0_6938,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4979,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5013,i_0_5019,i_0_5026,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4942,i_0_6962,i_0_6969,i_0_6973,i_0_6977,i_0_6981,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337,i_0_4417,i_0_4469,i_0_4763,i_0_4772,i_0_6025,i_0_6168,i_0_4466,i_0_3678,i_0_3679,i_0_4348,i_0_6145,i_0_2379,i_0_2533,i_0_2534,i_0_2596,i_0_2597,i_0_2688,i_0_3034,i_0_3183,i_0_3470,i_0_3548,i_0_3800,i_0_3827,i_0_4075,i_0_4076,i_0_4143,i_0_4242,i_0_4403,i_0_4456,i_0_6129,i_0_2761,i_0_3175,i_0_3176,i_0_3194,i_0_3195,i_0_3447]) ).
cnf(i_0_6984,plain,
relation(inclusion_relation(X1)),
inference(rename_variables,[],[i_0_4942]) ).
cnf(i_0_6985,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6986,plain,
( ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3)
| X3 != relation_rng_restriction(X4,X5)
| ~ relation(X5)
| ~ relation(X3)
| in(X2,X4) ),
inference(rename_variables,[],[i_0_3447]) ).
cnf(i_0_6987,plain,
inclusion_relation(omega) != relation_dom_restriction(esk171_0,empty_set),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_6857,i_0_6874,i_0_6877,i_0_6884,i_0_6888,i_0_6897,i_0_6901,i_0_6905,i_0_6908,i_0_6912,i_0_6916,i_0_6921,i_0_6924,i_0_6928,i_0_6949,i_0_6965,i_0_6968,i_0_6972,i_0_6976,i_0_6980,i_0_6985,i_0_6904,i_0_6909,i_0_6913,i_0_6917,i_0_6925,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6864,i_0_6934,i_0_6942,i_0_6955,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_6842,i_0_6883,i_0_6887,i_0_6891,i_0_6894,i_0_6945,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_6856,i_0_6867,i_0_6920,i_0_4983,i_0_5027,i_0_5028,i_0_5030,i_0_5033,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6843,i_0_6880,i_0_6938,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4979,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5013,i_0_5019,i_0_5026,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4942,i_0_6962,i_0_6969,i_0_6973,i_0_6977,i_0_6981,i_0_6984,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337,i_0_4417,i_0_4469,i_0_4763,i_0_4772,i_0_6025,i_0_6168,i_0_4466,i_0_3678,i_0_3679,i_0_4348,i_0_6145,i_0_2379,i_0_2533,i_0_2534,i_0_2596,i_0_2597,i_0_2688,i_0_3034,i_0_3183,i_0_3470,i_0_3548,i_0_3800,i_0_3827,i_0_4075,i_0_4076,i_0_4143,i_0_4242,i_0_4403,i_0_4456,i_0_6129,i_0_2761,i_0_3175,i_0_3176,i_0_3194,i_0_3195,i_0_3447,i_0_3448]) ).
cnf(i_0_6988,plain,
relation(inclusion_relation(X1)),
inference(rename_variables,[],[i_0_4942]) ).
cnf(i_0_6989,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6990,plain,
( ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3)
| X3 != relation_dom_restriction(X4,X5)
| ~ relation(X4)
| ~ relation(X3)
| in(X1,X5) ),
inference(rename_variables,[],[i_0_3448]) ).
cnf(i_0_6991,plain,
relstr_set_smaller(poset_of_lattice(esk176_0),empty_set,cast_to_el_of_LattPOSet(esk176_0,esk123_1(the_carrier(esk176_0)))),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_6857,i_0_6874,i_0_6877,i_0_6884,i_0_6888,i_0_6897,i_0_6901,i_0_6905,i_0_6908,i_0_6912,i_0_6916,i_0_6921,i_0_6924,i_0_6928,i_0_6949,i_0_6965,i_0_6968,i_0_6972,i_0_6976,i_0_6980,i_0_6985,i_0_6904,i_0_6909,i_0_6913,i_0_6917,i_0_6925,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6864,i_0_6934,i_0_6942,i_0_6955,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_6842,i_0_6883,i_0_6887,i_0_6891,i_0_6894,i_0_6945,i_0_6952,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_6856,i_0_6867,i_0_6920,i_0_4983,i_0_5027,i_0_5028,i_0_5030,i_0_5033,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6843,i_0_6880,i_0_6938,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4979,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5013,i_0_5019,i_0_5026,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4942,i_0_6962,i_0_6969,i_0_6973,i_0_6977,i_0_6981,i_0_6984,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337,i_0_4417,i_0_4469,i_0_4763,i_0_4772,i_0_6025,i_0_6168,i_0_4466,i_0_3678,i_0_3679,i_0_4348,i_0_6145,i_0_2379,i_0_2533,i_0_2534,i_0_2596,i_0_2597,i_0_2688,i_0_3034,i_0_3183,i_0_3470,i_0_3548,i_0_3800,i_0_3827,i_0_4075,i_0_4076,i_0_4143,i_0_4242,i_0_4403,i_0_4456,i_0_6129,i_0_2761,i_0_3175,i_0_3176,i_0_3194,i_0_3195,i_0_3447,i_0_3448,i_0_3658]) ).
cnf(i_0_6992,plain,
element(esk123_1(X1),X1),
inference(rename_variables,[],[i_0_4812]) ).
cnf(i_0_6993,plain,
( ~ element(X1,the_carrier(X2))
| relstr_set_smaller(poset_of_lattice(X2),X3,cast_to_el_of_LattPOSet(X2,X1))
| empty_carrier(X2)
| ~ latt_element_smaller(X2,X1,X3)
| ~ lattice(X2)
| ~ latt_str(X2) ),
inference(rename_variables,[],[i_0_3658]) ).
cnf(i_0_6994,plain,
relstr_element_smaller(poset_of_lattice(esk176_0),empty_set,cast_to_el_of_LattPOSet(esk176_0,esk123_1(the_carrier(esk176_0)))),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_6857,i_0_6874,i_0_6877,i_0_6884,i_0_6888,i_0_6897,i_0_6901,i_0_6905,i_0_6908,i_0_6912,i_0_6916,i_0_6921,i_0_6924,i_0_6928,i_0_6949,i_0_6965,i_0_6968,i_0_6972,i_0_6976,i_0_6980,i_0_6985,i_0_6904,i_0_6909,i_0_6913,i_0_6917,i_0_6925,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6864,i_0_6934,i_0_6942,i_0_6955,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_6842,i_0_6883,i_0_6887,i_0_6891,i_0_6894,i_0_6945,i_0_6952,i_0_6992,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_6856,i_0_6867,i_0_6920,i_0_4983,i_0_5027,i_0_5028,i_0_5030,i_0_5033,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6843,i_0_6880,i_0_6938,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4979,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5013,i_0_5019,i_0_5026,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4942,i_0_6962,i_0_6969,i_0_6973,i_0_6977,i_0_6981,i_0_6984,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337,i_0_4417,i_0_4469,i_0_4763,i_0_4772,i_0_6025,i_0_6168,i_0_4466,i_0_3678,i_0_3679,i_0_4348,i_0_6145,i_0_2379,i_0_2533,i_0_2534,i_0_2596,i_0_2597,i_0_2688,i_0_3034,i_0_3183,i_0_3470,i_0_3548,i_0_3800,i_0_3827,i_0_4075,i_0_4076,i_0_4143,i_0_4242,i_0_4403,i_0_4456,i_0_6129,i_0_2761,i_0_3175,i_0_3176,i_0_3194,i_0_3195,i_0_3447,i_0_3448,i_0_3658,i_0_3659]) ).
