TSTP Solution File: SEU204+2 by iProverMo---2.5-0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : SEU204+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 10:25:57 EDT 2022
% Result : Theorem 8.19s 8.40s
% Output : CNFRefutation 8.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 205
% Syntax : Number of formulae : 2010 ( 333 unt; 0 def)
% Number of atoms : 6475 (1550 equ)
% Maximal formula atoms : 38 ( 3 avg)
% Number of connectives : 7740 (3275 ~;3703 |; 338 &)
% ( 134 <=>; 290 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 11 ( 8 usr; 2 prp; 0-2 aty)
% Number of functors : 152 ( 152 usr; 13 con; 0-5 aty)
% Number of variables : 4995 ( 263 sgn1341 !; 38 ?)
% Comments :
%------------------------------------------------------------------------------
% Axioms transformation by autotheo
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ! [X3] :
( relation(X3)
=> ( X3 = relation_composition(X1,X2)
<=> ! [X4,X5] :
( in(ordered_pair(X4,X5),X3)
<=> ? [X6] :
( in(ordered_pair(X4,X6),X1)
& in(ordered_pair(X6,X5),X2) ) ) ) ) ) ),
file('<stdin>',d8_relat_1) ).
fof(c_0_1,axiom,
! [X1,X2] :
( relation(X2)
=> ! [X3] :
( relation(X3)
=> ( X3 = relation_rng_restriction(X1,X2)
<=> ! [X4,X5] :
( in(ordered_pair(X4,X5),X3)
<=> ( in(X5,X1)
& in(ordered_pair(X4,X5),X2) ) ) ) ) ),
file('<stdin>',d12_relat_1) ).
fof(c_0_2,axiom,
! [X1] :
( relation(X1)
=> ! [X2,X3] :
( relation(X3)
=> ( X3 = relation_dom_restriction(X1,X2)
<=> ! [X4,X5] :
( in(ordered_pair(X4,X5),X3)
<=> ( in(X4,X2)
& in(ordered_pair(X4,X5),X1) ) ) ) ) ),
file('<stdin>',d11_relat_1) ).
fof(c_0_3,axiom,
! [X1] :
( relation(X1)
=> ! [X2,X3] :
( X3 = relation_image(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(X5,X2) ) ) ) ),
file('<stdin>',d13_relat_1) ).
fof(c_0_4,axiom,
! [X1,X2,X3] :
( X3 = cartesian_product2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ? [X5,X6] :
( in(X5,X1)
& in(X6,X2)
& X4 = ordered_pair(X5,X6) ) ) ),
file('<stdin>',d2_zfmisc_1) ).
fof(c_0_5,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ! [X3] :
( element(X3,powerset(powerset(X1)))
=> ( X3 = complements_of_subsets(X1,X2)
<=> ! [X4] :
( element(X4,powerset(X1))
=> ( in(X4,X3)
<=> in(subset_complement(X1,X4),X2) ) ) ) ) ),
file('<stdin>',d8_setfam_1) ).
fof(c_0_6,axiom,
! [X1,X2,X3] :
( X3 = set_intersection2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& in(X4,X2) ) ) ),
file('<stdin>',d3_xboole_0) ).
fof(c_0_7,axiom,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
file('<stdin>',d4_xboole_0) ).
fof(c_0_8,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( X2 = relation_inverse(X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> in(ordered_pair(X4,X3),X1) ) ) ) ),
file('<stdin>',d7_relat_1) ).
fof(c_0_9,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( X1 = X2
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X1)
<=> in(ordered_pair(X3,X4),X2) ) ) ) ),
file('<stdin>',d2_relat_1) ).
fof(c_0_10,axiom,
! [X1,X2,X3] :
( X3 = set_union2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
| in(X4,X2) ) ) ),
file('<stdin>',d2_xboole_0) ).
fof(c_0_11,axiom,
! [X1,X2] :
( relation(X2)
=> ( X2 = identity_relation(X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(X3,X1)
& X3 = X4 ) ) ) ),
file('<stdin>',d10_relat_1) ).
fof(c_0_12,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
file('<stdin>',d2_tarski) ).
fof(c_0_13,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_rng(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X4,X3),X1) ) ) ),
file('<stdin>',d5_relat_1) ).
fof(c_0_14,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_dom(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X3,X4),X1) ) ) ),
file('<stdin>',d4_relat_1) ).
fof(c_0_15,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( subset(X1,X2)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X1)
=> in(ordered_pair(X3,X4),X2) ) ) ) ),
file('<stdin>',d3_relat_1) ).
fof(c_0_16,axiom,
! [X1,X2] :
( ( X1 != empty_set
=> ( X2 = set_meet(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ! [X4] :
( in(X4,X1)
=> in(X3,X4) ) ) ) )
& ( X1 = empty_set
=> ( X2 = set_meet(X1)
<=> X2 = empty_set ) ) ),
file('<stdin>',d1_setfam_1) ).
fof(c_0_17,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> element(subset_difference(X1,X2,X3),powerset(X1)) ),
file('<stdin>',dt_k6_subset_1) ).
fof(c_0_18,axiom,
! [X1,X2] :
( X2 = union(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X3,X4)
& in(X4,X1) ) ) ),
file('<stdin>',d4_tarski) ).
fof(c_0_19,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> subset_difference(X1,X2,X3) = set_difference(X2,X3) ),
file('<stdin>',redefinition_k6_subset_1) ).
fof(c_0_20,axiom,
! [X1,X2] :
( X2 = powerset(X1)
<=> ! [X3] :
( in(X3,X2)
<=> subset(X3,X1) ) ),
file('<stdin>',d1_zfmisc_1) ).
fof(c_0_21,axiom,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
<=> in(X3,X2) )
=> X1 = X2 ),
file('<stdin>',t2_tarski) ).
fof(c_0_22,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> element(complements_of_subsets(X1,X2),powerset(powerset(X1))) ),
file('<stdin>',dt_k7_setfam_1) ).
fof(c_0_23,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> element(meet_of_subsets(X1,X2),powerset(X1)) ),
file('<stdin>',dt_k6_setfam_1) ).
fof(c_0_24,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> element(union_of_subsets(X1,X2),powerset(X1)) ),
file('<stdin>',dt_k5_setfam_1) ).
fof(c_0_25,axiom,
! [X1] :
( relation(X1)
<=> ! [X2] :
~ ( in(X2,X1)
& ! [X3,X4] : X2 != ordered_pair(X3,X4) ) ),
file('<stdin>',d1_relat_1) ).
fof(c_0_26,axiom,
! [X1] :
? [X2] :
( in(X1,X2)
& ! [X3,X4] :
( ( in(X3,X2)
& subset(X4,X3) )
=> in(X4,X2) )
& ! [X3] :
~ ( in(X3,X2)
& ! [X4] :
~ ( in(X4,X2)
& ! [X5] :
( subset(X5,X3)
=> in(X5,X4) ) ) )
& ! [X3] :
~ ( subset(X3,X2)
& ~ are_equipotent(X3,X2)
& ~ in(X3,X2) ) ),
file('<stdin>',t9_tarski) ).
fof(c_0_27,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('<stdin>',d1_tarski) ).
fof(c_0_28,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2 ),
file('<stdin>',involutiveness_k7_setfam_1) ).
fof(c_0_29,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> element(subset_complement(X1,X2),powerset(X1)) ),
file('<stdin>',dt_k3_subset_1) ).
fof(c_0_30,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('<stdin>',d3_tarski) ).
fof(c_0_31,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,subset_complement(X1,X2)) = X2 ),
file('<stdin>',involutiveness_k3_subset_1) ).
fof(c_0_32,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> meet_of_subsets(X1,X2) = set_meet(X2) ),
file('<stdin>',redefinition_k6_setfam_1) ).
fof(c_0_33,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> union_of_subsets(X1,X2) = union(X2) ),
file('<stdin>',redefinition_k5_setfam_1) ).
fof(c_0_34,axiom,
! [X1,X2,X3] :
( ( in(X1,X2)
& element(X2,powerset(X3)) )
=> element(X1,X3) ),
file('<stdin>',t4_subset) ).
fof(c_0_35,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
file('<stdin>',t5_subset) ).
fof(c_0_36,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,X2) = set_difference(X1,X2) ),
file('<stdin>',d5_subset_1) ).
fof(c_0_37,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('<stdin>',d5_tarski) ).
fof(c_0_38,axiom,
! [X1,X2] :
( ( ~ empty(X1)
& ~ empty(X2) )
=> ~ empty(cartesian_product2(X1,X2)) ),
file('<stdin>',fc4_subset_1) ).
fof(c_0_39,axiom,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X2,X1)) ),
file('<stdin>',fc3_xboole_0) ).
fof(c_0_40,axiom,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X1,X2)) ),
file('<stdin>',fc2_xboole_0) ).
fof(c_0_41,axiom,
! [X1,X2] : ~ empty(unordered_pair(X1,X2)),
file('<stdin>',fc3_subset_1) ).
fof(c_0_42,axiom,
! [X1,X2] : ~ empty(ordered_pair(X1,X2)),
file('<stdin>',fc1_zfmisc_1) ).
fof(c_0_43,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('<stdin>',d10_xboole_0) ).
fof(c_0_44,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('<stdin>',t3_subset) ).
fof(c_0_45,axiom,
! [X1,X2] :
( proper_subset(X1,X2)
=> ~ proper_subset(X2,X1) ),
file('<stdin>',antisymmetry_r2_xboole_0) ).
fof(c_0_46,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('<stdin>',antisymmetry_r2_hidden) ).
fof(c_0_47,axiom,
! [X1,X2] :
( ( empty(X1)
& relation(X2) )
=> ( empty(relation_composition(X1,X2))
& relation(relation_composition(X1,X2)) ) ),
file('<stdin>',fc9_relat_1) ).
fof(c_0_48,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(set_union2(X1,X2)) ),
file('<stdin>',fc2_relat_1) ).
fof(c_0_49,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(set_intersection2(X1,X2)) ),
file('<stdin>',fc1_relat_1) ).
fof(c_0_50,axiom,
! [X1,X2] :
( ( empty(X1)
& relation(X2) )
=> ( empty(relation_composition(X2,X1))
& relation(relation_composition(X2,X1)) ) ),
file('<stdin>',fc10_relat_1) ).
fof(c_0_51,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(relation_composition(X1,X2)) ),
file('<stdin>',dt_k5_relat_1) ).
fof(c_0_52,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('<stdin>',t2_subset) ).
fof(c_0_53,axiom,
! [X1,X2] :
( ( ~ empty(X1)
=> ( element(X2,X1)
<=> in(X2,X1) ) )
& ( empty(X1)
=> ( element(X2,X1)
<=> empty(X2) ) ) ),
file('<stdin>',d2_subset_1) ).
fof(c_0_54,axiom,
! [X1,X2] :
( proper_subset(X1,X2)
<=> ( subset(X1,X2)
& X1 != X2 ) ),
file('<stdin>',d8_xboole_0) ).
fof(c_0_55,axiom,
! [X1,X2] :
( relation(X2)
=> relation(relation_rng_restriction(X1,X2)) ),
file('<stdin>',dt_k8_relat_1) ).
fof(c_0_56,axiom,
! [X1,X2] :
( relation(X1)
=> relation(relation_dom_restriction(X1,X2)) ),
file('<stdin>',dt_k7_relat_1) ).
fof(c_0_57,axiom,
! [X1] :
( relation(X1)
=> relation_field(X1) = set_union2(relation_dom(X1),relation_rng(X1)) ),
file('<stdin>',d6_relat_1) ).
fof(c_0_58,axiom,
! [X1,X2] :
( in(X1,X2)
=> element(X1,X2) ),
file('<stdin>',t1_subset) ).
fof(c_0_59,axiom,
! [X1,X2] :
( disjoint(X1,X2)
=> disjoint(X2,X1) ),
file('<stdin>',symmetry_r1_xboole_0) ).
fof(c_0_60,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_intersection2(X1,X2) = empty_set ),
file('<stdin>',d7_xboole_0) ).
fof(c_0_61,axiom,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
file('<stdin>',rc1_subset_1) ).
fof(c_0_62,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('<stdin>',t7_boole) ).
fof(c_0_63,axiom,
! [X1] :
( ( ~ empty(X1)
& relation(X1) )
=> ~ empty(relation_rng(X1)) ),
file('<stdin>',fc6_relat_1) ).
fof(c_0_64,axiom,
! [X1] :
( ( ~ empty(X1)
& relation(X1) )
=> ~ empty(relation_dom(X1)) ),
file('<stdin>',fc5_relat_1) ).
fof(c_0_65,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('<stdin>',commutativity_k3_xboole_0) ).
fof(c_0_66,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('<stdin>',commutativity_k2_xboole_0) ).
fof(c_0_67,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('<stdin>',commutativity_k2_tarski) ).
fof(c_0_68,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2) ),
file('<stdin>',rc2_subset_1) ).
fof(c_0_69,axiom,
! [X1] : element(cast_to_subset(X1),powerset(X1)),
file('<stdin>',dt_k2_subset_1) ).
fof(c_0_70,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('<stdin>',d1_xboole_0) ).
fof(c_0_71,axiom,
! [X1,X2] : ~ proper_subset(X1,X1),
file('<stdin>',irreflexivity_r2_xboole_0) ).
fof(c_0_72,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('<stdin>',existence_m1_subset_1) ).
fof(c_0_73,axiom,
! [X1] :
( relation(X1)
=> relation_inverse(relation_inverse(X1)) = X1 ),
file('<stdin>',involutiveness_k4_relat_1) ).
fof(c_0_74,axiom,
! [X1] :
( empty(X1)
=> ( empty(relation_rng(X1))
& relation(relation_rng(X1)) ) ),
file('<stdin>',fc8_relat_1) ).
fof(c_0_75,axiom,
! [X1] :
( empty(X1)
=> ( empty(relation_dom(X1))
& relation(relation_dom(X1)) ) ),
file('<stdin>',fc7_relat_1) ).
fof(c_0_76,axiom,
! [X1] :
( relation(X1)
=> relation(relation_inverse(X1)) ),
file('<stdin>',dt_k4_relat_1) ).
fof(c_0_77,axiom,
! [X1] : ~ empty(singleton(X1)),
file('<stdin>',fc2_subset_1) ).
fof(c_0_78,axiom,
! [X1] : ~ empty(powerset(X1)),
file('<stdin>',fc1_subset_1) ).
fof(c_0_79,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
file('<stdin>',t8_boole) ).
fof(c_0_80,axiom,
! [X1,X2] : set_intersection2(X1,X1) = X1,
file('<stdin>',idempotence_k3_xboole_0) ).
fof(c_0_81,axiom,
! [X1,X2] : set_union2(X1,X1) = X1,
file('<stdin>',idempotence_k2_xboole_0) ).
fof(c_0_82,axiom,
! [X1,X2] : subset(X1,X1),
file('<stdin>',reflexivity_r1_tarski) ).
fof(c_0_83,axiom,
! [X1] : set_difference(X1,empty_set) = X1,
file('<stdin>',t3_boole) ).
fof(c_0_84,axiom,
! [X1] : set_union2(X1,empty_set) = X1,
file('<stdin>',t1_boole) ).
fof(c_0_85,axiom,
! [X1] : set_difference(empty_set,X1) = empty_set,
file('<stdin>',t4_boole) ).
fof(c_0_86,axiom,
! [X1] : set_intersection2(X1,empty_set) = empty_set,
file('<stdin>',t2_boole) ).
fof(c_0_87,axiom,
! [X1] :
( empty(X1)
=> relation(X1) ),
file('<stdin>',cc1_relat_1) ).
fof(c_0_88,axiom,
! [X1] : relation(identity_relation(X1)),
file('<stdin>',dt_k6_relat_1) ).
fof(c_0_89,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('<stdin>',t6_boole) ).
fof(c_0_90,axiom,
! [X1] : cast_to_subset(X1) = X1,
file('<stdin>',d4_subset_1) ).
fof(c_0_91,axiom,
? [X1] : ~ empty(X1),
file('<stdin>',rc2_xboole_0) ).
fof(c_0_92,axiom,
? [X1] :
( ~ empty(X1)
& relation(X1) ),
file('<stdin>',rc2_relat_1) ).
fof(c_0_93,axiom,
? [X1] : empty(X1),
file('<stdin>',rc1_xboole_0) ).
fof(c_0_94,axiom,
? [X1] :
( empty(X1)
& relation(X1) ),
file('<stdin>',rc1_relat_1) ).
fof(c_0_95,axiom,
( empty(empty_set)
& relation(empty_set) ),
file('<stdin>',fc4_relat_1) ).
fof(c_0_96,axiom,
empty(empty_set),
file('<stdin>',fc1_xboole_0) ).
fof(c_0_97,axiom,
$true,
file('<stdin>',dt_m1_subset_1) ).
fof(c_0_98,axiom,
$true,
file('<stdin>',dt_k9_relat_1) ).
fof(c_0_99,axiom,
$true,
file('<stdin>',dt_k4_xboole_0) ).
fof(c_0_100,axiom,
$true,
file('<stdin>',dt_k4_tarski) ).
fof(c_0_101,axiom,
$true,
file('<stdin>',dt_k3_xboole_0) ).
fof(c_0_102,axiom,
$true,
file('<stdin>',dt_k3_tarski) ).
fof(c_0_103,axiom,
$true,
file('<stdin>',dt_k3_relat_1) ).
fof(c_0_104,axiom,
$true,
file('<stdin>',dt_k2_zfmisc_1) ).
fof(c_0_105,axiom,
$true,
file('<stdin>',dt_k2_xboole_0) ).
fof(c_0_106,axiom,
$true,
file('<stdin>',dt_k2_tarski) ).
fof(c_0_107,axiom,
$true,
file('<stdin>',dt_k2_relat_1) ).
fof(c_0_108,axiom,
$true,
file('<stdin>',dt_k1_zfmisc_1) ).
fof(c_0_109,axiom,
$true,
file('<stdin>',dt_k1_xboole_0) ).
fof(c_0_110,axiom,
$true,
file('<stdin>',dt_k1_tarski) ).
fof(c_0_111,axiom,
$true,
file('<stdin>',dt_k1_setfam_1) ).
fof(c_0_112,axiom,
$true,
file('<stdin>',dt_k1_relat_1) ).
fof(c_0_113,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ! [X3] :
( relation(X3)
=> ( X3 = relation_composition(X1,X2)
<=> ! [X4,X5] :
( in(ordered_pair(X4,X5),X3)
<=> ? [X6] :
( in(ordered_pair(X4,X6),X1)
& in(ordered_pair(X6,X5),X2) ) ) ) ) ) ),
c_0_0 ).
fof(c_0_114,axiom,
! [X1,X2] :
( relation(X2)
=> ! [X3] :
( relation(X3)
=> ( X3 = relation_rng_restriction(X1,X2)
<=> ! [X4,X5] :
( in(ordered_pair(X4,X5),X3)
<=> ( in(X5,X1)
& in(ordered_pair(X4,X5),X2) ) ) ) ) ),
c_0_1 ).
fof(c_0_115,axiom,
! [X1] :
( relation(X1)
=> ! [X2,X3] :
( relation(X3)
=> ( X3 = relation_dom_restriction(X1,X2)
<=> ! [X4,X5] :
( in(ordered_pair(X4,X5),X3)
<=> ( in(X4,X2)
& in(ordered_pair(X4,X5),X1) ) ) ) ) ),
c_0_2 ).
fof(c_0_116,axiom,
! [X1] :
( relation(X1)
=> ! [X2,X3] :
( X3 = relation_image(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(X5,X2) ) ) ) ),
c_0_3 ).
fof(c_0_117,axiom,
! [X1,X2,X3] :
( X3 = cartesian_product2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ? [X5,X6] :
( in(X5,X1)
& in(X6,X2)
& X4 = ordered_pair(X5,X6) ) ) ),
c_0_4 ).
fof(c_0_118,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ! [X3] :
( element(X3,powerset(powerset(X1)))
=> ( X3 = complements_of_subsets(X1,X2)
<=> ! [X4] :
( element(X4,powerset(X1))
=> ( in(X4,X3)
<=> in(subset_complement(X1,X4),X2) ) ) ) ) ),
c_0_5 ).
fof(c_0_119,axiom,
! [X1,X2,X3] :
( X3 = set_intersection2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& in(X4,X2) ) ) ),
c_0_6 ).
fof(c_0_120,plain,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_121,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( X2 = relation_inverse(X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> in(ordered_pair(X4,X3),X1) ) ) ) ),
c_0_8 ).
fof(c_0_122,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( X1 = X2
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X1)
<=> in(ordered_pair(X3,X4),X2) ) ) ) ),
c_0_9 ).
fof(c_0_123,axiom,
! [X1,X2,X3] :
( X3 = set_union2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
| in(X4,X2) ) ) ),
c_0_10 ).
fof(c_0_124,axiom,
! [X1,X2] :
( relation(X2)
=> ( X2 = identity_relation(X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(X3,X1)
& X3 = X4 ) ) ) ),
c_0_11 ).
fof(c_0_125,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
c_0_12 ).
fof(c_0_126,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_rng(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X4,X3),X1) ) ) ),
c_0_13 ).
fof(c_0_127,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_dom(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X3,X4),X1) ) ) ),
c_0_14 ).
fof(c_0_128,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( subset(X1,X2)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X1)
=> in(ordered_pair(X3,X4),X2) ) ) ) ),
c_0_15 ).
fof(c_0_129,axiom,
! [X1,X2] :
( ( X1 != empty_set
=> ( X2 = set_meet(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ! [X4] :
( in(X4,X1)
=> in(X3,X4) ) ) ) )
& ( X1 = empty_set
=> ( X2 = set_meet(X1)
<=> X2 = empty_set ) ) ),
c_0_16 ).
fof(c_0_130,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> element(subset_difference(X1,X2,X3),powerset(X1)) ),
c_0_17 ).
fof(c_0_131,axiom,
! [X1,X2] :
( X2 = union(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X3,X4)
& in(X4,X1) ) ) ),
c_0_18 ).
fof(c_0_132,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> subset_difference(X1,X2,X3) = set_difference(X2,X3) ),
c_0_19 ).
fof(c_0_133,axiom,
! [X1,X2] :
( X2 = powerset(X1)
<=> ! [X3] :
( in(X3,X2)
<=> subset(X3,X1) ) ),
c_0_20 ).
fof(c_0_134,axiom,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
<=> in(X3,X2) )
=> X1 = X2 ),
c_0_21 ).
fof(c_0_135,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> element(complements_of_subsets(X1,X2),powerset(powerset(X1))) ),
c_0_22 ).
fof(c_0_136,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> element(meet_of_subsets(X1,X2),powerset(X1)) ),
c_0_23 ).
fof(c_0_137,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> element(union_of_subsets(X1,X2),powerset(X1)) ),
c_0_24 ).
fof(c_0_138,axiom,
! [X1] :
( relation(X1)
<=> ! [X2] :
~ ( in(X2,X1)
& ! [X3,X4] : X2 != ordered_pair(X3,X4) ) ),
c_0_25 ).
fof(c_0_139,plain,
! [X1] :
? [X2] :
( in(X1,X2)
& ! [X3,X4] :
( ( in(X3,X2)
& subset(X4,X3) )
=> in(X4,X2) )
& ! [X3] :
~ ( in(X3,X2)
& ! [X4] :
~ ( in(X4,X2)
& ! [X5] :
( subset(X5,X3)
=> in(X5,X4) ) ) )
& ! [X3] :
~ ( subset(X3,X2)
& ~ are_equipotent(X3,X2)
& ~ in(X3,X2) ) ),
inference(fof_simplification,[status(thm)],[c_0_26]) ).
fof(c_0_140,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
c_0_27 ).
fof(c_0_141,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2 ),
c_0_28 ).
fof(c_0_142,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> element(subset_complement(X1,X2),powerset(X1)) ),
c_0_29 ).
fof(c_0_143,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
c_0_30 ).
fof(c_0_144,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,subset_complement(X1,X2)) = X2 ),
c_0_31 ).
fof(c_0_145,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> meet_of_subsets(X1,X2) = set_meet(X2) ),
c_0_32 ).
fof(c_0_146,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> union_of_subsets(X1,X2) = union(X2) ),
c_0_33 ).
fof(c_0_147,axiom,
! [X1,X2,X3] :
( ( in(X1,X2)
& element(X2,powerset(X3)) )
=> element(X1,X3) ),
c_0_34 ).
fof(c_0_148,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
c_0_35 ).
fof(c_0_149,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,X2) = set_difference(X1,X2) ),
c_0_36 ).
fof(c_0_150,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
c_0_37 ).
fof(c_0_151,plain,
! [X1,X2] :
( ( ~ empty(X1)
& ~ empty(X2) )
=> ~ empty(cartesian_product2(X1,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_38]) ).
fof(c_0_152,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X2,X1)) ),
inference(fof_simplification,[status(thm)],[c_0_39]) ).
fof(c_0_153,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X1,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_40]) ).
fof(c_0_154,plain,
! [X1,X2] : ~ empty(unordered_pair(X1,X2)),
inference(fof_simplification,[status(thm)],[c_0_41]) ).
fof(c_0_155,plain,
! [X1,X2] : ~ empty(ordered_pair(X1,X2)),
inference(fof_simplification,[status(thm)],[c_0_42]) ).
fof(c_0_156,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
c_0_43 ).
fof(c_0_157,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
c_0_44 ).
fof(c_0_158,plain,
! [X1,X2] :
( proper_subset(X1,X2)
=> ~ proper_subset(X2,X1) ),
inference(fof_simplification,[status(thm)],[c_0_45]) ).
fof(c_0_159,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[c_0_46]) ).
fof(c_0_160,axiom,
! [X1,X2] :
( ( empty(X1)
& relation(X2) )
=> ( empty(relation_composition(X1,X2))
& relation(relation_composition(X1,X2)) ) ),
c_0_47 ).
fof(c_0_161,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(set_union2(X1,X2)) ),
c_0_48 ).
fof(c_0_162,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(set_intersection2(X1,X2)) ),
c_0_49 ).
fof(c_0_163,axiom,
! [X1,X2] :
( ( empty(X1)
& relation(X2) )
=> ( empty(relation_composition(X2,X1))
& relation(relation_composition(X2,X1)) ) ),
c_0_50 ).
fof(c_0_164,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(relation_composition(X1,X2)) ),
c_0_51 ).
fof(c_0_165,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
c_0_52 ).
fof(c_0_166,plain,
! [X1,X2] :
( ( ~ empty(X1)
=> ( element(X2,X1)
<=> in(X2,X1) ) )
& ( empty(X1)
=> ( element(X2,X1)
<=> empty(X2) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_53]) ).
fof(c_0_167,axiom,
! [X1,X2] :
( proper_subset(X1,X2)
<=> ( subset(X1,X2)
& X1 != X2 ) ),
c_0_54 ).
fof(c_0_168,axiom,
! [X1,X2] :
( relation(X2)
=> relation(relation_rng_restriction(X1,X2)) ),
c_0_55 ).
fof(c_0_169,axiom,
! [X1,X2] :
( relation(X1)
=> relation(relation_dom_restriction(X1,X2)) ),
c_0_56 ).
fof(c_0_170,axiom,
! [X1] :
( relation(X1)
=> relation_field(X1) = set_union2(relation_dom(X1),relation_rng(X1)) ),
c_0_57 ).
fof(c_0_171,axiom,
! [X1,X2] :
( in(X1,X2)
=> element(X1,X2) ),
c_0_58 ).
fof(c_0_172,axiom,
! [X1,X2] :
( disjoint(X1,X2)
=> disjoint(X2,X1) ),
c_0_59 ).
fof(c_0_173,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_intersection2(X1,X2) = empty_set ),
c_0_60 ).
fof(c_0_174,plain,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
inference(fof_simplification,[status(thm)],[c_0_61]) ).
fof(c_0_175,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
c_0_62 ).
fof(c_0_176,plain,
! [X1] :
( ( ~ empty(X1)
& relation(X1) )
=> ~ empty(relation_rng(X1)) ),
inference(fof_simplification,[status(thm)],[c_0_63]) ).
fof(c_0_177,plain,
! [X1] :
( ( ~ empty(X1)
& relation(X1) )
=> ~ empty(relation_dom(X1)) ),
inference(fof_simplification,[status(thm)],[c_0_64]) ).
fof(c_0_178,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
c_0_65 ).
fof(c_0_179,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
c_0_66 ).
fof(c_0_180,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
c_0_67 ).
fof(c_0_181,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2) ),
c_0_68 ).
fof(c_0_182,axiom,
! [X1] : element(cast_to_subset(X1),powerset(X1)),
c_0_69 ).
fof(c_0_183,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[c_0_70]) ).
fof(c_0_184,plain,
! [X1,X2] : ~ proper_subset(X1,X1),
inference(fof_simplification,[status(thm)],[c_0_71]) ).
fof(c_0_185,axiom,
! [X1] :
? [X2] : element(X2,X1),
c_0_72 ).
fof(c_0_186,axiom,
! [X1] :
( relation(X1)
=> relation_inverse(relation_inverse(X1)) = X1 ),
c_0_73 ).
fof(c_0_187,axiom,
! [X1] :
( empty(X1)
=> ( empty(relation_rng(X1))
& relation(relation_rng(X1)) ) ),
c_0_74 ).
fof(c_0_188,axiom,
! [X1] :
( empty(X1)
=> ( empty(relation_dom(X1))
& relation(relation_dom(X1)) ) ),
c_0_75 ).
fof(c_0_189,axiom,
! [X1] :
( relation(X1)
=> relation(relation_inverse(X1)) ),
c_0_76 ).
fof(c_0_190,plain,
! [X1] : ~ empty(singleton(X1)),
inference(fof_simplification,[status(thm)],[c_0_77]) ).
fof(c_0_191,plain,
! [X1] : ~ empty(powerset(X1)),
inference(fof_simplification,[status(thm)],[c_0_78]) ).
fof(c_0_192,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
c_0_79 ).
fof(c_0_193,axiom,
! [X1,X2] : set_intersection2(X1,X1) = X1,
c_0_80 ).
fof(c_0_194,axiom,
! [X1,X2] : set_union2(X1,X1) = X1,
c_0_81 ).
fof(c_0_195,axiom,
! [X1,X2] : subset(X1,X1),
c_0_82 ).
fof(c_0_196,axiom,
! [X1] : set_difference(X1,empty_set) = X1,
c_0_83 ).
fof(c_0_197,axiom,
! [X1] : set_union2(X1,empty_set) = X1,
c_0_84 ).
fof(c_0_198,axiom,
! [X1] : set_difference(empty_set,X1) = empty_set,
c_0_85 ).
fof(c_0_199,axiom,
! [X1] : set_intersection2(X1,empty_set) = empty_set,
c_0_86 ).
fof(c_0_200,axiom,
! [X1] :
( empty(X1)
=> relation(X1) ),
c_0_87 ).
fof(c_0_201,axiom,
! [X1] : relation(identity_relation(X1)),
c_0_88 ).
fof(c_0_202,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
c_0_89 ).
fof(c_0_203,axiom,
! [X1] : cast_to_subset(X1) = X1,
c_0_90 ).
fof(c_0_204,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[c_0_91]) ).
fof(c_0_205,plain,
? [X1] :
( ~ empty(X1)
& relation(X1) ),
inference(fof_simplification,[status(thm)],[c_0_92]) ).
fof(c_0_206,axiom,
? [X1] : empty(X1),
c_0_93 ).
fof(c_0_207,axiom,
? [X1] :
( empty(X1)
& relation(X1) ),
c_0_94 ).
fof(c_0_208,axiom,
( empty(empty_set)
& relation(empty_set) ),
c_0_95 ).
fof(c_0_209,axiom,
empty(empty_set),
c_0_96 ).
fof(c_0_210,axiom,
$true,
c_0_97 ).
fof(c_0_211,axiom,
$true,
c_0_98 ).
fof(c_0_212,axiom,
$true,
c_0_99 ).
fof(c_0_213,axiom,
$true,
c_0_100 ).
fof(c_0_214,axiom,
$true,
c_0_101 ).
fof(c_0_215,axiom,
$true,
c_0_102 ).
fof(c_0_216,axiom,
$true,
c_0_103 ).
fof(c_0_217,axiom,
$true,
c_0_104 ).
fof(c_0_218,axiom,
$true,
c_0_105 ).
fof(c_0_219,axiom,
$true,
c_0_106 ).
fof(c_0_220,axiom,
$true,
c_0_107 ).
fof(c_0_221,axiom,
$true,
c_0_108 ).
fof(c_0_222,axiom,
$true,
c_0_109 ).
fof(c_0_223,axiom,
$true,
c_0_110 ).
fof(c_0_224,axiom,
$true,
c_0_111 ).
fof(c_0_225,axiom,
$true,
c_0_112 ).
fof(c_0_226,plain,
! [X7,X8,X9,X10,X11,X13,X14,X15,X18] :
( ( in(ordered_pair(X10,esk44_5(X7,X8,X9,X10,X11)),X7)
| ~ in(ordered_pair(X10,X11),X9)
| X9 != relation_composition(X7,X8)
| ~ relation(X9)
| ~ relation(X8)
| ~ relation(X7) )
& ( in(ordered_pair(esk44_5(X7,X8,X9,X10,X11),X11),X8)
| ~ in(ordered_pair(X10,X11),X9)
| X9 != relation_composition(X7,X8)
| ~ relation(X9)
| ~ relation(X8)
| ~ relation(X7) )
& ( ~ in(ordered_pair(X13,X15),X7)
| ~ in(ordered_pair(X15,X14),X8)
| in(ordered_pair(X13,X14),X9)
| X9 != relation_composition(X7,X8)
| ~ relation(X9)
| ~ relation(X8)
| ~ relation(X7) )
& ( ~ in(ordered_pair(esk45_3(X7,X8,X9),esk46_3(X7,X8,X9)),X9)
| ~ in(ordered_pair(esk45_3(X7,X8,X9),X18),X7)
| ~ in(ordered_pair(X18,esk46_3(X7,X8,X9)),X8)
| X9 = relation_composition(X7,X8)
| ~ relation(X9)
| ~ relation(X8)
| ~ relation(X7) )
& ( in(ordered_pair(esk45_3(X7,X8,X9),esk47_3(X7,X8,X9)),X7)
| in(ordered_pair(esk45_3(X7,X8,X9),esk46_3(X7,X8,X9)),X9)
| X9 = relation_composition(X7,X8)
| ~ relation(X9)
| ~ relation(X8)
| ~ relation(X7) )
& ( in(ordered_pair(esk47_3(X7,X8,X9),esk46_3(X7,X8,X9)),X8)
| in(ordered_pair(esk45_3(X7,X8,X9),esk46_3(X7,X8,X9)),X9)
| X9 = relation_composition(X7,X8)
| ~ relation(X9)
| ~ relation(X8)
| ~ relation(X7) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_113])])])])])]) ).
fof(c_0_227,plain,
! [X6,X7,X8,X9,X10,X11,X12] :
( ( in(X10,X6)
| ~ in(ordered_pair(X9,X10),X8)
| X8 != relation_rng_restriction(X6,X7)
| ~ relation(X8)
| ~ relation(X7) )
& ( in(ordered_pair(X9,X10),X7)
| ~ in(ordered_pair(X9,X10),X8)
| X8 != relation_rng_restriction(X6,X7)
| ~ relation(X8)
| ~ relation(X7) )
& ( ~ in(X12,X6)
| ~ in(ordered_pair(X11,X12),X7)
| in(ordered_pair(X11,X12),X8)
| X8 != relation_rng_restriction(X6,X7)
| ~ relation(X8)
| ~ relation(X7) )
& ( ~ in(ordered_pair(esk5_3(X6,X7,X8),esk6_3(X6,X7,X8)),X8)
| ~ in(esk6_3(X6,X7,X8),X6)
| ~ in(ordered_pair(esk5_3(X6,X7,X8),esk6_3(X6,X7,X8)),X7)
| X8 = relation_rng_restriction(X6,X7)
| ~ relation(X8)
| ~ relation(X7) )
& ( in(esk6_3(X6,X7,X8),X6)
| in(ordered_pair(esk5_3(X6,X7,X8),esk6_3(X6,X7,X8)),X8)
| X8 = relation_rng_restriction(X6,X7)
| ~ relation(X8)
| ~ relation(X7) )
& ( in(ordered_pair(esk5_3(X6,X7,X8),esk6_3(X6,X7,X8)),X7)
| in(ordered_pair(esk5_3(X6,X7,X8),esk6_3(X6,X7,X8)),X8)
| X8 = relation_rng_restriction(X6,X7)
| ~ relation(X8)
| ~ relation(X7) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_114])])])])])]) ).
fof(c_0_228,plain,
! [X6,X7,X8,X9,X10,X11,X12] :
( ( in(X9,X7)
| ~ in(ordered_pair(X9,X10),X8)
| X8 != relation_dom_restriction(X6,X7)
| ~ relation(X8)
| ~ relation(X6) )
& ( in(ordered_pair(X9,X10),X6)
| ~ in(ordered_pair(X9,X10),X8)
| X8 != relation_dom_restriction(X6,X7)
| ~ relation(X8)
| ~ relation(X6) )
& ( ~ in(X11,X7)
| ~ in(ordered_pair(X11,X12),X6)
| in(ordered_pair(X11,X12),X8)
| X8 != relation_dom_restriction(X6,X7)
| ~ relation(X8)
| ~ relation(X6) )
& ( ~ in(ordered_pair(esk3_3(X6,X7,X8),esk4_3(X6,X7,X8)),X8)
| ~ in(esk3_3(X6,X7,X8),X7)
| ~ in(ordered_pair(esk3_3(X6,X7,X8),esk4_3(X6,X7,X8)),X6)
| X8 = relation_dom_restriction(X6,X7)
| ~ relation(X8)
| ~ relation(X6) )
& ( in(esk3_3(X6,X7,X8),X7)
| in(ordered_pair(esk3_3(X6,X7,X8),esk4_3(X6,X7,X8)),X8)
| X8 = relation_dom_restriction(X6,X7)
| ~ relation(X8)
| ~ relation(X6) )
& ( in(ordered_pair(esk3_3(X6,X7,X8),esk4_3(X6,X7,X8)),X6)
| in(ordered_pair(esk3_3(X6,X7,X8),esk4_3(X6,X7,X8)),X8)
| X8 = relation_dom_restriction(X6,X7)
| ~ relation(X8)
| ~ relation(X6) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_115])])])])])]) ).
fof(c_0_229,plain,
! [X6,X7,X8,X9,X11,X12,X13,X14,X16] :
( ( in(ordered_pair(esk7_4(X6,X7,X8,X9),X9),X6)
| ~ in(X9,X8)
| X8 != relation_image(X6,X7)
| ~ relation(X6) )
& ( in(esk7_4(X6,X7,X8,X9),X7)
| ~ in(X9,X8)
| X8 != relation_image(X6,X7)
| ~ relation(X6) )
& ( ~ in(ordered_pair(X12,X11),X6)
| ~ in(X12,X7)
| in(X11,X8)
| X8 != relation_image(X6,X7)
| ~ relation(X6) )
& ( ~ in(esk8_3(X6,X13,X14),X14)
| ~ in(ordered_pair(X16,esk8_3(X6,X13,X14)),X6)
| ~ in(X16,X13)
| X14 = relation_image(X6,X13)
| ~ relation(X6) )
& ( in(ordered_pair(esk9_3(X6,X13,X14),esk8_3(X6,X13,X14)),X6)
| in(esk8_3(X6,X13,X14),X14)
| X14 = relation_image(X6,X13)
| ~ relation(X6) )
& ( in(esk9_3(X6,X13,X14),X13)
| in(esk8_3(X6,X13,X14),X14)
| X14 = relation_image(X6,X13)
| ~ relation(X6) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_116])])])])])]) ).
fof(c_0_230,plain,
! [X7,X8,X9,X10,X13,X14,X15,X16,X17,X18,X20,X21] :
( ( in(esk23_4(X7,X8,X9,X10),X7)
| ~ in(X10,X9)
| X9 != cartesian_product2(X7,X8) )
& ( in(esk24_4(X7,X8,X9,X10),X8)
| ~ in(X10,X9)
| X9 != cartesian_product2(X7,X8) )
& ( X10 = ordered_pair(esk23_4(X7,X8,X9,X10),esk24_4(X7,X8,X9,X10))
| ~ in(X10,X9)
| X9 != cartesian_product2(X7,X8) )
& ( ~ in(X14,X7)
| ~ in(X15,X8)
| X13 != ordered_pair(X14,X15)
| in(X13,X9)
| X9 != cartesian_product2(X7,X8) )
& ( ~ in(esk25_3(X16,X17,X18),X18)
| ~ in(X20,X16)
| ~ in(X21,X17)
| esk25_3(X16,X17,X18) != ordered_pair(X20,X21)
| X18 = cartesian_product2(X16,X17) )
& ( in(esk26_3(X16,X17,X18),X16)
| in(esk25_3(X16,X17,X18),X18)
| X18 = cartesian_product2(X16,X17) )
& ( in(esk27_3(X16,X17,X18),X17)
| in(esk25_3(X16,X17,X18),X18)
| X18 = cartesian_product2(X16,X17) )
& ( esk25_3(X16,X17,X18) = ordered_pair(esk26_3(X16,X17,X18),esk27_3(X16,X17,X18))
| in(esk25_3(X16,X17,X18),X18)
| X18 = cartesian_product2(X16,X17) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_117])])])])])]) ).
fof(c_0_231,plain,
! [X5,X6,X7,X8] :
( ( ~ in(X8,X7)
| in(subset_complement(X5,X8),X6)
| ~ element(X8,powerset(X5))
| X7 != complements_of_subsets(X5,X6)
| ~ element(X7,powerset(powerset(X5)))
| ~ element(X6,powerset(powerset(X5))) )
& ( ~ in(subset_complement(X5,X8),X6)
| in(X8,X7)
| ~ element(X8,powerset(X5))
| X7 != complements_of_subsets(X5,X6)
| ~ element(X7,powerset(powerset(X5)))
| ~ element(X6,powerset(powerset(X5))) )
& ( element(esk48_3(X5,X6,X7),powerset(X5))
| X7 = complements_of_subsets(X5,X6)
| ~ element(X7,powerset(powerset(X5)))
| ~ element(X6,powerset(powerset(X5))) )
& ( ~ in(esk48_3(X5,X6,X7),X7)
| ~ in(subset_complement(X5,esk48_3(X5,X6,X7)),X6)
| X7 = complements_of_subsets(X5,X6)
| ~ element(X7,powerset(powerset(X5)))
| ~ element(X6,powerset(powerset(X5))) )
& ( in(esk48_3(X5,X6,X7),X7)
| in(subset_complement(X5,esk48_3(X5,X6,X7)),X6)
| X7 = complements_of_subsets(X5,X6)
| ~ element(X7,powerset(powerset(X5)))
| ~ element(X6,powerset(powerset(X5))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_118])])])])]) ).
fof(c_0_232,plain,
! [X5,X6,X7,X8,X9,X10,X11,X12] :
( ( in(X8,X5)
| ~ in(X8,X7)
| X7 != set_intersection2(X5,X6) )
& ( in(X8,X6)
| ~ in(X8,X7)
| X7 != set_intersection2(X5,X6) )
& ( ~ in(X9,X5)
| ~ in(X9,X6)
| in(X9,X7)
| X7 != set_intersection2(X5,X6) )
& ( ~ in(esk31_3(X10,X11,X12),X12)
| ~ in(esk31_3(X10,X11,X12),X10)
| ~ in(esk31_3(X10,X11,X12),X11)
| X12 = set_intersection2(X10,X11) )
& ( in(esk31_3(X10,X11,X12),X10)
| in(esk31_3(X10,X11,X12),X12)
| X12 = set_intersection2(X10,X11) )
& ( in(esk31_3(X10,X11,X12),X11)
| in(esk31_3(X10,X11,X12),X12)
| X12 = set_intersection2(X10,X11) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_119])])])])])]) ).
fof(c_0_233,plain,
! [X5,X6,X7,X8,X9,X10,X11,X12] :
( ( in(X8,X5)
| ~ in(X8,X7)
| X7 != set_difference(X5,X6) )
& ( ~ in(X8,X6)
| ~ in(X8,X7)
| X7 != set_difference(X5,X6) )
& ( ~ in(X9,X5)
| in(X9,X6)
| in(X9,X7)
| X7 != set_difference(X5,X6) )
& ( ~ in(esk38_3(X10,X11,X12),X12)
| ~ in(esk38_3(X10,X11,X12),X10)
| in(esk38_3(X10,X11,X12),X11)
| X12 = set_difference(X10,X11) )
& ( in(esk38_3(X10,X11,X12),X10)
| in(esk38_3(X10,X11,X12),X12)
| X12 = set_difference(X10,X11) )
& ( ~ in(esk38_3(X10,X11,X12),X11)
| in(esk38_3(X10,X11,X12),X12)
| X12 = set_difference(X10,X11) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_120])])])])])]) ).
fof(c_0_234,plain,
! [X5,X6,X7,X8,X9,X10] :
( ( ~ in(ordered_pair(X7,X8),X6)
| in(ordered_pair(X8,X7),X5)
| X6 != relation_inverse(X5)
| ~ relation(X6)
| ~ relation(X5) )
& ( ~ in(ordered_pair(X10,X9),X5)
| in(ordered_pair(X9,X10),X6)
| X6 != relation_inverse(X5)
| ~ relation(X6)
| ~ relation(X5) )
& ( ~ in(ordered_pair(esk42_2(X5,X6),esk43_2(X5,X6)),X6)
| ~ in(ordered_pair(esk43_2(X5,X6),esk42_2(X5,X6)),X5)
| X6 = relation_inverse(X5)
| ~ relation(X6)
| ~ relation(X5) )
& ( in(ordered_pair(esk42_2(X5,X6),esk43_2(X5,X6)),X6)
| in(ordered_pair(esk43_2(X5,X6),esk42_2(X5,X6)),X5)
| X6 = relation_inverse(X5)
| ~ relation(X6)
| ~ relation(X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_121])])])])])]) ).
fof(c_0_235,plain,
! [X5,X6,X7,X8,X9,X10] :
( ( ~ in(ordered_pair(X7,X8),X5)
| in(ordered_pair(X7,X8),X6)
| X5 != X6
| ~ relation(X6)
| ~ relation(X5) )
& ( ~ in(ordered_pair(X9,X10),X6)
| in(ordered_pair(X9,X10),X5)
| X5 != X6
| ~ relation(X6)
| ~ relation(X5) )
& ( ~ in(ordered_pair(esk19_2(X5,X6),esk20_2(X5,X6)),X5)
| ~ in(ordered_pair(esk19_2(X5,X6),esk20_2(X5,X6)),X6)
| X5 = X6
| ~ relation(X6)
| ~ relation(X5) )
& ( in(ordered_pair(esk19_2(X5,X6),esk20_2(X5,X6)),X5)
| in(ordered_pair(esk19_2(X5,X6),esk20_2(X5,X6)),X6)
| X5 = X6
| ~ relation(X6)
| ~ relation(X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_122])])])])])]) ).
fof(c_0_236,plain,
! [X5,X6,X7,X8,X9,X10,X11,X12] :
( ( ~ in(X8,X7)
| in(X8,X5)
| in(X8,X6)
| X7 != set_union2(X5,X6) )
& ( ~ in(X9,X5)
| in(X9,X7)
| X7 != set_union2(X5,X6) )
& ( ~ in(X9,X6)
| in(X9,X7)
| X7 != set_union2(X5,X6) )
& ( ~ in(esk22_3(X10,X11,X12),X10)
| ~ in(esk22_3(X10,X11,X12),X12)
| X12 = set_union2(X10,X11) )
& ( ~ in(esk22_3(X10,X11,X12),X11)
| ~ in(esk22_3(X10,X11,X12),X12)
| X12 = set_union2(X10,X11) )
& ( in(esk22_3(X10,X11,X12),X12)
| in(esk22_3(X10,X11,X12),X10)
| in(esk22_3(X10,X11,X12),X11)
| X12 = set_union2(X10,X11) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_123])])])])])]) ).
fof(c_0_237,plain,
! [X5,X6,X7,X8,X9,X10] :
( ( in(X7,X5)
| ~ in(ordered_pair(X7,X8),X6)
| X6 != identity_relation(X5)
| ~ relation(X6) )
& ( X7 = X8
| ~ in(ordered_pair(X7,X8),X6)
| X6 != identity_relation(X5)
| ~ relation(X6) )
& ( ~ in(X9,X5)
| X9 != X10
| in(ordered_pair(X9,X10),X6)
| X6 != identity_relation(X5)
| ~ relation(X6) )
& ( ~ in(ordered_pair(esk1_2(X5,X6),esk2_2(X5,X6)),X6)
| ~ in(esk1_2(X5,X6),X5)
| esk1_2(X5,X6) != esk2_2(X5,X6)
| X6 = identity_relation(X5)
| ~ relation(X6) )
& ( in(esk1_2(X5,X6),X5)
| in(ordered_pair(esk1_2(X5,X6),esk2_2(X5,X6)),X6)
| X6 = identity_relation(X5)
| ~ relation(X6) )
& ( esk1_2(X5,X6) = esk2_2(X5,X6)
| in(ordered_pair(esk1_2(X5,X6),esk2_2(X5,X6)),X6)
| X6 = identity_relation(X5)
| ~ relation(X6) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_124])])])])])]) ).
fof(c_0_238,plain,
! [X5,X6,X7,X8,X9,X10,X11,X12] :
( ( ~ in(X8,X7)
| X8 = X5
| X8 = X6
| X7 != unordered_pair(X5,X6) )
& ( X9 != X5
| in(X9,X7)
| X7 != unordered_pair(X5,X6) )
& ( X9 != X6
| in(X9,X7)
| X7 != unordered_pair(X5,X6) )
& ( esk21_3(X10,X11,X12) != X10
| ~ in(esk21_3(X10,X11,X12),X12)
| X12 = unordered_pair(X10,X11) )
& ( esk21_3(X10,X11,X12) != X11
| ~ in(esk21_3(X10,X11,X12),X12)
| X12 = unordered_pair(X10,X11) )
& ( in(esk21_3(X10,X11,X12),X12)
| esk21_3(X10,X11,X12) = X10
| esk21_3(X10,X11,X12) = X11
| X12 = unordered_pair(X10,X11) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_125])])])])])]) ).
