TSTP Solution File: SEU177+2 by iProverMo---2.5-0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : SEU177+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n025.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 10:25:40 EDT 2022
% Result : Theorem 104.88s 105.12s
% Output : CNFRefutation 104.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 147
% Syntax : Number of formulae : 1333 ( 295 unt; 0 def)
% Number of atoms : 3720 (1080 equ)
% Maximal formula atoms : 32 ( 2 avg)
% Number of connectives : 4067 (1680 ~;1920 |; 221 &)
% ( 92 <=>; 154 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 8 usr; 2 prp; 0-2 aty)
% Number of functors : 98 ( 98 usr; 13 con; 0-4 aty)
% Number of variables : 3179 ( 180 sgn 963 !; 30 ?)
% Comments :
%------------------------------------------------------------------------------
% Axioms transformation by autotheo
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0,axiom,
! [X1,X2,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_1,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ! [X3] :
( element(X3,powerset(powerset(X1)))
=> ( X3 = complements_of_subsets(X1,X2)
<=> ! [X4] :
( element(X4,powerset(X1))
=> ( in(X4,X3)
<=> in(subset_complement(X1,X4),X2) ) ) ) ) ),
file('<stdin>',d8_setfam_1) ).
fof(c_0_2,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_3,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_4,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_5,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
file('<stdin>',d2_tarski) ).
fof(c_0_6,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_7,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_8,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_9,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_10,axiom,
! [X1,X2] :
( X2 = union(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X3,X4)
& in(X4,X1) ) ) ),
file('<stdin>',d4_tarski) ).
fof(c_0_11,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_12,axiom,
! [X1,X2] :
( X2 = powerset(X1)
<=> ! [X3] :
( in(X3,X2)
<=> subset(X3,X1) ) ),
file('<stdin>',d1_zfmisc_1) ).
fof(c_0_13,axiom,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
<=> in(X3,X2) )
=> X1 = X2 ),
file('<stdin>',t2_tarski) ).
fof(c_0_14,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_15,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_16,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_17,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_18,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('<stdin>',d1_tarski) ).
fof(c_0_19,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_20,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> element(subset_complement(X1,X2),powerset(X1)) ),
file('<stdin>',dt_k3_subset_1) ).
fof(c_0_21,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('<stdin>',d3_tarski) ).
fof(c_0_22,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,subset_complement(X1,X2)) = X2 ),
file('<stdin>',involutiveness_k3_subset_1) ).
fof(c_0_23,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_24,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> union_of_subsets(X1,X2) = union(X2) ),
file('<stdin>',redefinition_k5_setfam_1) ).
fof(c_0_25,axiom,
! [X1,X2,X3] :
( ( in(X1,X2)
& element(X2,powerset(X3)) )
=> element(X1,X3) ),
file('<stdin>',t4_subset) ).
fof(c_0_26,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
file('<stdin>',t5_subset) ).
fof(c_0_27,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,X2) = set_difference(X1,X2) ),
file('<stdin>',d5_subset_1) ).
fof(c_0_28,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('<stdin>',d5_tarski) ).
fof(c_0_29,axiom,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X2,X1)) ),
file('<stdin>',fc3_xboole_0) ).
fof(c_0_30,axiom,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X1,X2)) ),
file('<stdin>',fc2_xboole_0) ).
fof(c_0_31,axiom,
! [X1,X2] : ~ empty(unordered_pair(X1,X2)),
file('<stdin>',fc3_subset_1) ).
fof(c_0_32,axiom,
! [X1,X2] : ~ empty(ordered_pair(X1,X2)),
file('<stdin>',fc1_zfmisc_1) ).
fof(c_0_33,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('<stdin>',d10_xboole_0) ).
fof(c_0_34,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('<stdin>',t3_subset) ).
fof(c_0_35,axiom,
! [X1,X2] :
( proper_subset(X1,X2)
=> ~ proper_subset(X2,X1) ),
file('<stdin>',antisymmetry_r2_xboole_0) ).
fof(c_0_36,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('<stdin>',antisymmetry_r2_hidden) ).
fof(c_0_37,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('<stdin>',t2_subset) ).
fof(c_0_38,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_39,axiom,
! [X1,X2] :
( proper_subset(X1,X2)
<=> ( subset(X1,X2)
& X1 != X2 ) ),
file('<stdin>',d8_xboole_0) ).
fof(c_0_40,axiom,
! [X1,X2] :
( in(X1,X2)
=> element(X1,X2) ),
file('<stdin>',t1_subset) ).
fof(c_0_41,axiom,
! [X1,X2] :
( disjoint(X1,X2)
=> disjoint(X2,X1) ),
file('<stdin>',symmetry_r1_xboole_0) ).
fof(c_0_42,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_intersection2(X1,X2) = empty_set ),
file('<stdin>',d7_xboole_0) ).
fof(c_0_43,axiom,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
file('<stdin>',rc1_subset_1) ).
fof(c_0_44,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('<stdin>',t7_boole) ).
fof(c_0_45,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('<stdin>',commutativity_k3_xboole_0) ).
fof(c_0_46,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('<stdin>',commutativity_k2_xboole_0) ).
fof(c_0_47,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('<stdin>',commutativity_k2_tarski) ).
fof(c_0_48,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2) ),
file('<stdin>',rc2_subset_1) ).
fof(c_0_49,axiom,
! [X1] : element(cast_to_subset(X1),powerset(X1)),
file('<stdin>',dt_k2_subset_1) ).
fof(c_0_50,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('<stdin>',d1_xboole_0) ).
fof(c_0_51,axiom,
! [X1,X2] : ~ proper_subset(X1,X1),
file('<stdin>',irreflexivity_r2_xboole_0) ).
fof(c_0_52,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('<stdin>',existence_m1_subset_1) ).
fof(c_0_53,axiom,
! [X1] : ~ empty(singleton(X1)),
file('<stdin>',fc2_subset_1) ).
fof(c_0_54,axiom,
! [X1] : ~ empty(powerset(X1)),
file('<stdin>',fc1_subset_1) ).
fof(c_0_55,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
file('<stdin>',t8_boole) ).
fof(c_0_56,axiom,
! [X1,X2] : set_intersection2(X1,X1) = X1,
file('<stdin>',idempotence_k3_xboole_0) ).
fof(c_0_57,axiom,
! [X1,X2] : set_union2(X1,X1) = X1,
file('<stdin>',idempotence_k2_xboole_0) ).
fof(c_0_58,axiom,
! [X1,X2] : subset(X1,X1),
file('<stdin>',reflexivity_r1_tarski) ).
fof(c_0_59,axiom,
! [X1] : set_difference(X1,empty_set) = X1,
file('<stdin>',t3_boole) ).
fof(c_0_60,axiom,
! [X1] : set_union2(X1,empty_set) = X1,
file('<stdin>',t1_boole) ).
fof(c_0_61,axiom,
! [X1] : set_difference(empty_set,X1) = empty_set,
file('<stdin>',t4_boole) ).
fof(c_0_62,axiom,
! [X1] : set_intersection2(X1,empty_set) = empty_set,
file('<stdin>',t2_boole) ).
fof(c_0_63,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('<stdin>',t6_boole) ).
fof(c_0_64,axiom,
! [X1] : cast_to_subset(X1) = X1,
file('<stdin>',d4_subset_1) ).
fof(c_0_65,axiom,
? [X1] : ~ empty(X1),
file('<stdin>',rc2_xboole_0) ).
fof(c_0_66,axiom,
? [X1] : empty(X1),
file('<stdin>',rc1_xboole_0) ).
fof(c_0_67,axiom,
? [X1] :
( empty(X1)
& relation(X1) ),
file('<stdin>',rc1_relat_1) ).
fof(c_0_68,axiom,
empty(empty_set),
file('<stdin>',fc1_xboole_0) ).
fof(c_0_69,axiom,
$true,
file('<stdin>',dt_m1_subset_1) ).
fof(c_0_70,axiom,
$true,
file('<stdin>',dt_k4_xboole_0) ).
fof(c_0_71,axiom,
$true,
file('<stdin>',dt_k4_tarski) ).
fof(c_0_72,axiom,
$true,
file('<stdin>',dt_k3_xboole_0) ).
fof(c_0_73,axiom,
$true,
file('<stdin>',dt_k3_tarski) ).
fof(c_0_74,axiom,
$true,
file('<stdin>',dt_k2_zfmisc_1) ).
fof(c_0_75,axiom,
$true,
file('<stdin>',dt_k2_xboole_0) ).
fof(c_0_76,axiom,
$true,
file('<stdin>',dt_k2_tarski) ).
fof(c_0_77,axiom,
$true,
file('<stdin>',dt_k2_relat_1) ).
fof(c_0_78,axiom,
$true,
file('<stdin>',dt_k1_zfmisc_1) ).
fof(c_0_79,axiom,
$true,
file('<stdin>',dt_k1_xboole_0) ).
fof(c_0_80,axiom,
$true,
file('<stdin>',dt_k1_tarski) ).
fof(c_0_81,axiom,
$true,
file('<stdin>',dt_k1_setfam_1) ).
fof(c_0_82,axiom,
$true,
file('<stdin>',dt_k1_relat_1) ).
fof(c_0_83,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_0 ).
fof(c_0_84,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_1 ).
fof(c_0_85,axiom,
! [X1,X2,X3] :
( X3 = set_intersection2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& in(X4,X2) ) ) ),
c_0_2 ).
fof(c_0_86,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_3]) ).
fof(c_0_87,axiom,
! [X1,X2,X3] :
( X3 = set_union2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
| in(X4,X2) ) ) ),
c_0_4 ).
fof(c_0_88,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
c_0_5 ).
fof(c_0_89,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_rng(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X4,X3),X1) ) ) ),
c_0_6 ).
fof(c_0_90,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_dom(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X3,X4),X1) ) ) ),
c_0_7 ).
fof(c_0_91,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_8 ).
fof(c_0_92,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> element(subset_difference(X1,X2,X3),powerset(X1)) ),
c_0_9 ).
fof(c_0_93,axiom,
! [X1,X2] :
( X2 = union(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X3,X4)
& in(X4,X1) ) ) ),
c_0_10 ).
fof(c_0_94,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> subset_difference(X1,X2,X3) = set_difference(X2,X3) ),
c_0_11 ).
fof(c_0_95,axiom,
! [X1,X2] :
( X2 = powerset(X1)
<=> ! [X3] :
( in(X3,X2)
<=> subset(X3,X1) ) ),
c_0_12 ).
fof(c_0_96,axiom,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
<=> in(X3,X2) )
=> X1 = X2 ),
c_0_13 ).
fof(c_0_97,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> element(complements_of_subsets(X1,X2),powerset(powerset(X1))) ),
c_0_14 ).
fof(c_0_98,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> element(meet_of_subsets(X1,X2),powerset(X1)) ),
c_0_15 ).
fof(c_0_99,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> element(union_of_subsets(X1,X2),powerset(X1)) ),
c_0_16 ).
fof(c_0_100,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_17]) ).
fof(c_0_101,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
c_0_18 ).
fof(c_0_102,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2 ),
c_0_19 ).
fof(c_0_103,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> element(subset_complement(X1,X2),powerset(X1)) ),
c_0_20 ).
fof(c_0_104,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
c_0_21 ).
fof(c_0_105,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,subset_complement(X1,X2)) = X2 ),
c_0_22 ).
fof(c_0_106,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> meet_of_subsets(X1,X2) = set_meet(X2) ),
c_0_23 ).
fof(c_0_107,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> union_of_subsets(X1,X2) = union(X2) ),
c_0_24 ).
fof(c_0_108,axiom,
! [X1,X2,X3] :
( ( in(X1,X2)
& element(X2,powerset(X3)) )
=> element(X1,X3) ),
c_0_25 ).
fof(c_0_109,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
c_0_26 ).
fof(c_0_110,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,X2) = set_difference(X1,X2) ),
c_0_27 ).
fof(c_0_111,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
c_0_28 ).
fof(c_0_112,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X2,X1)) ),
inference(fof_simplification,[status(thm)],[c_0_29]) ).
fof(c_0_113,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X1,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_30]) ).
fof(c_0_114,plain,
! [X1,X2] : ~ empty(unordered_pair(X1,X2)),
inference(fof_simplification,[status(thm)],[c_0_31]) ).
fof(c_0_115,plain,
! [X1,X2] : ~ empty(ordered_pair(X1,X2)),
inference(fof_simplification,[status(thm)],[c_0_32]) ).
fof(c_0_116,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
c_0_33 ).
fof(c_0_117,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
c_0_34 ).
fof(c_0_118,plain,
! [X1,X2] :
( proper_subset(X1,X2)
=> ~ proper_subset(X2,X1) ),
inference(fof_simplification,[status(thm)],[c_0_35]) ).
fof(c_0_119,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[c_0_36]) ).
fof(c_0_120,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
c_0_37 ).
fof(c_0_121,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_38]) ).
fof(c_0_122,axiom,
! [X1,X2] :
( proper_subset(X1,X2)
<=> ( subset(X1,X2)
& X1 != X2 ) ),
c_0_39 ).
fof(c_0_123,axiom,
! [X1,X2] :
( in(X1,X2)
=> element(X1,X2) ),
c_0_40 ).
fof(c_0_124,axiom,
! [X1,X2] :
( disjoint(X1,X2)
=> disjoint(X2,X1) ),
c_0_41 ).
fof(c_0_125,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_intersection2(X1,X2) = empty_set ),
c_0_42 ).
fof(c_0_126,plain,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
inference(fof_simplification,[status(thm)],[c_0_43]) ).
fof(c_0_127,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
c_0_44 ).
fof(c_0_128,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
c_0_45 ).
fof(c_0_129,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
c_0_46 ).
fof(c_0_130,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
c_0_47 ).
fof(c_0_131,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2) ),
c_0_48 ).
fof(c_0_132,axiom,
! [X1] : element(cast_to_subset(X1),powerset(X1)),
c_0_49 ).
fof(c_0_133,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[c_0_50]) ).
fof(c_0_134,plain,
! [X1,X2] : ~ proper_subset(X1,X1),
inference(fof_simplification,[status(thm)],[c_0_51]) ).
fof(c_0_135,axiom,
! [X1] :
? [X2] : element(X2,X1),
c_0_52 ).
fof(c_0_136,plain,
! [X1] : ~ empty(singleton(X1)),
inference(fof_simplification,[status(thm)],[c_0_53]) ).
fof(c_0_137,plain,
! [X1] : ~ empty(powerset(X1)),
inference(fof_simplification,[status(thm)],[c_0_54]) ).
fof(c_0_138,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
c_0_55 ).
fof(c_0_139,axiom,
! [X1,X2] : set_intersection2(X1,X1) = X1,
c_0_56 ).
fof(c_0_140,axiom,
! [X1,X2] : set_union2(X1,X1) = X1,
c_0_57 ).
fof(c_0_141,axiom,
! [X1,X2] : subset(X1,X1),
c_0_58 ).
fof(c_0_142,axiom,
! [X1] : set_difference(X1,empty_set) = X1,
c_0_59 ).
fof(c_0_143,axiom,
! [X1] : set_union2(X1,empty_set) = X1,
c_0_60 ).
fof(c_0_144,axiom,
! [X1] : set_difference(empty_set,X1) = empty_set,
c_0_61 ).
fof(c_0_145,axiom,
! [X1] : set_intersection2(X1,empty_set) = empty_set,
c_0_62 ).
fof(c_0_146,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
c_0_63 ).
fof(c_0_147,axiom,
! [X1] : cast_to_subset(X1) = X1,
c_0_64 ).
fof(c_0_148,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[c_0_65]) ).
fof(c_0_149,axiom,
? [X1] : empty(X1),
c_0_66 ).
fof(c_0_150,axiom,
? [X1] :
( empty(X1)
& relation(X1) ),
c_0_67 ).
fof(c_0_151,axiom,
empty(empty_set),
c_0_68 ).
fof(c_0_152,axiom,
$true,
c_0_69 ).
fof(c_0_153,axiom,
$true,
c_0_70 ).
fof(c_0_154,axiom,
$true,
c_0_71 ).
fof(c_0_155,axiom,
$true,
c_0_72 ).
fof(c_0_156,axiom,
$true,
c_0_73 ).
fof(c_0_157,axiom,
$true,
c_0_74 ).
fof(c_0_158,axiom,
$true,
c_0_75 ).
fof(c_0_159,axiom,
$true,
c_0_76 ).
fof(c_0_160,axiom,
$true,
c_0_77 ).
fof(c_0_161,axiom,
$true,
c_0_78 ).
fof(c_0_162,axiom,
$true,
c_0_79 ).
fof(c_0_163,axiom,
$true,
c_0_80 ).
fof(c_0_164,axiom,
$true,
c_0_81 ).
fof(c_0_165,axiom,
$true,
c_0_82 ).
fof(c_0_166,plain,
! [X7,X8,X9,X10,X13,X14,X15,X16,X17,X18,X20,X21] :
( ( in(esk9_4(X7,X8,X9,X10),X7)
| ~ in(X10,X9)
| X9 != cartesian_product2(X7,X8) )
& ( in(esk10_4(X7,X8,X9,X10),X8)
| ~ in(X10,X9)
| X9 != cartesian_product2(X7,X8) )
& ( X10 = ordered_pair(esk9_4(X7,X8,X9,X10),esk10_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(esk11_3(X16,X17,X18),X18)
| ~ in(X20,X16)
| ~ in(X21,X17)
| esk11_3(X16,X17,X18) != ordered_pair(X20,X21)
| X18 = cartesian_product2(X16,X17) )
& ( in(esk12_3(X16,X17,X18),X16)
| in(esk11_3(X16,X17,X18),X18)
| X18 = cartesian_product2(X16,X17) )
& ( in(esk13_3(X16,X17,X18),X17)
| in(esk11_3(X16,X17,X18),X18)
| X18 = cartesian_product2(X16,X17) )
& ( esk11_3(X16,X17,X18) = ordered_pair(esk12_3(X16,X17,X18),esk13_3(X16,X17,X18))
| in(esk11_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_83])])])])])]) ).
fof(c_0_167,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(esk26_3(X5,X6,X7),powerset(X5))
| X7 = complements_of_subsets(X5,X6)
| ~ element(X7,powerset(powerset(X5)))
| ~ element(X6,powerset(powerset(X5))) )
& ( ~ in(esk26_3(X5,X6,X7),X7)
| ~ in(subset_complement(X5,esk26_3(X5,X6,X7)),X6)
| X7 = complements_of_subsets(X5,X6)
| ~ element(X7,powerset(powerset(X5)))
| ~ element(X6,powerset(powerset(X5))) )
& ( in(esk26_3(X5,X6,X7),X7)
| in(subset_complement(X5,esk26_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_84])])])])]) ).
fof(c_0_168,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(esk15_3(X10,X11,X12),X12)
| ~ in(esk15_3(X10,X11,X12),X10)
| ~ in(esk15_3(X10,X11,X12),X11)
| X12 = set_intersection2(X10,X11) )
& ( in(esk15_3(X10,X11,X12),X10)
| in(esk15_3(X10,X11,X12),X12)
| X12 = set_intersection2(X10,X11) )
& ( in(esk15_3(X10,X11,X12),X11)
| in(esk15_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_85])])])])])]) ).
fof(c_0_169,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(esk22_3(X10,X11,X12),X12)
| ~ in(esk22_3(X10,X11,X12),X10)
| in(esk22_3(X10,X11,X12),X11)
| X12 = set_difference(X10,X11) )
& ( in(esk22_3(X10,X11,X12),X10)
| in(esk22_3(X10,X11,X12),X12)
| X12 = set_difference(X10,X11) )
& ( ~ in(esk22_3(X10,X11,X12),X11)
| in(esk22_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_86])])])])])]) ).
fof(c_0_170,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(esk8_3(X10,X11,X12),X10)
| ~ in(esk8_3(X10,X11,X12),X12)
| X12 = set_union2(X10,X11) )
& ( ~ in(esk8_3(X10,X11,X12),X11)
| ~ in(esk8_3(X10,X11,X12),X12)
| X12 = set_union2(X10,X11) )
& ( in(esk8_3(X10,X11,X12),X12)
| in(esk8_3(X10,X11,X12),X10)
| in(esk8_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_87])])])])])]) ).
fof(c_0_171,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) )
& ( esk7_3(X10,X11,X12) != X10
| ~ in(esk7_3(X10,X11,X12),X12)
| X12 = unordered_pair(X10,X11) )
& ( esk7_3(X10,X11,X12) != X11
| ~ in(esk7_3(X10,X11,X12),X12)
| X12 = unordered_pair(X10,X11) )
& ( in(esk7_3(X10,X11,X12),X12)
| esk7_3(X10,X11,X12) = X10
| esk7_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_88])])])])])]) ).
fof(c_0_172,plain,
! [X5,X6,X7,X9,X10,X11,X13] :
( ( ~ in(X7,X6)
| in(ordered_pair(esk23_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(esk24_2(X5,X11),X11)
| ~ in(ordered_pair(X13,esk24_2(X5,X11)),X5)
| X11 = relation_rng(X5)
| ~ relation(X5) )
& ( in(esk24_2(X5,X11),X11)
| in(ordered_pair(esk25_2(X5,X11),esk24_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_89])])])])])]) ).
fof(c_0_173,plain,
! [X5,X6,X7,X9,X10,X11,X13] :
( ( ~ in(X7,X6)
| in(ordered_pair(X7,esk16_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(esk17_2(X5,X11),X11)
| ~ in(ordered_pair(esk17_2(X5,X11),X13),X5)
| X11 = relation_dom(X5)
| ~ relation(X5) )
& ( in(esk17_2(X5,X11),X11)
| in(ordered_pair(esk17_2(X5,X11),esk18_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_90])])])])])]) ).
fof(c_0_174,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(esk1_3(X5,X6,X9),X5)
| in(X9,X6)
| X6 != set_meet(X5)
| X5 = empty_set )
& ( ~ in(X9,esk1_3(X5,X6,X9))
| in(X9,X6)
| X6 != set_meet(X5)
| X5 = empty_set )
& ( in(esk3_2(X5,X11),X5)
| ~ in(esk2_2(X5,X11),X11)
| X11 = set_meet(X5)
| X5 = empty_set )
& ( ~ in(esk2_2(X5,X11),esk3_2(X5,X11))
| ~ in(esk2_2(X5,X11),X11)
| X11 = set_meet(X5)
| X5 = empty_set )
& ( in(esk2_2(X5,X11),X11)
| ~ in(X14,X5)
| in(esk2_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_91])])])])])]) ).
fof(c_0_175,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_92])]) ).
fof(c_0_176,plain,
! [X5,X6,X7,X9,X10,X11,X12,X14] :
( ( in(X7,esk19_3(X5,X6,X7))
| ~ in(X7,X6)
| X6 != union(X5) )
& ( in(esk19_3(X5,X6,X7),X5)
| ~ in(X7,X6)
| X6 != union(X5) )
& ( ~ in(X9,X10)
| ~ in(X10,X5)
| in(X9,X6)
| X6 != union(X5) )
& ( ~ in(esk20_2(X11,X12),X12)
| ~ in(esk20_2(X11,X12),X14)
| ~ in(X14,X11)
| X12 = union(X11) )
& ( in(esk20_2(X11,X12),esk21_2(X11,X12))
| in(esk20_2(X11,X12),X12)
| X12 = union(X11) )
& ( in(esk21_2(X11,X12),X11)
| in(esk20_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_93])])])])])]) ).
fof(c_0_177,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_94])]) ).
fof(c_0_178,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(esk6_2(X8,X9),X9)
| ~ subset(esk6_2(X8,X9),X8)
| X9 = powerset(X8) )
& ( in(esk6_2(X8,X9),X9)
| subset(esk6_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_95])])])])])]) ).
fof(c_0_179,plain,
! [X4,X5] :
( ( ~ in(esk33_2(X4,X5),X4)
| ~ in(esk33_2(X4,X5),X5)
| X4 = X5 )
& ( in(esk33_2(X4,X5),X4)
| in(esk33_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_96])])])]) ).
fof(c_0_180,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_97])]) ).
fof(c_0_181,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_98])]) ).
fof(c_0_182,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_99])]) ).
fof(c_0_183,plain,
! [X6,X8,X9,X10,X12,X13] :
( in(X6,esk34_1(X6))
& ( ~ in(X8,esk34_1(X6))
| ~ subset(X9,X8)
| in(X9,esk34_1(X6)) )
& ( in(esk35_2(X6,X10),esk34_1(X6))
| ~ in(X10,esk34_1(X6)) )
& ( ~ subset(X12,X10)
| in(X12,esk35_2(X6,X10))
| ~ in(X10,esk34_1(X6)) )
& ( ~ subset(X13,esk34_1(X6))
| are_equipotent(X13,esk34_1(X6))
| in(X13,esk34_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_100])])])])]) ).
fof(c_0_184,plain,
! [X4,X5,X6,X7,X8,X9] :
( ( ~ in(X6,X5)
| X6 = X4
| X5 != singleton(X4) )
& ( X7 != X4
| in(X7,X5)
| X5 != singleton(X4) )
& ( ~ in(esk4_2(X8,X9),X9)
| esk4_2(X8,X9) != X8
| X9 = singleton(X8) )
& ( in(esk4_2(X8,X9),X9)
| esk4_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_101])])])])])]) ).
fof(c_0_185,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_102])]) ).
fof(c_0_186,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_103])]) ).
fof(c_0_187,plain,
! [X4,X5,X6,X7,X8] :
( ( ~ subset(X4,X5)
| ~ in(X6,X4)
| in(X6,X5) )
& ( in(esk14_2(X7,X8),X7)
| subset(X7,X8) )
& ( ~ in(esk14_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_104])])])])])]) ).
fof(c_0_188,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_105])]) ).
fof(c_0_189,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_106])]) ).
fof(c_0_190,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_107])]) ).
fof(c_0_191,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_108])]) ).
fof(c_0_192,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_109])])])]) ).
fof(c_0_193,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_110])]) ).
fof(c_0_194,plain,
! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
inference(variable_rename,[status(thm)],[c_0_111]) ).
fof(c_0_195,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_112])])])]) ).
fof(c_0_196,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_113])])])]) ).
fof(c_0_197,plain,
! [X3,X4] : ~ empty(unordered_pair(X3,X4)),
inference(variable_rename,[status(thm)],[c_0_114]) ).
fof(c_0_198,plain,
! [X3,X4] : ~ empty(ordered_pair(X3,X4)),
inference(variable_rename,[status(thm)],[c_0_115]) ).
fof(c_0_199,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_116])])])])]) ).
fof(c_0_200,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_117])])])]) ).
fof(c_0_201,plain,
! [X3,X4] :
( ~ proper_subset(X3,X4)
| ~ proper_subset(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_118])]) ).
fof(c_0_202,plain,
! [X3,X4] :
( ~ in(X3,X4)
| ~ in(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_119])]) ).
fof(c_0_203,plain,
! [X3,X4] :
( ~ element(X3,X4)
| empty(X4)
| in(X3,X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_120])]) ).
fof(c_0_204,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_121])])])])]) ).
fof(c_0_205,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_122])])])])]) ).
fof(c_0_206,plain,
! [X3,X4] :
( ~ in(X3,X4)
| element(X3,X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_123])]) ).
fof(c_0_207,plain,
! [X3,X4] :
( ~ disjoint(X3,X4)
| disjoint(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_124])]) ).
fof(c_0_208,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_125])])])]) ).
fof(c_0_209,plain,
! [X3] :
( ( element(esk29_1(X3),powerset(X3))
| empty(X3) )
& ( ~ empty(esk29_1(X3))
| empty(X3) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_126])])])]) ).
fof(c_0_210,plain,
! [X3,X4] :
( ~ in(X3,X4)
| ~ empty(X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_127])]) ).
fof(c_0_211,plain,
! [X3,X4] : set_intersection2(X3,X4) = set_intersection2(X4,X3),
inference(variable_rename,[status(thm)],[c_0_128]) ).