cnf(i_0_6995,plain,
element(esk123_1(X1),X1),
inference(rename_variables,[],[i_0_4812]) ).
cnf(i_0_6996,plain,
( ~ element(X1,the_carrier(X2))
| relstr_element_smaller(poset_of_lattice(X2),X3,cast_to_el_of_LattPOSet(X2,X1))
| empty_carrier(X2)
| ~ latt_set_smaller(X2,X1,X3)
| ~ lattice(X2)
| ~ latt_str(X2) ),
inference(rename_variables,[],[i_0_3659]) ).
cnf(i_0_6997,plain,
~ in(X1,esk319_3(X2,empty_set,esk171_0)),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_6857,i_0_6874,i_0_6877,i_0_6884,i_0_6888,i_0_6897,i_0_6901,i_0_6905,i_0_6908,i_0_6912,i_0_6916,i_0_6921,i_0_6924,i_0_6928,i_0_6949,i_0_6965,i_0_6968,i_0_6972,i_0_6976,i_0_6980,i_0_6985,i_0_6989,i_0_6904,i_0_6909,i_0_6913,i_0_6917,i_0_6925,i_0_6929,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6864,i_0_6934,i_0_6942,i_0_6955,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_6842,i_0_6883,i_0_6887,i_0_6891,i_0_6894,i_0_6945,i_0_6952,i_0_6992,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_6856,i_0_6867,i_0_6920,i_0_4983,i_0_5027,i_0_5028,i_0_5030,i_0_5033,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6843,i_0_6880,i_0_6938,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4979,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5013,i_0_5019,i_0_5026,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4942,i_0_6962,i_0_6969,i_0_6973,i_0_6977,i_0_6981,i_0_6984,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337,i_0_4417,i_0_4469,i_0_4763,i_0_4772,i_0_6025,i_0_6168,i_0_4466,i_0_3678,i_0_3679,i_0_4348,i_0_6145,i_0_2379,i_0_2533,i_0_2534,i_0_2596,i_0_2597,i_0_2688,i_0_3034,i_0_3183,i_0_3470,i_0_3548,i_0_3800,i_0_3827,i_0_4075,i_0_4076,i_0_4143,i_0_4242,i_0_4403,i_0_4456,i_0_6129,i_0_2761,i_0_3175,i_0_3176,i_0_3194,i_0_3195,i_0_3447,i_0_3448,i_0_3658,i_0_3659,i_0_2352]) ).
cnf(i_0_6998,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_6999,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_7000,plain,
( in(unordered_pair(unordered_pair(apply(X1,esk317_3(X2,X3,X1)),apply(X1,esk318_3(X2,X3,X1))),unordered_pair(apply(X1,esk317_3(X2,X3,X1)),apply(X1,esk317_3(X2,X3,X1)))),X3)
| in(unordered_pair(unordered_pair(apply(X1,esk321_4(X2,X3,X1,X4)),apply(X1,esk322_4(X2,X3,X1,X4))),unordered_pair(apply(X1,esk321_4(X2,X3,X1,X4)),apply(X1,esk321_4(X2,X3,X1,X4)))),X3)
| ~ in(X4,esk319_3(X2,X3,X1))
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1) ),
inference(rename_variables,[],[i_0_2352]) ).
cnf(i_0_7001,plain,
empty_set = relation_composition(esk171_0,empty_set),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_6857,i_0_6874,i_0_6877,i_0_6884,i_0_6888,i_0_6897,i_0_6901,i_0_6905,i_0_6908,i_0_6912,i_0_6916,i_0_6921,i_0_6924,i_0_6928,i_0_6949,i_0_6965,i_0_6968,i_0_6972,i_0_6976,i_0_6980,i_0_6985,i_0_6989,i_0_6998,i_0_6904,i_0_6909,i_0_6913,i_0_6917,i_0_6925,i_0_6929,i_0_6999,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6864,i_0_6934,i_0_6942,i_0_6955,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_6842,i_0_6883,i_0_6887,i_0_6891,i_0_6894,i_0_6945,i_0_6952,i_0_6992,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_6856,i_0_6867,i_0_6920,i_0_4983,i_0_5027,i_0_5028,i_0_5030,i_0_5033,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6843,i_0_6880,i_0_6938,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4979,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5013,i_0_5019,i_0_5026,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4942,i_0_6962,i_0_6969,i_0_6973,i_0_6977,i_0_6981,i_0_6984,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337,i_0_4417,i_0_4469,i_0_4763,i_0_4772,i_0_6025,i_0_6168,i_0_4466,i_0_3678,i_0_3679,i_0_4348,i_0_6145,i_0_2379,i_0_2533,i_0_2534,i_0_2596,i_0_2597,i_0_2688,i_0_3034,i_0_3183,i_0_3470,i_0_3548,i_0_3800,i_0_3827,i_0_4075,i_0_4076,i_0_4143,i_0_4242,i_0_4403,i_0_4456,i_0_6129,i_0_2761,i_0_3175,i_0_3176,i_0_3194,i_0_3195,i_0_3447,i_0_3448,i_0_3658,i_0_3659,i_0_2352,i_0_2531]) ).
cnf(i_0_7002,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_7003,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_7004,plain,
( in(unordered_pair(unordered_pair(esk107_3(X1,X2,X3),esk108_3(X1,X2,X3)),unordered_pair(esk107_3(X1,X2,X3),esk107_3(X1,X2,X3))),X3)
| in(unordered_pair(unordered_pair(esk109_3(X1,X2,X3),esk108_3(X1,X2,X3)),unordered_pair(esk109_3(X1,X2,X3),esk109_3(X1,X2,X3))),X2)
| X3 = relation_composition(X1,X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1) ),
inference(rename_variables,[],[i_0_2531]) ).
cnf(i_0_7005,plain,
empty_set = relation_composition(empty_set,esk171_0),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_6857,i_0_6874,i_0_6877,i_0_6884,i_0_6888,i_0_6897,i_0_6901,i_0_6905,i_0_6908,i_0_6912,i_0_6916,i_0_6921,i_0_6924,i_0_6928,i_0_6949,i_0_6965,i_0_6968,i_0_6972,i_0_6976,i_0_6980,i_0_6985,i_0_6989,i_0_6998,i_0_7002,i_0_6904,i_0_6909,i_0_6913,i_0_6917,i_0_6925,i_0_6929,i_0_6999,i_0_7003,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6864,i_0_6934,i_0_6942,i_0_6955,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_6842,i_0_6883,i_0_6887,i_0_6891,i_0_6894,i_0_6945,i_0_6952,i_0_6992,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_6856,i_0_6867,i_0_6920,i_0_4983,i_0_5027,i_0_5028,i_0_5030,i_0_5033,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6843,i_0_6880,i_0_6938,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4979,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5013,i_0_5019,i_0_5026,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4942,i_0_6962,i_0_6969,i_0_6973,i_0_6977,i_0_6981,i_0_6984,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337,i_0_4417,i_0_4469,i_0_4763,i_0_4772,i_0_6025,i_0_6168,i_0_4466,i_0_3678,i_0_3679,i_0_4348,i_0_6145,i_0_2379,i_0_2533,i_0_2534,i_0_2596,i_0_2597,i_0_2688,i_0_3034,i_0_3183,i_0_3470,i_0_3548,i_0_3800,i_0_3827,i_0_4075,i_0_4076,i_0_4143,i_0_4242,i_0_4403,i_0_4456,i_0_6129,i_0_2761,i_0_3175,i_0_3176,i_0_3194,i_0_3195,i_0_3447,i_0_3448,i_0_3658,i_0_3659,i_0_2352,i_0_2531,i_0_2532]) ).