fof(c_0_239,plain,
! [X5,X6,X7,X9,X10,X11,X13] :
( ( ~ in(X7,X6)
| in(ordered_pair(esk39_3(X5,X6,X7),X7),X5)
| X6 != relation_rng(X5)
| ~ relation(X5) )
& ( ~ in(ordered_pair(X10,X9),X5)
| in(X9,X6)
| X6 != relation_rng(X5)
| ~ relation(X5) )
& ( ~ in(esk40_2(X5,X11),X11)
| ~ in(ordered_pair(X13,esk40_2(X5,X11)),X5)
| X11 = relation_rng(X5)
| ~ relation(X5) )
& ( in(esk40_2(X5,X11),X11)
| in(ordered_pair(esk41_2(X5,X11),esk40_2(X5,X11)),X5)
| X11 = relation_rng(X5)
| ~ relation(X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_126])])])])])]) ).
fof(c_0_240,plain,
! [X5,X6,X7,X9,X10,X11,X13] :
( ( ~ in(X7,X6)
| in(ordered_pair(X7,esk32_3(X5,X6,X7)),X5)
| X6 != relation_dom(X5)
| ~ relation(X5) )
& ( ~ in(ordered_pair(X9,X10),X5)
| in(X9,X6)
| X6 != relation_dom(X5)
| ~ relation(X5) )
& ( ~ in(esk33_2(X5,X11),X11)
| ~ in(ordered_pair(esk33_2(X5,X11),X13),X5)
| X11 = relation_dom(X5)
| ~ relation(X5) )
& ( in(esk33_2(X5,X11),X11)
| in(ordered_pair(esk33_2(X5,X11),esk34_2(X5,X11)),X5)
| X11 = relation_dom(X5)
| ~ relation(X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_127])])])])])]) ).
fof(c_0_241,plain,
! [X5,X6,X7,X8] :
( ( ~ subset(X5,X6)
| ~ in(ordered_pair(X7,X8),X5)
| in(ordered_pair(X7,X8),X6)
| ~ relation(X6)
| ~ relation(X5) )
& ( in(ordered_pair(esk28_2(X5,X6),esk29_2(X5,X6)),X5)
| subset(X5,X6)
| ~ relation(X6)
| ~ relation(X5) )
& ( ~ in(ordered_pair(esk28_2(X5,X6),esk29_2(X5,X6)),X6)
| subset(X5,X6)
| ~ relation(X6)
| ~ relation(X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_128])])])])]) ).
fof(c_0_242,plain,
! [X5,X6,X7,X8,X9,X11,X14,X15,X16,X17] :
( ( ~ in(X7,X6)
| ~ in(X8,X5)
| in(X7,X8)
| X6 != set_meet(X5)
| X5 = empty_set )
& ( in(esk13_3(X5,X6,X9),X5)
| in(X9,X6)
| X6 != set_meet(X5)
| X5 = empty_set )
& ( ~ in(X9,esk13_3(X5,X6,X9))
| in(X9,X6)
| X6 != set_meet(X5)
| X5 = empty_set )
& ( in(esk15_2(X5,X11),X5)
| ~ in(esk14_2(X5,X11),X11)
| X11 = set_meet(X5)
| X5 = empty_set )
& ( ~ in(esk14_2(X5,X11),esk15_2(X5,X11))
| ~ in(esk14_2(X5,X11),X11)
| X11 = set_meet(X5)
| X5 = empty_set )
& ( in(esk14_2(X5,X11),X11)
| ~ in(X14,X5)
| in(esk14_2(X5,X11),X14)
| X11 = set_meet(X5)
| X5 = empty_set )
& ( X16 != set_meet(X15)
| X16 = empty_set
| X15 != empty_set )
& ( X17 != empty_set
| X17 = set_meet(X15)
| X15 != empty_set ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_129])])])])])]) ).
fof(c_0_243,plain,
! [X4,X5,X6] :
( ~ element(X5,powerset(X4))
| ~ element(X6,powerset(X4))
| element(subset_difference(X4,X5,X6),powerset(X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_130])]) ).
fof(c_0_244,plain,
! [X5,X6,X7,X9,X10,X11,X12,X14] :
( ( in(X7,esk35_3(X5,X6,X7))
| ~ in(X7,X6)
| X6 != union(X5) )
& ( in(esk35_3(X5,X6,X7),X5)
| ~ in(X7,X6)
| X6 != union(X5) )
& ( ~ in(X9,X10)
| ~ in(X10,X5)
| in(X9,X6)
| X6 != union(X5) )
& ( ~ in(esk36_2(X11,X12),X12)
| ~ in(esk36_2(X11,X12),X14)
| ~ in(X14,X11)
| X12 = union(X11) )
& ( in(esk36_2(X11,X12),esk37_2(X11,X12))
| in(esk36_2(X11,X12),X12)
| X12 = union(X11) )
& ( in(esk37_2(X11,X12),X11)
| in(esk36_2(X11,X12),X12)
| X12 = union(X11) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_131])])])])])]) ).
fof(c_0_245,plain,
! [X4,X5,X6] :
( ~ element(X5,powerset(X4))
| ~ element(X6,powerset(X4))
| subset_difference(X4,X5,X6) = set_difference(X5,X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_132])]) ).
fof(c_0_246,plain,
! [X4,X5,X6,X7,X8,X9] :
( ( ~ in(X6,X5)
| subset(X6,X4)
| X5 != powerset(X4) )
& ( ~ subset(X7,X4)
| in(X7,X5)
| X5 != powerset(X4) )
& ( ~ in(esk18_2(X8,X9),X9)
| ~ subset(esk18_2(X8,X9),X8)
| X9 = powerset(X8) )
& ( in(esk18_2(X8,X9),X9)
| subset(esk18_2(X8,X9),X8)
| X9 = powerset(X8) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_133])])])])])]) ).
fof(c_0_247,plain,
! [X4,X5] :
( ( ~ in(esk56_2(X4,X5),X4)
| ~ in(esk56_2(X4,X5),X5)
| X4 = X5 )
& ( in(esk56_2(X4,X5),X4)
| in(esk56_2(X4,X5),X5)
| X4 = X5 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_134])])])]) ).
fof(c_0_248,plain,
! [X3,X4] :
( ~ element(X4,powerset(powerset(X3)))
| element(complements_of_subsets(X3,X4),powerset(powerset(X3))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_135])]) ).
fof(c_0_249,plain,
! [X3,X4] :
( ~ element(X4,powerset(powerset(X3)))
| element(meet_of_subsets(X3,X4),powerset(X3)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_136])]) ).
fof(c_0_250,plain,
! [X3,X4] :
( ~ element(X4,powerset(powerset(X3)))
| element(union_of_subsets(X3,X4),powerset(X3)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_137])]) ).
fof(c_0_251,plain,
! [X5,X6,X9,X11,X12] :
( ( ~ relation(X5)
| ~ in(X6,X5)
| X6 = ordered_pair(esk10_2(X5,X6),esk11_2(X5,X6)) )
& ( in(esk12_1(X9),X9)
| relation(X9) )
& ( esk12_1(X9) != ordered_pair(X11,X12)
| relation(X9) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_138])])])])])]) ).
fof(c_0_252,plain,
! [X6,X8,X9,X10,X12,X13] :
( in(X6,esk57_1(X6))
& ( ~ in(X8,esk57_1(X6))
| ~ subset(X9,X8)
| in(X9,esk57_1(X6)) )
& ( in(esk58_2(X6,X10),esk57_1(X6))
| ~ in(X10,esk57_1(X6)) )
& ( ~ subset(X12,X10)
| in(X12,esk58_2(X6,X10))
| ~ in(X10,esk57_1(X6)) )
& ( ~ subset(X13,esk57_1(X6))
| are_equipotent(X13,esk57_1(X6))
| in(X13,esk57_1(X6)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_139])])])])]) ).
fof(c_0_253,plain,
! [X4,X5,X6,X7,X8,X9] :
( ( ~ in(X6,X5)
| X6 = X4
| X5 != singleton(X4) )
& ( X7 != X4
| in(X7,X5)
| X5 != singleton(X4) )
& ( ~ in(esk16_2(X8,X9),X9)
| esk16_2(X8,X9) != X8
| X9 = singleton(X8) )
& ( in(esk16_2(X8,X9),X9)
| esk16_2(X8,X9) = X8
| X9 = singleton(X8) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_140])])])])])]) ).
fof(c_0_254,plain,
! [X3,X4] :
( ~ element(X4,powerset(powerset(X3)))
| complements_of_subsets(X3,complements_of_subsets(X3,X4)) = X4 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_141])]) ).
fof(c_0_255,plain,
! [X3,X4] :
( ~ element(X4,powerset(X3))
| element(subset_complement(X3,X4),powerset(X3)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_142])]) ).
fof(c_0_256,plain,
! [X4,X5,X6,X7,X8] :
( ( ~ subset(X4,X5)
| ~ in(X6,X4)
| in(X6,X5) )
& ( in(esk30_2(X7,X8),X7)
| subset(X7,X8) )
& ( ~ in(esk30_2(X7,X8),X8)
| subset(X7,X8) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_143])])])])])]) ).
fof(c_0_257,plain,
! [X3,X4] :
( ~ element(X4,powerset(X3))
| subset_complement(X3,subset_complement(X3,X4)) = X4 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_144])]) ).
fof(c_0_258,plain,
! [X3,X4] :
( ~ element(X4,powerset(powerset(X3)))
| meet_of_subsets(X3,X4) = set_meet(X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_145])]) ).
fof(c_0_259,plain,
! [X3,X4] :
( ~ element(X4,powerset(powerset(X3)))
| union_of_subsets(X3,X4) = union(X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_146])]) ).
fof(c_0_260,plain,
! [X4,X5,X6] :
( ~ in(X4,X5)
| ~ element(X5,powerset(X6))
| element(X4,X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_147])]) ).
fof(c_0_261,plain,
! [X4,X5,X6] :
( ~ in(X4,X5)
| ~ element(X5,powerset(X6))
| ~ empty(X6) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_148])])])]) ).
fof(c_0_262,plain,
! [X3,X4] :
( ~ element(X4,powerset(X3))
| subset_complement(X3,X4) = set_difference(X3,X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_149])]) ).
fof(c_0_263,plain,
! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
inference(variable_rename,[status(thm)],[c_0_150]) ).
fof(c_0_264,plain,
! [X3,X4] :
( empty(X3)
| empty(X4)
| ~ empty(cartesian_product2(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_151])]) ).
fof(c_0_265,plain,
! [X3,X4] :
( empty(X3)
| ~ empty(set_union2(X4,X3)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_152])])])]) ).
fof(c_0_266,plain,
! [X3,X4] :
( empty(X3)
| ~ empty(set_union2(X3,X4)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_153])])])]) ).
fof(c_0_267,plain,
! [X3,X4] : ~ empty(unordered_pair(X3,X4)),
inference(variable_rename,[status(thm)],[c_0_154]) ).
fof(c_0_268,plain,
! [X3,X4] : ~ empty(ordered_pair(X3,X4)),
inference(variable_rename,[status(thm)],[c_0_155]) ).
fof(c_0_269,plain,
! [X3,X4,X5,X6] :
( ( subset(X3,X4)
| X3 != X4 )
& ( subset(X4,X3)
| X3 != X4 )
& ( ~ subset(X5,X6)
| ~ subset(X6,X5)
| X5 = X6 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_156])])])])]) ).
fof(c_0_270,plain,
! [X3,X4,X5,X6] :
( ( ~ element(X3,powerset(X4))
| subset(X3,X4) )
& ( ~ subset(X5,X6)
| element(X5,powerset(X6)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_157])])])]) ).
fof(c_0_271,plain,
! [X3,X4] :
( ~ proper_subset(X3,X4)
| ~ proper_subset(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_158])]) ).
fof(c_0_272,plain,
! [X3,X4] :
( ~ in(X3,X4)
| ~ in(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_159])]) ).
fof(c_0_273,plain,
! [X3,X4] :
( ( empty(relation_composition(X3,X4))
| ~ empty(X3)
| ~ relation(X4) )
& ( relation(relation_composition(X3,X4))
| ~ empty(X3)
| ~ relation(X4) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_160])])]) ).
fof(c_0_274,plain,
! [X3,X4] :
( ~ relation(X3)
| ~ relation(X4)
| relation(set_union2(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_161])]) ).
fof(c_0_275,plain,
! [X3,X4] :
( ~ relation(X3)
| ~ relation(X4)
| relation(set_intersection2(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_162])]) ).
fof(c_0_276,plain,
! [X3,X4] :
( ( empty(relation_composition(X4,X3))
| ~ empty(X3)
| ~ relation(X4) )
& ( relation(relation_composition(X4,X3))
| ~ empty(X3)
| ~ relation(X4) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_163])])]) ).
fof(c_0_277,plain,
! [X3,X4] :
( ~ relation(X3)
| ~ relation(X4)
| relation(relation_composition(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_164])]) ).
fof(c_0_278,plain,
! [X3,X4] :
( ~ element(X3,X4)
| empty(X4)
| in(X3,X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_165])]) ).
fof(c_0_279,plain,
! [X3,X4,X5,X6,X7,X8] :
( ( ~ element(X4,X3)
| in(X4,X3)
| empty(X3) )
& ( ~ in(X5,X3)
| element(X5,X3)
| empty(X3) )
& ( ~ element(X7,X6)
| empty(X7)
| ~ empty(X6) )
& ( ~ empty(X8)
| element(X8,X6)
| ~ empty(X6) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_166])])])])]) ).
fof(c_0_280,plain,
! [X3,X4,X5,X6] :
( ( subset(X3,X4)
| ~ proper_subset(X3,X4) )
& ( X3 != X4
| ~ proper_subset(X3,X4) )
& ( ~ subset(X5,X6)
| X5 = X6
| proper_subset(X5,X6) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_167])])])])]) ).
fof(c_0_281,plain,
! [X3,X4] :
( ~ relation(X4)
| relation(relation_rng_restriction(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_168])]) ).
fof(c_0_282,plain,
! [X3,X4] :
( ~ relation(X3)
| relation(relation_dom_restriction(X3,X4)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_169])])])]) ).
fof(c_0_283,plain,
! [X2] :
( ~ relation(X2)
| relation_field(X2) = set_union2(relation_dom(X2),relation_rng(X2)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_170])]) ).
fof(c_0_284,plain,
! [X3,X4] :
( ~ in(X3,X4)
| element(X3,X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_171])]) ).
fof(c_0_285,plain,
! [X3,X4] :
( ~ disjoint(X3,X4)
| disjoint(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_172])]) ).
fof(c_0_286,plain,
! [X3,X4,X5,X6] :
( ( ~ disjoint(X3,X4)
| set_intersection2(X3,X4) = empty_set )
& ( set_intersection2(X5,X6) != empty_set
| disjoint(X5,X6) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_173])])])]) ).
fof(c_0_287,plain,
! [X3] :
( ( element(esk51_1(X3),powerset(X3))
| empty(X3) )
& ( ~ empty(esk51_1(X3))
| empty(X3) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_174])])])]) ).
fof(c_0_288,plain,
! [X3,X4] :
( ~ in(X3,X4)
| ~ empty(X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_175])]) ).
fof(c_0_289,plain,
! [X2] :
( empty(X2)
| ~ relation(X2)
| ~ empty(relation_rng(X2)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_176])]) ).
fof(c_0_290,plain,
! [X2] :
( empty(X2)
| ~ relation(X2)
| ~ empty(relation_dom(X2)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_177])]) ).
fof(c_0_291,plain,
! [X3,X4] : set_intersection2(X3,X4) = set_intersection2(X4,X3),
inference(variable_rename,[status(thm)],[c_0_178]) ).
fof(c_0_292,plain,
! [X3,X4] : set_union2(X3,X4) = set_union2(X4,X3),
inference(variable_rename,[status(thm)],[c_0_179]) ).
fof(c_0_293,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[c_0_180]) ).
fof(c_0_294,plain,
! [X3] :
( element(esk54_1(X3),powerset(X3))
& empty(esk54_1(X3)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_181])]) ).
fof(c_0_295,plain,
! [X2] : element(cast_to_subset(X2),powerset(X2)),
inference(variable_rename,[status(thm)],[c_0_182]) ).
fof(c_0_296,plain,
! [X3,X4,X5] :
( ( X3 != empty_set
| ~ in(X4,X3) )
& ( in(esk17_1(X5),X5)
| X5 = empty_set ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_183])])])])]) ).
fof(c_0_297,plain,
! [X3,X4] : ~ proper_subset(X3,X3),
inference(variable_rename,[status(thm)],[c_0_184]) ).
fof(c_0_298,plain,
! [X3] : element(esk49_1(X3),X3),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_185])]) ).
fof(c_0_299,plain,
! [X2] :
( ~ relation(X2)
| relation_inverse(relation_inverse(X2)) = X2 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_186])]) ).
fof(c_0_300,plain,
! [X2] :
( ( empty(relation_rng(X2))
| ~ empty(X2) )
& ( relation(relation_rng(X2))
| ~ empty(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_187])])]) ).
fof(c_0_301,plain,
! [X2] :
( ( empty(relation_dom(X2))
| ~ empty(X2) )
& ( relation(relation_dom(X2))
| ~ empty(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_188])])]) ).
fof(c_0_302,plain,
! [X2] :
( ~ relation(X2)
| relation(relation_inverse(X2)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_189])]) ).
fof(c_0_303,plain,
! [X2] : ~ empty(singleton(X2)),
inference(variable_rename,[status(thm)],[c_0_190]) ).
fof(c_0_304,plain,
! [X2] : ~ empty(powerset(X2)),
inference(variable_rename,[status(thm)],[c_0_191]) ).
fof(c_0_305,plain,
! [X3,X4] :
( ~ empty(X3)
| X3 = X4
| ~ empty(X4) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_192])])])]) ).
fof(c_0_306,plain,
! [X3,X4] : set_intersection2(X3,X3) = X3,
inference(variable_rename,[status(thm)],[c_0_193]) ).
fof(c_0_307,plain,
! [X3,X4] : set_union2(X3,X3) = X3,
inference(variable_rename,[status(thm)],[c_0_194]) ).
fof(c_0_308,plain,
! [X3,X4] : subset(X3,X3),
inference(variable_rename,[status(thm)],[c_0_195]) ).
fof(c_0_309,plain,
! [X2] : set_difference(X2,empty_set) = X2,
inference(variable_rename,[status(thm)],[c_0_196]) ).
fof(c_0_310,plain,
! [X2] : set_union2(X2,empty_set) = X2,
inference(variable_rename,[status(thm)],[c_0_197]) ).
fof(c_0_311,plain,
! [X2] : set_difference(empty_set,X2) = empty_set,
inference(variable_rename,[status(thm)],[c_0_198]) ).
fof(c_0_312,plain,
! [X2] : set_intersection2(X2,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[c_0_199]) ).
fof(c_0_313,plain,
! [X2] :
( ~ empty(X2)
| relation(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_200])]) ).
fof(c_0_314,plain,
! [X2] : relation(identity_relation(X2)),
inference(variable_rename,[status(thm)],[c_0_201]) ).
fof(c_0_315,plain,
! [X2] :
( ~ empty(X2)
| X2 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_202])]) ).
fof(c_0_316,plain,
! [X2] : cast_to_subset(X2) = X2,
inference(variable_rename,[status(thm)],[c_0_203]) ).
fof(c_0_317,plain,
~ empty(esk55_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_204])]) ).
fof(c_0_318,plain,
( ~ empty(esk53_0)
& relation(esk53_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_205])]) ).
fof(c_0_319,plain,
empty(esk52_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_206])]) ).
fof(c_0_320,plain,
( empty(esk50_0)
& relation(esk50_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_207])]) ).
fof(c_0_321,axiom,
( empty(empty_set)
& relation(empty_set) ),
c_0_208 ).
fof(c_0_322,axiom,
empty(empty_set),
c_0_209 ).
fof(c_0_323,axiom,
$true,
c_0_210 ).
fof(c_0_324,axiom,
$true,
c_0_211 ).
fof(c_0_325,axiom,
$true,
c_0_212 ).
fof(c_0_326,axiom,
$true,
c_0_213 ).
fof(c_0_327,axiom,
$true,
c_0_214 ).
fof(c_0_328,axiom,
$true,
c_0_215 ).
fof(c_0_329,axiom,
$true,
c_0_216 ).
fof(c_0_330,axiom,
$true,
c_0_217 ).
fof(c_0_331,axiom,
$true,
c_0_218 ).
fof(c_0_332,axiom,
$true,
c_0_219 ).
fof(c_0_333,axiom,
$true,
c_0_220 ).
fof(c_0_334,axiom,
$true,
c_0_221 ).
fof(c_0_335,axiom,
$true,
c_0_222 ).
fof(c_0_336,axiom,
$true,
c_0_223 ).
fof(c_0_337,axiom,
$true,
c_0_224 ).
fof(c_0_338,axiom,
$true,
c_0_225 ).
cnf(c_0_339,plain,
( in(ordered_pair(X4,esk44_5(X1,X2,X3,X4,X5)),X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X4,X5),X3) ),
inference(split_conjunct,[status(thm)],[c_0_226]) ).
cnf(c_0_340,plain,
( in(ordered_pair(esk44_5(X1,X2,X3,X4,X5),X5),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X4,X5),X3) ),
inference(split_conjunct,[status(thm)],[c_0_226]) ).
cnf(c_0_341,plain,
( X2 = relation_rng_restriction(X3,X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(esk5_3(X3,X1,X2),esk6_3(X3,X1,X2)),X1)
| ~ in(esk6_3(X3,X1,X2),X3)
| ~ in(ordered_pair(esk5_3(X3,X1,X2),esk6_3(X3,X1,X2)),X2) ),
inference(split_conjunct,[status(thm)],[c_0_227]) ).
cnf(c_0_342,plain,
( X2 = relation_dom_restriction(X1,X3)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(esk3_3(X1,X3,X2),esk4_3(X1,X3,X2)),X1)
| ~ in(esk3_3(X1,X3,X2),X3)
| ~ in(ordered_pair(esk3_3(X1,X3,X2),esk4_3(X1,X3,X2)),X2) ),
inference(split_conjunct,[status(thm)],[c_0_228]) ).
cnf(c_0_343,plain,
( X3 = relation_composition(X1,X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3)
| ~ in(ordered_pair(X4,esk46_3(X1,X2,X3)),X2)
| ~ in(ordered_pair(esk45_3(X1,X2,X3),X4),X1)
| ~ in(ordered_pair(esk45_3(X1,X2,X3),esk46_3(X1,X2,X3)),X3) ),
inference(split_conjunct,[status(thm)],[c_0_226]) ).
cnf(c_0_344,plain,
( in(ordered_pair(esk7_4(X1,X3,X2,X4),X4),X1)
| ~ relation(X1)
| X2 != relation_image(X1,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_229]) ).
cnf(c_0_345,plain,
( X4 = ordered_pair(esk23_4(X2,X3,X1,X4),esk24_4(X2,X3,X1,X4))
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_230]) ).
cnf(c_0_346,plain,
( X3 = relation_composition(X1,X2)
| in(ordered_pair(esk45_3(X1,X2,X3),esk46_3(X1,X2,X3)),X3)
| in(ordered_pair(esk45_3(X1,X2,X3),esk47_3(X1,X2,X3)),X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_226]) ).
cnf(c_0_347,plain,
( X3 = relation_composition(X1,X2)
| in(ordered_pair(esk45_3(X1,X2,X3),esk46_3(X1,X2,X3)),X3)
| in(ordered_pair(esk47_3(X1,X2,X3),esk46_3(X1,X2,X3)),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_226]) ).
cnf(c_0_348,plain,
( X2 = relation_rng_restriction(X3,X1)
| in(ordered_pair(esk5_3(X3,X1,X2),esk6_3(X3,X1,X2)),X2)
| in(ordered_pair(esk5_3(X3,X1,X2),esk6_3(X3,X1,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_227]) ).
cnf(c_0_349,plain,
( X2 = relation_dom_restriction(X1,X3)
| in(ordered_pair(esk3_3(X1,X3,X2),esk4_3(X1,X3,X2)),X2)
| in(ordered_pair(esk3_3(X1,X3,X2),esk4_3(X1,X3,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_228]) ).
cnf(c_0_350,plain,
( X3 = complements_of_subsets(X2,X1)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2)))
| ~ in(subset_complement(X2,esk48_3(X2,X1,X3)),X1)
| ~ in(esk48_3(X2,X1,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_231]) ).
cnf(c_0_351,plain,
( X2 = relation_image(X1,X3)
| ~ relation(X1)
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk8_3(X1,X3,X2)),X1)
| ~ in(esk8_3(X1,X3,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_229]) ).
cnf(c_0_352,plain,
( X2 = relation_rng_restriction(X3,X1)
| in(ordered_pair(esk5_3(X3,X1,X2),esk6_3(X3,X1,X2)),X2)
| in(esk6_3(X3,X1,X2),X3)
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_227]) ).
cnf(c_0_353,plain,
( X2 = relation_dom_restriction(X1,X3)
| in(ordered_pair(esk3_3(X1,X3,X2),esk4_3(X1,X3,X2)),X2)
| in(esk3_3(X1,X3,X2),X3)
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_228]) ).
cnf(c_0_354,plain,
( X2 = relation_image(X1,X3)
| in(esk8_3(X1,X3,X2),X2)
| in(ordered_pair(esk9_3(X1,X3,X2),esk8_3(X1,X3,X2)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_229]) ).
cnf(c_0_355,plain,
( X1 = set_intersection2(X2,X3)
| ~ in(esk31_3(X2,X3,X1),X3)
| ~ in(esk31_3(X2,X3,X1),X2)
| ~ in(esk31_3(X2,X3,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_232]) ).
cnf(c_0_356,plain,
( in(esk7_4(X1,X3,X2,X4),X3)
| ~ relation(X1)
| X2 != relation_image(X1,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_229]) ).
cnf(c_0_357,plain,
( in(esk23_4(X2,X3,X1,X4),X2)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_230]) ).
cnf(c_0_358,plain,
( in(esk24_4(X2,X3,X1,X4),X3)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_230]) ).
cnf(c_0_359,plain,
( X1 = set_difference(X2,X3)
| in(esk38_3(X2,X3,X1),X3)
| ~ in(esk38_3(X2,X3,X1),X2)
| ~ in(esk38_3(X2,X3,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_233]) ).
cnf(c_0_360,plain,
( X3 = complements_of_subsets(X2,X1)
| in(subset_complement(X2,esk48_3(X2,X1,X3)),X1)
| in(esk48_3(X2,X1,X3),X3)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_231]) ).
cnf(c_0_361,plain,
( X2 = relation_inverse(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(esk43_2(X1,X2),esk42_2(X1,X2)),X1)
| ~ in(ordered_pair(esk42_2(X1,X2),esk43_2(X1,X2)),X2) ),
inference(split_conjunct,[status(thm)],[c_0_234]) ).
cnf(c_0_362,plain,
( X1 = X2
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(esk19_2(X1,X2),esk20_2(X1,X2)),X2)
| ~ in(ordered_pair(esk19_2(X1,X2),esk20_2(X1,X2)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_235]) ).
cnf(c_0_363,plain,
( X1 = cartesian_product2(X2,X3)
| in(esk25_3(X2,X3,X1),X1)
| esk25_3(X2,X3,X1) = ordered_pair(esk26_3(X2,X3,X1),esk27_3(X2,X3,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_230]) ).
cnf(c_0_364,plain,
( X1 = set_union2(X2,X3)
| ~ in(esk22_3(X2,X3,X1),X1)
| ~ in(esk22_3(X2,X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_236]) ).
cnf(c_0_365,plain,
( X1 = set_union2(X2,X3)
| ~ in(esk22_3(X2,X3,X1),X1)
| ~ in(esk22_3(X2,X3,X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_236]) ).
cnf(c_0_366,plain,
( X1 = set_union2(X2,X3)
| in(esk22_3(X2,X3,X1),X3)
| in(esk22_3(X2,X3,X1),X2)
| in(esk22_3(X2,X3,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_236]) ).
cnf(c_0_367,plain,
( X1 = cartesian_product2(X2,X3)
| esk25_3(X2,X3,X1) != ordered_pair(X4,X5)
| ~ in(X5,X3)
| ~ in(X4,X2)
| ~ in(esk25_3(X2,X3,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_230]) ).
cnf(c_0_368,plain,
( X1 = identity_relation(X2)
| ~ relation(X1)
| esk1_2(X2,X1) != esk2_2(X2,X1)
| ~ in(esk1_2(X2,X1),X2)
| ~ in(ordered_pair(esk1_2(X2,X1),esk2_2(X2,X1)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_237]) ).
cnf(c_0_369,plain,
( X1 = set_difference(X2,X3)
| in(esk38_3(X2,X3,X1),X1)
| ~ in(esk38_3(X2,X3,X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_233]) ).
cnf(c_0_370,plain,
( X2 = relation_inverse(X1)
| in(ordered_pair(esk43_2(X1,X2),esk42_2(X1,X2)),X1)
| in(ordered_pair(esk42_2(X1,X2),esk43_2(X1,X2)),X2)
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_234]) ).
cnf(c_0_371,plain,
( X1 = X2
| in(ordered_pair(esk19_2(X1,X2),esk20_2(X1,X2)),X2)
| in(ordered_pair(esk19_2(X1,X2),esk20_2(X1,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_235]) ).
cnf(c_0_372,plain,
( X1 = unordered_pair(X2,X3)
| ~ in(esk21_3(X2,X3,X1),X1)
| esk21_3(X2,X3,X1) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_238]) ).
cnf(c_0_373,plain,
( X1 = unordered_pair(X2,X3)
| ~ in(esk21_3(X2,X3,X1),X1)
| esk21_3(X2,X3,X1) != X3 ),
inference(split_conjunct,[status(thm)],[c_0_238]) ).
cnf(c_0_374,plain,
( in(ordered_pair(esk39_3(X1,X2,X3),X3),X1)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_239]) ).
cnf(c_0_375,plain,
( in(ordered_pair(X3,esk32_3(X1,X2,X3)),X1)
| ~ relation(X1)
| X2 != relation_dom(X1)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_240]) ).
cnf(c_0_376,plain,
( X2 = relation_image(X1,X3)
| in(esk8_3(X1,X3,X2),X2)
| in(esk9_3(X1,X3,X2),X3)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_229]) ).
cnf(c_0_377,plain,
( X1 = set_difference(X2,X3)
| in(esk38_3(X2,X3,X1),X1)
| in(esk38_3(X2,X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_233]) ).
cnf(c_0_378,plain,
( X1 = set_intersection2(X2,X3)
| in(esk31_3(X2,X3,X1),X1)
| in(esk31_3(X2,X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_232]) ).
cnf(c_0_379,plain,
( X1 = set_intersection2(X2,X3)
| in(esk31_3(X2,X3,X1),X1)
| in(esk31_3(X2,X3,X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_232]) ).
cnf(c_0_380,plain,
( X1 = cartesian_product2(X2,X3)
| in(esk25_3(X2,X3,X1),X1)
| in(esk26_3(X2,X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_230]) ).
cnf(c_0_381,plain,
( X1 = cartesian_product2(X2,X3)
| in(esk25_3(X2,X3,X1),X1)
| in(esk27_3(X2,X3,X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_230]) ).
cnf(c_0_382,plain,
( subset(X1,X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(esk28_2(X1,X2),esk29_2(X1,X2)),X2) ),
inference(split_conjunct,[status(thm)],[c_0_241]) ).
cnf(c_0_383,plain,
( X1 = unordered_pair(X2,X3)
| esk21_3(X2,X3,X1) = X3
| esk21_3(X2,X3,X1) = X2
| in(esk21_3(X2,X3,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_238]) ).
cnf(c_0_384,plain,
( X3 = complements_of_subsets(X2,X1)
| element(esk48_3(X2,X1,X3),powerset(X2))
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_231]) ).
cnf(c_0_385,plain,
( in(X4,X3)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2)))
| X3 != complements_of_subsets(X2,X1)
| ~ element(X4,powerset(X2))
| ~ in(subset_complement(X2,X4),X1) ),
inference(split_conjunct,[status(thm)],[c_0_231]) ).
cnf(c_0_386,plain,
( in(subset_complement(X2,X4),X1)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2)))
| X3 != complements_of_subsets(X2,X1)
| ~ element(X4,powerset(X2))
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_231]) ).
cnf(c_0_387,plain,
( X2 = relation_rng(X1)
| ~ relation(X1)
| ~ in(ordered_pair(X3,esk40_2(X1,X2)),X1)
| ~ in(esk40_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_239]) ).
cnf(c_0_388,plain,
( X2 = relation_dom(X1)
| ~ relation(X1)
| ~ in(ordered_pair(esk33_2(X1,X2),X3),X1)
| ~ in(esk33_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_240]) ).
cnf(c_0_389,plain,
( X1 = empty_set
| in(X3,X2)
| X2 != set_meet(X1)
| ~ in(X3,esk13_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_242]) ).
cnf(c_0_390,plain,
( in(ordered_pair(X4,X5),X3)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X6,X5),X2)
| ~ in(ordered_pair(X4,X6),X1) ),
inference(split_conjunct,[status(thm)],[c_0_226]) ).
cnf(c_0_391,plain,
( X2 = relation_rng(X1)
| in(ordered_pair(esk41_2(X1,X2),esk40_2(X1,X2)),X1)
| in(esk40_2(X1,X2),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_239]) ).
cnf(c_0_392,plain,
( X2 = relation_dom(X1)
| in(ordered_pair(esk33_2(X1,X2),esk34_2(X1,X2)),X1)
| in(esk33_2(X1,X2),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_240]) ).
cnf(c_0_393,plain,
( X1 = identity_relation(X2)
| in(ordered_pair(esk1_2(X2,X1),esk2_2(X2,X1)),X1)
| in(esk1_2(X2,X1),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_237]) ).
cnf(c_0_394,plain,
( element(subset_difference(X1,X2,X3),powerset(X1))
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_243]) ).
cnf(c_0_395,plain,
( X1 = identity_relation(X2)
| in(ordered_pair(esk1_2(X2,X1),esk2_2(X2,X1)),X1)
| esk1_2(X2,X1) = esk2_2(X2,X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_237]) ).
cnf(c_0_396,plain,
( X1 = empty_set
| X2 = set_meet(X1)
| ~ in(esk14_2(X1,X2),X2)
| ~ in(esk14_2(X1,X2),esk15_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_242]) ).
cnf(c_0_397,plain,
( subset(X1,X2)
| in(ordered_pair(esk28_2(X1,X2),esk29_2(X1,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_241]) ).
cnf(c_0_398,plain,
( in(ordered_pair(X4,X5),X2)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_rng_restriction(X3,X1)
| ~ in(ordered_pair(X4,X5),X1)
| ~ in(X5,X3) ),
inference(split_conjunct,[status(thm)],[c_0_227]) ).
cnf(c_0_399,plain,
( in(ordered_pair(X4,X5),X2)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_dom_restriction(X1,X3)
| ~ in(ordered_pair(X4,X5),X1)
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_228]) ).
cnf(c_0_400,plain,
( X1 = union(X2)
| ~ in(X3,X2)
| ~ in(esk36_2(X2,X1),X3)
| ~ in(esk36_2(X2,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_244]) ).
cnf(c_0_401,plain,
( in(X3,esk35_3(X2,X1,X3))
| X1 != union(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_244]) ).
cnf(c_0_402,plain,
( in(esk35_3(X2,X1,X3),X2)
| X1 != union(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_244]) ).
cnf(c_0_403,plain,
( X1 = empty_set
| in(X3,X2)
| in(esk13_3(X1,X2,X3),X1)
| X2 != set_meet(X1) ),
inference(split_conjunct,[status(thm)],[c_0_242]) ).
cnf(c_0_404,plain,
( in(ordered_pair(X4,X5),X1)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_rng_restriction(X3,X1)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(split_conjunct,[status(thm)],[c_0_227]) ).
cnf(c_0_405,plain,
( in(ordered_pair(X4,X5),X1)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_dom_restriction(X1,X3)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(split_conjunct,[status(thm)],[c_0_228]) ).
cnf(c_0_406,plain,
( in(ordered_pair(X3,X4),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(X3,X4),X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_241]) ).
cnf(c_0_407,plain,
( subset_difference(X1,X2,X3) = set_difference(X2,X3)
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_245]) ).
cnf(c_0_408,plain,
( X1 = powerset(X2)
| ~ subset(esk18_2(X2,X1),X2)
| ~ in(esk18_2(X2,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_246]) ).
cnf(c_0_409,plain,
( in(X4,X2)
| ~ relation(X1)
| X2 != relation_image(X1,X3)
| ~ in(X5,X3)
| ~ in(ordered_pair(X5,X4),X1) ),
inference(split_conjunct,[status(thm)],[c_0_229]) ).
cnf(c_0_410,plain,
( X1 = X2
| ~ in(esk56_2(X1,X2),X2)
| ~ in(esk56_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_247]) ).
cnf(c_0_411,plain,
( in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_inverse(X1)
| ~ in(ordered_pair(X4,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_234]) ).
cnf(c_0_412,plain,
( in(ordered_pair(X3,X4),X2)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_inverse(X1)
| ~ in(ordered_pair(X4,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_234]) ).
cnf(c_0_413,plain,
( in(ordered_pair(X3,X4),X2)
| ~ relation(X1)
| ~ relation(X2)
| X1 != X2
| ~ in(ordered_pair(X3,X4),X1) ),
inference(split_conjunct,[status(thm)],[c_0_235]) ).
cnf(c_0_414,plain,
( in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ relation(X2)
| X1 != X2
| ~ in(ordered_pair(X3,X4),X2) ),
inference(split_conjunct,[status(thm)],[c_0_235]) ).
cnf(c_0_415,plain,
( in(X5,X3)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_rng_restriction(X3,X1)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(split_conjunct,[status(thm)],[c_0_227]) ).
cnf(c_0_416,plain,
( in(X4,X3)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_dom_restriction(X1,X3)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(split_conjunct,[status(thm)],[c_0_228]) ).
cnf(c_0_417,plain,
( X1 = union(X2)
| in(esk36_2(X2,X1),X1)
| in(esk36_2(X2,X1),esk37_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_244]) ).
cnf(c_0_418,plain,
( X1 = empty_set
| X2 = set_meet(X1)
| in(esk15_2(X1,X2),X1)
| ~ in(esk14_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_242]) ).
cnf(c_0_419,plain,
( X1 = empty_set
| X2 = set_meet(X1)
| in(esk14_2(X1,X2),X3)
| in(esk14_2(X1,X2),X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_242]) ).
cnf(c_0_420,plain,
( element(complements_of_subsets(X1,X2),powerset(powerset(X1)))
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_248]) ).
cnf(c_0_421,plain,
( in(X4,X1)
| X1 != cartesian_product2(X2,X3)
| X4 != ordered_pair(X5,X6)
| ~ in(X6,X3)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_230]) ).
cnf(c_0_422,plain,
( element(meet_of_subsets(X1,X2),powerset(X1))
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_249]) ).
cnf(c_0_423,plain,
( element(union_of_subsets(X1,X2),powerset(X1))
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_250]) ).
cnf(c_0_424,plain,
( X1 = ordered_pair(esk10_2(X2,X1),esk11_2(X2,X1))
| ~ in(X1,X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_251]) ).
cnf(c_0_425,plain,
( in(X3,esk58_2(X2,X1))
| ~ in(X1,esk57_1(X2))
| ~ subset(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_252]) ).
cnf(c_0_426,plain,
( in(X3,X2)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(ordered_pair(X4,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_239]) ).
cnf(c_0_427,plain,
( in(X3,X2)
| ~ relation(X1)
| X2 != relation_dom(X1)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(split_conjunct,[status(thm)],[c_0_240]) ).
cnf(c_0_428,plain,
( in(X3,X2)
| ~ relation(X1)
| X1 != identity_relation(X2)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(split_conjunct,[status(thm)],[c_0_237]) ).
cnf(c_0_429,plain,
( X1 = singleton(X2)
| esk16_2(X2,X1) != X2
| ~ in(esk16_2(X2,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_253]) ).
cnf(c_0_430,plain,
( complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_254]) ).
cnf(c_0_431,plain,
( X1 = union(X2)
| in(esk36_2(X2,X1),X1)
| in(esk37_2(X2,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_244]) ).
cnf(c_0_432,plain,
( X1 = powerset(X2)
| subset(esk18_2(X2,X1),X2)
| in(esk18_2(X2,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_246]) ).
cnf(c_0_433,plain,
( in(X4,X1)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_232]) ).
cnf(c_0_434,plain,
( X1 = X2
| in(esk56_2(X1,X2),X2)
| in(esk56_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_247]) ).
cnf(c_0_435,plain,
( in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| X1 != identity_relation(X2)
| X3 != X4
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_237]) ).
cnf(c_0_436,plain,
( X3 = X4
| ~ relation(X1)
| X1 != identity_relation(X2)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(split_conjunct,[status(thm)],[c_0_237]) ).
cnf(c_0_437,plain,
( in(esk58_2(X2,X1),esk57_1(X2))
| ~ in(X1,esk57_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_252]) ).
cnf(c_0_438,plain,
( element(subset_complement(X1,X2),powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_255]) ).
cnf(c_0_439,plain,
( subset(X1,X2)
| ~ in(esk30_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_256]) ).
cnf(c_0_440,plain,
( in(X1,esk57_1(X2))
| ~ subset(X1,X3)
| ~ in(X3,esk57_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_252]) ).
cnf(c_0_441,plain,
( in(X4,X1)
| in(X4,X3)
| X1 != set_difference(X2,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_233]) ).
cnf(c_0_442,plain,
( in(X4,X3)
| in(X4,X2)
| X1 != set_union2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_236]) ).
cnf(c_0_443,plain,
( in(X1,esk57_1(X2))
| are_equipotent(X1,esk57_1(X2))
| ~ subset(X1,esk57_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_252]) ).
cnf(c_0_444,plain,
( subset_complement(X1,subset_complement(X1,X2)) = X2
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_257]) ).
cnf(c_0_445,plain,
( X1 = empty_set
| in(X3,X4)
| X2 != set_meet(X1)
| ~ in(X4,X1)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_242]) ).
cnf(c_0_446,plain,
( meet_of_subsets(X1,X2) = set_meet(X2)
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_258]) ).
cnf(c_0_447,plain,
( union_of_subsets(X1,X2) = union(X2)
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_259]) ).
cnf(c_0_448,plain,
( element(X1,X2)
| ~ element(X3,powerset(X2))
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_260]) ).
cnf(c_0_449,plain,
( X1 != set_difference(X2,X3)
| ~ in(X4,X1)
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_233]) ).
cnf(c_0_450,plain,
( in(X3,X1)
| X1 != union(X2)
| ~ in(X4,X2)
| ~ in(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_244]) ).
cnf(c_0_451,plain,
( ~ empty(X1)
| ~ element(X2,powerset(X1))
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_261]) ).
cnf(c_0_452,plain,
( in(X4,X2)
| X1 != set_difference(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_233]) ).
cnf(c_0_453,plain,
( in(X4,X2)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_232]) ).
cnf(c_0_454,plain,
( in(X4,X3)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_232]) ).
cnf(c_0_455,plain,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_236]) ).
cnf(c_0_456,plain,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_236]) ).
cnf(c_0_457,plain,
( X1 = singleton(X2)
| esk16_2(X2,X1) = X2
| in(esk16_2(X2,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_253]) ).
cnf(c_0_458,plain,
( subset_complement(X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_262]) ).
cnf(c_0_459,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_263]) ).
cnf(c_0_460,plain,
( in(X1,X2)
| ~ in(X1,X3)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_256]) ).
cnf(c_0_461,plain,
( empty(X2)
| empty(X1)
| ~ empty(cartesian_product2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_264]) ).
cnf(c_0_462,plain,
( subset(X1,X2)
| in(esk30_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_256]) ).
cnf(c_0_463,plain,
( empty(X2)
| ~ empty(set_union2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_265]) ).
cnf(c_0_464,plain,
( empty(X1)
| ~ empty(set_union2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_266]) ).
cnf(c_0_465,plain,
( X4 = X3
| X4 = X2
| X1 != unordered_pair(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_238]) ).
cnf(c_0_466,plain,
~ empty(unordered_pair(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_267]) ).
cnf(c_0_467,plain,
~ empty(ordered_pair(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_268]) ).
cnf(c_0_468,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_269]) ).
cnf(c_0_469,plain,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_270]) ).
cnf(c_0_470,plain,
( subset(X3,X2)
| X1 != powerset(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_246]) ).
cnf(c_0_471,plain,
( in(X3,X1)
| X1 != powerset(X2)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_246]) ).
cnf(c_0_472,plain,
( ~ proper_subset(X1,X2)
| ~ proper_subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_271]) ).
cnf(c_0_473,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_272]) ).
cnf(c_0_474,plain,
( empty(relation_composition(X2,X1))
| ~ relation(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_273]) ).
cnf(c_0_475,plain,
( relation(relation_composition(X2,X1))
| ~ relation(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_273]) ).
cnf(c_0_476,plain,
( relation(set_union2(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_274]) ).
cnf(c_0_477,plain,
( relation(set_intersection2(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_275]) ).
cnf(c_0_478,plain,
( empty(relation_composition(X1,X2))
| ~ relation(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_276]) ).
cnf(c_0_479,plain,
( relation(relation_composition(X1,X2))
| ~ relation(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_276]) ).
cnf(c_0_480,plain,
( relation(relation_composition(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_277]) ).
cnf(c_0_481,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_270]) ).
cnf(c_0_482,plain,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_238]) ).
cnf(c_0_483,plain,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_238]) ).
cnf(c_0_484,plain,
( in(X1,X2)
| empty(X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_278]) ).
cnf(c_0_485,plain,
( empty(X1)
| in(X2,X1)
| ~ element(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_279]) ).
cnf(c_0_486,plain,
( empty(X1)
| element(X2,X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_279]) ).
cnf(c_0_487,plain,
( proper_subset(X1,X2)
| X1 = X2
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_280]) ).
cnf(c_0_488,plain,
( relation(relation_rng_restriction(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_281]) ).
cnf(c_0_489,plain,
( relation(relation_dom_restriction(X1,X2))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_282]) ).
cnf(c_0_490,plain,
( relation_field(X1) = set_union2(relation_dom(X1),relation_rng(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_283]) ).
cnf(c_0_491,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_284]) ).
cnf(c_0_492,plain,
( disjoint(X1,X2)
| ~ disjoint(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_285]) ).
cnf(c_0_493,plain,
( subset(X1,X2)
| ~ proper_subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_280]) ).
cnf(c_0_494,plain,
( set_intersection2(X1,X2) = empty_set
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_286]) ).
cnf(c_0_495,plain,
( disjoint(X1,X2)
| set_intersection2(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_286]) ).
cnf(c_0_496,plain,
( empty(X2)
| ~ empty(X1)
| ~ element(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_279]) ).
cnf(c_0_497,plain,
( X3 = X2
| X1 != singleton(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_253]) ).
cnf(c_0_498,plain,
( relation(X1)
| esk12_1(X1) != ordered_pair(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_251]) ).
cnf(c_0_499,plain,
( empty(X1)
| element(esk51_1(X1),powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_287]) ).
cnf(c_0_500,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_288]) ).
cnf(c_0_501,plain,
( element(X2,X1)
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_279]) ).
cnf(c_0_502,plain,
( empty(X1)
| ~ empty(relation_rng(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_289]) ).
cnf(c_0_503,plain,
( empty(X1)
| ~ empty(relation_dom(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_290]) ).
cnf(c_0_504,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_291]) ).
cnf(c_0_505,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_292]) ).
cnf(c_0_506,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_293]) ).
cnf(c_0_507,plain,
element(esk54_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_294]) ).
cnf(c_0_508,plain,
element(cast_to_subset(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_295]) ).
cnf(c_0_509,plain,
( in(X3,X1)
| X1 != singleton(X2)
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_253]) ).
cnf(c_0_510,plain,
( ~ proper_subset(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_280]) ).
cnf(c_0_511,plain,
( ~ in(X1,X2)
| X2 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_296]) ).
cnf(c_0_512,plain,
( relation(X1)
| in(esk12_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_251]) ).
cnf(c_0_513,plain,
~ proper_subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_297]) ).
cnf(c_0_514,plain,
( X1 = empty_set
| in(esk17_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_296]) ).
cnf(c_0_515,plain,
( empty(X1)
| ~ empty(esk51_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_287]) ).
cnf(c_0_516,plain,
in(X1,esk57_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_252]) ).
cnf(c_0_517,plain,
element(esk49_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_298]) ).
cnf(c_0_518,plain,
( relation_inverse(relation_inverse(X1)) = X1
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_299]) ).
cnf(c_0_519,plain,
( subset(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_269]) ).
cnf(c_0_520,plain,
( subset(X2,X1)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_269]) ).
cnf(c_0_521,plain,
( empty(relation_rng(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_300]) ).
cnf(c_0_522,plain,
( relation(relation_rng(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_300]) ).
cnf(c_0_523,plain,
( empty(relation_dom(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_301]) ).
cnf(c_0_524,plain,
( relation(relation_dom(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_301]) ).
cnf(c_0_525,plain,
( relation(relation_inverse(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_302]) ).
cnf(c_0_526,plain,
~ empty(singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_303]) ).
cnf(c_0_527,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_304]) ).
cnf(c_0_528,plain,
( X2 = X1
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_305]) ).
cnf(c_0_529,plain,
set_intersection2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_306]) ).
cnf(c_0_530,plain,
set_union2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_307]) ).
cnf(c_0_531,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_308]) ).
cnf(c_0_532,plain,
set_difference(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_309]) ).
cnf(c_0_533,plain,
set_union2(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_310]) ).
cnf(c_0_534,plain,
set_difference(empty_set,X1) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_311]) ).
cnf(c_0_535,plain,
set_intersection2(X1,empty_set) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_312]) ).
cnf(c_0_536,plain,
( X2 = empty_set
| X1 != empty_set
| X2 != set_meet(X1) ),
inference(split_conjunct,[status(thm)],[c_0_242]) ).
cnf(c_0_537,plain,
( relation(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_313]) ).
cnf(c_0_538,plain,
empty(esk54_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_294]) ).
cnf(c_0_539,plain,
relation(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_314]) ).
cnf(c_0_540,plain,
( X2 = set_meet(X1)
| X1 != empty_set
| X2 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_242]) ).
cnf(c_0_541,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_315]) ).
cnf(c_0_542,plain,
cast_to_subset(X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_316]) ).
cnf(c_0_543,plain,
~ empty(esk55_0),
inference(split_conjunct,[status(thm)],[c_0_317]) ).
