TSTP Solution File: SEU224+2 by iProverMo---2.5-0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : SEU224+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 10:26:11 EDT 2022
% Result : Theorem 10.93s 11.13s
% Output : CNFRefutation 10.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 246
% Syntax : Number of formulae : 2478 ( 389 unt; 0 def)
% Number of atoms : 8700 (1974 equ)
% Maximal formula atoms : 130 ( 3 avg)
% Number of connectives : 10818 (4596 ~;5130 |; 536 &)
% ( 158 <=>; 398 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 14 ( 11 usr; 2 prp; 0-2 aty)
% Number of functors : 178 ( 178 usr; 23 con; 0-5 aty)
% Number of variables : 5907 ( 297 sgn1574 !; 50 ?)
% Comments :
%------------------------------------------------------------------------------
% Axioms transformation by autotheo
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ! [X3] :
( relation(X3)
=> ( X3 = relation_composition(X1,X2)
<=> ! [X4,X5] :
( in(ordered_pair(X4,X5),X3)
<=> ? [X6] :
( in(ordered_pair(X4,X6),X1)
& in(ordered_pair(X6,X5),X2) ) ) ) ) ) ),
file('<stdin>',d8_relat_1) ).
fof(c_0_1,axiom,
! [X1,X2] :
( relation(X2)
=> ! [X3] :
( relation(X3)
=> ( X3 = relation_rng_restriction(X1,X2)
<=> ! [X4,X5] :
( in(ordered_pair(X4,X5),X3)
<=> ( in(X5,X1)
& in(ordered_pair(X4,X5),X2) ) ) ) ) ),
file('<stdin>',d12_relat_1) ).
fof(c_0_2,axiom,
! [X1] :
( relation(X1)
=> ! [X2,X3] :
( relation(X3)
=> ( X3 = relation_dom_restriction(X1,X2)
<=> ! [X4,X5] :
( in(ordered_pair(X4,X5),X3)
<=> ( in(X4,X2)
& in(ordered_pair(X4,X5),X1) ) ) ) ) ),
file('<stdin>',d11_relat_1) ).
fof(c_0_3,axiom,
! [X1] :
( relation(X1)
=> ! [X2,X3] :
( X3 = relation_inverse_image(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(ordered_pair(X4,X5),X1)
& in(X5,X2) ) ) ) ),
file('<stdin>',d14_relat_1) ).
fof(c_0_4,axiom,
! [X1] :
( relation(X1)
=> ! [X2,X3] :
( X3 = relation_image(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(X5,X2) ) ) ) ),
file('<stdin>',d13_relat_1) ).
fof(c_0_5,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_6,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_7,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_8,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_9,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( X2 = relation_inverse(X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> in(ordered_pair(X4,X3),X1) ) ) ) ),
file('<stdin>',d7_relat_1) ).
fof(c_0_10,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( X1 = X2
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X1)
<=> in(ordered_pair(X3,X4),X2) ) ) ) ),
file('<stdin>',d2_relat_1) ).
fof(c_0_11,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_12,axiom,
! [X1,X2] :
( relation(X2)
=> ( X2 = identity_relation(X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(X3,X1)
& X3 = X4 ) ) ) ),
file('<stdin>',d10_relat_1) ).
fof(c_0_13,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
file('<stdin>',d2_tarski) ).
fof(c_0_14,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_15,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_16,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( subset(X1,X2)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X1)
=> in(ordered_pair(X3,X4),X2) ) ) ) ),
file('<stdin>',d3_relat_1) ).
fof(c_0_17,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_18,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_19,axiom,
! [X1,X2] :
( X2 = union(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X3,X4)
& in(X4,X1) ) ) ),
file('<stdin>',d4_tarski) ).
fof(c_0_20,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_21,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
<=> ! [X2,X3] :
( ( in(X2,relation_dom(X1))
& in(X3,relation_dom(X1))
& apply(X1,X2) = apply(X1,X3) )
=> X2 = X3 ) ) ),
file('<stdin>',d8_funct_1) ).
fof(c_0_22,axiom,
! [X1,X2] :
( X2 = powerset(X1)
<=> ! [X3] :
( in(X3,X2)
<=> subset(X3,X1) ) ),
file('<stdin>',d1_zfmisc_1) ).