cnf(i_0_7006,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_7007,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_7008,plain,
( in(unordered_pair(unordered_pair(esk107_3(X1,X2,X3),esk108_3(X1,X2,X3)),unordered_pair(esk107_3(X1,X2,X3),esk107_3(X1,X2,X3))),X3)
| in(unordered_pair(unordered_pair(esk107_3(X1,X2,X3),esk109_3(X1,X2,X3)),unordered_pair(esk107_3(X1,X2,X3),esk107_3(X1,X2,X3))),X1)
| X3 = relation_composition(X1,X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1) ),
inference(rename_variables,[],[i_0_2532]) ).
cnf(i_0_7009,plain,
empty_set != relation_dom_restriction(inclusion_relation(omega),omega),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_6857,i_0_6874,i_0_6877,i_0_6884,i_0_6888,i_0_6897,i_0_6901,i_0_6905,i_0_6908,i_0_6912,i_0_6916,i_0_6921,i_0_6924,i_0_6928,i_0_6949,i_0_6965,i_0_6968,i_0_6972,i_0_6976,i_0_6980,i_0_6985,i_0_6989,i_0_6998,i_0_7002,i_0_7006,i_0_6904,i_0_6909,i_0_6913,i_0_6917,i_0_6925,i_0_6929,i_0_6999,i_0_7003,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6864,i_0_6934,i_0_6942,i_0_6955,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_6842,i_0_6883,i_0_6887,i_0_6891,i_0_6894,i_0_6945,i_0_6952,i_0_6992,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_6856,i_0_6867,i_0_6920,i_0_4983,i_0_5027,i_0_5028,i_0_5030,i_0_5033,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6843,i_0_6880,i_0_6938,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4979,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5013,i_0_5019,i_0_5026,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4942,i_0_6962,i_0_6969,i_0_6973,i_0_6977,i_0_6981,i_0_6984,i_0_6988,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337,i_0_4417,i_0_4469,i_0_4763,i_0_4772,i_0_6025,i_0_6168,i_0_4466,i_0_3678,i_0_3679,i_0_4348,i_0_6145,i_0_2379,i_0_2533,i_0_2534,i_0_2596,i_0_2597,i_0_2688,i_0_3034,i_0_3183,i_0_3470,i_0_3548,i_0_3800,i_0_3827,i_0_4075,i_0_4076,i_0_4143,i_0_4242,i_0_4403,i_0_4456,i_0_6129,i_0_2761,i_0_3175,i_0_3176,i_0_3194,i_0_3195,i_0_3447,i_0_3448,i_0_3658,i_0_3659,i_0_2352,i_0_2531,i_0_2532,i_0_3148]) ).
cnf(i_0_7010,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_7011,plain,
relation(inclusion_relation(X1)),
inference(rename_variables,[],[i_0_4942]) ).
cnf(i_0_7012,plain,
( ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3)
| in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X4)
| X4 != relation_dom_restriction(X3,X5)
| ~ relation(X4)
| ~ relation(X3)
| ~ in(X1,X5) ),
inference(rename_variables,[],[i_0_3148]) ).
cnf(i_0_7013,plain,
empty_set != relation_rng_restriction(omega,inclusion_relation(omega)),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_6857,i_0_6874,i_0_6877,i_0_6884,i_0_6888,i_0_6897,i_0_6901,i_0_6905,i_0_6908,i_0_6912,i_0_6916,i_0_6921,i_0_6924,i_0_6928,i_0_6949,i_0_6965,i_0_6968,i_0_6972,i_0_6976,i_0_6980,i_0_6985,i_0_6989,i_0_6998,i_0_7002,i_0_7006,i_0_7010,i_0_6904,i_0_6909,i_0_6913,i_0_6917,i_0_6925,i_0_6929,i_0_6999,i_0_7003,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6864,i_0_6934,i_0_6942,i_0_6955,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_6842,i_0_6883,i_0_6887,i_0_6891,i_0_6894,i_0_6945,i_0_6952,i_0_6992,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_6856,i_0_6867,i_0_6920,i_0_4983,i_0_5027,i_0_5028,i_0_5030,i_0_5033,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6843,i_0_6880,i_0_6938,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4979,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5013,i_0_5019,i_0_5026,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4942,i_0_6962,i_0_6969,i_0_6973,i_0_6977,i_0_6981,i_0_6984,i_0_6988,i_0_7011,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337,i_0_4417,i_0_4469,i_0_4763,i_0_4772,i_0_6025,i_0_6168,i_0_4466,i_0_3678,i_0_3679,i_0_4348,i_0_6145,i_0_2379,i_0_2533,i_0_2534,i_0_2596,i_0_2597,i_0_2688,i_0_3034,i_0_3183,i_0_3470,i_0_3548,i_0_3800,i_0_3827,i_0_4075,i_0_4076,i_0_4143,i_0_4242,i_0_4403,i_0_4456,i_0_6129,i_0_2761,i_0_3175,i_0_3176,i_0_3194,i_0_3195,i_0_3447,i_0_3448,i_0_3658,i_0_3659,i_0_2352,i_0_2531,i_0_2532,i_0_3148,i_0_3149]) ).
cnf(i_0_7014,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_7015,plain,
relation(inclusion_relation(X1)),
inference(rename_variables,[],[i_0_4942]) ).
cnf(i_0_7016,plain,
( ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3)
| in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X4)
| X4 != relation_rng_restriction(X5,X3)
| ~ relation(X4)
| ~ relation(X3)
| ~ in(X2,X5) ),
inference(rename_variables,[],[i_0_3149]) ).
cnf(i_0_7017,plain,
empty_set != inclusion_relation(omega),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_6857,i_0_6874,i_0_6877,i_0_6884,i_0_6888,i_0_6897,i_0_6901,i_0_6905,i_0_6908,i_0_6912,i_0_6916,i_0_6921,i_0_6924,i_0_6928,i_0_6949,i_0_6965,i_0_6968,i_0_6972,i_0_6976,i_0_6980,i_0_6985,i_0_6989,i_0_6998,i_0_7002,i_0_7006,i_0_7010,i_0_7014,i_0_6904,i_0_6909,i_0_6913,i_0_6917,i_0_6925,i_0_6929,i_0_6999,i_0_7003,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6864,i_0_6934,i_0_6942,i_0_6955,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_6842,i_0_6883,i_0_6887,i_0_6891,i_0_6894,i_0_6945,i_0_6952,i_0_6992,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_6856,i_0_6867,i_0_6920,i_0_4983,i_0_5027,i_0_5028,i_0_5030,i_0_5033,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6843,i_0_6880,i_0_6938,i_0_6961,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4979,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5013,i_0_5019,i_0_5026,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4942,i_0_6962,i_0_6969,i_0_6973,i_0_6977,i_0_6981,i_0_6984,i_0_6988,i_0_7011,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337,i_0_4417,i_0_4469,i_0_4763,i_0_4772,i_0_6025,i_0_6168,i_0_4466,i_0_3678,i_0_3679,i_0_4348,i_0_6145,i_0_2379,i_0_2533,i_0_2534,i_0_2596,i_0_2597,i_0_2688,i_0_3034,i_0_3183,i_0_3470,i_0_3548,i_0_3800,i_0_3827,i_0_4075,i_0_4076,i_0_4143,i_0_4242,i_0_4403,i_0_4456,i_0_6129,i_0_2761,i_0_3175,i_0_3176,i_0_3194,i_0_3195,i_0_3447,i_0_3448,i_0_3658,i_0_3659,i_0_2352,i_0_2531,i_0_2532,i_0_3148,i_0_3149,i_0_3630]) ).
cnf(i_0_7018,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_7019,plain,
subset(X1,X1),
inference(rename_variables,[],[i_0_4880]) ).