fof(c_0_212,plain,
! [X3,X4] : set_union2(X3,X4) = set_union2(X4,X3),
inference(variable_rename,[status(thm)],[c_0_129]) ).
fof(c_0_213,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[c_0_130]) ).
fof(c_0_214,plain,
! [X3] :
( element(esk31_1(X3),powerset(X3))
& empty(esk31_1(X3)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_131])]) ).
fof(c_0_215,plain,
! [X2] : element(cast_to_subset(X2),powerset(X2)),
inference(variable_rename,[status(thm)],[c_0_132]) ).
fof(c_0_216,plain,
! [X3,X4,X5] :
( ( X3 != empty_set
| ~ in(X4,X3) )
& ( in(esk5_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_133])])])])]) ).
fof(c_0_217,plain,
! [X3,X4] : ~ proper_subset(X3,X3),
inference(variable_rename,[status(thm)],[c_0_134]) ).
fof(c_0_218,plain,
! [X3] : element(esk27_1(X3),X3),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_135])]) ).
fof(c_0_219,plain,
! [X2] : ~ empty(singleton(X2)),
inference(variable_rename,[status(thm)],[c_0_136]) ).
fof(c_0_220,plain,
! [X2] : ~ empty(powerset(X2)),
inference(variable_rename,[status(thm)],[c_0_137]) ).
fof(c_0_221,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_138])])])]) ).
fof(c_0_222,plain,
! [X3,X4] : set_intersection2(X3,X3) = X3,
inference(variable_rename,[status(thm)],[c_0_139]) ).
fof(c_0_223,plain,
! [X3,X4] : set_union2(X3,X3) = X3,
inference(variable_rename,[status(thm)],[c_0_140]) ).
fof(c_0_224,plain,
! [X3,X4] : subset(X3,X3),
inference(variable_rename,[status(thm)],[c_0_141]) ).
fof(c_0_225,plain,
! [X2] : set_difference(X2,empty_set) = X2,
inference(variable_rename,[status(thm)],[c_0_142]) ).
fof(c_0_226,plain,
! [X2] : set_union2(X2,empty_set) = X2,
inference(variable_rename,[status(thm)],[c_0_143]) ).
fof(c_0_227,plain,
! [X2] : set_difference(empty_set,X2) = empty_set,
inference(variable_rename,[status(thm)],[c_0_144]) ).
fof(c_0_228,plain,
! [X2] : set_intersection2(X2,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[c_0_145]) ).
fof(c_0_229,plain,
! [X2] :
( ~ empty(X2)
| X2 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_146])]) ).
fof(c_0_230,plain,
! [X2] : cast_to_subset(X2) = X2,
inference(variable_rename,[status(thm)],[c_0_147]) ).
fof(c_0_231,plain,
~ empty(esk32_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_148])]) ).
fof(c_0_232,plain,
empty(esk30_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_149])]) ).
fof(c_0_233,plain,
( empty(esk28_0)
& relation(esk28_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_150])]) ).
fof(c_0_234,axiom,
empty(empty_set),
c_0_151 ).
fof(c_0_235,axiom,
$true,
c_0_152 ).
fof(c_0_236,axiom,
$true,
c_0_153 ).
fof(c_0_237,axiom,
$true,
c_0_154 ).
fof(c_0_238,axiom,
$true,
c_0_155 ).
fof(c_0_239,axiom,
$true,
c_0_156 ).
fof(c_0_240,axiom,
$true,
c_0_157 ).
fof(c_0_241,axiom,
$true,
c_0_158 ).
fof(c_0_242,axiom,
$true,
c_0_159 ).
fof(c_0_243,axiom,
$true,
c_0_160 ).
fof(c_0_244,axiom,
$true,
c_0_161 ).
fof(c_0_245,axiom,
$true,
c_0_162 ).
fof(c_0_246,axiom,
$true,
c_0_163 ).
fof(c_0_247,axiom,
$true,
c_0_164 ).
fof(c_0_248,axiom,
$true,
c_0_165 ).
cnf(c_0_249,plain,
( X4 = ordered_pair(esk9_4(X2,X3,X1,X4),esk10_4(X2,X3,X1,X4))
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_166]) ).
cnf(c_0_250,plain,
( X3 = complements_of_subsets(X2,X1)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2)))
| ~ in(subset_complement(X2,esk26_3(X2,X1,X3)),X1)
| ~ in(esk26_3(X2,X1,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_167]) ).
cnf(c_0_251,plain,
( X1 = set_intersection2(X2,X3)
| ~ in(esk15_3(X2,X3,X1),X3)
| ~ in(esk15_3(X2,X3,X1),X2)
| ~ in(esk15_3(X2,X3,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_168]) ).
cnf(c_0_252,plain,
( in(esk9_4(X2,X3,X1,X4),X2)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_166]) ).
cnf(c_0_253,plain,
( in(esk10_4(X2,X3,X1,X4),X3)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_166]) ).
cnf(c_0_254,plain,
( X1 = set_difference(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_169]) ).
cnf(c_0_255,plain,
( X3 = complements_of_subsets(X2,X1)
| in(subset_complement(X2,esk26_3(X2,X1,X3)),X1)
| in(esk26_3(X2,X1,X3),X3)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_167]) ).
cnf(c_0_256,plain,
( X1 = cartesian_product2(X2,X3)
| in(esk11_3(X2,X3,X1),X1)
| esk11_3(X2,X3,X1) = ordered_pair(esk12_3(X2,X3,X1),esk13_3(X2,X3,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_166]) ).
cnf(c_0_257,plain,
( X1 = set_union2(X2,X3)
| ~ in(esk8_3(X2,X3,X1),X1)
| ~ in(esk8_3(X2,X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_170]) ).
cnf(c_0_258,plain,
( X1 = set_union2(X2,X3)
| ~ in(esk8_3(X2,X3,X1),X1)
| ~ in(esk8_3(X2,X3,X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_170]) ).
cnf(c_0_259,plain,
( X1 = set_union2(X2,X3)
| in(esk8_3(X2,X3,X1),X3)
| in(esk8_3(X2,X3,X1),X2)
| in(esk8_3(X2,X3,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_170]) ).
cnf(c_0_260,plain,
( X1 = cartesian_product2(X2,X3)
| esk11_3(X2,X3,X1) != ordered_pair(X4,X5)
| ~ in(X5,X3)
| ~ in(X4,X2)
| ~ in(esk11_3(X2,X3,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_166]) ).
cnf(c_0_261,plain,
( X1 = set_difference(X2,X3)
| in(esk22_3(X2,X3,X1),X1)
| ~ in(esk22_3(X2,X3,X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_169]) ).
cnf(c_0_262,plain,
( X1 = unordered_pair(X2,X3)
| ~ in(esk7_3(X2,X3,X1),X1)
| esk7_3(X2,X3,X1) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_171]) ).
cnf(c_0_263,plain,
( X1 = unordered_pair(X2,X3)
| ~ in(esk7_3(X2,X3,X1),X1)
| esk7_3(X2,X3,X1) != X3 ),
inference(split_conjunct,[status(thm)],[c_0_171]) ).
cnf(c_0_264,plain,
( in(ordered_pair(esk23_3(X1,X2,X3),X3),X1)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_172]) ).
cnf(c_0_265,plain,
( in(ordered_pair(X3,esk16_3(X1,X2,X3)),X1)
| ~ relation(X1)
| X2 != relation_dom(X1)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_173]) ).
cnf(c_0_266,plain,
( X1 = set_difference(X2,X3)
| in(esk22_3(X2,X3,X1),X1)
| in(esk22_3(X2,X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_169]) ).
cnf(c_0_267,plain,
( X1 = set_intersection2(X2,X3)
| in(esk15_3(X2,X3,X1),X1)
| in(esk15_3(X2,X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_168]) ).
cnf(c_0_268,plain,
( X1 = set_intersection2(X2,X3)
| in(esk15_3(X2,X3,X1),X1)
| in(esk15_3(X2,X3,X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_168]) ).
cnf(c_0_269,plain,
( X1 = cartesian_product2(X2,X3)
| in(esk11_3(X2,X3,X1),X1)
| in(esk12_3(X2,X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_166]) ).
cnf(c_0_270,plain,
( X1 = cartesian_product2(X2,X3)
| in(esk11_3(X2,X3,X1),X1)
| in(esk13_3(X2,X3,X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_166]) ).
cnf(c_0_271,plain,
( X1 = unordered_pair(X2,X3)
| esk7_3(X2,X3,X1) = X3
| esk7_3(X2,X3,X1) = X2
| in(esk7_3(X2,X3,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_171]) ).
cnf(c_0_272,plain,
( X3 = complements_of_subsets(X2,X1)
| element(esk26_3(X2,X1,X3),powerset(X2))
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_167]) ).
cnf(c_0_273,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_167]) ).
cnf(c_0_274,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_167]) ).
cnf(c_0_275,plain,
( X2 = relation_rng(X1)
| ~ relation(X1)
| ~ in(ordered_pair(X3,esk24_2(X1,X2)),X1)
| ~ in(esk24_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_172]) ).
cnf(c_0_276,plain,
( X2 = relation_dom(X1)
| ~ relation(X1)
| ~ in(ordered_pair(esk17_2(X1,X2),X3),X1)
| ~ in(esk17_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_173]) ).
cnf(c_0_277,plain,
( X1 = empty_set
| in(X3,X2)
| X2 != set_meet(X1)
| ~ in(X3,esk1_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_174]) ).
cnf(c_0_278,plain,
( X2 = relation_rng(X1)
| in(ordered_pair(esk25_2(X1,X2),esk24_2(X1,X2)),X1)
| in(esk24_2(X1,X2),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_172]) ).
cnf(c_0_279,plain,
( X2 = relation_dom(X1)
| in(ordered_pair(esk17_2(X1,X2),esk18_2(X1,X2)),X1)
| in(esk17_2(X1,X2),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_173]) ).
cnf(c_0_280,plain,
( element(subset_difference(X1,X2,X3),powerset(X1))
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_175]) ).
cnf(c_0_281,plain,
( X1 = empty_set
| X2 = set_meet(X1)
| ~ in(esk2_2(X1,X2),X2)
| ~ in(esk2_2(X1,X2),esk3_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_174]) ).
cnf(c_0_282,plain,
( X1 = union(X2)
| ~ in(X3,X2)
| ~ in(esk20_2(X2,X1),X3)
| ~ in(esk20_2(X2,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_176]) ).
cnf(c_0_283,plain,
( in(X3,esk19_3(X2,X1,X3))
| X1 != union(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_176]) ).
cnf(c_0_284,plain,
( in(esk19_3(X2,X1,X3),X2)
| X1 != union(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_176]) ).
cnf(c_0_285,plain,
( X1 = empty_set
| in(X3,X2)
| in(esk1_3(X1,X2,X3),X1)
| X2 != set_meet(X1) ),
inference(split_conjunct,[status(thm)],[c_0_174]) ).
cnf(c_0_286,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_177]) ).
cnf(c_0_287,plain,
( X1 = powerset(X2)
| ~ subset(esk6_2(X2,X1),X2)
| ~ in(esk6_2(X2,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_178]) ).
cnf(c_0_288,plain,
( X1 = X2
| ~ in(esk33_2(X1,X2),X2)
| ~ in(esk33_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_179]) ).
cnf(c_0_289,plain,
( X1 = union(X2)
| in(esk20_2(X2,X1),X1)
| in(esk20_2(X2,X1),esk21_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_176]) ).
cnf(c_0_290,plain,
( X1 = empty_set
| X2 = set_meet(X1)
| in(esk3_2(X1,X2),X1)
| ~ in(esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_174]) ).
cnf(c_0_291,plain,
( X1 = empty_set
| X2 = set_meet(X1)
| in(esk2_2(X1,X2),X3)
| in(esk2_2(X1,X2),X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_174]) ).
cnf(c_0_292,plain,
( element(complements_of_subsets(X1,X2),powerset(powerset(X1)))
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_180]) ).
cnf(c_0_293,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_166]) ).
cnf(c_0_294,plain,
( element(meet_of_subsets(X1,X2),powerset(X1))
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_181]) ).
cnf(c_0_295,plain,
( element(union_of_subsets(X1,X2),powerset(X1))
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_182]) ).
cnf(c_0_296,plain,
( in(X3,esk35_2(X2,X1))
| ~ in(X1,esk34_1(X2))
| ~ subset(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_183]) ).
cnf(c_0_297,plain,
( in(X3,X2)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(ordered_pair(X4,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_172]) ).
cnf(c_0_298,plain,
( in(X3,X2)
| ~ relation(X1)
| X2 != relation_dom(X1)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(split_conjunct,[status(thm)],[c_0_173]) ).
cnf(c_0_299,plain,
( X1 = singleton(X2)
| esk4_2(X2,X1) != X2
| ~ in(esk4_2(X2,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_184]) ).
cnf(c_0_300,plain,
( complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_185]) ).
cnf(c_0_301,plain,
( X1 = union(X2)
| in(esk20_2(X2,X1),X1)
| in(esk21_2(X2,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_176]) ).
cnf(c_0_302,plain,
( X1 = powerset(X2)
| subset(esk6_2(X2,X1),X2)
| in(esk6_2(X2,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_178]) ).
cnf(c_0_303,plain,
( in(X4,X1)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_168]) ).
cnf(c_0_304,plain,
( X1 = X2
| in(esk33_2(X1,X2),X2)
| in(esk33_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_179]) ).
cnf(c_0_305,plain,
( in(esk35_2(X2,X1),esk34_1(X2))
| ~ in(X1,esk34_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_183]) ).
cnf(c_0_306,plain,
( element(subset_complement(X1,X2),powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_186]) ).
cnf(c_0_307,plain,
( subset(X1,X2)
| ~ in(esk14_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_187]) ).
cnf(c_0_308,plain,
( in(X1,esk34_1(X2))
| ~ subset(X1,X3)
| ~ in(X3,esk34_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_183]) ).
cnf(c_0_309,plain,
( in(X4,X1)
| in(X4,X3)
| X1 != set_difference(X2,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_169]) ).
cnf(c_0_310,plain,
( in(X4,X3)
| in(X4,X2)
| X1 != set_union2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_170]) ).
cnf(c_0_311,plain,
( in(X1,esk34_1(X2))
| are_equipotent(X1,esk34_1(X2))
| ~ subset(X1,esk34_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_183]) ).
cnf(c_0_312,plain,
( subset_complement(X1,subset_complement(X1,X2)) = X2
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_188]) ).
cnf(c_0_313,plain,
( X1 = empty_set
| in(X3,X4)
| X2 != set_meet(X1)
| ~ in(X4,X1)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_174]) ).
cnf(c_0_314,plain,
( meet_of_subsets(X1,X2) = set_meet(X2)
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_189]) ).
cnf(c_0_315,plain,
( union_of_subsets(X1,X2) = union(X2)
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_190]) ).
cnf(c_0_316,plain,
( element(X1,X2)
| ~ element(X3,powerset(X2))
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_191]) ).
cnf(c_0_317,plain,
( X1 != set_difference(X2,X3)
| ~ in(X4,X1)
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_169]) ).
cnf(c_0_318,plain,
( in(X3,X1)
| X1 != union(X2)
| ~ in(X4,X2)
| ~ in(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_176]) ).
cnf(c_0_319,plain,
( ~ empty(X1)
| ~ element(X2,powerset(X1))
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_192]) ).
cnf(c_0_320,plain,
( in(X4,X2)
| X1 != set_difference(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_169]) ).
cnf(c_0_321,plain,
( in(X4,X2)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_168]) ).
cnf(c_0_322,plain,
( in(X4,X3)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_168]) ).
cnf(c_0_323,plain,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_170]) ).
cnf(c_0_324,plain,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_170]) ).
cnf(c_0_325,plain,
( X1 = singleton(X2)
| esk4_2(X2,X1) = X2
| in(esk4_2(X2,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_184]) ).
cnf(c_0_326,plain,
( subset_complement(X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_193]) ).
cnf(c_0_327,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_194]) ).
cnf(c_0_328,plain,
( in(X1,X2)
| ~ in(X1,X3)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_187]) ).
cnf(c_0_329,plain,
( subset(X1,X2)
| in(esk14_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_187]) ).
cnf(c_0_330,plain,
( empty(X2)
| ~ empty(set_union2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_195]) ).
cnf(c_0_331,plain,
( empty(X1)
| ~ empty(set_union2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_196]) ).
cnf(c_0_332,plain,
( X4 = X3
| X4 = X2
| X1 != unordered_pair(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_171]) ).
cnf(c_0_333,plain,
~ empty(unordered_pair(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_197]) ).
cnf(c_0_334,plain,
~ empty(ordered_pair(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_198]) ).
cnf(c_0_335,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_199]) ).
cnf(c_0_336,plain,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_200]) ).
cnf(c_0_337,plain,
( subset(X3,X2)
| X1 != powerset(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_178]) ).
cnf(c_0_338,plain,
( in(X3,X1)
| X1 != powerset(X2)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_178]) ).
cnf(c_0_339,plain,
( ~ proper_subset(X1,X2)
| ~ proper_subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_201]) ).
cnf(c_0_340,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_202]) ).
cnf(c_0_341,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_200]) ).
cnf(c_0_342,plain,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_171]) ).
cnf(c_0_343,plain,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_171]) ).
cnf(c_0_344,plain,
( in(X1,X2)
| empty(X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_203]) ).
cnf(c_0_345,plain,
( empty(X1)
| in(X2,X1)
| ~ element(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_204]) ).
cnf(c_0_346,plain,
( empty(X1)
| element(X2,X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_204]) ).
cnf(c_0_347,plain,
( proper_subset(X1,X2)
| X1 = X2
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_205]) ).
cnf(c_0_348,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_206]) ).
cnf(c_0_349,plain,
( disjoint(X1,X2)
| ~ disjoint(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_207]) ).
cnf(c_0_350,plain,
( subset(X1,X2)
| ~ proper_subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_205]) ).
cnf(c_0_351,plain,
( set_intersection2(X1,X2) = empty_set
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_208]) ).
cnf(c_0_352,plain,
( disjoint(X1,X2)
| set_intersection2(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_208]) ).
cnf(c_0_353,plain,
( empty(X2)
| ~ empty(X1)
| ~ element(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_204]) ).
cnf(c_0_354,plain,
( X3 = X2
| X1 != singleton(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_184]) ).
cnf(c_0_355,plain,
( empty(X1)
| element(esk29_1(X1),powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_209]) ).
cnf(c_0_356,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_210]) ).
cnf(c_0_357,plain,
( element(X2,X1)
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_204]) ).
cnf(c_0_358,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_211]) ).
cnf(c_0_359,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_212]) ).
cnf(c_0_360,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_213]) ).
cnf(c_0_361,plain,
element(esk31_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_214]) ).
cnf(c_0_362,plain,
element(cast_to_subset(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_215]) ).
cnf(c_0_363,plain,
( in(X3,X1)
| X1 != singleton(X2)
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_184]) ).
cnf(c_0_364,plain,
( ~ proper_subset(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_205]) ).
cnf(c_0_365,plain,
( ~ in(X1,X2)
| X2 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_216]) ).
cnf(c_0_366,plain,
~ proper_subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_217]) ).
cnf(c_0_367,plain,
( X1 = empty_set
| in(esk5_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_216]) ).
cnf(c_0_368,plain,
( empty(X1)
| ~ empty(esk29_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_209]) ).
cnf(c_0_369,plain,
in(X1,esk34_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_183]) ).
cnf(c_0_370,plain,
element(esk27_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_218]) ).
cnf(c_0_371,plain,
( subset(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_199]) ).
cnf(c_0_372,plain,
( subset(X2,X1)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_199]) ).
cnf(c_0_373,plain,
~ empty(singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_219]) ).
cnf(c_0_374,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_220]) ).
cnf(c_0_375,plain,
( X2 = X1
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_221]) ).
cnf(c_0_376,plain,
set_intersection2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_222]) ).
cnf(c_0_377,plain,
set_union2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_223]) ).
cnf(c_0_378,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_224]) ).
cnf(c_0_379,plain,
set_difference(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_225]) ).
cnf(c_0_380,plain,
set_union2(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_226]) ).
cnf(c_0_381,plain,
set_difference(empty_set,X1) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_227]) ).
cnf(c_0_382,plain,
set_intersection2(X1,empty_set) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_228]) ).
cnf(c_0_383,plain,
( X2 = empty_set
| X1 != empty_set
| X2 != set_meet(X1) ),
inference(split_conjunct,[status(thm)],[c_0_174]) ).
cnf(c_0_384,plain,
empty(esk31_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_214]) ).
cnf(c_0_385,plain,
( X2 = set_meet(X1)
| X1 != empty_set
| X2 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_174]) ).
cnf(c_0_386,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_229]) ).
cnf(c_0_387,plain,
cast_to_subset(X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_230]) ).
cnf(c_0_388,plain,
~ empty(esk32_0),
inference(split_conjunct,[status(thm)],[c_0_231]) ).
cnf(c_0_389,plain,
empty(esk30_0),
inference(split_conjunct,[status(thm)],[c_0_232]) ).
cnf(c_0_390,plain,
empty(esk28_0),
inference(split_conjunct,[status(thm)],[c_0_233]) ).
cnf(c_0_391,plain,
relation(esk28_0),
inference(split_conjunct,[status(thm)],[c_0_233]) ).
cnf(c_0_392,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[c_0_234]) ).
cnf(c_0_393,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_235]) ).
cnf(c_0_394,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_236]) ).
cnf(c_0_395,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_237]) ).
cnf(c_0_396,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_238]) ).
cnf(c_0_397,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_239]) ).
cnf(c_0_398,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_240]) ).
cnf(c_0_399,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_241]) ).
cnf(c_0_400,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_242]) ).
cnf(c_0_401,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_243]) ).
cnf(c_0_402,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_244]) ).
cnf(c_0_403,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_245]) ).
cnf(c_0_404,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_246]) ).
cnf(c_0_405,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_247]) ).
cnf(c_0_406,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_248]) ).
cnf(c_0_407,plain,
( ordered_pair(esk9_4(X2,X3,X1,X4),esk10_4(X2,X3,X1,X4)) = X4
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
c_0_249,
[final] ).
cnf(c_0_408,plain,
( X3 = complements_of_subsets(X2,X1)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2)))
| ~ in(subset_complement(X2,esk26_3(X2,X1,X3)),X1)
| ~ in(esk26_3(X2,X1,X3),X3) ),
c_0_250,
[final] ).
cnf(c_0_409,plain,
( X1 = set_intersection2(X2,X3)
| ~ in(esk15_3(X2,X3,X1),X3)
| ~ in(esk15_3(X2,X3,X1),X2)
| ~ in(esk15_3(X2,X3,X1),X1) ),
c_0_251,
[final] ).
cnf(c_0_410,plain,
( in(esk9_4(X2,X3,X1,X4),X2)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
c_0_252,
[final] ).
cnf(c_0_411,plain,
( in(esk10_4(X2,X3,X1,X4),X3)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
c_0_253,
[final] ).
cnf(c_0_412,plain,
( X1 = set_difference(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_254,
[final] ).
cnf(c_0_413,plain,
( X3 = complements_of_subsets(X2,X1)
| in(subset_complement(X2,esk26_3(X2,X1,X3)),X1)
| in(esk26_3(X2,X1,X3),X3)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2))) ),
c_0_255,
[final] ).
cnf(c_0_414,plain,
( X1 = cartesian_product2(X2,X3)
| in(esk11_3(X2,X3,X1),X1)
| ordered_pair(esk12_3(X2,X3,X1),esk13_3(X2,X3,X1)) = esk11_3(X2,X3,X1) ),
c_0_256,
[final] ).
cnf(c_0_415,plain,
( X1 = set_union2(X2,X3)
| ~ in(esk8_3(X2,X3,X1),X1)
| ~ in(esk8_3(X2,X3,X1),X2) ),
c_0_257,
[final] ).
cnf(c_0_416,plain,
( X1 = set_union2(X2,X3)
| ~ in(esk8_3(X2,X3,X1),X1)
| ~ in(esk8_3(X2,X3,X1),X3) ),
c_0_258,
[final] ).
cnf(c_0_417,plain,
( X1 = set_union2(X2,X3)
| in(esk8_3(X2,X3,X1),X3)
| in(esk8_3(X2,X3,X1),X2)
| in(esk8_3(X2,X3,X1),X1) ),
c_0_259,
[final] ).
cnf(c_0_418,plain,
( X1 = cartesian_product2(X2,X3)
| esk11_3(X2,X3,X1) != ordered_pair(X4,X5)
| ~ in(X5,X3)
| ~ in(X4,X2)
| ~ in(esk11_3(X2,X3,X1),X1) ),
c_0_260,
[final] ).
cnf(c_0_419,plain,
( X1 = set_difference(X2,X3)
| in(esk22_3(X2,X3,X1),X1)
| ~ in(esk22_3(X2,X3,X1),X3) ),
c_0_261,
[final] ).
cnf(c_0_420,plain,
( X1 = unordered_pair(X2,X3)
| ~ in(esk7_3(X2,X3,X1),X1)
| esk7_3(X2,X3,X1) != X2 ),
c_0_262,
[final] ).
cnf(c_0_421,plain,
( X1 = unordered_pair(X2,X3)
| ~ in(esk7_3(X2,X3,X1),X1)
| esk7_3(X2,X3,X1) != X3 ),
c_0_263,
[final] ).
cnf(c_0_422,plain,
( in(ordered_pair(esk23_3(X1,X2,X3),X3),X1)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(X3,X2) ),
c_0_264,
[final] ).
cnf(c_0_423,plain,
( in(ordered_pair(X3,esk16_3(X1,X2,X3)),X1)
| ~ relation(X1)
| X2 != relation_dom(X1)
| ~ in(X3,X2) ),
c_0_265,
[final] ).
cnf(c_0_424,plain,
( X1 = set_difference(X2,X3)
| in(esk22_3(X2,X3,X1),X1)
| in(esk22_3(X2,X3,X1),X2) ),
c_0_266,
[final] ).
cnf(c_0_425,plain,
( X1 = set_intersection2(X2,X3)
| in(esk15_3(X2,X3,X1),X1)
| in(esk15_3(X2,X3,X1),X2) ),
c_0_267,
[final] ).
cnf(c_0_426,plain,
( X1 = set_intersection2(X2,X3)
| in(esk15_3(X2,X3,X1),X1)
| in(esk15_3(X2,X3,X1),X3) ),
c_0_268,
[final] ).
cnf(c_0_427,plain,
( X1 = cartesian_product2(X2,X3)
| in(esk11_3(X2,X3,X1),X1)
| in(esk12_3(X2,X3,X1),X2) ),
c_0_269,
[final] ).
cnf(c_0_428,plain,
( X1 = cartesian_product2(X2,X3)
| in(esk11_3(X2,X3,X1),X1)
| in(esk13_3(X2,X3,X1),X3) ),
c_0_270,
[final] ).
cnf(c_0_429,plain,
( X1 = unordered_pair(X2,X3)
| esk7_3(X2,X3,X1) = X3
| esk7_3(X2,X3,X1) = X2
| in(esk7_3(X2,X3,X1),X1) ),
c_0_271,
[final] ).
cnf(c_0_430,plain,
( X3 = complements_of_subsets(X2,X1)
| element(esk26_3(X2,X1,X3),powerset(X2))
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2))) ),
c_0_272,
[final] ).
cnf(c_0_431,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_273,
[final] ).
cnf(c_0_432,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_274,
[final] ).
cnf(c_0_433,plain,
( X2 = relation_rng(X1)
| ~ relation(X1)
| ~ in(ordered_pair(X3,esk24_2(X1,X2)),X1)
| ~ in(esk24_2(X1,X2),X2) ),
c_0_275,
[final] ).
cnf(c_0_434,plain,
( X2 = relation_dom(X1)
| ~ relation(X1)
| ~ in(ordered_pair(esk17_2(X1,X2),X3),X1)
| ~ in(esk17_2(X1,X2),X2) ),
c_0_276,
[final] ).