fof(c_0_23,axiom,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
<=> in(X3,X2) )
=> X1 = X2 ),
file('<stdin>',t2_tarski) ).
fof(c_0_24,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2,X3] :
( ( in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> in(ordered_pair(X2,X3),X1) ) )
& ( ~ in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> X3 = empty_set ) ) ) ),
file('<stdin>',d4_funct_1) ).
fof(c_0_25,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_26,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_27,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_28,axiom,
! [X1] :
( relation(X1)
<=> ! [X2] :
~ ( in(X2,X1)
& ! [X3,X4] : X2 != ordered_pair(X3,X4) ) ),
file('<stdin>',d1_relat_1) ).
fof(c_0_29,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_30,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('<stdin>',d1_tarski) ).
fof(c_0_31,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_32,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> element(subset_complement(X1,X2),powerset(X1)) ),
file('<stdin>',dt_k3_subset_1) ).
fof(c_0_33,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('<stdin>',d3_tarski) ).
fof(c_0_34,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,subset_complement(X1,X2)) = X2 ),
file('<stdin>',involutiveness_k3_subset_1) ).
fof(c_0_35,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_36,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> union_of_subsets(X1,X2) = union(X2) ),
file('<stdin>',redefinition_k5_setfam_1) ).
fof(c_0_37,axiom,
! [X1,X2,X3] :
( ( in(X1,X2)
& element(X2,powerset(X3)) )
=> element(X1,X3) ),
file('<stdin>',t4_subset) ).
fof(c_0_38,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
file('<stdin>',t5_subset) ).
fof(c_0_39,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,X2) = set_difference(X1,X2) ),
file('<stdin>',d5_subset_1) ).
fof(c_0_40,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('<stdin>',d5_tarski) ).
fof(c_0_41,axiom,
! [X1,X2] :
( ( relation(X1)
& function(X1)
& relation(X2)
& function(X2) )
=> ( relation(relation_composition(X1,X2))
& function(relation_composition(X1,X2)) ) ),
file('<stdin>',fc1_funct_1) ).
fof(c_0_42,axiom,
! [X1,X2] :
( ( ~ empty(X1)
& ~ empty(X2) )
=> ~ empty(cartesian_product2(X1,X2)) ),
file('<stdin>',fc4_subset_1) ).
fof(c_0_43,axiom,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X2,X1)) ),
file('<stdin>',fc3_xboole_0) ).
fof(c_0_44,axiom,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X1,X2)) ),
file('<stdin>',fc2_xboole_0) ).
fof(c_0_45,axiom,
! [X1,X2] : ~ empty(unordered_pair(X1,X2)),
file('<stdin>',fc3_subset_1) ).
fof(c_0_46,axiom,
! [X1,X2] : ~ empty(ordered_pair(X1,X2)),
file('<stdin>',fc1_zfmisc_1) ).
fof(c_0_47,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('<stdin>',d10_xboole_0) ).
fof(c_0_48,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('<stdin>',t3_subset) ).
fof(c_0_49,axiom,
! [X1,X2] :
( proper_subset(X1,X2)
=> ~ proper_subset(X2,X1) ),
file('<stdin>',antisymmetry_r2_xboole_0) ).
fof(c_0_50,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('<stdin>',antisymmetry_r2_hidden) ).
fof(c_0_51,axiom,
! [X1,X2] :
( ( empty(X1)
& relation(X2) )
=> ( empty(relation_composition(X1,X2))
& relation(relation_composition(X1,X2)) ) ),
file('<stdin>',fc9_relat_1) ).
fof(c_0_52,axiom,
! [X1,X2] :
( ( relation(X1)
& function(X1) )
=> ( relation(relation_dom_restriction(X1,X2))
& function(relation_dom_restriction(X1,X2)) ) ),
file('<stdin>',fc4_funct_1) ).
fof(c_0_53,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(set_union2(X1,X2)) ),
file('<stdin>',fc2_relat_1) ).
fof(c_0_54,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(set_intersection2(X1,X2)) ),
file('<stdin>',fc1_relat_1) ).