cnf(i_0_7020,plain,
( in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3)
| X3 != inclusion_relation(X4)
| ~ relation(X3)
| ~ in(X2,X4)
| ~ in(X1,X4)
| ~ subset(X1,X2) ),
inference(rename_variables,[],[i_0_3630]) ).
cnf(i_0_7021,plain,
~ empty(esk142_2(esk166_0,esk166_0)),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_4270,i_0_4272,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_6857,i_0_6874,i_0_6877,i_0_6884,i_0_6888,i_0_6897,i_0_6901,i_0_6905,i_0_6908,i_0_6912,i_0_6916,i_0_6921,i_0_6924,i_0_6928,i_0_6949,i_0_6965,i_0_6968,i_0_6972,i_0_6976,i_0_6980,i_0_6985,i_0_6989,i_0_6998,i_0_7002,i_0_7006,i_0_7010,i_0_7014,i_0_6904,i_0_6909,i_0_6913,i_0_6917,i_0_6925,i_0_6929,i_0_6999,i_0_7003,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6864,i_0_6934,i_0_6942,i_0_6955,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_6842,i_0_6883,i_0_6887,i_0_6891,i_0_6894,i_0_6945,i_0_6952,i_0_6992,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_6856,i_0_6867,i_0_6920,i_0_4983,i_0_5027,i_0_5028,i_0_5030,i_0_5033,i_0_4727,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6843,i_0_6880,i_0_6938,i_0_6961,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4979,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5013,i_0_5019,i_0_5026,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4942,i_0_6962,i_0_6969,i_0_6973,i_0_6977,i_0_6981,i_0_6984,i_0_6988,i_0_7011,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337,i_0_4417,i_0_4469,i_0_4763,i_0_4772,i_0_6025,i_0_6168,i_0_4466,i_0_3678,i_0_3679,i_0_4348,i_0_6145,i_0_2379,i_0_2533,i_0_2534,i_0_2596,i_0_2597,i_0_2688,i_0_3034,i_0_3183,i_0_3470,i_0_3548,i_0_3800,i_0_3827,i_0_4075,i_0_4076,i_0_4143,i_0_4242,i_0_4403,i_0_4456,i_0_6129,i_0_2761,i_0_3175,i_0_3176,i_0_3194,i_0_3195,i_0_3447,i_0_3448,i_0_3658,i_0_3659,i_0_2352,i_0_2531,i_0_2532,i_0_3148,i_0_3149,i_0_3630,i_0_3772]) ).
cnf(i_0_7022,plain,
function(esk142_2(X1,X2)),
inference(rename_variables,[],[i_0_4727]) ).
cnf(i_0_7023,plain,
quasi_total(esk142_2(X1,X2),X1,X2),
inference(rename_variables,[],[i_0_4270]) ).
cnf(i_0_7024,plain,
relation_of2(esk142_2(X1,X2),X1,X2),
inference(rename_variables,[],[i_0_4272]) ).
cnf(i_0_7025,plain,
( ~ function(X1)
| ~ quasi_total(X1,X2,X3)
| ~ relation_of2(X1,X2,X3)
| empty(X2)
| empty(X3)
| ~ empty(X1) ),
inference(rename_variables,[],[i_0_3772]) ).
cnf(i_0_7026,plain,
inclusion_relation(omega) != relation_composition(empty_set,esk171_0),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_4270,i_0_4272,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_6857,i_0_6874,i_0_6877,i_0_6884,i_0_6888,i_0_6897,i_0_6901,i_0_6905,i_0_6908,i_0_6912,i_0_6916,i_0_6921,i_0_6924,i_0_6928,i_0_6949,i_0_6965,i_0_6968,i_0_6972,i_0_6976,i_0_6980,i_0_6985,i_0_6989,i_0_6998,i_0_7002,i_0_7006,i_0_7010,i_0_7014,i_0_7018,i_0_6904,i_0_6909,i_0_6913,i_0_6917,i_0_6925,i_0_6929,i_0_6999,i_0_7003,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6864,i_0_6934,i_0_6942,i_0_6955,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_6842,i_0_6883,i_0_6887,i_0_6891,i_0_6894,i_0_6945,i_0_6952,i_0_6992,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_6856,i_0_6867,i_0_6920,i_0_4983,i_0_5027,i_0_5028,i_0_5030,i_0_5033,i_0_4727,i_0_4881,i_0_4957,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6843,i_0_6880,i_0_6938,i_0_6961,i_0_6222,i_0_4393,i_0_4398,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4979,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5013,i_0_5019,i_0_5026,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4942,i_0_6962,i_0_6969,i_0_6973,i_0_6977,i_0_6981,i_0_6984,i_0_6988,i_0_7011,i_0_7015,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337,i_0_4417,i_0_4469,i_0_4763,i_0_4772,i_0_6025,i_0_6168,i_0_4466,i_0_3678,i_0_3679,i_0_4348,i_0_6145,i_0_2379,i_0_2533,i_0_2534,i_0_2596,i_0_2597,i_0_2688,i_0_3034,i_0_3183,i_0_3470,i_0_3548,i_0_3800,i_0_3827,i_0_4075,i_0_4076,i_0_4143,i_0_4242,i_0_4403,i_0_4456,i_0_6129,i_0_2761,i_0_3175,i_0_3176,i_0_3194,i_0_3195,i_0_3447,i_0_3448,i_0_3658,i_0_3659,i_0_2352,i_0_2531,i_0_2532,i_0_3148,i_0_3149,i_0_3630,i_0_3772,i_0_2419]) ).
cnf(i_0_7027,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_7028,plain,
relation(inclusion_relation(X1)),
inference(rename_variables,[],[i_0_4942]) ).
cnf(i_0_7029,plain,
( ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3)
| in(unordered_pair(unordered_pair(X1,esk106_5(X4,X5,X3,X1,X2)),unordered_pair(X1,X1)),X4)
| X3 != relation_composition(X4,X5)
| ~ relation(X3)
| ~ relation(X5)
| ~ relation(X4) ),
inference(rename_variables,[],[i_0_2419]) ).
cnf(i_0_7030,plain,
onto(identity_relation(empty_set),empty_set,empty_set),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_4270,i_0_4272,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_6857,i_0_6874,i_0_6877,i_0_6884,i_0_6888,i_0_6897,i_0_6901,i_0_6905,i_0_6908,i_0_6912,i_0_6916,i_0_6921,i_0_6924,i_0_6928,i_0_6949,i_0_6965,i_0_6968,i_0_6972,i_0_6976,i_0_6980,i_0_6985,i_0_6989,i_0_6998,i_0_7002,i_0_7006,i_0_7010,i_0_7014,i_0_7018,i_0_6904,i_0_6909,i_0_6913,i_0_6917,i_0_6925,i_0_6929,i_0_6999,i_0_7003,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6864,i_0_6934,i_0_6942,i_0_6955,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_6842,i_0_6883,i_0_6887,i_0_6891,i_0_6894,i_0_6945,i_0_6952,i_0_6992,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_6856,i_0_6867,i_0_6920,i_0_4983,i_0_5027,i_0_5028,i_0_5030,i_0_5033,i_0_4727,i_0_4881,i_0_4957,i_0_6817,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6843,i_0_6880,i_0_6938,i_0_6961,i_0_6222,i_0_4393,i_0_4398,i_0_6818,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4979,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5013,i_0_5019,i_0_5026,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_6677,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4942,i_0_6962,i_0_6969,i_0_6973,i_0_6977,i_0_6981,i_0_6984,i_0_6988,i_0_7011,i_0_7015,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337,i_0_4417,i_0_4469,i_0_4763,i_0_4772,i_0_6025,i_0_6168,i_0_4466,i_0_3678,i_0_3679,i_0_4348,i_0_6145,i_0_2379,i_0_2533,i_0_2534,i_0_2596,i_0_2597,i_0_2688,i_0_3034,i_0_3183,i_0_3470,i_0_3548,i_0_3800,i_0_3827,i_0_4075,i_0_4076,i_0_4143,i_0_4242,i_0_4403,i_0_4456,i_0_6129,i_0_2761,i_0_3175,i_0_3176,i_0_3194,i_0_3195,i_0_3447,i_0_3448,i_0_3658,i_0_3659,i_0_2352,i_0_2531,i_0_2532,i_0_3148,i_0_3149,i_0_3630,i_0_3772,i_0_2419,i_0_3285]) ).