cnf(c_0_544,plain,
~ empty(esk53_0),
inference(split_conjunct,[status(thm)],[c_0_318]) ).
cnf(c_0_545,plain,
relation(esk53_0),
inference(split_conjunct,[status(thm)],[c_0_318]) ).
cnf(c_0_546,plain,
empty(esk52_0),
inference(split_conjunct,[status(thm)],[c_0_319]) ).
cnf(c_0_547,plain,
empty(esk50_0),
inference(split_conjunct,[status(thm)],[c_0_320]) ).
cnf(c_0_548,plain,
relation(esk50_0),
inference(split_conjunct,[status(thm)],[c_0_320]) ).
cnf(c_0_549,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[c_0_321]) ).
cnf(c_0_550,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[c_0_321]) ).
cnf(c_0_551,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[c_0_322]) ).
cnf(c_0_552,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_323]) ).
cnf(c_0_553,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_324]) ).
cnf(c_0_554,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_325]) ).
cnf(c_0_555,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_326]) ).
cnf(c_0_556,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_327]) ).
cnf(c_0_557,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_328]) ).
cnf(c_0_558,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_329]) ).
cnf(c_0_559,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_330]) ).
cnf(c_0_560,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_331]) ).
cnf(c_0_561,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_332]) ).
cnf(c_0_562,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_333]) ).
cnf(c_0_563,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_334]) ).
cnf(c_0_564,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_335]) ).
cnf(c_0_565,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_336]) ).
cnf(c_0_566,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_337]) ).
cnf(c_0_567,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_338]) ).
cnf(c_0_568,plain,
( in(ordered_pair(X4,esk44_5(X1,X2,X3,X4,X5)),X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X4,X5),X3) ),
c_0_339,
[final] ).
cnf(c_0_569,plain,
( in(ordered_pair(esk44_5(X1,X2,X3,X4,X5),X5),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X4,X5),X3) ),
c_0_340,
[final] ).
cnf(c_0_570,plain,
( X2 = relation_rng_restriction(X3,X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(esk5_3(X3,X1,X2),esk6_3(X3,X1,X2)),X1)
| ~ in(esk6_3(X3,X1,X2),X3)
| ~ in(ordered_pair(esk5_3(X3,X1,X2),esk6_3(X3,X1,X2)),X2) ),
c_0_341,
[final] ).
cnf(c_0_571,plain,
( X2 = relation_dom_restriction(X1,X3)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(esk3_3(X1,X3,X2),esk4_3(X1,X3,X2)),X1)
| ~ in(esk3_3(X1,X3,X2),X3)
| ~ in(ordered_pair(esk3_3(X1,X3,X2),esk4_3(X1,X3,X2)),X2) ),
c_0_342,
[final] ).
cnf(c_0_572,plain,
( X3 = relation_composition(X1,X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3)
| ~ in(ordered_pair(X4,esk46_3(X1,X2,X3)),X2)
| ~ in(ordered_pair(esk45_3(X1,X2,X3),X4),X1)
| ~ in(ordered_pair(esk45_3(X1,X2,X3),esk46_3(X1,X2,X3)),X3) ),
c_0_343,
[final] ).
cnf(c_0_573,plain,
( in(ordered_pair(esk7_4(X1,X3,X2,X4),X4),X1)
| ~ relation(X1)
| X2 != relation_image(X1,X3)
| ~ in(X4,X2) ),
c_0_344,
[final] ).
cnf(c_0_574,plain,
( ordered_pair(esk23_4(X2,X3,X1,X4),esk24_4(X2,X3,X1,X4)) = X4
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
c_0_345,
[final] ).
cnf(c_0_575,plain,
( X3 = relation_composition(X1,X2)
| in(ordered_pair(esk45_3(X1,X2,X3),esk46_3(X1,X2,X3)),X3)
| in(ordered_pair(esk45_3(X1,X2,X3),esk47_3(X1,X2,X3)),X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3) ),
c_0_346,
[final] ).
cnf(c_0_576,plain,
( X3 = relation_composition(X1,X2)
| in(ordered_pair(esk45_3(X1,X2,X3),esk46_3(X1,X2,X3)),X3)
| in(ordered_pair(esk47_3(X1,X2,X3),esk46_3(X1,X2,X3)),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3) ),
c_0_347,
[final] ).
cnf(c_0_577,plain,
( X2 = relation_rng_restriction(X3,X1)
| in(ordered_pair(esk5_3(X3,X1,X2),esk6_3(X3,X1,X2)),X2)
| in(ordered_pair(esk5_3(X3,X1,X2),esk6_3(X3,X1,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
c_0_348,
[final] ).
cnf(c_0_578,plain,
( X2 = relation_dom_restriction(X1,X3)
| in(ordered_pair(esk3_3(X1,X3,X2),esk4_3(X1,X3,X2)),X2)
| in(ordered_pair(esk3_3(X1,X3,X2),esk4_3(X1,X3,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
c_0_349,
[final] ).
cnf(c_0_579,plain,
( X3 = complements_of_subsets(X2,X1)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2)))
| ~ in(subset_complement(X2,esk48_3(X2,X1,X3)),X1)
| ~ in(esk48_3(X2,X1,X3),X3) ),
c_0_350,
[final] ).
cnf(c_0_580,plain,
( X2 = relation_image(X1,X3)
| ~ relation(X1)
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk8_3(X1,X3,X2)),X1)
| ~ in(esk8_3(X1,X3,X2),X2) ),
c_0_351,
[final] ).
cnf(c_0_581,plain,
( X2 = relation_rng_restriction(X3,X1)
| in(ordered_pair(esk5_3(X3,X1,X2),esk6_3(X3,X1,X2)),X2)
| in(esk6_3(X3,X1,X2),X3)
| ~ relation(X1)
| ~ relation(X2) ),
c_0_352,
[final] ).
cnf(c_0_582,plain,
( X2 = relation_dom_restriction(X1,X3)
| in(ordered_pair(esk3_3(X1,X3,X2),esk4_3(X1,X3,X2)),X2)
| in(esk3_3(X1,X3,X2),X3)
| ~ relation(X1)
| ~ relation(X2) ),
c_0_353,
[final] ).
cnf(c_0_583,plain,
( X2 = relation_image(X1,X3)
| in(esk8_3(X1,X3,X2),X2)
| in(ordered_pair(esk9_3(X1,X3,X2),esk8_3(X1,X3,X2)),X1)
| ~ relation(X1) ),
c_0_354,
[final] ).
cnf(c_0_584,plain,
( X1 = set_intersection2(X2,X3)
| ~ in(esk31_3(X2,X3,X1),X3)
| ~ in(esk31_3(X2,X3,X1),X2)
| ~ in(esk31_3(X2,X3,X1),X1) ),
c_0_355,
[final] ).
cnf(c_0_585,plain,
( in(esk7_4(X1,X3,X2,X4),X3)
| ~ relation(X1)
| X2 != relation_image(X1,X3)
| ~ in(X4,X2) ),
c_0_356,
[final] ).
cnf(c_0_586,plain,
( in(esk23_4(X2,X3,X1,X4),X2)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
c_0_357,
[final] ).
cnf(c_0_587,plain,
( in(esk24_4(X2,X3,X1,X4),X3)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
c_0_358,
[final] ).
cnf(c_0_588,plain,
( X1 = set_difference(X2,X3)
| in(esk38_3(X2,X3,X1),X3)
| ~ in(esk38_3(X2,X3,X1),X2)
| ~ in(esk38_3(X2,X3,X1),X1) ),
c_0_359,
[final] ).
cnf(c_0_589,plain,
( X3 = complements_of_subsets(X2,X1)
| in(subset_complement(X2,esk48_3(X2,X1,X3)),X1)
| in(esk48_3(X2,X1,X3),X3)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2))) ),
c_0_360,
[final] ).
cnf(c_0_590,plain,
( X2 = relation_inverse(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(esk43_2(X1,X2),esk42_2(X1,X2)),X1)
| ~ in(ordered_pair(esk42_2(X1,X2),esk43_2(X1,X2)),X2) ),
c_0_361,
[final] ).
cnf(c_0_591,plain,
( X1 = X2
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(esk19_2(X1,X2),esk20_2(X1,X2)),X2)
| ~ in(ordered_pair(esk19_2(X1,X2),esk20_2(X1,X2)),X1) ),
c_0_362,
[final] ).
cnf(c_0_592,plain,
( X1 = cartesian_product2(X2,X3)
| in(esk25_3(X2,X3,X1),X1)
| ordered_pair(esk26_3(X2,X3,X1),esk27_3(X2,X3,X1)) = esk25_3(X2,X3,X1) ),
c_0_363,
[final] ).
cnf(c_0_593,plain,
( X1 = set_union2(X2,X3)
| ~ in(esk22_3(X2,X3,X1),X1)
| ~ in(esk22_3(X2,X3,X1),X2) ),
c_0_364,
[final] ).
cnf(c_0_594,plain,
( X1 = set_union2(X2,X3)
| ~ in(esk22_3(X2,X3,X1),X1)
| ~ in(esk22_3(X2,X3,X1),X3) ),
c_0_365,
[final] ).
cnf(c_0_595,plain,
( X1 = set_union2(X2,X3)
| in(esk22_3(X2,X3,X1),X3)
| in(esk22_3(X2,X3,X1),X2)
| in(esk22_3(X2,X3,X1),X1) ),
c_0_366,
[final] ).
cnf(c_0_596,plain,
( X1 = cartesian_product2(X2,X3)
| esk25_3(X2,X3,X1) != ordered_pair(X4,X5)
| ~ in(X5,X3)
| ~ in(X4,X2)
| ~ in(esk25_3(X2,X3,X1),X1) ),
c_0_367,
[final] ).
cnf(c_0_597,plain,
( X1 = identity_relation(X2)
| ~ relation(X1)
| esk2_2(X2,X1) != esk1_2(X2,X1)
| ~ in(esk1_2(X2,X1),X2)
| ~ in(ordered_pair(esk1_2(X2,X1),esk2_2(X2,X1)),X1) ),
c_0_368,
[final] ).
cnf(c_0_598,plain,
( X1 = set_difference(X2,X3)
| in(esk38_3(X2,X3,X1),X1)
| ~ in(esk38_3(X2,X3,X1),X3) ),
c_0_369,
[final] ).
cnf(c_0_599,plain,
( X2 = relation_inverse(X1)
| in(ordered_pair(esk43_2(X1,X2),esk42_2(X1,X2)),X1)
| in(ordered_pair(esk42_2(X1,X2),esk43_2(X1,X2)),X2)
| ~ relation(X1)
| ~ relation(X2) ),
c_0_370,
[final] ).
cnf(c_0_600,plain,
( X1 = X2
| in(ordered_pair(esk19_2(X1,X2),esk20_2(X1,X2)),X2)
| in(ordered_pair(esk19_2(X1,X2),esk20_2(X1,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
c_0_371,
[final] ).
cnf(c_0_601,plain,
( X1 = unordered_pair(X2,X3)
| ~ in(esk21_3(X2,X3,X1),X1)
| esk21_3(X2,X3,X1) != X2 ),
c_0_372,
[final] ).
cnf(c_0_602,plain,
( X1 = unordered_pair(X2,X3)
| ~ in(esk21_3(X2,X3,X1),X1)
| esk21_3(X2,X3,X1) != X3 ),
c_0_373,
[final] ).
cnf(c_0_603,plain,
( in(ordered_pair(esk39_3(X1,X2,X3),X3),X1)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(X3,X2) ),
c_0_374,
[final] ).
cnf(c_0_604,plain,
( in(ordered_pair(X3,esk32_3(X1,X2,X3)),X1)
| ~ relation(X1)
| X2 != relation_dom(X1)
| ~ in(X3,X2) ),
c_0_375,
[final] ).
cnf(c_0_605,plain,
( X2 = relation_image(X1,X3)
| in(esk8_3(X1,X3,X2),X2)
| in(esk9_3(X1,X3,X2),X3)
| ~ relation(X1) ),
c_0_376,
[final] ).
cnf(c_0_606,plain,
( X1 = set_difference(X2,X3)
| in(esk38_3(X2,X3,X1),X1)
| in(esk38_3(X2,X3,X1),X2) ),
c_0_377,
[final] ).
cnf(c_0_607,plain,
( X1 = set_intersection2(X2,X3)
| in(esk31_3(X2,X3,X1),X1)
| in(esk31_3(X2,X3,X1),X2) ),
c_0_378,
[final] ).
cnf(c_0_608,plain,
( X1 = set_intersection2(X2,X3)
| in(esk31_3(X2,X3,X1),X1)
| in(esk31_3(X2,X3,X1),X3) ),
c_0_379,
[final] ).
cnf(c_0_609,plain,
( X1 = cartesian_product2(X2,X3)
| in(esk25_3(X2,X3,X1),X1)
| in(esk26_3(X2,X3,X1),X2) ),
c_0_380,
[final] ).
cnf(c_0_610,plain,
( X1 = cartesian_product2(X2,X3)
| in(esk25_3(X2,X3,X1),X1)
| in(esk27_3(X2,X3,X1),X3) ),
c_0_381,
[final] ).
cnf(c_0_611,plain,
( subset(X1,X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(esk28_2(X1,X2),esk29_2(X1,X2)),X2) ),
c_0_382,
[final] ).
cnf(c_0_612,plain,
( X1 = unordered_pair(X2,X3)
| esk21_3(X2,X3,X1) = X3
| esk21_3(X2,X3,X1) = X2
| in(esk21_3(X2,X3,X1),X1) ),
c_0_383,
[final] ).
cnf(c_0_613,plain,
( X3 = complements_of_subsets(X2,X1)
| element(esk48_3(X2,X1,X3),powerset(X2))
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2))) ),
c_0_384,
[final] ).
cnf(c_0_614,plain,
( in(X4,X3)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2)))
| X3 != complements_of_subsets(X2,X1)
| ~ element(X4,powerset(X2))
| ~ in(subset_complement(X2,X4),X1) ),
c_0_385,
[final] ).
cnf(c_0_615,plain,
( in(subset_complement(X2,X4),X1)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2)))
| X3 != complements_of_subsets(X2,X1)
| ~ element(X4,powerset(X2))
| ~ in(X4,X3) ),
c_0_386,
[final] ).
cnf(c_0_616,plain,
( X2 = relation_rng(X1)
| ~ relation(X1)
| ~ in(ordered_pair(X3,esk40_2(X1,X2)),X1)
| ~ in(esk40_2(X1,X2),X2) ),
c_0_387,
[final] ).
cnf(c_0_617,plain,
( X2 = relation_dom(X1)
| ~ relation(X1)
| ~ in(ordered_pair(esk33_2(X1,X2),X3),X1)
| ~ in(esk33_2(X1,X2),X2) ),
c_0_388,
[final] ).
cnf(c_0_618,plain,
( X1 = empty_set
| in(X3,X2)
| X2 != set_meet(X1)
| ~ in(X3,esk13_3(X1,X2,X3)) ),
c_0_389,
[final] ).
cnf(c_0_619,plain,
( in(ordered_pair(X4,X5),X3)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X6,X5),X2)
| ~ in(ordered_pair(X4,X6),X1) ),
c_0_390,
[final] ).
cnf(c_0_620,plain,
( X2 = relation_rng(X1)
| in(ordered_pair(esk41_2(X1,X2),esk40_2(X1,X2)),X1)
| in(esk40_2(X1,X2),X2)
| ~ relation(X1) ),
c_0_391,
[final] ).
cnf(c_0_621,plain,
( X2 = relation_dom(X1)
| in(ordered_pair(esk33_2(X1,X2),esk34_2(X1,X2)),X1)
| in(esk33_2(X1,X2),X2)
| ~ relation(X1) ),
c_0_392,
[final] ).
cnf(c_0_622,plain,
( X1 = identity_relation(X2)
| in(ordered_pair(esk1_2(X2,X1),esk2_2(X2,X1)),X1)
| in(esk1_2(X2,X1),X2)
| ~ relation(X1) ),
c_0_393,
[final] ).
cnf(c_0_623,plain,
( element(subset_difference(X1,X2,X3),powerset(X1))
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
c_0_394,
[final] ).
cnf(c_0_624,plain,
( X1 = identity_relation(X2)
| in(ordered_pair(esk1_2(X2,X1),esk2_2(X2,X1)),X1)
| esk2_2(X2,X1) = esk1_2(X2,X1)
| ~ relation(X1) ),
c_0_395,
[final] ).
cnf(c_0_625,plain,
( X1 = empty_set
| X2 = set_meet(X1)
| ~ in(esk14_2(X1,X2),X2)
| ~ in(esk14_2(X1,X2),esk15_2(X1,X2)) ),
c_0_396,
[final] ).
cnf(c_0_626,plain,
( subset(X1,X2)
| in(ordered_pair(esk28_2(X1,X2),esk29_2(X1,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
c_0_397,
[final] ).
cnf(c_0_627,plain,
( in(ordered_pair(X4,X5),X2)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_rng_restriction(X3,X1)
| ~ in(ordered_pair(X4,X5),X1)
| ~ in(X5,X3) ),
c_0_398,
[final] ).
cnf(c_0_628,plain,
( in(ordered_pair(X4,X5),X2)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_dom_restriction(X1,X3)
| ~ in(ordered_pair(X4,X5),X1)
| ~ in(X4,X3) ),
c_0_399,
[final] ).
cnf(c_0_629,plain,
( X1 = union(X2)
| ~ in(X3,X2)
| ~ in(esk36_2(X2,X1),X3)
| ~ in(esk36_2(X2,X1),X1) ),
c_0_400,
[final] ).
cnf(c_0_630,plain,
( in(X3,esk35_3(X2,X1,X3))
| X1 != union(X2)
| ~ in(X3,X1) ),
c_0_401,
[final] ).
cnf(c_0_631,plain,
( in(esk35_3(X2,X1,X3),X2)
| X1 != union(X2)
| ~ in(X3,X1) ),
c_0_402,
[final] ).
cnf(c_0_632,plain,
( X1 = empty_set
| in(X3,X2)
| in(esk13_3(X1,X2,X3),X1)
| X2 != set_meet(X1) ),
c_0_403,
[final] ).
cnf(c_0_633,plain,
( in(ordered_pair(X4,X5),X1)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_rng_restriction(X3,X1)
| ~ in(ordered_pair(X4,X5),X2) ),
c_0_404,
[final] ).
cnf(c_0_634,plain,
( in(ordered_pair(X4,X5),X1)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_dom_restriction(X1,X3)
| ~ in(ordered_pair(X4,X5),X2) ),
c_0_405,
[final] ).
cnf(c_0_635,plain,
( in(ordered_pair(X3,X4),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(X3,X4),X1)
| ~ subset(X1,X2) ),
c_0_406,
[final] ).
cnf(c_0_636,plain,
( subset_difference(X1,X2,X3) = set_difference(X2,X3)
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
c_0_407,
[final] ).
cnf(c_0_637,plain,
( X1 = powerset(X2)
| ~ subset(esk18_2(X2,X1),X2)
| ~ in(esk18_2(X2,X1),X1) ),
c_0_408,
[final] ).
cnf(c_0_638,plain,
( in(X4,X2)
| ~ relation(X1)
| X2 != relation_image(X1,X3)
| ~ in(X5,X3)
| ~ in(ordered_pair(X5,X4),X1) ),
c_0_409,
[final] ).
cnf(c_0_639,plain,
( X1 = X2
| ~ in(esk56_2(X1,X2),X2)
| ~ in(esk56_2(X1,X2),X1) ),
c_0_410,
[final] ).
cnf(c_0_640,plain,
( in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_inverse(X1)
| ~ in(ordered_pair(X4,X3),X2) ),
c_0_411,
[final] ).
cnf(c_0_641,plain,
( in(ordered_pair(X3,X4),X2)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_inverse(X1)
| ~ in(ordered_pair(X4,X3),X1) ),
c_0_412,
[final] ).
cnf(c_0_642,plain,
( in(ordered_pair(X3,X4),X2)
| ~ relation(X1)
| ~ relation(X2)
| X1 != X2
| ~ in(ordered_pair(X3,X4),X1) ),
c_0_413,
[final] ).
cnf(c_0_643,plain,
( in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ relation(X2)
| X1 != X2
| ~ in(ordered_pair(X3,X4),X2) ),
c_0_414,
[final] ).
cnf(c_0_644,plain,
( in(X5,X3)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_rng_restriction(X3,X1)
| ~ in(ordered_pair(X4,X5),X2) ),
c_0_415,
[final] ).
cnf(c_0_645,plain,
( in(X4,X3)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_dom_restriction(X1,X3)
| ~ in(ordered_pair(X4,X5),X2) ),
c_0_416,
[final] ).
cnf(c_0_646,plain,
( X1 = union(X2)
| in(esk36_2(X2,X1),X1)
| in(esk36_2(X2,X1),esk37_2(X2,X1)) ),
c_0_417,
[final] ).
cnf(c_0_647,plain,
( X1 = empty_set
| X2 = set_meet(X1)
| in(esk15_2(X1,X2),X1)
| ~ in(esk14_2(X1,X2),X2) ),
c_0_418,
[final] ).
cnf(c_0_648,plain,
( X1 = empty_set
| X2 = set_meet(X1)
| in(esk14_2(X1,X2),X3)
| in(esk14_2(X1,X2),X2)
| ~ in(X3,X1) ),
c_0_419,
[final] ).
cnf(c_0_649,plain,
( element(complements_of_subsets(X1,X2),powerset(powerset(X1)))
| ~ element(X2,powerset(powerset(X1))) ),
c_0_420,
[final] ).
cnf(c_0_650,plain,
( in(X4,X1)
| X1 != cartesian_product2(X2,X3)
| X4 != ordered_pair(X5,X6)
| ~ in(X6,X3)
| ~ in(X5,X2) ),
c_0_421,
[final] ).
cnf(c_0_651,plain,
( element(meet_of_subsets(X1,X2),powerset(X1))
| ~ element(X2,powerset(powerset(X1))) ),
c_0_422,
[final] ).
cnf(c_0_652,plain,
( element(union_of_subsets(X1,X2),powerset(X1))
| ~ element(X2,powerset(powerset(X1))) ),
c_0_423,
[final] ).
cnf(c_0_653,plain,
( ordered_pair(esk10_2(X2,X1),esk11_2(X2,X1)) = X1
| ~ in(X1,X2)
| ~ relation(X2) ),
c_0_424,
[final] ).
cnf(c_0_654,plain,
( in(X3,esk58_2(X2,X1))
| ~ in(X1,esk57_1(X2))
| ~ subset(X3,X1) ),
c_0_425,
[final] ).
cnf(c_0_655,plain,
( in(X3,X2)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(ordered_pair(X4,X3),X1) ),
c_0_426,
[final] ).
cnf(c_0_656,plain,
( in(X3,X2)
| ~ relation(X1)
| X2 != relation_dom(X1)
| ~ in(ordered_pair(X3,X4),X1) ),
c_0_427,
[final] ).
cnf(c_0_657,plain,
( in(X3,X2)
| ~ relation(X1)
| X1 != identity_relation(X2)
| ~ in(ordered_pair(X3,X4),X1) ),
c_0_428,
[final] ).
cnf(c_0_658,plain,
( X1 = singleton(X2)
| esk16_2(X2,X1) != X2
| ~ in(esk16_2(X2,X1),X1) ),
c_0_429,
[final] ).
cnf(c_0_659,plain,
( complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2
| ~ element(X2,powerset(powerset(X1))) ),
c_0_430,
[final] ).
cnf(c_0_660,plain,
( X1 = union(X2)
| in(esk36_2(X2,X1),X1)
| in(esk37_2(X2,X1),X2) ),
c_0_431,
[final] ).
cnf(c_0_661,plain,
( X1 = powerset(X2)
| subset(esk18_2(X2,X1),X2)
| in(esk18_2(X2,X1),X1) ),
c_0_432,
[final] ).
cnf(c_0_662,plain,
( in(X4,X1)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X3)
| ~ in(X4,X2) ),
c_0_433,
[final] ).
cnf(c_0_663,plain,
( X1 = X2
| in(esk56_2(X1,X2),X2)
| in(esk56_2(X1,X2),X1) ),
c_0_434,
[final] ).
cnf(c_0_664,plain,
( in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| X1 != identity_relation(X2)
| X3 != X4
| ~ in(X3,X2) ),
c_0_435,
[final] ).
cnf(c_0_665,plain,
( X3 = X4
| ~ relation(X1)
| X1 != identity_relation(X2)
| ~ in(ordered_pair(X3,X4),X1) ),
c_0_436,
[final] ).
cnf(c_0_666,plain,
( in(esk58_2(X2,X1),esk57_1(X2))
| ~ in(X1,esk57_1(X2)) ),
c_0_437,
[final] ).
cnf(c_0_667,plain,
( element(subset_complement(X1,X2),powerset(X1))
| ~ element(X2,powerset(X1)) ),
c_0_438,
[final] ).
cnf(c_0_668,plain,
( subset(X1,X2)
| ~ in(esk30_2(X1,X2),X2) ),
c_0_439,
[final] ).
cnf(c_0_669,plain,
( in(X1,esk57_1(X2))
| ~ subset(X1,X3)
| ~ in(X3,esk57_1(X2)) ),
c_0_440,
[final] ).
cnf(c_0_670,plain,
( in(X4,X1)
| in(X4,X3)
| X1 != set_difference(X2,X3)
| ~ in(X4,X2) ),
c_0_441,
[final] ).
cnf(c_0_671,plain,
( in(X4,X3)
| in(X4,X2)
| X1 != set_union2(X2,X3)
| ~ in(X4,X1) ),
c_0_442,
[final] ).
cnf(c_0_672,plain,
( in(X1,esk57_1(X2))
| are_equipotent(X1,esk57_1(X2))
| ~ subset(X1,esk57_1(X2)) ),
c_0_443,
[final] ).
cnf(c_0_673,plain,
( subset_complement(X1,subset_complement(X1,X2)) = X2
| ~ element(X2,powerset(X1)) ),
c_0_444,
[final] ).
cnf(c_0_674,plain,
( X1 = empty_set
| in(X3,X4)
| X2 != set_meet(X1)
| ~ in(X4,X1)
| ~ in(X3,X2) ),
c_0_445,
[final] ).
cnf(c_0_675,plain,
( meet_of_subsets(X1,X2) = set_meet(X2)
| ~ element(X2,powerset(powerset(X1))) ),
c_0_446,
[final] ).
cnf(c_0_676,plain,
( union_of_subsets(X1,X2) = union(X2)
| ~ element(X2,powerset(powerset(X1))) ),
c_0_447,
[final] ).
cnf(c_0_677,plain,
( element(X1,X2)
| ~ element(X3,powerset(X2))
| ~ in(X1,X3) ),
c_0_448,
[final] ).
cnf(c_0_678,plain,
( X1 != set_difference(X2,X3)
| ~ in(X4,X1)
| ~ in(X4,X3) ),
c_0_449,
[final] ).
cnf(c_0_679,plain,
( in(X3,X1)
| X1 != union(X2)
| ~ in(X4,X2)
| ~ in(X3,X4) ),
c_0_450,
[final] ).
cnf(c_0_680,plain,
( ~ empty(X1)
| ~ element(X2,powerset(X1))
| ~ in(X3,X2) ),
c_0_451,
[final] ).
cnf(c_0_681,plain,
( in(X4,X2)
| X1 != set_difference(X2,X3)
| ~ in(X4,X1) ),
c_0_452,
[final] ).
cnf(c_0_682,plain,
( in(X4,X2)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X1) ),
c_0_453,
[final] ).
cnf(c_0_683,plain,
( in(X4,X3)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X1) ),
c_0_454,
[final] ).
cnf(c_0_684,plain,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X2) ),
c_0_455,
[final] ).
cnf(c_0_685,plain,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X3) ),
c_0_456,
[final] ).
cnf(c_0_686,plain,
( X1 = singleton(X2)
| esk16_2(X2,X1) = X2
| in(esk16_2(X2,X1),X1) ),
c_0_457,
[final] ).
cnf(c_0_687,plain,
( subset_complement(X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X1)) ),
c_0_458,
[final] ).
cnf(c_0_688,plain,
unordered_pair(unordered_pair(X1,X2),singleton(X1)) = ordered_pair(X1,X2),
c_0_459,
[final] ).
cnf(c_0_689,plain,
( in(X1,X2)
| ~ in(X1,X3)
| ~ subset(X3,X2) ),
c_0_460,
[final] ).
cnf(c_0_690,plain,
( empty(X2)
| empty(X1)
| ~ empty(cartesian_product2(X1,X2)) ),
c_0_461,
[final] ).
cnf(c_0_691,plain,
( subset(X1,X2)
| in(esk30_2(X1,X2),X1) ),
c_0_462,
[final] ).
cnf(c_0_692,plain,
( empty(X2)
| ~ empty(set_union2(X1,X2)) ),
c_0_463,
[final] ).
cnf(c_0_693,plain,
( empty(X1)
| ~ empty(set_union2(X1,X2)) ),
c_0_464,
[final] ).
cnf(c_0_694,plain,
( X4 = X3
| X4 = X2
| X1 != unordered_pair(X2,X3)
| ~ in(X4,X1) ),
c_0_465,
[final] ).
cnf(c_0_695,plain,
~ empty(unordered_pair(X1,X2)),
c_0_466,
[final] ).
cnf(c_0_696,plain,
~ empty(ordered_pair(X1,X2)),
c_0_467,
[final] ).
cnf(c_0_697,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
c_0_468,
[final] ).
cnf(c_0_698,plain,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
c_0_469,
[final] ).
cnf(c_0_699,plain,
( subset(X3,X2)
| X1 != powerset(X2)
| ~ in(X3,X1) ),
c_0_470,
[final] ).
cnf(c_0_700,plain,
( in(X3,X1)
| X1 != powerset(X2)
| ~ subset(X3,X2) ),
c_0_471,
[final] ).
cnf(c_0_701,plain,
( ~ proper_subset(X1,X2)
| ~ proper_subset(X2,X1) ),
c_0_472,
[final] ).
cnf(c_0_702,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
c_0_473,
[final] ).
cnf(c_0_703,plain,
( empty(relation_composition(X2,X1))
| ~ relation(X1)
| ~ empty(X2) ),
c_0_474,
[final] ).
cnf(c_0_704,plain,
( relation(relation_composition(X2,X1))
| ~ relation(X1)
| ~ empty(X2) ),
c_0_475,
[final] ).
cnf(c_0_705,plain,
( relation(set_union2(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
c_0_476,
[final] ).
cnf(c_0_706,plain,
( relation(set_intersection2(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
c_0_477,
[final] ).
cnf(c_0_707,plain,
( empty(relation_composition(X1,X2))
| ~ relation(X1)
| ~ empty(X2) ),
c_0_478,
[final] ).
cnf(c_0_708,plain,
( relation(relation_composition(X1,X2))
| ~ relation(X1)
| ~ empty(X2) ),
c_0_479,
[final] ).
cnf(c_0_709,plain,
( relation(relation_composition(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
c_0_480,
[final] ).
cnf(c_0_710,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
c_0_481,
[final] ).
cnf(c_0_711,plain,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X2 ),
c_0_482,
[final] ).
cnf(c_0_712,plain,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X3 ),
c_0_483,
[final] ).
cnf(c_0_713,plain,
( in(X1,X2)
| empty(X2)
| ~ element(X1,X2) ),
c_0_484,
[final] ).
cnf(c_0_714,plain,
( empty(X1)
| in(X2,X1)
| ~ element(X2,X1) ),
c_0_485,
[final] ).
cnf(c_0_715,plain,
( empty(X1)
| element(X2,X1)
| ~ in(X2,X1) ),
c_0_486,
[final] ).
cnf(c_0_716,plain,
( proper_subset(X1,X2)
| X1 = X2
| ~ subset(X1,X2) ),
c_0_487,
[final] ).
cnf(c_0_717,plain,
( relation(relation_rng_restriction(X1,X2))
| ~ relation(X2) ),
c_0_488,
[final] ).
cnf(c_0_718,plain,
( relation(relation_dom_restriction(X1,X2))
| ~ relation(X1) ),
c_0_489,
[final] ).
cnf(c_0_719,plain,
( set_union2(relation_dom(X1),relation_rng(X1)) = relation_field(X1)
| ~ relation(X1) ),
c_0_490,
[final] ).
cnf(c_0_720,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
c_0_491,
[final] ).
cnf(c_0_721,plain,
( disjoint(X1,X2)
| ~ disjoint(X2,X1) ),
c_0_492,
[final] ).
cnf(c_0_722,plain,
( subset(X1,X2)
| ~ proper_subset(X1,X2) ),
c_0_493,
[final] ).
cnf(c_0_723,plain,
( set_intersection2(X1,X2) = empty_set
| ~ disjoint(X1,X2) ),
c_0_494,
[final] ).
cnf(c_0_724,plain,
( disjoint(X1,X2)
| set_intersection2(X1,X2) != empty_set ),
c_0_495,
[final] ).
cnf(c_0_725,plain,
( empty(X2)
| ~ empty(X1)
| ~ element(X2,X1) ),
c_0_496,
[final] ).
cnf(c_0_726,plain,
( X3 = X2
| X1 != singleton(X2)
| ~ in(X3,X1) ),
c_0_497,
[final] ).
cnf(c_0_727,plain,
( relation(X1)
| esk12_1(X1) != ordered_pair(X2,X3) ),
c_0_498,
[final] ).
cnf(c_0_728,plain,
( empty(X1)
| element(esk51_1(X1),powerset(X1)) ),
c_0_499,
[final] ).
cnf(c_0_729,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
c_0_500,
[final] ).
cnf(c_0_730,plain,
( element(X2,X1)
| ~ empty(X1)
| ~ empty(X2) ),
c_0_501,
[final] ).
cnf(c_0_731,plain,
( empty(X1)
| ~ empty(relation_rng(X1))
| ~ relation(X1) ),
c_0_502,
[final] ).
cnf(c_0_732,plain,
( empty(X1)
| ~ empty(relation_dom(X1))
| ~ relation(X1) ),
c_0_503,
[final] ).
cnf(c_0_733,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
c_0_504,
[final] ).
cnf(c_0_734,plain,
set_union2(X1,X2) = set_union2(X2,X1),
c_0_505,
[final] ).
cnf(c_0_735,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
c_0_506,
[final] ).
cnf(c_0_736,plain,
element(esk54_1(X1),powerset(X1)),
c_0_507,
[final] ).
cnf(c_0_737,plain,
element(cast_to_subset(X1),powerset(X1)),
c_0_508,
[final] ).
cnf(c_0_738,plain,
( in(X3,X1)
| X1 != singleton(X2)
| X3 != X2 ),
c_0_509,
[final] ).
cnf(c_0_739,plain,
( ~ proper_subset(X1,X2)
| X1 != X2 ),
c_0_510,
[final] ).
cnf(c_0_740,plain,
( ~ in(X1,X2)
| X2 != empty_set ),
c_0_511,
[final] ).
cnf(c_0_741,plain,
( relation(X1)
| in(esk12_1(X1),X1) ),
c_0_512,
[final] ).
cnf(c_0_742,plain,
~ proper_subset(X1,X1),
c_0_513,
[final] ).
cnf(c_0_743,plain,
( X1 = empty_set
| in(esk17_1(X1),X1) ),
c_0_514,
[final] ).
cnf(c_0_744,plain,
( empty(X1)
| ~ empty(esk51_1(X1)) ),
c_0_515,
[final] ).
cnf(c_0_745,plain,
in(X1,esk57_1(X1)),
c_0_516,
[final] ).
cnf(c_0_746,plain,
element(esk49_1(X1),X1),
c_0_517,
[final] ).
cnf(c_0_747,plain,
( relation_inverse(relation_inverse(X1)) = X1
| ~ relation(X1) ),
c_0_518,
[final] ).
cnf(c_0_748,plain,
( subset(X1,X2)
| X1 != X2 ),
c_0_519,
[final] ).
cnf(c_0_749,plain,
( subset(X2,X1)
| X1 != X2 ),
c_0_520,
[final] ).
cnf(c_0_750,plain,
( empty(relation_rng(X1))
| ~ empty(X1) ),
c_0_521,
[final] ).
cnf(c_0_751,plain,
( relation(relation_rng(X1))
| ~ empty(X1) ),
c_0_522,
[final] ).
cnf(c_0_752,plain,
( empty(relation_dom(X1))
| ~ empty(X1) ),
c_0_523,
[final] ).
cnf(c_0_753,plain,
( relation(relation_dom(X1))
| ~ empty(X1) ),
c_0_524,
[final] ).
cnf(c_0_754,plain,
( relation(relation_inverse(X1))
| ~ relation(X1) ),
c_0_525,
[final] ).
cnf(c_0_755,plain,
~ empty(singleton(X1)),
c_0_526,
[final] ).
cnf(c_0_756,plain,
~ empty(powerset(X1)),
c_0_527,
[final] ).
cnf(c_0_757,plain,
( X2 = X1
| ~ empty(X1)
| ~ empty(X2) ),
c_0_528,
[final] ).
cnf(c_0_758,plain,
set_intersection2(X1,X1) = X1,
c_0_529,
[final] ).
cnf(c_0_759,plain,
set_union2(X1,X1) = X1,
c_0_530,
[final] ).
cnf(c_0_760,plain,
subset(X1,X1),
c_0_531,
[final] ).
cnf(c_0_761,plain,
set_difference(X1,empty_set) = X1,
c_0_532,
[final] ).
cnf(c_0_762,plain,
set_union2(X1,empty_set) = X1,
c_0_533,
[final] ).
cnf(c_0_763,plain,
set_difference(empty_set,X1) = empty_set,
c_0_534,
[final] ).
cnf(c_0_764,plain,
set_intersection2(X1,empty_set) = empty_set,
c_0_535,
[final] ).
cnf(c_0_765,plain,
( X2 = empty_set
| X1 != empty_set
| X2 != set_meet(X1) ),
c_0_536,
[final] ).
cnf(c_0_766,plain,
( relation(X1)
| ~ empty(X1) ),
c_0_537,
[final] ).
cnf(c_0_767,plain,
empty(esk54_1(X1)),
c_0_538,
[final] ).
cnf(c_0_768,plain,
relation(identity_relation(X1)),
c_0_539,
[final] ).
cnf(c_0_769,plain,
( X2 = set_meet(X1)
| X1 != empty_set
| X2 != empty_set ),
c_0_540,
[final] ).
cnf(c_0_770,plain,
( X1 = empty_set
| ~ empty(X1) ),
c_0_541,
[final] ).
cnf(c_0_771,plain,
cast_to_subset(X1) = X1,
c_0_542,
[final] ).
cnf(c_0_772,plain,
~ empty(esk55_0),
c_0_543,
[final] ).
cnf(c_0_773,plain,
~ empty(esk53_0),
c_0_544,
[final] ).
cnf(c_0_774,plain,
relation(esk53_0),
c_0_545,
[final] ).
cnf(c_0_775,plain,
empty(esk52_0),
c_0_546,
[final] ).
cnf(c_0_776,plain,
empty(esk50_0),
c_0_547,
[final] ).
cnf(c_0_777,plain,
relation(esk50_0),
c_0_548,
[final] ).
cnf(c_0_778,plain,
empty(empty_set),
c_0_549,
[final] ).
cnf(c_0_779,plain,
relation(empty_set),
c_0_550,
[final] ).
cnf(c_0_780,plain,
empty(empty_set),
c_0_551,
[final] ).
cnf(c_0_781,plain,
$true,
c_0_552,
[final] ).
cnf(c_0_782,plain,
$true,
c_0_553,
[final] ).
cnf(c_0_783,plain,
$true,
c_0_554,
[final] ).
cnf(c_0_784,plain,
$true,
c_0_555,
[final] ).
cnf(c_0_785,plain,
$true,
c_0_556,
[final] ).
cnf(c_0_786,plain,
$true,
c_0_557,
[final] ).
cnf(c_0_787,plain,
$true,
c_0_558,
[final] ).
cnf(c_0_788,plain,
$true,
c_0_559,
[final] ).
cnf(c_0_789,plain,
$true,
c_0_560,
[final] ).
cnf(c_0_790,plain,
$true,
c_0_561,
[final] ).
cnf(c_0_791,plain,
$true,
c_0_562,
[final] ).
cnf(c_0_792,plain,
$true,
c_0_563,
[final] ).
cnf(c_0_793,plain,
$true,
c_0_564,
[final] ).
cnf(c_0_794,plain,
$true,
c_0_565,
[final] ).
cnf(c_0_795,plain,
$true,
c_0_566,
[final] ).
cnf(c_0_796,plain,
$true,
c_0_567,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_568_0,axiom,
( in(ordered_pair(X4,sk1_esk44_5(X1,X2,X3,X4,X5)),X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X4,X5),X3) ),
inference(literals_permutation,[status(thm)],[c_0_568]) ).
cnf(c_0_568_1,axiom,
( ~ relation(X1)
| in(ordered_pair(X4,sk1_esk44_5(X1,X2,X3,X4,X5)),X1)
| ~ relation(X2)
| ~ relation(X3)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X4,X5),X3) ),
inference(literals_permutation,[status(thm)],[c_0_568]) ).
cnf(c_0_568_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,sk1_esk44_5(X1,X2,X3,X4,X5)),X1)
| ~ relation(X3)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X4,X5),X3) ),
inference(literals_permutation,[status(thm)],[c_0_568]) ).
cnf(c_0_568_3,axiom,
( ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,sk1_esk44_5(X1,X2,X3,X4,X5)),X1)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X4,X5),X3) ),
inference(literals_permutation,[status(thm)],[c_0_568]) ).
cnf(c_0_568_4,axiom,
( X3 != relation_composition(X1,X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,sk1_esk44_5(X1,X2,X3,X4,X5)),X1)
| ~ in(ordered_pair(X4,X5),X3) ),
inference(literals_permutation,[status(thm)],[c_0_568]) ).
cnf(c_0_568_5,axiom,
( ~ in(ordered_pair(X4,X5),X3)
| X3 != relation_composition(X1,X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,sk1_esk44_5(X1,X2,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_568]) ).
cnf(c_0_569_0,axiom,
( in(ordered_pair(sk1_esk44_5(X1,X2,X3,X4,X5),X5),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X4,X5),X3) ),
inference(literals_permutation,[status(thm)],[c_0_569]) ).
cnf(c_0_569_1,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk44_5(X1,X2,X3,X4,X5),X5),X2)
| ~ relation(X2)
| ~ relation(X3)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X4,X5),X3) ),
inference(literals_permutation,[status(thm)],[c_0_569]) ).
cnf(c_0_569_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk44_5(X1,X2,X3,X4,X5),X5),X2)
| ~ relation(X3)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X4,X5),X3) ),
inference(literals_permutation,[status(thm)],[c_0_569]) ).
cnf(c_0_569_3,axiom,
( ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk44_5(X1,X2,X3,X4,X5),X5),X2)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X4,X5),X3) ),
inference(literals_permutation,[status(thm)],[c_0_569]) ).
cnf(c_0_569_4,axiom,
( X3 != relation_composition(X1,X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk44_5(X1,X2,X3,X4,X5),X5),X2)
| ~ in(ordered_pair(X4,X5),X3) ),
inference(literals_permutation,[status(thm)],[c_0_569]) ).
cnf(c_0_569_5,axiom,
( ~ in(ordered_pair(X4,X5),X3)
| X3 != relation_composition(X1,X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk44_5(X1,X2,X3,X4,X5),X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_569]) ).
cnf(c_0_570_0,axiom,
( X2 = relation_rng_restriction(X3,X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(sk1_esk5_3(X3,X1,X2),sk1_esk6_3(X3,X1,X2)),X1)
| ~ in(sk1_esk6_3(X3,X1,X2),X3)
| ~ in(ordered_pair(sk1_esk5_3(X3,X1,X2),sk1_esk6_3(X3,X1,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_570]) ).
cnf(c_0_570_1,axiom,
( ~ relation(X1)
| X2 = relation_rng_restriction(X3,X1)
| ~ relation(X2)
| ~ in(ordered_pair(sk1_esk5_3(X3,X1,X2),sk1_esk6_3(X3,X1,X2)),X1)
| ~ in(sk1_esk6_3(X3,X1,X2),X3)
| ~ in(ordered_pair(sk1_esk5_3(X3,X1,X2),sk1_esk6_3(X3,X1,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_570]) ).
cnf(c_0_570_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| X2 = relation_rng_restriction(X3,X1)
| ~ in(ordered_pair(sk1_esk5_3(X3,X1,X2),sk1_esk6_3(X3,X1,X2)),X1)
| ~ in(sk1_esk6_3(X3,X1,X2),X3)
| ~ in(ordered_pair(sk1_esk5_3(X3,X1,X2),sk1_esk6_3(X3,X1,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_570]) ).
cnf(c_0_570_3,axiom,
( ~ in(ordered_pair(sk1_esk5_3(X3,X1,X2),sk1_esk6_3(X3,X1,X2)),X1)
| ~ relation(X2)
| ~ relation(X1)
| X2 = relation_rng_restriction(X3,X1)
| ~ in(sk1_esk6_3(X3,X1,X2),X3)
| ~ in(ordered_pair(sk1_esk5_3(X3,X1,X2),sk1_esk6_3(X3,X1,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_570]) ).
cnf(c_0_570_4,axiom,
( ~ in(sk1_esk6_3(X3,X1,X2),X3)
| ~ in(ordered_pair(sk1_esk5_3(X3,X1,X2),sk1_esk6_3(X3,X1,X2)),X1)
| ~ relation(X2)
| ~ relation(X1)
| X2 = relation_rng_restriction(X3,X1)
| ~ in(ordered_pair(sk1_esk5_3(X3,X1,X2),sk1_esk6_3(X3,X1,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_570]) ).
cnf(c_0_570_5,axiom,
( ~ in(ordered_pair(sk1_esk5_3(X3,X1,X2),sk1_esk6_3(X3,X1,X2)),X2)
| ~ in(sk1_esk6_3(X3,X1,X2),X3)
| ~ in(ordered_pair(sk1_esk5_3(X3,X1,X2),sk1_esk6_3(X3,X1,X2)),X1)
| ~ relation(X2)
| ~ relation(X1)
| X2 = relation_rng_restriction(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_570]) ).
cnf(c_0_571_0,axiom,
( X2 = relation_dom_restriction(X1,X3)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X1)
| ~ in(sk1_esk3_3(X1,X3,X2),X3)
| ~ in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_571]) ).
cnf(c_0_571_1,axiom,
( ~ relation(X1)
| X2 = relation_dom_restriction(X1,X3)
| ~ relation(X2)
| ~ in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X1)
| ~ in(sk1_esk3_3(X1,X3,X2),X3)
| ~ in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_571]) ).
cnf(c_0_571_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| X2 = relation_dom_restriction(X1,X3)
| ~ in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X1)
| ~ in(sk1_esk3_3(X1,X3,X2),X3)
| ~ in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_571]) ).
cnf(c_0_571_3,axiom,
( ~ in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X1)
| ~ relation(X2)
| ~ relation(X1)
| X2 = relation_dom_restriction(X1,X3)
| ~ in(sk1_esk3_3(X1,X3,X2),X3)
| ~ in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_571]) ).
cnf(c_0_571_4,axiom,
( ~ in(sk1_esk3_3(X1,X3,X2),X3)
| ~ in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X1)
| ~ relation(X2)
| ~ relation(X1)
| X2 = relation_dom_restriction(X1,X3)
| ~ in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_571]) ).
cnf(c_0_571_5,axiom,
( ~ in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X2)
| ~ in(sk1_esk3_3(X1,X3,X2),X3)
| ~ in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X1)
| ~ relation(X2)
| ~ relation(X1)
| X2 = relation_dom_restriction(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_571]) ).
cnf(c_0_572_0,axiom,
( X3 = relation_composition(X1,X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3)
| ~ in(ordered_pair(X4,sk1_esk46_3(X1,X2,X3)),X2)
| ~ in(ordered_pair(sk1_esk45_3(X1,X2,X3),X4),X1)
| ~ in(ordered_pair(sk1_esk45_3(X1,X2,X3),sk1_esk46_3(X1,X2,X3)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_572]) ).
cnf(c_0_572_1,axiom,
( ~ relation(X1)
| X3 = relation_composition(X1,X2)
| ~ relation(X2)
| ~ relation(X3)
| ~ in(ordered_pair(X4,sk1_esk46_3(X1,X2,X3)),X2)
| ~ in(ordered_pair(sk1_esk45_3(X1,X2,X3),X4),X1)
| ~ in(ordered_pair(sk1_esk45_3(X1,X2,X3),sk1_esk46_3(X1,X2,X3)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_572]) ).
cnf(c_0_572_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| X3 = relation_composition(X1,X2)
| ~ relation(X3)
| ~ in(ordered_pair(X4,sk1_esk46_3(X1,X2,X3)),X2)
| ~ in(ordered_pair(sk1_esk45_3(X1,X2,X3),X4),X1)
| ~ in(ordered_pair(sk1_esk45_3(X1,X2,X3),sk1_esk46_3(X1,X2,X3)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_572]) ).
cnf(c_0_572_3,axiom,
( ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| X3 = relation_composition(X1,X2)
| ~ in(ordered_pair(X4,sk1_esk46_3(X1,X2,X3)),X2)
| ~ in(ordered_pair(sk1_esk45_3(X1,X2,X3),X4),X1)
| ~ in(ordered_pair(sk1_esk45_3(X1,X2,X3),sk1_esk46_3(X1,X2,X3)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_572]) ).
cnf(c_0_572_4,axiom,
( ~ in(ordered_pair(X4,sk1_esk46_3(X1,X2,X3)),X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| X3 = relation_composition(X1,X2)
| ~ in(ordered_pair(sk1_esk45_3(X1,X2,X3),X4),X1)
| ~ in(ordered_pair(sk1_esk45_3(X1,X2,X3),sk1_esk46_3(X1,X2,X3)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_572]) ).
cnf(c_0_572_5,axiom,
( ~ in(ordered_pair(sk1_esk45_3(X1,X2,X3),X4),X1)
| ~ in(ordered_pair(X4,sk1_esk46_3(X1,X2,X3)),X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| X3 = relation_composition(X1,X2)
| ~ in(ordered_pair(sk1_esk45_3(X1,X2,X3),sk1_esk46_3(X1,X2,X3)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_572]) ).