fof(c_0_55,axiom,
! [X1,X2] :
( ( relation(X1)
& relation_empty_yielding(X1) )
=> ( relation(relation_dom_restriction(X1,X2))
& relation_empty_yielding(relation_dom_restriction(X1,X2)) ) ),
file('<stdin>',fc13_relat_1) ).
fof(c_0_56,axiom,
! [X1,X2] :
( ( empty(X1)
& relation(X2) )
=> ( empty(relation_composition(X2,X1))
& relation(relation_composition(X2,X1)) ) ),
file('<stdin>',fc10_relat_1) ).
fof(c_0_57,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(relation_composition(X1,X2)) ),
file('<stdin>',dt_k5_relat_1) ).
fof(c_0_58,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('<stdin>',t2_subset) ).
fof(c_0_59,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_60,axiom,
! [X1,X2] :
( proper_subset(X1,X2)
<=> ( subset(X1,X2)
& X1 != X2 ) ),
file('<stdin>',d8_xboole_0) ).
fof(c_0_61,axiom,
! [X1,X2] :
( relation(X2)
=> relation(relation_rng_restriction(X1,X2)) ),
file('<stdin>',dt_k8_relat_1) ).
fof(c_0_62,axiom,
! [X1,X2] :
( relation(X1)
=> relation(relation_dom_restriction(X1,X2)) ),
file('<stdin>',dt_k7_relat_1) ).
fof(c_0_63,axiom,
! [X1] :
( relation(X1)
=> relation_field(X1) = set_union2(relation_dom(X1),relation_rng(X1)) ),
file('<stdin>',d6_relat_1) ).
fof(c_0_64,axiom,
! [X1,X2] :
( in(X1,X2)
=> element(X1,X2) ),
file('<stdin>',t1_subset) ).
fof(c_0_65,axiom,
! [X1,X2] :
( disjoint(X1,X2)
=> disjoint(X2,X1) ),
file('<stdin>',symmetry_r1_xboole_0) ).
fof(c_0_66,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_intersection2(X1,X2) = empty_set ),
file('<stdin>',d7_xboole_0) ).
fof(c_0_67,axiom,
! [X1] :
( ( relation(X1)
& function(X1)
& one_to_one(X1) )
=> ( relation(relation_inverse(X1))
& function(relation_inverse(X1)) ) ),
file('<stdin>',fc3_funct_1) ).
fof(c_0_68,axiom,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
file('<stdin>',rc1_subset_1) ).
fof(c_0_69,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('<stdin>',t7_boole) ).
fof(c_0_70,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> function_inverse(X1) = relation_inverse(X1) ) ),
file('<stdin>',d9_funct_1) ).
fof(c_0_71,axiom,
! [X1] :
( ( ~ empty(X1)
& relation(X1) )
=> ~ empty(relation_rng(X1)) ),
file('<stdin>',fc6_relat_1) ).
fof(c_0_72,axiom,
! [X1] :
( ( ~ empty(X1)
& relation(X1) )
=> ~ empty(relation_dom(X1)) ),
file('<stdin>',fc5_relat_1) ).
fof(c_0_73,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('<stdin>',commutativity_k3_xboole_0) ).
fof(c_0_74,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('<stdin>',commutativity_k2_xboole_0) ).
fof(c_0_75,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('<stdin>',commutativity_k2_tarski) ).
fof(c_0_76,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2) ),
file('<stdin>',rc2_subset_1) ).
fof(c_0_77,axiom,
! [X1] : element(cast_to_subset(X1),powerset(X1)),
file('<stdin>',dt_k2_subset_1) ).
fof(c_0_78,axiom,
! [X1] :
( ( relation(X1)
& empty(X1)
& function(X1) )
=> ( relation(X1)
& function(X1)
& one_to_one(X1) ) ),
file('<stdin>',cc2_funct_1) ).
fof(c_0_79,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('<stdin>',d1_xboole_0) ).
fof(c_0_80,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( relation(function_inverse(X1))
& function(function_inverse(X1)) ) ),
file('<stdin>',dt_k2_funct_1) ).
fof(c_0_81,axiom,
! [X1,X2] : ~ proper_subset(X1,X1),
file('<stdin>',irreflexivity_r2_xboole_0) ).
fof(c_0_82,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('<stdin>',existence_m1_subset_1) ).