cnf(i_0_7031,plain,
function(identity_relation(X1)),
inference(rename_variables,[],[i_0_4957]) ).
cnf(i_0_7032,plain,
v1_partfun1(identity_relation(X1),X1,X1),
inference(rename_variables,[],[i_0_4398]) ).
cnf(i_0_7033,plain,
reflexive(identity_relation(X1)),
inference(rename_variables,[],[i_0_4931]) ).
cnf(i_0_7034,plain,
( ~ function(X1)
| ~ v1_partfun1(X1,X2,X2)
| ~ reflexive(X1)
| ~ quasi_total(X1,X2,X2)
| ~ relation_of2(X1,X2,X2)
| onto(X1,X2,X2) ),
inference(rename_variables,[],[i_0_3285]) ).
cnf(i_0_7035,plain,
bijective(identity_relation(empty_set),empty_set,empty_set),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_4270,i_0_4272,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_6857,i_0_6874,i_0_6877,i_0_6884,i_0_6888,i_0_6897,i_0_6901,i_0_6905,i_0_6908,i_0_6912,i_0_6916,i_0_6921,i_0_6924,i_0_6928,i_0_6949,i_0_6965,i_0_6968,i_0_6972,i_0_6976,i_0_6980,i_0_6985,i_0_6989,i_0_6998,i_0_7002,i_0_7006,i_0_7010,i_0_7014,i_0_7018,i_0_6904,i_0_6909,i_0_6913,i_0_6917,i_0_6925,i_0_6929,i_0_6999,i_0_7003,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6864,i_0_6934,i_0_6942,i_0_6955,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_6842,i_0_6883,i_0_6887,i_0_6891,i_0_6894,i_0_6945,i_0_6952,i_0_6992,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_6856,i_0_6867,i_0_6920,i_0_4983,i_0_5027,i_0_5028,i_0_5030,i_0_5033,i_0_4727,i_0_4881,i_0_4957,i_0_6817,i_0_7031,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6843,i_0_6880,i_0_6938,i_0_6961,i_0_6222,i_0_4393,i_0_4398,i_0_6818,i_0_7032,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4979,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5013,i_0_5019,i_0_5026,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_6677,i_0_7033,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4942,i_0_6962,i_0_6969,i_0_6973,i_0_6977,i_0_6981,i_0_6984,i_0_6988,i_0_7011,i_0_7015,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337,i_0_4417,i_0_4469,i_0_4763,i_0_4772,i_0_6025,i_0_6168,i_0_4466,i_0_3678,i_0_3679,i_0_4348,i_0_6145,i_0_2379,i_0_2533,i_0_2534,i_0_2596,i_0_2597,i_0_2688,i_0_3034,i_0_3183,i_0_3470,i_0_3548,i_0_3800,i_0_3827,i_0_4075,i_0_4076,i_0_4143,i_0_4242,i_0_4403,i_0_4456,i_0_6129,i_0_2761,i_0_3175,i_0_3176,i_0_3194,i_0_3195,i_0_3447,i_0_3448,i_0_3658,i_0_3659,i_0_2352,i_0_2531,i_0_2532,i_0_3148,i_0_3149,i_0_3630,i_0_3772,i_0_2419,i_0_3285,i_0_3286]) ).
cnf(i_0_7036,plain,
function(identity_relation(X1)),
inference(rename_variables,[],[i_0_4957]) ).
cnf(i_0_7037,plain,
v1_partfun1(identity_relation(X1),X1,X1),
inference(rename_variables,[],[i_0_4398]) ).
cnf(i_0_7038,plain,
reflexive(identity_relation(X1)),
inference(rename_variables,[],[i_0_4931]) ).
cnf(i_0_7039,plain,
( ~ function(X1)
| ~ v1_partfun1(X1,X2,X2)
| ~ reflexive(X1)
| ~ quasi_total(X1,X2,X2)
| ~ relation_of2(X1,X2,X2)
| bijective(X1,X2,X2) ),
inference(rename_variables,[],[i_0_3286]) ).
cnf(i_0_7040,plain,
one_to_one(identity_relation(empty_set)),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_4270,i_0_4272,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_6857,i_0_6874,i_0_6877,i_0_6884,i_0_6888,i_0_6897,i_0_6901,i_0_6905,i_0_6908,i_0_6912,i_0_6916,i_0_6921,i_0_6924,i_0_6928,i_0_6949,i_0_6965,i_0_6968,i_0_6972,i_0_6976,i_0_6980,i_0_6985,i_0_6989,i_0_6998,i_0_7002,i_0_7006,i_0_7010,i_0_7014,i_0_7018,i_0_6904,i_0_6909,i_0_6913,i_0_6917,i_0_6925,i_0_6929,i_0_6999,i_0_7003,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6864,i_0_6934,i_0_6942,i_0_6955,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_6842,i_0_6883,i_0_6887,i_0_6891,i_0_6894,i_0_6945,i_0_6952,i_0_6992,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_6856,i_0_6867,i_0_6920,i_0_4983,i_0_5027,i_0_5028,i_0_5030,i_0_5033,i_0_4727,i_0_4881,i_0_4957,i_0_6817,i_0_7031,i_0_7036,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6843,i_0_6880,i_0_6938,i_0_6961,i_0_6222,i_0_4393,i_0_4398,i_0_6818,i_0_7032,i_0_7037,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4979,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5008,i_0_5010,i_0_5013,i_0_5019,i_0_5026,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_6677,i_0_7033,i_0_7038,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4942,i_0_6962,i_0_6969,i_0_6973,i_0_6977,i_0_6981,i_0_6984,i_0_6988,i_0_7011,i_0_7015,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337,i_0_4417,i_0_4469,i_0_4763,i_0_4772,i_0_6025,i_0_6168,i_0_4466,i_0_3678,i_0_3679,i_0_4348,i_0_6145,i_0_2379,i_0_2533,i_0_2534,i_0_2596,i_0_2597,i_0_2688,i_0_3034,i_0_3183,i_0_3470,i_0_3548,i_0_3800,i_0_3827,i_0_4075,i_0_4076,i_0_4143,i_0_4242,i_0_4403,i_0_4456,i_0_6129,i_0_2761,i_0_3175,i_0_3176,i_0_3194,i_0_3195,i_0_3447,i_0_3448,i_0_3658,i_0_3659,i_0_2352,i_0_2531,i_0_2532,i_0_3148,i_0_3149,i_0_3630,i_0_3772,i_0_2419,i_0_3285,i_0_3286,i_0_3459]) ).
cnf(i_0_7041,plain,
function(identity_relation(X1)),
inference(rename_variables,[],[i_0_4957]) ).
cnf(i_0_7042,plain,
reflexive(identity_relation(X1)),
inference(rename_variables,[],[i_0_4931]) ).
cnf(i_0_7043,plain,
v1_partfun1(identity_relation(X1),X1,X1),
inference(rename_variables,[],[i_0_4398]) ).
cnf(i_0_7044,plain,
( ~ function(X1)
| ~ reflexive(X1)
| ~ quasi_total(X1,X2,X2)
| ~ relation_of2(X1,X2,X2)
| ~ v1_partfun1(X1,X2,X2)
| one_to_one(X1) ),
inference(rename_variables,[],[i_0_3459]) ).