cnf(c_0_572_6,axiom,
( ~ in(ordered_pair(sk1_esk45_3(X1,X2,X3),sk1_esk46_3(X1,X2,X3)),X3)
| ~ in(ordered_pair(sk1_esk45_3(X1,X2,X3),X4),X1)
| ~ in(ordered_pair(X4,sk1_esk46_3(X1,X2,X3)),X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| X3 = relation_composition(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_572]) ).
cnf(c_0_573_0,axiom,
( in(ordered_pair(sk1_esk7_4(X1,X3,X2,X4),X4),X1)
| ~ relation(X1)
| X2 != relation_image(X1,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_573]) ).
cnf(c_0_573_1,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk7_4(X1,X3,X2,X4),X4),X1)
| X2 != relation_image(X1,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_573]) ).
cnf(c_0_573_2,axiom,
( X2 != relation_image(X1,X3)
| ~ relation(X1)
| in(ordered_pair(sk1_esk7_4(X1,X3,X2,X4),X4),X1)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_573]) ).
cnf(c_0_573_3,axiom,
( ~ in(X4,X2)
| X2 != relation_image(X1,X3)
| ~ relation(X1)
| in(ordered_pair(sk1_esk7_4(X1,X3,X2,X4),X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_573]) ).
cnf(c_0_574_0,axiom,
( ordered_pair(sk1_esk23_4(X2,X3,X1,X4),sk1_esk24_4(X2,X3,X1,X4)) = X4
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_574]) ).
cnf(c_0_574_1,axiom,
( X1 != cartesian_product2(X2,X3)
| ordered_pair(sk1_esk23_4(X2,X3,X1,X4),sk1_esk24_4(X2,X3,X1,X4)) = X4
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_574]) ).
cnf(c_0_574_2,axiom,
( ~ in(X4,X1)
| X1 != cartesian_product2(X2,X3)
| ordered_pair(sk1_esk23_4(X2,X3,X1,X4),sk1_esk24_4(X2,X3,X1,X4)) = X4 ),
inference(literals_permutation,[status(thm)],[c_0_574]) ).
cnf(c_0_575_0,axiom,
( X3 = relation_composition(X1,X2)
| in(ordered_pair(sk1_esk45_3(X1,X2,X3),sk1_esk46_3(X1,X2,X3)),X3)
| in(ordered_pair(sk1_esk45_3(X1,X2,X3),sk1_esk47_3(X1,X2,X3)),X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_575]) ).
cnf(c_0_575_1,axiom,
( in(ordered_pair(sk1_esk45_3(X1,X2,X3),sk1_esk46_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2)
| in(ordered_pair(sk1_esk45_3(X1,X2,X3),sk1_esk47_3(X1,X2,X3)),X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_575]) ).
cnf(c_0_575_2,axiom,
( in(ordered_pair(sk1_esk45_3(X1,X2,X3),sk1_esk47_3(X1,X2,X3)),X1)
| in(ordered_pair(sk1_esk45_3(X1,X2,X3),sk1_esk46_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_575]) ).
cnf(c_0_575_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk45_3(X1,X2,X3),sk1_esk47_3(X1,X2,X3)),X1)
| in(ordered_pair(sk1_esk45_3(X1,X2,X3),sk1_esk46_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2)
| ~ relation(X2)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_575]) ).
cnf(c_0_575_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk45_3(X1,X2,X3),sk1_esk47_3(X1,X2,X3)),X1)
| in(ordered_pair(sk1_esk45_3(X1,X2,X3),sk1_esk46_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_575]) ).
cnf(c_0_575_5,axiom,
( ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk45_3(X1,X2,X3),sk1_esk47_3(X1,X2,X3)),X1)
| in(ordered_pair(sk1_esk45_3(X1,X2,X3),sk1_esk46_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_575]) ).
cnf(c_0_576_0,axiom,
( X3 = relation_composition(X1,X2)
| in(ordered_pair(sk1_esk45_3(X1,X2,X3),sk1_esk46_3(X1,X2,X3)),X3)
| in(ordered_pair(sk1_esk47_3(X1,X2,X3),sk1_esk46_3(X1,X2,X3)),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_576]) ).
cnf(c_0_576_1,axiom,
( in(ordered_pair(sk1_esk45_3(X1,X2,X3),sk1_esk46_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2)
| in(ordered_pair(sk1_esk47_3(X1,X2,X3),sk1_esk46_3(X1,X2,X3)),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_576]) ).
cnf(c_0_576_2,axiom,
( in(ordered_pair(sk1_esk47_3(X1,X2,X3),sk1_esk46_3(X1,X2,X3)),X2)
| in(ordered_pair(sk1_esk45_3(X1,X2,X3),sk1_esk46_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_576]) ).
cnf(c_0_576_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk47_3(X1,X2,X3),sk1_esk46_3(X1,X2,X3)),X2)
| in(ordered_pair(sk1_esk45_3(X1,X2,X3),sk1_esk46_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2)
| ~ relation(X2)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_576]) ).
cnf(c_0_576_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk47_3(X1,X2,X3),sk1_esk46_3(X1,X2,X3)),X2)
| in(ordered_pair(sk1_esk45_3(X1,X2,X3),sk1_esk46_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_576]) ).
cnf(c_0_576_5,axiom,
( ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk47_3(X1,X2,X3),sk1_esk46_3(X1,X2,X3)),X2)
| in(ordered_pair(sk1_esk45_3(X1,X2,X3),sk1_esk46_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_576]) ).
cnf(c_0_577_0,axiom,
( X2 = relation_rng_restriction(X3,X1)
| in(ordered_pair(sk1_esk5_3(X3,X1,X2),sk1_esk6_3(X3,X1,X2)),X2)
| in(ordered_pair(sk1_esk5_3(X3,X1,X2),sk1_esk6_3(X3,X1,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_577]) ).
cnf(c_0_577_1,axiom,
( in(ordered_pair(sk1_esk5_3(X3,X1,X2),sk1_esk6_3(X3,X1,X2)),X2)
| X2 = relation_rng_restriction(X3,X1)
| in(ordered_pair(sk1_esk5_3(X3,X1,X2),sk1_esk6_3(X3,X1,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_577]) ).
cnf(c_0_577_2,axiom,
( in(ordered_pair(sk1_esk5_3(X3,X1,X2),sk1_esk6_3(X3,X1,X2)),X1)
| in(ordered_pair(sk1_esk5_3(X3,X1,X2),sk1_esk6_3(X3,X1,X2)),X2)
| X2 = relation_rng_restriction(X3,X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_577]) ).
cnf(c_0_577_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk5_3(X3,X1,X2),sk1_esk6_3(X3,X1,X2)),X1)
| in(ordered_pair(sk1_esk5_3(X3,X1,X2),sk1_esk6_3(X3,X1,X2)),X2)
| X2 = relation_rng_restriction(X3,X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_577]) ).
cnf(c_0_577_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk5_3(X3,X1,X2),sk1_esk6_3(X3,X1,X2)),X1)
| in(ordered_pair(sk1_esk5_3(X3,X1,X2),sk1_esk6_3(X3,X1,X2)),X2)
| X2 = relation_rng_restriction(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_577]) ).
cnf(c_0_578_0,axiom,
( X2 = relation_dom_restriction(X1,X3)
| in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X2)
| in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_578]) ).
cnf(c_0_578_1,axiom,
( in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X2)
| X2 = relation_dom_restriction(X1,X3)
| in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_578]) ).
cnf(c_0_578_2,axiom,
( in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X1)
| in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X2)
| X2 = relation_dom_restriction(X1,X3)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_578]) ).
cnf(c_0_578_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X1)
| in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X2)
| X2 = relation_dom_restriction(X1,X3)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_578]) ).
cnf(c_0_578_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X1)
| in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X2)
| X2 = relation_dom_restriction(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_578]) ).
cnf(c_0_579_0,axiom,
( X3 = complements_of_subsets(X2,X1)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2)))
| ~ in(subset_complement(X2,sk1_esk48_3(X2,X1,X3)),X1)
| ~ in(sk1_esk48_3(X2,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_579]) ).
cnf(c_0_579_1,axiom,
( ~ element(X1,powerset(powerset(X2)))
| X3 = complements_of_subsets(X2,X1)
| ~ element(X3,powerset(powerset(X2)))
| ~ in(subset_complement(X2,sk1_esk48_3(X2,X1,X3)),X1)
| ~ in(sk1_esk48_3(X2,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_579]) ).
cnf(c_0_579_2,axiom,
( ~ element(X3,powerset(powerset(X2)))
| ~ element(X1,powerset(powerset(X2)))
| X3 = complements_of_subsets(X2,X1)
| ~ in(subset_complement(X2,sk1_esk48_3(X2,X1,X3)),X1)
| ~ in(sk1_esk48_3(X2,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_579]) ).
cnf(c_0_579_3,axiom,
( ~ in(subset_complement(X2,sk1_esk48_3(X2,X1,X3)),X1)
| ~ element(X3,powerset(powerset(X2)))
| ~ element(X1,powerset(powerset(X2)))
| X3 = complements_of_subsets(X2,X1)
| ~ in(sk1_esk48_3(X2,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_579]) ).
cnf(c_0_579_4,axiom,
( ~ in(sk1_esk48_3(X2,X1,X3),X3)
| ~ in(subset_complement(X2,sk1_esk48_3(X2,X1,X3)),X1)
| ~ element(X3,powerset(powerset(X2)))
| ~ element(X1,powerset(powerset(X2)))
| X3 = complements_of_subsets(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_579]) ).
cnf(c_0_580_0,axiom,
( X2 = relation_image(X1,X3)
| ~ relation(X1)
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,sk1_esk8_3(X1,X3,X2)),X1)
| ~ in(sk1_esk8_3(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_580]) ).
cnf(c_0_580_1,axiom,
( ~ relation(X1)
| X2 = relation_image(X1,X3)
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,sk1_esk8_3(X1,X3,X2)),X1)
| ~ in(sk1_esk8_3(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_580]) ).
cnf(c_0_580_2,axiom,
( ~ in(X4,X3)
| ~ relation(X1)
| X2 = relation_image(X1,X3)
| ~ in(ordered_pair(X4,sk1_esk8_3(X1,X3,X2)),X1)
| ~ in(sk1_esk8_3(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_580]) ).
cnf(c_0_580_3,axiom,
( ~ in(ordered_pair(X4,sk1_esk8_3(X1,X3,X2)),X1)
| ~ in(X4,X3)
| ~ relation(X1)
| X2 = relation_image(X1,X3)
| ~ in(sk1_esk8_3(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_580]) ).
cnf(c_0_580_4,axiom,
( ~ in(sk1_esk8_3(X1,X3,X2),X2)
| ~ in(ordered_pair(X4,sk1_esk8_3(X1,X3,X2)),X1)
| ~ in(X4,X3)
| ~ relation(X1)
| X2 = relation_image(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_580]) ).
cnf(c_0_581_0,axiom,
( X2 = relation_rng_restriction(X3,X1)
| in(ordered_pair(sk1_esk5_3(X3,X1,X2),sk1_esk6_3(X3,X1,X2)),X2)
| in(sk1_esk6_3(X3,X1,X2),X3)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_581]) ).
cnf(c_0_581_1,axiom,
( in(ordered_pair(sk1_esk5_3(X3,X1,X2),sk1_esk6_3(X3,X1,X2)),X2)
| X2 = relation_rng_restriction(X3,X1)
| in(sk1_esk6_3(X3,X1,X2),X3)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_581]) ).
cnf(c_0_581_2,axiom,
( in(sk1_esk6_3(X3,X1,X2),X3)
| in(ordered_pair(sk1_esk5_3(X3,X1,X2),sk1_esk6_3(X3,X1,X2)),X2)
| X2 = relation_rng_restriction(X3,X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_581]) ).
cnf(c_0_581_3,axiom,
( ~ relation(X1)
| in(sk1_esk6_3(X3,X1,X2),X3)
| in(ordered_pair(sk1_esk5_3(X3,X1,X2),sk1_esk6_3(X3,X1,X2)),X2)
| X2 = relation_rng_restriction(X3,X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_581]) ).
cnf(c_0_581_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(sk1_esk6_3(X3,X1,X2),X3)
| in(ordered_pair(sk1_esk5_3(X3,X1,X2),sk1_esk6_3(X3,X1,X2)),X2)
| X2 = relation_rng_restriction(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_581]) ).
cnf(c_0_582_0,axiom,
( X2 = relation_dom_restriction(X1,X3)
| in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X2)
| in(sk1_esk3_3(X1,X3,X2),X3)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_582]) ).
cnf(c_0_582_1,axiom,
( in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X2)
| X2 = relation_dom_restriction(X1,X3)
| in(sk1_esk3_3(X1,X3,X2),X3)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_582]) ).
cnf(c_0_582_2,axiom,
( in(sk1_esk3_3(X1,X3,X2),X3)
| in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X2)
| X2 = relation_dom_restriction(X1,X3)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_582]) ).
cnf(c_0_582_3,axiom,
( ~ relation(X1)
| in(sk1_esk3_3(X1,X3,X2),X3)
| in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X2)
| X2 = relation_dom_restriction(X1,X3)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_582]) ).
cnf(c_0_582_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(sk1_esk3_3(X1,X3,X2),X3)
| in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X2)
| X2 = relation_dom_restriction(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_582]) ).
cnf(c_0_583_0,axiom,
( X2 = relation_image(X1,X3)
| in(sk1_esk8_3(X1,X3,X2),X2)
| in(ordered_pair(sk1_esk9_3(X1,X3,X2),sk1_esk8_3(X1,X3,X2)),X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_583]) ).
cnf(c_0_583_1,axiom,
( in(sk1_esk8_3(X1,X3,X2),X2)
| X2 = relation_image(X1,X3)
| in(ordered_pair(sk1_esk9_3(X1,X3,X2),sk1_esk8_3(X1,X3,X2)),X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_583]) ).
cnf(c_0_583_2,axiom,
( in(ordered_pair(sk1_esk9_3(X1,X3,X2),sk1_esk8_3(X1,X3,X2)),X1)
| in(sk1_esk8_3(X1,X3,X2),X2)
| X2 = relation_image(X1,X3)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_583]) ).
cnf(c_0_583_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk9_3(X1,X3,X2),sk1_esk8_3(X1,X3,X2)),X1)
| in(sk1_esk8_3(X1,X3,X2),X2)
| X2 = relation_image(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_583]) ).
cnf(c_0_584_0,axiom,
( X1 = set_intersection2(X2,X3)
| ~ in(sk1_esk31_3(X2,X3,X1),X3)
| ~ in(sk1_esk31_3(X2,X3,X1),X2)
| ~ in(sk1_esk31_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_584]) ).
cnf(c_0_584_1,axiom,
( ~ in(sk1_esk31_3(X2,X3,X1),X3)
| X1 = set_intersection2(X2,X3)
| ~ in(sk1_esk31_3(X2,X3,X1),X2)
| ~ in(sk1_esk31_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_584]) ).
cnf(c_0_584_2,axiom,
( ~ in(sk1_esk31_3(X2,X3,X1),X2)
| ~ in(sk1_esk31_3(X2,X3,X1),X3)
| X1 = set_intersection2(X2,X3)
| ~ in(sk1_esk31_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_584]) ).
cnf(c_0_584_3,axiom,
( ~ in(sk1_esk31_3(X2,X3,X1),X1)
| ~ in(sk1_esk31_3(X2,X3,X1),X2)
| ~ in(sk1_esk31_3(X2,X3,X1),X3)
| X1 = set_intersection2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_584]) ).
cnf(c_0_585_0,axiom,
( in(sk1_esk7_4(X1,X3,X2,X4),X3)
| ~ relation(X1)
| X2 != relation_image(X1,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_585]) ).
cnf(c_0_585_1,axiom,
( ~ relation(X1)
| in(sk1_esk7_4(X1,X3,X2,X4),X3)
| X2 != relation_image(X1,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_585]) ).
cnf(c_0_585_2,axiom,
( X2 != relation_image(X1,X3)
| ~ relation(X1)
| in(sk1_esk7_4(X1,X3,X2,X4),X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_585]) ).
cnf(c_0_585_3,axiom,
( ~ in(X4,X2)
| X2 != relation_image(X1,X3)
| ~ relation(X1)
| in(sk1_esk7_4(X1,X3,X2,X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_585]) ).
cnf(c_0_586_0,axiom,
( in(sk1_esk23_4(X2,X3,X1,X4),X2)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_586]) ).
cnf(c_0_586_1,axiom,
( X1 != cartesian_product2(X2,X3)
| in(sk1_esk23_4(X2,X3,X1,X4),X2)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_586]) ).
cnf(c_0_586_2,axiom,
( ~ in(X4,X1)
| X1 != cartesian_product2(X2,X3)
| in(sk1_esk23_4(X2,X3,X1,X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_586]) ).
cnf(c_0_587_0,axiom,
( in(sk1_esk24_4(X2,X3,X1,X4),X3)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_587]) ).
cnf(c_0_587_1,axiom,
( X1 != cartesian_product2(X2,X3)
| in(sk1_esk24_4(X2,X3,X1,X4),X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_587]) ).
cnf(c_0_587_2,axiom,
( ~ in(X4,X1)
| X1 != cartesian_product2(X2,X3)
| in(sk1_esk24_4(X2,X3,X1,X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_587]) ).
cnf(c_0_588_0,axiom,
( X1 = set_difference(X2,X3)
| in(sk1_esk38_3(X2,X3,X1),X3)
| ~ in(sk1_esk38_3(X2,X3,X1),X2)
| ~ in(sk1_esk38_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_588]) ).
cnf(c_0_588_1,axiom,
( in(sk1_esk38_3(X2,X3,X1),X3)
| X1 = set_difference(X2,X3)
| ~ in(sk1_esk38_3(X2,X3,X1),X2)
| ~ in(sk1_esk38_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_588]) ).
cnf(c_0_588_2,axiom,
( ~ in(sk1_esk38_3(X2,X3,X1),X2)
| in(sk1_esk38_3(X2,X3,X1),X3)
| X1 = set_difference(X2,X3)
| ~ in(sk1_esk38_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_588]) ).
cnf(c_0_588_3,axiom,
( ~ in(sk1_esk38_3(X2,X3,X1),X1)
| ~ in(sk1_esk38_3(X2,X3,X1),X2)
| in(sk1_esk38_3(X2,X3,X1),X3)
| X1 = set_difference(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_588]) ).
cnf(c_0_589_0,axiom,
( X3 = complements_of_subsets(X2,X1)
| in(subset_complement(X2,sk1_esk48_3(X2,X1,X3)),X1)
| in(sk1_esk48_3(X2,X1,X3),X3)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_589]) ).
cnf(c_0_589_1,axiom,
( in(subset_complement(X2,sk1_esk48_3(X2,X1,X3)),X1)
| X3 = complements_of_subsets(X2,X1)
| in(sk1_esk48_3(X2,X1,X3),X3)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_589]) ).
cnf(c_0_589_2,axiom,
( in(sk1_esk48_3(X2,X1,X3),X3)
| in(subset_complement(X2,sk1_esk48_3(X2,X1,X3)),X1)
| X3 = complements_of_subsets(X2,X1)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_589]) ).
cnf(c_0_589_3,axiom,
( ~ element(X1,powerset(powerset(X2)))
| in(sk1_esk48_3(X2,X1,X3),X3)
| in(subset_complement(X2,sk1_esk48_3(X2,X1,X3)),X1)
| X3 = complements_of_subsets(X2,X1)
| ~ element(X3,powerset(powerset(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_589]) ).
cnf(c_0_589_4,axiom,
( ~ element(X3,powerset(powerset(X2)))
| ~ element(X1,powerset(powerset(X2)))
| in(sk1_esk48_3(X2,X1,X3),X3)
| in(subset_complement(X2,sk1_esk48_3(X2,X1,X3)),X1)
| X3 = complements_of_subsets(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_589]) ).
cnf(c_0_590_0,axiom,
( X2 = relation_inverse(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(sk1_esk43_2(X1,X2),sk1_esk42_2(X1,X2)),X1)
| ~ in(ordered_pair(sk1_esk42_2(X1,X2),sk1_esk43_2(X1,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_590]) ).
cnf(c_0_590_1,axiom,
( ~ relation(X1)
| X2 = relation_inverse(X1)
| ~ relation(X2)
| ~ in(ordered_pair(sk1_esk43_2(X1,X2),sk1_esk42_2(X1,X2)),X1)
| ~ in(ordered_pair(sk1_esk42_2(X1,X2),sk1_esk43_2(X1,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_590]) ).
cnf(c_0_590_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| X2 = relation_inverse(X1)
| ~ in(ordered_pair(sk1_esk43_2(X1,X2),sk1_esk42_2(X1,X2)),X1)
| ~ in(ordered_pair(sk1_esk42_2(X1,X2),sk1_esk43_2(X1,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_590]) ).
cnf(c_0_590_3,axiom,
( ~ in(ordered_pair(sk1_esk43_2(X1,X2),sk1_esk42_2(X1,X2)),X1)
| ~ relation(X2)
| ~ relation(X1)
| X2 = relation_inverse(X1)
| ~ in(ordered_pair(sk1_esk42_2(X1,X2),sk1_esk43_2(X1,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_590]) ).
cnf(c_0_590_4,axiom,
( ~ in(ordered_pair(sk1_esk42_2(X1,X2),sk1_esk43_2(X1,X2)),X2)
| ~ in(ordered_pair(sk1_esk43_2(X1,X2),sk1_esk42_2(X1,X2)),X1)
| ~ relation(X2)
| ~ relation(X1)
| X2 = relation_inverse(X1) ),
inference(literals_permutation,[status(thm)],[c_0_590]) ).
cnf(c_0_591_0,axiom,
( X1 = X2
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(sk1_esk19_2(X1,X2),sk1_esk20_2(X1,X2)),X2)
| ~ in(ordered_pair(sk1_esk19_2(X1,X2),sk1_esk20_2(X1,X2)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_591]) ).
cnf(c_0_591_1,axiom,
( ~ relation(X1)
| X1 = X2
| ~ relation(X2)
| ~ in(ordered_pair(sk1_esk19_2(X1,X2),sk1_esk20_2(X1,X2)),X2)
| ~ in(ordered_pair(sk1_esk19_2(X1,X2),sk1_esk20_2(X1,X2)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_591]) ).
cnf(c_0_591_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| X1 = X2
| ~ in(ordered_pair(sk1_esk19_2(X1,X2),sk1_esk20_2(X1,X2)),X2)
| ~ in(ordered_pair(sk1_esk19_2(X1,X2),sk1_esk20_2(X1,X2)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_591]) ).
cnf(c_0_591_3,axiom,
( ~ in(ordered_pair(sk1_esk19_2(X1,X2),sk1_esk20_2(X1,X2)),X2)
| ~ relation(X2)
| ~ relation(X1)
| X1 = X2
| ~ in(ordered_pair(sk1_esk19_2(X1,X2),sk1_esk20_2(X1,X2)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_591]) ).
cnf(c_0_591_4,axiom,
( ~ in(ordered_pair(sk1_esk19_2(X1,X2),sk1_esk20_2(X1,X2)),X1)
| ~ in(ordered_pair(sk1_esk19_2(X1,X2),sk1_esk20_2(X1,X2)),X2)
| ~ relation(X2)
| ~ relation(X1)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_591]) ).
cnf(c_0_592_0,axiom,
( X1 = cartesian_product2(X2,X3)
| in(sk1_esk25_3(X2,X3,X1),X1)
| ordered_pair(sk1_esk26_3(X2,X3,X1),sk1_esk27_3(X2,X3,X1)) = sk1_esk25_3(X2,X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_592]) ).
cnf(c_0_592_1,axiom,
( in(sk1_esk25_3(X2,X3,X1),X1)
| X1 = cartesian_product2(X2,X3)
| ordered_pair(sk1_esk26_3(X2,X3,X1),sk1_esk27_3(X2,X3,X1)) = sk1_esk25_3(X2,X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_592]) ).
cnf(c_0_592_2,axiom,
( ordered_pair(sk1_esk26_3(X2,X3,X1),sk1_esk27_3(X2,X3,X1)) = sk1_esk25_3(X2,X3,X1)
| in(sk1_esk25_3(X2,X3,X1),X1)
| X1 = cartesian_product2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_592]) ).
cnf(c_0_593_0,axiom,
( X1 = set_union2(X2,X3)
| ~ in(sk1_esk22_3(X2,X3,X1),X1)
| ~ in(sk1_esk22_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_593]) ).
cnf(c_0_593_1,axiom,
( ~ in(sk1_esk22_3(X2,X3,X1),X1)
| X1 = set_union2(X2,X3)
| ~ in(sk1_esk22_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_593]) ).
cnf(c_0_593_2,axiom,
( ~ in(sk1_esk22_3(X2,X3,X1),X2)
| ~ in(sk1_esk22_3(X2,X3,X1),X1)
| X1 = set_union2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_593]) ).
cnf(c_0_594_0,axiom,
( X1 = set_union2(X2,X3)
| ~ in(sk1_esk22_3(X2,X3,X1),X1)
| ~ in(sk1_esk22_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_594]) ).
cnf(c_0_594_1,axiom,
( ~ in(sk1_esk22_3(X2,X3,X1),X1)
| X1 = set_union2(X2,X3)
| ~ in(sk1_esk22_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_594]) ).
cnf(c_0_594_2,axiom,
( ~ in(sk1_esk22_3(X2,X3,X1),X3)
| ~ in(sk1_esk22_3(X2,X3,X1),X1)
| X1 = set_union2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_594]) ).
cnf(c_0_595_0,axiom,
( X1 = set_union2(X2,X3)
| in(sk1_esk22_3(X2,X3,X1),X3)
| in(sk1_esk22_3(X2,X3,X1),X2)
| in(sk1_esk22_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_595]) ).
cnf(c_0_595_1,axiom,
( in(sk1_esk22_3(X2,X3,X1),X3)
| X1 = set_union2(X2,X3)
| in(sk1_esk22_3(X2,X3,X1),X2)
| in(sk1_esk22_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_595]) ).
cnf(c_0_595_2,axiom,
( in(sk1_esk22_3(X2,X3,X1),X2)
| in(sk1_esk22_3(X2,X3,X1),X3)
| X1 = set_union2(X2,X3)
| in(sk1_esk22_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_595]) ).
cnf(c_0_595_3,axiom,
( in(sk1_esk22_3(X2,X3,X1),X1)
| in(sk1_esk22_3(X2,X3,X1),X2)
| in(sk1_esk22_3(X2,X3,X1),X3)
| X1 = set_union2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_595]) ).
cnf(c_0_596_0,axiom,
( X1 = cartesian_product2(X2,X3)
| sk1_esk25_3(X2,X3,X1) != ordered_pair(X4,X5)
| ~ in(X5,X3)
| ~ in(X4,X2)
| ~ in(sk1_esk25_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_596]) ).
cnf(c_0_596_1,axiom,
( sk1_esk25_3(X2,X3,X1) != ordered_pair(X4,X5)
| X1 = cartesian_product2(X2,X3)
| ~ in(X5,X3)
| ~ in(X4,X2)
| ~ in(sk1_esk25_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_596]) ).
cnf(c_0_596_2,axiom,
( ~ in(X5,X3)
| sk1_esk25_3(X2,X3,X1) != ordered_pair(X4,X5)
| X1 = cartesian_product2(X2,X3)
| ~ in(X4,X2)
| ~ in(sk1_esk25_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_596]) ).
cnf(c_0_596_3,axiom,
( ~ in(X4,X2)
| ~ in(X5,X3)
| sk1_esk25_3(X2,X3,X1) != ordered_pair(X4,X5)
| X1 = cartesian_product2(X2,X3)
| ~ in(sk1_esk25_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_596]) ).
cnf(c_0_596_4,axiom,
( ~ in(sk1_esk25_3(X2,X3,X1),X1)
| ~ in(X4,X2)
| ~ in(X5,X3)
| sk1_esk25_3(X2,X3,X1) != ordered_pair(X4,X5)
| X1 = cartesian_product2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_596]) ).
cnf(c_0_597_0,axiom,
( X1 = identity_relation(X2)
| ~ relation(X1)
| sk1_esk2_2(X2,X1) != sk1_esk1_2(X2,X1)
| ~ in(sk1_esk1_2(X2,X1),X2)
| ~ in(ordered_pair(sk1_esk1_2(X2,X1),sk1_esk2_2(X2,X1)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_597]) ).
cnf(c_0_597_1,axiom,
( ~ relation(X1)
| X1 = identity_relation(X2)
| sk1_esk2_2(X2,X1) != sk1_esk1_2(X2,X1)
| ~ in(sk1_esk1_2(X2,X1),X2)
| ~ in(ordered_pair(sk1_esk1_2(X2,X1),sk1_esk2_2(X2,X1)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_597]) ).
cnf(c_0_597_2,axiom,
( sk1_esk2_2(X2,X1) != sk1_esk1_2(X2,X1)
| ~ relation(X1)
| X1 = identity_relation(X2)
| ~ in(sk1_esk1_2(X2,X1),X2)
| ~ in(ordered_pair(sk1_esk1_2(X2,X1),sk1_esk2_2(X2,X1)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_597]) ).
cnf(c_0_597_3,axiom,
( ~ in(sk1_esk1_2(X2,X1),X2)
| sk1_esk2_2(X2,X1) != sk1_esk1_2(X2,X1)
| ~ relation(X1)
| X1 = identity_relation(X2)
| ~ in(ordered_pair(sk1_esk1_2(X2,X1),sk1_esk2_2(X2,X1)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_597]) ).
cnf(c_0_597_4,axiom,
( ~ in(ordered_pair(sk1_esk1_2(X2,X1),sk1_esk2_2(X2,X1)),X1)
| ~ in(sk1_esk1_2(X2,X1),X2)
| sk1_esk2_2(X2,X1) != sk1_esk1_2(X2,X1)
| ~ relation(X1)
| X1 = identity_relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_597]) ).
cnf(c_0_598_0,axiom,
( X1 = set_difference(X2,X3)
| in(sk1_esk38_3(X2,X3,X1),X1)
| ~ in(sk1_esk38_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_598]) ).
cnf(c_0_598_1,axiom,
( in(sk1_esk38_3(X2,X3,X1),X1)
| X1 = set_difference(X2,X3)
| ~ in(sk1_esk38_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_598]) ).
cnf(c_0_598_2,axiom,
( ~ in(sk1_esk38_3(X2,X3,X1),X3)
| in(sk1_esk38_3(X2,X3,X1),X1)
| X1 = set_difference(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_598]) ).
cnf(c_0_599_0,axiom,
( X2 = relation_inverse(X1)
| in(ordered_pair(sk1_esk43_2(X1,X2),sk1_esk42_2(X1,X2)),X1)
| in(ordered_pair(sk1_esk42_2(X1,X2),sk1_esk43_2(X1,X2)),X2)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_599]) ).
cnf(c_0_599_1,axiom,
( in(ordered_pair(sk1_esk43_2(X1,X2),sk1_esk42_2(X1,X2)),X1)
| X2 = relation_inverse(X1)
| in(ordered_pair(sk1_esk42_2(X1,X2),sk1_esk43_2(X1,X2)),X2)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_599]) ).
cnf(c_0_599_2,axiom,
( in(ordered_pair(sk1_esk42_2(X1,X2),sk1_esk43_2(X1,X2)),X2)
| in(ordered_pair(sk1_esk43_2(X1,X2),sk1_esk42_2(X1,X2)),X1)
| X2 = relation_inverse(X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_599]) ).
cnf(c_0_599_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk42_2(X1,X2),sk1_esk43_2(X1,X2)),X2)
| in(ordered_pair(sk1_esk43_2(X1,X2),sk1_esk42_2(X1,X2)),X1)
| X2 = relation_inverse(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_599]) ).
cnf(c_0_599_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk42_2(X1,X2),sk1_esk43_2(X1,X2)),X2)
| in(ordered_pair(sk1_esk43_2(X1,X2),sk1_esk42_2(X1,X2)),X1)
| X2 = relation_inverse(X1) ),
inference(literals_permutation,[status(thm)],[c_0_599]) ).
cnf(c_0_600_0,axiom,
( X1 = X2
| in(ordered_pair(sk1_esk19_2(X1,X2),sk1_esk20_2(X1,X2)),X2)
| in(ordered_pair(sk1_esk19_2(X1,X2),sk1_esk20_2(X1,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_600]) ).
cnf(c_0_600_1,axiom,
( in(ordered_pair(sk1_esk19_2(X1,X2),sk1_esk20_2(X1,X2)),X2)
| X1 = X2
| in(ordered_pair(sk1_esk19_2(X1,X2),sk1_esk20_2(X1,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_600]) ).
cnf(c_0_600_2,axiom,
( in(ordered_pair(sk1_esk19_2(X1,X2),sk1_esk20_2(X1,X2)),X1)
| in(ordered_pair(sk1_esk19_2(X1,X2),sk1_esk20_2(X1,X2)),X2)
| X1 = X2
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_600]) ).
cnf(c_0_600_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk19_2(X1,X2),sk1_esk20_2(X1,X2)),X1)
| in(ordered_pair(sk1_esk19_2(X1,X2),sk1_esk20_2(X1,X2)),X2)
| X1 = X2
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_600]) ).
cnf(c_0_600_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk19_2(X1,X2),sk1_esk20_2(X1,X2)),X1)
| in(ordered_pair(sk1_esk19_2(X1,X2),sk1_esk20_2(X1,X2)),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_600]) ).
cnf(c_0_601_0,axiom,
( X1 = unordered_pair(X2,X3)
| ~ in(sk1_esk21_3(X2,X3,X1),X1)
| sk1_esk21_3(X2,X3,X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_601]) ).
cnf(c_0_601_1,axiom,
( ~ in(sk1_esk21_3(X2,X3,X1),X1)
| X1 = unordered_pair(X2,X3)
| sk1_esk21_3(X2,X3,X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_601]) ).
cnf(c_0_601_2,axiom,
( sk1_esk21_3(X2,X3,X1) != X2
| ~ in(sk1_esk21_3(X2,X3,X1),X1)
| X1 = unordered_pair(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_601]) ).
cnf(c_0_602_0,axiom,
( X1 = unordered_pair(X2,X3)
| ~ in(sk1_esk21_3(X2,X3,X1),X1)
| sk1_esk21_3(X2,X3,X1) != X3 ),
inference(literals_permutation,[status(thm)],[c_0_602]) ).
cnf(c_0_602_1,axiom,
( ~ in(sk1_esk21_3(X2,X3,X1),X1)
| X1 = unordered_pair(X2,X3)
| sk1_esk21_3(X2,X3,X1) != X3 ),
inference(literals_permutation,[status(thm)],[c_0_602]) ).
cnf(c_0_602_2,axiom,
( sk1_esk21_3(X2,X3,X1) != X3
| ~ in(sk1_esk21_3(X2,X3,X1),X1)
| X1 = unordered_pair(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_602]) ).
cnf(c_0_603_0,axiom,
( in(ordered_pair(sk1_esk39_3(X1,X2,X3),X3),X1)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_603]) ).
cnf(c_0_603_1,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk39_3(X1,X2,X3),X3),X1)
| X2 != relation_rng(X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_603]) ).
cnf(c_0_603_2,axiom,
( X2 != relation_rng(X1)
| ~ relation(X1)
| in(ordered_pair(sk1_esk39_3(X1,X2,X3),X3),X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_603]) ).
cnf(c_0_603_3,axiom,
( ~ in(X3,X2)
| X2 != relation_rng(X1)
| ~ relation(X1)
| in(ordered_pair(sk1_esk39_3(X1,X2,X3),X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_603]) ).
cnf(c_0_604_0,axiom,
( in(ordered_pair(X3,sk1_esk32_3(X1,X2,X3)),X1)
| ~ relation(X1)
| X2 != relation_dom(X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_604]) ).
cnf(c_0_604_1,axiom,
( ~ relation(X1)
| in(ordered_pair(X3,sk1_esk32_3(X1,X2,X3)),X1)
| X2 != relation_dom(X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_604]) ).
cnf(c_0_604_2,axiom,
( X2 != relation_dom(X1)
| ~ relation(X1)
| in(ordered_pair(X3,sk1_esk32_3(X1,X2,X3)),X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_604]) ).
cnf(c_0_604_3,axiom,
( ~ in(X3,X2)
| X2 != relation_dom(X1)
| ~ relation(X1)
| in(ordered_pair(X3,sk1_esk32_3(X1,X2,X3)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_604]) ).
cnf(c_0_605_0,axiom,
( X2 = relation_image(X1,X3)
| in(sk1_esk8_3(X1,X3,X2),X2)
| in(sk1_esk9_3(X1,X3,X2),X3)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_605]) ).
cnf(c_0_605_1,axiom,
( in(sk1_esk8_3(X1,X3,X2),X2)
| X2 = relation_image(X1,X3)
| in(sk1_esk9_3(X1,X3,X2),X3)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_605]) ).
cnf(c_0_605_2,axiom,
( in(sk1_esk9_3(X1,X3,X2),X3)
| in(sk1_esk8_3(X1,X3,X2),X2)
| X2 = relation_image(X1,X3)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_605]) ).
cnf(c_0_605_3,axiom,
( ~ relation(X1)
| in(sk1_esk9_3(X1,X3,X2),X3)
| in(sk1_esk8_3(X1,X3,X2),X2)
| X2 = relation_image(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_605]) ).
cnf(c_0_606_0,axiom,
( X1 = set_difference(X2,X3)
| in(sk1_esk38_3(X2,X3,X1),X1)
| in(sk1_esk38_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_606]) ).
cnf(c_0_606_1,axiom,
( in(sk1_esk38_3(X2,X3,X1),X1)
| X1 = set_difference(X2,X3)
| in(sk1_esk38_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_606]) ).
cnf(c_0_606_2,axiom,
( in(sk1_esk38_3(X2,X3,X1),X2)
| in(sk1_esk38_3(X2,X3,X1),X1)
| X1 = set_difference(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_606]) ).
cnf(c_0_607_0,axiom,
( X1 = set_intersection2(X2,X3)
| in(sk1_esk31_3(X2,X3,X1),X1)
| in(sk1_esk31_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_607]) ).
cnf(c_0_607_1,axiom,
( in(sk1_esk31_3(X2,X3,X1),X1)
| X1 = set_intersection2(X2,X3)
| in(sk1_esk31_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_607]) ).
cnf(c_0_607_2,axiom,
( in(sk1_esk31_3(X2,X3,X1),X2)
| in(sk1_esk31_3(X2,X3,X1),X1)
| X1 = set_intersection2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_607]) ).
cnf(c_0_608_0,axiom,
( X1 = set_intersection2(X2,X3)
| in(sk1_esk31_3(X2,X3,X1),X1)
| in(sk1_esk31_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_608]) ).
cnf(c_0_608_1,axiom,
( in(sk1_esk31_3(X2,X3,X1),X1)
| X1 = set_intersection2(X2,X3)
| in(sk1_esk31_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_608]) ).
cnf(c_0_608_2,axiom,
( in(sk1_esk31_3(X2,X3,X1),X3)
| in(sk1_esk31_3(X2,X3,X1),X1)
| X1 = set_intersection2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_608]) ).
cnf(c_0_609_0,axiom,
( X1 = cartesian_product2(X2,X3)
| in(sk1_esk25_3(X2,X3,X1),X1)
| in(sk1_esk26_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_609]) ).
cnf(c_0_609_1,axiom,
( in(sk1_esk25_3(X2,X3,X1),X1)
| X1 = cartesian_product2(X2,X3)
| in(sk1_esk26_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_609]) ).
cnf(c_0_609_2,axiom,
( in(sk1_esk26_3(X2,X3,X1),X2)
| in(sk1_esk25_3(X2,X3,X1),X1)
| X1 = cartesian_product2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_609]) ).
cnf(c_0_610_0,axiom,
( X1 = cartesian_product2(X2,X3)
| in(sk1_esk25_3(X2,X3,X1),X1)
| in(sk1_esk27_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_610]) ).
cnf(c_0_610_1,axiom,
( in(sk1_esk25_3(X2,X3,X1),X1)
| X1 = cartesian_product2(X2,X3)
| in(sk1_esk27_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_610]) ).
cnf(c_0_610_2,axiom,
( in(sk1_esk27_3(X2,X3,X1),X3)
| in(sk1_esk25_3(X2,X3,X1),X1)
| X1 = cartesian_product2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_610]) ).
cnf(c_0_611_0,axiom,
( subset(X1,X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(sk1_esk28_2(X1,X2),sk1_esk29_2(X1,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_611]) ).
cnf(c_0_611_1,axiom,
( ~ relation(X1)
| subset(X1,X2)
| ~ relation(X2)
| ~ in(ordered_pair(sk1_esk28_2(X1,X2),sk1_esk29_2(X1,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_611]) ).
cnf(c_0_611_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| subset(X1,X2)
| ~ in(ordered_pair(sk1_esk28_2(X1,X2),sk1_esk29_2(X1,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_611]) ).
cnf(c_0_611_3,axiom,
( ~ in(ordered_pair(sk1_esk28_2(X1,X2),sk1_esk29_2(X1,X2)),X2)
| ~ relation(X2)
| ~ relation(X1)
| subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_611]) ).
cnf(c_0_612_0,axiom,
( X1 = unordered_pair(X2,X3)
| sk1_esk21_3(X2,X3,X1) = X3
| sk1_esk21_3(X2,X3,X1) = X2
| in(sk1_esk21_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_612]) ).
cnf(c_0_612_1,axiom,
( sk1_esk21_3(X2,X3,X1) = X3
| X1 = unordered_pair(X2,X3)
| sk1_esk21_3(X2,X3,X1) = X2
| in(sk1_esk21_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_612]) ).
cnf(c_0_612_2,axiom,
( sk1_esk21_3(X2,X3,X1) = X2
| sk1_esk21_3(X2,X3,X1) = X3
| X1 = unordered_pair(X2,X3)
| in(sk1_esk21_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_612]) ).
cnf(c_0_612_3,axiom,
( in(sk1_esk21_3(X2,X3,X1),X1)
| sk1_esk21_3(X2,X3,X1) = X2
| sk1_esk21_3(X2,X3,X1) = X3
| X1 = unordered_pair(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_612]) ).
cnf(c_0_613_0,axiom,
( X3 = complements_of_subsets(X2,X1)
| element(sk1_esk48_3(X2,X1,X3),powerset(X2))
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_613]) ).
cnf(c_0_613_1,axiom,
( element(sk1_esk48_3(X2,X1,X3),powerset(X2))
| X3 = complements_of_subsets(X2,X1)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_613]) ).
cnf(c_0_613_2,axiom,
( ~ element(X1,powerset(powerset(X2)))
| element(sk1_esk48_3(X2,X1,X3),powerset(X2))
| X3 = complements_of_subsets(X2,X1)
| ~ element(X3,powerset(powerset(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_613]) ).
cnf(c_0_613_3,axiom,
( ~ element(X3,powerset(powerset(X2)))
| ~ element(X1,powerset(powerset(X2)))
| element(sk1_esk48_3(X2,X1,X3),powerset(X2))
| X3 = complements_of_subsets(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_613]) ).
cnf(c_0_614_0,axiom,
( in(X4,X3)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2)))
| X3 != complements_of_subsets(X2,X1)
| ~ element(X4,powerset(X2))
| ~ in(subset_complement(X2,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_614]) ).
cnf(c_0_614_1,axiom,
( ~ element(X1,powerset(powerset(X2)))
| in(X4,X3)
| ~ element(X3,powerset(powerset(X2)))
| X3 != complements_of_subsets(X2,X1)
| ~ element(X4,powerset(X2))
| ~ in(subset_complement(X2,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_614]) ).
cnf(c_0_614_2,axiom,
( ~ element(X3,powerset(powerset(X2)))
| ~ element(X1,powerset(powerset(X2)))
| in(X4,X3)
| X3 != complements_of_subsets(X2,X1)
| ~ element(X4,powerset(X2))
| ~ in(subset_complement(X2,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_614]) ).
cnf(c_0_614_3,axiom,
( X3 != complements_of_subsets(X2,X1)
| ~ element(X3,powerset(powerset(X2)))
| ~ element(X1,powerset(powerset(X2)))
| in(X4,X3)
| ~ element(X4,powerset(X2))
| ~ in(subset_complement(X2,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_614]) ).
cnf(c_0_614_4,axiom,
( ~ element(X4,powerset(X2))
| X3 != complements_of_subsets(X2,X1)
| ~ element(X3,powerset(powerset(X2)))
| ~ element(X1,powerset(powerset(X2)))
| in(X4,X3)
| ~ in(subset_complement(X2,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_614]) ).
cnf(c_0_614_5,axiom,
( ~ in(subset_complement(X2,X4),X1)
| ~ element(X4,powerset(X2))
| X3 != complements_of_subsets(X2,X1)
| ~ element(X3,powerset(powerset(X2)))
| ~ element(X1,powerset(powerset(X2)))
| in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_614]) ).
cnf(c_0_615_0,axiom,
( in(subset_complement(X2,X4),X1)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2)))
| X3 != complements_of_subsets(X2,X1)
| ~ element(X4,powerset(X2))
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_615]) ).
cnf(c_0_615_1,axiom,
( ~ element(X1,powerset(powerset(X2)))
| in(subset_complement(X2,X4),X1)
| ~ element(X3,powerset(powerset(X2)))
| X3 != complements_of_subsets(X2,X1)
| ~ element(X4,powerset(X2))
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_615]) ).
cnf(c_0_615_2,axiom,
( ~ element(X3,powerset(powerset(X2)))
| ~ element(X1,powerset(powerset(X2)))
| in(subset_complement(X2,X4),X1)
| X3 != complements_of_subsets(X2,X1)
| ~ element(X4,powerset(X2))
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_615]) ).
cnf(c_0_615_3,axiom,
( X3 != complements_of_subsets(X2,X1)
| ~ element(X3,powerset(powerset(X2)))
| ~ element(X1,powerset(powerset(X2)))
| in(subset_complement(X2,X4),X1)
| ~ element(X4,powerset(X2))
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_615]) ).
cnf(c_0_615_4,axiom,
( ~ element(X4,powerset(X2))
| X3 != complements_of_subsets(X2,X1)
| ~ element(X3,powerset(powerset(X2)))
| ~ element(X1,powerset(powerset(X2)))
| in(subset_complement(X2,X4),X1)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_615]) ).
cnf(c_0_615_5,axiom,
( ~ in(X4,X3)
| ~ element(X4,powerset(X2))
| X3 != complements_of_subsets(X2,X1)
| ~ element(X3,powerset(powerset(X2)))
| ~ element(X1,powerset(powerset(X2)))
| in(subset_complement(X2,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_615]) ).
cnf(c_0_616_0,axiom,
( X2 = relation_rng(X1)
| ~ relation(X1)
| ~ in(ordered_pair(X3,sk1_esk40_2(X1,X2)),X1)
| ~ in(sk1_esk40_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_616]) ).
cnf(c_0_616_1,axiom,
( ~ relation(X1)
| X2 = relation_rng(X1)
| ~ in(ordered_pair(X3,sk1_esk40_2(X1,X2)),X1)
| ~ in(sk1_esk40_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_616]) ).
cnf(c_0_616_2,axiom,
( ~ in(ordered_pair(X3,sk1_esk40_2(X1,X2)),X1)
| ~ relation(X1)
| X2 = relation_rng(X1)
| ~ in(sk1_esk40_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_616]) ).
cnf(c_0_616_3,axiom,
( ~ in(sk1_esk40_2(X1,X2),X2)
| ~ in(ordered_pair(X3,sk1_esk40_2(X1,X2)),X1)
| ~ relation(X1)
| X2 = relation_rng(X1) ),
inference(literals_permutation,[status(thm)],[c_0_616]) ).
cnf(c_0_617_0,axiom,
( X2 = relation_dom(X1)
| ~ relation(X1)
| ~ in(ordered_pair(sk1_esk33_2(X1,X2),X3),X1)
| ~ in(sk1_esk33_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_617]) ).
cnf(c_0_617_1,axiom,
( ~ relation(X1)
| X2 = relation_dom(X1)
| ~ in(ordered_pair(sk1_esk33_2(X1,X2),X3),X1)
| ~ in(sk1_esk33_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_617]) ).
cnf(c_0_617_2,axiom,
( ~ in(ordered_pair(sk1_esk33_2(X1,X2),X3),X1)
| ~ relation(X1)
| X2 = relation_dom(X1)
| ~ in(sk1_esk33_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_617]) ).
cnf(c_0_617_3,axiom,
( ~ in(sk1_esk33_2(X1,X2),X2)
| ~ in(ordered_pair(sk1_esk33_2(X1,X2),X3),X1)
| ~ relation(X1)
| X2 = relation_dom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_617]) ).
cnf(c_0_618_0,axiom,
( X1 = empty_set
| in(X3,X2)
| X2 != set_meet(X1)
| ~ in(X3,sk1_esk13_3(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_618]) ).
cnf(c_0_618_1,axiom,
( in(X3,X2)
| X1 = empty_set
| X2 != set_meet(X1)
| ~ in(X3,sk1_esk13_3(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_618]) ).
cnf(c_0_618_2,axiom,
( X2 != set_meet(X1)
| in(X3,X2)
| X1 = empty_set
| ~ in(X3,sk1_esk13_3(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_618]) ).
cnf(c_0_618_3,axiom,
( ~ in(X3,sk1_esk13_3(X1,X2,X3))
| X2 != set_meet(X1)
| in(X3,X2)
| X1 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_618]) ).
cnf(c_0_619_0,axiom,
( in(ordered_pair(X4,X5),X3)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X6,X5),X2)
| ~ in(ordered_pair(X4,X6),X1) ),
inference(literals_permutation,[status(thm)],[c_0_619]) ).
cnf(c_0_619_1,axiom,
( ~ relation(X1)
| in(ordered_pair(X4,X5),X3)
| ~ relation(X2)
| ~ relation(X3)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X6,X5),X2)
| ~ in(ordered_pair(X4,X6),X1) ),
inference(literals_permutation,[status(thm)],[c_0_619]) ).
cnf(c_0_619_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X3)
| ~ relation(X3)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X6,X5),X2)
| ~ in(ordered_pair(X4,X6),X1) ),
inference(literals_permutation,[status(thm)],[c_0_619]) ).
cnf(c_0_619_3,axiom,
( ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X3)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X6,X5),X2)
| ~ in(ordered_pair(X4,X6),X1) ),
inference(literals_permutation,[status(thm)],[c_0_619]) ).
cnf(c_0_619_4,axiom,
( X3 != relation_composition(X1,X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X3)
| ~ in(ordered_pair(X6,X5),X2)
| ~ in(ordered_pair(X4,X6),X1) ),
inference(literals_permutation,[status(thm)],[c_0_619]) ).