fof(c_0_83,axiom,
! [X1] :
( relation(X1)
=> relation_inverse(relation_inverse(X1)) = X1 ),
file('<stdin>',involutiveness_k4_relat_1) ).
fof(c_0_84,axiom,
! [X1] :
( empty(X1)
=> ( empty(relation_rng(X1))
& relation(relation_rng(X1)) ) ),
file('<stdin>',fc8_relat_1) ).
fof(c_0_85,axiom,
! [X1] :
( empty(X1)
=> ( empty(relation_dom(X1))
& relation(relation_dom(X1)) ) ),
file('<stdin>',fc7_relat_1) ).
fof(c_0_86,axiom,
! [X1] :
( empty(X1)
=> ( empty(relation_inverse(X1))
& relation(relation_inverse(X1)) ) ),
file('<stdin>',fc11_relat_1) ).
fof(c_0_87,axiom,
! [X1] :
( relation(X1)
=> relation(relation_inverse(X1)) ),
file('<stdin>',dt_k4_relat_1) ).
fof(c_0_88,axiom,
! [X1] : ~ empty(singleton(X1)),
file('<stdin>',fc2_subset_1) ).
fof(c_0_89,axiom,
! [X1] : ~ empty(powerset(X1)),
file('<stdin>',fc1_subset_1) ).
fof(c_0_90,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
file('<stdin>',t8_boole) ).
fof(c_0_91,axiom,
! [X1,X2] : set_intersection2(X1,X1) = X1,
file('<stdin>',idempotence_k3_xboole_0) ).
fof(c_0_92,axiom,
! [X1,X2] : set_union2(X1,X1) = X1,
file('<stdin>',idempotence_k2_xboole_0) ).
fof(c_0_93,axiom,
! [X1,X2] : subset(X1,X1),
file('<stdin>',reflexivity_r1_tarski) ).
fof(c_0_94,axiom,
! [X1] : set_difference(X1,empty_set) = X1,
file('<stdin>',t3_boole) ).
fof(c_0_95,axiom,
! [X1] : set_union2(X1,empty_set) = X1,
file('<stdin>',t1_boole) ).
fof(c_0_96,axiom,
! [X1] : set_difference(empty_set,X1) = empty_set,
file('<stdin>',t4_boole) ).
fof(c_0_97,axiom,
! [X1] : set_intersection2(X1,empty_set) = empty_set,
file('<stdin>',t2_boole) ).
fof(c_0_98,axiom,
! [X1] :
( empty(X1)
=> relation(X1) ),
file('<stdin>',cc1_relat_1) ).
fof(c_0_99,axiom,
! [X1] :
( empty(X1)
=> function(X1) ),
file('<stdin>',cc1_funct_1) ).
fof(c_0_100,axiom,
! [X1] :
( relation(identity_relation(X1))
& function(identity_relation(X1)) ),
file('<stdin>',fc2_funct_1) ).
fof(c_0_101,axiom,
! [X1] : relation(identity_relation(X1)),
file('<stdin>',dt_k6_relat_1) ).
fof(c_0_102,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('<stdin>',t6_boole) ).
fof(c_0_103,axiom,
! [X1] : cast_to_subset(X1) = X1,
file('<stdin>',d4_subset_1) ).
fof(c_0_104,axiom,
? [X1] : ~ empty(X1),
file('<stdin>',rc2_xboole_0) ).
fof(c_0_105,axiom,
? [X1] :
( ~ empty(X1)
& relation(X1) ),
file('<stdin>',rc2_relat_1) ).
fof(c_0_106,axiom,
? [X1] :
( relation(X1)
& relation_empty_yielding(X1) ),
file('<stdin>',rc3_relat_1) ).
fof(c_0_107,axiom,
? [X1] :
( relation(X1)
& function(X1)
& one_to_one(X1) ),
file('<stdin>',rc3_funct_1) ).
fof(c_0_108,axiom,
? [X1] :
( relation(X1)
& empty(X1)
& function(X1) ),
file('<stdin>',rc2_funct_1) ).
fof(c_0_109,axiom,
? [X1] : empty(X1),
file('<stdin>',rc1_xboole_0) ).