cnf(c_0_435,plain,
( X1 = empty_set
| in(X3,X2)
| X2 != set_meet(X1)
| ~ in(X3,esk1_3(X1,X2,X3)) ),
c_0_277,
[final] ).
cnf(c_0_436,plain,
( X2 = relation_rng(X1)
| in(ordered_pair(esk25_2(X1,X2),esk24_2(X1,X2)),X1)
| in(esk24_2(X1,X2),X2)
| ~ relation(X1) ),
c_0_278,
[final] ).
cnf(c_0_437,plain,
( X2 = relation_dom(X1)
| in(ordered_pair(esk17_2(X1,X2),esk18_2(X1,X2)),X1)
| in(esk17_2(X1,X2),X2)
| ~ relation(X1) ),
c_0_279,
[final] ).
cnf(c_0_438,plain,
( element(subset_difference(X1,X2,X3),powerset(X1))
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
c_0_280,
[final] ).
cnf(c_0_439,plain,
( X1 = empty_set
| X2 = set_meet(X1)
| ~ in(esk2_2(X1,X2),X2)
| ~ in(esk2_2(X1,X2),esk3_2(X1,X2)) ),
c_0_281,
[final] ).
cnf(c_0_440,plain,
( X1 = union(X2)
| ~ in(X3,X2)
| ~ in(esk20_2(X2,X1),X3)
| ~ in(esk20_2(X2,X1),X1) ),
c_0_282,
[final] ).
cnf(c_0_441,plain,
( in(X3,esk19_3(X2,X1,X3))
| X1 != union(X2)
| ~ in(X3,X1) ),
c_0_283,
[final] ).
cnf(c_0_442,plain,
( in(esk19_3(X2,X1,X3),X2)
| X1 != union(X2)
| ~ in(X3,X1) ),
c_0_284,
[final] ).
cnf(c_0_443,plain,
( X1 = empty_set
| in(X3,X2)
| in(esk1_3(X1,X2,X3),X1)
| X2 != set_meet(X1) ),
c_0_285,
[final] ).
cnf(c_0_444,plain,
( subset_difference(X1,X2,X3) = set_difference(X2,X3)
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
c_0_286,
[final] ).
cnf(c_0_445,plain,
( X1 = powerset(X2)
| ~ subset(esk6_2(X2,X1),X2)
| ~ in(esk6_2(X2,X1),X1) ),
c_0_287,
[final] ).
cnf(c_0_446,plain,
( X1 = X2
| ~ in(esk33_2(X1,X2),X2)
| ~ in(esk33_2(X1,X2),X1) ),
c_0_288,
[final] ).
cnf(c_0_447,plain,
( X1 = union(X2)
| in(esk20_2(X2,X1),X1)
| in(esk20_2(X2,X1),esk21_2(X2,X1)) ),
c_0_289,
[final] ).
cnf(c_0_448,plain,
( X1 = empty_set
| X2 = set_meet(X1)
| in(esk3_2(X1,X2),X1)
| ~ in(esk2_2(X1,X2),X2) ),
c_0_290,
[final] ).
cnf(c_0_449,plain,
( X1 = empty_set
| X2 = set_meet(X1)
| in(esk2_2(X1,X2),X3)
| in(esk2_2(X1,X2),X2)
| ~ in(X3,X1) ),
c_0_291,
[final] ).
cnf(c_0_450,plain,
( element(complements_of_subsets(X1,X2),powerset(powerset(X1)))
| ~ element(X2,powerset(powerset(X1))) ),
c_0_292,
[final] ).
cnf(c_0_451,plain,
( in(X4,X1)
| X1 != cartesian_product2(X2,X3)
| X4 != ordered_pair(X5,X6)
| ~ in(X6,X3)
| ~ in(X5,X2) ),
c_0_293,
[final] ).
cnf(c_0_452,plain,
( element(meet_of_subsets(X1,X2),powerset(X1))
| ~ element(X2,powerset(powerset(X1))) ),
c_0_294,
[final] ).
cnf(c_0_453,plain,
( element(union_of_subsets(X1,X2),powerset(X1))
| ~ element(X2,powerset(powerset(X1))) ),
c_0_295,
[final] ).
cnf(c_0_454,plain,
( in(X3,esk35_2(X2,X1))
| ~ in(X1,esk34_1(X2))
| ~ subset(X3,X1) ),
c_0_296,
[final] ).
cnf(c_0_455,plain,
( in(X3,X2)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(ordered_pair(X4,X3),X1) ),
c_0_297,
[final] ).
cnf(c_0_456,plain,
( in(X3,X2)
| ~ relation(X1)
| X2 != relation_dom(X1)
| ~ in(ordered_pair(X3,X4),X1) ),
c_0_298,
[final] ).
cnf(c_0_457,plain,
( X1 = singleton(X2)
| esk4_2(X2,X1) != X2
| ~ in(esk4_2(X2,X1),X1) ),
c_0_299,
[final] ).
cnf(c_0_458,plain,
( complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2
| ~ element(X2,powerset(powerset(X1))) ),
c_0_300,
[final] ).
cnf(c_0_459,plain,
( X1 = union(X2)
| in(esk20_2(X2,X1),X1)
| in(esk21_2(X2,X1),X2) ),
c_0_301,
[final] ).
cnf(c_0_460,plain,
( X1 = powerset(X2)
| subset(esk6_2(X2,X1),X2)
| in(esk6_2(X2,X1),X1) ),
c_0_302,
[final] ).
cnf(c_0_461,plain,
( in(X4,X1)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X3)
| ~ in(X4,X2) ),
c_0_303,
[final] ).
cnf(c_0_462,plain,
( X1 = X2
| in(esk33_2(X1,X2),X2)
| in(esk33_2(X1,X2),X1) ),
c_0_304,
[final] ).
cnf(c_0_463,plain,
( in(esk35_2(X2,X1),esk34_1(X2))
| ~ in(X1,esk34_1(X2)) ),
c_0_305,
[final] ).
cnf(c_0_464,plain,
( element(subset_complement(X1,X2),powerset(X1))
| ~ element(X2,powerset(X1)) ),
c_0_306,
[final] ).
cnf(c_0_465,plain,
( subset(X1,X2)
| ~ in(esk14_2(X1,X2),X2) ),
c_0_307,
[final] ).
cnf(c_0_466,plain,
( in(X1,esk34_1(X2))
| ~ subset(X1,X3)
| ~ in(X3,esk34_1(X2)) ),
c_0_308,
[final] ).
cnf(c_0_467,plain,
( in(X4,X1)
| in(X4,X3)
| X1 != set_difference(X2,X3)
| ~ in(X4,X2) ),
c_0_309,
[final] ).
cnf(c_0_468,plain,
( in(X4,X3)
| in(X4,X2)
| X1 != set_union2(X2,X3)
| ~ in(X4,X1) ),
c_0_310,
[final] ).
cnf(c_0_469,plain,
( in(X1,esk34_1(X2))
| are_equipotent(X1,esk34_1(X2))
| ~ subset(X1,esk34_1(X2)) ),
c_0_311,
[final] ).
cnf(c_0_470,plain,
( subset_complement(X1,subset_complement(X1,X2)) = X2
| ~ element(X2,powerset(X1)) ),
c_0_312,
[final] ).
cnf(c_0_471,plain,
( X1 = empty_set
| in(X3,X4)
| X2 != set_meet(X1)
| ~ in(X4,X1)
| ~ in(X3,X2) ),
c_0_313,
[final] ).
cnf(c_0_472,plain,
( meet_of_subsets(X1,X2) = set_meet(X2)
| ~ element(X2,powerset(powerset(X1))) ),
c_0_314,
[final] ).
cnf(c_0_473,plain,
( union_of_subsets(X1,X2) = union(X2)
| ~ element(X2,powerset(powerset(X1))) ),
c_0_315,
[final] ).
cnf(c_0_474,plain,
( element(X1,X2)
| ~ element(X3,powerset(X2))
| ~ in(X1,X3) ),
c_0_316,
[final] ).
cnf(c_0_475,plain,
( X1 != set_difference(X2,X3)
| ~ in(X4,X1)
| ~ in(X4,X3) ),
c_0_317,
[final] ).
cnf(c_0_476,plain,
( in(X3,X1)
| X1 != union(X2)
| ~ in(X4,X2)
| ~ in(X3,X4) ),
c_0_318,
[final] ).
cnf(c_0_477,plain,
( ~ empty(X1)
| ~ element(X2,powerset(X1))
| ~ in(X3,X2) ),
c_0_319,
[final] ).
cnf(c_0_478,plain,
( in(X4,X2)
| X1 != set_difference(X2,X3)
| ~ in(X4,X1) ),
c_0_320,
[final] ).
cnf(c_0_479,plain,
( in(X4,X2)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X1) ),
c_0_321,
[final] ).
cnf(c_0_480,plain,
( in(X4,X3)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X1) ),
c_0_322,
[final] ).
cnf(c_0_481,plain,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X2) ),
c_0_323,
[final] ).
cnf(c_0_482,plain,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X3) ),
c_0_324,
[final] ).
cnf(c_0_483,plain,
( X1 = singleton(X2)
| esk4_2(X2,X1) = X2
| in(esk4_2(X2,X1),X1) ),
c_0_325,
[final] ).
cnf(c_0_484,plain,
( subset_complement(X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X1)) ),
c_0_326,
[final] ).
cnf(c_0_485,plain,
unordered_pair(unordered_pair(X1,X2),singleton(X1)) = ordered_pair(X1,X2),
c_0_327,
[final] ).
cnf(c_0_486,plain,
( in(X1,X2)
| ~ in(X1,X3)
| ~ subset(X3,X2) ),
c_0_328,
[final] ).
cnf(c_0_487,plain,
( subset(X1,X2)
| in(esk14_2(X1,X2),X1) ),
c_0_329,
[final] ).
cnf(c_0_488,plain,
( empty(X2)
| ~ empty(set_union2(X1,X2)) ),
c_0_330,
[final] ).
cnf(c_0_489,plain,
( empty(X1)
| ~ empty(set_union2(X1,X2)) ),
c_0_331,
[final] ).
cnf(c_0_490,plain,
( X4 = X3
| X4 = X2
| X1 != unordered_pair(X2,X3)
| ~ in(X4,X1) ),
c_0_332,
[final] ).
cnf(c_0_491,plain,
~ empty(unordered_pair(X1,X2)),
c_0_333,
[final] ).
cnf(c_0_492,plain,
~ empty(ordered_pair(X1,X2)),
c_0_334,
[final] ).
cnf(c_0_493,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
c_0_335,
[final] ).
cnf(c_0_494,plain,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
c_0_336,
[final] ).
cnf(c_0_495,plain,
( subset(X3,X2)
| X1 != powerset(X2)
| ~ in(X3,X1) ),
c_0_337,
[final] ).
cnf(c_0_496,plain,
( in(X3,X1)
| X1 != powerset(X2)
| ~ subset(X3,X2) ),
c_0_338,
[final] ).
cnf(c_0_497,plain,
( ~ proper_subset(X1,X2)
| ~ proper_subset(X2,X1) ),
c_0_339,
[final] ).
cnf(c_0_498,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
c_0_340,
[final] ).
cnf(c_0_499,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
c_0_341,
[final] ).
cnf(c_0_500,plain,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X2 ),
c_0_342,
[final] ).
cnf(c_0_501,plain,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X3 ),
c_0_343,
[final] ).
cnf(c_0_502,plain,
( in(X1,X2)
| empty(X2)
| ~ element(X1,X2) ),
c_0_344,
[final] ).
cnf(c_0_503,plain,
( empty(X1)
| in(X2,X1)
| ~ element(X2,X1) ),
c_0_345,
[final] ).
cnf(c_0_504,plain,
( empty(X1)
| element(X2,X1)
| ~ in(X2,X1) ),
c_0_346,
[final] ).
cnf(c_0_505,plain,
( proper_subset(X1,X2)
| X1 = X2
| ~ subset(X1,X2) ),
c_0_347,
[final] ).
cnf(c_0_506,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
c_0_348,
[final] ).
cnf(c_0_507,plain,
( disjoint(X1,X2)
| ~ disjoint(X2,X1) ),
c_0_349,
[final] ).
cnf(c_0_508,plain,
( subset(X1,X2)
| ~ proper_subset(X1,X2) ),
c_0_350,
[final] ).
cnf(c_0_509,plain,
( set_intersection2(X1,X2) = empty_set
| ~ disjoint(X1,X2) ),
c_0_351,
[final] ).
cnf(c_0_510,plain,
( disjoint(X1,X2)
| set_intersection2(X1,X2) != empty_set ),
c_0_352,
[final] ).
cnf(c_0_511,plain,
( empty(X2)
| ~ empty(X1)
| ~ element(X2,X1) ),
c_0_353,
[final] ).
cnf(c_0_512,plain,
( X3 = X2
| X1 != singleton(X2)
| ~ in(X3,X1) ),
c_0_354,
[final] ).
cnf(c_0_513,plain,
( empty(X1)
| element(esk29_1(X1),powerset(X1)) ),
c_0_355,
[final] ).
cnf(c_0_514,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
c_0_356,
[final] ).
cnf(c_0_515,plain,
( element(X2,X1)
| ~ empty(X1)
| ~ empty(X2) ),
c_0_357,
[final] ).
cnf(c_0_516,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
c_0_358,
[final] ).
cnf(c_0_517,plain,
set_union2(X1,X2) = set_union2(X2,X1),
c_0_359,
[final] ).
cnf(c_0_518,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
c_0_360,
[final] ).
cnf(c_0_519,plain,
element(esk31_1(X1),powerset(X1)),
c_0_361,
[final] ).
cnf(c_0_520,plain,
element(cast_to_subset(X1),powerset(X1)),
c_0_362,
[final] ).
cnf(c_0_521,plain,
( in(X3,X1)
| X1 != singleton(X2)
| X3 != X2 ),
c_0_363,
[final] ).
cnf(c_0_522,plain,
( ~ proper_subset(X1,X2)
| X1 != X2 ),
c_0_364,
[final] ).
cnf(c_0_523,plain,
( ~ in(X1,X2)
| X2 != empty_set ),
c_0_365,
[final] ).
cnf(c_0_524,plain,
~ proper_subset(X1,X1),
c_0_366,
[final] ).
cnf(c_0_525,plain,
( X1 = empty_set
| in(esk5_1(X1),X1) ),
c_0_367,
[final] ).
cnf(c_0_526,plain,
( empty(X1)
| ~ empty(esk29_1(X1)) ),
c_0_368,
[final] ).
cnf(c_0_527,plain,
in(X1,esk34_1(X1)),
c_0_369,
[final] ).
cnf(c_0_528,plain,
element(esk27_1(X1),X1),
c_0_370,
[final] ).
cnf(c_0_529,plain,
( subset(X1,X2)
| X1 != X2 ),
c_0_371,
[final] ).
cnf(c_0_530,plain,
( subset(X2,X1)
| X1 != X2 ),
c_0_372,
[final] ).
cnf(c_0_531,plain,
~ empty(singleton(X1)),
c_0_373,
[final] ).
cnf(c_0_532,plain,
~ empty(powerset(X1)),
c_0_374,
[final] ).
cnf(c_0_533,plain,
( X2 = X1
| ~ empty(X1)
| ~ empty(X2) ),
c_0_375,
[final] ).
cnf(c_0_534,plain,
set_intersection2(X1,X1) = X1,
c_0_376,
[final] ).
cnf(c_0_535,plain,
set_union2(X1,X1) = X1,
c_0_377,
[final] ).
cnf(c_0_536,plain,
subset(X1,X1),
c_0_378,
[final] ).
cnf(c_0_537,plain,
set_difference(X1,empty_set) = X1,
c_0_379,
[final] ).
cnf(c_0_538,plain,
set_union2(X1,empty_set) = X1,
c_0_380,
[final] ).
cnf(c_0_539,plain,
set_difference(empty_set,X1) = empty_set,
c_0_381,
[final] ).
cnf(c_0_540,plain,
set_intersection2(X1,empty_set) = empty_set,
c_0_382,
[final] ).
cnf(c_0_541,plain,
( X2 = empty_set
| X1 != empty_set
| X2 != set_meet(X1) ),
c_0_383,
[final] ).
cnf(c_0_542,plain,
empty(esk31_1(X1)),
c_0_384,
[final] ).
cnf(c_0_543,plain,
( X2 = set_meet(X1)
| X1 != empty_set
| X2 != empty_set ),
c_0_385,
[final] ).
cnf(c_0_544,plain,
( X1 = empty_set
| ~ empty(X1) ),
c_0_386,
[final] ).
cnf(c_0_545,plain,
cast_to_subset(X1) = X1,
c_0_387,
[final] ).
cnf(c_0_546,plain,
~ empty(esk32_0),
c_0_388,
[final] ).
cnf(c_0_547,plain,
empty(esk30_0),
c_0_389,
[final] ).
cnf(c_0_548,plain,
empty(esk28_0),
c_0_390,
[final] ).
cnf(c_0_549,plain,
relation(esk28_0),
c_0_391,
[final] ).
cnf(c_0_550,plain,
empty(empty_set),
c_0_392,
[final] ).
cnf(c_0_551,plain,
$true,
c_0_393,
[final] ).
cnf(c_0_552,plain,
$true,
c_0_394,
[final] ).
cnf(c_0_553,plain,
$true,
c_0_395,
[final] ).
cnf(c_0_554,plain,
$true,
c_0_396,
[final] ).
cnf(c_0_555,plain,
$true,
c_0_397,
[final] ).
cnf(c_0_556,plain,
$true,
c_0_398,
[final] ).
cnf(c_0_557,plain,
$true,
c_0_399,
[final] ).
cnf(c_0_558,plain,
$true,
c_0_400,
[final] ).
cnf(c_0_559,plain,
$true,
c_0_401,
[final] ).
cnf(c_0_560,plain,
$true,
c_0_402,
[final] ).
cnf(c_0_561,plain,
$true,
c_0_403,
[final] ).
cnf(c_0_562,plain,
$true,
c_0_404,
[final] ).
cnf(c_0_563,plain,
$true,
c_0_405,
[final] ).
cnf(c_0_564,plain,
$true,
c_0_406,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_407_0,axiom,
( ordered_pair(sk1_esk9_4(X2,X3,X1,X4),sk1_esk10_4(X2,X3,X1,X4)) = X4
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_407]) ).
cnf(c_0_407_1,axiom,
( X1 != cartesian_product2(X2,X3)
| ordered_pair(sk1_esk9_4(X2,X3,X1,X4),sk1_esk10_4(X2,X3,X1,X4)) = X4
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_407]) ).
cnf(c_0_407_2,axiom,
( ~ in(X4,X1)
| X1 != cartesian_product2(X2,X3)
| ordered_pair(sk1_esk9_4(X2,X3,X1,X4),sk1_esk10_4(X2,X3,X1,X4)) = X4 ),
inference(literals_permutation,[status(thm)],[c_0_407]) ).
cnf(c_0_408_0,axiom,
( X3 = complements_of_subsets(X2,X1)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2)))
| ~ in(subset_complement(X2,sk1_esk26_3(X2,X1,X3)),X1)
| ~ in(sk1_esk26_3(X2,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_408]) ).
cnf(c_0_408_1,axiom,
( ~ element(X1,powerset(powerset(X2)))
| X3 = complements_of_subsets(X2,X1)
| ~ element(X3,powerset(powerset(X2)))
| ~ in(subset_complement(X2,sk1_esk26_3(X2,X1,X3)),X1)
| ~ in(sk1_esk26_3(X2,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_408]) ).
cnf(c_0_408_2,axiom,
( ~ element(X3,powerset(powerset(X2)))
| ~ element(X1,powerset(powerset(X2)))
| X3 = complements_of_subsets(X2,X1)
| ~ in(subset_complement(X2,sk1_esk26_3(X2,X1,X3)),X1)
| ~ in(sk1_esk26_3(X2,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_408]) ).
cnf(c_0_408_3,axiom,
( ~ in(subset_complement(X2,sk1_esk26_3(X2,X1,X3)),X1)
| ~ element(X3,powerset(powerset(X2)))
| ~ element(X1,powerset(powerset(X2)))
| X3 = complements_of_subsets(X2,X1)
| ~ in(sk1_esk26_3(X2,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_408]) ).
cnf(c_0_408_4,axiom,
( ~ in(sk1_esk26_3(X2,X1,X3),X3)
| ~ in(subset_complement(X2,sk1_esk26_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_408]) ).
cnf(c_0_409_0,axiom,
( X1 = set_intersection2(X2,X3)
| ~ in(sk1_esk15_3(X2,X3,X1),X3)
| ~ in(sk1_esk15_3(X2,X3,X1),X2)
| ~ in(sk1_esk15_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_409]) ).
cnf(c_0_409_1,axiom,
( ~ in(sk1_esk15_3(X2,X3,X1),X3)
| X1 = set_intersection2(X2,X3)
| ~ in(sk1_esk15_3(X2,X3,X1),X2)
| ~ in(sk1_esk15_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_409]) ).
cnf(c_0_409_2,axiom,
( ~ in(sk1_esk15_3(X2,X3,X1),X2)
| ~ in(sk1_esk15_3(X2,X3,X1),X3)
| X1 = set_intersection2(X2,X3)
| ~ in(sk1_esk15_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_409]) ).
cnf(c_0_409_3,axiom,
( ~ in(sk1_esk15_3(X2,X3,X1),X1)
| ~ in(sk1_esk15_3(X2,X3,X1),X2)
| ~ in(sk1_esk15_3(X2,X3,X1),X3)
| X1 = set_intersection2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_409]) ).
cnf(c_0_410_0,axiom,
( in(sk1_esk9_4(X2,X3,X1,X4),X2)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_410]) ).
cnf(c_0_410_1,axiom,
( X1 != cartesian_product2(X2,X3)
| in(sk1_esk9_4(X2,X3,X1,X4),X2)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_410]) ).
cnf(c_0_410_2,axiom,
( ~ in(X4,X1)
| X1 != cartesian_product2(X2,X3)
| in(sk1_esk9_4(X2,X3,X1,X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_410]) ).
cnf(c_0_411_0,axiom,
( in(sk1_esk10_4(X2,X3,X1,X4),X3)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_411]) ).
cnf(c_0_411_1,axiom,
( X1 != cartesian_product2(X2,X3)
| in(sk1_esk10_4(X2,X3,X1,X4),X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_411]) ).
cnf(c_0_411_2,axiom,
( ~ in(X4,X1)
| X1 != cartesian_product2(X2,X3)
| in(sk1_esk10_4(X2,X3,X1,X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_411]) ).
cnf(c_0_412_0,axiom,
( X1 = set_difference(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_412]) ).
cnf(c_0_412_1,axiom,
( in(sk1_esk22_3(X2,X3,X1),X3)
| X1 = set_difference(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_412]) ).
cnf(c_0_412_2,axiom,
( ~ in(sk1_esk22_3(X2,X3,X1),X2)
| in(sk1_esk22_3(X2,X3,X1),X3)
| X1 = set_difference(X2,X3)
| ~ in(sk1_esk22_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_412]) ).
cnf(c_0_412_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_difference(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_412]) ).
cnf(c_0_413_0,axiom,
( X3 = complements_of_subsets(X2,X1)
| in(subset_complement(X2,sk1_esk26_3(X2,X1,X3)),X1)
| in(sk1_esk26_3(X2,X1,X3),X3)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_413]) ).
cnf(c_0_413_1,axiom,
( in(subset_complement(X2,sk1_esk26_3(X2,X1,X3)),X1)
| X3 = complements_of_subsets(X2,X1)
| in(sk1_esk26_3(X2,X1,X3),X3)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_413]) ).
cnf(c_0_413_2,axiom,
( in(sk1_esk26_3(X2,X1,X3),X3)
| in(subset_complement(X2,sk1_esk26_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_413]) ).
cnf(c_0_413_3,axiom,
( ~ element(X1,powerset(powerset(X2)))
| in(sk1_esk26_3(X2,X1,X3),X3)
| in(subset_complement(X2,sk1_esk26_3(X2,X1,X3)),X1)
| X3 = complements_of_subsets(X2,X1)
| ~ element(X3,powerset(powerset(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_413]) ).
cnf(c_0_413_4,axiom,
( ~ element(X3,powerset(powerset(X2)))
| ~ element(X1,powerset(powerset(X2)))
| in(sk1_esk26_3(X2,X1,X3),X3)
| in(subset_complement(X2,sk1_esk26_3(X2,X1,X3)),X1)
| X3 = complements_of_subsets(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_413]) ).
cnf(c_0_414_0,axiom,
( X1 = cartesian_product2(X2,X3)
| in(sk1_esk11_3(X2,X3,X1),X1)
| ordered_pair(sk1_esk12_3(X2,X3,X1),sk1_esk13_3(X2,X3,X1)) = sk1_esk11_3(X2,X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_414]) ).
cnf(c_0_414_1,axiom,
( in(sk1_esk11_3(X2,X3,X1),X1)
| X1 = cartesian_product2(X2,X3)
| ordered_pair(sk1_esk12_3(X2,X3,X1),sk1_esk13_3(X2,X3,X1)) = sk1_esk11_3(X2,X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_414]) ).
cnf(c_0_414_2,axiom,
( ordered_pair(sk1_esk12_3(X2,X3,X1),sk1_esk13_3(X2,X3,X1)) = sk1_esk11_3(X2,X3,X1)
| in(sk1_esk11_3(X2,X3,X1),X1)
| X1 = cartesian_product2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_414]) ).
cnf(c_0_415_0,axiom,
( X1 = set_union2(X2,X3)
| ~ in(sk1_esk8_3(X2,X3,X1),X1)
| ~ in(sk1_esk8_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_415]) ).
cnf(c_0_415_1,axiom,
( ~ in(sk1_esk8_3(X2,X3,X1),X1)
| X1 = set_union2(X2,X3)
| ~ in(sk1_esk8_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_415]) ).
cnf(c_0_415_2,axiom,
( ~ in(sk1_esk8_3(X2,X3,X1),X2)
| ~ in(sk1_esk8_3(X2,X3,X1),X1)
| X1 = set_union2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_415]) ).
cnf(c_0_416_0,axiom,
( X1 = set_union2(X2,X3)
| ~ in(sk1_esk8_3(X2,X3,X1),X1)
| ~ in(sk1_esk8_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_416]) ).
cnf(c_0_416_1,axiom,
( ~ in(sk1_esk8_3(X2,X3,X1),X1)
| X1 = set_union2(X2,X3)
| ~ in(sk1_esk8_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_416]) ).
cnf(c_0_416_2,axiom,
( ~ in(sk1_esk8_3(X2,X3,X1),X3)
| ~ in(sk1_esk8_3(X2,X3,X1),X1)
| X1 = set_union2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_416]) ).
cnf(c_0_417_0,axiom,
( X1 = set_union2(X2,X3)
| in(sk1_esk8_3(X2,X3,X1),X3)
| in(sk1_esk8_3(X2,X3,X1),X2)
| in(sk1_esk8_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_417]) ).
cnf(c_0_417_1,axiom,
( in(sk1_esk8_3(X2,X3,X1),X3)
| X1 = set_union2(X2,X3)
| in(sk1_esk8_3(X2,X3,X1),X2)
| in(sk1_esk8_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_417]) ).
cnf(c_0_417_2,axiom,
( in(sk1_esk8_3(X2,X3,X1),X2)
| in(sk1_esk8_3(X2,X3,X1),X3)
| X1 = set_union2(X2,X3)
| in(sk1_esk8_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_417]) ).
cnf(c_0_417_3,axiom,
( in(sk1_esk8_3(X2,X3,X1),X1)
| in(sk1_esk8_3(X2,X3,X1),X2)
| in(sk1_esk8_3(X2,X3,X1),X3)
| X1 = set_union2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_417]) ).