cnf(c_0_619_5,axiom,
( ~ in(ordered_pair(X6,X5),X2)
| X3 != relation_composition(X1,X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X3)
| ~ in(ordered_pair(X4,X6),X1) ),
inference(literals_permutation,[status(thm)],[c_0_619]) ).
cnf(c_0_619_6,axiom,
( ~ in(ordered_pair(X4,X6),X1)
| ~ in(ordered_pair(X6,X5),X2)
| X3 != relation_composition(X1,X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X3) ),
inference(literals_permutation,[status(thm)],[c_0_619]) ).
cnf(c_0_620_0,axiom,
( X2 = relation_rng(X1)
| in(ordered_pair(sk1_esk41_2(X1,X2),sk1_esk40_2(X1,X2)),X1)
| in(sk1_esk40_2(X1,X2),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_620]) ).
cnf(c_0_620_1,axiom,
( in(ordered_pair(sk1_esk41_2(X1,X2),sk1_esk40_2(X1,X2)),X1)
| X2 = relation_rng(X1)
| in(sk1_esk40_2(X1,X2),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_620]) ).
cnf(c_0_620_2,axiom,
( in(sk1_esk40_2(X1,X2),X2)
| in(ordered_pair(sk1_esk41_2(X1,X2),sk1_esk40_2(X1,X2)),X1)
| X2 = relation_rng(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_620]) ).
cnf(c_0_620_3,axiom,
( ~ relation(X1)
| in(sk1_esk40_2(X1,X2),X2)
| in(ordered_pair(sk1_esk41_2(X1,X2),sk1_esk40_2(X1,X2)),X1)
| X2 = relation_rng(X1) ),
inference(literals_permutation,[status(thm)],[c_0_620]) ).
cnf(c_0_621_0,axiom,
( X2 = relation_dom(X1)
| in(ordered_pair(sk1_esk33_2(X1,X2),sk1_esk34_2(X1,X2)),X1)
| in(sk1_esk33_2(X1,X2),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_621]) ).
cnf(c_0_621_1,axiom,
( in(ordered_pair(sk1_esk33_2(X1,X2),sk1_esk34_2(X1,X2)),X1)
| X2 = relation_dom(X1)
| in(sk1_esk33_2(X1,X2),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_621]) ).
cnf(c_0_621_2,axiom,
( in(sk1_esk33_2(X1,X2),X2)
| in(ordered_pair(sk1_esk33_2(X1,X2),sk1_esk34_2(X1,X2)),X1)
| X2 = relation_dom(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_621]) ).
cnf(c_0_621_3,axiom,
( ~ relation(X1)
| in(sk1_esk33_2(X1,X2),X2)
| in(ordered_pair(sk1_esk33_2(X1,X2),sk1_esk34_2(X1,X2)),X1)
| X2 = relation_dom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_621]) ).
cnf(c_0_622_0,axiom,
( X1 = identity_relation(X2)
| in(ordered_pair(sk1_esk1_2(X2,X1),sk1_esk2_2(X2,X1)),X1)
| in(sk1_esk1_2(X2,X1),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_622]) ).
cnf(c_0_622_1,axiom,
( in(ordered_pair(sk1_esk1_2(X2,X1),sk1_esk2_2(X2,X1)),X1)
| X1 = identity_relation(X2)
| in(sk1_esk1_2(X2,X1),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_622]) ).
cnf(c_0_622_2,axiom,
( in(sk1_esk1_2(X2,X1),X2)
| in(ordered_pair(sk1_esk1_2(X2,X1),sk1_esk2_2(X2,X1)),X1)
| X1 = identity_relation(X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_622]) ).
cnf(c_0_622_3,axiom,
( ~ relation(X1)
| in(sk1_esk1_2(X2,X1),X2)
| in(ordered_pair(sk1_esk1_2(X2,X1),sk1_esk2_2(X2,X1)),X1)
| X1 = identity_relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_622]) ).
cnf(c_0_623_0,axiom,
( element(subset_difference(X1,X2,X3),powerset(X1))
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_623]) ).
cnf(c_0_623_1,axiom,
( ~ element(X3,powerset(X1))
| element(subset_difference(X1,X2,X3),powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_623]) ).
cnf(c_0_623_2,axiom,
( ~ element(X2,powerset(X1))
| ~ element(X3,powerset(X1))
| element(subset_difference(X1,X2,X3),powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_623]) ).
cnf(c_0_624_0,axiom,
( X1 = identity_relation(X2)
| in(ordered_pair(sk1_esk1_2(X2,X1),sk1_esk2_2(X2,X1)),X1)
| sk1_esk2_2(X2,X1) = sk1_esk1_2(X2,X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_624]) ).
cnf(c_0_624_1,axiom,
( in(ordered_pair(sk1_esk1_2(X2,X1),sk1_esk2_2(X2,X1)),X1)
| X1 = identity_relation(X2)
| sk1_esk2_2(X2,X1) = sk1_esk1_2(X2,X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_624]) ).
cnf(c_0_624_2,axiom,
( sk1_esk2_2(X2,X1) = sk1_esk1_2(X2,X1)
| in(ordered_pair(sk1_esk1_2(X2,X1),sk1_esk2_2(X2,X1)),X1)
| X1 = identity_relation(X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_624]) ).
cnf(c_0_624_3,axiom,
( ~ relation(X1)
| sk1_esk2_2(X2,X1) = sk1_esk1_2(X2,X1)
| in(ordered_pair(sk1_esk1_2(X2,X1),sk1_esk2_2(X2,X1)),X1)
| X1 = identity_relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_624]) ).
cnf(c_0_625_0,axiom,
( X1 = empty_set
| X2 = set_meet(X1)
| ~ in(sk1_esk14_2(X1,X2),X2)
| ~ in(sk1_esk14_2(X1,X2),sk1_esk15_2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_625]) ).
cnf(c_0_625_1,axiom,
( X2 = set_meet(X1)
| X1 = empty_set
| ~ in(sk1_esk14_2(X1,X2),X2)
| ~ in(sk1_esk14_2(X1,X2),sk1_esk15_2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_625]) ).
cnf(c_0_625_2,axiom,
( ~ in(sk1_esk14_2(X1,X2),X2)
| X2 = set_meet(X1)
| X1 = empty_set
| ~ in(sk1_esk14_2(X1,X2),sk1_esk15_2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_625]) ).
cnf(c_0_625_3,axiom,
( ~ in(sk1_esk14_2(X1,X2),sk1_esk15_2(X1,X2))
| ~ in(sk1_esk14_2(X1,X2),X2)
| X2 = set_meet(X1)
| X1 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_625]) ).
cnf(c_0_626_0,axiom,
( subset(X1,X2)
| in(ordered_pair(sk1_esk28_2(X1,X2),sk1_esk29_2(X1,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_626]) ).
cnf(c_0_626_1,axiom,
( in(ordered_pair(sk1_esk28_2(X1,X2),sk1_esk29_2(X1,X2)),X1)
| subset(X1,X2)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_626]) ).
cnf(c_0_626_2,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk28_2(X1,X2),sk1_esk29_2(X1,X2)),X1)
| subset(X1,X2)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_626]) ).
cnf(c_0_626_3,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk28_2(X1,X2),sk1_esk29_2(X1,X2)),X1)
| subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_626]) ).
cnf(c_0_627_0,axiom,
( in(ordered_pair(X4,X5),X2)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_rng_restriction(X3,X1)
| ~ in(ordered_pair(X4,X5),X1)
| ~ in(X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_627]) ).
cnf(c_0_627_1,axiom,
( ~ relation(X1)
| in(ordered_pair(X4,X5),X2)
| ~ relation(X2)
| X2 != relation_rng_restriction(X3,X1)
| ~ in(ordered_pair(X4,X5),X1)
| ~ in(X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_627]) ).
cnf(c_0_627_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X2)
| X2 != relation_rng_restriction(X3,X1)
| ~ in(ordered_pair(X4,X5),X1)
| ~ in(X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_627]) ).
cnf(c_0_627_3,axiom,
( X2 != relation_rng_restriction(X3,X1)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X2)
| ~ in(ordered_pair(X4,X5),X1)
| ~ in(X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_627]) ).
cnf(c_0_627_4,axiom,
( ~ in(ordered_pair(X4,X5),X1)
| X2 != relation_rng_restriction(X3,X1)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X2)
| ~ in(X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_627]) ).
cnf(c_0_627_5,axiom,
( ~ in(X5,X3)
| ~ in(ordered_pair(X4,X5),X1)
| X2 != relation_rng_restriction(X3,X1)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_627]) ).
cnf(c_0_628_0,axiom,
( in(ordered_pair(X4,X5),X2)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_dom_restriction(X1,X3)
| ~ in(ordered_pair(X4,X5),X1)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_628]) ).
cnf(c_0_628_1,axiom,
( ~ relation(X1)
| in(ordered_pair(X4,X5),X2)
| ~ relation(X2)
| X2 != relation_dom_restriction(X1,X3)
| ~ in(ordered_pair(X4,X5),X1)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_628]) ).
cnf(c_0_628_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X2)
| X2 != relation_dom_restriction(X1,X3)
| ~ in(ordered_pair(X4,X5),X1)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_628]) ).
cnf(c_0_628_3,axiom,
( X2 != relation_dom_restriction(X1,X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X2)
| ~ in(ordered_pair(X4,X5),X1)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_628]) ).
cnf(c_0_628_4,axiom,
( ~ in(ordered_pair(X4,X5),X1)
| X2 != relation_dom_restriction(X1,X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X2)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_628]) ).
cnf(c_0_628_5,axiom,
( ~ in(X4,X3)
| ~ in(ordered_pair(X4,X5),X1)
| X2 != relation_dom_restriction(X1,X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_628]) ).
cnf(c_0_629_0,axiom,
( X1 = union(X2)
| ~ in(X3,X2)
| ~ in(sk1_esk36_2(X2,X1),X3)
| ~ in(sk1_esk36_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_629]) ).
cnf(c_0_629_1,axiom,
( ~ in(X3,X2)
| X1 = union(X2)
| ~ in(sk1_esk36_2(X2,X1),X3)
| ~ in(sk1_esk36_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_629]) ).
cnf(c_0_629_2,axiom,
( ~ in(sk1_esk36_2(X2,X1),X3)
| ~ in(X3,X2)
| X1 = union(X2)
| ~ in(sk1_esk36_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_629]) ).
cnf(c_0_629_3,axiom,
( ~ in(sk1_esk36_2(X2,X1),X1)
| ~ in(sk1_esk36_2(X2,X1),X3)
| ~ in(X3,X2)
| X1 = union(X2) ),
inference(literals_permutation,[status(thm)],[c_0_629]) ).
cnf(c_0_630_0,axiom,
( in(X3,sk1_esk35_3(X2,X1,X3))
| X1 != union(X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_630]) ).
cnf(c_0_630_1,axiom,
( X1 != union(X2)
| in(X3,sk1_esk35_3(X2,X1,X3))
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_630]) ).
cnf(c_0_630_2,axiom,
( ~ in(X3,X1)
| X1 != union(X2)
| in(X3,sk1_esk35_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_630]) ).
cnf(c_0_631_0,axiom,
( in(sk1_esk35_3(X2,X1,X3),X2)
| X1 != union(X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_631]) ).
cnf(c_0_631_1,axiom,
( X1 != union(X2)
| in(sk1_esk35_3(X2,X1,X3),X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_631]) ).
cnf(c_0_631_2,axiom,
( ~ in(X3,X1)
| X1 != union(X2)
| in(sk1_esk35_3(X2,X1,X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_631]) ).
cnf(c_0_632_0,axiom,
( X1 = empty_set
| in(X3,X2)
| in(sk1_esk13_3(X1,X2,X3),X1)
| X2 != set_meet(X1) ),
inference(literals_permutation,[status(thm)],[c_0_632]) ).
cnf(c_0_632_1,axiom,
( in(X3,X2)
| X1 = empty_set
| in(sk1_esk13_3(X1,X2,X3),X1)
| X2 != set_meet(X1) ),
inference(literals_permutation,[status(thm)],[c_0_632]) ).
cnf(c_0_632_2,axiom,
( in(sk1_esk13_3(X1,X2,X3),X1)
| in(X3,X2)
| X1 = empty_set
| X2 != set_meet(X1) ),
inference(literals_permutation,[status(thm)],[c_0_632]) ).
cnf(c_0_632_3,axiom,
( X2 != set_meet(X1)
| in(sk1_esk13_3(X1,X2,X3),X1)
| in(X3,X2)
| X1 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_632]) ).
cnf(c_0_633_0,axiom,
( in(ordered_pair(X4,X5),X1)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_rng_restriction(X3,X1)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_633]) ).
cnf(c_0_633_1,axiom,
( ~ relation(X1)
| in(ordered_pair(X4,X5),X1)
| ~ relation(X2)
| X2 != relation_rng_restriction(X3,X1)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_633]) ).
cnf(c_0_633_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X1)
| X2 != relation_rng_restriction(X3,X1)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_633]) ).
cnf(c_0_633_3,axiom,
( X2 != relation_rng_restriction(X3,X1)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X1)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_633]) ).
cnf(c_0_633_4,axiom,
( ~ in(ordered_pair(X4,X5),X2)
| X2 != relation_rng_restriction(X3,X1)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X1) ),
inference(literals_permutation,[status(thm)],[c_0_633]) ).
cnf(c_0_634_0,axiom,
( in(ordered_pair(X4,X5),X1)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_dom_restriction(X1,X3)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_634]) ).
cnf(c_0_634_1,axiom,
( ~ relation(X1)
| in(ordered_pair(X4,X5),X1)
| ~ relation(X2)
| X2 != relation_dom_restriction(X1,X3)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_634]) ).
cnf(c_0_634_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X1)
| X2 != relation_dom_restriction(X1,X3)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_634]) ).
cnf(c_0_634_3,axiom,
( X2 != relation_dom_restriction(X1,X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X1)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_634]) ).
cnf(c_0_634_4,axiom,
( ~ in(ordered_pair(X4,X5),X2)
| X2 != relation_dom_restriction(X1,X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X1) ),
inference(literals_permutation,[status(thm)],[c_0_634]) ).
cnf(c_0_635_0,axiom,
( in(ordered_pair(X3,X4),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(X3,X4),X1)
| ~ subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_635]) ).
cnf(c_0_635_1,axiom,
( ~ relation(X1)
| in(ordered_pair(X3,X4),X2)
| ~ relation(X2)
| ~ in(ordered_pair(X3,X4),X1)
| ~ subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_635]) ).
cnf(c_0_635_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X3,X4),X1)
| ~ subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_635]) ).
cnf(c_0_635_3,axiom,
( ~ in(ordered_pair(X3,X4),X1)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X2)
| ~ subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_635]) ).
cnf(c_0_635_4,axiom,
( ~ subset(X1,X2)
| ~ in(ordered_pair(X3,X4),X1)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_635]) ).
cnf(c_0_636_0,axiom,
( subset_difference(X1,X2,X3) = set_difference(X2,X3)
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_636]) ).
cnf(c_0_636_1,axiom,
( ~ element(X3,powerset(X1))
| subset_difference(X1,X2,X3) = set_difference(X2,X3)
| ~ element(X2,powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_636]) ).
cnf(c_0_636_2,axiom,
( ~ element(X2,powerset(X1))
| ~ element(X3,powerset(X1))
| subset_difference(X1,X2,X3) = set_difference(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_636]) ).
cnf(c_0_637_0,axiom,
( X1 = powerset(X2)
| ~ subset(sk1_esk18_2(X2,X1),X2)
| ~ in(sk1_esk18_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_637]) ).
cnf(c_0_637_1,axiom,
( ~ subset(sk1_esk18_2(X2,X1),X2)
| X1 = powerset(X2)
| ~ in(sk1_esk18_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_637]) ).
cnf(c_0_637_2,axiom,
( ~ in(sk1_esk18_2(X2,X1),X1)
| ~ subset(sk1_esk18_2(X2,X1),X2)
| X1 = powerset(X2) ),
inference(literals_permutation,[status(thm)],[c_0_637]) ).
cnf(c_0_638_0,axiom,
( in(X4,X2)
| ~ relation(X1)
| X2 != relation_image(X1,X3)
| ~ in(X5,X3)
| ~ in(ordered_pair(X5,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_638]) ).
cnf(c_0_638_1,axiom,
( ~ relation(X1)
| in(X4,X2)
| X2 != relation_image(X1,X3)
| ~ in(X5,X3)
| ~ in(ordered_pair(X5,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_638]) ).
cnf(c_0_638_2,axiom,
( X2 != relation_image(X1,X3)
| ~ relation(X1)
| in(X4,X2)
| ~ in(X5,X3)
| ~ in(ordered_pair(X5,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_638]) ).
cnf(c_0_638_3,axiom,
( ~ in(X5,X3)
| X2 != relation_image(X1,X3)
| ~ relation(X1)
| in(X4,X2)
| ~ in(ordered_pair(X5,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_638]) ).
cnf(c_0_638_4,axiom,
( ~ in(ordered_pair(X5,X4),X1)
| ~ in(X5,X3)
| X2 != relation_image(X1,X3)
| ~ relation(X1)
| in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_638]) ).
cnf(c_0_639_0,axiom,
( X1 = X2
| ~ in(sk1_esk56_2(X1,X2),X2)
| ~ in(sk1_esk56_2(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_639]) ).
cnf(c_0_639_1,axiom,
( ~ in(sk1_esk56_2(X1,X2),X2)
| X1 = X2
| ~ in(sk1_esk56_2(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_639]) ).
cnf(c_0_639_2,axiom,
( ~ in(sk1_esk56_2(X1,X2),X1)
| ~ in(sk1_esk56_2(X1,X2),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_639]) ).
cnf(c_0_640_0,axiom,
( in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_inverse(X1)
| ~ in(ordered_pair(X4,X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_640]) ).
cnf(c_0_640_1,axiom,
( ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| ~ relation(X2)
| X2 != relation_inverse(X1)
| ~ in(ordered_pair(X4,X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_640]) ).
cnf(c_0_640_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| X2 != relation_inverse(X1)
| ~ in(ordered_pair(X4,X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_640]) ).
cnf(c_0_640_3,axiom,
( X2 != relation_inverse(X1)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| ~ in(ordered_pair(X4,X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_640]) ).
cnf(c_0_640_4,axiom,
( ~ in(ordered_pair(X4,X3),X2)
| X2 != relation_inverse(X1)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_640]) ).
cnf(c_0_641_0,axiom,
( in(ordered_pair(X3,X4),X2)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_inverse(X1)
| ~ in(ordered_pair(X4,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_641]) ).
cnf(c_0_641_1,axiom,
( ~ relation(X1)
| in(ordered_pair(X3,X4),X2)
| ~ relation(X2)
| X2 != relation_inverse(X1)
| ~ in(ordered_pair(X4,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_641]) ).
cnf(c_0_641_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X2)
| X2 != relation_inverse(X1)
| ~ in(ordered_pair(X4,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_641]) ).
cnf(c_0_641_3,axiom,
( X2 != relation_inverse(X1)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X4,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_641]) ).
cnf(c_0_641_4,axiom,
( ~ in(ordered_pair(X4,X3),X1)
| X2 != relation_inverse(X1)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_641]) ).
cnf(c_0_642_0,axiom,
( in(ordered_pair(X3,X4),X2)
| ~ relation(X1)
| ~ relation(X2)
| X1 != X2
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_642]) ).
cnf(c_0_642_1,axiom,
( ~ relation(X1)
| in(ordered_pair(X3,X4),X2)
| ~ relation(X2)
| X1 != X2
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_642]) ).
cnf(c_0_642_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X2)
| X1 != X2
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_642]) ).
cnf(c_0_642_3,axiom,
( X1 != X2
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_642]) ).
cnf(c_0_642_4,axiom,
( ~ in(ordered_pair(X3,X4),X1)
| X1 != X2
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_642]) ).
cnf(c_0_643_0,axiom,
( in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ relation(X2)
| X1 != X2
| ~ in(ordered_pair(X3,X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_643]) ).
cnf(c_0_643_1,axiom,
( ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| ~ relation(X2)
| X1 != X2
| ~ in(ordered_pair(X3,X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_643]) ).
cnf(c_0_643_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| X1 != X2
| ~ in(ordered_pair(X3,X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_643]) ).
cnf(c_0_643_3,axiom,
( X1 != X2
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| ~ in(ordered_pair(X3,X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_643]) ).
cnf(c_0_643_4,axiom,
( ~ in(ordered_pair(X3,X4),X2)
| X1 != X2
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_643]) ).
cnf(c_0_644_0,axiom,
( in(X5,X3)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_rng_restriction(X3,X1)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_644]) ).
cnf(c_0_644_1,axiom,
( ~ relation(X1)
| in(X5,X3)
| ~ relation(X2)
| X2 != relation_rng_restriction(X3,X1)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_644]) ).
cnf(c_0_644_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(X5,X3)
| X2 != relation_rng_restriction(X3,X1)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_644]) ).
cnf(c_0_644_3,axiom,
( X2 != relation_rng_restriction(X3,X1)
| ~ relation(X2)
| ~ relation(X1)
| in(X5,X3)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_644]) ).
cnf(c_0_644_4,axiom,
( ~ in(ordered_pair(X4,X5),X2)
| X2 != relation_rng_restriction(X3,X1)
| ~ relation(X2)
| ~ relation(X1)
| in(X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_644]) ).
cnf(c_0_645_0,axiom,
( in(X4,X3)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_dom_restriction(X1,X3)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_645]) ).
cnf(c_0_645_1,axiom,
( ~ relation(X1)
| in(X4,X3)
| ~ relation(X2)
| X2 != relation_dom_restriction(X1,X3)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_645]) ).
cnf(c_0_645_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(X4,X3)
| X2 != relation_dom_restriction(X1,X3)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_645]) ).
cnf(c_0_645_3,axiom,
( X2 != relation_dom_restriction(X1,X3)
| ~ relation(X2)
| ~ relation(X1)
| in(X4,X3)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_645]) ).
cnf(c_0_645_4,axiom,
( ~ in(ordered_pair(X4,X5),X2)
| X2 != relation_dom_restriction(X1,X3)
| ~ relation(X2)
| ~ relation(X1)
| in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_645]) ).
cnf(c_0_646_0,axiom,
( X1 = union(X2)
| in(sk1_esk36_2(X2,X1),X1)
| in(sk1_esk36_2(X2,X1),sk1_esk37_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_646]) ).
cnf(c_0_646_1,axiom,
( in(sk1_esk36_2(X2,X1),X1)
| X1 = union(X2)
| in(sk1_esk36_2(X2,X1),sk1_esk37_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_646]) ).
cnf(c_0_646_2,axiom,
( in(sk1_esk36_2(X2,X1),sk1_esk37_2(X2,X1))
| in(sk1_esk36_2(X2,X1),X1)
| X1 = union(X2) ),
inference(literals_permutation,[status(thm)],[c_0_646]) ).
cnf(c_0_647_0,axiom,
( X1 = empty_set
| X2 = set_meet(X1)
| in(sk1_esk15_2(X1,X2),X1)
| ~ in(sk1_esk14_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_647]) ).
cnf(c_0_647_1,axiom,
( X2 = set_meet(X1)
| X1 = empty_set
| in(sk1_esk15_2(X1,X2),X1)
| ~ in(sk1_esk14_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_647]) ).
cnf(c_0_647_2,axiom,
( in(sk1_esk15_2(X1,X2),X1)
| X2 = set_meet(X1)
| X1 = empty_set
| ~ in(sk1_esk14_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_647]) ).
cnf(c_0_647_3,axiom,
( ~ in(sk1_esk14_2(X1,X2),X2)
| in(sk1_esk15_2(X1,X2),X1)
| X2 = set_meet(X1)
| X1 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_647]) ).
cnf(c_0_648_0,axiom,
( X1 = empty_set
| X2 = set_meet(X1)
| in(sk1_esk14_2(X1,X2),X3)
| in(sk1_esk14_2(X1,X2),X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_648]) ).
cnf(c_0_648_1,axiom,
( X2 = set_meet(X1)
| X1 = empty_set
| in(sk1_esk14_2(X1,X2),X3)
| in(sk1_esk14_2(X1,X2),X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_648]) ).
cnf(c_0_648_2,axiom,
( in(sk1_esk14_2(X1,X2),X3)
| X2 = set_meet(X1)
| X1 = empty_set
| in(sk1_esk14_2(X1,X2),X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_648]) ).
cnf(c_0_648_3,axiom,
( in(sk1_esk14_2(X1,X2),X2)
| in(sk1_esk14_2(X1,X2),X3)
| X2 = set_meet(X1)
| X1 = empty_set
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_648]) ).
cnf(c_0_648_4,axiom,
( ~ in(X3,X1)
| in(sk1_esk14_2(X1,X2),X2)
| in(sk1_esk14_2(X1,X2),X3)
| X2 = set_meet(X1)
| X1 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_648]) ).
cnf(c_0_649_0,axiom,
( element(complements_of_subsets(X1,X2),powerset(powerset(X1)))
| ~ element(X2,powerset(powerset(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_649]) ).
cnf(c_0_649_1,axiom,
( ~ element(X2,powerset(powerset(X1)))
| element(complements_of_subsets(X1,X2),powerset(powerset(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_649]) ).
cnf(c_0_650_0,axiom,
( in(X4,X1)
| X1 != cartesian_product2(X2,X3)
| X4 != ordered_pair(X5,X6)
| ~ in(X6,X3)
| ~ in(X5,X2) ),
inference(literals_permutation,[status(thm)],[c_0_650]) ).
cnf(c_0_650_1,axiom,
( X1 != cartesian_product2(X2,X3)
| in(X4,X1)
| X4 != ordered_pair(X5,X6)
| ~ in(X6,X3)
| ~ in(X5,X2) ),
inference(literals_permutation,[status(thm)],[c_0_650]) ).
cnf(c_0_650_2,axiom,
( X4 != ordered_pair(X5,X6)
| X1 != cartesian_product2(X2,X3)
| in(X4,X1)
| ~ in(X6,X3)
| ~ in(X5,X2) ),
inference(literals_permutation,[status(thm)],[c_0_650]) ).
cnf(c_0_650_3,axiom,
( ~ in(X6,X3)
| X4 != ordered_pair(X5,X6)
| X1 != cartesian_product2(X2,X3)
| in(X4,X1)
| ~ in(X5,X2) ),
inference(literals_permutation,[status(thm)],[c_0_650]) ).
cnf(c_0_650_4,axiom,
( ~ in(X5,X2)
| ~ in(X6,X3)
| X4 != ordered_pair(X5,X6)
| X1 != cartesian_product2(X2,X3)
| in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_650]) ).
cnf(c_0_651_0,axiom,
( element(meet_of_subsets(X1,X2),powerset(X1))
| ~ element(X2,powerset(powerset(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_651]) ).
cnf(c_0_651_1,axiom,
( ~ element(X2,powerset(powerset(X1)))
| element(meet_of_subsets(X1,X2),powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_651]) ).
cnf(c_0_652_0,axiom,
( element(union_of_subsets(X1,X2),powerset(X1))
| ~ element(X2,powerset(powerset(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_652]) ).
cnf(c_0_652_1,axiom,
( ~ element(X2,powerset(powerset(X1)))
| element(union_of_subsets(X1,X2),powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_652]) ).
cnf(c_0_653_0,axiom,
( ordered_pair(sk1_esk10_2(X2,X1),sk1_esk11_2(X2,X1)) = X1
| ~ in(X1,X2)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_653]) ).
cnf(c_0_653_1,axiom,
( ~ in(X1,X2)
| ordered_pair(sk1_esk10_2(X2,X1),sk1_esk11_2(X2,X1)) = X1
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_653]) ).
cnf(c_0_653_2,axiom,
( ~ relation(X2)
| ~ in(X1,X2)
| ordered_pair(sk1_esk10_2(X2,X1),sk1_esk11_2(X2,X1)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_653]) ).
cnf(c_0_654_0,axiom,
( in(X3,sk1_esk58_2(X2,X1))
| ~ in(X1,sk1_esk57_1(X2))
| ~ subset(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_654]) ).
cnf(c_0_654_1,axiom,
( ~ in(X1,sk1_esk57_1(X2))
| in(X3,sk1_esk58_2(X2,X1))
| ~ subset(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_654]) ).
cnf(c_0_654_2,axiom,
( ~ subset(X3,X1)
| ~ in(X1,sk1_esk57_1(X2))
| in(X3,sk1_esk58_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_654]) ).
cnf(c_0_655_0,axiom,
( in(X3,X2)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(ordered_pair(X4,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_655]) ).
cnf(c_0_655_1,axiom,
( ~ relation(X1)
| in(X3,X2)
| X2 != relation_rng(X1)
| ~ in(ordered_pair(X4,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_655]) ).
cnf(c_0_655_2,axiom,
( X2 != relation_rng(X1)
| ~ relation(X1)
| in(X3,X2)
| ~ in(ordered_pair(X4,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_655]) ).
cnf(c_0_655_3,axiom,
( ~ in(ordered_pair(X4,X3),X1)
| X2 != relation_rng(X1)
| ~ relation(X1)
| in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_655]) ).
cnf(c_0_656_0,axiom,
( in(X3,X2)
| ~ relation(X1)
| X2 != relation_dom(X1)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_656]) ).
cnf(c_0_656_1,axiom,
( ~ relation(X1)
| in(X3,X2)
| X2 != relation_dom(X1)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_656]) ).
cnf(c_0_656_2,axiom,
( X2 != relation_dom(X1)
| ~ relation(X1)
| in(X3,X2)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_656]) ).
cnf(c_0_656_3,axiom,
( ~ in(ordered_pair(X3,X4),X1)
| X2 != relation_dom(X1)
| ~ relation(X1)
| in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_656]) ).
cnf(c_0_657_0,axiom,
( in(X3,X2)
| ~ relation(X1)
| X1 != identity_relation(X2)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_657]) ).
cnf(c_0_657_1,axiom,
( ~ relation(X1)
| in(X3,X2)
| X1 != identity_relation(X2)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_657]) ).
cnf(c_0_657_2,axiom,
( X1 != identity_relation(X2)
| ~ relation(X1)
| in(X3,X2)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_657]) ).
cnf(c_0_657_3,axiom,
( ~ in(ordered_pair(X3,X4),X1)
| X1 != identity_relation(X2)
| ~ relation(X1)
| in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_657]) ).
cnf(c_0_658_0,axiom,
( X1 = singleton(X2)
| sk1_esk16_2(X2,X1) != X2
| ~ in(sk1_esk16_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_658]) ).
cnf(c_0_658_1,axiom,
( sk1_esk16_2(X2,X1) != X2
| X1 = singleton(X2)
| ~ in(sk1_esk16_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_658]) ).
cnf(c_0_658_2,axiom,
( ~ in(sk1_esk16_2(X2,X1),X1)
| sk1_esk16_2(X2,X1) != X2
| X1 = singleton(X2) ),
inference(literals_permutation,[status(thm)],[c_0_658]) ).
cnf(c_0_659_0,axiom,
( complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2
| ~ element(X2,powerset(powerset(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_659]) ).
cnf(c_0_659_1,axiom,
( ~ element(X2,powerset(powerset(X1)))
| complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_659]) ).
cnf(c_0_660_0,axiom,
( X1 = union(X2)
| in(sk1_esk36_2(X2,X1),X1)
| in(sk1_esk37_2(X2,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_660]) ).
cnf(c_0_660_1,axiom,
( in(sk1_esk36_2(X2,X1),X1)
| X1 = union(X2)
| in(sk1_esk37_2(X2,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_660]) ).
cnf(c_0_660_2,axiom,
( in(sk1_esk37_2(X2,X1),X2)
| in(sk1_esk36_2(X2,X1),X1)
| X1 = union(X2) ),
inference(literals_permutation,[status(thm)],[c_0_660]) ).
cnf(c_0_661_0,axiom,
( X1 = powerset(X2)
| subset(sk1_esk18_2(X2,X1),X2)
| in(sk1_esk18_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_661]) ).
cnf(c_0_661_1,axiom,
( subset(sk1_esk18_2(X2,X1),X2)
| X1 = powerset(X2)
| in(sk1_esk18_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_661]) ).
cnf(c_0_661_2,axiom,
( in(sk1_esk18_2(X2,X1),X1)
| subset(sk1_esk18_2(X2,X1),X2)
| X1 = powerset(X2) ),
inference(literals_permutation,[status(thm)],[c_0_661]) ).
cnf(c_0_662_0,axiom,
( in(X4,X1)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_662]) ).
cnf(c_0_662_1,axiom,
( X1 != set_intersection2(X2,X3)
| in(X4,X1)
| ~ in(X4,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_662]) ).
cnf(c_0_662_2,axiom,
( ~ in(X4,X3)
| X1 != set_intersection2(X2,X3)
| in(X4,X1)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_662]) ).
cnf(c_0_662_3,axiom,
( ~ in(X4,X2)
| ~ in(X4,X3)
| X1 != set_intersection2(X2,X3)
| in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_662]) ).
cnf(c_0_663_0,axiom,
( X1 = X2
| in(sk1_esk56_2(X1,X2),X2)
| in(sk1_esk56_2(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_663]) ).
cnf(c_0_663_1,axiom,
( in(sk1_esk56_2(X1,X2),X2)
| X1 = X2
| in(sk1_esk56_2(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_663]) ).
cnf(c_0_663_2,axiom,
( in(sk1_esk56_2(X1,X2),X1)
| in(sk1_esk56_2(X1,X2),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_663]) ).
cnf(c_0_664_0,axiom,
( in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| X1 != identity_relation(X2)
| X3 != X4
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_664]) ).
cnf(c_0_664_1,axiom,
( ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| X1 != identity_relation(X2)
| X3 != X4
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_664]) ).
cnf(c_0_664_2,axiom,
( X1 != identity_relation(X2)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| X3 != X4
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_664]) ).
cnf(c_0_664_3,axiom,
( X3 != X4
| X1 != identity_relation(X2)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_664]) ).
cnf(c_0_664_4,axiom,
( ~ in(X3,X2)
| X3 != X4
| X1 != identity_relation(X2)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_664]) ).
cnf(c_0_665_0,axiom,
( X3 = X4
| ~ relation(X1)
| X1 != identity_relation(X2)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_665]) ).
cnf(c_0_665_1,axiom,
( ~ relation(X1)
| X3 = X4
| X1 != identity_relation(X2)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_665]) ).
cnf(c_0_665_2,axiom,
( X1 != identity_relation(X2)
| ~ relation(X1)
| X3 = X4
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_665]) ).
cnf(c_0_665_3,axiom,
( ~ in(ordered_pair(X3,X4),X1)
| X1 != identity_relation(X2)
| ~ relation(X1)
| X3 = X4 ),
inference(literals_permutation,[status(thm)],[c_0_665]) ).
cnf(c_0_666_0,axiom,
( in(sk1_esk58_2(X2,X1),sk1_esk57_1(X2))
| ~ in(X1,sk1_esk57_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_666]) ).
cnf(c_0_666_1,axiom,
( ~ in(X1,sk1_esk57_1(X2))
| in(sk1_esk58_2(X2,X1),sk1_esk57_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_666]) ).
cnf(c_0_667_0,axiom,
( element(subset_complement(X1,X2),powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_667]) ).
cnf(c_0_667_1,axiom,
( ~ element(X2,powerset(X1))
| element(subset_complement(X1,X2),powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_667]) ).
cnf(c_0_668_0,axiom,
( subset(X1,X2)
| ~ in(sk1_esk30_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_668]) ).
cnf(c_0_668_1,axiom,
( ~ in(sk1_esk30_2(X1,X2),X2)
| subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_668]) ).
cnf(c_0_669_0,axiom,
( in(X1,sk1_esk57_1(X2))
| ~ subset(X1,X3)
| ~ in(X3,sk1_esk57_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_669]) ).
cnf(c_0_669_1,axiom,
( ~ subset(X1,X3)
| in(X1,sk1_esk57_1(X2))
| ~ in(X3,sk1_esk57_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_669]) ).
cnf(c_0_669_2,axiom,
( ~ in(X3,sk1_esk57_1(X2))
| ~ subset(X1,X3)
| in(X1,sk1_esk57_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_669]) ).
cnf(c_0_670_0,axiom,
( in(X4,X1)
| in(X4,X3)
| X1 != set_difference(X2,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_670]) ).
cnf(c_0_670_1,axiom,
( in(X4,X3)
| in(X4,X1)
| X1 != set_difference(X2,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_670]) ).
cnf(c_0_670_2,axiom,
( X1 != set_difference(X2,X3)
| in(X4,X3)
| in(X4,X1)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_670]) ).
cnf(c_0_670_3,axiom,
( ~ in(X4,X2)
| X1 != set_difference(X2,X3)
| in(X4,X3)
| in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_670]) ).
cnf(c_0_671_0,axiom,
( in(X4,X3)
| in(X4,X2)
| X1 != set_union2(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_671]) ).
cnf(c_0_671_1,axiom,
( in(X4,X2)
| in(X4,X3)
| X1 != set_union2(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_671]) ).
cnf(c_0_671_2,axiom,
( X1 != set_union2(X2,X3)
| in(X4,X2)
| in(X4,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_671]) ).
cnf(c_0_671_3,axiom,
( ~ in(X4,X1)
| X1 != set_union2(X2,X3)
| in(X4,X2)
| in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_671]) ).
cnf(c_0_672_0,axiom,
( in(X1,sk1_esk57_1(X2))
| are_equipotent(X1,sk1_esk57_1(X2))
| ~ subset(X1,sk1_esk57_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_672]) ).
cnf(c_0_672_1,axiom,
( are_equipotent(X1,sk1_esk57_1(X2))
| in(X1,sk1_esk57_1(X2))
| ~ subset(X1,sk1_esk57_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_672]) ).
cnf(c_0_672_2,axiom,
( ~ subset(X1,sk1_esk57_1(X2))
| are_equipotent(X1,sk1_esk57_1(X2))
| in(X1,sk1_esk57_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_672]) ).
cnf(c_0_673_0,axiom,
( subset_complement(X1,subset_complement(X1,X2)) = X2
| ~ element(X2,powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_673]) ).
cnf(c_0_673_1,axiom,
( ~ element(X2,powerset(X1))
| subset_complement(X1,subset_complement(X1,X2)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_673]) ).
cnf(c_0_674_0,axiom,
( X1 = empty_set
| in(X3,X4)
| X2 != set_meet(X1)
| ~ in(X4,X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_674]) ).
cnf(c_0_674_1,axiom,
( in(X3,X4)
| X1 = empty_set
| X2 != set_meet(X1)
| ~ in(X4,X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_674]) ).
cnf(c_0_674_2,axiom,
( X2 != set_meet(X1)
| in(X3,X4)
| X1 = empty_set
| ~ in(X4,X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_674]) ).
cnf(c_0_674_3,axiom,
( ~ in(X4,X1)
| X2 != set_meet(X1)
| in(X3,X4)
| X1 = empty_set
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_674]) ).
cnf(c_0_674_4,axiom,
( ~ in(X3,X2)
| ~ in(X4,X1)
| X2 != set_meet(X1)
| in(X3,X4)
| X1 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_674]) ).
cnf(c_0_675_0,axiom,
( meet_of_subsets(X1,X2) = set_meet(X2)
| ~ element(X2,powerset(powerset(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_675]) ).
cnf(c_0_675_1,axiom,
( ~ element(X2,powerset(powerset(X1)))
| meet_of_subsets(X1,X2) = set_meet(X2) ),
inference(literals_permutation,[status(thm)],[c_0_675]) ).
cnf(c_0_676_0,axiom,
( union_of_subsets(X1,X2) = union(X2)
| ~ element(X2,powerset(powerset(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_676]) ).
cnf(c_0_676_1,axiom,
( ~ element(X2,powerset(powerset(X1)))
| union_of_subsets(X1,X2) = union(X2) ),
inference(literals_permutation,[status(thm)],[c_0_676]) ).
cnf(c_0_677_0,axiom,
( element(X1,X2)
| ~ element(X3,powerset(X2))
| ~ in(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_677]) ).
cnf(c_0_677_1,axiom,
( ~ element(X3,powerset(X2))
| element(X1,X2)
| ~ in(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_677]) ).
cnf(c_0_677_2,axiom,
( ~ in(X1,X3)
| ~ element(X3,powerset(X2))
| element(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_677]) ).
cnf(c_0_678_0,axiom,
( X1 != set_difference(X2,X3)
| ~ in(X4,X1)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_678]) ).
cnf(c_0_678_1,axiom,
( ~ in(X4,X1)
| X1 != set_difference(X2,X3)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_678]) ).
cnf(c_0_678_2,axiom,
( ~ in(X4,X3)
| ~ in(X4,X1)
| X1 != set_difference(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_678]) ).
cnf(c_0_679_0,axiom,
( in(X3,X1)
| X1 != union(X2)
| ~ in(X4,X2)
| ~ in(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_679]) ).
cnf(c_0_679_1,axiom,
( X1 != union(X2)
| in(X3,X1)
| ~ in(X4,X2)
| ~ in(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_679]) ).
cnf(c_0_679_2,axiom,
( ~ in(X4,X2)
| X1 != union(X2)
| in(X3,X1)
| ~ in(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_679]) ).
cnf(c_0_679_3,axiom,
( ~ in(X3,X4)
| ~ in(X4,X2)
| X1 != union(X2)
| in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_679]) ).
cnf(c_0_680_0,axiom,
( ~ empty(X1)
| ~ element(X2,powerset(X1))
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_680]) ).
cnf(c_0_680_1,axiom,
( ~ element(X2,powerset(X1))
| ~ empty(X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_680]) ).
cnf(c_0_680_2,axiom,
( ~ in(X3,X2)
| ~ element(X2,powerset(X1))
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_680]) ).
cnf(c_0_681_0,axiom,
( in(X4,X2)
| X1 != set_difference(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_681]) ).
cnf(c_0_681_1,axiom,
( X1 != set_difference(X2,X3)
| in(X4,X2)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_681]) ).
cnf(c_0_681_2,axiom,
( ~ in(X4,X1)
| X1 != set_difference(X2,X3)
| in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_681]) ).
cnf(c_0_682_0,axiom,
( in(X4,X2)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_682]) ).
cnf(c_0_682_1,axiom,
( X1 != set_intersection2(X2,X3)
| in(X4,X2)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_682]) ).
cnf(c_0_682_2,axiom,
( ~ in(X4,X1)
| X1 != set_intersection2(X2,X3)
| in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_682]) ).
cnf(c_0_683_0,axiom,
( in(X4,X3)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_683]) ).
cnf(c_0_683_1,axiom,
( X1 != set_intersection2(X2,X3)
| in(X4,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_683]) ).
cnf(c_0_683_2,axiom,
( ~ in(X4,X1)
| X1 != set_intersection2(X2,X3)
| in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_683]) ).
cnf(c_0_684_0,axiom,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_684]) ).
cnf(c_0_684_1,axiom,
( X1 != set_union2(X2,X3)
| in(X4,X1)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_684]) ).
cnf(c_0_684_2,axiom,
( ~ in(X4,X2)
| X1 != set_union2(X2,X3)
| in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_684]) ).
cnf(c_0_685_0,axiom,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_685]) ).
cnf(c_0_685_1,axiom,
( X1 != set_union2(X2,X3)
| in(X4,X1)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_685]) ).
cnf(c_0_685_2,axiom,
( ~ in(X4,X3)
| X1 != set_union2(X2,X3)
| in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_685]) ).
cnf(c_0_686_0,axiom,
( X1 = singleton(X2)
| sk1_esk16_2(X2,X1) = X2
| in(sk1_esk16_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_686]) ).
cnf(c_0_686_1,axiom,
( sk1_esk16_2(X2,X1) = X2
| X1 = singleton(X2)
| in(sk1_esk16_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_686]) ).
cnf(c_0_686_2,axiom,
( in(sk1_esk16_2(X2,X1),X1)
| sk1_esk16_2(X2,X1) = X2
| X1 = singleton(X2) ),
inference(literals_permutation,[status(thm)],[c_0_686]) ).
cnf(c_0_687_0,axiom,
( subset_complement(X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_687]) ).
cnf(c_0_687_1,axiom,
( ~ element(X2,powerset(X1))
| subset_complement(X1,X2) = set_difference(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_687]) ).
cnf(c_0_689_0,axiom,
( in(X1,X2)
| ~ in(X1,X3)
| ~ subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_689]) ).
cnf(c_0_689_1,axiom,
( ~ in(X1,X3)
| in(X1,X2)
| ~ subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_689]) ).
cnf(c_0_689_2,axiom,
( ~ subset(X3,X2)
| ~ in(X1,X3)
| in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_689]) ).
cnf(c_0_690_0,axiom,
( empty(X2)
| empty(X1)
| ~ empty(cartesian_product2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_690]) ).
cnf(c_0_690_1,axiom,
( empty(X1)
| empty(X2)
| ~ empty(cartesian_product2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_690]) ).
cnf(c_0_690_2,axiom,
( ~ empty(cartesian_product2(X1,X2))
| empty(X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_690]) ).
cnf(c_0_691_0,axiom,
( subset(X1,X2)
| in(sk1_esk30_2(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_691]) ).
cnf(c_0_691_1,axiom,
( in(sk1_esk30_2(X1,X2),X1)
| subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_691]) ).
cnf(c_0_692_0,axiom,
( empty(X2)
| ~ empty(set_union2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_692]) ).
cnf(c_0_692_1,axiom,
( ~ empty(set_union2(X1,X2))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_692]) ).
cnf(c_0_693_0,axiom,
( empty(X1)
| ~ empty(set_union2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_693]) ).
cnf(c_0_693_1,axiom,
( ~ empty(set_union2(X1,X2))
| empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_693]) ).
cnf(c_0_694_0,axiom,
( X4 = X3
| X4 = X2
| X1 != unordered_pair(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_694]) ).
cnf(c_0_694_1,axiom,
( X4 = X2
| X4 = X3
| X1 != unordered_pair(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_694]) ).
cnf(c_0_694_2,axiom,
( X1 != unordered_pair(X2,X3)
| X4 = X2
| X4 = X3
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_694]) ).
cnf(c_0_694_3,axiom,
( ~ in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 = X2
| X4 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_694]) ).
cnf(c_0_697_0,axiom,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_697]) ).
cnf(c_0_697_1,axiom,
( ~ subset(X2,X1)
| X1 = X2
| ~ subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_697]) ).
cnf(c_0_697_2,axiom,
( ~ subset(X1,X2)
| ~ subset(X2,X1)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_697]) ).
cnf(c_0_698_0,axiom,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_698]) ).
cnf(c_0_698_1,axiom,
( ~ element(X1,powerset(X2))
| subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_698]) ).
cnf(c_0_699_0,axiom,
( subset(X3,X2)
| X1 != powerset(X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_699]) ).
cnf(c_0_699_1,axiom,
( X1 != powerset(X2)
| subset(X3,X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_699]) ).
cnf(c_0_699_2,axiom,
( ~ in(X3,X1)
| X1 != powerset(X2)
| subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_699]) ).
cnf(c_0_700_0,axiom,
( in(X3,X1)
| X1 != powerset(X2)
| ~ subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_700]) ).
cnf(c_0_700_1,axiom,
( X1 != powerset(X2)
| in(X3,X1)
| ~ subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_700]) ).
cnf(c_0_700_2,axiom,
( ~ subset(X3,X2)
| X1 != powerset(X2)
| in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_700]) ).
cnf(c_0_701_0,axiom,
( ~ proper_subset(X1,X2)
| ~ proper_subset(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_701]) ).
cnf(c_0_701_1,axiom,
( ~ proper_subset(X2,X1)
| ~ proper_subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_701]) ).
cnf(c_0_702_0,axiom,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_702]) ).
cnf(c_0_702_1,axiom,
( ~ in(X2,X1)
| ~ in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_702]) ).
cnf(c_0_703_0,axiom,
( empty(relation_composition(X2,X1))
| ~ relation(X1)
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_703]) ).
cnf(c_0_703_1,axiom,
( ~ relation(X1)
| empty(relation_composition(X2,X1))
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_703]) ).
cnf(c_0_703_2,axiom,
( ~ empty(X2)
| ~ relation(X1)
| empty(relation_composition(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_703]) ).
cnf(c_0_704_0,axiom,
( relation(relation_composition(X2,X1))
| ~ relation(X1)
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_704]) ).
cnf(c_0_704_1,axiom,
( ~ relation(X1)
| relation(relation_composition(X2,X1))
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_704]) ).
cnf(c_0_704_2,axiom,
( ~ empty(X2)
| ~ relation(X1)
| relation(relation_composition(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_704]) ).
cnf(c_0_705_0,axiom,
( relation(set_union2(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_705]) ).
cnf(c_0_705_1,axiom,
( ~ relation(X2)
| relation(set_union2(X1,X2))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_705]) ).
cnf(c_0_705_2,axiom,
( ~ relation(X1)
| ~ relation(X2)
| relation(set_union2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_705]) ).
cnf(c_0_706_0,axiom,
( relation(set_intersection2(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_706]) ).
cnf(c_0_706_1,axiom,
( ~ relation(X2)
| relation(set_intersection2(X1,X2))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_706]) ).
cnf(c_0_706_2,axiom,
( ~ relation(X1)
| ~ relation(X2)
| relation(set_intersection2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_706]) ).
cnf(c_0_707_0,axiom,
( empty(relation_composition(X1,X2))
| ~ relation(X1)
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_707]) ).
cnf(c_0_707_1,axiom,
( ~ relation(X1)
| empty(relation_composition(X1,X2))
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_707]) ).
cnf(c_0_707_2,axiom,
( ~ empty(X2)
| ~ relation(X1)
| empty(relation_composition(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_707]) ).
cnf(c_0_708_0,axiom,
( relation(relation_composition(X1,X2))
| ~ relation(X1)
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_708]) ).
cnf(c_0_708_1,axiom,
( ~ relation(X1)
| relation(relation_composition(X1,X2))
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_708]) ).
cnf(c_0_708_2,axiom,
( ~ empty(X2)
| ~ relation(X1)
| relation(relation_composition(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_708]) ).
cnf(c_0_709_0,axiom,
( relation(relation_composition(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_709]) ).
cnf(c_0_709_1,axiom,
( ~ relation(X2)
| relation(relation_composition(X1,X2))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_709]) ).