cnf(i_0_7045,plain,
equipotent(relation_inverse_image(empty_set,X1),empty_set),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_4270,i_0_4272,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_6857,i_0_6874,i_0_6877,i_0_6884,i_0_6888,i_0_6897,i_0_6901,i_0_6905,i_0_6908,i_0_6912,i_0_6916,i_0_6921,i_0_6924,i_0_6928,i_0_6949,i_0_6965,i_0_6968,i_0_6972,i_0_6976,i_0_6980,i_0_6985,i_0_6989,i_0_6998,i_0_7002,i_0_7006,i_0_7010,i_0_7014,i_0_7018,i_0_6904,i_0_6909,i_0_6913,i_0_6917,i_0_6925,i_0_6929,i_0_6999,i_0_7003,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6864,i_0_6934,i_0_6942,i_0_6955,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_6842,i_0_6883,i_0_6887,i_0_6891,i_0_6894,i_0_6945,i_0_6952,i_0_6992,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_6856,i_0_6867,i_0_6920,i_0_4983,i_0_5027,i_0_5028,i_0_5030,i_0_5033,i_0_4727,i_0_4881,i_0_4957,i_0_6817,i_0_7031,i_0_7036,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_5090,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6843,i_0_6880,i_0_6938,i_0_6961,i_0_6222,i_0_4393,i_0_4398,i_0_6818,i_0_7032,i_0_7037,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4979,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5007,i_0_5008,i_0_5010,i_0_5013,i_0_5019,i_0_5026,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_6677,i_0_7033,i_0_7038,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4942,i_0_6962,i_0_6969,i_0_6973,i_0_6977,i_0_6981,i_0_6984,i_0_6988,i_0_7011,i_0_7015,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337,i_0_4417,i_0_4469,i_0_4763,i_0_4772,i_0_6025,i_0_6168,i_0_4466,i_0_3678,i_0_3679,i_0_4348,i_0_6145,i_0_2379,i_0_2533,i_0_2534,i_0_2596,i_0_2597,i_0_2688,i_0_3034,i_0_3183,i_0_3470,i_0_3548,i_0_3800,i_0_3827,i_0_4075,i_0_4076,i_0_4143,i_0_4242,i_0_4403,i_0_4456,i_0_6129,i_0_2761,i_0_3175,i_0_3176,i_0_3194,i_0_3195,i_0_3447,i_0_3448,i_0_3658,i_0_3659,i_0_2352,i_0_2531,i_0_2532,i_0_3148,i_0_3149,i_0_3630,i_0_3772,i_0_2419,i_0_3285,i_0_3286,i_0_3459,i_0_4454]) ).
cnf(i_0_7046,plain,
( relation_dom(X1) != X2
| relation_rng(X1) != X3
| ~ function(X1)
| ~ one_to_one(X1)
| equipotent(X2,X3)
| ~ relation(X1) ),
inference(rename_variables,[],[i_0_4454]) ).
cnf(i_0_7047,plain,
empty_set != relation_composition(inclusion_relation(omega),inclusion_relation(omega)),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_4270,i_0_4272,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_6857,i_0_6874,i_0_6877,i_0_6884,i_0_6888,i_0_6897,i_0_6901,i_0_6905,i_0_6908,i_0_6912,i_0_6916,i_0_6921,i_0_6924,i_0_6928,i_0_6949,i_0_6965,i_0_6968,i_0_6972,i_0_6976,i_0_6980,i_0_6985,i_0_6989,i_0_6998,i_0_7002,i_0_7006,i_0_7010,i_0_7014,i_0_7018,i_0_7027,i_0_6904,i_0_6909,i_0_6913,i_0_6917,i_0_6925,i_0_6929,i_0_6999,i_0_7003,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6864,i_0_6934,i_0_6942,i_0_6955,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_6842,i_0_6883,i_0_6887,i_0_6891,i_0_6894,i_0_6945,i_0_6952,i_0_6992,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_6856,i_0_6867,i_0_6920,i_0_4983,i_0_5027,i_0_5028,i_0_5030,i_0_5033,i_0_4727,i_0_4881,i_0_4957,i_0_6817,i_0_7031,i_0_7036,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_5090,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6843,i_0_6880,i_0_6938,i_0_6961,i_0_6222,i_0_4393,i_0_4398,i_0_6818,i_0_7032,i_0_7037,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4979,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5007,i_0_5008,i_0_5010,i_0_5013,i_0_5019,i_0_5026,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_6677,i_0_7033,i_0_7038,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4942,i_0_6962,i_0_6969,i_0_6973,i_0_6977,i_0_6981,i_0_6984,i_0_6988,i_0_7011,i_0_7015,i_0_7028,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337,i_0_4417,i_0_4469,i_0_4763,i_0_4772,i_0_6025,i_0_6168,i_0_4466,i_0_3678,i_0_3679,i_0_4348,i_0_6145,i_0_2379,i_0_2533,i_0_2534,i_0_2596,i_0_2597,i_0_2688,i_0_3034,i_0_3183,i_0_3470,i_0_3548,i_0_3800,i_0_3827,i_0_4075,i_0_4076,i_0_4143,i_0_4242,i_0_4403,i_0_4456,i_0_6129,i_0_2761,i_0_3175,i_0_3176,i_0_3194,i_0_3195,i_0_3447,i_0_3448,i_0_3658,i_0_3659,i_0_2352,i_0_2531,i_0_2532,i_0_3148,i_0_3149,i_0_3630,i_0_3772,i_0_2419,i_0_3285,i_0_3286,i_0_3459,i_0_4454,i_0_2970]) ).
cnf(i_0_7048,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_6218]) ).
cnf(i_0_7049,plain,
relation(inclusion_relation(X1)),
inference(rename_variables,[],[i_0_4942]) ).
cnf(i_0_7050,plain,
( ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3)
| in(unordered_pair(unordered_pair(X1,X4),unordered_pair(X1,X1)),X5)
| ~ in(unordered_pair(unordered_pair(X2,X4),unordered_pair(X2,X2)),X6)
| X5 != relation_composition(X3,X6)
| ~ relation(X5)
| ~ relation(X6)
| ~ relation(X3) ),
inference(rename_variables,[],[i_0_2970]) ).