cnf(c_0_418_0,axiom,
( X1 = cartesian_product2(X2,X3)
| sk1_esk11_3(X2,X3,X1) != ordered_pair(X4,X5)
| ~ in(X5,X3)
| ~ in(X4,X2)
| ~ in(sk1_esk11_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_418]) ).
cnf(c_0_418_1,axiom,
( sk1_esk11_3(X2,X3,X1) != ordered_pair(X4,X5)
| X1 = cartesian_product2(X2,X3)
| ~ in(X5,X3)
| ~ in(X4,X2)
| ~ in(sk1_esk11_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_418]) ).
cnf(c_0_418_2,axiom,
( ~ in(X5,X3)
| sk1_esk11_3(X2,X3,X1) != ordered_pair(X4,X5)
| X1 = cartesian_product2(X2,X3)
| ~ in(X4,X2)
| ~ in(sk1_esk11_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_418]) ).
cnf(c_0_418_3,axiom,
( ~ in(X4,X2)
| ~ in(X5,X3)
| sk1_esk11_3(X2,X3,X1) != ordered_pair(X4,X5)
| X1 = cartesian_product2(X2,X3)
| ~ in(sk1_esk11_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_418]) ).
cnf(c_0_418_4,axiom,
( ~ in(sk1_esk11_3(X2,X3,X1),X1)
| ~ in(X4,X2)
| ~ in(X5,X3)
| sk1_esk11_3(X2,X3,X1) != ordered_pair(X4,X5)
| X1 = cartesian_product2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_418]) ).
cnf(c_0_419_0,axiom,
( X1 = set_difference(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_419]) ).
cnf(c_0_419_1,axiom,
( in(sk1_esk22_3(X2,X3,X1),X1)
| X1 = set_difference(X2,X3)
| ~ in(sk1_esk22_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_419]) ).
cnf(c_0_419_2,axiom,
( ~ in(sk1_esk22_3(X2,X3,X1),X3)
| in(sk1_esk22_3(X2,X3,X1),X1)
| X1 = set_difference(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_419]) ).
cnf(c_0_420_0,axiom,
( X1 = unordered_pair(X2,X3)
| ~ in(sk1_esk7_3(X2,X3,X1),X1)
| sk1_esk7_3(X2,X3,X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_420]) ).
cnf(c_0_420_1,axiom,
( ~ in(sk1_esk7_3(X2,X3,X1),X1)
| X1 = unordered_pair(X2,X3)
| sk1_esk7_3(X2,X3,X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_420]) ).
cnf(c_0_420_2,axiom,
( sk1_esk7_3(X2,X3,X1) != X2
| ~ in(sk1_esk7_3(X2,X3,X1),X1)
| X1 = unordered_pair(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_420]) ).
cnf(c_0_421_0,axiom,
( X1 = unordered_pair(X2,X3)
| ~ in(sk1_esk7_3(X2,X3,X1),X1)
| sk1_esk7_3(X2,X3,X1) != X3 ),
inference(literals_permutation,[status(thm)],[c_0_421]) ).
cnf(c_0_421_1,axiom,
( ~ in(sk1_esk7_3(X2,X3,X1),X1)
| X1 = unordered_pair(X2,X3)
| sk1_esk7_3(X2,X3,X1) != X3 ),
inference(literals_permutation,[status(thm)],[c_0_421]) ).
cnf(c_0_421_2,axiom,
( sk1_esk7_3(X2,X3,X1) != X3
| ~ in(sk1_esk7_3(X2,X3,X1),X1)
| X1 = unordered_pair(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_421]) ).
cnf(c_0_422_0,axiom,
( in(ordered_pair(sk1_esk23_3(X1,X2,X3),X3),X1)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_422]) ).
cnf(c_0_422_1,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk23_3(X1,X2,X3),X3),X1)
| X2 != relation_rng(X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_422]) ).
cnf(c_0_422_2,axiom,
( X2 != relation_rng(X1)
| ~ relation(X1)
| in(ordered_pair(sk1_esk23_3(X1,X2,X3),X3),X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_422]) ).
cnf(c_0_422_3,axiom,
( ~ in(X3,X2)
| X2 != relation_rng(X1)
| ~ relation(X1)
| in(ordered_pair(sk1_esk23_3(X1,X2,X3),X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_422]) ).
cnf(c_0_423_0,axiom,
( in(ordered_pair(X3,sk1_esk16_3(X1,X2,X3)),X1)
| ~ relation(X1)
| X2 != relation_dom(X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_423]) ).
cnf(c_0_423_1,axiom,
( ~ relation(X1)
| in(ordered_pair(X3,sk1_esk16_3(X1,X2,X3)),X1)
| X2 != relation_dom(X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_423]) ).
cnf(c_0_423_2,axiom,
( X2 != relation_dom(X1)
| ~ relation(X1)
| in(ordered_pair(X3,sk1_esk16_3(X1,X2,X3)),X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_423]) ).
cnf(c_0_423_3,axiom,
( ~ in(X3,X2)
| X2 != relation_dom(X1)
| ~ relation(X1)
| in(ordered_pair(X3,sk1_esk16_3(X1,X2,X3)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_423]) ).
cnf(c_0_424_0,axiom,
( X1 = set_difference(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_424]) ).
cnf(c_0_424_1,axiom,
( in(sk1_esk22_3(X2,X3,X1),X1)
| X1 = set_difference(X2,X3)
| in(sk1_esk22_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_424]) ).
cnf(c_0_424_2,axiom,
( in(sk1_esk22_3(X2,X3,X1),X2)
| in(sk1_esk22_3(X2,X3,X1),X1)
| X1 = set_difference(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_424]) ).
cnf(c_0_425_0,axiom,
( X1 = set_intersection2(X2,X3)
| in(sk1_esk15_3(X2,X3,X1),X1)
| in(sk1_esk15_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_425]) ).
cnf(c_0_425_1,axiom,
( in(sk1_esk15_3(X2,X3,X1),X1)
| X1 = set_intersection2(X2,X3)
| in(sk1_esk15_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_425]) ).
cnf(c_0_425_2,axiom,
( in(sk1_esk15_3(X2,X3,X1),X2)
| in(sk1_esk15_3(X2,X3,X1),X1)
| X1 = set_intersection2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_425]) ).
cnf(c_0_426_0,axiom,
( X1 = set_intersection2(X2,X3)
| in(sk1_esk15_3(X2,X3,X1),X1)
| in(sk1_esk15_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_426]) ).
cnf(c_0_426_1,axiom,
( in(sk1_esk15_3(X2,X3,X1),X1)
| X1 = set_intersection2(X2,X3)
| in(sk1_esk15_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_426]) ).
cnf(c_0_426_2,axiom,
( in(sk1_esk15_3(X2,X3,X1),X3)
| in(sk1_esk15_3(X2,X3,X1),X1)
| X1 = set_intersection2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_426]) ).
cnf(c_0_427_0,axiom,
( X1 = cartesian_product2(X2,X3)
| in(sk1_esk11_3(X2,X3,X1),X1)
| in(sk1_esk12_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_427]) ).
cnf(c_0_427_1,axiom,
( in(sk1_esk11_3(X2,X3,X1),X1)
| X1 = cartesian_product2(X2,X3)
| in(sk1_esk12_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_427]) ).
cnf(c_0_427_2,axiom,
( in(sk1_esk12_3(X2,X3,X1),X2)
| in(sk1_esk11_3(X2,X3,X1),X1)
| X1 = cartesian_product2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_427]) ).
cnf(c_0_428_0,axiom,
( X1 = cartesian_product2(X2,X3)
| in(sk1_esk11_3(X2,X3,X1),X1)
| in(sk1_esk13_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_428]) ).
cnf(c_0_428_1,axiom,
( in(sk1_esk11_3(X2,X3,X1),X1)
| X1 = cartesian_product2(X2,X3)
| in(sk1_esk13_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_428]) ).
cnf(c_0_428_2,axiom,
( in(sk1_esk13_3(X2,X3,X1),X3)
| in(sk1_esk11_3(X2,X3,X1),X1)
| X1 = cartesian_product2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_428]) ).
cnf(c_0_429_0,axiom,
( X1 = unordered_pair(X2,X3)
| sk1_esk7_3(X2,X3,X1) = X3
| sk1_esk7_3(X2,X3,X1) = X2
| in(sk1_esk7_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_429]) ).
cnf(c_0_429_1,axiom,
( sk1_esk7_3(X2,X3,X1) = X3
| X1 = unordered_pair(X2,X3)
| sk1_esk7_3(X2,X3,X1) = X2
| in(sk1_esk7_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_429]) ).
cnf(c_0_429_2,axiom,
( sk1_esk7_3(X2,X3,X1) = X2
| sk1_esk7_3(X2,X3,X1) = X3
| X1 = unordered_pair(X2,X3)
| in(sk1_esk7_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_429]) ).
cnf(c_0_429_3,axiom,
( in(sk1_esk7_3(X2,X3,X1),X1)
| sk1_esk7_3(X2,X3,X1) = X2
| sk1_esk7_3(X2,X3,X1) = X3
| X1 = unordered_pair(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_429]) ).
cnf(c_0_430_0,axiom,
( X3 = complements_of_subsets(X2,X1)
| element(sk1_esk26_3(X2,X1,X3),powerset(X2))
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_430]) ).
cnf(c_0_430_1,axiom,
( element(sk1_esk26_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_430]) ).
cnf(c_0_430_2,axiom,
( ~ element(X1,powerset(powerset(X2)))
| element(sk1_esk26_3(X2,X1,X3),powerset(X2))
| X3 = complements_of_subsets(X2,X1)
| ~ element(X3,powerset(powerset(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_430]) ).
cnf(c_0_430_3,axiom,
( ~ element(X3,powerset(powerset(X2)))
| ~ element(X1,powerset(powerset(X2)))
| element(sk1_esk26_3(X2,X1,X3),powerset(X2))
| X3 = complements_of_subsets(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_430]) ).
cnf(c_0_431_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_431]) ).
cnf(c_0_431_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_431]) ).
cnf(c_0_431_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_431]) ).
cnf(c_0_431_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_431]) ).
cnf(c_0_431_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_431]) ).
cnf(c_0_431_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_431]) ).
cnf(c_0_432_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_432]) ).
cnf(c_0_432_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_432]) ).
cnf(c_0_432_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_432]) ).
cnf(c_0_432_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_432]) ).
cnf(c_0_432_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_432]) ).
cnf(c_0_432_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_432]) ).
cnf(c_0_433_0,axiom,
( X2 = relation_rng(X1)
| ~ relation(X1)
| ~ in(ordered_pair(X3,sk1_esk24_2(X1,X2)),X1)
| ~ in(sk1_esk24_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_433]) ).
cnf(c_0_433_1,axiom,
( ~ relation(X1)
| X2 = relation_rng(X1)
| ~ in(ordered_pair(X3,sk1_esk24_2(X1,X2)),X1)
| ~ in(sk1_esk24_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_433]) ).
cnf(c_0_433_2,axiom,
( ~ in(ordered_pair(X3,sk1_esk24_2(X1,X2)),X1)
| ~ relation(X1)
| X2 = relation_rng(X1)
| ~ in(sk1_esk24_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_433]) ).
cnf(c_0_433_3,axiom,
( ~ in(sk1_esk24_2(X1,X2),X2)
| ~ in(ordered_pair(X3,sk1_esk24_2(X1,X2)),X1)
| ~ relation(X1)
| X2 = relation_rng(X1) ),
inference(literals_permutation,[status(thm)],[c_0_433]) ).
cnf(c_0_434_0,axiom,
( X2 = relation_dom(X1)
| ~ relation(X1)
| ~ in(ordered_pair(sk1_esk17_2(X1,X2),X3),X1)
| ~ in(sk1_esk17_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_434]) ).
cnf(c_0_434_1,axiom,
( ~ relation(X1)
| X2 = relation_dom(X1)
| ~ in(ordered_pair(sk1_esk17_2(X1,X2),X3),X1)
| ~ in(sk1_esk17_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_434]) ).
cnf(c_0_434_2,axiom,
( ~ in(ordered_pair(sk1_esk17_2(X1,X2),X3),X1)
| ~ relation(X1)
| X2 = relation_dom(X1)
| ~ in(sk1_esk17_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_434]) ).
cnf(c_0_434_3,axiom,
( ~ in(sk1_esk17_2(X1,X2),X2)
| ~ in(ordered_pair(sk1_esk17_2(X1,X2),X3),X1)
| ~ relation(X1)
| X2 = relation_dom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_434]) ).
cnf(c_0_435_0,axiom,
( X1 = empty_set
| in(X3,X2)
| X2 != set_meet(X1)
| ~ in(X3,sk1_esk1_3(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_435]) ).
cnf(c_0_435_1,axiom,
( in(X3,X2)
| X1 = empty_set
| X2 != set_meet(X1)
| ~ in(X3,sk1_esk1_3(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_435]) ).
cnf(c_0_435_2,axiom,
( X2 != set_meet(X1)
| in(X3,X2)
| X1 = empty_set
| ~ in(X3,sk1_esk1_3(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_435]) ).
cnf(c_0_435_3,axiom,
( ~ in(X3,sk1_esk1_3(X1,X2,X3))
| X2 != set_meet(X1)
| in(X3,X2)
| X1 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_435]) ).
cnf(c_0_436_0,axiom,
( X2 = relation_rng(X1)
| in(ordered_pair(sk1_esk25_2(X1,X2),sk1_esk24_2(X1,X2)),X1)
| in(sk1_esk24_2(X1,X2),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_436]) ).
cnf(c_0_436_1,axiom,
( in(ordered_pair(sk1_esk25_2(X1,X2),sk1_esk24_2(X1,X2)),X1)
| X2 = relation_rng(X1)
| in(sk1_esk24_2(X1,X2),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_436]) ).
cnf(c_0_436_2,axiom,
( in(sk1_esk24_2(X1,X2),X2)
| in(ordered_pair(sk1_esk25_2(X1,X2),sk1_esk24_2(X1,X2)),X1)
| X2 = relation_rng(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_436]) ).
cnf(c_0_436_3,axiom,
( ~ relation(X1)
| in(sk1_esk24_2(X1,X2),X2)
| in(ordered_pair(sk1_esk25_2(X1,X2),sk1_esk24_2(X1,X2)),X1)
| X2 = relation_rng(X1) ),
inference(literals_permutation,[status(thm)],[c_0_436]) ).
cnf(c_0_437_0,axiom,
( X2 = relation_dom(X1)
| in(ordered_pair(sk1_esk17_2(X1,X2),sk1_esk18_2(X1,X2)),X1)
| in(sk1_esk17_2(X1,X2),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_437]) ).
cnf(c_0_437_1,axiom,
( in(ordered_pair(sk1_esk17_2(X1,X2),sk1_esk18_2(X1,X2)),X1)
| X2 = relation_dom(X1)
| in(sk1_esk17_2(X1,X2),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_437]) ).
cnf(c_0_437_2,axiom,
( in(sk1_esk17_2(X1,X2),X2)
| in(ordered_pair(sk1_esk17_2(X1,X2),sk1_esk18_2(X1,X2)),X1)
| X2 = relation_dom(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_437]) ).
cnf(c_0_437_3,axiom,
( ~ relation(X1)
| in(sk1_esk17_2(X1,X2),X2)
| in(ordered_pair(sk1_esk17_2(X1,X2),sk1_esk18_2(X1,X2)),X1)
| X2 = relation_dom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_437]) ).
cnf(c_0_438_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_438]) ).
cnf(c_0_438_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_438]) ).
cnf(c_0_438_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_438]) ).
cnf(c_0_439_0,axiom,
( X1 = empty_set
| X2 = set_meet(X1)
| ~ in(sk1_esk2_2(X1,X2),X2)
| ~ in(sk1_esk2_2(X1,X2),sk1_esk3_2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_439]) ).
cnf(c_0_439_1,axiom,
( X2 = set_meet(X1)
| X1 = empty_set
| ~ in(sk1_esk2_2(X1,X2),X2)
| ~ in(sk1_esk2_2(X1,X2),sk1_esk3_2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_439]) ).
cnf(c_0_439_2,axiom,
( ~ in(sk1_esk2_2(X1,X2),X2)
| X2 = set_meet(X1)
| X1 = empty_set
| ~ in(sk1_esk2_2(X1,X2),sk1_esk3_2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_439]) ).
cnf(c_0_439_3,axiom,
( ~ in(sk1_esk2_2(X1,X2),sk1_esk3_2(X1,X2))
| ~ in(sk1_esk2_2(X1,X2),X2)
| X2 = set_meet(X1)
| X1 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_439]) ).
cnf(c_0_440_0,axiom,
( X1 = union(X2)
| ~ in(X3,X2)
| ~ in(sk1_esk20_2(X2,X1),X3)
| ~ in(sk1_esk20_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_440]) ).
cnf(c_0_440_1,axiom,
( ~ in(X3,X2)
| X1 = union(X2)
| ~ in(sk1_esk20_2(X2,X1),X3)
| ~ in(sk1_esk20_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_440]) ).
cnf(c_0_440_2,axiom,
( ~ in(sk1_esk20_2(X2,X1),X3)
| ~ in(X3,X2)
| X1 = union(X2)
| ~ in(sk1_esk20_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_440]) ).
cnf(c_0_440_3,axiom,
( ~ in(sk1_esk20_2(X2,X1),X1)
| ~ in(sk1_esk20_2(X2,X1),X3)
| ~ in(X3,X2)
| X1 = union(X2) ),
inference(literals_permutation,[status(thm)],[c_0_440]) ).
cnf(c_0_441_0,axiom,
( in(X3,sk1_esk19_3(X2,X1,X3))
| X1 != union(X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_441]) ).
cnf(c_0_441_1,axiom,
( X1 != union(X2)
| in(X3,sk1_esk19_3(X2,X1,X3))
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_441]) ).
cnf(c_0_441_2,axiom,
( ~ in(X3,X1)
| X1 != union(X2)
| in(X3,sk1_esk19_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_441]) ).
cnf(c_0_442_0,axiom,
( in(sk1_esk19_3(X2,X1,X3),X2)
| X1 != union(X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_442]) ).
cnf(c_0_442_1,axiom,
( X1 != union(X2)
| in(sk1_esk19_3(X2,X1,X3),X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_442]) ).
cnf(c_0_442_2,axiom,
( ~ in(X3,X1)
| X1 != union(X2)
| in(sk1_esk19_3(X2,X1,X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_442]) ).
cnf(c_0_443_0,axiom,
( X1 = empty_set
| in(X3,X2)
| in(sk1_esk1_3(X1,X2,X3),X1)
| X2 != set_meet(X1) ),
inference(literals_permutation,[status(thm)],[c_0_443]) ).
cnf(c_0_443_1,axiom,
( in(X3,X2)
| X1 = empty_set
| in(sk1_esk1_3(X1,X2,X3),X1)
| X2 != set_meet(X1) ),
inference(literals_permutation,[status(thm)],[c_0_443]) ).
cnf(c_0_443_2,axiom,
( in(sk1_esk1_3(X1,X2,X3),X1)
| in(X3,X2)
| X1 = empty_set
| X2 != set_meet(X1) ),
inference(literals_permutation,[status(thm)],[c_0_443]) ).
cnf(c_0_443_3,axiom,
( X2 != set_meet(X1)
| in(sk1_esk1_3(X1,X2,X3),X1)
| in(X3,X2)
| X1 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_443]) ).
cnf(c_0_444_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_444]) ).
cnf(c_0_444_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_444]) ).
cnf(c_0_444_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_444]) ).
cnf(c_0_445_0,axiom,
( X1 = powerset(X2)
| ~ subset(sk1_esk6_2(X2,X1),X2)
| ~ in(sk1_esk6_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_445]) ).
cnf(c_0_445_1,axiom,
( ~ subset(sk1_esk6_2(X2,X1),X2)
| X1 = powerset(X2)
| ~ in(sk1_esk6_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_445]) ).
cnf(c_0_445_2,axiom,
( ~ in(sk1_esk6_2(X2,X1),X1)
| ~ subset(sk1_esk6_2(X2,X1),X2)
| X1 = powerset(X2) ),
inference(literals_permutation,[status(thm)],[c_0_445]) ).
cnf(c_0_446_0,axiom,
( X1 = X2
| ~ in(sk1_esk33_2(X1,X2),X2)
| ~ in(sk1_esk33_2(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_446]) ).
cnf(c_0_446_1,axiom,
( ~ in(sk1_esk33_2(X1,X2),X2)
| X1 = X2
| ~ in(sk1_esk33_2(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_446]) ).
cnf(c_0_446_2,axiom,
( ~ in(sk1_esk33_2(X1,X2),X1)
| ~ in(sk1_esk33_2(X1,X2),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_446]) ).
cnf(c_0_447_0,axiom,
( X1 = union(X2)
| in(sk1_esk20_2(X2,X1),X1)
| in(sk1_esk20_2(X2,X1),sk1_esk21_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_447]) ).
cnf(c_0_447_1,axiom,
( in(sk1_esk20_2(X2,X1),X1)
| X1 = union(X2)
| in(sk1_esk20_2(X2,X1),sk1_esk21_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_447]) ).
cnf(c_0_447_2,axiom,
( in(sk1_esk20_2(X2,X1),sk1_esk21_2(X2,X1))
| in(sk1_esk20_2(X2,X1),X1)
| X1 = union(X2) ),
inference(literals_permutation,[status(thm)],[c_0_447]) ).
cnf(c_0_448_0,axiom,
( X1 = empty_set
| X2 = set_meet(X1)
| in(sk1_esk3_2(X1,X2),X1)
| ~ in(sk1_esk2_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_448]) ).
cnf(c_0_448_1,axiom,
( X2 = set_meet(X1)
| X1 = empty_set
| in(sk1_esk3_2(X1,X2),X1)
| ~ in(sk1_esk2_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_448]) ).
cnf(c_0_448_2,axiom,
( in(sk1_esk3_2(X1,X2),X1)
| X2 = set_meet(X1)
| X1 = empty_set
| ~ in(sk1_esk2_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_448]) ).
cnf(c_0_448_3,axiom,
( ~ in(sk1_esk2_2(X1,X2),X2)
| in(sk1_esk3_2(X1,X2),X1)
| X2 = set_meet(X1)
| X1 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_448]) ).
cnf(c_0_449_0,axiom,
( X1 = empty_set
| X2 = set_meet(X1)
| in(sk1_esk2_2(X1,X2),X3)
| in(sk1_esk2_2(X1,X2),X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_449]) ).
cnf(c_0_449_1,axiom,
( X2 = set_meet(X1)
| X1 = empty_set
| in(sk1_esk2_2(X1,X2),X3)
| in(sk1_esk2_2(X1,X2),X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_449]) ).
cnf(c_0_449_2,axiom,
( in(sk1_esk2_2(X1,X2),X3)
| X2 = set_meet(X1)
| X1 = empty_set
| in(sk1_esk2_2(X1,X2),X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_449]) ).
cnf(c_0_449_3,axiom,
( in(sk1_esk2_2(X1,X2),X2)
| in(sk1_esk2_2(X1,X2),X3)
| X2 = set_meet(X1)
| X1 = empty_set
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_449]) ).
cnf(c_0_449_4,axiom,
( ~ in(X3,X1)
| in(sk1_esk2_2(X1,X2),X2)
| in(sk1_esk2_2(X1,X2),X3)
| X2 = set_meet(X1)
| X1 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_449]) ).
cnf(c_0_450_0,axiom,
( element(complements_of_subsets(X1,X2),powerset(powerset(X1)))
| ~ element(X2,powerset(powerset(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_450]) ).
cnf(c_0_450_1,axiom,
( ~ element(X2,powerset(powerset(X1)))
| element(complements_of_subsets(X1,X2),powerset(powerset(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_450]) ).
cnf(c_0_451_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_451]) ).
cnf(c_0_451_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_451]) ).
cnf(c_0_451_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_451]) ).
cnf(c_0_451_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_451]) ).
cnf(c_0_451_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_451]) ).
cnf(c_0_452_0,axiom,
( element(meet_of_subsets(X1,X2),powerset(X1))
| ~ element(X2,powerset(powerset(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_452]) ).
cnf(c_0_452_1,axiom,
( ~ element(X2,powerset(powerset(X1)))
| element(meet_of_subsets(X1,X2),powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_452]) ).
cnf(c_0_453_0,axiom,
( element(union_of_subsets(X1,X2),powerset(X1))
| ~ element(X2,powerset(powerset(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_453]) ).
cnf(c_0_453_1,axiom,
( ~ element(X2,powerset(powerset(X1)))
| element(union_of_subsets(X1,X2),powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_453]) ).
cnf(c_0_454_0,axiom,
( in(X3,sk1_esk35_2(X2,X1))
| ~ in(X1,sk1_esk34_1(X2))
| ~ subset(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_454]) ).
cnf(c_0_454_1,axiom,
( ~ in(X1,sk1_esk34_1(X2))
| in(X3,sk1_esk35_2(X2,X1))
| ~ subset(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_454]) ).
cnf(c_0_454_2,axiom,
( ~ subset(X3,X1)
| ~ in(X1,sk1_esk34_1(X2))
| in(X3,sk1_esk35_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_454]) ).
cnf(c_0_455_0,axiom,
( in(X3,X2)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(ordered_pair(X4,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_455]) ).
cnf(c_0_455_1,axiom,
( ~ relation(X1)
| in(X3,X2)
| X2 != relation_rng(X1)
| ~ in(ordered_pair(X4,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_455]) ).
cnf(c_0_455_2,axiom,
( X2 != relation_rng(X1)
| ~ relation(X1)
| in(X3,X2)
| ~ in(ordered_pair(X4,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_455]) ).
cnf(c_0_455_3,axiom,
( ~ in(ordered_pair(X4,X3),X1)
| X2 != relation_rng(X1)
| ~ relation(X1)
| in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_455]) ).
cnf(c_0_456_0,axiom,
( in(X3,X2)
| ~ relation(X1)
| X2 != relation_dom(X1)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_456]) ).
cnf(c_0_456_1,axiom,
( ~ relation(X1)
| in(X3,X2)
| X2 != relation_dom(X1)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_456]) ).
cnf(c_0_456_2,axiom,
( X2 != relation_dom(X1)
| ~ relation(X1)
| in(X3,X2)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_456]) ).
cnf(c_0_456_3,axiom,
( ~ in(ordered_pair(X3,X4),X1)
| X2 != relation_dom(X1)
| ~ relation(X1)
| in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_456]) ).
cnf(c_0_457_0,axiom,
( X1 = singleton(X2)
| sk1_esk4_2(X2,X1) != X2
| ~ in(sk1_esk4_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_457]) ).
cnf(c_0_457_1,axiom,
( sk1_esk4_2(X2,X1) != X2
| X1 = singleton(X2)
| ~ in(sk1_esk4_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_457]) ).
cnf(c_0_457_2,axiom,
( ~ in(sk1_esk4_2(X2,X1),X1)
| sk1_esk4_2(X2,X1) != X2
| X1 = singleton(X2) ),
inference(literals_permutation,[status(thm)],[c_0_457]) ).
cnf(c_0_458_0,axiom,
( complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2
| ~ element(X2,powerset(powerset(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_458]) ).
cnf(c_0_458_1,axiom,
( ~ element(X2,powerset(powerset(X1)))
| complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_458]) ).
cnf(c_0_459_0,axiom,
( X1 = union(X2)
| in(sk1_esk20_2(X2,X1),X1)
| in(sk1_esk21_2(X2,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_459]) ).
cnf(c_0_459_1,axiom,
( in(sk1_esk20_2(X2,X1),X1)
| X1 = union(X2)
| in(sk1_esk21_2(X2,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_459]) ).
cnf(c_0_459_2,axiom,
( in(sk1_esk21_2(X2,X1),X2)
| in(sk1_esk20_2(X2,X1),X1)
| X1 = union(X2) ),
inference(literals_permutation,[status(thm)],[c_0_459]) ).