cnf(c_0_709_2,axiom,
( ~ relation(X1)
| ~ relation(X2)
| relation(relation_composition(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_709]) ).
cnf(c_0_710_0,axiom,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_710]) ).
cnf(c_0_710_1,axiom,
( ~ subset(X1,X2)
| element(X1,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_710]) ).
cnf(c_0_711_0,axiom,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_711]) ).
cnf(c_0_711_1,axiom,
( X1 != unordered_pair(X2,X3)
| in(X4,X1)
| X4 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_711]) ).
cnf(c_0_711_2,axiom,
( X4 != X2
| X1 != unordered_pair(X2,X3)
| in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_711]) ).
cnf(c_0_712_0,axiom,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_712]) ).
cnf(c_0_712_1,axiom,
( X1 != unordered_pair(X2,X3)
| in(X4,X1)
| X4 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_712]) ).
cnf(c_0_712_2,axiom,
( X4 != X3
| X1 != unordered_pair(X2,X3)
| in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_712]) ).
cnf(c_0_713_0,axiom,
( in(X1,X2)
| empty(X2)
| ~ element(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_713]) ).
cnf(c_0_713_1,axiom,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_713]) ).
cnf(c_0_713_2,axiom,
( ~ element(X1,X2)
| empty(X2)
| in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_713]) ).
cnf(c_0_714_0,axiom,
( empty(X1)
| in(X2,X1)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_714]) ).
cnf(c_0_714_1,axiom,
( in(X2,X1)
| empty(X1)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_714]) ).
cnf(c_0_714_2,axiom,
( ~ element(X2,X1)
| in(X2,X1)
| empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_714]) ).
cnf(c_0_715_0,axiom,
( empty(X1)
| element(X2,X1)
| ~ in(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_715]) ).
cnf(c_0_715_1,axiom,
( element(X2,X1)
| empty(X1)
| ~ in(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_715]) ).
cnf(c_0_715_2,axiom,
( ~ in(X2,X1)
| element(X2,X1)
| empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_715]) ).
cnf(c_0_716_0,axiom,
( proper_subset(X1,X2)
| X1 = X2
| ~ subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_716]) ).
cnf(c_0_716_1,axiom,
( X1 = X2
| proper_subset(X1,X2)
| ~ subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_716]) ).
cnf(c_0_716_2,axiom,
( ~ subset(X1,X2)
| X1 = X2
| proper_subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_716]) ).
cnf(c_0_717_0,axiom,
( relation(relation_rng_restriction(X1,X2))
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_717]) ).
cnf(c_0_717_1,axiom,
( ~ relation(X2)
| relation(relation_rng_restriction(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_717]) ).
cnf(c_0_718_0,axiom,
( relation(relation_dom_restriction(X1,X2))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_718]) ).
cnf(c_0_718_1,axiom,
( ~ relation(X1)
| relation(relation_dom_restriction(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_718]) ).
cnf(c_0_719_0,axiom,
( set_union2(relation_dom(X1),relation_rng(X1)) = relation_field(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_719]) ).
cnf(c_0_719_1,axiom,
( ~ relation(X1)
| set_union2(relation_dom(X1),relation_rng(X1)) = relation_field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_719]) ).
cnf(c_0_720_0,axiom,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_720]) ).
cnf(c_0_720_1,axiom,
( ~ in(X1,X2)
| element(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_720]) ).
cnf(c_0_721_0,axiom,
( disjoint(X1,X2)
| ~ disjoint(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_721]) ).
cnf(c_0_721_1,axiom,
( ~ disjoint(X2,X1)
| disjoint(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_721]) ).
cnf(c_0_722_0,axiom,
( subset(X1,X2)
| ~ proper_subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_722]) ).
cnf(c_0_722_1,axiom,
( ~ proper_subset(X1,X2)
| subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_722]) ).
cnf(c_0_723_0,axiom,
( set_intersection2(X1,X2) = empty_set
| ~ disjoint(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_723]) ).
cnf(c_0_723_1,axiom,
( ~ disjoint(X1,X2)
| set_intersection2(X1,X2) = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_723]) ).
cnf(c_0_724_0,axiom,
( disjoint(X1,X2)
| set_intersection2(X1,X2) != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_724]) ).
cnf(c_0_724_1,axiom,
( set_intersection2(X1,X2) != empty_set
| disjoint(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_724]) ).
cnf(c_0_725_0,axiom,
( empty(X2)
| ~ empty(X1)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_725]) ).
cnf(c_0_725_1,axiom,
( ~ empty(X1)
| empty(X2)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_725]) ).
cnf(c_0_725_2,axiom,
( ~ element(X2,X1)
| ~ empty(X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_725]) ).
cnf(c_0_726_0,axiom,
( X3 = X2
| X1 != singleton(X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_726]) ).
cnf(c_0_726_1,axiom,
( X1 != singleton(X2)
| X3 = X2
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_726]) ).
cnf(c_0_726_2,axiom,
( ~ in(X3,X1)
| X1 != singleton(X2)
| X3 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_726]) ).
cnf(c_0_727_0,axiom,
( relation(X1)
| sk1_esk12_1(X1) != ordered_pair(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_727]) ).
cnf(c_0_727_1,axiom,
( sk1_esk12_1(X1) != ordered_pair(X2,X3)
| relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_727]) ).
cnf(c_0_728_0,axiom,
( empty(X1)
| element(sk1_esk51_1(X1),powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_728]) ).
cnf(c_0_728_1,axiom,
( element(sk1_esk51_1(X1),powerset(X1))
| empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_728]) ).
cnf(c_0_729_0,axiom,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_729]) ).
cnf(c_0_729_1,axiom,
( ~ in(X2,X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_729]) ).
cnf(c_0_730_0,axiom,
( element(X2,X1)
| ~ empty(X1)
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_730]) ).
cnf(c_0_730_1,axiom,
( ~ empty(X1)
| element(X2,X1)
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_730]) ).
cnf(c_0_730_2,axiom,
( ~ empty(X2)
| ~ empty(X1)
| element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_730]) ).
cnf(c_0_731_0,axiom,
( empty(X1)
| ~ empty(relation_rng(X1))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_731]) ).
cnf(c_0_731_1,axiom,
( ~ empty(relation_rng(X1))
| empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_731]) ).
cnf(c_0_731_2,axiom,
( ~ relation(X1)
| ~ empty(relation_rng(X1))
| empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_731]) ).
cnf(c_0_732_0,axiom,
( empty(X1)
| ~ empty(relation_dom(X1))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_732]) ).
cnf(c_0_732_1,axiom,
( ~ empty(relation_dom(X1))
| empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_732]) ).
cnf(c_0_732_2,axiom,
( ~ relation(X1)
| ~ empty(relation_dom(X1))
| empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_732]) ).
cnf(c_0_738_0,axiom,
( in(X3,X1)
| X1 != singleton(X2)
| X3 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_738]) ).
cnf(c_0_738_1,axiom,
( X1 != singleton(X2)
| in(X3,X1)
| X3 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_738]) ).
cnf(c_0_738_2,axiom,
( X3 != X2
| X1 != singleton(X2)
| in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_738]) ).
cnf(c_0_739_0,axiom,
( ~ proper_subset(X1,X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_739]) ).
cnf(c_0_739_1,axiom,
( X1 != X2
| ~ proper_subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_739]) ).
cnf(c_0_740_0,axiom,
( ~ in(X1,X2)
| X2 != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_740]) ).
cnf(c_0_740_1,axiom,
( X2 != empty_set
| ~ in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_740]) ).
cnf(c_0_741_0,axiom,
( relation(X1)
| in(sk1_esk12_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_741]) ).
cnf(c_0_741_1,axiom,
( in(sk1_esk12_1(X1),X1)
| relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_741]) ).
cnf(c_0_743_0,axiom,
( X1 = empty_set
| in(sk1_esk17_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_743]) ).
cnf(c_0_743_1,axiom,
( in(sk1_esk17_1(X1),X1)
| X1 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_743]) ).
cnf(c_0_744_0,axiom,
( empty(X1)
| ~ empty(sk1_esk51_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_744]) ).
cnf(c_0_744_1,axiom,
( ~ empty(sk1_esk51_1(X1))
| empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_744]) ).
cnf(c_0_747_0,axiom,
( relation_inverse(relation_inverse(X1)) = X1
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_747]) ).
cnf(c_0_747_1,axiom,
( ~ relation(X1)
| relation_inverse(relation_inverse(X1)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_747]) ).
cnf(c_0_748_0,axiom,
( subset(X1,X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_748]) ).
cnf(c_0_748_1,axiom,
( X1 != X2
| subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_748]) ).
cnf(c_0_749_0,axiom,
( subset(X2,X1)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_749]) ).
cnf(c_0_749_1,axiom,
( X1 != X2
| subset(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_749]) ).
cnf(c_0_750_0,axiom,
( empty(relation_rng(X1))
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_750]) ).
cnf(c_0_750_1,axiom,
( ~ empty(X1)
| empty(relation_rng(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_750]) ).
cnf(c_0_751_0,axiom,
( relation(relation_rng(X1))
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_751]) ).
cnf(c_0_751_1,axiom,
( ~ empty(X1)
| relation(relation_rng(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_751]) ).
cnf(c_0_752_0,axiom,
( empty(relation_dom(X1))
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_752]) ).
cnf(c_0_752_1,axiom,
( ~ empty(X1)
| empty(relation_dom(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_752]) ).
cnf(c_0_753_0,axiom,
( relation(relation_dom(X1))
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_753]) ).
cnf(c_0_753_1,axiom,
( ~ empty(X1)
| relation(relation_dom(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_753]) ).
cnf(c_0_754_0,axiom,
( relation(relation_inverse(X1))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_754]) ).
cnf(c_0_754_1,axiom,
( ~ relation(X1)
| relation(relation_inverse(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_754]) ).
cnf(c_0_757_0,axiom,
( X2 = X1
| ~ empty(X1)
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_757]) ).
cnf(c_0_757_1,axiom,
( ~ empty(X1)
| X2 = X1
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_757]) ).
cnf(c_0_757_2,axiom,
( ~ empty(X2)
| ~ empty(X1)
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_757]) ).
cnf(c_0_765_0,axiom,
( X2 = empty_set
| X1 != empty_set
| X2 != set_meet(X1) ),
inference(literals_permutation,[status(thm)],[c_0_765]) ).
cnf(c_0_765_1,axiom,
( X1 != empty_set
| X2 = empty_set
| X2 != set_meet(X1) ),
inference(literals_permutation,[status(thm)],[c_0_765]) ).
cnf(c_0_765_2,axiom,
( X2 != set_meet(X1)
| X1 != empty_set
| X2 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_765]) ).
cnf(c_0_766_0,axiom,
( relation(X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_766]) ).
cnf(c_0_766_1,axiom,
( ~ empty(X1)
| relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_766]) ).
cnf(c_0_769_0,axiom,
( X2 = set_meet(X1)
| X1 != empty_set
| X2 != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_769]) ).
cnf(c_0_769_1,axiom,
( X1 != empty_set
| X2 = set_meet(X1)
| X2 != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_769]) ).
cnf(c_0_769_2,axiom,
( X2 != empty_set
| X1 != empty_set
| X2 = set_meet(X1) ),
inference(literals_permutation,[status(thm)],[c_0_769]) ).
cnf(c_0_770_0,axiom,
( X1 = empty_set
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_770]) ).
cnf(c_0_770_1,axiom,
( ~ empty(X1)
| X1 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_770]) ).
cnf(c_0_695_0,axiom,
~ empty(unordered_pair(X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_695]) ).
cnf(c_0_696_0,axiom,
~ empty(ordered_pair(X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_696]) ).
cnf(c_0_742_0,axiom,
~ proper_subset(X1,X1),
inference(literals_permutation,[status(thm)],[c_0_742]) ).
cnf(c_0_755_0,axiom,
~ empty(singleton(X1)),
inference(literals_permutation,[status(thm)],[c_0_755]) ).
cnf(c_0_756_0,axiom,
~ empty(powerset(X1)),
inference(literals_permutation,[status(thm)],[c_0_756]) ).
cnf(c_0_772_0,axiom,
~ empty(sk1_esk55_0),
inference(literals_permutation,[status(thm)],[c_0_772]) ).
cnf(c_0_773_0,axiom,
~ empty(sk1_esk53_0),
inference(literals_permutation,[status(thm)],[c_0_773]) ).
cnf(c_0_688_0,axiom,
unordered_pair(unordered_pair(X1,X2),singleton(X1)) = ordered_pair(X1,X2),
inference(literals_permutation,[status(thm)],[c_0_688]) ).
cnf(c_0_733_0,axiom,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(literals_permutation,[status(thm)],[c_0_733]) ).
cnf(c_0_734_0,axiom,
set_union2(X1,X2) = set_union2(X2,X1),
inference(literals_permutation,[status(thm)],[c_0_734]) ).
cnf(c_0_735_0,axiom,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(literals_permutation,[status(thm)],[c_0_735]) ).
cnf(c_0_736_0,axiom,
element(sk1_esk54_1(X1),powerset(X1)),
inference(literals_permutation,[status(thm)],[c_0_736]) ).
cnf(c_0_737_0,axiom,
element(cast_to_subset(X1),powerset(X1)),
inference(literals_permutation,[status(thm)],[c_0_737]) ).
cnf(c_0_745_0,axiom,
in(X1,sk1_esk57_1(X1)),
inference(literals_permutation,[status(thm)],[c_0_745]) ).
cnf(c_0_746_0,axiom,
element(sk1_esk49_1(X1),X1),
inference(literals_permutation,[status(thm)],[c_0_746]) ).
cnf(c_0_758_0,axiom,
set_intersection2(X1,X1) = X1,
inference(literals_permutation,[status(thm)],[c_0_758]) ).
cnf(c_0_759_0,axiom,
set_union2(X1,X1) = X1,
inference(literals_permutation,[status(thm)],[c_0_759]) ).
cnf(c_0_760_0,axiom,
subset(X1,X1),
inference(literals_permutation,[status(thm)],[c_0_760]) ).
cnf(c_0_761_0,axiom,
set_difference(X1,empty_set) = X1,
inference(literals_permutation,[status(thm)],[c_0_761]) ).
cnf(c_0_762_0,axiom,
set_union2(X1,empty_set) = X1,
inference(literals_permutation,[status(thm)],[c_0_762]) ).
cnf(c_0_763_0,axiom,
set_difference(empty_set,X1) = empty_set,
inference(literals_permutation,[status(thm)],[c_0_763]) ).
cnf(c_0_764_0,axiom,
set_intersection2(X1,empty_set) = empty_set,
inference(literals_permutation,[status(thm)],[c_0_764]) ).
cnf(c_0_767_0,axiom,
empty(sk1_esk54_1(X1)),
inference(literals_permutation,[status(thm)],[c_0_767]) ).
cnf(c_0_768_0,axiom,
relation(identity_relation(X1)),
inference(literals_permutation,[status(thm)],[c_0_768]) ).
cnf(c_0_771_0,axiom,
cast_to_subset(X1) = X1,
inference(literals_permutation,[status(thm)],[c_0_771]) ).
cnf(c_0_774_0,axiom,
relation(sk1_esk53_0),
inference(literals_permutation,[status(thm)],[c_0_774]) ).
cnf(c_0_775_0,axiom,
empty(sk1_esk52_0),
inference(literals_permutation,[status(thm)],[c_0_775]) ).
cnf(c_0_776_0,axiom,
empty(sk1_esk50_0),
inference(literals_permutation,[status(thm)],[c_0_776]) ).
cnf(c_0_777_0,axiom,
relation(sk1_esk50_0),
inference(literals_permutation,[status(thm)],[c_0_777]) ).
cnf(c_0_778_0,axiom,
empty(empty_set),
inference(literals_permutation,[status(thm)],[c_0_778]) ).
cnf(c_0_779_0,axiom,
relation(empty_set),
inference(literals_permutation,[status(thm)],[c_0_779]) ).
cnf(c_0_780_0,axiom,
empty(empty_set),
inference(literals_permutation,[status(thm)],[c_0_780]) ).
cnf(c_0_781_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_781]) ).
cnf(c_0_782_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_782]) ).
cnf(c_0_783_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_783]) ).
cnf(c_0_784_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_784]) ).
cnf(c_0_785_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_785]) ).
cnf(c_0_786_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_786]) ).
cnf(c_0_787_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_787]) ).
cnf(c_0_788_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_788]) ).
cnf(c_0_789_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_789]) ).
cnf(c_0_790_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_790]) ).
cnf(c_0_791_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_791]) ).
cnf(c_0_792_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_792]) ).
cnf(c_0_793_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_793]) ).
cnf(c_0_794_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_794]) ).
cnf(c_0_795_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_795]) ).
cnf(c_0_796_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_796]) ).
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_001,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_image(X3,X2))
<=> ? [X4] :
( in(X4,relation_dom(X3))
& in(ordered_pair(X4,X1),X3)
& in(X4,X2) ) ) ),
file('<stdin>',t143_relat_1) ).
fof(c_0_1_002,lemma,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ( X2 != empty_set
=> union_of_subsets(X1,complements_of_subsets(X1,X2)) = subset_difference(X1,cast_to_subset(X1),meet_of_subsets(X1,X2)) ) ),
file('<stdin>',t48_setfam_1) ).
fof(c_0_2_003,lemma,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ( X2 != empty_set
=> subset_difference(X1,cast_to_subset(X1),union_of_subsets(X1,X2)) = meet_of_subsets(X1,complements_of_subsets(X1,X2)) ) ),
file('<stdin>',t47_setfam_1) ).
fof(c_0_3_004,lemma,
! [X1,X2,X3,X4] :
( relation(X4)
=> ( in(ordered_pair(X1,X2),relation_composition(identity_relation(X3),X4))
<=> ( in(X1,X3)
& in(ordered_pair(X1,X2),X4) ) ) ),
file('<stdin>',t74_relat_1) ).
fof(c_0_4_005,lemma,
! [X1,X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( element(X3,powerset(X1))
=> ( disjoint(X2,X3)
<=> subset(X2,subset_complement(X1,X3)) ) ) ),
file('<stdin>',t43_subset_1) ).
fof(c_0_5_006,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_dom(relation_dom_restriction(X3,X2)))
<=> ( in(X1,X2)
& in(X1,relation_dom(X3)) ) ) ),
file('<stdin>',t86_relat_1) ).
fof(c_0_6_007,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_rng(relation_rng_restriction(X2,X3)))
<=> ( in(X1,X2)
& in(X1,relation_rng(X3)) ) ) ),
file('<stdin>',t115_relat_1) ).
fof(c_0_7_008,lemma,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X1,X3)
& in(X2,X4) ) ),
file('<stdin>',t106_zfmisc_1) ).
fof(c_0_8_009,lemma,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X1,X3)
& in(X2,X4) ) ),
file('<stdin>',l55_zfmisc_1) ).
fof(c_0_9_010,lemma,
! [X1,X2,X3] :
( element(X3,powerset(X1))
=> ~ ( in(X2,subset_complement(X1,X3))
& in(X2,X3) ) ),
file('<stdin>',t54_subset_1) ).
fof(c_0_10_011,lemma,
! [X1,X2,X3,X4] :
( ( subset(X1,X2)
& subset(X3,X4) )
=> subset(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) ),
file('<stdin>',t119_zfmisc_1) ).
fof(c_0_11_012,lemma,
! [X1] :
( X1 != empty_set
=> ! [X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( element(X3,X1)
=> ( ~ in(X3,X2)
=> in(X3,subset_complement(X1,X2)) ) ) ) ),
file('<stdin>',t50_subset_1) ).
fof(c_0_12_013,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> subset(relation_rng(relation_composition(X1,X2)),relation_rng(X2)) ) ),
file('<stdin>',t45_relat_1) ).
fof(c_0_13_014,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> subset(relation_dom(relation_composition(X1,X2)),relation_dom(X1)) ) ),
file('<stdin>',t44_relat_1) ).
fof(c_0_14_015,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X1,X2),X3)
=> ( in(X1,relation_field(X3))
& in(X2,relation_field(X3)) ) ) ),
file('<stdin>',t30_relat_1) ).
fof(c_0_15_016,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X1,X2),X3)
=> ( in(X1,relation_dom(X3))
& in(X2,relation_rng(X3)) ) ) ),
file('<stdin>',t20_relat_1) ).
fof(c_0_16_017,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( subset(relation_dom(X1),relation_rng(X2))
=> relation_rng(relation_composition(X2,X1)) = relation_rng(X1) ) ) ),
file('<stdin>',t47_relat_1) ).
fof(c_0_17_018,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( subset(relation_rng(X1),relation_dom(X2))
=> relation_dom(relation_composition(X1,X2)) = relation_dom(X1) ) ) ),
file('<stdin>',t46_relat_1) ).
fof(c_0_18_019,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> ( in(X3,X1)
| subset(X1,set_difference(X2,singleton(X3))) ) ),
file('<stdin>',l3_zfmisc_1) ).
fof(c_0_19_020,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_difference(X1,X3),set_difference(X2,X3)) ),
file('<stdin>',t33_xboole_1) ).
fof(c_0_20_021,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_intersection2(X1,X3),set_intersection2(X2,X3)) ),
file('<stdin>',t26_xboole_1) ).
fof(c_0_21_022,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> ( subset(cartesian_product2(X1,X3),cartesian_product2(X2,X3))
& subset(cartesian_product2(X3,X1),cartesian_product2(X3,X2)) ) ),
file('<stdin>',t118_zfmisc_1) ).
fof(c_0_22_023,lemma,
! [X1,X2,X3] :
( relation(X3)
=> relation_dom_restriction(relation_rng_restriction(X1,X3),X2) = relation_rng_restriction(X1,relation_dom_restriction(X3,X2)) ),
file('<stdin>',t140_relat_1) ).
fof(c_0_23_024,lemma,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
& ~ ( ? [X3] : in(X3,set_intersection2(X1,X2))
& disjoint(X1,X2) ) ),
file('<stdin>',t4_xboole_0) ).
fof(c_0_24_025,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X3,X2) )
=> subset(set_union2(X1,X3),X2) ),
file('<stdin>',t8_xboole_1) ).
fof(c_0_25_026,lemma,
! [X1,X2,X3] :
( subset(unordered_pair(X1,X2),X3)
<=> ( in(X1,X3)
& in(X2,X3) ) ),
file('<stdin>',t38_zfmisc_1) ).
fof(c_0_26_027,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X1,X3) )
=> subset(X1,set_intersection2(X2,X3)) ),
file('<stdin>',t19_xboole_1) ).
fof(c_0_27_028,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_rng(relation_dom_restriction(X2,X1)),relation_rng(X2)) ),
file('<stdin>',t99_relat_1) ).
fof(c_0_28_029,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_rng(relation_rng_restriction(X1,X2)),relation_rng(X2)) ),
file('<stdin>',t118_relat_1) ).
fof(c_0_29_030,lemma,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
=> in(X3,X2) )
=> element(X1,powerset(X2)) ),
file('<stdin>',l71_subset_1) ).
fof(c_0_30_031,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_rng(relation_rng_restriction(X1,X2)),X1) ),
file('<stdin>',t116_relat_1) ).
fof(c_0_31_032,lemma,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ~ ( X2 != empty_set
& complements_of_subsets(X1,X2) = empty_set ) ),
file('<stdin>',t46_setfam_1) ).
fof(c_0_32_033,lemma,
! [X1] :
? [X2] :
( in(X1,X2)
& ! [X3,X4] :
( ( in(X3,X2)
& subset(X4,X3) )
=> in(X4,X2) )
& ! [X3] :
( in(X3,X2)
=> in(powerset(X3),X2) )
& ! [X3] :
~ ( subset(X3,X2)
& ~ are_equipotent(X3,X2)
& ~ in(X3,X2) ) ),
file('<stdin>',t136_zfmisc_1) ).
fof(c_0_33_034,lemma,
! [X1] :
( relation(X1)
=> ( ! [X2,X3] : ~ in(ordered_pair(X2,X3),X1)
=> X1 = empty_set ) ),
file('<stdin>',t56_relat_1) ).
fof(c_0_34_035,lemma,
! [X1] :
( relation(X1)
=> subset(X1,cartesian_product2(relation_dom(X1),relation_rng(X1))) ),
file('<stdin>',t21_relat_1) ).
fof(c_0_35_036,lemma,
! [X1,X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( in(X3,X2)
=> in(X3,X1) ) ),
file('<stdin>',l3_subset_1) ).
fof(c_0_36_037,lemma,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] :
~ ( in(X3,X1)
& in(X3,X2) ) )
& ~ ( ? [X3] :
( in(X3,X1)
& in(X3,X2) )
& disjoint(X1,X2) ) ),
file('<stdin>',t3_xboole_0) ).
fof(c_0_37_038,lemma,
! [X1,X2] :
( subset(X1,X2)
=> X2 = set_union2(X1,set_difference(X2,X1)) ),
file('<stdin>',t45_xboole_1) ).
fof(c_0_38_039,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( subset(X1,X2)
=> ( subset(relation_dom(X1),relation_dom(X2))
& subset(relation_rng(X1),relation_rng(X2)) ) ) ) ),
file('<stdin>',t25_relat_1) ).
fof(c_0_39_040,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& disjoint(X2,X3) )
=> disjoint(X1,X3) ),
file('<stdin>',t63_xboole_1) ).
fof(c_0_40_041,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ),
file('<stdin>',t1_xboole_1) ).
fof(c_0_41_042,conjecture,
! [X1,X2] :
( relation(X2)
=> subset(relation_image(X2,X1),relation_rng(X2)) ),
file('<stdin>',t144_relat_1) ).
fof(c_0_42_043,lemma,
! [X1,X2] :
( relation(X2)
=> relation_dom(relation_dom_restriction(X2,X1)) = set_intersection2(relation_dom(X2),X1) ),
file('<stdin>',t90_relat_1) ).
fof(c_0_43_044,lemma,
! [X1,X2] :
( relation(X2)
=> relation_rng(relation_rng_restriction(X1,X2)) = set_intersection2(relation_rng(X2),X1) ),
file('<stdin>',t119_relat_1) ).
fof(c_0_44_045,lemma,
! [X1,X2] :
( set_difference(X1,singleton(X2)) = X1
<=> ~ in(X2,X1) ),
file('<stdin>',t65_zfmisc_1) ).
fof(c_0_45_046,lemma,
! [X1,X2] :
~ ( disjoint(singleton(X1),X2)
& in(X1,X2) ),
file('<stdin>',l25_zfmisc_1) ).
fof(c_0_46_047,lemma,
! [X1,X2] : set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
file('<stdin>',t48_xboole_1) ).
fof(c_0_47_048,lemma,
! [X1,X2] : set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
file('<stdin>',t40_xboole_1) ).
fof(c_0_48_049,lemma,
! [X1,X2] : set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
file('<stdin>',t39_xboole_1) ).
fof(c_0_49_050,lemma,
! [X1,X2,X3,X4] :
~ ( unordered_pair(X1,X2) = unordered_pair(X3,X4)
& X1 != X3
& X1 != X4 ),
file('<stdin>',t10_zfmisc_1) ).
fof(c_0_50_051,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_dom_restriction(X2,X1),X2) ),
file('<stdin>',t88_relat_1) ).
fof(c_0_51_052,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_rng_restriction(X1,X2),X2) ),
file('<stdin>',t117_relat_1) ).
fof(c_0_52_053,lemma,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
file('<stdin>',t37_zfmisc_1) ).
fof(c_0_53_054,lemma,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
file('<stdin>',l2_zfmisc_1) ).
fof(c_0_54_055,lemma,
! [X1,X2,X3,X4] :
( ordered_pair(X1,X2) = ordered_pair(X3,X4)
=> ( X1 = X3
& X2 = X4 ) ),
file('<stdin>',t33_zfmisc_1) ).
fof(c_0_55_056,lemma,
! [X1,X2] :
~ ( subset(X1,X2)
& proper_subset(X2,X1) ),
file('<stdin>',t60_xboole_1) ).
fof(c_0_56_057,lemma,
! [X1,X2] :
( subset(singleton(X1),singleton(X2))
=> X1 = X2 ),
file('<stdin>',t6_zfmisc_1) ).
fof(c_0_57_058,lemma,
! [X1,X2] :
( in(X1,X2)
=> set_union2(singleton(X1),X2) = X2 ),
file('<stdin>',t46_zfmisc_1) ).
fof(c_0_58_059,lemma,
! [X1,X2] :
( in(X1,X2)
=> set_union2(singleton(X1),X2) = X2 ),
file('<stdin>',l23_zfmisc_1) ).
fof(c_0_59_060,lemma,
! [X1,X2] :
( in(X1,X2)
=> subset(X1,union(X2)) ),
file('<stdin>',t92_zfmisc_1) ).
fof(c_0_60_061,lemma,
! [X1,X2] :
( in(X1,X2)
=> subset(X1,union(X2)) ),
file('<stdin>',l50_zfmisc_1) ).
fof(c_0_61_062,lemma,
! [X1,X2] :
( relation(X2)
=> relation_dom_restriction(X2,X1) = relation_composition(identity_relation(X1),X2) ),
file('<stdin>',t94_relat_1) ).
fof(c_0_62_063,lemma,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
file('<stdin>',t7_xboole_1) ).
fof(c_0_63_064,lemma,
! [X1,X2] : subset(set_difference(X1,X2),X1),
file('<stdin>',t36_xboole_1) ).
fof(c_0_64_065,lemma,
! [X1,X2] : subset(set_intersection2(X1,X2),X1),
file('<stdin>',t17_xboole_1) ).
fof(c_0_65_066,lemma,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
file('<stdin>',t39_zfmisc_1) ).
fof(c_0_66_067,lemma,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
file('<stdin>',l4_zfmisc_1) ).
fof(c_0_67_068,lemma,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_difference(X1,X2) = X1 ),
file('<stdin>',t83_xboole_1) ).
fof(c_0_68_069,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_intersection2(X1,X2) = X1 ),
file('<stdin>',t28_xboole_1) ).
fof(c_0_69_070,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_union2(X1,X2) = X2 ),
file('<stdin>',t12_xboole_1) ).
fof(c_0_70_071,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('<stdin>',t37_xboole_1) ).
fof(c_0_71_072,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('<stdin>',l32_xboole_1) ).
fof(c_0_72_073,lemma,
! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
file('<stdin>',l28_zfmisc_1) ).
fof(c_0_73_074,lemma,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X2 = X3 ),
file('<stdin>',t9_zfmisc_1) ).
fof(c_0_74_075,lemma,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X1 = X2 ),
file('<stdin>',t8_zfmisc_1) ).
fof(c_0_75_076,lemma,
! [X1] :
( subset(X1,empty_set)
=> X1 = empty_set ),
file('<stdin>',t3_xboole_1) ).
fof(c_0_76_077,lemma,
! [X1] :
( relation(X1)
=> ( relation_rng(X1) = relation_dom(relation_inverse(X1))
& relation_dom(X1) = relation_rng(relation_inverse(X1)) ) ),
file('<stdin>',t37_relat_1) ).
fof(c_0_77_078,lemma,
! [X1] :
( relation(X1)
=> ( relation_dom(X1) = empty_set
<=> relation_rng(X1) = empty_set ) ),
file('<stdin>',t65_relat_1) ).
fof(c_0_78_079,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('<stdin>',t69_enumset1) ).
fof(c_0_79_080,lemma,
! [X1] :
( relation(X1)
=> ( ( relation_dom(X1) = empty_set
| relation_rng(X1) = empty_set )
=> X1 = empty_set ) ),
file('<stdin>',t64_relat_1) ).
fof(c_0_80_081,lemma,
! [X1] : subset(empty_set,X1),
file('<stdin>',t2_xboole_1) ).
fof(c_0_81_082,lemma,
! [X1] : union(powerset(X1)) = X1,
file('<stdin>',t99_zfmisc_1) ).
fof(c_0_82_083,lemma,
! [X1] :
( relation_dom(identity_relation(X1)) = X1
& relation_rng(identity_relation(X1)) = X1 ),
file('<stdin>',t71_relat_1) ).
fof(c_0_83_084,lemma,
! [X1] : singleton(X1) != empty_set,
file('<stdin>',l1_zfmisc_1) ).
fof(c_0_84_085,lemma,
powerset(empty_set) = singleton(empty_set),
file('<stdin>',t1_zfmisc_1) ).
fof(c_0_85_086,lemma,
( relation_dom(empty_set) = empty_set
& relation_rng(empty_set) = empty_set ),
file('<stdin>',t60_relat_1) ).
fof(c_0_86_087,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_image(X3,X2))
<=> ? [X4] :
( in(X4,relation_dom(X3))
& in(ordered_pair(X4,X1),X3)
& in(X4,X2) ) ) ),
c_0_0 ).
fof(c_0_87_088,lemma,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ( X2 != empty_set
=> union_of_subsets(X1,complements_of_subsets(X1,X2)) = subset_difference(X1,cast_to_subset(X1),meet_of_subsets(X1,X2)) ) ),
c_0_1 ).
fof(c_0_88_089,lemma,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ( X2 != empty_set
=> subset_difference(X1,cast_to_subset(X1),union_of_subsets(X1,X2)) = meet_of_subsets(X1,complements_of_subsets(X1,X2)) ) ),
c_0_2 ).
fof(c_0_89_090,lemma,
! [X1,X2,X3,X4] :
( relation(X4)
=> ( in(ordered_pair(X1,X2),relation_composition(identity_relation(X3),X4))
<=> ( in(X1,X3)
& in(ordered_pair(X1,X2),X4) ) ) ),
c_0_3 ).
fof(c_0_90_091,lemma,
! [X1,X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( element(X3,powerset(X1))
=> ( disjoint(X2,X3)
<=> subset(X2,subset_complement(X1,X3)) ) ) ),
c_0_4 ).
fof(c_0_91_092,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_dom(relation_dom_restriction(X3,X2)))
<=> ( in(X1,X2)
& in(X1,relation_dom(X3)) ) ) ),
c_0_5 ).
fof(c_0_92_093,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_rng(relation_rng_restriction(X2,X3)))
<=> ( in(X1,X2)
& in(X1,relation_rng(X3)) ) ) ),
c_0_6 ).
fof(c_0_93_094,lemma,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X1,X3)
& in(X2,X4) ) ),
c_0_7 ).
fof(c_0_94_095,lemma,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X1,X3)
& in(X2,X4) ) ),
c_0_8 ).
fof(c_0_95_096,lemma,
! [X1,X2,X3] :
( element(X3,powerset(X1))
=> ~ ( in(X2,subset_complement(X1,X3))
& in(X2,X3) ) ),
c_0_9 ).
fof(c_0_96_097,lemma,
! [X1,X2,X3,X4] :
( ( subset(X1,X2)
& subset(X3,X4) )
=> subset(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) ),
c_0_10 ).
fof(c_0_97_098,lemma,
! [X1] :
( X1 != empty_set
=> ! [X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( element(X3,X1)
=> ( ~ in(X3,X2)
=> in(X3,subset_complement(X1,X2)) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_98_099,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> subset(relation_rng(relation_composition(X1,X2)),relation_rng(X2)) ) ),
c_0_12 ).
fof(c_0_99_100,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> subset(relation_dom(relation_composition(X1,X2)),relation_dom(X1)) ) ),
c_0_13 ).
fof(c_0_100_101,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X1,X2),X3)
=> ( in(X1,relation_field(X3))
& in(X2,relation_field(X3)) ) ) ),
c_0_14 ).
fof(c_0_101_102,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X1,X2),X3)
=> ( in(X1,relation_dom(X3))
& in(X2,relation_rng(X3)) ) ) ),
c_0_15 ).
fof(c_0_102_103,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( subset(relation_dom(X1),relation_rng(X2))
=> relation_rng(relation_composition(X2,X1)) = relation_rng(X1) ) ) ),
c_0_16 ).
fof(c_0_103_104,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( subset(relation_rng(X1),relation_dom(X2))
=> relation_dom(relation_composition(X1,X2)) = relation_dom(X1) ) ) ),
c_0_17 ).
fof(c_0_104_105,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> ( in(X3,X1)
| subset(X1,set_difference(X2,singleton(X3))) ) ),
c_0_18 ).
fof(c_0_105_106,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_difference(X1,X3),set_difference(X2,X3)) ),
c_0_19 ).
fof(c_0_106_107,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_intersection2(X1,X3),set_intersection2(X2,X3)) ),
c_0_20 ).
fof(c_0_107_108,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> ( subset(cartesian_product2(X1,X3),cartesian_product2(X2,X3))
& subset(cartesian_product2(X3,X1),cartesian_product2(X3,X2)) ) ),
c_0_21 ).
fof(c_0_108_109,lemma,
! [X1,X2,X3] :
( relation(X3)
=> relation_dom_restriction(relation_rng_restriction(X1,X3),X2) = relation_rng_restriction(X1,relation_dom_restriction(X3,X2)) ),
c_0_22 ).
fof(c_0_109_110,lemma,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
& ~ ( ? [X3] : in(X3,set_intersection2(X1,X2))
& disjoint(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[c_0_23]) ).
fof(c_0_110_111,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X3,X2) )
=> subset(set_union2(X1,X3),X2) ),
c_0_24 ).
fof(c_0_111_112,lemma,
! [X1,X2,X3] :
( subset(unordered_pair(X1,X2),X3)
<=> ( in(X1,X3)
& in(X2,X3) ) ),
c_0_25 ).
fof(c_0_112_113,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X1,X3) )
=> subset(X1,set_intersection2(X2,X3)) ),
c_0_26 ).
fof(c_0_113_114,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_rng(relation_dom_restriction(X2,X1)),relation_rng(X2)) ),
c_0_27 ).
fof(c_0_114_115,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_rng(relation_rng_restriction(X1,X2)),relation_rng(X2)) ),
c_0_28 ).
fof(c_0_115_116,lemma,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
=> in(X3,X2) )
=> element(X1,powerset(X2)) ),
c_0_29 ).
fof(c_0_116_117,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_rng(relation_rng_restriction(X1,X2)),X1) ),
c_0_30 ).
fof(c_0_117_118,lemma,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ~ ( X2 != empty_set
& complements_of_subsets(X1,X2) = empty_set ) ),
c_0_31 ).
fof(c_0_118_119,lemma,
! [X1] :
? [X2] :
( in(X1,X2)
& ! [X3,X4] :
( ( in(X3,X2)
& subset(X4,X3) )
=> in(X4,X2) )
& ! [X3] :
( in(X3,X2)
=> in(powerset(X3),X2) )
& ! [X3] :
~ ( subset(X3,X2)
& ~ are_equipotent(X3,X2)
& ~ in(X3,X2) ) ),
inference(fof_simplification,[status(thm)],[c_0_32]) ).
fof(c_0_119_120,lemma,
! [X1] :
( relation(X1)
=> ( ! [X2,X3] : ~ in(ordered_pair(X2,X3),X1)
=> X1 = empty_set ) ),
inference(fof_simplification,[status(thm)],[c_0_33]) ).
fof(c_0_120_121,lemma,
! [X1] :
( relation(X1)
=> subset(X1,cartesian_product2(relation_dom(X1),relation_rng(X1))) ),
c_0_34 ).
fof(c_0_121_122,lemma,
! [X1,X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( in(X3,X2)
=> in(X3,X1) ) ),
c_0_35 ).
fof(c_0_122_123,lemma,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] :
~ ( in(X3,X1)
& in(X3,X2) ) )
& ~ ( ? [X3] :
( in(X3,X1)
& in(X3,X2) )
& disjoint(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[c_0_36]) ).
fof(c_0_123_124,lemma,
! [X1,X2] :
( subset(X1,X2)
=> X2 = set_union2(X1,set_difference(X2,X1)) ),
c_0_37 ).
fof(c_0_124_125,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( subset(X1,X2)
=> ( subset(relation_dom(X1),relation_dom(X2))
& subset(relation_rng(X1),relation_rng(X2)) ) ) ) ),
c_0_38 ).
fof(c_0_125_126,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& disjoint(X2,X3) )
=> disjoint(X1,X3) ),
c_0_39 ).
fof(c_0_126_127,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ),
c_0_40 ).
fof(c_0_127_128,negated_conjecture,
~ ! [X1,X2] :
( relation(X2)
=> subset(relation_image(X2,X1),relation_rng(X2)) ),
inference(assume_negation,[status(cth)],[c_0_41]) ).
fof(c_0_128_129,lemma,
! [X1,X2] :
( relation(X2)
=> relation_dom(relation_dom_restriction(X2,X1)) = set_intersection2(relation_dom(X2),X1) ),
c_0_42 ).
fof(c_0_129_130,lemma,
! [X1,X2] :
( relation(X2)
=> relation_rng(relation_rng_restriction(X1,X2)) = set_intersection2(relation_rng(X2),X1) ),
c_0_43 ).
fof(c_0_130_131,lemma,
! [X1,X2] :
( set_difference(X1,singleton(X2)) = X1
<=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[c_0_44]) ).
fof(c_0_131_132,lemma,
! [X1,X2] :
~ ( disjoint(singleton(X1),X2)
& in(X1,X2) ),
c_0_45 ).
fof(c_0_132_133,lemma,
! [X1,X2] : set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
c_0_46 ).
fof(c_0_133_134,lemma,
! [X1,X2] : set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
c_0_47 ).
fof(c_0_134_135,lemma,
! [X1,X2] : set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
c_0_48 ).
fof(c_0_135_136,lemma,
! [X1,X2,X3,X4] :
~ ( unordered_pair(X1,X2) = unordered_pair(X3,X4)
& X1 != X3
& X1 != X4 ),
c_0_49 ).
fof(c_0_136_137,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_dom_restriction(X2,X1),X2) ),
c_0_50 ).
fof(c_0_137_138,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_rng_restriction(X1,X2),X2) ),
c_0_51 ).
fof(c_0_138_139,lemma,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
c_0_52 ).
fof(c_0_139_140,lemma,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
c_0_53 ).
fof(c_0_140_141,lemma,
! [X1,X2,X3,X4] :
( ordered_pair(X1,X2) = ordered_pair(X3,X4)
=> ( X1 = X3
& X2 = X4 ) ),
c_0_54 ).
fof(c_0_141_142,lemma,
! [X1,X2] :
~ ( subset(X1,X2)
& proper_subset(X2,X1) ),
c_0_55 ).
fof(c_0_142_143,lemma,
! [X1,X2] :
( subset(singleton(X1),singleton(X2))
=> X1 = X2 ),
c_0_56 ).
fof(c_0_143_144,lemma,
! [X1,X2] :
( in(X1,X2)
=> set_union2(singleton(X1),X2) = X2 ),
c_0_57 ).
fof(c_0_144_145,lemma,
! [X1,X2] :
( in(X1,X2)
=> set_union2(singleton(X1),X2) = X2 ),
c_0_58 ).
fof(c_0_145_146,lemma,
! [X1,X2] :
( in(X1,X2)
=> subset(X1,union(X2)) ),
c_0_59 ).
fof(c_0_146_147,lemma,
! [X1,X2] :
( in(X1,X2)
=> subset(X1,union(X2)) ),
c_0_60 ).
fof(c_0_147_148,lemma,
! [X1,X2] :
( relation(X2)
=> relation_dom_restriction(X2,X1) = relation_composition(identity_relation(X1),X2) ),
c_0_61 ).
fof(c_0_148_149,lemma,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
c_0_62 ).
fof(c_0_149_150,lemma,
! [X1,X2] : subset(set_difference(X1,X2),X1),
c_0_63 ).
fof(c_0_150_151,lemma,
! [X1,X2] : subset(set_intersection2(X1,X2),X1),
c_0_64 ).
fof(c_0_151_152,lemma,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
c_0_65 ).
fof(c_0_152_153,lemma,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
c_0_66 ).
fof(c_0_153_154,lemma,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_difference(X1,X2) = X1 ),
c_0_67 ).
fof(c_0_154_155,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_intersection2(X1,X2) = X1 ),
c_0_68 ).
fof(c_0_155_156,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_union2(X1,X2) = X2 ),
c_0_69 ).
fof(c_0_156_157,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
c_0_70 ).
fof(c_0_157_158,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
c_0_71 ).
fof(c_0_158_159,lemma,
! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
inference(fof_simplification,[status(thm)],[c_0_72]) ).
fof(c_0_159_160,lemma,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X2 = X3 ),
c_0_73 ).
fof(c_0_160_161,lemma,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X1 = X2 ),
c_0_74 ).
fof(c_0_161_162,lemma,
! [X1] :
( subset(X1,empty_set)
=> X1 = empty_set ),
c_0_75 ).
fof(c_0_162_163,lemma,
! [X1] :
( relation(X1)
=> ( relation_rng(X1) = relation_dom(relation_inverse(X1))
& relation_dom(X1) = relation_rng(relation_inverse(X1)) ) ),
c_0_76 ).
fof(c_0_163_164,lemma,
! [X1] :
( relation(X1)
=> ( relation_dom(X1) = empty_set
<=> relation_rng(X1) = empty_set ) ),
c_0_77 ).
fof(c_0_164_165,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
c_0_78 ).
fof(c_0_165_166,lemma,
! [X1] :
( relation(X1)
=> ( ( relation_dom(X1) = empty_set
| relation_rng(X1) = empty_set )
=> X1 = empty_set ) ),
c_0_79 ).
fof(c_0_166_167,lemma,
! [X1] : subset(empty_set,X1),
c_0_80 ).
fof(c_0_167_168,lemma,
! [X1] : union(powerset(X1)) = X1,
c_0_81 ).
fof(c_0_168_169,lemma,
! [X1] :
( relation_dom(identity_relation(X1)) = X1
& relation_rng(identity_relation(X1)) = X1 ),
c_0_82 ).
fof(c_0_169_170,lemma,
! [X1] : singleton(X1) != empty_set,
c_0_83 ).
fof(c_0_170_171,lemma,
powerset(empty_set) = singleton(empty_set),
c_0_84 ).
fof(c_0_171_172,lemma,
( relation_dom(empty_set) = empty_set
& relation_rng(empty_set) = empty_set ),
c_0_85 ).
fof(c_0_172_173,lemma,
! [X5,X6,X7,X9] :
( ( in(esk3_3(X5,X6,X7),relation_dom(X7))
| ~ in(X5,relation_image(X7,X6))
| ~ relation(X7) )
& ( in(ordered_pair(esk3_3(X5,X6,X7),X5),X7)
| ~ in(X5,relation_image(X7,X6))
| ~ relation(X7) )
& ( in(esk3_3(X5,X6,X7),X6)
| ~ in(X5,relation_image(X7,X6))
| ~ relation(X7) )
& ( ~ in(X9,relation_dom(X7))
| ~ in(ordered_pair(X9,X5),X7)
| ~ in(X9,X6)
| in(X5,relation_image(X7,X6))
| ~ relation(X7) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_86])])])])]) ).
fof(c_0_173_174,lemma,
! [X3,X4] :
( ~ element(X4,powerset(powerset(X3)))
| X4 = empty_set
| union_of_subsets(X3,complements_of_subsets(X3,X4)) = subset_difference(X3,cast_to_subset(X3),meet_of_subsets(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_87])]) ).
fof(c_0_174_175,lemma,
! [X3,X4] :
( ~ element(X4,powerset(powerset(X3)))
| X4 = empty_set
| subset_difference(X3,cast_to_subset(X3),union_of_subsets(X3,X4)) = meet_of_subsets(X3,complements_of_subsets(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_88])]) ).
fof(c_0_175_176,lemma,
! [X5,X6,X7,X8] :
( ( in(X5,X7)
| ~ in(ordered_pair(X5,X6),relation_composition(identity_relation(X7),X8))
| ~ relation(X8) )
& ( in(ordered_pair(X5,X6),X8)
| ~ in(ordered_pair(X5,X6),relation_composition(identity_relation(X7),X8))
| ~ relation(X8) )
& ( ~ in(X5,X7)
| ~ in(ordered_pair(X5,X6),X8)
| in(ordered_pair(X5,X6),relation_composition(identity_relation(X7),X8))
| ~ relation(X8) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_89])])]) ).
fof(c_0_176_177,lemma,
! [X4,X5,X6] :
( ( ~ disjoint(X5,X6)
| subset(X5,subset_complement(X4,X6))
| ~ element(X6,powerset(X4))
| ~ element(X5,powerset(X4)) )
& ( ~ subset(X5,subset_complement(X4,X6))
| disjoint(X5,X6)
| ~ element(X6,powerset(X4))
| ~ element(X5,powerset(X4)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_90])])])]) ).
fof(c_0_177_178,lemma,
! [X4,X5,X6] :
( ( in(X4,X5)
| ~ in(X4,relation_dom(relation_dom_restriction(X6,X5)))
| ~ relation(X6) )
& ( in(X4,relation_dom(X6))
| ~ in(X4,relation_dom(relation_dom_restriction(X6,X5)))
| ~ relation(X6) )
& ( ~ in(X4,X5)
| ~ in(X4,relation_dom(X6))
| in(X4,relation_dom(relation_dom_restriction(X6,X5)))
| ~ relation(X6) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_91])])]) ).
fof(c_0_178_179,lemma,
! [X4,X5,X6] :
( ( in(X4,X5)
| ~ in(X4,relation_rng(relation_rng_restriction(X5,X6)))
| ~ relation(X6) )
& ( in(X4,relation_rng(X6))
| ~ in(X4,relation_rng(relation_rng_restriction(X5,X6)))
| ~ relation(X6) )
& ( ~ in(X4,X5)
| ~ in(X4,relation_rng(X6))
| in(X4,relation_rng(relation_rng_restriction(X5,X6)))
| ~ relation(X6) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_92])])]) ).
fof(c_0_179_180,lemma,
! [X5,X6,X7,X8,X9,X10,X11,X12] :
( ( in(X5,X7)
| ~ in(ordered_pair(X5,X6),cartesian_product2(X7,X8)) )
& ( in(X6,X8)
| ~ in(ordered_pair(X5,X6),cartesian_product2(X7,X8)) )
& ( ~ in(X9,X11)
| ~ in(X10,X12)
| in(ordered_pair(X9,X10),cartesian_product2(X11,X12)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_93])])])])]) ).
fof(c_0_180_181,lemma,
! [X5,X6,X7,X8,X9,X10,X11,X12] :
( ( in(X5,X7)
| ~ in(ordered_pair(X5,X6),cartesian_product2(X7,X8)) )
& ( in(X6,X8)
| ~ in(ordered_pair(X5,X6),cartesian_product2(X7,X8)) )
& ( ~ in(X9,X11)
| ~ in(X10,X12)
| in(ordered_pair(X9,X10),cartesian_product2(X11,X12)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_94])])])])]) ).