fof(c_0_110,axiom,
? [X1] :
( empty(X1)
& relation(X1) ),
file('<stdin>',rc1_relat_1) ).
fof(c_0_111,axiom,
? [X1] :
( relation(X1)
& function(X1) ),
file('<stdin>',rc1_funct_1) ).
fof(c_0_112,axiom,
( empty(empty_set)
& relation(empty_set) ),
file('<stdin>',fc4_relat_1) ).
fof(c_0_113,axiom,
empty(empty_set),
file('<stdin>',fc1_xboole_0) ).
fof(c_0_114,axiom,
( empty(empty_set)
& relation(empty_set)
& relation_empty_yielding(empty_set) ),
file('<stdin>',fc12_relat_1) ).
fof(c_0_115,axiom,
$true,
file('<stdin>',dt_m1_subset_1) ).
fof(c_0_116,axiom,
$true,
file('<stdin>',dt_k9_relat_1) ).
fof(c_0_117,axiom,
$true,
file('<stdin>',dt_k4_xboole_0) ).
fof(c_0_118,axiom,
$true,
file('<stdin>',dt_k4_tarski) ).
fof(c_0_119,axiom,
$true,
file('<stdin>',dt_k3_xboole_0) ).
fof(c_0_120,axiom,
$true,
file('<stdin>',dt_k3_tarski) ).
fof(c_0_121,axiom,
$true,
file('<stdin>',dt_k3_relat_1) ).
fof(c_0_122,axiom,
$true,
file('<stdin>',dt_k2_zfmisc_1) ).
fof(c_0_123,axiom,
$true,
file('<stdin>',dt_k2_xboole_0) ).
fof(c_0_124,axiom,
$true,
file('<stdin>',dt_k2_tarski) ).
fof(c_0_125,axiom,
$true,
file('<stdin>',dt_k2_relat_1) ).
fof(c_0_126,axiom,
$true,
file('<stdin>',dt_k1_zfmisc_1) ).
fof(c_0_127,axiom,
$true,
file('<stdin>',dt_k1_xboole_0) ).
fof(c_0_128,axiom,
$true,
file('<stdin>',dt_k1_tarski) ).
fof(c_0_129,axiom,
$true,
file('<stdin>',dt_k1_setfam_1) ).
fof(c_0_130,axiom,
$true,
file('<stdin>',dt_k1_relat_1) ).
fof(c_0_131,axiom,
$true,
file('<stdin>',dt_k1_funct_1) ).
fof(c_0_132,axiom,
$true,
file('<stdin>',dt_k10_relat_1) ).
fof(c_0_133,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ! [X3] :
( relation(X3)
=> ( X3 = relation_composition(X1,X2)
<=> ! [X4,X5] :
( in(ordered_pair(X4,X5),X3)
<=> ? [X6] :
( in(ordered_pair(X4,X6),X1)
& in(ordered_pair(X6,X5),X2) ) ) ) ) ) ),
c_0_0 ).
fof(c_0_134,axiom,
! [X1,X2] :
( relation(X2)
=> ! [X3] :
( relation(X3)
=> ( X3 = relation_rng_restriction(X1,X2)
<=> ! [X4,X5] :
( in(ordered_pair(X4,X5),X3)
<=> ( in(X5,X1)
& in(ordered_pair(X4,X5),X2) ) ) ) ) ),
c_0_1 ).
fof(c_0_135,axiom,
! [X1] :
( relation(X1)
=> ! [X2,X3] :
( relation(X3)
=> ( X3 = relation_dom_restriction(X1,X2)
<=> ! [X4,X5] :
( in(ordered_pair(X4,X5),X3)
<=> ( in(X4,X2)
& in(ordered_pair(X4,X5),X1) ) ) ) ) ),
c_0_2 ).
fof(c_0_136,axiom,
! [X1] :
( relation(X1)
=> ! [X2,X3] :
( X3 = relation_inverse_image(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(ordered_pair(X4,X5),X1)
& in(X5,X2) ) ) ) ),
c_0_3 ).
fof(c_0_137,axiom,
! [X1] :
( relation(X1)
=> ! [X2,X3] :
( X3 = relation_image(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(X5,X2) ) ) ) ),
c_0_4 ).
fof(c_0_138,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_5 ).
fof(c_0_139,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_6 ).