cnf(c_0_460_0,axiom,
( X1 = powerset(X2)
| subset(sk1_esk6_2(X2,X1),X2)
| in(sk1_esk6_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_460]) ).
cnf(c_0_460_1,axiom,
( subset(sk1_esk6_2(X2,X1),X2)
| X1 = powerset(X2)
| in(sk1_esk6_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_460]) ).
cnf(c_0_460_2,axiom,
( in(sk1_esk6_2(X2,X1),X1)
| subset(sk1_esk6_2(X2,X1),X2)
| X1 = powerset(X2) ),
inference(literals_permutation,[status(thm)],[c_0_460]) ).
cnf(c_0_461_0,axiom,
( in(X4,X1)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_461]) ).
cnf(c_0_461_1,axiom,
( X1 != set_intersection2(X2,X3)
| in(X4,X1)
| ~ in(X4,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_461]) ).
cnf(c_0_461_2,axiom,
( ~ in(X4,X3)
| X1 != set_intersection2(X2,X3)
| in(X4,X1)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_461]) ).
cnf(c_0_461_3,axiom,
( ~ in(X4,X2)
| ~ in(X4,X3)
| X1 != set_intersection2(X2,X3)
| in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_461]) ).
cnf(c_0_462_0,axiom,
( X1 = X2
| in(sk1_esk33_2(X1,X2),X2)
| in(sk1_esk33_2(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_462]) ).
cnf(c_0_462_1,axiom,
( in(sk1_esk33_2(X1,X2),X2)
| X1 = X2
| in(sk1_esk33_2(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_462]) ).
cnf(c_0_462_2,axiom,
( in(sk1_esk33_2(X1,X2),X1)
| in(sk1_esk33_2(X1,X2),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_462]) ).
cnf(c_0_463_0,axiom,
( in(sk1_esk35_2(X2,X1),sk1_esk34_1(X2))
| ~ in(X1,sk1_esk34_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_463]) ).
cnf(c_0_463_1,axiom,
( ~ in(X1,sk1_esk34_1(X2))
| in(sk1_esk35_2(X2,X1),sk1_esk34_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_463]) ).
cnf(c_0_464_0,axiom,
( element(subset_complement(X1,X2),powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_464]) ).
cnf(c_0_464_1,axiom,
( ~ element(X2,powerset(X1))
| element(subset_complement(X1,X2),powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_464]) ).
cnf(c_0_465_0,axiom,
( subset(X1,X2)
| ~ in(sk1_esk14_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_465]) ).
cnf(c_0_465_1,axiom,
( ~ in(sk1_esk14_2(X1,X2),X2)
| subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_465]) ).
cnf(c_0_466_0,axiom,
( in(X1,sk1_esk34_1(X2))
| ~ subset(X1,X3)
| ~ in(X3,sk1_esk34_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_466]) ).
cnf(c_0_466_1,axiom,
( ~ subset(X1,X3)
| in(X1,sk1_esk34_1(X2))
| ~ in(X3,sk1_esk34_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_466]) ).
cnf(c_0_466_2,axiom,
( ~ in(X3,sk1_esk34_1(X2))
| ~ subset(X1,X3)
| in(X1,sk1_esk34_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_466]) ).
cnf(c_0_467_0,axiom,
( in(X4,X1)
| in(X4,X3)
| X1 != set_difference(X2,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_467]) ).
cnf(c_0_467_1,axiom,
( in(X4,X3)
| in(X4,X1)
| X1 != set_difference(X2,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_467]) ).
cnf(c_0_467_2,axiom,
( X1 != set_difference(X2,X3)
| in(X4,X3)
| in(X4,X1)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_467]) ).
cnf(c_0_467_3,axiom,
( ~ in(X4,X2)
| X1 != set_difference(X2,X3)
| in(X4,X3)
| in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_467]) ).
cnf(c_0_468_0,axiom,
( in(X4,X3)
| in(X4,X2)
| X1 != set_union2(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_468]) ).
cnf(c_0_468_1,axiom,
( in(X4,X2)
| in(X4,X3)
| X1 != set_union2(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_468]) ).
cnf(c_0_468_2,axiom,
( X1 != set_union2(X2,X3)
| in(X4,X2)
| in(X4,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_468]) ).
cnf(c_0_468_3,axiom,
( ~ in(X4,X1)
| X1 != set_union2(X2,X3)
| in(X4,X2)
| in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_468]) ).
cnf(c_0_469_0,axiom,
( in(X1,sk1_esk34_1(X2))
| are_equipotent(X1,sk1_esk34_1(X2))
| ~ subset(X1,sk1_esk34_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_469]) ).
cnf(c_0_469_1,axiom,
( are_equipotent(X1,sk1_esk34_1(X2))
| in(X1,sk1_esk34_1(X2))
| ~ subset(X1,sk1_esk34_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_469]) ).
cnf(c_0_469_2,axiom,
( ~ subset(X1,sk1_esk34_1(X2))
| are_equipotent(X1,sk1_esk34_1(X2))
| in(X1,sk1_esk34_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_469]) ).
cnf(c_0_470_0,axiom,
( subset_complement(X1,subset_complement(X1,X2)) = X2
| ~ element(X2,powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_470]) ).
cnf(c_0_470_1,axiom,
( ~ element(X2,powerset(X1))
| subset_complement(X1,subset_complement(X1,X2)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_470]) ).
cnf(c_0_471_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_471]) ).
cnf(c_0_471_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_471]) ).
cnf(c_0_471_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_471]) ).
cnf(c_0_471_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_471]) ).
cnf(c_0_471_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_471]) ).
cnf(c_0_472_0,axiom,
( meet_of_subsets(X1,X2) = set_meet(X2)
| ~ element(X2,powerset(powerset(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_472]) ).
cnf(c_0_472_1,axiom,
( ~ element(X2,powerset(powerset(X1)))
| meet_of_subsets(X1,X2) = set_meet(X2) ),
inference(literals_permutation,[status(thm)],[c_0_472]) ).
cnf(c_0_473_0,axiom,
( union_of_subsets(X1,X2) = union(X2)
| ~ element(X2,powerset(powerset(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_473]) ).
cnf(c_0_473_1,axiom,
( ~ element(X2,powerset(powerset(X1)))
| union_of_subsets(X1,X2) = union(X2) ),
inference(literals_permutation,[status(thm)],[c_0_473]) ).
cnf(c_0_474_0,axiom,
( element(X1,X2)
| ~ element(X3,powerset(X2))
| ~ in(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_474]) ).
cnf(c_0_474_1,axiom,
( ~ element(X3,powerset(X2))
| element(X1,X2)
| ~ in(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_474]) ).
cnf(c_0_474_2,axiom,
( ~ in(X1,X3)
| ~ element(X3,powerset(X2))
| element(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_474]) ).
cnf(c_0_475_0,axiom,
( X1 != set_difference(X2,X3)
| ~ in(X4,X1)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_475]) ).
cnf(c_0_475_1,axiom,
( ~ in(X4,X1)
| X1 != set_difference(X2,X3)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_475]) ).
cnf(c_0_475_2,axiom,
( ~ in(X4,X3)
| ~ in(X4,X1)
| X1 != set_difference(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_475]) ).
cnf(c_0_476_0,axiom,
( in(X3,X1)
| X1 != union(X2)
| ~ in(X4,X2)
| ~ in(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_476]) ).
cnf(c_0_476_1,axiom,
( X1 != union(X2)
| in(X3,X1)
| ~ in(X4,X2)
| ~ in(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_476]) ).
cnf(c_0_476_2,axiom,
( ~ in(X4,X2)
| X1 != union(X2)
| in(X3,X1)
| ~ in(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_476]) ).
cnf(c_0_476_3,axiom,
( ~ in(X3,X4)
| ~ in(X4,X2)
| X1 != union(X2)
| in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_476]) ).
cnf(c_0_477_0,axiom,
( ~ empty(X1)
| ~ element(X2,powerset(X1))
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_477]) ).
cnf(c_0_477_1,axiom,
( ~ element(X2,powerset(X1))
| ~ empty(X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_477]) ).
cnf(c_0_477_2,axiom,
( ~ in(X3,X2)
| ~ element(X2,powerset(X1))
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_477]) ).
cnf(c_0_478_0,axiom,
( in(X4,X2)
| X1 != set_difference(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_478]) ).
cnf(c_0_478_1,axiom,
( X1 != set_difference(X2,X3)
| in(X4,X2)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_478]) ).
cnf(c_0_478_2,axiom,
( ~ in(X4,X1)
| X1 != set_difference(X2,X3)
| in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_478]) ).
cnf(c_0_479_0,axiom,
( in(X4,X2)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_479]) ).
cnf(c_0_479_1,axiom,
( X1 != set_intersection2(X2,X3)
| in(X4,X2)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_479]) ).
cnf(c_0_479_2,axiom,
( ~ in(X4,X1)
| X1 != set_intersection2(X2,X3)
| in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_479]) ).
cnf(c_0_480_0,axiom,
( in(X4,X3)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_480]) ).
cnf(c_0_480_1,axiom,
( X1 != set_intersection2(X2,X3)
| in(X4,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_480]) ).
cnf(c_0_480_2,axiom,
( ~ in(X4,X1)
| X1 != set_intersection2(X2,X3)
| in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_480]) ).
cnf(c_0_481_0,axiom,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_481]) ).
cnf(c_0_481_1,axiom,
( X1 != set_union2(X2,X3)
| in(X4,X1)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_481]) ).
cnf(c_0_481_2,axiom,
( ~ in(X4,X2)
| X1 != set_union2(X2,X3)
| in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_481]) ).
cnf(c_0_482_0,axiom,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_482]) ).
cnf(c_0_482_1,axiom,
( X1 != set_union2(X2,X3)
| in(X4,X1)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_482]) ).
cnf(c_0_482_2,axiom,
( ~ in(X4,X3)
| X1 != set_union2(X2,X3)
| in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_482]) ).
cnf(c_0_483_0,axiom,
( X1 = singleton(X2)
| sk1_esk4_2(X2,X1) = X2
| in(sk1_esk4_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_483]) ).
cnf(c_0_483_1,axiom,
( sk1_esk4_2(X2,X1) = X2
| X1 = singleton(X2)
| in(sk1_esk4_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_483]) ).
cnf(c_0_483_2,axiom,
( in(sk1_esk4_2(X2,X1),X1)
| sk1_esk4_2(X2,X1) = X2
| X1 = singleton(X2) ),
inference(literals_permutation,[status(thm)],[c_0_483]) ).
cnf(c_0_484_0,axiom,
( subset_complement(X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_484]) ).
cnf(c_0_484_1,axiom,
( ~ element(X2,powerset(X1))
| subset_complement(X1,X2) = set_difference(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_484]) ).
cnf(c_0_486_0,axiom,
( in(X1,X2)
| ~ in(X1,X3)
| ~ subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_486]) ).
cnf(c_0_486_1,axiom,
( ~ in(X1,X3)
| in(X1,X2)
| ~ subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_486]) ).
cnf(c_0_486_2,axiom,
( ~ subset(X3,X2)
| ~ in(X1,X3)
| in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_486]) ).
cnf(c_0_487_0,axiom,
( subset(X1,X2)
| in(sk1_esk14_2(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_487]) ).
cnf(c_0_487_1,axiom,
( in(sk1_esk14_2(X1,X2),X1)
| subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_487]) ).
cnf(c_0_488_0,axiom,
( empty(X2)
| ~ empty(set_union2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_488]) ).
cnf(c_0_488_1,axiom,
( ~ empty(set_union2(X1,X2))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_488]) ).
cnf(c_0_489_0,axiom,
( empty(X1)
| ~ empty(set_union2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_489]) ).
cnf(c_0_489_1,axiom,
( ~ empty(set_union2(X1,X2))
| empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_489]) ).
cnf(c_0_490_0,axiom,
( X4 = X3
| X4 = X2
| X1 != unordered_pair(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_490]) ).
cnf(c_0_490_1,axiom,
( X4 = X2
| X4 = X3
| X1 != unordered_pair(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_490]) ).
cnf(c_0_490_2,axiom,
( X1 != unordered_pair(X2,X3)
| X4 = X2
| X4 = X3
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_490]) ).
cnf(c_0_490_3,axiom,
( ~ in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 = X2
| X4 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_490]) ).
cnf(c_0_493_0,axiom,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_493]) ).
cnf(c_0_493_1,axiom,
( ~ subset(X2,X1)
| X1 = X2
| ~ subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_493]) ).
cnf(c_0_493_2,axiom,
( ~ subset(X1,X2)
| ~ subset(X2,X1)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_493]) ).
cnf(c_0_494_0,axiom,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_494]) ).
cnf(c_0_494_1,axiom,
( ~ element(X1,powerset(X2))
| subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_494]) ).
cnf(c_0_495_0,axiom,
( subset(X3,X2)
| X1 != powerset(X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_495]) ).
cnf(c_0_495_1,axiom,
( X1 != powerset(X2)
| subset(X3,X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_495]) ).
cnf(c_0_495_2,axiom,
( ~ in(X3,X1)
| X1 != powerset(X2)
| subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_495]) ).
cnf(c_0_496_0,axiom,
( in(X3,X1)
| X1 != powerset(X2)
| ~ subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_496]) ).
cnf(c_0_496_1,axiom,
( X1 != powerset(X2)
| in(X3,X1)
| ~ subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_496]) ).
cnf(c_0_496_2,axiom,
( ~ subset(X3,X2)
| X1 != powerset(X2)
| in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_496]) ).
cnf(c_0_497_0,axiom,
( ~ proper_subset(X1,X2)
| ~ proper_subset(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_497]) ).
cnf(c_0_497_1,axiom,
( ~ proper_subset(X2,X1)
| ~ proper_subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_497]) ).
cnf(c_0_498_0,axiom,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_498]) ).
cnf(c_0_498_1,axiom,
( ~ in(X2,X1)
| ~ in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_498]) ).
cnf(c_0_499_0,axiom,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_499]) ).
cnf(c_0_499_1,axiom,
( ~ subset(X1,X2)
| element(X1,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_499]) ).
cnf(c_0_500_0,axiom,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_500]) ).
cnf(c_0_500_1,axiom,
( X1 != unordered_pair(X2,X3)
| in(X4,X1)
| X4 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_500]) ).
cnf(c_0_500_2,axiom,
( X4 != X2
| X1 != unordered_pair(X2,X3)
| in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_500]) ).
cnf(c_0_501_0,axiom,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_501]) ).
cnf(c_0_501_1,axiom,
( X1 != unordered_pair(X2,X3)
| in(X4,X1)
| X4 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_501]) ).
cnf(c_0_501_2,axiom,
( X4 != X3
| X1 != unordered_pair(X2,X3)
| in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_501]) ).
cnf(c_0_502_0,axiom,
( in(X1,X2)
| empty(X2)
| ~ element(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_502]) ).
cnf(c_0_502_1,axiom,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_502]) ).
cnf(c_0_502_2,axiom,
( ~ element(X1,X2)
| empty(X2)
| in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_502]) ).
cnf(c_0_503_0,axiom,
( empty(X1)
| in(X2,X1)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_503]) ).
cnf(c_0_503_1,axiom,
( in(X2,X1)
| empty(X1)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_503]) ).
cnf(c_0_503_2,axiom,
( ~ element(X2,X1)
| in(X2,X1)
| empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_503]) ).
cnf(c_0_504_0,axiom,
( empty(X1)
| element(X2,X1)
| ~ in(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_504]) ).
cnf(c_0_504_1,axiom,
( element(X2,X1)
| empty(X1)
| ~ in(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_504]) ).
cnf(c_0_504_2,axiom,
( ~ in(X2,X1)
| element(X2,X1)
| empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_504]) ).
cnf(c_0_505_0,axiom,
( proper_subset(X1,X2)
| X1 = X2
| ~ subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_505]) ).
cnf(c_0_505_1,axiom,
( X1 = X2
| proper_subset(X1,X2)
| ~ subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_505]) ).
cnf(c_0_505_2,axiom,
( ~ subset(X1,X2)
| X1 = X2
| proper_subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_505]) ).
cnf(c_0_506_0,axiom,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_506]) ).
cnf(c_0_506_1,axiom,
( ~ in(X1,X2)
| element(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_506]) ).
cnf(c_0_507_0,axiom,
( disjoint(X1,X2)
| ~ disjoint(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_507]) ).
cnf(c_0_507_1,axiom,
( ~ disjoint(X2,X1)
| disjoint(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_507]) ).
cnf(c_0_508_0,axiom,
( subset(X1,X2)
| ~ proper_subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_508]) ).
cnf(c_0_508_1,axiom,
( ~ proper_subset(X1,X2)
| subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_508]) ).
cnf(c_0_509_0,axiom,
( set_intersection2(X1,X2) = empty_set
| ~ disjoint(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_509]) ).
cnf(c_0_509_1,axiom,
( ~ disjoint(X1,X2)
| set_intersection2(X1,X2) = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_509]) ).
cnf(c_0_510_0,axiom,
( disjoint(X1,X2)
| set_intersection2(X1,X2) != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_510]) ).
cnf(c_0_510_1,axiom,
( set_intersection2(X1,X2) != empty_set
| disjoint(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_510]) ).
cnf(c_0_511_0,axiom,
( empty(X2)
| ~ empty(X1)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_511]) ).
cnf(c_0_511_1,axiom,
( ~ empty(X1)
| empty(X2)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_511]) ).
cnf(c_0_511_2,axiom,
( ~ element(X2,X1)
| ~ empty(X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_511]) ).
cnf(c_0_512_0,axiom,
( X3 = X2
| X1 != singleton(X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_512]) ).
cnf(c_0_512_1,axiom,
( X1 != singleton(X2)
| X3 = X2
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_512]) ).
cnf(c_0_512_2,axiom,
( ~ in(X3,X1)
| X1 != singleton(X2)
| X3 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_512]) ).
cnf(c_0_513_0,axiom,
( empty(X1)
| element(sk1_esk29_1(X1),powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_513]) ).
cnf(c_0_513_1,axiom,
( element(sk1_esk29_1(X1),powerset(X1))
| empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_513]) ).
cnf(c_0_514_0,axiom,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_514]) ).
cnf(c_0_514_1,axiom,
( ~ in(X2,X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_514]) ).
cnf(c_0_515_0,axiom,
( element(X2,X1)
| ~ empty(X1)
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_515]) ).
cnf(c_0_515_1,axiom,
( ~ empty(X1)
| element(X2,X1)
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_515]) ).
cnf(c_0_515_2,axiom,
( ~ empty(X2)
| ~ empty(X1)
| element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_515]) ).
cnf(c_0_521_0,axiom,
( in(X3,X1)
| X1 != singleton(X2)
| X3 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_521]) ).
cnf(c_0_521_1,axiom,
( X1 != singleton(X2)
| in(X3,X1)
| X3 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_521]) ).
cnf(c_0_521_2,axiom,
( X3 != X2
| X1 != singleton(X2)
| in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_521]) ).
cnf(c_0_522_0,axiom,
( ~ proper_subset(X1,X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_522]) ).
cnf(c_0_522_1,axiom,
( X1 != X2
| ~ proper_subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_522]) ).
cnf(c_0_523_0,axiom,
( ~ in(X1,X2)
| X2 != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_523]) ).
cnf(c_0_523_1,axiom,
( X2 != empty_set
| ~ in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_523]) ).
cnf(c_0_525_0,axiom,
( X1 = empty_set
| in(sk1_esk5_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_525]) ).
cnf(c_0_525_1,axiom,
( in(sk1_esk5_1(X1),X1)
| X1 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_525]) ).
cnf(c_0_526_0,axiom,
( empty(X1)
| ~ empty(sk1_esk29_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_526]) ).
cnf(c_0_526_1,axiom,
( ~ empty(sk1_esk29_1(X1))
| empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_526]) ).
cnf(c_0_529_0,axiom,
( subset(X1,X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_529]) ).
cnf(c_0_529_1,axiom,
( X1 != X2
| subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_529]) ).
cnf(c_0_530_0,axiom,
( subset(X2,X1)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_530]) ).
cnf(c_0_530_1,axiom,
( X1 != X2
| subset(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_530]) ).
cnf(c_0_533_0,axiom,
( X2 = X1
| ~ empty(X1)
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_533]) ).
cnf(c_0_533_1,axiom,
( ~ empty(X1)
| X2 = X1
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_533]) ).
cnf(c_0_533_2,axiom,
( ~ empty(X2)
| ~ empty(X1)
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_533]) ).
cnf(c_0_541_0,axiom,
( X2 = empty_set
| X1 != empty_set
| X2 != set_meet(X1) ),
inference(literals_permutation,[status(thm)],[c_0_541]) ).
cnf(c_0_541_1,axiom,
( X1 != empty_set
| X2 = empty_set
| X2 != set_meet(X1) ),
inference(literals_permutation,[status(thm)],[c_0_541]) ).
cnf(c_0_541_2,axiom,
( X2 != set_meet(X1)
| X1 != empty_set
| X2 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_541]) ).
cnf(c_0_543_0,axiom,
( X2 = set_meet(X1)
| X1 != empty_set
| X2 != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_543]) ).
cnf(c_0_543_1,axiom,
( X1 != empty_set
| X2 = set_meet(X1)
| X2 != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_543]) ).
cnf(c_0_543_2,axiom,
( X2 != empty_set
| X1 != empty_set
| X2 = set_meet(X1) ),
inference(literals_permutation,[status(thm)],[c_0_543]) ).
cnf(c_0_544_0,axiom,
( X1 = empty_set
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_544]) ).
cnf(c_0_544_1,axiom,
( ~ empty(X1)
| X1 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_544]) ).
cnf(c_0_491_0,axiom,
~ empty(unordered_pair(X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_491]) ).
cnf(c_0_492_0,axiom,
~ empty(ordered_pair(X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_492]) ).
cnf(c_0_524_0,axiom,
~ proper_subset(X1,X1),
inference(literals_permutation,[status(thm)],[c_0_524]) ).
cnf(c_0_531_0,axiom,
~ empty(singleton(X1)),
inference(literals_permutation,[status(thm)],[c_0_531]) ).
cnf(c_0_532_0,axiom,
~ empty(powerset(X1)),
inference(literals_permutation,[status(thm)],[c_0_532]) ).
cnf(c_0_546_0,axiom,
~ empty(sk1_esk32_0),
inference(literals_permutation,[status(thm)],[c_0_546]) ).
cnf(c_0_485_0,axiom,
unordered_pair(unordered_pair(X1,X2),singleton(X1)) = ordered_pair(X1,X2),
inference(literals_permutation,[status(thm)],[c_0_485]) ).
cnf(c_0_516_0,axiom,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(literals_permutation,[status(thm)],[c_0_516]) ).
cnf(c_0_517_0,axiom,
set_union2(X1,X2) = set_union2(X2,X1),
inference(literals_permutation,[status(thm)],[c_0_517]) ).
cnf(c_0_518_0,axiom,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(literals_permutation,[status(thm)],[c_0_518]) ).
cnf(c_0_519_0,axiom,
element(sk1_esk31_1(X1),powerset(X1)),
inference(literals_permutation,[status(thm)],[c_0_519]) ).
cnf(c_0_520_0,axiom,
element(cast_to_subset(X1),powerset(X1)),
inference(literals_permutation,[status(thm)],[c_0_520]) ).
cnf(c_0_527_0,axiom,
in(X1,sk1_esk34_1(X1)),
inference(literals_permutation,[status(thm)],[c_0_527]) ).
cnf(c_0_528_0,axiom,
element(sk1_esk27_1(X1),X1),
inference(literals_permutation,[status(thm)],[c_0_528]) ).
cnf(c_0_534_0,axiom,
set_intersection2(X1,X1) = X1,
inference(literals_permutation,[status(thm)],[c_0_534]) ).
cnf(c_0_535_0,axiom,
set_union2(X1,X1) = X1,
inference(literals_permutation,[status(thm)],[c_0_535]) ).
cnf(c_0_536_0,axiom,
subset(X1,X1),
inference(literals_permutation,[status(thm)],[c_0_536]) ).
cnf(c_0_537_0,axiom,
set_difference(X1,empty_set) = X1,
inference(literals_permutation,[status(thm)],[c_0_537]) ).
cnf(c_0_538_0,axiom,
set_union2(X1,empty_set) = X1,
inference(literals_permutation,[status(thm)],[c_0_538]) ).
cnf(c_0_539_0,axiom,
set_difference(empty_set,X1) = empty_set,
inference(literals_permutation,[status(thm)],[c_0_539]) ).
cnf(c_0_540_0,axiom,
set_intersection2(X1,empty_set) = empty_set,
inference(literals_permutation,[status(thm)],[c_0_540]) ).
cnf(c_0_542_0,axiom,
empty(sk1_esk31_1(X1)),
inference(literals_permutation,[status(thm)],[c_0_542]) ).
cnf(c_0_545_0,axiom,
cast_to_subset(X1) = X1,
inference(literals_permutation,[status(thm)],[c_0_545]) ).
cnf(c_0_547_0,axiom,
empty(sk1_esk30_0),
inference(literals_permutation,[status(thm)],[c_0_547]) ).
cnf(c_0_548_0,axiom,
empty(sk1_esk28_0),
inference(literals_permutation,[status(thm)],[c_0_548]) ).
cnf(c_0_549_0,axiom,
relation(sk1_esk28_0),
inference(literals_permutation,[status(thm)],[c_0_549]) ).
cnf(c_0_550_0,axiom,
empty(empty_set),
inference(literals_permutation,[status(thm)],[c_0_550]) ).
cnf(c_0_551_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_551]) ).
cnf(c_0_552_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_552]) ).
cnf(c_0_553_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_553]) ).
cnf(c_0_554_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_554]) ).
cnf(c_0_555_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_555]) ).
cnf(c_0_556_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_556]) ).
cnf(c_0_557_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_557]) ).
cnf(c_0_558_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_558]) ).
cnf(c_0_559_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_559]) ).
cnf(c_0_560_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_560]) ).
cnf(c_0_561_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_561]) ).
cnf(c_0_562_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_562]) ).
cnf(c_0_563_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_563]) ).
cnf(c_0_564_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_564]) ).