cnf(i_0_7051,plain,
below_refl(esk176_0,cast_to_el_of_lattice(esk176_0,esk123_1(the_carrier(poset_of_lattice(esk176_0)))),cast_to_el_of_lattice(esk176_0,esk123_1(the_carrier(poset_of_lattice(esk176_0))))),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_4270,i_0_4272,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_6857,i_0_6874,i_0_6877,i_0_6884,i_0_6888,i_0_6897,i_0_6901,i_0_6905,i_0_6908,i_0_6912,i_0_6916,i_0_6921,i_0_6924,i_0_6928,i_0_6949,i_0_6965,i_0_6968,i_0_6972,i_0_6976,i_0_6980,i_0_6985,i_0_6989,i_0_6998,i_0_7002,i_0_7006,i_0_7010,i_0_7014,i_0_7018,i_0_7027,i_0_6904,i_0_6909,i_0_6913,i_0_6917,i_0_6925,i_0_6929,i_0_6999,i_0_7003,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6864,i_0_6934,i_0_6942,i_0_6955,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_6842,i_0_6883,i_0_6887,i_0_6891,i_0_6894,i_0_6945,i_0_6952,i_0_6992,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_6856,i_0_6867,i_0_6920,i_0_4983,i_0_5027,i_0_5028,i_0_5030,i_0_5033,i_0_4727,i_0_4881,i_0_4957,i_0_6817,i_0_7031,i_0_7036,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_5090,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6843,i_0_6880,i_0_6938,i_0_6961,i_0_6222,i_0_4393,i_0_4398,i_0_6818,i_0_7032,i_0_7037,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4979,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5007,i_0_5008,i_0_5010,i_0_5013,i_0_5019,i_0_5020,i_0_5021,i_0_5023,i_0_5026,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_6677,i_0_7033,i_0_7038,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4942,i_0_6962,i_0_6969,i_0_6973,i_0_6977,i_0_6981,i_0_6984,i_0_6988,i_0_7011,i_0_7015,i_0_7028,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337,i_0_4417,i_0_4469,i_0_4763,i_0_4772,i_0_6025,i_0_6168,i_0_4466,i_0_3678,i_0_3679,i_0_4348,i_0_6145,i_0_2379,i_0_2533,i_0_2534,i_0_2596,i_0_2597,i_0_2688,i_0_3034,i_0_3183,i_0_3470,i_0_3548,i_0_3800,i_0_3827,i_0_4075,i_0_4076,i_0_4143,i_0_4242,i_0_4403,i_0_4456,i_0_6129,i_0_2761,i_0_3175,i_0_3176,i_0_3194,i_0_3195,i_0_3447,i_0_3448,i_0_3658,i_0_3659,i_0_2352,i_0_2531,i_0_2532,i_0_3148,i_0_3149,i_0_3630,i_0_3772,i_0_2419,i_0_3285,i_0_3286,i_0_3459,i_0_4454,i_0_2970,i_0_3910]) ).
cnf(i_0_7052,plain,
( ~ element(X1,the_carrier(X2))
| ~ element(X3,the_carrier(X2))
| ~ meet_commutative(X2)
| ~ meet_absorbing(X2)
| ~ join_absorbing(X2)
| ~ latt_str(X2)
| below_refl(X2,X1,X1)
| empty_carrier(X2) ),
inference(rename_variables,[],[i_0_3910]) ).
cnf(i_0_7053,plain,
below(esk176_0,cast_to_el_of_lattice(esk176_0,esk123_1(the_carrier(poset_of_lattice(esk176_0)))),cast_to_el_of_lattice(esk176_0,esk123_1(the_carrier(poset_of_lattice(esk176_0))))),
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_4270,i_0_4272,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_6857,i_0_6874,i_0_6877,i_0_6884,i_0_6888,i_0_6897,i_0_6901,i_0_6905,i_0_6908,i_0_6912,i_0_6916,i_0_6921,i_0_6924,i_0_6928,i_0_6949,i_0_6965,i_0_6968,i_0_6972,i_0_6976,i_0_6980,i_0_6985,i_0_6989,i_0_6998,i_0_7002,i_0_7006,i_0_7010,i_0_7014,i_0_7018,i_0_7027,i_0_6904,i_0_6909,i_0_6913,i_0_6917,i_0_6925,i_0_6929,i_0_6999,i_0_7003,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6864,i_0_6934,i_0_6942,i_0_6955,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_6842,i_0_6883,i_0_6887,i_0_6891,i_0_6894,i_0_6945,i_0_6952,i_0_6992,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_6856,i_0_6867,i_0_6920,i_0_4983,i_0_5027,i_0_5028,i_0_5030,i_0_5033,i_0_4727,i_0_4881,i_0_4957,i_0_6817,i_0_7031,i_0_7036,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_5090,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6843,i_0_6880,i_0_6938,i_0_6961,i_0_6222,i_0_4393,i_0_4398,i_0_6818,i_0_7032,i_0_7037,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4979,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5007,i_0_5008,i_0_5010,i_0_5013,i_0_5019,i_0_5020,i_0_5021,i_0_5023,i_0_5026,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_6677,i_0_7033,i_0_7038,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4942,i_0_6962,i_0_6969,i_0_6973,i_0_6977,i_0_6981,i_0_6984,i_0_6988,i_0_7011,i_0_7015,i_0_7028,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_3806,i_0_4025,i_0_4040,i_0_4302,i_0_4303,i_0_4337,i_0_4417,i_0_4469,i_0_4763,i_0_4772,i_0_6025,i_0_6168,i_0_4466,i_0_3678,i_0_3679,i_0_4348,i_0_6145,i_0_2379,i_0_2533,i_0_2534,i_0_2596,i_0_2597,i_0_2688,i_0_3034,i_0_3183,i_0_3470,i_0_3548,i_0_3800,i_0_3827,i_0_4075,i_0_4076,i_0_4143,i_0_4242,i_0_4403,i_0_4456,i_0_6129,i_0_2761,i_0_3175,i_0_3176,i_0_3194,i_0_3195,i_0_3447,i_0_3448,i_0_3658,i_0_3659,i_0_2352,i_0_2531,i_0_2532,i_0_3148,i_0_3149,i_0_3630,i_0_3772,i_0_2419,i_0_3285,i_0_3286,i_0_3459,i_0_4454,i_0_2970,i_0_3910,i_0_3589]) ).
cnf(i_0_7054,plain,
( ~ element(X1,the_carrier(X2))
| ~ element(X3,the_carrier(X2))
| empty_carrier(X2)
| ~ below_refl(X2,X1,X3)
| ~ meet_commutative(X2)
| ~ meet_absorbing(X2)
| ~ join_absorbing(X2)
| ~ latt_str(X2)
| below(X2,X1,X3) ),
inference(rename_variables,[],[i_0_3589]) ).
cnf(i_0_7055,plain,
$false,