fof(c_0_181_182,lemma,
! [X4,X5,X6] :
( ~ element(X6,powerset(X4))
| ~ in(X5,subset_complement(X4,X6))
| ~ in(X5,X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_95])]) ).
fof(c_0_182_183,lemma,
! [X5,X6,X7,X8] :
( ~ subset(X5,X6)
| ~ subset(X7,X8)
| subset(cartesian_product2(X5,X7),cartesian_product2(X6,X8)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_96])]) ).
fof(c_0_183_184,lemma,
! [X4,X5,X6] :
( X4 = empty_set
| ~ element(X5,powerset(X4))
| ~ element(X6,X4)
| in(X6,X5)
| in(X6,subset_complement(X4,X5)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_97])])]) ).
fof(c_0_184_185,lemma,
! [X3,X4] :
( ~ relation(X3)
| ~ relation(X4)
| subset(relation_rng(relation_composition(X3,X4)),relation_rng(X4)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_98])])]) ).
fof(c_0_185_186,lemma,
! [X3,X4] :
( ~ relation(X3)
| ~ relation(X4)
| subset(relation_dom(relation_composition(X3,X4)),relation_dom(X3)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_99])])]) ).
fof(c_0_186_187,lemma,
! [X4,X5,X6] :
( ( in(X4,relation_field(X6))
| ~ in(ordered_pair(X4,X5),X6)
| ~ relation(X6) )
& ( in(X5,relation_field(X6))
| ~ in(ordered_pair(X4,X5),X6)
| ~ relation(X6) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_100])])]) ).
fof(c_0_187_188,lemma,
! [X4,X5,X6] :
( ( in(X4,relation_dom(X6))
| ~ in(ordered_pair(X4,X5),X6)
| ~ relation(X6) )
& ( in(X5,relation_rng(X6))
| ~ in(ordered_pair(X4,X5),X6)
| ~ relation(X6) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_101])])]) ).
fof(c_0_188_189,lemma,
! [X3,X4] :
( ~ relation(X3)
| ~ relation(X4)
| ~ subset(relation_dom(X3),relation_rng(X4))
| relation_rng(relation_composition(X4,X3)) = relation_rng(X3) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_102])])]) ).
fof(c_0_189_190,lemma,
! [X3,X4] :
( ~ relation(X3)
| ~ relation(X4)
| ~ subset(relation_rng(X3),relation_dom(X4))
| relation_dom(relation_composition(X3,X4)) = relation_dom(X3) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_103])])]) ).
fof(c_0_190_191,lemma,
! [X4,X5,X6] :
( ~ subset(X4,X5)
| in(X6,X4)
| subset(X4,set_difference(X5,singleton(X6))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_104])])])]) ).
fof(c_0_191_192,lemma,
! [X4,X5,X6] :
( ~ subset(X4,X5)
| subset(set_difference(X4,X6),set_difference(X5,X6)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_105])])])]) ).
fof(c_0_192_193,lemma,
! [X4,X5,X6] :
( ~ subset(X4,X5)
| subset(set_intersection2(X4,X6),set_intersection2(X5,X6)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_106])])])]) ).
fof(c_0_193_194,lemma,
! [X4,X5,X6,X7] :
( ( subset(cartesian_product2(X4,X6),cartesian_product2(X5,X6))
| ~ subset(X4,X5) )
& ( subset(cartesian_product2(X7,X4),cartesian_product2(X7,X5))
| ~ subset(X4,X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_107])])])])]) ).
fof(c_0_194_195,lemma,
! [X4,X5,X6] :
( ~ relation(X6)
| relation_dom_restriction(relation_rng_restriction(X4,X6),X5) = relation_rng_restriction(X4,relation_dom_restriction(X6,X5)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_108])]) ).
fof(c_0_195_196,lemma,
! [X4,X5,X7,X8,X9] :
( ( disjoint(X4,X5)
| in(esk7_2(X4,X5),set_intersection2(X4,X5)) )
& ( ~ in(X9,set_intersection2(X7,X8))
| ~ disjoint(X7,X8) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_109])])])])]) ).
fof(c_0_196_197,lemma,
! [X4,X5,X6] :
( ~ subset(X4,X5)
| ~ subset(X6,X5)
| subset(set_union2(X4,X6),X5) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_110])]) ).
fof(c_0_197_198,lemma,
! [X4,X5,X6,X7,X8,X9] :
( ( in(X4,X6)
| ~ subset(unordered_pair(X4,X5),X6) )
& ( in(X5,X6)
| ~ subset(unordered_pair(X4,X5),X6) )
& ( ~ in(X7,X9)
| ~ in(X8,X9)
| subset(unordered_pair(X7,X8),X9) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_111])])])])]) ).
fof(c_0_198_199,lemma,
! [X4,X5,X6] :
( ~ subset(X4,X5)
| ~ subset(X4,X6)
| subset(X4,set_intersection2(X5,X6)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_112])]) ).
fof(c_0_199_200,lemma,
! [X3,X4] :
( ~ relation(X4)
| subset(relation_rng(relation_dom_restriction(X4,X3)),relation_rng(X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_113])]) ).
fof(c_0_200_201,lemma,
! [X3,X4] :
( ~ relation(X4)
| subset(relation_rng(relation_rng_restriction(X3,X4)),relation_rng(X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_114])]) ).
fof(c_0_201_202,lemma,
! [X4,X5] :
( ( in(esk1_2(X4,X5),X4)
| element(X4,powerset(X5)) )
& ( ~ in(esk1_2(X4,X5),X5)
| element(X4,powerset(X5)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_115])])])]) ).
fof(c_0_202_203,lemma,
! [X3,X4] :
( ~ relation(X4)
| subset(relation_rng(relation_rng_restriction(X3,X4)),X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_116])]) ).
fof(c_0_203_204,lemma,
! [X3,X4] :
( ~ element(X4,powerset(powerset(X3)))
| X4 = empty_set
| complements_of_subsets(X3,X4) != empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_117])]) ).
fof(c_0_204_205,lemma,
! [X5,X7,X8,X9,X10] :
( in(X5,esk2_1(X5))
& ( ~ in(X7,esk2_1(X5))
| ~ subset(X8,X7)
| in(X8,esk2_1(X5)) )
& ( ~ in(X9,esk2_1(X5))
| in(powerset(X9),esk2_1(X5)) )
& ( ~ subset(X10,esk2_1(X5))
| are_equipotent(X10,esk2_1(X5))
| in(X10,esk2_1(X5)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_118])])])]) ).
fof(c_0_205_206,lemma,
! [X4] :
( ~ relation(X4)
| in(ordered_pair(esk8_1(X4),esk9_1(X4)),X4)
| X4 = empty_set ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_119])])]) ).
fof(c_0_206_207,lemma,
! [X2] :
( ~ relation(X2)
| subset(X2,cartesian_product2(relation_dom(X2),relation_rng(X2))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_120])]) ).
fof(c_0_207_208,lemma,
! [X4,X5,X6] :
( ~ element(X5,powerset(X4))
| ~ in(X6,X5)
| in(X6,X4) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_121])])]) ).
fof(c_0_208_209,lemma,
! [X4,X5,X7,X8,X9] :
( ( in(esk6_2(X4,X5),X4)
| disjoint(X4,X5) )
& ( in(esk6_2(X4,X5),X5)
| disjoint(X4,X5) )
& ( ~ in(X9,X7)
| ~ in(X9,X8)
| ~ disjoint(X7,X8) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_122])])])])])]) ).
fof(c_0_209_210,lemma,
! [X3,X4] :
( ~ subset(X3,X4)
| X4 = set_union2(X3,set_difference(X4,X3)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_123])]) ).
fof(c_0_210_211,lemma,
! [X3,X4] :
( ( subset(relation_dom(X3),relation_dom(X4))
| ~ subset(X3,X4)
| ~ relation(X4)
| ~ relation(X3) )
& ( subset(relation_rng(X3),relation_rng(X4))
| ~ subset(X3,X4)
| ~ relation(X4)
| ~ relation(X3) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_124])])])]) ).
fof(c_0_211_212,lemma,
! [X4,X5,X6] :
( ~ subset(X4,X5)
| ~ disjoint(X5,X6)
| disjoint(X4,X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_125])]) ).
fof(c_0_212_213,lemma,
! [X4,X5,X6] :
( ~ subset(X4,X5)
| ~ subset(X5,X6)
| subset(X4,X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_126])]) ).
fof(c_0_213_214,negated_conjecture,
( relation(esk5_0)
& ~ subset(relation_image(esk5_0,esk4_0),relation_rng(esk5_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_127])])]) ).
fof(c_0_214_215,lemma,
! [X3,X4] :
( ~ relation(X4)
| relation_dom(relation_dom_restriction(X4,X3)) = set_intersection2(relation_dom(X4),X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_128])]) ).
fof(c_0_215_216,lemma,
! [X3,X4] :
( ~ relation(X4)
| relation_rng(relation_rng_restriction(X3,X4)) = set_intersection2(relation_rng(X4),X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_129])]) ).
fof(c_0_216_217,lemma,
! [X3,X4,X5,X6] :
( ( set_difference(X3,singleton(X4)) != X3
| ~ in(X4,X3) )
& ( in(X6,X5)
| set_difference(X5,singleton(X6)) = X5 ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_130])])])]) ).
fof(c_0_217_218,lemma,
! [X3,X4] :
( ~ disjoint(singleton(X3),X4)
| ~ in(X3,X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_131])]) ).
fof(c_0_218_219,lemma,
! [X3,X4] : set_difference(X3,set_difference(X3,X4)) = set_intersection2(X3,X4),
inference(variable_rename,[status(thm)],[c_0_132]) ).
fof(c_0_219_220,lemma,
! [X3,X4] : set_difference(set_union2(X3,X4),X4) = set_difference(X3,X4),
inference(variable_rename,[status(thm)],[c_0_133]) ).
fof(c_0_220_221,lemma,
! [X3,X4] : set_union2(X3,set_difference(X4,X3)) = set_union2(X3,X4),
inference(variable_rename,[status(thm)],[c_0_134]) ).
fof(c_0_221_222,lemma,
! [X5,X6,X7,X8] :
( unordered_pair(X5,X6) != unordered_pair(X7,X8)
| X5 = X7
| X5 = X8 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_135])]) ).
fof(c_0_222_223,lemma,
! [X3,X4] :
( ~ relation(X4)
| subset(relation_dom_restriction(X4,X3),X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_136])]) ).
fof(c_0_223_224,lemma,
! [X3,X4] :
( ~ relation(X4)
| subset(relation_rng_restriction(X3,X4),X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_137])]) ).
fof(c_0_224_225,lemma,
! [X3,X4,X5,X6] :
( ( ~ subset(singleton(X3),X4)
| in(X3,X4) )
& ( ~ in(X5,X6)
| subset(singleton(X5),X6) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_138])])])]) ).
fof(c_0_225_226,lemma,
! [X3,X4,X5,X6] :
( ( ~ subset(singleton(X3),X4)
| in(X3,X4) )
& ( ~ in(X5,X6)
| subset(singleton(X5),X6) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_139])])])]) ).
fof(c_0_226_227,lemma,
! [X5,X6,X7,X8] :
( ( X5 = X7
| ordered_pair(X5,X6) != ordered_pair(X7,X8) )
& ( X6 = X8
| ordered_pair(X5,X6) != ordered_pair(X7,X8) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_140])])]) ).
fof(c_0_227_228,lemma,
! [X3,X4] :
( ~ subset(X3,X4)
| ~ proper_subset(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_141])]) ).
fof(c_0_228_229,lemma,
! [X3,X4] :
( ~ subset(singleton(X3),singleton(X4))
| X3 = X4 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_142])]) ).
fof(c_0_229_230,lemma,
! [X3,X4] :
( ~ in(X3,X4)
| set_union2(singleton(X3),X4) = X4 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_143])]) ).
fof(c_0_230_231,lemma,
! [X3,X4] :
( ~ in(X3,X4)
| set_union2(singleton(X3),X4) = X4 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_144])]) ).
fof(c_0_231_232,lemma,
! [X3,X4] :
( ~ in(X3,X4)
| subset(X3,union(X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_145])]) ).
fof(c_0_232_233,lemma,
! [X3,X4] :
( ~ in(X3,X4)
| subset(X3,union(X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_146])]) ).
fof(c_0_233_234,lemma,
! [X3,X4] :
( ~ relation(X4)
| relation_dom_restriction(X4,X3) = relation_composition(identity_relation(X3),X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_147])]) ).
fof(c_0_234_235,lemma,
! [X3,X4] : subset(X3,set_union2(X3,X4)),
inference(variable_rename,[status(thm)],[c_0_148]) ).
fof(c_0_235_236,lemma,
! [X3,X4] : subset(set_difference(X3,X4),X3),
inference(variable_rename,[status(thm)],[c_0_149]) ).
fof(c_0_236_237,lemma,
! [X3,X4] : subset(set_intersection2(X3,X4),X3),
inference(variable_rename,[status(thm)],[c_0_150]) ).
fof(c_0_237_238,lemma,
! [X3,X4,X5,X6] :
( ( ~ subset(X3,singleton(X4))
| X3 = empty_set
| X3 = singleton(X4) )
& ( X5 != empty_set
| subset(X5,singleton(X6)) )
& ( X5 != singleton(X6)
| subset(X5,singleton(X6)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_151])])])])]) ).
fof(c_0_238_239,lemma,
! [X3,X4,X5,X6] :
( ( ~ subset(X3,singleton(X4))
| X3 = empty_set
| X3 = singleton(X4) )
& ( X5 != empty_set
| subset(X5,singleton(X6)) )
& ( X5 != singleton(X6)
| subset(X5,singleton(X6)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_152])])])])]) ).
fof(c_0_239_240,lemma,
! [X3,X4,X5,X6] :
( ( ~ disjoint(X3,X4)
| set_difference(X3,X4) = X3 )
& ( set_difference(X5,X6) != X5
| disjoint(X5,X6) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_153])])])]) ).
fof(c_0_240_241,lemma,
! [X3,X4] :
( ~ subset(X3,X4)
| set_intersection2(X3,X4) = X3 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_154])]) ).
fof(c_0_241_242,lemma,
! [X3,X4] :
( ~ subset(X3,X4)
| set_union2(X3,X4) = X4 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_155])]) ).
fof(c_0_242_243,lemma,
! [X3,X4,X5,X6] :
( ( set_difference(X3,X4) != empty_set
| subset(X3,X4) )
& ( ~ subset(X5,X6)
| set_difference(X5,X6) = empty_set ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_156])])])]) ).
fof(c_0_243_244,lemma,
! [X3,X4,X5,X6] :
( ( set_difference(X3,X4) != empty_set
| subset(X3,X4) )
& ( ~ subset(X5,X6)
| set_difference(X5,X6) = empty_set ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_157])])])]) ).
fof(c_0_244_245,lemma,
! [X3,X4] :
( in(X3,X4)
| disjoint(singleton(X3),X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_158])]) ).
fof(c_0_245_246,lemma,
! [X4,X5,X6] :
( singleton(X4) != unordered_pair(X5,X6)
| X5 = X6 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_159])]) ).
fof(c_0_246_247,lemma,
! [X4,X5,X6] :
( singleton(X4) != unordered_pair(X5,X6)
| X4 = X5 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_160])])])]) ).
fof(c_0_247_248,lemma,
! [X2] :
( ~ subset(X2,empty_set)
| X2 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_161])]) ).
fof(c_0_248_249,lemma,
! [X2] :
( ( relation_rng(X2) = relation_dom(relation_inverse(X2))
| ~ relation(X2) )
& ( relation_dom(X2) = relation_rng(relation_inverse(X2))
| ~ relation(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_162])])]) ).
fof(c_0_249_250,lemma,
! [X2] :
( ( relation_dom(X2) != empty_set
| relation_rng(X2) = empty_set
| ~ relation(X2) )
& ( relation_rng(X2) != empty_set
| relation_dom(X2) = empty_set
| ~ relation(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_163])])]) ).
fof(c_0_250_251,lemma,
! [X2] : unordered_pair(X2,X2) = singleton(X2),
inference(variable_rename,[status(thm)],[c_0_164]) ).
fof(c_0_251_252,lemma,
! [X2] :
( ( relation_dom(X2) != empty_set
| X2 = empty_set
| ~ relation(X2) )
& ( relation_rng(X2) != empty_set
| X2 = empty_set
| ~ relation(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_165])])]) ).
fof(c_0_252_253,lemma,
! [X2] : subset(empty_set,X2),
inference(variable_rename,[status(thm)],[c_0_166]) ).
fof(c_0_253_254,lemma,
! [X2] : union(powerset(X2)) = X2,
inference(variable_rename,[status(thm)],[c_0_167]) ).
fof(c_0_254_255,lemma,
! [X2,X3] :
( relation_dom(identity_relation(X2)) = X2
& relation_rng(identity_relation(X3)) = X3 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_168])])]) ).
fof(c_0_255_256,lemma,
! [X2] : singleton(X2) != empty_set,
inference(variable_rename,[status(thm)],[c_0_169]) ).
fof(c_0_256_257,lemma,
powerset(empty_set) = singleton(empty_set),
c_0_170 ).
fof(c_0_257_258,lemma,
( relation_dom(empty_set) = empty_set
& relation_rng(empty_set) = empty_set ),
c_0_171 ).
cnf(c_0_258_259,lemma,
( in(ordered_pair(esk3_3(X2,X3,X1),X2),X1)
| ~ relation(X1)
| ~ in(X2,relation_image(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_172]) ).
cnf(c_0_259_260,lemma,
( in(esk3_3(X2,X3,X1),relation_dom(X1))
| ~ relation(X1)
| ~ in(X2,relation_image(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_172]) ).
cnf(c_0_260_261,lemma,
( in(esk3_3(X2,X3,X1),X3)
| ~ relation(X1)
| ~ in(X2,relation_image(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_172]) ).
cnf(c_0_261_262,lemma,
( union_of_subsets(X1,complements_of_subsets(X1,X2)) = subset_difference(X1,cast_to_subset(X1),meet_of_subsets(X1,X2))
| X2 = empty_set
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_173]) ).
cnf(c_0_262_263,lemma,
( subset_difference(X1,cast_to_subset(X1),union_of_subsets(X1,X2)) = meet_of_subsets(X1,complements_of_subsets(X1,X2))
| X2 = empty_set
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_174]) ).
cnf(c_0_263_264,lemma,
( in(ordered_pair(X2,X3),relation_composition(identity_relation(X4),X1))
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1)
| ~ in(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_175]) ).
cnf(c_0_264_265,lemma,
( in(ordered_pair(X2,X3),X1)
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),relation_composition(identity_relation(X4),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_175]) ).
cnf(c_0_265_266,lemma,
( in(X2,relation_image(X1,X3))
| ~ relation(X1)
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,X2),X1)
| ~ in(X4,relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_172]) ).
cnf(c_0_266_267,lemma,
( in(X2,X4)
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),relation_composition(identity_relation(X4),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_175]) ).
cnf(c_0_267_268,lemma,
( disjoint(X1,X3)
| ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2))
| ~ subset(X1,subset_complement(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_176]) ).
cnf(c_0_268_269,lemma,
( in(X2,relation_dom(X1))
| ~ relation(X1)
| ~ in(X2,relation_dom(relation_dom_restriction(X1,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_177]) ).
cnf(c_0_269_270,lemma,
( in(X2,relation_rng(X1))
| ~ relation(X1)
| ~ in(X2,relation_rng(relation_rng_restriction(X3,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_178]) ).
cnf(c_0_270_271,lemma,
( in(X2,X3)
| ~ relation(X1)
| ~ in(X2,relation_dom(relation_dom_restriction(X1,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_177]) ).
cnf(c_0_271_272,lemma,
( in(X2,X3)
| ~ relation(X1)
| ~ in(X2,relation_rng(relation_rng_restriction(X3,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_178]) ).
cnf(c_0_272_273,lemma,
( in(X2,relation_dom(relation_dom_restriction(X1,X3)))
| ~ relation(X1)
| ~ in(X2,relation_dom(X1))
| ~ in(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_177]) ).
cnf(c_0_273_274,lemma,
( in(X2,relation_rng(relation_rng_restriction(X3,X1)))
| ~ relation(X1)
| ~ in(X2,relation_rng(X1))
| ~ in(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_178]) ).
cnf(c_0_274_275,lemma,
( subset(X1,subset_complement(X2,X3))
| ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2))
| ~ disjoint(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_176]) ).
cnf(c_0_275_276,lemma,
( in(X1,X3)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_179]) ).
cnf(c_0_276_277,lemma,
( in(X2,X4)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_179]) ).
cnf(c_0_277_278,lemma,
( in(X1,X3)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_180]) ).
cnf(c_0_278_279,lemma,
( in(X2,X4)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_180]) ).
cnf(c_0_279_280,lemma,
( ~ in(X1,X2)
| ~ in(X1,subset_complement(X3,X2))
| ~ element(X2,powerset(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_181]) ).
cnf(c_0_280_281,lemma,
( subset(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
| ~ subset(X2,X4)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_182]) ).
cnf(c_0_281_282,lemma,
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_179]) ).
cnf(c_0_282_283,lemma,
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_180]) ).
cnf(c_0_283_284,lemma,
( in(X1,subset_complement(X2,X3))
| in(X1,X3)
| X2 = empty_set
| ~ element(X1,X2)
| ~ element(X3,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_183]) ).
cnf(c_0_284_285,lemma,
( subset(relation_rng(relation_composition(X1,X2)),relation_rng(X2))
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_184]) ).
cnf(c_0_285_286,lemma,
( subset(relation_dom(relation_composition(X1,X2)),relation_dom(X1))
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_185]) ).
cnf(c_0_286_287,lemma,
( in(X2,relation_field(X1))
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_186]) ).
cnf(c_0_287_288,lemma,
( in(X3,relation_field(X1))
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_186]) ).
cnf(c_0_288_289,lemma,
( in(X2,relation_dom(X1))
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_187]) ).
cnf(c_0_289_290,lemma,
( in(X3,relation_rng(X1))
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_187]) ).
cnf(c_0_290_291,lemma,
( relation_rng(relation_composition(X1,X2)) = relation_rng(X2)
| ~ subset(relation_dom(X2),relation_rng(X1))
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_188]) ).
cnf(c_0_291_292,lemma,
( relation_dom(relation_composition(X1,X2)) = relation_dom(X1)
| ~ subset(relation_rng(X1),relation_dom(X2))
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_189]) ).
cnf(c_0_292_293,lemma,
( subset(X1,set_difference(X2,singleton(X3)))
| in(X3,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_190]) ).
cnf(c_0_293_294,lemma,
( subset(set_difference(X1,X2),set_difference(X3,X2))
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_191]) ).
cnf(c_0_294_295,lemma,
( subset(set_intersection2(X1,X2),set_intersection2(X3,X2))
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_192]) ).
cnf(c_0_295_296,lemma,
( subset(cartesian_product2(X1,X3),cartesian_product2(X2,X3))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_193]) ).
cnf(c_0_296_297,lemma,
( subset(cartesian_product2(X3,X1),cartesian_product2(X3,X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_193]) ).
cnf(c_0_297_298,lemma,
( relation_dom_restriction(relation_rng_restriction(X1,X2),X3) = relation_rng_restriction(X1,relation_dom_restriction(X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_194]) ).
cnf(c_0_298_299,lemma,
( ~ disjoint(X1,X2)
| ~ in(X3,set_intersection2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_195]) ).
cnf(c_0_299_300,lemma,
( subset(set_union2(X1,X2),X3)
| ~ subset(X2,X3)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_196]) ).
cnf(c_0_300_301,lemma,
( subset(unordered_pair(X1,X2),X3)
| ~ in(X2,X3)
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_197]) ).
cnf(c_0_301_302,lemma,
( subset(X1,set_intersection2(X2,X3))
| ~ subset(X1,X3)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_198]) ).
cnf(c_0_302_303,lemma,
( subset(relation_rng(relation_dom_restriction(X1,X2)),relation_rng(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_199]) ).
cnf(c_0_303_304,lemma,
( subset(relation_rng(relation_rng_restriction(X1,X2)),relation_rng(X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_200]) ).
cnf(c_0_304_305,lemma,
( element(X1,powerset(X2))
| ~ in(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_201]) ).
cnf(c_0_305_306,lemma,
( in(esk7_2(X1,X2),set_intersection2(X1,X2))
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_195]) ).
cnf(c_0_306_307,lemma,
( subset(relation_rng(relation_rng_restriction(X1,X2)),X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_202]) ).
cnf(c_0_307_308,lemma,
( in(X1,X3)
| ~ subset(unordered_pair(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_197]) ).
cnf(c_0_308_309,lemma,
( in(X2,X3)
| ~ subset(unordered_pair(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_197]) ).
cnf(c_0_309_310,lemma,
( X2 = empty_set
| complements_of_subsets(X1,X2) != empty_set
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_203]) ).
cnf(c_0_310_311,lemma,
( in(X1,esk2_1(X2))
| ~ subset(X1,X3)
| ~ in(X3,esk2_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_204]) ).
cnf(c_0_311_312,lemma,
( X1 = empty_set
| in(ordered_pair(esk8_1(X1),esk9_1(X1)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_205]) ).
cnf(c_0_312_313,lemma,
( in(X1,esk2_1(X2))
| are_equipotent(X1,esk2_1(X2))
| ~ subset(X1,esk2_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_204]) ).
cnf(c_0_313_314,lemma,
( subset(X1,cartesian_product2(relation_dom(X1),relation_rng(X1)))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_206]) ).
cnf(c_0_314_315,lemma,
( in(X1,X2)
| ~ in(X1,X3)
| ~ element(X3,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_207]) ).
cnf(c_0_315_316,lemma,
( ~ disjoint(X1,X2)
| ~ in(X3,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_208]) ).
cnf(c_0_316_317,lemma,
( X1 = set_union2(X2,set_difference(X1,X2))
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_209]) ).
cnf(c_0_317_318,lemma,
( subset(relation_dom(X1),relation_dom(X2))
| ~ relation(X1)
| ~ relation(X2)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_210]) ).
cnf(c_0_318_319,lemma,
( subset(relation_rng(X1),relation_rng(X2))
| ~ relation(X1)
| ~ relation(X2)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_210]) ).
cnf(c_0_319_320,lemma,
( element(X1,powerset(X2))
| in(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_201]) ).
cnf(c_0_320_321,lemma,
( disjoint(X1,X2)
| ~ disjoint(X3,X2)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_211]) ).
cnf(c_0_321_322,lemma,
( subset(X1,X2)
| ~ subset(X3,X2)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_212]) ).
cnf(c_0_322_323,lemma,
( in(powerset(X1),esk2_1(X2))
| ~ in(X1,esk2_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_204]) ).
cnf(c_0_323_324,negated_conjecture,
~ subset(relation_image(esk5_0,esk4_0),relation_rng(esk5_0)),
inference(split_conjunct,[status(thm)],[c_0_213]) ).
cnf(c_0_324_325,lemma,
( relation_dom(relation_dom_restriction(X1,X2)) = set_intersection2(relation_dom(X1),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_214]) ).
cnf(c_0_325_326,lemma,
( relation_rng(relation_rng_restriction(X1,X2)) = set_intersection2(relation_rng(X2),X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_215]) ).
cnf(c_0_326_327,lemma,
( ~ in(X1,X2)
| set_difference(X2,singleton(X1)) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_216]) ).
cnf(c_0_327_328,lemma,
( ~ in(X1,X2)
| ~ disjoint(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_217]) ).
cnf(c_0_328_329,lemma,
( disjoint(X1,X2)
| in(esk6_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_208]) ).
cnf(c_0_329_330,lemma,
( disjoint(X1,X2)
| in(esk6_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_208]) ).
cnf(c_0_330_331,lemma,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_218]) ).
cnf(c_0_331_332,lemma,
set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_219]) ).
cnf(c_0_332_333,lemma,
set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_220]) ).
cnf(c_0_333_334,lemma,
( X1 = X2
| X1 = X3
| unordered_pair(X1,X4) != unordered_pair(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_221]) ).
cnf(c_0_334_335,lemma,
( subset(relation_dom_restriction(X1,X2),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_222]) ).
cnf(c_0_335_336,lemma,
( subset(relation_rng_restriction(X1,X2),X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_223]) ).
cnf(c_0_336_337,lemma,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_224]) ).
cnf(c_0_337_338,lemma,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_225]) ).
cnf(c_0_338_339,lemma,
( X1 = X3
| ordered_pair(X1,X2) != ordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_226]) ).
cnf(c_0_339_340,lemma,
( X2 = X4
| ordered_pair(X1,X2) != ordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_226]) ).
cnf(c_0_340_341,lemma,
( ~ proper_subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_227]) ).
cnf(c_0_341_342,lemma,
( X1 = X2
| ~ subset(singleton(X1),singleton(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_228]) ).
cnf(c_0_342_343,lemma,
( set_union2(singleton(X1),X2) = X2
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_229]) ).
cnf(c_0_343_344,lemma,
( set_union2(singleton(X1),X2) = X2
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_230]) ).
cnf(c_0_344_345,lemma,
( subset(X1,union(X2))
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_231]) ).
cnf(c_0_345_346,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_224]) ).
cnf(c_0_346_347,lemma,
( subset(X1,union(X2))
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_232]) ).
cnf(c_0_347_348,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_225]) ).
cnf(c_0_348_349,lemma,
( relation_dom_restriction(X1,X2) = relation_composition(identity_relation(X2),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_233]) ).
cnf(c_0_349_350,lemma,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_234]) ).
cnf(c_0_350_351,lemma,
subset(set_difference(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_235]) ).
cnf(c_0_351_352,lemma,
subset(set_intersection2(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_236]) ).
cnf(c_0_352_353,lemma,
( X1 = singleton(X2)
| X1 = empty_set
| ~ subset(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_237]) ).
cnf(c_0_353_354,lemma,
( X1 = singleton(X2)
| X1 = empty_set
| ~ subset(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_238]) ).
cnf(c_0_354_355,lemma,
( disjoint(X1,X2)
| set_difference(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_239]) ).
cnf(c_0_355_356,lemma,
( set_difference(X1,X2) = X1
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_239]) ).
cnf(c_0_356_357,lemma,
( set_intersection2(X1,X2) = X1
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_240]) ).
cnf(c_0_357_358,lemma,
( set_union2(X1,X2) = X2
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_241]) ).
cnf(c_0_358_359,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_242]) ).
cnf(c_0_359_360,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_242]) ).
cnf(c_0_360_361,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_243]) ).
cnf(c_0_361_362,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_243]) ).
cnf(c_0_362_363,lemma,
( set_difference(X1,singleton(X2)) = X1
| in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_216]) ).
cnf(c_0_363_364,lemma,
( disjoint(singleton(X1),X2)
| in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_244]) ).
cnf(c_0_364_365,lemma,
( X1 = X2
| singleton(X3) != unordered_pair(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_245]) ).
cnf(c_0_365_366,lemma,
( X1 = X2
| singleton(X1) != unordered_pair(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_246]) ).
cnf(c_0_366_367,lemma,
( subset(X1,singleton(X2))
| X1 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[c_0_237]) ).
cnf(c_0_367_368,lemma,
( subset(X1,singleton(X2))
| X1 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[c_0_238]) ).
cnf(c_0_368_369,lemma,
( subset(X1,singleton(X2))
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_237]) ).
cnf(c_0_369_370,lemma,
( subset(X1,singleton(X2))
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_238]) ).
cnf(c_0_370_371,lemma,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
inference(split_conjunct,[status(thm)],[c_0_247]) ).
cnf(c_0_371_372,lemma,
( relation_rng(X1) = relation_dom(relation_inverse(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_248]) ).
cnf(c_0_372_373,lemma,
( relation_dom(X1) = relation_rng(relation_inverse(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_248]) ).
cnf(c_0_373_374,lemma,
in(X1,esk2_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_204]) ).
cnf(c_0_374_375,lemma,
( relation_rng(X1) = empty_set
| ~ relation(X1)
| relation_dom(X1) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_249]) ).
cnf(c_0_375_376,lemma,
( relation_dom(X1) = empty_set
| ~ relation(X1)
| relation_rng(X1) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_249]) ).
cnf(c_0_376_377,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[c_0_250]) ).
cnf(c_0_377_378,lemma,
( X1 = empty_set
| ~ relation(X1)
| relation_dom(X1) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_251]) ).
cnf(c_0_378_379,lemma,
( X1 = empty_set
| ~ relation(X1)
| relation_rng(X1) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_251]) ).
cnf(c_0_379_380,lemma,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[c_0_252]) ).
cnf(c_0_380_381,lemma,
union(powerset(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_253]) ).
cnf(c_0_381_382,lemma,
relation_dom(identity_relation(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_254]) ).
cnf(c_0_382_383,lemma,
relation_rng(identity_relation(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_254]) ).
cnf(c_0_383_384,lemma,
singleton(X1) != empty_set,
inference(split_conjunct,[status(thm)],[c_0_255]) ).
cnf(c_0_384_385,lemma,
powerset(empty_set) = singleton(empty_set),
inference(split_conjunct,[status(thm)],[c_0_256]) ).
cnf(c_0_385_386,lemma,
relation_dom(empty_set) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_257]) ).
cnf(c_0_386_387,lemma,
relation_rng(empty_set) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_257]) ).
cnf(c_0_387_388,negated_conjecture,
relation(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_213]) ).
cnf(c_0_388_389,lemma,
( in(ordered_pair(esk3_3(X2,X3,X1),X2),X1)
| ~ relation(X1)
| ~ in(X2,relation_image(X1,X3)) ),
c_0_258,
[final] ).
cnf(c_0_389_390,lemma,
( in(esk3_3(X2,X3,X1),relation_dom(X1))
| ~ relation(X1)
| ~ in(X2,relation_image(X1,X3)) ),
c_0_259,
[final] ).
cnf(c_0_390_391,lemma,
( in(esk3_3(X2,X3,X1),X3)
| ~ relation(X1)
| ~ in(X2,relation_image(X1,X3)) ),
c_0_260,
[final] ).
cnf(c_0_391_392,lemma,
( subset_difference(X1,cast_to_subset(X1),meet_of_subsets(X1,X2)) = union_of_subsets(X1,complements_of_subsets(X1,X2))
| X2 = empty_set
| ~ element(X2,powerset(powerset(X1))) ),
c_0_261,
[final] ).
cnf(c_0_392_393,lemma,
( subset_difference(X1,cast_to_subset(X1),union_of_subsets(X1,X2)) = meet_of_subsets(X1,complements_of_subsets(X1,X2))
| X2 = empty_set
| ~ element(X2,powerset(powerset(X1))) ),
c_0_262,
[final] ).
cnf(c_0_393_394,lemma,
( in(ordered_pair(X2,X3),relation_composition(identity_relation(X4),X1))
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1)
| ~ in(X2,X4) ),
c_0_263,
[final] ).
cnf(c_0_394_395,lemma,
( in(ordered_pair(X2,X3),X1)
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),relation_composition(identity_relation(X4),X1)) ),
c_0_264,
[final] ).
cnf(c_0_395_396,lemma,
( in(X2,relation_image(X1,X3))
| ~ relation(X1)
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,X2),X1)
| ~ in(X4,relation_dom(X1)) ),
c_0_265,
[final] ).
cnf(c_0_396_397,lemma,
( in(X2,X4)
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),relation_composition(identity_relation(X4),X1)) ),
c_0_266,
[final] ).
cnf(c_0_397_398,lemma,
( disjoint(X1,X3)
| ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2))
| ~ subset(X1,subset_complement(X2,X3)) ),
c_0_267,
[final] ).
cnf(c_0_398_399,lemma,
( in(X2,relation_dom(X1))
| ~ relation(X1)
| ~ in(X2,relation_dom(relation_dom_restriction(X1,X3))) ),
c_0_268,
[final] ).
cnf(c_0_399_400,lemma,
( in(X2,relation_rng(X1))
| ~ relation(X1)
| ~ in(X2,relation_rng(relation_rng_restriction(X3,X1))) ),
c_0_269,
[final] ).
cnf(c_0_400_401,lemma,
( in(X2,X3)
| ~ relation(X1)
| ~ in(X2,relation_dom(relation_dom_restriction(X1,X3))) ),
c_0_270,
[final] ).
cnf(c_0_401_402,lemma,
( in(X2,X3)
| ~ relation(X1)
| ~ in(X2,relation_rng(relation_rng_restriction(X3,X1))) ),
c_0_271,
[final] ).
cnf(c_0_402_403,lemma,
( in(X2,relation_dom(relation_dom_restriction(X1,X3)))
| ~ relation(X1)
| ~ in(X2,relation_dom(X1))
| ~ in(X2,X3) ),
c_0_272,
[final] ).
cnf(c_0_403_404,lemma,
( in(X2,relation_rng(relation_rng_restriction(X3,X1)))
| ~ relation(X1)
| ~ in(X2,relation_rng(X1))
| ~ in(X2,X3) ),
c_0_273,
[final] ).
cnf(c_0_404_405,lemma,
( subset(X1,subset_complement(X2,X3))
| ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2))
| ~ disjoint(X1,X3) ),
c_0_274,
[final] ).
cnf(c_0_405_406,lemma,
( in(X1,X3)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
c_0_275,
[final] ).
cnf(c_0_406_407,lemma,
( in(X2,X4)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
c_0_276,
[final] ).
cnf(c_0_407_408,lemma,
( in(X1,X3)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
c_0_277,
[final] ).
cnf(c_0_408_409,lemma,
( in(X2,X4)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
c_0_278,
[final] ).
cnf(c_0_409_410,lemma,
( ~ in(X1,X2)
| ~ in(X1,subset_complement(X3,X2))
| ~ element(X2,powerset(X3)) ),
c_0_279,
[final] ).
cnf(c_0_410_411,lemma,
( subset(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
| ~ subset(X2,X4)
| ~ subset(X1,X3) ),
c_0_280,
[final] ).
cnf(c_0_411_412,lemma,
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
c_0_281,
[final] ).
cnf(c_0_412_413,lemma,
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
c_0_282,
[final] ).
cnf(c_0_413_414,lemma,
( in(X1,subset_complement(X2,X3))
| in(X1,X3)
| X2 = empty_set
| ~ element(X1,X2)
| ~ element(X3,powerset(X2)) ),
c_0_283,
[final] ).
cnf(c_0_414_415,lemma,
( subset(relation_rng(relation_composition(X1,X2)),relation_rng(X2))
| ~ relation(X2)
| ~ relation(X1) ),
c_0_284,
[final] ).
cnf(c_0_415_416,lemma,
( subset(relation_dom(relation_composition(X1,X2)),relation_dom(X1))
| ~ relation(X2)
| ~ relation(X1) ),
c_0_285,
[final] ).
cnf(c_0_416_417,lemma,
( in(X2,relation_field(X1))
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
c_0_286,
[final] ).
cnf(c_0_417_418,lemma,
( in(X3,relation_field(X1))
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
c_0_287,
[final] ).
cnf(c_0_418_419,lemma,
( in(X2,relation_dom(X1))
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
c_0_288,
[final] ).
cnf(c_0_419_420,lemma,
( in(X3,relation_rng(X1))
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
c_0_289,
[final] ).
cnf(c_0_420_421,lemma,
( relation_rng(relation_composition(X1,X2)) = relation_rng(X2)
| ~ subset(relation_dom(X2),relation_rng(X1))
| ~ relation(X1)
| ~ relation(X2) ),
c_0_290,
[final] ).
cnf(c_0_421_422,lemma,
( relation_dom(relation_composition(X1,X2)) = relation_dom(X1)
| ~ subset(relation_rng(X1),relation_dom(X2))
| ~ relation(X2)
| ~ relation(X1) ),
c_0_291,
[final] ).
cnf(c_0_422_423,lemma,
( subset(X1,set_difference(X2,singleton(X3)))
| in(X3,X1)
| ~ subset(X1,X2) ),
c_0_292,
[final] ).
cnf(c_0_423_424,lemma,
( subset(set_difference(X1,X2),set_difference(X3,X2))
| ~ subset(X1,X3) ),
c_0_293,
[final] ).
cnf(c_0_424_425,lemma,
( subset(set_intersection2(X1,X2),set_intersection2(X3,X2))
| ~ subset(X1,X3) ),
c_0_294,
[final] ).
cnf(c_0_425_426,lemma,
( subset(cartesian_product2(X1,X3),cartesian_product2(X2,X3))
| ~ subset(X1,X2) ),
c_0_295,
[final] ).
cnf(c_0_426_427,lemma,
( subset(cartesian_product2(X3,X1),cartesian_product2(X3,X2))
| ~ subset(X1,X2) ),
c_0_296,
[final] ).
cnf(c_0_427_428,lemma,
( relation_dom_restriction(relation_rng_restriction(X1,X2),X3) = relation_rng_restriction(X1,relation_dom_restriction(X2,X3))
| ~ relation(X2) ),
c_0_297,
[final] ).
cnf(c_0_428_429,lemma,
( ~ disjoint(X1,X2)
| ~ in(X3,set_intersection2(X1,X2)) ),
c_0_298,
[final] ).
cnf(c_0_429_430,lemma,
( subset(set_union2(X1,X2),X3)
| ~ subset(X2,X3)
| ~ subset(X1,X3) ),
c_0_299,
[final] ).
cnf(c_0_430_431,lemma,
( subset(unordered_pair(X1,X2),X3)
| ~ in(X2,X3)
| ~ in(X1,X3) ),
c_0_300,
[final] ).
cnf(c_0_431_432,lemma,
( subset(X1,set_intersection2(X2,X3))
| ~ subset(X1,X3)
| ~ subset(X1,X2) ),
c_0_301,
[final] ).
cnf(c_0_432_433,lemma,
( subset(relation_rng(relation_dom_restriction(X1,X2)),relation_rng(X1))
| ~ relation(X1) ),
c_0_302,
[final] ).
cnf(c_0_433_434,lemma,
( subset(relation_rng(relation_rng_restriction(X1,X2)),relation_rng(X2))
| ~ relation(X2) ),
c_0_303,
[final] ).
cnf(c_0_434_435,lemma,
( element(X1,powerset(X2))
| ~ in(esk1_2(X1,X2),X2) ),
c_0_304,
[final] ).
cnf(c_0_435_436,lemma,
( in(esk7_2(X1,X2),set_intersection2(X1,X2))
| disjoint(X1,X2) ),
c_0_305,
[final] ).
cnf(c_0_436_437,lemma,
( subset(relation_rng(relation_rng_restriction(X1,X2)),X1)
| ~ relation(X2) ),
c_0_306,
[final] ).
cnf(c_0_437_438,lemma,
( in(X1,X3)
| ~ subset(unordered_pair(X1,X2),X3) ),
c_0_307,
[final] ).
cnf(c_0_438_439,lemma,
( in(X2,X3)
| ~ subset(unordered_pair(X1,X2),X3) ),
c_0_308,
[final] ).
cnf(c_0_439_440,lemma,
( X2 = empty_set
| complements_of_subsets(X1,X2) != empty_set
| ~ element(X2,powerset(powerset(X1))) ),
c_0_309,
[final] ).
cnf(c_0_440_441,lemma,
( in(X1,esk2_1(X2))
| ~ subset(X1,X3)
| ~ in(X3,esk2_1(X2)) ),
c_0_310,
[final] ).
cnf(c_0_441_442,lemma,
( X1 = empty_set
| in(ordered_pair(esk8_1(X1),esk9_1(X1)),X1)
| ~ relation(X1) ),
c_0_311,
[final] ).
cnf(c_0_442_443,lemma,
( in(X1,esk2_1(X2))
| are_equipotent(X1,esk2_1(X2))
| ~ subset(X1,esk2_1(X2)) ),
c_0_312,
[final] ).
cnf(c_0_443_444,lemma,
( subset(X1,cartesian_product2(relation_dom(X1),relation_rng(X1)))
| ~ relation(X1) ),
c_0_313,
[final] ).
cnf(c_0_444_445,lemma,
( in(X1,X2)
| ~ in(X1,X3)
| ~ element(X3,powerset(X2)) ),
c_0_314,
[final] ).
cnf(c_0_445_446,lemma,
( ~ disjoint(X1,X2)
| ~ in(X3,X2)
| ~ in(X3,X1) ),
c_0_315,
[final] ).
cnf(c_0_446_447,lemma,
( set_union2(X2,set_difference(X1,X2)) = X1
| ~ subset(X2,X1) ),
c_0_316,
[final] ).
cnf(c_0_447_448,lemma,
( subset(relation_dom(X1),relation_dom(X2))
| ~ relation(X1)
| ~ relation(X2)
| ~ subset(X1,X2) ),
c_0_317,
[final] ).
cnf(c_0_448_449,lemma,
( subset(relation_rng(X1),relation_rng(X2))
| ~ relation(X1)
| ~ relation(X2)
| ~ subset(X1,X2) ),
c_0_318,
[final] ).
cnf(c_0_449_450,lemma,
( element(X1,powerset(X2))
| in(esk1_2(X1,X2),X1) ),
c_0_319,
[final] ).
cnf(c_0_450_451,lemma,
( disjoint(X1,X2)
| ~ disjoint(X3,X2)
| ~ subset(X1,X3) ),
c_0_320,
[final] ).
cnf(c_0_451_452,lemma,
( subset(X1,X2)
| ~ subset(X3,X2)
| ~ subset(X1,X3) ),
c_0_321,
[final] ).
cnf(c_0_452_453,lemma,
( in(powerset(X1),esk2_1(X2))
| ~ in(X1,esk2_1(X2)) ),
c_0_322,
[final] ).
cnf(c_0_453_454,negated_conjecture,
~ subset(relation_image(esk5_0,esk4_0),relation_rng(esk5_0)),
c_0_323,
[final] ).
cnf(c_0_454_455,lemma,
( relation_dom(relation_dom_restriction(X1,X2)) = set_intersection2(relation_dom(X1),X2)
| ~ relation(X1) ),
c_0_324,
[final] ).
cnf(c_0_455_456,lemma,
( relation_rng(relation_rng_restriction(X1,X2)) = set_intersection2(relation_rng(X2),X1)
| ~ relation(X2) ),
c_0_325,
[final] ).
cnf(c_0_456_457,lemma,
( ~ in(X1,X2)
| set_difference(X2,singleton(X1)) != X2 ),
c_0_326,
[final] ).
cnf(c_0_457_458,lemma,
( ~ in(X1,X2)
| ~ disjoint(singleton(X1),X2) ),
c_0_327,
[final] ).
cnf(c_0_458_459,lemma,
( disjoint(X1,X2)
| in(esk6_2(X1,X2),X1) ),
c_0_328,
[final] ).
cnf(c_0_459_460,lemma,
( disjoint(X1,X2)
| in(esk6_2(X1,X2),X2) ),
c_0_329,
[final] ).
cnf(c_0_460_461,lemma,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
c_0_330,
[final] ).
cnf(c_0_461_462,lemma,
set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
c_0_331,
[final] ).
cnf(c_0_462_463,lemma,
set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
c_0_332,
[final] ).
cnf(c_0_463_464,lemma,
( X1 = X2
| X1 = X3
| unordered_pair(X1,X4) != unordered_pair(X3,X2) ),
c_0_333,
[final] ).
cnf(c_0_464_465,lemma,
( subset(relation_dom_restriction(X1,X2),X1)
| ~ relation(X1) ),
c_0_334,
[final] ).
cnf(c_0_465_466,lemma,
( subset(relation_rng_restriction(X1,X2),X2)
| ~ relation(X2) ),
c_0_335,
[final] ).
cnf(c_0_466_467,lemma,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
c_0_336,
[final] ).
cnf(c_0_467_468,lemma,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
c_0_337,
[final] ).
cnf(c_0_468_469,lemma,
( X1 = X3
| ordered_pair(X1,X2) != ordered_pair(X3,X4) ),
c_0_338,
[final] ).
cnf(c_0_469_470,lemma,
( X2 = X4
| ordered_pair(X1,X2) != ordered_pair(X3,X4) ),
c_0_339,
[final] ).
cnf(c_0_470_471,lemma,
( ~ proper_subset(X1,X2)
| ~ subset(X2,X1) ),
c_0_340,
[final] ).
cnf(c_0_471_472,lemma,
( X1 = X2
| ~ subset(singleton(X1),singleton(X2)) ),
c_0_341,
[final] ).
cnf(c_0_472_473,lemma,
( set_union2(singleton(X1),X2) = X2
| ~ in(X1,X2) ),
c_0_342,
[final] ).
cnf(c_0_473_474,lemma,
( set_union2(singleton(X1),X2) = X2
| ~ in(X1,X2) ),
c_0_343,
[final] ).
cnf(c_0_474_475,lemma,
( subset(X1,union(X2))
| ~ in(X1,X2) ),
c_0_344,
[final] ).
cnf(c_0_475_476,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
c_0_345,
[final] ).
cnf(c_0_476_477,lemma,
( subset(X1,union(X2))
| ~ in(X1,X2) ),
c_0_346,
[final] ).
cnf(c_0_477_478,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
c_0_347,
[final] ).
cnf(c_0_478_479,lemma,
( relation_composition(identity_relation(X2),X1) = relation_dom_restriction(X1,X2)
| ~ relation(X1) ),
c_0_348,
[final] ).
cnf(c_0_479_480,lemma,
subset(X1,set_union2(X1,X2)),
c_0_349,
[final] ).
cnf(c_0_480_481,lemma,
subset(set_difference(X1,X2),X1),
c_0_350,
[final] ).
cnf(c_0_481_482,lemma,
subset(set_intersection2(X1,X2),X1),
c_0_351,
[final] ).
cnf(c_0_482_483,lemma,
( X1 = singleton(X2)
| X1 = empty_set
| ~ subset(X1,singleton(X2)) ),
c_0_352,
[final] ).
cnf(c_0_483_484,lemma,
( X1 = singleton(X2)
| X1 = empty_set
| ~ subset(X1,singleton(X2)) ),
c_0_353,
[final] ).
cnf(c_0_484_485,lemma,
( disjoint(X1,X2)
| set_difference(X1,X2) != X1 ),
c_0_354,
[final] ).
cnf(c_0_485_486,lemma,
( set_difference(X1,X2) = X1
| ~ disjoint(X1,X2) ),
c_0_355,
[final] ).
cnf(c_0_486_487,lemma,
( set_intersection2(X1,X2) = X1
| ~ subset(X1,X2) ),
c_0_356,
[final] ).
cnf(c_0_487_488,lemma,
( set_union2(X1,X2) = X2
| ~ subset(X1,X2) ),
c_0_357,
[final] ).