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_001,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_1_002,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_2_003,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_3_004,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_4_005,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_5_006,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_6_007,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_7_008,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_8_009,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_9_010,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_difference(X1,X3),set_difference(X2,X3)) ),
file('<stdin>',t33_xboole_1) ).
fof(c_0_10_011,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_intersection2(X1,X3),set_intersection2(X2,X3)) ),
file('<stdin>',t26_xboole_1) ).
fof(c_0_11_012,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_12_013,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_13_014,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X3,X2) )
=> subset(set_union2(X1,X3),X2) ),
file('<stdin>',t8_xboole_1) ).
fof(c_0_14_015,lemma,
! [X1,X2,X3] :
( subset(unordered_pair(X1,X2),X3)
<=> ( in(X1,X3)
& in(X2,X3) ) ),
file('<stdin>',t38_zfmisc_1) ).
fof(c_0_15_016,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X1,X3) )
=> subset(X1,set_intersection2(X2,X3)) ),
file('<stdin>',t19_xboole_1) ).
fof(c_0_16_017,lemma,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
=> in(X3,X2) )
=> element(X1,powerset(X2)) ),
file('<stdin>',l71_subset_1) ).
fof(c_0_17_018,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_18_019,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_19_020,lemma,
! [X1,X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( in(X3,X2)
=> in(X3,X1) ) ),
file('<stdin>',l3_subset_1) ).
fof(c_0_20_021,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_21_022,lemma,
! [X1,X2] :
( subset(X1,X2)
=> X2 = set_union2(X1,set_difference(X2,X1)) ),
file('<stdin>',t45_xboole_1) ).
fof(c_0_22_023,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& disjoint(X2,X3) )
=> disjoint(X1,X3) ),
file('<stdin>',t63_xboole_1) ).
fof(c_0_23_024,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ),
file('<stdin>',t1_xboole_1) ).
fof(c_0_24_025,lemma,
! [X1,X2] :
( set_difference(X1,singleton(X2)) = X1
<=> ~ in(X2,X1) ),
file('<stdin>',t65_zfmisc_1) ).
fof(c_0_25_026,lemma,
! [X1,X2] :
~ ( disjoint(singleton(X1),X2)
& in(X1,X2) ),
file('<stdin>',l25_zfmisc_1) ).
fof(c_0_26_027,lemma,
! [X1,X2] : set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
file('<stdin>',t48_xboole_1) ).
fof(c_0_27_028,lemma,
! [X1,X2] : set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
file('<stdin>',t40_xboole_1) ).
fof(c_0_28_029,lemma,
! [X1,X2] : set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
file('<stdin>',t39_xboole_1) ).
fof(c_0_29_030,conjecture,
! [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_30_031,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_31_032,lemma,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
file('<stdin>',t37_zfmisc_1) ).
fof(c_0_32_033,lemma,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
file('<stdin>',l2_zfmisc_1) ).
fof(c_0_33_034,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_34_035,lemma,
! [X1,X2] :
~ ( subset(X1,X2)
& proper_subset(X2,X1) ),
file('<stdin>',t60_xboole_1) ).
fof(c_0_35_036,lemma,
! [X1,X2] :
( subset(singleton(X1),singleton(X2))
=> X1 = X2 ),
file('<stdin>',t6_zfmisc_1) ).
fof(c_0_36_037,lemma,
! [X1,X2] :
( in(X1,X2)
=> set_union2(singleton(X1),X2) = X2 ),
file('<stdin>',t46_zfmisc_1) ).
fof(c_0_37_038,lemma,
! [X1,X2] :
( in(X1,X2)
=> set_union2(singleton(X1),X2) = X2 ),
file('<stdin>',l23_zfmisc_1) ).
fof(c_0_38_039,lemma,
! [X1,X2] :
( in(X1,X2)
=> subset(X1,union(X2)) ),
file('<stdin>',t92_zfmisc_1) ).
fof(c_0_39_040,lemma,
! [X1,X2] :
( in(X1,X2)
=> subset(X1,union(X2)) ),
file('<stdin>',l50_zfmisc_1) ).
fof(c_0_40_041,lemma,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
file('<stdin>',t7_xboole_1) ).
fof(c_0_41_042,lemma,
! [X1,X2] : subset(set_difference(X1,X2),X1),
file('<stdin>',t36_xboole_1) ).
fof(c_0_42_043,lemma,
! [X1,X2] : subset(set_intersection2(X1,X2),X1),
file('<stdin>',t17_xboole_1) ).
fof(c_0_43_044,lemma,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
file('<stdin>',t39_zfmisc_1) ).
fof(c_0_44_045,lemma,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
file('<stdin>',l4_zfmisc_1) ).
fof(c_0_45_046,lemma,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_difference(X1,X2) = X1 ),
file('<stdin>',t83_xboole_1) ).
fof(c_0_46_047,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_intersection2(X1,X2) = X1 ),
file('<stdin>',t28_xboole_1) ).
fof(c_0_47_048,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_union2(X1,X2) = X2 ),
file('<stdin>',t12_xboole_1) ).
fof(c_0_48_049,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('<stdin>',t37_xboole_1) ).
fof(c_0_49_050,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('<stdin>',l32_xboole_1) ).
fof(c_0_50_051,lemma,
! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
file('<stdin>',l28_zfmisc_1) ).
fof(c_0_51_052,lemma,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X2 = X3 ),
file('<stdin>',t9_zfmisc_1) ).
fof(c_0_52_053,lemma,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X1 = X2 ),
file('<stdin>',t8_zfmisc_1) ).
fof(c_0_53_054,lemma,
! [X1] :
( subset(X1,empty_set)
=> X1 = empty_set ),
file('<stdin>',t3_xboole_1) ).
fof(c_0_54_055,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('<stdin>',t69_enumset1) ).
fof(c_0_55_056,lemma,
! [X1] : subset(empty_set,X1),
file('<stdin>',t2_xboole_1) ).
fof(c_0_56_057,lemma,
! [X1] : union(powerset(X1)) = X1,
file('<stdin>',t99_zfmisc_1) ).
fof(c_0_57_058,lemma,
! [X1] : singleton(X1) != empty_set,
file('<stdin>',l1_zfmisc_1) ).
fof(c_0_58_059,lemma,
powerset(empty_set) = singleton(empty_set),
file('<stdin>',t1_zfmisc_1) ).
fof(c_0_59_060,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_0 ).
fof(c_0_60_061,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_1 ).
fof(c_0_61_062,lemma,
! [X1,X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( element(X3,powerset(X1))
=> ( disjoint(X2,X3)
<=> subset(X2,subset_complement(X1,X3)) ) ) ),
c_0_2 ).
fof(c_0_62_063,lemma,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X1,X3)
& in(X2,X4) ) ),
c_0_3 ).
fof(c_0_63_064,lemma,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X1,X3)
& in(X2,X4) ) ),
c_0_4 ).
fof(c_0_64_065,lemma,
! [X1,X2,X3] :
( element(X3,powerset(X1))
=> ~ ( in(X2,subset_complement(X1,X3))
& in(X2,X3) ) ),
c_0_5 ).
fof(c_0_65_066,lemma,
! [X1,X2,X3,X4] :
( ( subset(X1,X2)
& subset(X3,X4) )
=> subset(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) ),
c_0_6 ).
fof(c_0_66_067,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_7]) ).
fof(c_0_67_068,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> ( in(X3,X1)
| subset(X1,set_difference(X2,singleton(X3))) ) ),
c_0_8 ).
fof(c_0_68_069,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_difference(X1,X3),set_difference(X2,X3)) ),
c_0_9 ).
fof(c_0_69_070,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_intersection2(X1,X3),set_intersection2(X2,X3)) ),
c_0_10 ).
fof(c_0_70_071,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_11 ).
fof(c_0_71_072,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_12]) ).
fof(c_0_72_073,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X3,X2) )
=> subset(set_union2(X1,X3),X2) ),
c_0_13 ).
fof(c_0_73_074,lemma,
! [X1,X2,X3] :
( subset(unordered_pair(X1,X2),X3)
<=> ( in(X1,X3)
& in(X2,X3) ) ),
c_0_14 ).
fof(c_0_74_075,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X1,X3) )
=> subset(X1,set_intersection2(X2,X3)) ),
c_0_15 ).
fof(c_0_75_076,lemma,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
=> in(X3,X2) )
=> element(X1,powerset(X2)) ),
c_0_16 ).
fof(c_0_76_077,lemma,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ~ ( X2 != empty_set
& complements_of_subsets(X1,X2) = empty_set ) ),
c_0_17 ).
fof(c_0_77_078,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_18]) ).
fof(c_0_78_079,lemma,
! [X1,X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( in(X3,X2)
=> in(X3,X1) ) ),
c_0_19 ).
fof(c_0_79_080,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_20]) ).
fof(c_0_80_081,lemma,
! [X1,X2] :
( subset(X1,X2)
=> X2 = set_union2(X1,set_difference(X2,X1)) ),
c_0_21 ).
fof(c_0_81_082,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& disjoint(X2,X3) )
=> disjoint(X1,X3) ),
c_0_22 ).
fof(c_0_82_083,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ),
c_0_23 ).
fof(c_0_83_084,lemma,
! [X1,X2] :
( set_difference(X1,singleton(X2)) = X1
<=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[c_0_24]) ).
fof(c_0_84_085,lemma,
! [X1,X2] :
~ ( disjoint(singleton(X1),X2)
& in(X1,X2) ),
c_0_25 ).
fof(c_0_85_086,lemma,
! [X1,X2] : set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
c_0_26 ).
fof(c_0_86_087,lemma,
! [X1,X2] : set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
c_0_27 ).
fof(c_0_87_088,lemma,
! [X1,X2] : set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
c_0_28 ).
fof(c_0_88_089,negated_conjecture,
~ ! [X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X1,X2),X3)
=> ( in(X1,relation_dom(X3))
& in(X2,relation_rng(X3)) ) ) ),
inference(assume_negation,[status(cth)],[c_0_29]) ).
fof(c_0_89_090,lemma,
! [X1,X2,X3,X4] :
~ ( unordered_pair(X1,X2) = unordered_pair(X3,X4)
& X1 != X3
& X1 != X4 ),
c_0_30 ).
fof(c_0_90_091,lemma,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
c_0_31 ).
fof(c_0_91_092,lemma,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
c_0_32 ).
fof(c_0_92_093,lemma,
! [X1,X2,X3,X4] :
( ordered_pair(X1,X2) = ordered_pair(X3,X4)
=> ( X1 = X3
& X2 = X4 ) ),
c_0_33 ).
fof(c_0_93_094,lemma,
! [X1,X2] :
~ ( subset(X1,X2)
& proper_subset(X2,X1) ),
c_0_34 ).
fof(c_0_94_095,lemma,
! [X1,X2] :
( subset(singleton(X1),singleton(X2))
=> X1 = X2 ),
c_0_35 ).
fof(c_0_95_096,lemma,
! [X1,X2] :
( in(X1,X2)
=> set_union2(singleton(X1),X2) = X2 ),
c_0_36 ).
fof(c_0_96_097,lemma,
! [X1,X2] :
( in(X1,X2)
=> set_union2(singleton(X1),X2) = X2 ),
c_0_37 ).
fof(c_0_97_098,lemma,
! [X1,X2] :
( in(X1,X2)
=> subset(X1,union(X2)) ),
c_0_38 ).
fof(c_0_98_099,lemma,
! [X1,X2] :
( in(X1,X2)
=> subset(X1,union(X2)) ),
c_0_39 ).
fof(c_0_99_100,lemma,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
c_0_40 ).
fof(c_0_100_101,lemma,
! [X1,X2] : subset(set_difference(X1,X2),X1),
c_0_41 ).
fof(c_0_101_102,lemma,
! [X1,X2] : subset(set_intersection2(X1,X2),X1),
c_0_42 ).
fof(c_0_102_103,lemma,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
c_0_43 ).
fof(c_0_103_104,lemma,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
c_0_44 ).
fof(c_0_104_105,lemma,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_difference(X1,X2) = X1 ),
c_0_45 ).
fof(c_0_105_106,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_intersection2(X1,X2) = X1 ),
c_0_46 ).
fof(c_0_106_107,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_union2(X1,X2) = X2 ),
c_0_47 ).
fof(c_0_107_108,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
c_0_48 ).
fof(c_0_108_109,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
c_0_49 ).
fof(c_0_109_110,lemma,
! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
inference(fof_simplification,[status(thm)],[c_0_50]) ).
fof(c_0_110_111,lemma,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X2 = X3 ),
c_0_51 ).
fof(c_0_111_112,lemma,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X1 = X2 ),
c_0_52 ).
fof(c_0_112_113,lemma,
! [X1] :
( subset(X1,empty_set)
=> X1 = empty_set ),
c_0_53 ).
fof(c_0_113_114,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
c_0_54 ).
fof(c_0_114_115,lemma,
! [X1] : subset(empty_set,X1),
c_0_55 ).
fof(c_0_115_116,lemma,
! [X1] : union(powerset(X1)) = X1,
c_0_56 ).
fof(c_0_116_117,lemma,
! [X1] : singleton(X1) != empty_set,
c_0_57 ).
fof(c_0_117_118,lemma,
powerset(empty_set) = singleton(empty_set),
c_0_58 ).
fof(c_0_118_119,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_59])]) ).
fof(c_0_119_120,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_60])]) ).
fof(c_0_120_121,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_61])])])]) ).
fof(c_0_121_122,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_62])])])])]) ).
fof(c_0_122_123,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_63])])])])]) ).
fof(c_0_123_124,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_64])]) ).
fof(c_0_124_125,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_65])]) ).
fof(c_0_125_126,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_66])])]) ).
fof(c_0_126_127,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_67])])])]) ).
fof(c_0_127_128,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_68])])])]) ).
fof(c_0_128_129,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_69])])])]) ).
fof(c_0_129_130,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_70])])])])]) ).
fof(c_0_130_131,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_71])])])])]) ).
fof(c_0_131_132,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_72])]) ).
fof(c_0_132_133,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_73])])])])]) ).
fof(c_0_133_134,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_74])]) ).
fof(c_0_134_135,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_75])])])]) ).
fof(c_0_135_136,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_76])]) ).
fof(c_0_136_137,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_77])])])]) ).
fof(c_0_137_138,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_78])])]) ).
fof(c_0_138_139,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_79])])])])])]) ).
fof(c_0_139_140,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_80])]) ).
fof(c_0_140_141,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_81])]) ).
fof(c_0_141_142,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_82])]) ).
fof(c_0_142_143,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_83])])])]) ).
fof(c_0_143_144,lemma,
! [X3,X4] :
( ~ disjoint(singleton(X3),X4)
| ~ in(X3,X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_84])]) ).
fof(c_0_144_145,lemma,
! [X3,X4] : set_difference(X3,set_difference(X3,X4)) = set_intersection2(X3,X4),
inference(variable_rename,[status(thm)],[c_0_85]) ).
fof(c_0_145_146,lemma,
! [X3,X4] : set_difference(set_union2(X3,X4),X4) = set_difference(X3,X4),
inference(variable_rename,[status(thm)],[c_0_86]) ).
fof(c_0_146_147,lemma,
! [X3,X4] : set_union2(X3,set_difference(X4,X3)) = set_union2(X3,X4),
inference(variable_rename,[status(thm)],[c_0_87]) ).
fof(c_0_147_148,negated_conjecture,
( relation(esk5_0)
& in(ordered_pair(esk3_0,esk4_0),esk5_0)
& ( ~ in(esk3_0,relation_dom(esk5_0))
| ~ in(esk4_0,relation_rng(esk5_0)) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_88])])]) ).
fof(c_0_148_149,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_89])]) ).
fof(c_0_149_150,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_90])])])]) ).
fof(c_0_150_151,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_91])])])]) ).
fof(c_0_151_152,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_92])])]) ).
fof(c_0_152_153,lemma,
! [X3,X4] :
( ~ subset(X3,X4)
| ~ proper_subset(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_93])]) ).
fof(c_0_153_154,lemma,
! [X3,X4] :
( ~ subset(singleton(X3),singleton(X4))
| X3 = X4 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_94])]) ).
fof(c_0_154_155,lemma,
! [X3,X4] :
( ~ in(X3,X4)
| set_union2(singleton(X3),X4) = X4 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_95])]) ).
fof(c_0_155_156,lemma,
! [X3,X4] :
( ~ in(X3,X4)
| set_union2(singleton(X3),X4) = X4 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_96])]) ).
fof(c_0_156_157,lemma,
! [X3,X4] :
( ~ in(X3,X4)
| subset(X3,union(X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_97])]) ).
fof(c_0_157_158,lemma,
! [X3,X4] :
( ~ in(X3,X4)
| subset(X3,union(X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_98])]) ).
fof(c_0_158_159,lemma,
! [X3,X4] : subset(X3,set_union2(X3,X4)),
inference(variable_rename,[status(thm)],[c_0_99]) ).
fof(c_0_159_160,lemma,
! [X3,X4] : subset(set_difference(X3,X4),X3),
inference(variable_rename,[status(thm)],[c_0_100]) ).
fof(c_0_160_161,lemma,
! [X3,X4] : subset(set_intersection2(X3,X4),X3),
inference(variable_rename,[status(thm)],[c_0_101]) ).
fof(c_0_161_162,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_102])])])])]) ).
fof(c_0_162_163,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_103])])])])]) ).
fof(c_0_163_164,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_104])])])]) ).
fof(c_0_164_165,lemma,
! [X3,X4] :
( ~ subset(X3,X4)
| set_intersection2(X3,X4) = X3 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_105])]) ).
fof(c_0_165_166,lemma,
! [X3,X4] :
( ~ subset(X3,X4)
| set_union2(X3,X4) = X4 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_106])]) ).
fof(c_0_166_167,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_107])])])]) ).
fof(c_0_167_168,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_108])])])]) ).
fof(c_0_168_169,lemma,
! [X3,X4] :
( in(X3,X4)
| disjoint(singleton(X3),X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_109])]) ).
fof(c_0_169_170,lemma,
! [X4,X5,X6] :
( singleton(X4) != unordered_pair(X5,X6)
| X5 = X6 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_110])]) ).
fof(c_0_170_171,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_111])])])]) ).
fof(c_0_171_172,lemma,
! [X2] :
( ~ subset(X2,empty_set)
| X2 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_112])]) ).
fof(c_0_172_173,lemma,
! [X2] : unordered_pair(X2,X2) = singleton(X2),
inference(variable_rename,[status(thm)],[c_0_113]) ).
fof(c_0_173_174,lemma,
! [X2] : subset(empty_set,X2),
inference(variable_rename,[status(thm)],[c_0_114]) ).
fof(c_0_174_175,lemma,
! [X2] : union(powerset(X2)) = X2,
inference(variable_rename,[status(thm)],[c_0_115]) ).
fof(c_0_175_176,lemma,
! [X2] : singleton(X2) != empty_set,
inference(variable_rename,[status(thm)],[c_0_116]) ).
fof(c_0_176_177,lemma,
powerset(empty_set) = singleton(empty_set),
c_0_117 ).
cnf(c_0_177_178,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_118]) ).
cnf(c_0_178_179,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_119]) ).
cnf(c_0_179_180,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_120]) ).
cnf(c_0_180_181,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_120]) ).
cnf(c_0_181_182,lemma,
( in(X1,X3)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_121]) ).
cnf(c_0_182_183,lemma,
( in(X2,X4)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_121]) ).
cnf(c_0_183_184,lemma,
( in(X1,X3)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_122]) ).
cnf(c_0_184_185,lemma,
( in(X2,X4)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_122]) ).
cnf(c_0_185_186,lemma,
( ~ in(X1,X2)
| ~ in(X1,subset_complement(X3,X2))
| ~ element(X2,powerset(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_123]) ).
cnf(c_0_186_187,lemma,
( subset(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
| ~ subset(X2,X4)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_124]) ).
cnf(c_0_187_188,lemma,
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_121]) ).
cnf(c_0_188_189,lemma,
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_122]) ).
cnf(c_0_189_190,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_125]) ).
cnf(c_0_190_191,lemma,
( subset(X1,set_difference(X2,singleton(X3)))
| in(X3,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_126]) ).
cnf(c_0_191_192,lemma,
( subset(set_difference(X1,X2),set_difference(X3,X2))
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_127]) ).
cnf(c_0_192_193,lemma,
( subset(set_intersection2(X1,X2),set_intersection2(X3,X2))
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_128]) ).
cnf(c_0_193_194,lemma,
( subset(cartesian_product2(X1,X3),cartesian_product2(X2,X3))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_129]) ).
cnf(c_0_194_195,lemma,
( subset(cartesian_product2(X3,X1),cartesian_product2(X3,X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_129]) ).
cnf(c_0_195_196,lemma,
( ~ disjoint(X1,X2)
| ~ in(X3,set_intersection2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_130]) ).
cnf(c_0_196_197,lemma,
( subset(set_union2(X1,X2),X3)
| ~ subset(X2,X3)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_131]) ).
cnf(c_0_197_198,lemma,
( subset(unordered_pair(X1,X2),X3)
| ~ in(X2,X3)
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_132]) ).
cnf(c_0_198_199,lemma,
( subset(X1,set_intersection2(X2,X3))
| ~ subset(X1,X3)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_133]) ).
cnf(c_0_199_200,lemma,
( element(X1,powerset(X2))
| ~ in(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_134]) ).
cnf(c_0_200_201,lemma,
( in(esk7_2(X1,X2),set_intersection2(X1,X2))
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_130]) ).
cnf(c_0_201_202,lemma,
( in(X1,X3)
| ~ subset(unordered_pair(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_132]) ).
cnf(c_0_202_203,lemma,
( in(X2,X3)
| ~ subset(unordered_pair(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_132]) ).
cnf(c_0_203_204,lemma,
( X2 = empty_set
| complements_of_subsets(X1,X2) != empty_set
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_135]) ).
cnf(c_0_204_205,lemma,
( in(X1,esk2_1(X2))
| ~ subset(X1,X3)
| ~ in(X3,esk2_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_136]) ).
cnf(c_0_205_206,lemma,
( in(X1,esk2_1(X2))
| are_equipotent(X1,esk2_1(X2))
| ~ subset(X1,esk2_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_136]) ).
cnf(c_0_206_207,lemma,
( in(X1,X2)
| ~ in(X1,X3)
| ~ element(X3,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_137]) ).
cnf(c_0_207_208,lemma,
( ~ disjoint(X1,X2)
| ~ in(X3,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_138]) ).
cnf(c_0_208_209,lemma,
( X1 = set_union2(X2,set_difference(X1,X2))
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_139]) ).
cnf(c_0_209_210,lemma,
( element(X1,powerset(X2))
| in(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_134]) ).
cnf(c_0_210_211,lemma,
( disjoint(X1,X2)
| ~ disjoint(X3,X2)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_140]) ).
cnf(c_0_211_212,lemma,
( subset(X1,X2)
| ~ subset(X3,X2)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_141]) ).
cnf(c_0_212_213,lemma,
( in(powerset(X1),esk2_1(X2))
| ~ in(X1,esk2_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_136]) ).
cnf(c_0_213_214,lemma,
( ~ in(X1,X2)
| set_difference(X2,singleton(X1)) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_142]) ).
cnf(c_0_214_215,lemma,
( ~ in(X1,X2)
| ~ disjoint(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_143]) ).
cnf(c_0_215_216,lemma,
( disjoint(X1,X2)
| in(esk6_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_138]) ).
cnf(c_0_216_217,lemma,
( disjoint(X1,X2)
| in(esk6_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_138]) ).
cnf(c_0_217_218,lemma,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_144]) ).
cnf(c_0_218_219,lemma,
set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_145]) ).
cnf(c_0_219_220,lemma,
set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_146]) ).
cnf(c_0_220_221,negated_conjecture,
( ~ in(esk4_0,relation_rng(esk5_0))
| ~ in(esk3_0,relation_dom(esk5_0)) ),
inference(split_conjunct,[status(thm)],[c_0_147]) ).
cnf(c_0_221_222,lemma,
( X1 = X2
| X1 = X3
| unordered_pair(X1,X4) != unordered_pair(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_148]) ).
cnf(c_0_222_223,lemma,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_149]) ).
cnf(c_0_223_224,lemma,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_150]) ).
cnf(c_0_224_225,lemma,
( X1 = X3
| ordered_pair(X1,X2) != ordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_151]) ).
cnf(c_0_225_226,lemma,
( X2 = X4
| ordered_pair(X1,X2) != ordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_151]) ).
cnf(c_0_226_227,lemma,
( ~ proper_subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_152]) ).
cnf(c_0_227_228,lemma,
( X1 = X2
| ~ subset(singleton(X1),singleton(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_153]) ).
cnf(c_0_228_229,lemma,
( set_union2(singleton(X1),X2) = X2
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_154]) ).
cnf(c_0_229_230,lemma,
( set_union2(singleton(X1),X2) = X2
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_155]) ).
cnf(c_0_230_231,lemma,
( subset(X1,union(X2))
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_156]) ).
cnf(c_0_231_232,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_149]) ).
cnf(c_0_232_233,lemma,
( subset(X1,union(X2))
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_157]) ).
cnf(c_0_233_234,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_150]) ).
cnf(c_0_234_235,lemma,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_158]) ).
cnf(c_0_235_236,lemma,
subset(set_difference(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_159]) ).
cnf(c_0_236_237,lemma,
subset(set_intersection2(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_160]) ).
cnf(c_0_237_238,lemma,
( X1 = singleton(X2)
| X1 = empty_set
| ~ subset(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_161]) ).
cnf(c_0_238_239,lemma,
( X1 = singleton(X2)
| X1 = empty_set
| ~ subset(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_162]) ).
cnf(c_0_239_240,lemma,
( disjoint(X1,X2)
| set_difference(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_163]) ).
cnf(c_0_240_241,lemma,
( set_difference(X1,X2) = X1
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_163]) ).
cnf(c_0_241_242,lemma,
( set_intersection2(X1,X2) = X1
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_164]) ).
cnf(c_0_242_243,lemma,
( set_union2(X1,X2) = X2
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_165]) ).
cnf(c_0_243_244,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_166]) ).
cnf(c_0_244_245,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_166]) ).
cnf(c_0_245_246,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_167]) ).
cnf(c_0_246_247,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_167]) ).
cnf(c_0_247_248,lemma,
( set_difference(X1,singleton(X2)) = X1
| in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_142]) ).
cnf(c_0_248_249,lemma,
( disjoint(singleton(X1),X2)
| in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_168]) ).
cnf(c_0_249_250,negated_conjecture,
in(ordered_pair(esk3_0,esk4_0),esk5_0),
inference(split_conjunct,[status(thm)],[c_0_147]) ).
cnf(c_0_250_251,lemma,
( X1 = X2
| singleton(X3) != unordered_pair(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_169]) ).
cnf(c_0_251_252,lemma,
( X1 = X2
| singleton(X1) != unordered_pair(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_170]) ).
cnf(c_0_252_253,lemma,
( subset(X1,singleton(X2))
| X1 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[c_0_161]) ).
cnf(c_0_253_254,lemma,
( subset(X1,singleton(X2))
| X1 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[c_0_162]) ).
cnf(c_0_254_255,lemma,
( subset(X1,singleton(X2))
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_161]) ).
cnf(c_0_255_256,lemma,
( subset(X1,singleton(X2))
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_162]) ).
cnf(c_0_256_257,lemma,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
inference(split_conjunct,[status(thm)],[c_0_171]) ).
cnf(c_0_257_258,lemma,
in(X1,esk2_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_136]) ).
cnf(c_0_258_259,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[c_0_172]) ).
cnf(c_0_259_260,lemma,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[c_0_173]) ).
cnf(c_0_260_261,lemma,
union(powerset(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_174]) ).
cnf(c_0_261_262,lemma,
singleton(X1) != empty_set,
inference(split_conjunct,[status(thm)],[c_0_175]) ).
cnf(c_0_262_263,lemma,
powerset(empty_set) = singleton(empty_set),
inference(split_conjunct,[status(thm)],[c_0_176]) ).
cnf(c_0_263_264,negated_conjecture,
relation(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_147]) ).
cnf(c_0_264_265,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_177,
[final] ).
cnf(c_0_265_266,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_178,
[final] ).
cnf(c_0_266_267,lemma,
( disjoint(X1,X3)
| ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2))
| ~ subset(X1,subset_complement(X2,X3)) ),
c_0_179,
[final] ).
cnf(c_0_267_268,lemma,
( subset(X1,subset_complement(X2,X3))
| ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2))
| ~ disjoint(X1,X3) ),
c_0_180,
[final] ).
cnf(c_0_268_269,lemma,
( in(X1,X3)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
c_0_181,
[final] ).
cnf(c_0_269_270,lemma,
( in(X2,X4)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
c_0_182,
[final] ).
cnf(c_0_270_271,lemma,
( in(X1,X3)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
c_0_183,
[final] ).
cnf(c_0_271_272,lemma,
( in(X2,X4)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
c_0_184,
[final] ).
cnf(c_0_272_273,lemma,
( ~ in(X1,X2)
| ~ in(X1,subset_complement(X3,X2))
| ~ element(X2,powerset(X3)) ),
c_0_185,
[final] ).
cnf(c_0_273_274,lemma,
( subset(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
| ~ subset(X2,X4)
| ~ subset(X1,X3) ),
c_0_186,
[final] ).
cnf(c_0_274_275,lemma,
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
c_0_187,
[final] ).
cnf(c_0_275_276,lemma,
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
c_0_188,
[final] ).
cnf(c_0_276_277,lemma,
( in(X1,subset_complement(X2,X3))
| in(X1,X3)
| X2 = empty_set
| ~ element(X1,X2)
| ~ element(X3,powerset(X2)) ),
c_0_189,
[final] ).