inference(scs_inference,[],[i_0_4869,i_0_5086,i_0_4399,i_0_4270,i_0_4272,i_0_6218,i_0_6319,i_0_6322,i_0_6325,i_0_6499,i_0_6536,i_0_6622,i_0_6625,i_0_6628,i_0_6631,i_0_6634,i_0_6637,i_0_6640,i_0_6646,i_0_6691,i_0_6694,i_0_6697,i_0_6706,i_0_6709,i_0_6716,i_0_6721,i_0_6746,i_0_6756,i_0_6759,i_0_6762,i_0_6766,i_0_6770,i_0_6773,i_0_6776,i_0_6779,i_0_6783,i_0_6786,i_0_6789,i_0_6792,i_0_6797,i_0_6801,i_0_6806,i_0_6809,i_0_6812,i_0_6831,i_0_6835,i_0_6838,i_0_6857,i_0_6874,i_0_6877,i_0_6884,i_0_6888,i_0_6897,i_0_6901,i_0_6905,i_0_6908,i_0_6912,i_0_6916,i_0_6921,i_0_6924,i_0_6928,i_0_6949,i_0_6965,i_0_6968,i_0_6972,i_0_6976,i_0_6980,i_0_6985,i_0_6989,i_0_6998,i_0_7002,i_0_7006,i_0_7010,i_0_7014,i_0_7018,i_0_7027,i_0_6904,i_0_6909,i_0_6913,i_0_6917,i_0_6925,i_0_6929,i_0_6999,i_0_7003,i_0_4878,i_0_6274,i_0_6360,i_0_6388,i_0_6391,i_0_6394,i_0_6449,i_0_6451,i_0_6489,i_0_6492,i_0_6495,i_0_6498,i_0_6518,i_0_6527,i_0_6530,i_0_6533,i_0_6542,i_0_6548,i_0_6616,i_0_6619,i_0_6653,i_0_6657,i_0_6659,i_0_6661,i_0_6663,i_0_6665,i_0_6668,i_0_6670,i_0_6680,i_0_6682,i_0_6763,i_0_6767,i_0_6780,i_0_6793,i_0_6796,i_0_6800,i_0_6822,i_0_6827,i_0_6832,i_0_6850,i_0_6853,i_0_6860,i_0_6864,i_0_6934,i_0_6942,i_0_6955,i_0_6821,i_0_6826,i_0_4761,i_0_4768,i_0_6235,i_0_6238,i_0_6241,i_0_6244,i_0_6247,i_0_6258,i_0_6261,i_0_6453,i_0_6481,i_0_6484,i_0_6502,i_0_6505,i_0_6512,i_0_6515,i_0_6524,i_0_6553,i_0_6556,i_0_6559,i_0_6565,i_0_6574,i_0_6586,i_0_4769,i_0_6460,i_0_6463,i_0_6562,i_0_6568,i_0_6577,i_0_4770,i_0_6571,i_0_6580,i_0_4812,i_0_6277,i_0_6280,i_0_6283,i_0_6286,i_0_6399,i_0_6402,i_0_6405,i_0_6408,i_0_6413,i_0_6416,i_0_6419,i_0_6422,i_0_6425,i_0_6428,i_0_6431,i_0_6434,i_0_6437,i_0_6440,i_0_6443,i_0_6446,i_0_6583,i_0_6595,i_0_6842,i_0_6883,i_0_6887,i_0_6891,i_0_6894,i_0_6945,i_0_6952,i_0_6992,i_0_4813,i_0_6478,i_0_4882,i_0_6375,i_0_6823,i_0_6828,i_0_6856,i_0_6867,i_0_6920,i_0_4983,i_0_5027,i_0_5028,i_0_5030,i_0_5033,i_0_4727,i_0_4881,i_0_4957,i_0_6817,i_0_7031,i_0_7036,i_0_4597,i_0_4920,i_0_4921,i_0_6604,i_0_4888,i_0_5090,i_0_4646,i_0_4797,i_0_6684,i_0_4879,i_0_4880,i_0_6232,i_0_6345,i_0_6348,i_0_6509,i_0_6700,i_0_6843,i_0_6880,i_0_6938,i_0_6961,i_0_6222,i_0_4393,i_0_4398,i_0_6818,i_0_7032,i_0_7037,i_0_4887,i_0_4584,i_0_6539,i_0_4811,i_0_6731,i_0_6734,i_0_6737,i_0_6740,i_0_4814,i_0_6508,i_0_6645,i_0_4815,i_0_4603,i_0_6545,i_0_4979,i_0_4994,i_0_4999,i_0_5002,i_0_5003,i_0_5004,i_0_5007,i_0_5008,i_0_5010,i_0_5013,i_0_5019,i_0_5020,i_0_5021,i_0_5023,i_0_5026,i_0_5034,i_0_5040,i_0_5042,i_0_5047,i_0_5049,i_0_5050,i_0_5054,i_0_5056,i_0_5057,i_0_5058,i_0_5067,i_0_5068,i_0_5069,i_0_5070,i_0_5071,i_0_5072,i_0_5073,i_0_5074,i_0_5075,i_0_5076,i_0_5080,i_0_4798,i_0_4926,i_0_4931,i_0_6677,i_0_7033,i_0_7038,i_0_4934,i_0_4936,i_0_4937,i_0_4938,i_0_6605,i_0_4942,i_0_6962,i_0_6969,i_0_6973,i_0_6977,i_0_6981,i_0_6984,i_0_6988,i_0_7011,i_0_7015,i_0_7028,i_0_4945,i_0_4894,i_0_3963,i_0_4069,i_0_4070,i_0_4105,i_0_4150,i_0_4151,i_0_4173,i_0_4222,i_0_4223,i_0_4287,i_0_4288,i_0_4328,i_0_4329,i_0_4402,i_0_4491,i_0_4512,i_0_4652,i_0_4729,i_0_4774,i_0_4785,i_0_4786,i_0_4787,i_0_4788,i_0_4801,i_0_4802,i_0_4834,i_0_4835,i_0_4897,i_0_4898,i_0_4901,i_0_4904,i_0_4907,i_0_4908,i_0_4909,i_0_4910,i_0_4912,i_0_4914,i_0_4916,i_0_6030,i_0_6031,i_0_6148,i_0_6167,i_0_6186,i_0_6193,i_0_6194,i_0_6195,i_0_6208,i_0_5093,i_0_3962,i_0_4005,i_0_4293,i_0_4294,i_0_4295,i_0_4429,i_0_4430,i_0_4431,i_0_4579,i_0_4620,i_0_4647,i_0_4650,i_0_4654,i_0_4775,i_0_4776,i_0_4874,i_0_4891,i_0_4892,i_0_4893,i_0_4895,i_0_4896,i_0_4974,i_0_4976,i_0_4977,i_0_6213,i_0_4589,i_0_4683,i_0_4684,i_0_4685,i_0_4687,i_0_4688,i_0_4689,i_0_4690,i_0_4691,i_0_4692,i_0_4693,i_0_4694,i_0_4695,i_0_4696,i_0_4698,i_0_4699,i_0_4700,i_0_5782,i_0_5783,i_0_3789,i_0_3790,i_0_3791,i_0_3834,i_0_3835,i_0_3874,i_0_3997,i_0_3998,i_0_4012,i_0_4061,i_0_4062,i_0_4068,i_0_4071,i_0_4072,i_0_4098,i_0_4128,i_0_4129,i_0_4130,i_0_4141,i_0_4147,i_0_4148,i_0_4165,i_0_4330,i_0_4331,i_0_4332,i_0_4340,i_0_4369,i_0_4389,i_0_4390,i_0_4391,i_0_4407,i_0_4426,i_0_4477,i_0_4485,i_0_4508,i_0_4540,i_0_4551,i_0_4552,i_0_4553,i_0_4554,i_0_4555,i_0_4556,i_0_4557,i_0_4558,i_0_4559,i_0_4560,i_0_4561,i_0_4562,i_0_4563,i_0_4564,i_0_4565,i_0_4566,i_0_4754,i_0_4828,i_0_4830,i_0_4870,i_0_4871,i_0_4890,i_0_4973,i_0_5861,i_0_5925,i_0_5931,i_0_6019,i_0_6026,i_0_6027,i_0_6141,i_0_6180,i_0_6181,i_0_6188,i_0_6207,i_0_5094,i_0_5690,i_0_5691,i_0_5698,i_0_5699,i_0_5700,i_0_5701,i_0_5702,i_0_5703,i_0_5708,i_0_5709,i_0_5723,i_0_5726,i_0_5727,i_0_5740,i_0_5744,i_0_5821,i_0_5822,i_0_5823,i_0_5824,i_0_5829,i_0_5837,i_0_3016,i_0_3018,i_0_3145,i_0_3836,i_0_3869,i_0_4371,i_0_4372,i_0_4373,i_0_4374,i_0_4375,i_0_4376,i_0_4377,i_0_4378,i_0_4406,i_0_4509,i_0_4535,i_0_4536,i_0_4537,i_0_4538,i_0_4539,i_0_4705,i_0_5807,i_0_5808,i_0_5809,i_0_5810,i_0_5811,i_0_5812,i_0_5816,i_0_3691,i_0_3692,i_0_2461,i_0_2589,i_0_2598,i_0_2599,i_0_2616,i_0_2622,i_0_2994,i_0_2995,i_0_2996,i_0_2998,i_0_3041,i_0_3042,i_0_3116,i_0_3212,i_0_3490,i_0_3491,i_0_3576,i_0_3614,i_0_3673,i_0_3674,i_0_3761,i_0_3770,i_0_3797,i_0_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[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU355+2 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n001.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 03:00:18 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 17.83/10.87 % Version : CSE_E---1.7
% 17.83/10.87 % Problem : theBenchmark.p
% 17.83/10.87 % SZS status Theorem for theBenchmark.p
% 17.83/10.87 % SZS output start CNFRefutation
% See solution above
% 48.82/28.02 % Total time : 10.518s
%------------------------------------------------------------------------------