cnf(c_0_488_489,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
c_0_358,
[final] ).
cnf(c_0_489_490,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
c_0_359,
[final] ).
cnf(c_0_490_491,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
c_0_360,
[final] ).
cnf(c_0_491_492,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
c_0_361,
[final] ).
cnf(c_0_492_493,lemma,
( set_difference(X1,singleton(X2)) = X1
| in(X2,X1) ),
c_0_362,
[final] ).
cnf(c_0_493_494,lemma,
( disjoint(singleton(X1),X2)
| in(X1,X2) ),
c_0_363,
[final] ).
cnf(c_0_494_495,lemma,
( X1 = X2
| singleton(X3) != unordered_pair(X1,X2) ),
c_0_364,
[final] ).
cnf(c_0_495_496,lemma,
( X1 = X2
| singleton(X1) != unordered_pair(X2,X3) ),
c_0_365,
[final] ).
cnf(c_0_496_497,lemma,
( subset(X1,singleton(X2))
| X1 != singleton(X2) ),
c_0_366,
[final] ).
cnf(c_0_497_498,lemma,
( subset(X1,singleton(X2))
| X1 != singleton(X2) ),
c_0_367,
[final] ).
cnf(c_0_498_499,lemma,
( subset(X1,singleton(X2))
| X1 != empty_set ),
c_0_368,
[final] ).
cnf(c_0_499_500,lemma,
( subset(X1,singleton(X2))
| X1 != empty_set ),
c_0_369,
[final] ).
cnf(c_0_500_501,lemma,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
c_0_370,
[final] ).
cnf(c_0_501_502,lemma,
( relation_dom(relation_inverse(X1)) = relation_rng(X1)
| ~ relation(X1) ),
c_0_371,
[final] ).
cnf(c_0_502_503,lemma,
( relation_rng(relation_inverse(X1)) = relation_dom(X1)
| ~ relation(X1) ),
c_0_372,
[final] ).
cnf(c_0_503_504,lemma,
in(X1,esk2_1(X1)),
c_0_373,
[final] ).
cnf(c_0_504_505,lemma,
( relation_rng(X1) = empty_set
| ~ relation(X1)
| relation_dom(X1) != empty_set ),
c_0_374,
[final] ).
cnf(c_0_505_506,lemma,
( relation_dom(X1) = empty_set
| ~ relation(X1)
| relation_rng(X1) != empty_set ),
c_0_375,
[final] ).
cnf(c_0_506_507,lemma,
unordered_pair(X1,X1) = singleton(X1),
c_0_376,
[final] ).
cnf(c_0_507_508,lemma,
( X1 = empty_set
| ~ relation(X1)
| relation_dom(X1) != empty_set ),
c_0_377,
[final] ).
cnf(c_0_508_509,lemma,
( X1 = empty_set
| ~ relation(X1)
| relation_rng(X1) != empty_set ),
c_0_378,
[final] ).
cnf(c_0_509_510,lemma,
subset(empty_set,X1),
c_0_379,
[final] ).
cnf(c_0_510_511,lemma,
union(powerset(X1)) = X1,
c_0_380,
[final] ).
cnf(c_0_511_512,lemma,
relation_dom(identity_relation(X1)) = X1,
c_0_381,
[final] ).
cnf(c_0_512_513,lemma,
relation_rng(identity_relation(X1)) = X1,
c_0_382,
[final] ).
cnf(c_0_513_514,lemma,
singleton(X1) != empty_set,
c_0_383,
[final] ).
cnf(c_0_514_515,lemma,
powerset(empty_set) = singleton(empty_set),
c_0_384,
[final] ).
cnf(c_0_515_516,lemma,
relation_dom(empty_set) = empty_set,
c_0_385,
[final] ).
cnf(c_0_516_517,lemma,
relation_rng(empty_set) = empty_set,
c_0_386,
[final] ).
cnf(c_0_517_518,negated_conjecture,
relation(esk5_0),
c_0_387,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_703,plain,
( ~ relation(X0)
| ~ in(ordered_pair(X1,X2),X0)
| in(X2,relation_rng(X0)) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_b1c7de.p',c_0_419) ).
cnf(c_1106,plain,
( ~ relation(X0)
| ~ in(ordered_pair(X1,X2),X0)
| in(X2,relation_rng(X0)) ),
inference(copy,[status(esa)],[c_703]) ).
cnf(c_1335,plain,
( ~ relation(X0)
| ~ in(ordered_pair(X1,X2),X0)
| in(X2,relation_rng(X0)) ),
inference(copy,[status(esa)],[c_1106]) ).
cnf(c_1518,plain,
( ~ relation(X0)
| ~ in(ordered_pair(X1,X2),X0)
| in(X2,relation_rng(X0)) ),
inference(copy,[status(esa)],[c_1335]) ).
cnf(c_1575,plain,
( ~ relation(X0)
| ~ in(ordered_pair(X1,X2),X0)
| in(X2,relation_rng(X0)) ),
inference(copy,[status(esa)],[c_1518]) ).
cnf(c_2364,plain,
( ~ relation(X0)
| ~ in(ordered_pair(X1,X2),X0)
| in(X2,relation_rng(X0)) ),
inference(copy,[status(esa)],[c_1575]) ).
cnf(c_285907,plain,
( ~ relation(sk2_esk5_0)
| ~ in(ordered_pair(sk2_esk3_3(sk1_esk30_2(relation_image(sk2_esk5_0,sk2_esk4_0),relation_rng(sk2_esk5_0)),sk2_esk4_0,sk2_esk5_0),sk1_esk30_2(relation_image(sk2_esk5_0,sk2_esk4_0),relation_rng(sk2_esk5_0))),sk2_esk5_0)
| in(sk1_esk30_2(relation_image(sk2_esk5_0,sk2_esk4_0),relation_rng(sk2_esk5_0)),relation_rng(sk2_esk5_0)) ),
inference(instantiation,[status(thm)],[c_2364]) ).
cnf(c_672,plain,
( ~ relation(X0)
| in(ordered_pair(sk2_esk3_3(X1,X2,X0),X1),X0)
| ~ in(X1,relation_image(X0,X2)) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_b1c7de.p',c_0_388) ).
cnf(c_1044,plain,
( ~ relation(X0)
| in(ordered_pair(sk2_esk3_3(X1,X2,X0),X1),X0)
| ~ in(X1,relation_image(X0,X2)) ),
inference(copy,[status(esa)],[c_672]) ).
cnf(c_1308,plain,
( ~ relation(X0)
| in(ordered_pair(sk2_esk3_3(X1,X2,X0),X1),X0)
| ~ in(X1,relation_image(X0,X2)) ),
inference(copy,[status(esa)],[c_1044]) ).
cnf(c_1545,plain,
( ~ relation(X0)
| in(ordered_pair(sk2_esk3_3(X1,X2,X0),X1),X0)
| ~ in(X1,relation_image(X0,X2)) ),
inference(copy,[status(esa)],[c_1308]) ).
cnf(c_1548,plain,
( ~ relation(X0)
| in(ordered_pair(sk2_esk3_3(X1,X2,X0),X1),X0)
| ~ in(X1,relation_image(X0,X2)) ),
inference(copy,[status(esa)],[c_1545]) ).
cnf(c_2337,plain,
( ~ relation(X0)
| in(ordered_pair(sk2_esk3_3(X1,X2,X0),X1),X0)
| ~ in(X1,relation_image(X0,X2)) ),
inference(copy,[status(esa)],[c_1548]) ).
cnf(c_283648,plain,
( ~ relation(sk2_esk5_0)
| in(ordered_pair(sk2_esk3_3(sk1_esk30_2(relation_image(sk2_esk5_0,sk2_esk4_0),relation_rng(sk2_esk5_0)),sk2_esk4_0,sk2_esk5_0),sk1_esk30_2(relation_image(sk2_esk5_0,sk2_esk4_0),relation_rng(sk2_esk5_0))),sk2_esk5_0)
| ~ in(sk1_esk30_2(relation_image(sk2_esk5_0,sk2_esk4_0),relation_rng(sk2_esk5_0)),relation_image(sk2_esk5_0,sk2_esk4_0)) ),
inference(instantiation,[status(thm)],[c_2337]) ).
cnf(c_257,plain,
( subset(X0,X1)
| ~ in(sk1_esk30_2(X0,X1),X1) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_b1c7de.p',c_0_668_1) ).
cnf(c_1920,plain,
( subset(X0,X1)
| ~ in(sk1_esk30_2(X0,X1),X1) ),
inference(copy,[status(esa)],[c_257]) ).
cnf(c_90008,plain,
( subset(relation_image(sk2_esk5_0,sk2_esk4_0),relation_rng(sk2_esk5_0))
| ~ in(sk1_esk30_2(relation_image(sk2_esk5_0,sk2_esk4_0),relation_rng(sk2_esk5_0)),relation_rng(sk2_esk5_0)) ),
inference(instantiation,[status(thm)],[c_1920]) ).
cnf(c_191,plain,
( subset(X0,X1)
| in(sk1_esk30_2(X0,X1),X0) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_b1c7de.p',c_0_691_1) ).
cnf(c_1854,plain,
( subset(X0,X1)
| in(sk1_esk30_2(X0,X1),X0) ),
inference(copy,[status(esa)],[c_191]) ).
cnf(c_90003,plain,
( subset(relation_image(sk2_esk5_0,sk2_esk4_0),relation_rng(sk2_esk5_0))
| in(sk1_esk30_2(relation_image(sk2_esk5_0,sk2_esk4_0),relation_rng(sk2_esk5_0)),relation_image(sk2_esk5_0,sk2_esk4_0)) ),
inference(instantiation,[status(thm)],[c_1854]) ).
cnf(c_784,negated_conjecture,
~ subset(relation_image(sk2_esk5_0,sk2_esk4_0),relation_rng(sk2_esk5_0)),
file('/export/starexec/sandbox/tmp/iprover_modulo_b1c7de.p',c_0_453) ).
cnf(c_801,negated_conjecture,
relation(sk2_esk5_0),
file('/export/starexec/sandbox/tmp/iprover_modulo_b1c7de.p',c_0_517) ).
cnf(contradiction,plain,
$false,
inference(minisat,[status(thm)],[c_285907,c_283648,c_90008,c_90003,c_784,c_801]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU204+2 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : iprover_modulo %s %d
% 0.13/0.34 % Computer : n010.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jun 19 11:47:37 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.34 % Running in mono-core mode
% 0.19/0.44 % Orienting using strategy Equiv(ClausalAll)
% 0.19/0.44 % FOF problem with conjecture
% 0.19/0.44 % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format " --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_352014.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_b1c7de.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_f470fb | grep -v "SZS"
% 0.19/0.46
% 0.19/0.46 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.19/0.46
% 0.19/0.46 %
% 0.19/0.46 % ------ iProver source info
% 0.19/0.46
% 0.19/0.46 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.19/0.46 % git: non_committed_changes: true
% 0.19/0.46 % git: last_make_outside_of_git: true
% 0.19/0.46
% 0.19/0.46 %
% 0.19/0.46 % ------ Input Options
% 0.19/0.46
% 0.19/0.46 % --out_options all
% 0.19/0.46 % --tptp_safe_out true
% 0.19/0.46 % --problem_path ""
% 0.19/0.46 % --include_path ""
% 0.19/0.46 % --clausifier .//eprover
% 0.19/0.46 % --clausifier_options --tstp-format
% 0.19/0.46 % --stdin false
% 0.19/0.46 % --dbg_backtrace false
% 0.19/0.46 % --dbg_dump_prop_clauses false
% 0.19/0.46 % --dbg_dump_prop_clauses_file -
% 0.19/0.46 % --dbg_out_stat false
% 0.19/0.46
% 0.19/0.46 % ------ General Options
% 0.19/0.46
% 0.19/0.46 % --fof false
% 0.19/0.46 % --time_out_real 150.
% 0.19/0.46 % --time_out_prep_mult 0.2
% 0.19/0.46 % --time_out_virtual -1.
% 0.19/0.46 % --schedule none
% 0.19/0.46 % --ground_splitting input
% 0.19/0.46 % --splitting_nvd 16
% 0.19/0.46 % --non_eq_to_eq false
% 0.19/0.46 % --prep_gs_sim true
% 0.19/0.46 % --prep_unflatten false
% 0.19/0.46 % --prep_res_sim true
% 0.19/0.46 % --prep_upred true
% 0.19/0.46 % --res_sim_input true
% 0.19/0.46 % --clause_weak_htbl true
% 0.19/0.46 % --gc_record_bc_elim false
% 0.19/0.46 % --symbol_type_check false
% 0.19/0.46 % --clausify_out false
% 0.19/0.46 % --large_theory_mode false
% 0.19/0.46 % --prep_sem_filter none
% 0.19/0.46 % --prep_sem_filter_out false
% 0.19/0.46 % --preprocessed_out false
% 0.19/0.46 % --sub_typing false
% 0.19/0.46 % --brand_transform false
% 0.19/0.46 % --pure_diseq_elim true
% 0.19/0.46 % --min_unsat_core false
% 0.19/0.46 % --pred_elim true
% 0.19/0.46 % --add_important_lit false
% 0.19/0.46 % --soft_assumptions false
% 0.19/0.46 % --reset_solvers false
% 0.19/0.46 % --bc_imp_inh []
% 0.19/0.46 % --conj_cone_tolerance 1.5
% 0.19/0.46 % --prolific_symb_bound 500
% 0.19/0.46 % --lt_threshold 2000
% 0.19/0.46
% 0.19/0.46 % ------ SAT Options
% 0.19/0.46
% 0.19/0.46 % --sat_mode false
% 0.19/0.46 % --sat_fm_restart_options ""
% 0.19/0.46 % --sat_gr_def false
% 0.19/0.46 % --sat_epr_types true
% 0.19/0.46 % --sat_non_cyclic_types false
% 0.19/0.46 % --sat_finite_models false
% 0.19/0.46 % --sat_fm_lemmas false
% 0.19/0.46 % --sat_fm_prep false
% 0.19/0.46 % --sat_fm_uc_incr true
% 0.19/0.46 % --sat_out_model small
% 0.19/0.46 % --sat_out_clauses false
% 0.19/0.46
% 0.19/0.46 % ------ QBF Options
% 0.19/0.46
% 0.19/0.46 % --qbf_mode false
% 0.19/0.46 % --qbf_elim_univ true
% 0.19/0.46 % --qbf_sk_in true
% 0.19/0.46 % --qbf_pred_elim true
% 0.19/0.46 % --qbf_split 32
% 0.19/0.46
% 0.19/0.46 % ------ BMC1 Options
% 0.19/0.46
% 0.19/0.46 % --bmc1_incremental false
% 0.19/0.46 % --bmc1_axioms reachable_all
% 0.19/0.46 % --bmc1_min_bound 0
% 0.19/0.46 % --bmc1_max_bound -1
% 0.19/0.46 % --bmc1_max_bound_default -1
% 0.19/0.46 % --bmc1_symbol_reachability true
% 0.19/0.46 % --bmc1_property_lemmas false
% 0.19/0.46 % --bmc1_k_induction false
% 0.19/0.46 % --bmc1_non_equiv_states false
% 0.19/0.46 % --bmc1_deadlock false
% 0.19/0.46 % --bmc1_ucm false
% 0.19/0.46 % --bmc1_add_unsat_core none
% 0.19/0.46 % --bmc1_unsat_core_children false
% 0.19/0.46 % --bmc1_unsat_core_extrapolate_axioms false
% 0.19/0.46 % --bmc1_out_stat full
% 0.19/0.46 % --bmc1_ground_init false
% 0.19/0.46 % --bmc1_pre_inst_next_state false
% 0.19/0.46 % --bmc1_pre_inst_state false
% 0.19/0.46 % --bmc1_pre_inst_reach_state false
% 0.19/0.46 % --bmc1_out_unsat_core false
% 0.19/0.46 % --bmc1_aig_witness_out false
% 0.19/0.46 % --bmc1_verbose false
% 0.19/0.46 % --bmc1_dump_clauses_tptp false
% 0.19/0.47 % --bmc1_dump_unsat_core_tptp false
% 0.19/0.47 % --bmc1_dump_file -
% 0.19/0.47 % --bmc1_ucm_expand_uc_limit 128
% 0.19/0.47 % --bmc1_ucm_n_expand_iterations 6
% 0.19/0.47 % --bmc1_ucm_extend_mode 1
% 0.19/0.47 % --bmc1_ucm_init_mode 2
% 0.19/0.47 % --bmc1_ucm_cone_mode none
% 0.19/0.47 % --bmc1_ucm_reduced_relation_type 0
% 0.19/0.47 % --bmc1_ucm_relax_model 4
% 0.19/0.47 % --bmc1_ucm_full_tr_after_sat true
% 0.19/0.47 % --bmc1_ucm_expand_neg_assumptions false
% 0.19/0.47 % --bmc1_ucm_layered_model none
% 0.19/0.47 % --bmc1_ucm_max_lemma_size 10
% 0.19/0.47
% 0.19/0.47 % ------ AIG Options
% 0.19/0.47
% 0.19/0.47 % --aig_mode false
% 0.19/0.47
% 0.19/0.47 % ------ Instantiation Options
% 0.19/0.47
% 0.19/0.47 % --instantiation_flag true
% 0.19/0.47 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.19/0.47 % --inst_solver_per_active 750
% 0.19/0.47 % --inst_solver_calls_frac 0.5
% 0.19/0.47 % --inst_passive_queue_type priority_queues
% 0.19/0.47 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.19/0.47 % --inst_passive_queues_freq [25;2]
% 0.19/0.47 % --inst_dismatching true
% 0.19/0.47 % --inst_eager_unprocessed_to_passive true
% 0.19/0.47 % --inst_prop_sim_given true
% 0.19/0.47 % --inst_prop_sim_new false
% 0.19/0.47 % --inst_orphan_elimination true
% 0.19/0.47 % --inst_learning_loop_flag true
% 0.19/0.47 % --inst_learning_start 3000
% 0.19/0.47 % --inst_learning_factor 2
% 0.19/0.47 % --inst_start_prop_sim_after_learn 3
% 0.19/0.47 % --inst_sel_renew solver
% 0.19/0.47 % --inst_lit_activity_flag true
% 0.19/0.47 % --inst_out_proof true
% 0.19/0.47
% 0.19/0.47 % ------ Resolution Options
% 0.19/0.47
% 0.19/0.47 % --resolution_flag true
% 0.19/0.47 % --res_lit_sel kbo_max
% 0.19/0.47 % --res_to_prop_solver none
% 0.19/0.47 % --res_prop_simpl_new false
% 0.19/0.47 % --res_prop_simpl_given false
% 0.19/0.47 % --res_passive_queue_type priority_queues
% 0.19/0.47 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.19/0.47 % --res_passive_queues_freq [15;5]
% 0.19/0.47 % --res_forward_subs full
% 0.19/0.47 % --res_backward_subs full
% 0.19/0.47 % --res_forward_subs_resolution true
% 0.19/0.47 % --res_backward_subs_resolution true
% 0.19/0.47 % --res_orphan_elimination false
% 0.19/0.47 % --res_time_limit 1000.
% 0.19/0.47 % --res_out_proof true
% 0.19/0.47 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_352014.s
% 0.19/0.47 % --modulo true
% 0.19/0.47
% 0.19/0.47 % ------ Combination Options
% 0.19/0.47
% 0.19/0.47 % --comb_res_mult 1000
% 0.19/0.47 % --comb_inst_mult 300
% 0.19/0.47 % ------
% 0.19/0.47
% 0.19/0.47 % ------ Parsing...%
% 0.19/0.47
% 0.19/0.47
% 0.19/0.47 % ------ Statistics
% 0.19/0.47
% 0.19/0.47 % ------ General
% 0.19/0.47
% 0.19/0.47 % num_of_input_clauses: 141
% 0.19/0.47 % num_of_input_neg_conjectures: 0
% 0.19/0.47 % num_of_splits: 0
% 0.19/0.47 % num_of_split_atoms: 0
% 0.19/0.47 % num_of_sem_filtered_clauses: 0
% 0.19/0.47 % num_of_subtypes: 0
% 0.19/0.47 % monotx_restored_types: 0
% 0.19/0.47 % sat_num_of_epr_types: 0
% 0.19/0.47 % sat_num_of_non_cyclic_types: 0
% 0.19/0.47 % sat_guarded_non_collapsed_types: 0
% 0.19/0.47 % is_epr: 0
% 0.19/0.47 % is_horn: 0
% 0.19/0.47 % has_eq: 0
% 0.19/0.47 % num_pure_diseq_elim: 0
% 0.19/0.47 % simp_replaced_by: 0
% 0.19/0.47 % res_preprocessed: 0
% 0.19/0.47 % prep_upred: 0
% 0.19/0.47 % prep_unflattend: 0
% 0.19/0.47 % pred_elim_cands: 0
% 0.19/0.47 % pred_elim: 0
% 0.19/0.47 % pred_elim_cl: 0
% 0.19/0.47 % pred_elim_cycles: 0
% 0.19/0.47 % forced_gc_time: 0
% 0.19/0.47 % gc_basic_clause_elim: 0
% 0.19/0.47 % parsing_time: 0.
% 0.19/0.47 % sem_filter_time: 0.
% 0.19/0.47 % pred_elim_time: 0.
% 0.19/0.47 % out_proof_time: 0.
% 0.19/0.47 % monotx_time: 0.
% 0.19/0.47 % subtype_inf_time: 0.
% 0.19/0.47 % unif_index_cands_time: 0.
% 0.19/0.47 % uFatal error: exception Failure("Parse error in: /export/starexec/sandbox/tmp/iprover_modulo_b1c7de.p line: 144 near token: '!='")
% 0.19/0.47 nif_index_add_time: 0.
% 0.19/0.47 % total_time: 0.021
% 0.19/0.47 % num_of_symbols: 70
% 0.19/0.47 % num_of_terms: 348
% 0.19/0.47
% 0.19/0.47 % ------ Propositional Solver
% 0.19/0.47
% 0.19/0.47 % prop_solver_calls: 0
% 0.19/0.47 % prop_fast_solver_calls: 0
% 0.19/0.47 % prop_num_of_clauses: 0
% 0.19/0.47 % prop_preprocess_simplified: 0
% 0.19/0.47 % prop_fo_subsumed: 0
% 0.19/0.47 % prop_solver_time: 0.
% 0.19/0.47 % prop_fast_solver_time: 0.
% 0.19/0.47 % prop_unsat_core_time: 0.
% 0.19/0.47
% 0.19/0.47 % ------ QBF
% 0.19/0.47
% 0.19/0.47 % qbf_q_res: 0
% 0.19/0.47 % qbf_num_tautologies: 0
% 0.19/0.47 % qbf_prep_cycles: 0
% 0.19/0.47
% 0.19/0.47 % ------ BMC1
% 0.19/0.47
% 0.19/0.47 % bmc1_current_bound: -1
% 0.19/0.47 % bmc1_last_solved_bound: -1
% 0.19/0.47 % bmc1_unsat_core_size: -1
% 0.19/0.47 % bmc1_unsat_core_parents_size: -1
% 0.19/0.47 % bmc1_merge_next_fun: 0
% 0.19/0.47 % bmc1_unsat_core_clauses_time: 0.
% 0.19/0.47
% 0.19/0.47 % ------ Instantiation
% 0.19/0.47
% 0.19/0.47 % inst_num_of_clauses: undef
% 0.19/0.47 % inst_num_in_passive: undef
% 0.19/0.47 % inst_num_in_active: 0
% 0.19/0.47 % inst_num_in_unprocessed: 0
% 0.19/0.47 % inst_num_of_loops: 0
% 0.19/0.47 % inst_num_of_learning_restarts: 0
% 0.19/0.47 % inst_num_moves_active_passive: 0
% 0.19/0.47 % inst_lit_activity: 0
% 0.19/0.47 % inst_lit_activity_moves: 0
% 0.19/0.47 % inst_num_tautologies: 0
% 0.19/0.47 % inst_num_prop_implied: 0
% 0.19/0.47 % inst_num_existing_simplified: 0
% 0.19/0.47 % inst_num_eq_res_simplified: 0
% 0.19/0.47 % inst_num_child_elim: 0
% 0.19/0.47 % inst_num_of_dismatching_blockings: 0
% 0.19/0.47 % inst_num_of_non_proper_insts: 0
% 0.19/0.47 % inst_num_of_duplicates: 0
% 0.19/0.47 % inst_inst_num_from_inst_to_res: 0
% 0.19/0.47 % inst_dismatching_checking_time: 0.
% 0.19/0.47
% 0.19/0.47 % ------ Resolution
% 0.19/0.47
% 0.19/0.47 % res_num_of_clauses: undef
% 0.19/0.47 % res_num_in_passive: undef
% 0.19/0.47 % res_num_in_active: 0
% 0.19/0.47 % res_num_of_loops: 0
% 0.19/0.47 % res_forward_subset_subsumed: 0
% 0.19/0.47 % res_backward_subset_subsumed: 0
% 0.19/0.47 % res_forward_subsumed: 0
% 0.19/0.47 % res_backward_subsumed: 0
% 0.19/0.47 % res_forward_subsumption_resolution: 0
% 0.19/0.47 % res_backward_subsumption_resolution: 0
% 0.19/0.47 % res_clause_to_clause_subsumption: 0
% 0.19/0.47 % res_orphan_elimination: 0
% 0.19/0.47 % res_tautology_del: 0
% 0.19/0.47 % res_num_eq_res_simplified: 0
% 0.19/0.47 % res_num_sel_changes: 0
% 0.19/0.47 % res_moves_from_active_to_pass: 0
% 0.19/0.47
% 0.19/0.47 % Status Unknown
% 0.19/0.54 % Orienting using strategy ClausalAll
% 0.19/0.54 % FOF problem with conjecture
% 0.19/0.54 % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format " --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_352014.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_b1c7de.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_74c92e | grep -v "SZS"
% 0.19/0.57
% 0.19/0.57 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.19/0.57
% 0.19/0.57 %
% 0.19/0.57 % ------ iProver source info
% 0.19/0.57
% 0.19/0.57 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.19/0.57 % git: non_committed_changes: true
% 0.19/0.57 % git: last_make_outside_of_git: true
% 0.19/0.57
% 0.19/0.57 %
% 0.19/0.57 % ------ Input Options
% 0.19/0.57
% 0.19/0.57 % --out_options all
% 0.19/0.57 % --tptp_safe_out true
% 0.19/0.57 % --problem_path ""
% 0.19/0.57 % --include_path ""
% 0.19/0.57 % --clausifier .//eprover
% 0.19/0.57 % --clausifier_options --tstp-format
% 0.19/0.57 % --stdin false
% 0.19/0.57 % --dbg_backtrace false
% 0.19/0.57 % --dbg_dump_prop_clauses false
% 0.19/0.57 % --dbg_dump_prop_clauses_file -
% 0.19/0.57 % --dbg_out_stat false
% 0.19/0.57
% 0.19/0.57 % ------ General Options
% 0.19/0.57
% 0.19/0.57 % --fof false
% 0.19/0.57 % --time_out_real 150.
% 0.19/0.57 % --time_out_prep_mult 0.2
% 0.19/0.57 % --time_out_virtual -1.
% 0.19/0.57 % --schedule none
% 0.19/0.57 % --ground_splitting input
% 0.19/0.57 % --splitting_nvd 16
% 0.19/0.57 % --non_eq_to_eq false
% 0.19/0.57 % --prep_gs_sim true
% 0.19/0.57 % --prep_unflatten false
% 0.19/0.57 % --prep_res_sim true
% 0.19/0.57 % --prep_upred true
% 0.19/0.57 % --res_sim_input true
% 0.19/0.57 % --clause_weak_htbl true
% 0.19/0.57 % --gc_record_bc_elim false
% 0.19/0.57 % --symbol_type_check false
% 0.19/0.57 % --clausify_out false
% 0.19/0.57 % --large_theory_mode false
% 0.19/0.57 % --prep_sem_filter none
% 0.19/0.57 % --prep_sem_filter_out false
% 0.19/0.57 % --preprocessed_out false
% 0.19/0.57 % --sub_typing false
% 0.19/0.57 % --brand_transform false
% 0.19/0.57 % --pure_diseq_elim true
% 0.19/0.57 % --min_unsat_core false
% 0.19/0.57 % --pred_elim true
% 0.19/0.57 % --add_important_lit false
% 0.19/0.57 % --soft_assumptions false
% 0.19/0.57 % --reset_solvers false
% 0.19/0.57 % --bc_imp_inh []
% 0.19/0.57 % --conj_cone_tolerance 1.5
% 0.19/0.57 % --prolific_symb_bound 500
% 0.19/0.57 % --lt_threshold 2000
% 0.19/0.57
% 0.19/0.57 % ------ SAT Options
% 0.19/0.57
% 0.19/0.57 % --sat_mode false
% 0.19/0.57 % --sat_fm_restart_options ""
% 0.19/0.57 % --sat_gr_def false
% 0.19/0.57 % --sat_epr_types true
% 0.19/0.57 % --sat_non_cyclic_types false
% 0.19/0.57 % --sat_finite_models false
% 0.19/0.57 % --sat_fm_lemmas false
% 0.19/0.57 % --sat_fm_prep false
% 0.19/0.57 % --sat_fm_uc_incr true
% 0.19/0.57 % --sat_out_model small
% 0.19/0.57 % --sat_out_clauses false
% 0.19/0.57
% 0.19/0.57 % ------ QBF Options
% 0.19/0.57
% 0.19/0.57 % --qbf_mode false
% 0.19/0.57 % --qbf_elim_univ true
% 0.19/0.57 % --qbf_sk_in true
% 0.19/0.57 % --qbf_pred_elim true
% 0.19/0.57 % --qbf_split 32
% 0.19/0.57
% 0.19/0.57 % ------ BMC1 Options
% 0.19/0.57
% 0.19/0.57 % --bmc1_incremental false
% 0.19/0.57 % --bmc1_axioms reachable_all
% 0.19/0.57 % --bmc1_min_bound 0
% 0.19/0.57 % --bmc1_max_bound -1
% 0.19/0.57 % --bmc1_max_bound_default -1
% 0.19/0.57 % --bmc1_symbol_reachability true
% 0.19/0.57 % --bmc1_property_lemmas false
% 0.19/0.57 % --bmc1_k_induction false
% 0.19/0.57 % --bmc1_non_equiv_states false
% 0.19/0.57 % --bmc1_deadlock false
% 0.19/0.57 % --bmc1_ucm false
% 0.19/0.57 % --bmc1_add_unsat_core none
% 0.19/0.57 % --bmc1_unsat_core_children false
% 0.19/0.57 % --bmc1_unsat_core_extrapolate_axioms false
% 0.19/0.57 % --bmc1_out_stat full
% 0.19/0.57 % --bmc1_ground_init false
% 0.19/0.57 % --bmc1_pre_inst_next_state false
% 0.19/0.57 % --bmc1_pre_inst_state false
% 0.19/0.57 % --bmc1_pre_inst_reach_state false
% 0.19/0.57 % --bmc1_out_unsat_core false
% 0.19/0.57 % --bmc1_aig_witness_out false
% 0.19/0.57 % --bmc1_verbose false
% 0.19/0.57 % --bmc1_dump_clauses_tptp false
% 0.75/1.08 % --bmc1_dump_unsat_core_tptp false
% 0.75/1.08 % --bmc1_dump_file -
% 0.75/1.08 % --bmc1_ucm_expand_uc_limit 128
% 0.75/1.08 % --bmc1_ucm_n_expand_iterations 6
% 0.75/1.08 % --bmc1_ucm_extend_mode 1
% 0.75/1.08 % --bmc1_ucm_init_mode 2
% 0.75/1.08 % --bmc1_ucm_cone_mode none
% 0.75/1.08 % --bmc1_ucm_reduced_relation_type 0
% 0.75/1.08 % --bmc1_ucm_relax_model 4
% 0.75/1.08 % --bmc1_ucm_full_tr_after_sat true
% 0.75/1.08 % --bmc1_ucm_expand_neg_assumptions false
% 0.75/1.08 % --bmc1_ucm_layered_model none
% 0.75/1.08 % --bmc1_ucm_max_lemma_size 10
% 0.75/1.08
% 0.75/1.08 % ------ AIG Options
% 0.75/1.08
% 0.75/1.08 % --aig_mode false
% 0.75/1.08
% 0.75/1.08 % ------ Instantiation Options
% 0.75/1.08
% 0.75/1.08 % --instantiation_flag true
% 0.75/1.08 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.75/1.08 % --inst_solver_per_active 750
% 0.75/1.08 % --inst_solver_calls_frac 0.5
% 0.75/1.08 % --inst_passive_queue_type priority_queues
% 0.75/1.08 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.75/1.08 % --inst_passive_queues_freq [25;2]
% 0.75/1.08 % --inst_dismatching true
% 0.75/1.08 % --inst_eager_unprocessed_to_passive true
% 0.75/1.08 % --inst_prop_sim_given true
% 0.75/1.08 % --inst_prop_sim_new false
% 0.75/1.08 % --inst_orphan_elimination true
% 0.75/1.08 % --inst_learning_loop_flag true
% 0.75/1.08 % --inst_learning_start 3000
% 0.75/1.08 % --inst_learning_factor 2
% 0.75/1.08 % --inst_start_prop_sim_after_learn 3
% 0.75/1.08 % --inst_sel_renew solver
% 0.75/1.08 % --inst_lit_activity_flag true
% 0.75/1.08 % --inst_out_proof true
% 0.75/1.08
% 0.75/1.08 % ------ Resolution Options
% 0.75/1.08
% 0.75/1.08 % --resolution_flag true
% 0.75/1.08 % --res_lit_sel kbo_max
% 0.75/1.08 % --res_to_prop_solver none
% 0.75/1.08 % --res_prop_simpl_new false
% 0.75/1.08 % --res_prop_simpl_given false
% 0.75/1.08 % --res_passive_queue_type priority_queues
% 0.75/1.08 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.75/1.08 % --res_passive_queues_freq [15;5]
% 0.75/1.08 % --res_forward_subs full
% 0.75/1.08 % --res_backward_subs full
% 0.75/1.08 % --res_forward_subs_resolution true
% 0.75/1.08 % --res_backward_subs_resolution true
% 0.75/1.08 % --res_orphan_elimination false
% 0.75/1.08 % --res_time_limit 1000.
% 0.75/1.08 % --res_out_proof true
% 0.75/1.08 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_352014.s
% 0.75/1.08 % --modulo true
% 0.75/1.08
% 0.75/1.08 % ------ Combination Options
% 0.75/1.08
% 0.75/1.08 % --comb_res_mult 1000
% 0.75/1.08 % --comb_inst_mult 300
% 0.75/1.08 % ------
% 0.75/1.08
% 0.75/1.08 % ------ Parsing...% successful
% 0.75/1.08
% 0.75/1.08 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e pe_s pe:1:0s pe:2:0s pe_e snvd_s sp: 0 0s snvd_e %
% 0.75/1.08
% 0.75/1.08 % ------ Proving...
% 0.75/1.08 % ------ Problem Properties
% 0.75/1.08
% 0.75/1.08 %
% 0.75/1.08 % EPR false
% 0.75/1.08 % Horn false
% 0.75/1.08 % Has equality true
% 0.75/1.08
% 0.75/1.08 % % ------ Input Options Time Limit: Unbounded
% 0.75/1.08
% 0.75/1.08
% 0.75/1.08 Compiling...
% 0.75/1.08 Loading plugin: done.
% 0.75/1.08 Compiling...
% 0.75/1.08 Loading plugin: done.
% 0.75/1.08 Compiling...
% 0.75/1.08 Loading plugin: done.
% 0.75/1.08 Compiling...
% 0.75/1.08 Loading plugin: done.
% 0.75/1.08 % % ------ Current options:
% 0.75/1.08
% 0.75/1.08 % ------ Input Options
% 0.75/1.08
% 0.75/1.08 % --out_options all
% 0.75/1.08 % --tptp_safe_out true
% 0.75/1.08 % --problem_path ""
% 0.75/1.08 % --include_path ""
% 0.75/1.08 % --clausifier .//eprover
% 0.75/1.08 % --clausifier_options --tstp-format
% 0.75/1.08 % --stdin false
% 0.75/1.08 % --dbg_backtrace false
% 0.75/1.08 % --dbg_dump_prop_clauses false
% 0.75/1.08 % --dbg_dump_prop_clauses_file -
% 0.75/1.08 % --dbg_out_stat false
% 0.75/1.08
% 0.75/1.08 % ------ General Options
% 0.75/1.08
% 0.75/1.08 % --fof false
% 0.75/1.08 % --time_out_real 150.
% 0.75/1.08 % --time_out_prep_mult 0.2
% 0.75/1.08 % --time_out_virtual -1.
% 0.75/1.08 % --schedule none
% 0.75/1.08 % --ground_splitting input
% 0.75/1.08 % --splitting_nvd 16
% 0.75/1.08 % --non_eq_to_eq false
% 0.75/1.08 % --prep_gs_sim true
% 0.75/1.08 % --prep_unflatten false
% 0.75/1.08 % --prep_res_sim true
% 0.75/1.08 % --prep_upred true
% 0.75/1.08 % --res_sim_input true
% 0.75/1.08 % --clause_weak_htbl true
% 0.75/1.08 % --gc_record_bc_elim false
% 0.75/1.08 % --symbol_type_check false
% 0.75/1.08 % --clausify_out false
% 0.75/1.08 % --large_theory_mode false
% 0.75/1.08 % --prep_sem_filter none
% 0.75/1.08 % --prep_sem_filter_out false
% 0.75/1.08 % --preprocessed_out false
% 0.75/1.08 % --sub_typing false
% 0.75/1.08 % --brand_transform false
% 0.75/1.08 % --pure_diseq_elim true
% 0.75/1.08 % --min_unsat_core false
% 0.75/1.08 % --pred_elim true
% 0.75/1.08 % --add_important_lit false
% 0.75/1.08 % --soft_assumptions false
% 0.75/1.08 % --reset_solvers false
% 0.75/1.08 % --bc_imp_inh []
% 0.75/1.08 % --conj_cone_tolerance 1.5
% 0.75/1.08 % --prolific_symb_bound 500
% 0.75/1.08 % --lt_threshold 2000
% 0.75/1.08
% 0.75/1.08 % ------ SAT Options
% 0.75/1.08
% 0.75/1.08 % --sat_mode false
% 0.75/1.08 % --sat_fm_restart_options ""
% 0.75/1.08 % --sat_gr_def false
% 0.75/1.08 % --sat_epr_types true
% 0.75/1.08 % --sat_non_cyclic_types false
% 0.75/1.08 % --sat_finite_models false
% 0.75/1.08 % --sat_fm_lemmas false
% 0.75/1.08 % --sat_fm_prep false
% 0.75/1.08 % --sat_fm_uc_incr true
% 0.75/1.08 % --sat_out_model small
% 0.75/1.08 % --sat_out_clauses false
% 0.75/1.08
% 0.75/1.08 % ------ QBF Options
% 0.75/1.08
% 0.75/1.08 % --qbf_mode false
% 0.75/1.08 % --qbf_elim_univ true
% 0.75/1.08 % --qbf_sk_in true
% 0.75/1.08 % --qbf_pred_elim true
% 0.75/1.08 % --qbf_split 32
% 0.75/1.08
% 0.75/1.08 % ------ BMC1 Options
% 0.75/1.08
% 0.75/1.08 % --bmc1_incremental false
% 0.75/1.08 % --bmc1_axioms reachable_all
% 0.75/1.08 % --bmc1_min_bound 0
% 0.75/1.08 % --bmc1_max_bound -1
% 0.75/1.08 % --bmc1_max_bound_default -1
% 0.75/1.08 % --bmc1_symbol_reachability true
% 0.75/1.08 % --bmc1_property_lemmas false
% 0.75/1.08 % --bmc1_k_induction false
% 0.75/1.08 % --bmc1_non_equiv_states false
% 0.75/1.08 % --bmc1_deadlock false
% 0.75/1.08 % --bmc1_ucm false
% 0.75/1.08 % --bmc1_add_unsat_core none
% 0.75/1.08 % --bmc1_unsat_core_children false
% 0.75/1.08 % --bmc1_unsat_core_extrapolate_axioms false
% 0.75/1.08 % --bmc1_out_stat full
% 0.75/1.08 % --bmc1_ground_init false
% 0.75/1.08 % --bmc1_pre_inst_next_state false
% 0.75/1.08 % --bmc1_pre_inst_state false
% 0.75/1.08 % --bmc1_pre_inst_reach_state false
% 0.75/1.08 % --bmc1_out_unsat_core false
% 0.75/1.08 % --bmc1_aig_witness_out false
% 0.75/1.08 % --bmc1_verbose false
% 0.75/1.08 % --bmc1_dump_clauses_tptp false
% 0.75/1.08 % --bmc1_dump_unsat_core_tptp false
% 0.75/1.08 % --bmc1_dump_file -
% 0.75/1.08 % --bmc1_ucm_expand_uc_limit 128
% 0.75/1.08 % --bmc1_ucm_n_expand_iterations 6
% 0.75/1.08 % --bmc1_ucm_extend_mode 1
% 0.75/1.08 % --bmc1_ucm_init_mode 2
% 0.75/1.08 % --bmc1_ucm_cone_mode none
% 0.75/1.08 % --bmc1_ucm_reduced_relation_type 0
% 0.75/1.08 % --bmc1_ucm_relax_model 4
% 0.75/1.08 % --bmc1_ucm_full_tr_after_sat true
% 0.75/1.08 % --bmc1_ucm_expand_neg_assumptions false
% 0.75/1.08 % --bmc1_ucm_layered_model none
% 0.75/1.08 % --bmc1_ucm_max_lemma_size 10
% 0.75/1.08
% 0.75/1.08 % ------ AIG Options
% 0.75/1.08
% 0.75/1.08 % --aig_mode false
% 0.75/1.08
% 0.75/1.08 % ------ Instantiation Options
% 0.75/1.08
% 0.75/1.08 % --instantiation_flag true
% 0.75/1.08 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.75/1.08 % --inst_solver_per_active 750
% 0.75/1.08 % --inst_solver_calls_frac 0.5
% 0.75/1.08 % --inst_passive_queue_type priority_queues
% 0.75/1.08 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.75/1.08 % --inst_passive_queues_freq [25;2]
% 8.19/8.40 % --inst_dismatching true
% 8.19/8.40 % --inst_eager_unprocessed_to_passive true
% 8.19/8.40 % --inst_prop_sim_given true
% 8.19/8.40 % --inst_prop_sim_new false
% 8.19/8.40 % --inst_orphan_elimination true
% 8.19/8.40 % --inst_learning_loop_flag true
% 8.19/8.40 % --inst_learning_start 3000
% 8.19/8.40 % --inst_learning_factor 2
% 8.19/8.40 % --inst_start_prop_sim_after_learn 3
% 8.19/8.40 % --inst_sel_renew solver
% 8.19/8.40 % --inst_lit_activity_flag true
% 8.19/8.40 % --inst_out_proof true
% 8.19/8.40
% 8.19/8.40 % ------ Resolution Options
% 8.19/8.40
% 8.19/8.40 % --resolution_flag true
% 8.19/8.40 % --res_lit_sel kbo_max
% 8.19/8.40 % --res_to_prop_solver none
% 8.19/8.40 % --res_prop_simpl_new false
% 8.19/8.40 % --res_prop_simpl_given false
% 8.19/8.40 % --res_passive_queue_type priority_queues
% 8.19/8.40 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 8.19/8.40 % --res_passive_queues_freq [15;5]
% 8.19/8.40 % --res_forward_subs full
% 8.19/8.40 % --res_backward_subs full
% 8.19/8.40 % --res_forward_subs_resolution true
% 8.19/8.40 % --res_backward_subs_resolution true
% 8.19/8.40 % --res_orphan_elimination false
% 8.19/8.40 % --res_time_limit 1000.
% 8.19/8.40 % --res_out_proof true
% 8.19/8.40 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_352014.s
% 8.19/8.40 % --modulo true
% 8.19/8.40
% 8.19/8.40 % ------ Combination Options
% 8.19/8.40
% 8.19/8.40 % --comb_res_mult 1000
% 8.19/8.40 % --comb_inst_mult 300
% 8.19/8.40 % ------
% 8.19/8.40
% 8.19/8.40
% 8.19/8.40
% 8.19/8.40 % ------ Proving...
% 8.19/8.40 %
% 8.19/8.40
% 8.19/8.40
% 8.19/8.40 % ------ Statistics
% 8.19/8.40
% 8.19/8.40 % ------ General
% 8.19/8.40
% 8.19/8.40 % num_of_input_clauses: 802
% 8.19/8.40 % num_of_input_neg_conjectures: 2
% 8.19/8.40 % num_of_splits: 0
% 8.19/8.40 % num_of_split_atoms: 0
% 8.19/8.40 % num_of_sem_filtered_clauses: 0
% 8.19/8.40 % num_of_subtypes: 0
% 8.19/8.40 % monotx_restored_types: 0
% 8.19/8.40 % sat_num_of_epr_types: 0
% 8.19/8.40 % sat_num_of_non_cyclic_types: 0
% 8.19/8.40 % sat_guarded_non_collapsed_types: 0
% 8.19/8.40 % is_epr: 0
% 8.19/8.40 % is_horn: 0
% 8.19/8.40 % has_eq: 1
% 8.19/8.40 % num_pure_diseq_elim: 0
% 8.19/8.40 % simp_replaced_by: 0
% 8.19/8.40 % res_preprocessed: 132
% 8.19/8.40 % prep_upred: 0
% 8.19/8.40 % prep_unflattend: 0
% 8.19/8.40 % pred_elim_cands: 5
% 8.19/8.40 % pred_elim: 2
% 8.19/8.40 % pred_elim_cl: 2
% 8.19/8.40 % pred_elim_cycles: 3
% 8.19/8.40 % forced_gc_time: 0
% 8.19/8.40 % gc_basic_clause_elim: 0
% 8.19/8.40 % parsing_time: 0.041
% 8.19/8.40 % sem_filter_time: 0.
% 8.19/8.40 % pred_elim_time: 0.001
% 8.19/8.40 % out_proof_time: 0.001
% 8.19/8.40 % monotx_time: 0.
% 8.19/8.40 % subtype_inf_time: 0.
% 8.19/8.40 % unif_index_cands_time: 0.048
% 8.19/8.40 % unif_index_add_time: 0.006
% 8.19/8.40 % total_time: 7.846
% 8.19/8.40 % num_of_symbols: 126
% 8.19/8.40 % num_of_terms: 278320
% 8.19/8.40
% 8.19/8.40 % ------ Propositional Solver
% 8.19/8.40
% 8.19/8.40 % prop_solver_calls: 4
% 8.19/8.40 % prop_fast_solver_calls: 591
% 8.19/8.40 % prop_num_of_clauses: 2671
% 8.19/8.40 % prop_preprocess_simplified: 7254
% 8.19/8.40 % prop_fo_subsumed: 1
% 8.19/8.40 % prop_solver_time: 0.
% 8.19/8.40 % prop_fast_solver_time: 0.
% 8.19/8.40 % prop_unsat_core_time: 0.
% 8.19/8.40
% 8.19/8.40 % ------ QBF
% 8.19/8.40
% 8.19/8.40 % qbf_q_res: 0
% 8.19/8.40 % qbf_num_tautologies: 0
% 8.19/8.40 % qbf_prep_cycles: 0
% 8.19/8.40
% 8.19/8.40 % ------ BMC1
% 8.19/8.40
% 8.19/8.40 % bmc1_current_bound: -1
% 8.19/8.40 % bmc1_last_solved_bound: -1
% 8.19/8.40 % bmc1_unsat_core_size: -1
% 8.19/8.40 % bmc1_unsat_core_parents_size: -1
% 8.19/8.40 % bmc1_merge_next_fun: 0
% 8.19/8.40 % bmc1_unsat_core_clauses_time: 0.
% 8.19/8.40
% 8.19/8.40 % ------ Instantiation
% 8.19/8.40
% 8.19/8.40 % inst_num_of_clauses: 1889
% 8.19/8.40 % inst_num_in_passive: 1317
% 8.19/8.40 % inst_num_in_active: 438
% 8.19/8.40 % inst_num_in_unprocessed: 129
% 8.19/8.40 % inst_num_of_loops: 442
% 8.19/8.40 % inst_num_of_learning_restarts: 0
% 8.19/8.40 % inst_num_moves_active_passive: 2
% 8.19/8.40 % inst_lit_activity: 213
% 8.19/8.40 % inst_lit_activity_moves: 0
% 8.19/8.40 % inst_num_tautologies: 0
% 8.19/8.40 % inst_num_prop_implied: 0
% 8.19/8.40 % inst_num_existing_simplified: 0
% 8.19/8.40 % inst_num_eq_res_simplified: 0
% 8.19/8.40 % inst_num_child_elim: 0
% 8.19/8.40 % inst_num_of_dismatching_blockings: 355
% 8.19/8.40 % inst_num_of_non_proper_insts: 911
% 8.19/8.40 % inst_num_of_duplicates: 1665
% 8.19/8.40 % inst_inst_num_from_inst_to_res: 0
% 8.19/8.40 % inst_dismatching_checking_time: 0.001
% 8.19/8.40
% 8.19/8.40 % ------ Resolution
% 8.19/8.40
% 8.19/8.40 % res_num_of_clauses: 126636
% 8.19/8.40 % res_num_in_passive: 124051
% 8.19/8.40 % res_num_in_active: 2076
% 8.19/8.40 % res_num_of_loops: 2000
% 8.19/8.40 % res_forward_subset_subsumed: 6095
% 8.19/8.40 % res_backward_subset_subsumed: 7
% 8.19/8.40 % res_forward_subsumed: 222
% 8.19/8.40 % res_backward_subsumed: 3
% 8.19/8.40 % res_forward_subsumption_resolution: 117
% 8.19/8.40 % res_backward_subsumption_resolution: 3
% 8.19/8.40 % res_clause_to_clause_subsumption: 19530
% 8.19/8.40 % res_orphan_elimination: 0
% 8.19/8.40 % res_tautology_del: 302
% 8.19/8.40 % res_num_eq_res_simplified: 0
% 8.19/8.40 % res_num_sel_changes: 0
% 8.19/8.40 % res_moves_from_active_to_pass: 0
% 8.19/8.40
% 8.19/8.40 % Status Unsatisfiable
% 8.19/8.40 % SZS status Theorem
% 8.19/8.40 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------