cnf(c_0_277_278,lemma,
( subset(X1,set_difference(X2,singleton(X3)))
| in(X3,X1)
| ~ subset(X1,X2) ),
c_0_190,
[final] ).
cnf(c_0_278_279,lemma,
( subset(set_difference(X1,X2),set_difference(X3,X2))
| ~ subset(X1,X3) ),
c_0_191,
[final] ).
cnf(c_0_279_280,lemma,
( subset(set_intersection2(X1,X2),set_intersection2(X3,X2))
| ~ subset(X1,X3) ),
c_0_192,
[final] ).
cnf(c_0_280_281,lemma,
( subset(cartesian_product2(X1,X3),cartesian_product2(X2,X3))
| ~ subset(X1,X2) ),
c_0_193,
[final] ).
cnf(c_0_281_282,lemma,
( subset(cartesian_product2(X3,X1),cartesian_product2(X3,X2))
| ~ subset(X1,X2) ),
c_0_194,
[final] ).
cnf(c_0_282_283,lemma,
( ~ disjoint(X1,X2)
| ~ in(X3,set_intersection2(X1,X2)) ),
c_0_195,
[final] ).
cnf(c_0_283_284,lemma,
( subset(set_union2(X1,X2),X3)
| ~ subset(X2,X3)
| ~ subset(X1,X3) ),
c_0_196,
[final] ).
cnf(c_0_284_285,lemma,
( subset(unordered_pair(X1,X2),X3)
| ~ in(X2,X3)
| ~ in(X1,X3) ),
c_0_197,
[final] ).
cnf(c_0_285_286,lemma,
( subset(X1,set_intersection2(X2,X3))
| ~ subset(X1,X3)
| ~ subset(X1,X2) ),
c_0_198,
[final] ).
cnf(c_0_286_287,lemma,
( element(X1,powerset(X2))
| ~ in(esk1_2(X1,X2),X2) ),
c_0_199,
[final] ).
cnf(c_0_287_288,lemma,
( in(esk7_2(X1,X2),set_intersection2(X1,X2))
| disjoint(X1,X2) ),
c_0_200,
[final] ).
cnf(c_0_288_289,lemma,
( in(X1,X3)
| ~ subset(unordered_pair(X1,X2),X3) ),
c_0_201,
[final] ).
cnf(c_0_289_290,lemma,
( in(X2,X3)
| ~ subset(unordered_pair(X1,X2),X3) ),
c_0_202,
[final] ).
cnf(c_0_290_291,lemma,
( X2 = empty_set
| complements_of_subsets(X1,X2) != empty_set
| ~ element(X2,powerset(powerset(X1))) ),
c_0_203,
[final] ).
cnf(c_0_291_292,lemma,
( in(X1,esk2_1(X2))
| ~ subset(X1,X3)
| ~ in(X3,esk2_1(X2)) ),
c_0_204,
[final] ).
cnf(c_0_292_293,lemma,
( in(X1,esk2_1(X2))
| are_equipotent(X1,esk2_1(X2))
| ~ subset(X1,esk2_1(X2)) ),
c_0_205,
[final] ).
cnf(c_0_293_294,lemma,
( in(X1,X2)
| ~ in(X1,X3)
| ~ element(X3,powerset(X2)) ),
c_0_206,
[final] ).
cnf(c_0_294_295,lemma,
( ~ disjoint(X1,X2)
| ~ in(X3,X2)
| ~ in(X3,X1) ),
c_0_207,
[final] ).
cnf(c_0_295_296,lemma,
( set_union2(X2,set_difference(X1,X2)) = X1
| ~ subset(X2,X1) ),
c_0_208,
[final] ).
cnf(c_0_296_297,lemma,
( element(X1,powerset(X2))
| in(esk1_2(X1,X2),X1) ),
c_0_209,
[final] ).
cnf(c_0_297_298,lemma,
( disjoint(X1,X2)
| ~ disjoint(X3,X2)
| ~ subset(X1,X3) ),
c_0_210,
[final] ).
cnf(c_0_298_299,lemma,
( subset(X1,X2)
| ~ subset(X3,X2)
| ~ subset(X1,X3) ),
c_0_211,
[final] ).
cnf(c_0_299_300,lemma,
( in(powerset(X1),esk2_1(X2))
| ~ in(X1,esk2_1(X2)) ),
c_0_212,
[final] ).
cnf(c_0_300_301,lemma,
( ~ in(X1,X2)
| set_difference(X2,singleton(X1)) != X2 ),
c_0_213,
[final] ).
cnf(c_0_301_302,lemma,
( ~ in(X1,X2)
| ~ disjoint(singleton(X1),X2) ),
c_0_214,
[final] ).
cnf(c_0_302_303,lemma,
( disjoint(X1,X2)
| in(esk6_2(X1,X2),X1) ),
c_0_215,
[final] ).
cnf(c_0_303_304,lemma,
( disjoint(X1,X2)
| in(esk6_2(X1,X2),X2) ),
c_0_216,
[final] ).
cnf(c_0_304_305,lemma,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
c_0_217,
[final] ).
cnf(c_0_305_306,lemma,
set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
c_0_218,
[final] ).
cnf(c_0_306_307,lemma,
set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
c_0_219,
[final] ).
cnf(c_0_307_308,negated_conjecture,
( ~ in(esk4_0,relation_rng(esk5_0))
| ~ in(esk3_0,relation_dom(esk5_0)) ),
c_0_220,
[final] ).
cnf(c_0_308_309,lemma,
( X1 = X2
| X1 = X3
| unordered_pair(X1,X4) != unordered_pair(X3,X2) ),
c_0_221,
[final] ).
cnf(c_0_309_310,lemma,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
c_0_222,
[final] ).
cnf(c_0_310_311,lemma,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
c_0_223,
[final] ).
cnf(c_0_311_312,lemma,
( X1 = X3
| ordered_pair(X1,X2) != ordered_pair(X3,X4) ),
c_0_224,
[final] ).
cnf(c_0_312_313,lemma,
( X2 = X4
| ordered_pair(X1,X2) != ordered_pair(X3,X4) ),
c_0_225,
[final] ).
cnf(c_0_313_314,lemma,
( ~ proper_subset(X1,X2)
| ~ subset(X2,X1) ),
c_0_226,
[final] ).
cnf(c_0_314_315,lemma,
( X1 = X2
| ~ subset(singleton(X1),singleton(X2)) ),
c_0_227,
[final] ).
cnf(c_0_315_316,lemma,
( set_union2(singleton(X1),X2) = X2
| ~ in(X1,X2) ),
c_0_228,
[final] ).
cnf(c_0_316_317,lemma,
( set_union2(singleton(X1),X2) = X2
| ~ in(X1,X2) ),
c_0_229,
[final] ).
cnf(c_0_317_318,lemma,
( subset(X1,union(X2))
| ~ in(X1,X2) ),
c_0_230,
[final] ).
cnf(c_0_318_319,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
c_0_231,
[final] ).
cnf(c_0_319_320,lemma,
( subset(X1,union(X2))
| ~ in(X1,X2) ),
c_0_232,
[final] ).
cnf(c_0_320_321,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
c_0_233,
[final] ).
cnf(c_0_321_322,lemma,
subset(X1,set_union2(X1,X2)),
c_0_234,
[final] ).
cnf(c_0_322_323,lemma,
subset(set_difference(X1,X2),X1),
c_0_235,
[final] ).
cnf(c_0_323_324,lemma,
subset(set_intersection2(X1,X2),X1),
c_0_236,
[final] ).
cnf(c_0_324_325,lemma,
( X1 = singleton(X2)
| X1 = empty_set
| ~ subset(X1,singleton(X2)) ),
c_0_237,
[final] ).
cnf(c_0_325_326,lemma,
( X1 = singleton(X2)
| X1 = empty_set
| ~ subset(X1,singleton(X2)) ),
c_0_238,
[final] ).
cnf(c_0_326_327,lemma,
( disjoint(X1,X2)
| set_difference(X1,X2) != X1 ),
c_0_239,
[final] ).
cnf(c_0_327_328,lemma,
( set_difference(X1,X2) = X1
| ~ disjoint(X1,X2) ),
c_0_240,
[final] ).
cnf(c_0_328_329,lemma,
( set_intersection2(X1,X2) = X1
| ~ subset(X1,X2) ),
c_0_241,
[final] ).
cnf(c_0_329_330,lemma,
( set_union2(X1,X2) = X2
| ~ subset(X1,X2) ),
c_0_242,
[final] ).
cnf(c_0_330_331,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
c_0_243,
[final] ).
cnf(c_0_331_332,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
c_0_244,
[final] ).
cnf(c_0_332_333,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
c_0_245,
[final] ).
cnf(c_0_333_334,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
c_0_246,
[final] ).
cnf(c_0_334_335,lemma,
( set_difference(X1,singleton(X2)) = X1
| in(X2,X1) ),
c_0_247,
[final] ).
cnf(c_0_335_336,lemma,
( disjoint(singleton(X1),X2)
| in(X1,X2) ),
c_0_248,
[final] ).
cnf(c_0_336_337,negated_conjecture,
in(ordered_pair(esk3_0,esk4_0),esk5_0),
c_0_249,
[final] ).
cnf(c_0_337_338,lemma,
( X1 = X2
| singleton(X3) != unordered_pair(X1,X2) ),
c_0_250,
[final] ).
cnf(c_0_338_339,lemma,
( X1 = X2
| singleton(X1) != unordered_pair(X2,X3) ),
c_0_251,
[final] ).
cnf(c_0_339_340,lemma,
( subset(X1,singleton(X2))
| X1 != singleton(X2) ),
c_0_252,
[final] ).
cnf(c_0_340_341,lemma,
( subset(X1,singleton(X2))
| X1 != singleton(X2) ),
c_0_253,
[final] ).
cnf(c_0_341_342,lemma,
( subset(X1,singleton(X2))
| X1 != empty_set ),
c_0_254,
[final] ).
cnf(c_0_342_343,lemma,
( subset(X1,singleton(X2))
| X1 != empty_set ),
c_0_255,
[final] ).
cnf(c_0_343_344,lemma,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
c_0_256,
[final] ).
cnf(c_0_344_345,lemma,
in(X1,esk2_1(X1)),
c_0_257,
[final] ).
cnf(c_0_345_346,lemma,
unordered_pair(X1,X1) = singleton(X1),
c_0_258,
[final] ).
cnf(c_0_346_347,lemma,
subset(empty_set,X1),
c_0_259,
[final] ).
cnf(c_0_347_348,lemma,
union(powerset(X1)) = X1,
c_0_260,
[final] ).
cnf(c_0_348_349,lemma,
singleton(X1) != empty_set,
c_0_261,
[final] ).
cnf(c_0_349_350,lemma,
powerset(empty_set) = singleton(empty_set),
c_0_262,
[final] ).
cnf(c_0_350_351,negated_conjecture,
relation(esk5_0),
c_0_263,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_220,plain,
( in(X0,X1)
| ~ relation(X2)
| X1 != relation_dom(X2)
| ~ in(ordered_pair(X0,X3),X2) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_111001.p',c_0_456_3) ).
cnf(c_2392777,plain,
( in(X0,X1)
| ~ relation(X2)
| X1 != relation_dom(X2)
| ~ in(ordered_pair(X0,X3),X2) ),
inference(copy,[status(esa)],[c_220]) ).
cnf(c_2393656,plain,
( ~ relation(sk2_esk5_0)
| ~ in(ordered_pair(X0,X1),sk2_esk5_0)
| in(X0,X2)
| X2 != relation_dom(sk2_esk5_0) ),
inference(instantiation,[status(thm)],[c_2392777]) ).
cnf(c_2394049,plain,
( ~ relation(sk2_esk5_0)
| ~ in(ordered_pair(sk2_esk3_0,sk2_esk4_0),sk2_esk5_0)
| in(sk2_esk3_0,X0)
| X0 != relation_dom(sk2_esk5_0) ),
inference(instantiation,[status(thm)],[c_2393656]) ).
cnf(c_2754715,plain,
( ~ relation(sk2_esk5_0)
| ~ in(ordered_pair(sk2_esk3_0,sk2_esk4_0),sk2_esk5_0)
| in(sk2_esk3_0,relation_dom(sk2_esk5_0))
| relation_dom(sk2_esk5_0) != relation_dom(sk2_esk5_0) ),
inference(instantiation,[status(thm)],[c_2394049]) ).
cnf(c_2756456,plain,
( ~ relation(sk2_esk5_0)
| ~ in(ordered_pair(sk2_esk3_0,sk2_esk4_0),sk2_esk5_0)
| in(sk2_esk3_0,relation_dom(sk2_esk5_0)) ),
inference(equality_resolution_simp,[status(esa)],[c_2754715]) ).
cnf(c_224,plain,
( in(X0,X1)
| ~ relation(X2)
| X1 != relation_rng(X2)
| ~ in(ordered_pair(X3,X0),X2) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_111001.p',c_0_455_3) ).
cnf(c_2392781,plain,
( in(X0,X1)
| ~ relation(X2)
| X1 != relation_rng(X2)
| ~ in(ordered_pair(X3,X0),X2) ),
inference(copy,[status(esa)],[c_224]) ).
cnf(c_2393664,plain,
( ~ relation(sk2_esk5_0)
| ~ in(ordered_pair(X0,X1),sk2_esk5_0)
| in(X1,X2)
| X2 != relation_rng(sk2_esk5_0) ),
inference(instantiation,[status(thm)],[c_2392781]) ).
cnf(c_2394051,plain,
( ~ relation(sk2_esk5_0)
| ~ in(ordered_pair(sk2_esk3_0,sk2_esk4_0),sk2_esk5_0)
| in(sk2_esk4_0,X0)
| X0 != relation_rng(sk2_esk5_0) ),
inference(instantiation,[status(thm)],[c_2393664]) ).
cnf(c_2394809,plain,
( ~ relation(sk2_esk5_0)
| ~ in(ordered_pair(sk2_esk3_0,sk2_esk4_0),sk2_esk5_0)
| in(sk2_esk4_0,relation_rng(sk2_esk5_0))
| relation_rng(sk2_esk5_0) != relation_rng(sk2_esk5_0) ),
inference(instantiation,[status(thm)],[c_2394051]) ).
cnf(c_2754664,plain,
( ~ relation(sk2_esk5_0)
| ~ in(ordered_pair(sk2_esk3_0,sk2_esk4_0),sk2_esk5_0)
| in(sk2_esk4_0,relation_rng(sk2_esk5_0)) ),
inference(equality_resolution_simp,[status(esa)],[c_2394809]) ).
cnf(c_441,negated_conjecture,
( ~ in(sk2_esk4_0,relation_rng(sk2_esk5_0))
| ~ in(sk2_esk3_0,relation_dom(sk2_esk5_0)) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_111001.p',c_0_307) ).
cnf(c_481,negated_conjecture,
in(ordered_pair(sk2_esk3_0,sk2_esk4_0),sk2_esk5_0),
file('/export/starexec/sandbox/tmp/iprover_modulo_111001.p',c_0_336) ).
cnf(c_487,negated_conjecture,
relation(sk2_esk5_0),
file('/export/starexec/sandbox/tmp/iprover_modulo_111001.p',c_0_350) ).
cnf(contradiction,plain,
$false,
inference(minisat,[status(thm)],[c_2756456,c_2754664,c_441,c_481,c_487]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU177+2 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.13 % Command : iprover_modulo %s %d
% 0.14/0.34 % Computer : n025.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jun 20 14:24:00 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 % Running in mono-core mode
% 0.20/0.43 % Orienting using strategy Equiv(ClausalAll)
% 0.20/0.43 % FOF problem with conjecture
% 0.20/0.43 % 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_c6279f.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_111001.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_6b50d6 | grep -v "SZS"
% 0.20/0.45
% 0.20/0.45 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.20/0.45
% 0.20/0.45 %
% 0.20/0.45 % ------ iProver source info
% 0.20/0.45
% 0.20/0.45 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.20/0.45 % git: non_committed_changes: true
% 0.20/0.45 % git: last_make_outside_of_git: true
% 0.20/0.45
% 0.20/0.45 %
% 0.20/0.45 % ------ Input Options
% 0.20/0.45
% 0.20/0.45 % --out_options all
% 0.20/0.45 % --tptp_safe_out true
% 0.20/0.45 % --problem_path ""
% 0.20/0.45 % --include_path ""
% 0.20/0.45 % --clausifier .//eprover
% 0.20/0.45 % --clausifier_options --tstp-format
% 0.20/0.45 % --stdin false
% 0.20/0.45 % --dbg_backtrace false
% 0.20/0.45 % --dbg_dump_prop_clauses false
% 0.20/0.45 % --dbg_dump_prop_clauses_file -
% 0.20/0.45 % --dbg_out_stat false
% 0.20/0.45
% 0.20/0.45 % ------ General Options
% 0.20/0.45
% 0.20/0.45 % --fof false
% 0.20/0.45 % --time_out_real 150.
% 0.20/0.45 % --time_out_prep_mult 0.2
% 0.20/0.45 % --time_out_virtual -1.
% 0.20/0.45 % --schedule none
% 0.20/0.45 % --ground_splitting input
% 0.20/0.45 % --splitting_nvd 16
% 0.20/0.45 % --non_eq_to_eq false
% 0.20/0.45 % --prep_gs_sim true
% 0.20/0.45 % --prep_unflatten false
% 0.20/0.45 % --prep_res_sim true
% 0.20/0.45 % --prep_upred true
% 0.20/0.45 % --res_sim_input true
% 0.20/0.45 % --clause_weak_htbl true
% 0.20/0.45 % --gc_record_bc_elim false
% 0.20/0.45 % --symbol_type_check false
% 0.20/0.45 % --clausify_out false
% 0.20/0.45 % --large_theory_mode false
% 0.20/0.45 % --prep_sem_filter none
% 0.20/0.45 % --prep_sem_filter_out false
% 0.20/0.45 % --preprocessed_out false
% 0.20/0.45 % --sub_typing false
% 0.20/0.45 % --brand_transform false
% 0.20/0.45 % --pure_diseq_elim true
% 0.20/0.45 % --min_unsat_core false
% 0.20/0.45 % --pred_elim true
% 0.20/0.45 % --add_important_lit false
% 0.20/0.45 % --soft_assumptions false
% 0.20/0.45 % --reset_solvers false
% 0.20/0.45 % --bc_imp_inh []
% 0.20/0.45 % --conj_cone_tolerance 1.5
% 0.20/0.45 % --prolific_symb_bound 500
% 0.20/0.45 % --lt_threshold 2000
% 0.20/0.45
% 0.20/0.45 % ------ SAT Options
% 0.20/0.45
% 0.20/0.45 % --sat_mode false
% 0.20/0.45 % --sat_fm_restart_options ""
% 0.20/0.45 % --sat_gr_def false
% 0.20/0.45 % --sat_epr_types true
% 0.20/0.45 % --sat_non_cyclic_types false
% 0.20/0.45 % --sat_finite_models false
% 0.20/0.45 % --sat_fm_lemmas false
% 0.20/0.45 % --sat_fm_prep false
% 0.20/0.45 % --sat_fm_uc_incr true
% 0.20/0.45 % --sat_out_model small
% 0.20/0.45 % --sat_out_clauses false
% 0.20/0.45
% 0.20/0.45 % ------ QBF Options
% 0.20/0.45
% 0.20/0.45 % --qbf_mode false
% 0.20/0.45 % --qbf_elim_univ true
% 0.20/0.45 % --qbf_sk_in true
% 0.20/0.45 % --qbf_pred_elim true
% 0.20/0.45 % --qbf_split 32
% 0.20/0.45
% 0.20/0.45 % ------ BMC1 Options
% 0.20/0.45
% 0.20/0.45 % --bmc1_incremental false
% 0.20/0.45 % --bmc1_axioms reachable_all
% 0.20/0.45 % --bmc1_min_bound 0
% 0.20/0.45 % --bmc1_max_bound -1
% 0.20/0.45 % --bmc1_max_bound_default -1
% 0.20/0.45 % --bmc1_symbol_reachability true
% 0.20/0.45 % --bmc1_property_lemmas false
% 0.20/0.45 % --bmc1_k_induction false
% 0.20/0.45 % --bmc1_non_equiv_states false
% 0.20/0.45 % --bmc1_deadlock false
% 0.20/0.45 % --bmc1_ucm false
% 0.20/0.45 % --bmc1_add_unsat_core none
% 0.20/0.45 % --bmc1_unsat_core_children false
% 0.20/0.45 % --bmc1_unsat_core_extrapolate_axioms false
% 0.20/0.45 % --bmc1_out_stat full
% 0.20/0.45 % --bmc1_ground_init false
% 0.20/0.45 % --bmc1_pre_inst_next_state false
% 0.20/0.45 % --bmc1_pre_inst_state false
% 0.20/0.45 % --bmc1_pre_inst_reach_state false
% 0.20/0.45 % --bmc1_out_unsat_core false
% 0.20/0.45 % --bmc1_aig_witness_out false
% 0.20/0.45 % --bmc1_verbose false
% 0.20/0.45 % --bmc1_dump_clauses_tptp false
% 0.20/0.46 % --bmc1_dump_unsat_core_tptp false
% 0.20/0.46 % --bmc1_dump_file -
% 0.20/0.46 % --bmc1_ucm_expand_uc_limit 128
% 0.20/0.46 % --bmc1_ucm_n_expand_iterations 6
% 0.20/0.46 % --bmc1_ucm_extend_mode 1
% 0.20/0.46 % --bmc1_ucm_init_mode 2
% 0.20/0.46 % --bmc1_ucm_cone_mode none
% 0.20/0.46 % --bmc1_ucm_reduced_relation_type 0
% 0.20/0.46 % --bmc1_ucm_relax_model 4
% 0.20/0.46 % --bmc1_ucm_full_tr_after_sat true
% 0.20/0.46 % --bmc1_ucm_expand_neg_assumptions false
% 0.20/0.46 % --bmc1_ucm_layered_model none
% 0.20/0.46 % --bmc1_ucm_max_lemma_size 10
% 0.20/0.46
% 0.20/0.46 % ------ AIG Options
% 0.20/0.46
% 0.20/0.46 % --aig_mode false
% 0.20/0.46
% 0.20/0.46 % ------ Instantiation Options
% 0.20/0.46
% 0.20/0.46 % --instantiation_flag true
% 0.20/0.46 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.20/0.46 % --inst_solver_per_active 750
% 0.20/0.46 % --inst_solver_calls_frac 0.5
% 0.20/0.46 % --inst_passive_queue_type priority_queues
% 0.20/0.46 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.20/0.46 % --inst_passive_queues_freq [25;2]
% 0.20/0.46 % --inst_dismatching true
% 0.20/0.46 % --inst_eager_unprocessed_to_passive true
% 0.20/0.46 % --inst_prop_sim_given true
% 0.20/0.46 % --inst_prop_sim_new false
% 0.20/0.46 % --inst_orphan_elimination true
% 0.20/0.46 % --inst_learning_loop_flag true
% 0.20/0.46 % --inst_learning_start 3000
% 0.20/0.46 % --inst_learning_factor 2
% 0.20/0.46 % --inst_start_prop_sim_after_learn 3
% 0.20/0.46 % --inst_sel_renew solver
% 0.20/0.46 % --inst_lit_activity_flag true
% 0.20/0.46 % --inst_out_proof true
% 0.20/0.46
% 0.20/0.46 % ------ Resolution Options
% 0.20/0.46
% 0.20/0.46 % --resolution_flag true
% 0.20/0.46 % --res_lit_sel kbo_max
% 0.20/0.46 % --res_to_prop_solver none
% 0.20/0.46 % --res_prop_simpl_new false
% 0.20/0.46 % --res_prop_simpl_given false
% 0.20/0.46 % --res_passive_queue_type priority_queues
% 0.20/0.46 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.20/0.46 % --res_passive_queues_freq [15;5]
% 0.20/0.46 % --res_forward_subs full
% 0.20/0.46 % --res_backward_subs full
% 0.20/0.46 % --res_forward_subs_resolution true
% 0.20/0.46 % --res_backward_subs_resolution true
% 0.20/0.46 % --res_orphan_elimination false
% 0.20/0.46 % --res_time_limit 1000.
% 0.20/0.46 % --res_out_proof true
% 0.20/0.46 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_c6279f.s
% 0.20/0.46 % --modulo true
% 0.20/0.46
% 0.20/0.46 % ------ Combination Options
% 0.20/0.46
% 0.20/0.46 % --comb_res_mult 1000
% 0.20/0.46 % --comb_inst_mult 300
% 0.20/0.46 % ------
% 0.20/0.46
% 0.20/0.46 % ------ Parsing...%
% 0.20/0.46
% 0.20/0.46
% 0.20/0.46 % ------ Statistics
% 0.20/0.46
% 0.20/0.46 % ------ General
% 0.20/0.46
% 0.20/0.46 % num_of_input_clauses: 104
% 0.20/0.46 % num_of_input_neg_conjectures: 0
% 0.20/0.46 % num_of_splits: 0
% 0.20/0.46 % num_of_split_atoms: 0
% 0.20/0.46 % num_of_sem_filtered_clauses: 0
% 0.20/0.46 % num_of_subtypes: 0
% 0.20/0.46 % monotx_restored_types: 0
% 0.20/0.46 % sat_num_of_epr_types: 0
% 0.20/0.46 % sat_num_of_non_cyclic_types: 0
% 0.20/0.46 % sat_guarded_non_collapsed_types: 0
% 0.20/0.46 % is_epr: 0
% 0.20/0.46 % is_horn: 0
% 0.20/0.46 % has_eq: 0
% 0.20/0.46 % num_pure_diseq_elim: 0
% 0.20/0.46 % simp_replaced_by: 0
% 0.20/0.46 % res_preprocessed: 0
% 0.20/0.46 % prep_upred: 0
% 0.20/0.46 % prep_unflattend: 0
% 0.20/0.46 % pred_elim_cands: 0
% 0.20/0.46 % pred_elim: 0
% 0.20/0.46 % pred_elim_cl: 0
% 0.20/0.46 % pred_elim_cycles: 0
% 0.20/0.46 % forced_gc_time: 0
% 0.20/0.46 % gc_basic_clause_elim: 0
% 0.20/0.46 % parsing_time: 0.
% 0.20/0.46 % sem_filter_time: 0.
% 0.20/0.46 % pred_elim_time: 0.
% 0.20/0.46 % out_proof_time: 0.
% 0.20/0.46 % monotx_time: 0.
% 0.20/0.46 % subtype_inf_time: 0.
% 0.20/0.46 % unif_index_cands_time: 0.
% 0.20/0.46 % uFatal error: exception Failure("Parse error in: /export/starexec/sandbox/tmp/iprover_modulo_111001.p line: 107 near token: '!='")
% 0.20/0.46 nif_index_add_time: 0.
% 0.20/0.46 % total_time: 0.021
% 0.20/0.46 % num_of_symbols: 59
% 0.20/0.46 % num_of_terms: 282
% 0.20/0.46
% 0.20/0.46 % ------ Propositional Solver
% 0.20/0.46
% 0.20/0.46 % prop_solver_calls: 0
% 0.20/0.46 % prop_fast_solver_calls: 0
% 0.20/0.46 % prop_num_of_clauses: 0
% 0.20/0.46 % prop_preprocess_simplified: 0
% 0.20/0.46 % prop_fo_subsumed: 0
% 0.20/0.46 % prop_solver_time: 0.
% 0.20/0.46 % prop_fast_solver_time: 0.
% 0.20/0.46 % prop_unsat_core_time: 0.
% 0.20/0.46
% 0.20/0.46 % ------ QBF
% 0.20/0.46
% 0.20/0.46 % qbf_q_res: 0
% 0.20/0.46 % qbf_num_tautologies: 0
% 0.20/0.46 % qbf_prep_cycles: 0
% 0.20/0.46
% 0.20/0.46 % ------ BMC1
% 0.20/0.46
% 0.20/0.46 % bmc1_current_bound: -1
% 0.20/0.46 % bmc1_last_solved_bound: -1
% 0.20/0.46 % bmc1_unsat_core_size: -1
% 0.20/0.46 % bmc1_unsat_core_parents_size: -1
% 0.20/0.46 % bmc1_merge_next_fun: 0
% 0.20/0.46 % bmc1_unsat_core_clauses_time: 0.
% 0.20/0.46
% 0.20/0.46 % ------ Instantiation
% 0.20/0.46
% 0.20/0.46 % inst_num_of_clauses: undef
% 0.20/0.46 % inst_num_in_passive: undef
% 0.20/0.46 % inst_num_in_active: 0
% 0.20/0.46 % inst_num_in_unprocessed: 0
% 0.20/0.46 % inst_num_of_loops: 0
% 0.20/0.46 % inst_num_of_learning_restarts: 0
% 0.20/0.46 % inst_num_moves_active_passive: 0
% 0.20/0.46 % inst_lit_activity: 0
% 0.20/0.46 % inst_lit_activity_moves: 0
% 0.20/0.46 % inst_num_tautologies: 0
% 0.20/0.46 % inst_num_prop_implied: 0
% 0.20/0.46 % inst_num_existing_simplified: 0
% 0.20/0.46 % inst_num_eq_res_simplified: 0
% 0.20/0.46 % inst_num_child_elim: 0
% 0.20/0.46 % inst_num_of_dismatching_blockings: 0
% 0.20/0.46 % inst_num_of_non_proper_insts: 0
% 0.20/0.46 % inst_num_of_duplicates: 0
% 0.20/0.46 % inst_inst_num_from_inst_to_res: 0
% 0.20/0.46 % inst_dismatching_checking_time: 0.
% 0.20/0.46
% 0.20/0.46 % ------ Resolution
% 0.20/0.46
% 0.20/0.46 % res_num_of_clauses: undef
% 0.20/0.46 % res_num_in_passive: undef
% 0.20/0.46 % res_num_in_active: 0
% 0.20/0.46 % res_num_of_loops: 0
% 0.20/0.46 % res_forward_subset_subsumed: 0
% 0.20/0.46 % res_backward_subset_subsumed: 0
% 0.20/0.46 % res_forward_subsumed: 0
% 0.20/0.46 % res_backward_subsumed: 0
% 0.20/0.46 % res_forward_subsumption_resolution: 0
% 0.20/0.46 % res_backward_subsumption_resolution: 0
% 0.20/0.46 % res_clause_to_clause_subsumption: 0
% 0.20/0.46 % res_orphan_elimination: 0
% 0.20/0.46 % res_tautology_del: 0
% 0.20/0.46 % res_num_eq_res_simplified: 0
% 0.20/0.46 % res_num_sel_changes: 0
% 0.20/0.46 % res_moves_from_active_to_pass: 0
% 0.20/0.46
% 0.20/0.46 % Status Unknown
% 0.34/0.53 % Orienting using strategy ClausalAll
% 0.34/0.53 % FOF problem with conjecture
% 0.34/0.53 % 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_c6279f.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_111001.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_e4df5c | grep -v "SZS"
% 0.37/0.55
% 0.37/0.55 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.37/0.55
% 0.37/0.55 %
% 0.37/0.55 % ------ iProver source info
% 0.37/0.55
% 0.37/0.55 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.37/0.55 % git: non_committed_changes: true
% 0.37/0.55 % git: last_make_outside_of_git: true
% 0.37/0.55
% 0.37/0.55 %
% 0.37/0.55 % ------ Input Options
% 0.37/0.55
% 0.37/0.55 % --out_options all
% 0.37/0.55 % --tptp_safe_out true
% 0.37/0.55 % --problem_path ""
% 0.37/0.55 % --include_path ""
% 0.37/0.55 % --clausifier .//eprover
% 0.37/0.55 % --clausifier_options --tstp-format
% 0.37/0.55 % --stdin false
% 0.37/0.55 % --dbg_backtrace false
% 0.37/0.55 % --dbg_dump_prop_clauses false
% 0.37/0.55 % --dbg_dump_prop_clauses_file -
% 0.37/0.55 % --dbg_out_stat false
% 0.37/0.55
% 0.37/0.55 % ------ General Options
% 0.37/0.55
% 0.37/0.55 % --fof false
% 0.37/0.55 % --time_out_real 150.
% 0.37/0.55 % --time_out_prep_mult 0.2
% 0.37/0.55 % --time_out_virtual -1.
% 0.37/0.55 % --schedule none
% 0.37/0.55 % --ground_splitting input
% 0.37/0.55 % --splitting_nvd 16
% 0.37/0.55 % --non_eq_to_eq false
% 0.37/0.55 % --prep_gs_sim true
% 0.37/0.55 % --prep_unflatten false
% 0.37/0.55 % --prep_res_sim true
% 0.37/0.55 % --prep_upred true
% 0.37/0.55 % --res_sim_input true
% 0.37/0.55 % --clause_weak_htbl true
% 0.37/0.55 % --gc_record_bc_elim false
% 0.37/0.55 % --symbol_type_check false
% 0.37/0.55 % --clausify_out false
% 0.37/0.55 % --large_theory_mode false
% 0.37/0.55 % --prep_sem_filter none
% 0.37/0.55 % --prep_sem_filter_out false
% 0.37/0.55 % --preprocessed_out false
% 0.37/0.55 % --sub_typing false
% 0.37/0.55 % --brand_transform false
% 0.37/0.55 % --pure_diseq_elim true
% 0.37/0.55 % --min_unsat_core false
% 0.37/0.55 % --pred_elim true
% 0.37/0.55 % --add_important_lit false
% 0.37/0.55 % --soft_assumptions false
% 0.37/0.55 % --reset_solvers false
% 0.37/0.55 % --bc_imp_inh []
% 0.37/0.55 % --conj_cone_tolerance 1.5
% 0.37/0.55 % --prolific_symb_bound 500
% 0.37/0.55 % --lt_threshold 2000
% 0.37/0.55
% 0.37/0.55 % ------ SAT Options
% 0.37/0.55
% 0.37/0.55 % --sat_mode false
% 0.37/0.55 % --sat_fm_restart_options ""
% 0.37/0.55 % --sat_gr_def false
% 0.37/0.55 % --sat_epr_types true
% 0.37/0.55 % --sat_non_cyclic_types false
% 0.37/0.55 % --sat_finite_models false
% 0.37/0.55 % --sat_fm_lemmas false
% 0.37/0.55 % --sat_fm_prep false
% 0.37/0.55 % --sat_fm_uc_incr true
% 0.37/0.55 % --sat_out_model small
% 0.37/0.55 % --sat_out_clauses false
% 0.37/0.55
% 0.37/0.55 % ------ QBF Options
% 0.37/0.55
% 0.37/0.55 % --qbf_mode false
% 0.37/0.55 % --qbf_elim_univ true
% 0.37/0.55 % --qbf_sk_in true
% 0.37/0.55 % --qbf_pred_elim true
% 0.37/0.55 % --qbf_split 32
% 0.37/0.55
% 0.37/0.55 % ------ BMC1 Options
% 0.37/0.55
% 0.37/0.55 % --bmc1_incremental false
% 0.37/0.55 % --bmc1_axioms reachable_all
% 0.37/0.55 % --bmc1_min_bound 0
% 0.37/0.55 % --bmc1_max_bound -1
% 0.37/0.55 % --bmc1_max_bound_default -1
% 0.37/0.55 % --bmc1_symbol_reachability true
% 0.37/0.55 % --bmc1_property_lemmas false
% 0.37/0.55 % --bmc1_k_induction false
% 0.37/0.55 % --bmc1_non_equiv_states false
% 0.37/0.55 % --bmc1_deadlock false
% 0.37/0.55 % --bmc1_ucm false
% 0.37/0.55 % --bmc1_add_unsat_core none
% 0.37/0.55 % --bmc1_unsat_core_children false
% 0.37/0.55 % --bmc1_unsat_core_extrapolate_axioms false
% 0.37/0.55 % --bmc1_out_stat full
% 0.37/0.55 % --bmc1_ground_init false
% 0.37/0.55 % --bmc1_pre_inst_next_state false
% 0.37/0.55 % --bmc1_pre_inst_state false
% 0.37/0.55 % --bmc1_pre_inst_reach_state false
% 0.37/0.55 % --bmc1_out_unsat_core false
% 0.37/0.55 % --bmc1_aig_witness_out false
% 0.37/0.55 % --bmc1_verbose false
% 0.37/0.55 % --bmc1_dump_clauses_tptp false
% 0.37/0.99 % --bmc1_dump_unsat_core_tptp false
% 0.37/0.99 % --bmc1_dump_file -
% 0.37/0.99 % --bmc1_ucm_expand_uc_limit 128
% 0.37/0.99 % --bmc1_ucm_n_expand_iterations 6
% 0.37/0.99 % --bmc1_ucm_extend_mode 1
% 0.37/0.99 % --bmc1_ucm_init_mode 2
% 0.37/0.99 % --bmc1_ucm_cone_mode none
% 0.37/0.99 % --bmc1_ucm_reduced_relation_type 0
% 0.37/0.99 % --bmc1_ucm_relax_model 4
% 0.37/0.99 % --bmc1_ucm_full_tr_after_sat true
% 0.37/0.99 % --bmc1_ucm_expand_neg_assumptions false
% 0.37/0.99 % --bmc1_ucm_layered_model none
% 0.37/0.99 % --bmc1_ucm_max_lemma_size 10
% 0.37/0.99
% 0.37/0.99 % ------ AIG Options
% 0.37/0.99
% 0.37/0.99 % --aig_mode false
% 0.37/0.99
% 0.37/0.99 % ------ Instantiation Options
% 0.37/0.99
% 0.37/0.99 % --instantiation_flag true
% 0.37/0.99 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.37/0.99 % --inst_solver_per_active 750
% 0.37/0.99 % --inst_solver_calls_frac 0.5
% 0.37/0.99 % --inst_passive_queue_type priority_queues
% 0.37/0.99 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.37/0.99 % --inst_passive_queues_freq [25;2]
% 0.37/0.99 % --inst_dismatching true
% 0.37/0.99 % --inst_eager_unprocessed_to_passive true
% 0.37/0.99 % --inst_prop_sim_given true
% 0.37/0.99 % --inst_prop_sim_new false
% 0.37/0.99 % --inst_orphan_elimination true
% 0.37/0.99 % --inst_learning_loop_flag true
% 0.37/0.99 % --inst_learning_start 3000
% 0.37/0.99 % --inst_learning_factor 2
% 0.37/0.99 % --inst_start_prop_sim_after_learn 3
% 0.37/0.99 % --inst_sel_renew solver
% 0.37/0.99 % --inst_lit_activity_flag true
% 0.37/0.99 % --inst_out_proof true
% 0.37/0.99
% 0.37/0.99 % ------ Resolution Options
% 0.37/0.99
% 0.37/0.99 % --resolution_flag true
% 0.37/0.99 % --res_lit_sel kbo_max
% 0.37/0.99 % --res_to_prop_solver none
% 0.37/0.99 % --res_prop_simpl_new false
% 0.37/0.99 % --res_prop_simpl_given false
% 0.37/0.99 % --res_passive_queue_type priority_queues
% 0.37/0.99 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.37/0.99 % --res_passive_queues_freq [15;5]
% 0.37/0.99 % --res_forward_subs full
% 0.37/0.99 % --res_backward_subs full
% 0.37/0.99 % --res_forward_subs_resolution true
% 0.37/0.99 % --res_backward_subs_resolution true
% 0.37/0.99 % --res_orphan_elimination false
% 0.37/0.99 % --res_time_limit 1000.
% 0.37/0.99 % --res_out_proof true
% 0.37/0.99 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_c6279f.s
% 0.37/0.99 % --modulo true
% 0.37/0.99
% 0.37/0.99 % ------ Combination Options
% 0.37/0.99
% 0.37/0.99 % --comb_res_mult 1000
% 0.37/0.99 % --comb_inst_mult 300
% 0.37/0.99 % ------
% 0.37/0.99
% 0.37/0.99 % ------ Parsing...% successful
% 0.37/0.99
% 0.37/0.99 % ------ 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 %
% 0.37/0.99
% 0.37/0.99 % ------ Proving...
% 0.37/0.99 % ------ Problem Properties
% 0.37/0.99
% 0.37/0.99 %
% 0.37/0.99 % EPR false
% 0.37/0.99 % Horn false
% 0.37/0.99 % Has equality true
% 0.37/0.99
% 0.37/0.99 % % ------ Input Options Time Limit: Unbounded
% 0.37/0.99
% 0.37/0.99
% 0.37/0.99 Compiling...
% 0.37/0.99 Loading plugin: done.
% 0.37/0.99 Compiling...
% 0.37/0.99 Loading plugin: done.
% 0.37/0.99 Compiling...
% 0.37/0.99 Loading plugin: done.
% 0.37/0.99 Compiling...
% 0.37/0.99 Loading plugin: done.
% 0.37/0.99 % % ------ Current options:
% 0.37/0.99
% 0.37/0.99 % ------ Input Options
% 0.37/0.99
% 0.37/0.99 % --out_options all
% 0.37/0.99 % --tptp_safe_out true
% 0.37/0.99 % --problem_path ""
% 0.37/0.99 % --include_path ""
% 0.37/0.99 % --clausifier .//eprover
% 0.37/0.99 % --clausifier_options --tstp-format
% 0.37/0.99 % --stdin false
% 0.37/0.99 % --dbg_backtrace false
% 0.37/0.99 % --dbg_dump_prop_clauses false
% 0.37/0.99 % --dbg_dump_prop_clauses_file -
% 0.37/0.99 % --dbg_out_stat false
% 0.37/0.99
% 0.37/0.99 % ------ General Options
% 0.37/0.99
% 0.37/0.99 % --fof false
% 0.37/0.99 % --time_out_real 150.
% 0.37/0.99 % --time_out_prep_mult 0.2
% 0.37/0.99 % --time_out_virtual -1.
% 0.37/0.99 % --schedule none
% 0.37/0.99 % --ground_splitting input
% 0.37/0.99 % --splitting_nvd 16
% 0.37/0.99 % --non_eq_to_eq false
% 0.37/0.99 % --prep_gs_sim true
% 0.37/0.99 % --prep_unflatten false
% 0.37/0.99 % --prep_res_sim true
% 0.37/0.99 % --prep_upred true
% 0.37/0.99 % --res_sim_input true
% 0.37/0.99 % --clause_weak_htbl true
% 0.37/0.99 % --gc_record_bc_elim false
% 0.37/0.99 % --symbol_type_check false
% 0.37/0.99 % --clausify_out false
% 0.37/0.99 % --large_theory_mode false
% 0.37/0.99 % --prep_sem_filter none
% 0.37/0.99 % --prep_sem_filter_out false
% 0.37/0.99 % --preprocessed_out false
% 0.37/0.99 % --sub_typing false
% 0.37/0.99 % --brand_transform false
% 0.37/0.99 % --pure_diseq_elim true
% 0.37/0.99 % --min_unsat_core false
% 0.37/0.99 % --pred_elim true
% 0.37/0.99 % --add_important_lit false
% 0.37/0.99 % --soft_assumptions false
% 0.37/0.99 % --reset_solvers false
% 0.37/0.99 % --bc_imp_inh []
% 0.37/0.99 % --conj_cone_tolerance 1.5
% 0.37/0.99 % --prolific_symb_bound 500
% 0.37/0.99 % --lt_threshold 2000
% 0.37/0.99
% 0.37/0.99 % ------ SAT Options
% 0.37/0.99
% 0.37/0.99 % --sat_mode false
% 0.37/0.99 % --sat_fm_restart_options ""
% 0.37/0.99 % --sat_gr_def false
% 0.37/0.99 % --sat_epr_types true
% 0.37/0.99 % --sat_non_cyclic_types false
% 0.37/0.99 % --sat_finite_models false
% 0.37/0.99 % --sat_fm_lemmas false
% 0.37/0.99 % --sat_fm_prep false
% 0.37/0.99 % --sat_fm_uc_incr true
% 0.37/0.99 % --sat_out_model small
% 0.37/0.99 % --sat_out_clauses false
% 0.37/0.99
% 0.37/0.99 % ------ QBF Options
% 0.37/0.99
% 0.37/0.99 % --qbf_mode false
% 0.37/0.99 % --qbf_elim_univ true
% 0.37/0.99 % --qbf_sk_in true
% 0.37/0.99 % --qbf_pred_elim true
% 0.37/0.99 % --qbf_split 32
% 0.37/0.99
% 0.37/0.99 % ------ BMC1 Options
% 0.37/0.99
% 0.37/0.99 % --bmc1_incremental false
% 0.37/0.99 % --bmc1_axioms reachable_all
% 0.37/0.99 % --bmc1_min_bound 0
% 0.37/0.99 % --bmc1_max_bound -1
% 0.37/0.99 % --bmc1_max_bound_default -1
% 0.37/0.99 % --bmc1_symbol_reachability true
% 0.37/0.99 % --bmc1_property_lemmas false
% 0.37/0.99 % --bmc1_k_induction false
% 0.37/0.99 % --bmc1_non_equiv_states false
% 0.37/0.99 % --bmc1_deadlock false
% 0.37/0.99 % --bmc1_ucm false
% 0.37/0.99 % --bmc1_add_unsat_core none
% 0.37/0.99 % --bmc1_unsat_core_children false
% 0.37/0.99 % --bmc1_unsat_core_extrapolate_axioms false
% 0.37/0.99 % --bmc1_out_stat full
% 0.37/0.99 % --bmc1_ground_init false
% 0.37/0.99 % --bmc1_pre_inst_next_state false
% 0.37/0.99 % --bmc1_pre_inst_state false
% 0.37/0.99 % --bmc1_pre_inst_reach_state false
% 0.37/0.99 % --bmc1_out_unsat_core false
% 0.37/0.99 % --bmc1_aig_witness_out false
% 0.37/0.99 % --bmc1_verbose false
% 0.37/0.99 % --bmc1_dump_clauses_tptp false
% 0.37/0.99 % --bmc1_dump_unsat_core_tptp false
% 0.37/0.99 % --bmc1_dump_file -
% 0.37/0.99 % --bmc1_ucm_expand_uc_limit 128
% 0.37/0.99 % --bmc1_ucm_n_expand_iterations 6
% 0.37/0.99 % --bmc1_ucm_extend_mode 1
% 0.37/0.99 % --bmc1_ucm_init_mode 2
% 0.37/0.99 % --bmc1_ucm_cone_mode none
% 0.37/0.99 % --bmc1_ucm_reduced_relation_type 0
% 0.37/0.99 % --bmc1_ucm_relax_model 4
% 0.37/0.99 % --bmc1_ucm_full_tr_after_sat true
% 0.37/0.99 % --bmc1_ucm_expand_neg_assumptions false
% 0.37/0.99 % --bmc1_ucm_layered_model none
% 0.37/0.99 % --bmc1_ucm_max_lemma_size 10
% 0.37/0.99
% 0.37/0.99 % ------ AIG Options
% 0.37/0.99
% 0.37/0.99 % --aig_mode false
% 0.37/0.99
% 0.37/0.99 % ------ Instantiation Options
% 0.37/0.99
% 0.37/0.99 % --instantiation_flag true
% 0.37/0.99 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.37/0.99 % --inst_solver_per_active 750
% 0.37/0.99 % --inst_solver_calls_frac 0.5
% 0.37/0.99 % --inst_passive_queue_type priority_queues
% 0.37/0.99 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.37/0.99 % --inst_passive_queues_freq [25;2]
% 104.88/105.11 % --inst_dismatching true
% 104.88/105.11 % --inst_eager_unprocessed_to_passive true
% 104.88/105.11 % --inst_prop_sim_given true
% 104.88/105.11 % --inst_prop_sim_new false
% 104.88/105.11 % --inst_orphan_elimination true
% 104.88/105.11 % --inst_learning_loop_flag true
% 104.88/105.11 % --inst_learning_start 3000
% 104.88/105.11 % --inst_learning_factor 2
% 104.88/105.11 % --inst_start_prop_sim_after_learn 3
% 104.88/105.11 % --inst_sel_renew solver
% 104.88/105.11 % --inst_lit_activity_flag true
% 104.88/105.11 % --inst_out_proof true
% 104.88/105.11
% 104.88/105.11 % ------ Resolution Options
% 104.88/105.11
% 104.88/105.11 % --resolution_flag true
% 104.88/105.11 % --res_lit_sel kbo_max
% 104.88/105.11 % --res_to_prop_solver none
% 104.88/105.11 % --res_prop_simpl_new false
% 104.88/105.11 % --res_prop_simpl_given false
% 104.88/105.11 % --res_passive_queue_type priority_queues
% 104.88/105.11 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 104.88/105.11 % --res_passive_queues_freq [15;5]
% 104.88/105.11 % --res_forward_subs full
% 104.88/105.11 % --res_backward_subs full
% 104.88/105.11 % --res_forward_subs_resolution true
% 104.88/105.11 % --res_backward_subs_resolution true
% 104.88/105.11 % --res_orphan_elimination false
% 104.88/105.11 % --res_time_limit 1000.
% 104.88/105.11 % --res_out_proof true
% 104.88/105.11 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_c6279f.s
% 104.88/105.11 % --modulo true
% 104.88/105.11
% 104.88/105.11 % ------ Combination Options
% 104.88/105.11
% 104.88/105.11 % --comb_res_mult 1000
% 104.88/105.11 % --comb_inst_mult 300
% 104.88/105.11 % ------
% 104.88/105.11
% 104.88/105.11
% 104.88/105.11
% 104.88/105.11 % ------ Proving...
% 104.88/105.11 %
% 104.88/105.11
% 104.88/105.11
% 104.88/105.11 % ------ Statistics
% 104.88/105.11
% 104.88/105.11 % ------ General
% 104.88/105.11
% 104.88/105.11 % num_of_input_clauses: 488
% 104.88/105.11 % num_of_input_neg_conjectures: 3
% 104.88/105.11 % num_of_splits: 0
% 104.88/105.11 % num_of_split_atoms: 0
% 104.88/105.11 % num_of_sem_filtered_clauses: 0
% 104.88/105.11 % num_of_subtypes: 0
% 104.88/105.11 % monotx_restored_types: 0
% 104.88/105.11 % sat_num_of_epr_types: 0
% 104.88/105.11 % sat_num_of_non_cyclic_types: 0
% 104.88/105.11 % sat_guarded_non_collapsed_types: 0
% 104.88/105.11 % is_epr: 0
% 104.88/105.11 % is_horn: 0
% 104.88/105.11 % has_eq: 1
% 104.88/105.11 % num_pure_diseq_elim: 0
% 104.88/105.11 % simp_replaced_by: 2
% 104.88/105.11 % res_preprocessed: 90
% 104.88/105.11 % prep_upred: 0
% 104.88/105.11 % prep_unflattend: 0
% 104.88/105.11 % pred_elim_cands: 5
% 104.88/105.11 % pred_elim: 2
% 104.88/105.11 % pred_elim_cl: 2
% 104.88/105.11 % pred_elim_cycles: 3
% 104.88/105.11 % forced_gc_time: 0
% 104.88/105.11 % gc_basic_clause_elim: 0
% 104.88/105.11 % parsing_time: 0.02
% 104.88/105.11 % sem_filter_time: 0.
% 104.88/105.11 % pred_elim_time: 0.001
% 104.88/105.11 % out_proof_time: 0.004
% 104.88/105.11 % monotx_time: 0.
% 104.88/105.11 % subtype_inf_time: 0.
% 104.88/105.11 % unif_index_cands_time: 0.771
% 104.88/105.11 % unif_index_add_time: 0.056
% 104.88/105.11 % total_time: 104.579
% 104.88/105.11 % num_of_symbols: 94
% 104.88/105.11 % num_of_terms: 2186385
% 104.88/105.11
% 104.88/105.11 % ------ Propositional Solver
% 104.88/105.11
% 104.88/105.11 % prop_solver_calls: 21
% 104.88/105.11 % prop_fast_solver_calls: 352
% 104.88/105.11 % prop_num_of_clauses: 33032
% 104.88/105.11 % prop_preprocess_simplified: 44240
% 104.88/105.11 % prop_fo_subsumed: 0
% 104.88/105.11 % prop_solver_time: 0.019
% 104.88/105.11 % prop_fast_solver_time: 0.
% 104.88/105.11 % prop_unsat_core_time: 0.004
% 104.88/105.11
% 104.88/105.11 % ------ QBF
% 104.88/105.11
% 104.88/105.11 % qbf_q_res: 0
% 104.88/105.11 % qbf_num_tautologies: 0
% 104.88/105.11 % qbf_prep_cycles: 0
% 104.88/105.11
% 104.88/105.11 % ------ BMC1
% 104.88/105.11
% 104.88/105.11 % bmc1_current_bound: -1
% 104.88/105.11 % bmc1_last_solved_bound: -1
% 104.88/105.11 % bmc1_unsat_core_size: -1
% 104.88/105.11 % bmc1_unsat_core_parents_size: -1
% 104.88/105.11 % bmc1_merge_next_fun: 0
% 104.88/105.11 % bmc1_unsat_core_clauses_time: 0.
% 104.88/105.11
% 104.88/105.11 % ------ Instantiation
% 104.88/105.11
% 104.88/105.11 % inst_num_of_clauses: 2487
% 104.88/105.12 % inst_num_in_passive: 2048
% 104.88/105.12 % inst_num_in_active: 405
% 104.88/105.12 % inst_num_in_unprocessed: 30
% 104.88/105.12 % inst_num_of_loops: 413
% 104.88/105.12 % inst_num_of_learning_restarts: 1
% 104.88/105.12 % inst_num_moves_active_passive: 5
% 104.88/105.12 % inst_lit_activity: 975
% 104.88/105.12 % inst_lit_activity_moves: 0
% 104.88/105.12 % inst_num_tautologies: 1
% 104.88/105.12 % inst_num_prop_implied: 0
% 104.88/105.12 % inst_num_existing_simplified: 0
% 104.88/105.12 % inst_num_eq_res_simplified: 2
% 104.88/105.12 % inst_num_child_elim: 0
% 104.88/105.12 % inst_num_of_dismatching_blockings: 519
% 104.88/105.12 % inst_num_of_non_proper_insts: 1191
% 104.88/105.12 % inst_num_of_duplicates: 1635
% 104.88/105.12 % inst_inst_num_from_inst_to_res: 0
% 104.88/105.12 % inst_dismatching_checking_time: 0.246
% 104.88/105.12
% 104.88/105.12 % ------ Resolution
% 104.88/105.12
% 104.88/105.12 % res_num_of_clauses: 1228459
% 104.88/105.12 % res_num_in_passive: 1219229
% 104.88/105.12 % res_num_in_active: 10308
% 104.88/105.12 % res_num_of_loops: 12000
% 104.88/105.12 % res_forward_subset_subsumed: 75501
% 104.88/105.12 % res_backward_subset_subsumed: 1462
% 104.88/105.12 % res_forward_subsumed: 1713
% 104.88/105.12 % res_backward_subsumed: 72
% 104.88/105.12 % res_forward_subsumption_resolution: 254
% 104.88/105.12 % res_backward_subsumption_resolution: 23
% 104.88/105.12 % res_clause_to_clause_subsumption: 222488
% 104.88/105.12 % res_orphan_elimination: 0
% 104.88/105.12 % res_tautology_del: 1365
% 104.88/105.12 % res_num_eq_res_simplified: 27
% 104.88/105.12 % res_num_sel_changes: 0
% 104.88/105.12 % res_moves_from_active_to_pass: 0
% 104.88/105.12
% 104.88/105.12 % Status Unsatisfiable
% 104.88/105.12 % SZS status Theorem
% 104.88/105.12 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------