fof(c_0_140,axiom,
! [X1,X2,X3] :
( X3 = set_intersection2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& in(X4,X2) ) ) ),
c_0_7 ).
fof(c_0_141,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_8]) ).
fof(c_0_142,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( X2 = relation_inverse(X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> in(ordered_pair(X4,X3),X1) ) ) ) ),
c_0_9 ).
fof(c_0_143,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( X1 = X2
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X1)
<=> in(ordered_pair(X3,X4),X2) ) ) ) ),
c_0_10 ).
fof(c_0_144,axiom,
! [X1,X2,X3] :
( X3 = set_union2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
| in(X4,X2) ) ) ),
c_0_11 ).
fof(c_0_145,axiom,
! [X1,X2] :
( relation(X2)
=> ( X2 = identity_relation(X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(X3,X1)
& X3 = X4 ) ) ) ),
c_0_12 ).
fof(c_0_146,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
c_0_13 ).
fof(c_0_147,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_rng(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X4,X3),X1) ) ) ),
c_0_14 ).
fof(c_0_148,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_dom(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X3,X4),X1) ) ) ),
c_0_15 ).
fof(c_0_149,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( subset(X1,X2)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X1)
=> in(ordered_pair(X3,X4),X2) ) ) ) ),
c_0_16 ).
fof(c_0_150,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_17 ).
fof(c_0_151,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> element(subset_difference(X1,X2,X3),powerset(X1)) ),
c_0_18 ).
fof(c_0_152,axiom,
! [X1,X2] :
( X2 = union(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X3,X4)
& in(X4,X1) ) ) ),
c_0_19 ).
fof(c_0_153,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> subset_difference(X1,X2,X3) = set_difference(X2,X3) ),
c_0_20 ).
fof(c_0_154,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
<=> ! [X2,X3] :
( ( in(X2,relation_dom(X1))
& in(X3,relation_dom(X1))
& apply(X1,X2) = apply(X1,X3) )
=> X2 = X3 ) ) ),
c_0_21 ).
fof(c_0_155,axiom,
! [X1,X2] :
( X2 = powerset(X1)
<=> ! [X3] :
( in(X3,X2)
<=> subset(X3,X1) ) ),
c_0_22 ).
fof(c_0_156,axiom,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
<=> in(X3,X2) )
=> X1 = X2 ),
c_0_23 ).
fof(c_0_157,plain,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2,X3] :
( ( in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> in(ordered_pair(X2,X3),X1) ) )
& ( ~ in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> X3 = empty_set ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_24]) ).
fof(c_0_158,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> element(complements_of_subsets(X1,X2),powerset(powerset(X1))) ),
c_0_25 ).
fof(c_0_159,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> element(meet_of_subsets(X1,X2),powerset(X1)) ),
c_0_26 ).
fof(c_0_160,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> element(union_of_subsets(X1,X2),powerset(X1)) ),
c_0_27 ).
fof(c_0_161,axiom,
! [X1] :
( relation(X1)
<=> ! [X2] :
~ ( in(X2,X1)
& ! [X3,X4] : X2 != ordered_pair(X3,X4) ) ),
c_0_28 ).
fof(c_0_162,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_29]) ).
fof(c_0_163,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
c_0_30 ).
fof(c_0_164,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2 ),
c_0_31 ).
fof(c_0_165,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> element(subset_complement(X1,X2),powerset(X1)) ),
c_0_32 ).
fof(c_0_166,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
c_0_33 ).
fof(c_0_167,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,subset_complement(X1,X2)) = X2 ),
c_0_34 ).
fof(c_0_168,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> meet_of_subsets(X1,X2) = set_meet(X2) ),
c_0_35 ).
fof(c_0_169,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> union_of_subsets(X1,X2) = union(X2) ),
c_0_36 ).
fof(c_0_170,axiom,
! [X1,X2,X3] :
( ( in(X1,X2)
& element(X2,powerset(X3)) )
=> element(X1,X3) ),
c_0_37 ).
fof(c_0_171,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
c_0_38 ).
fof(c_0_172,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,X2) = set_difference(X1,X2) ),
c_0_39 ).
fof(c_0_173,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
c_0_40 ).
fof(c_0_174,axiom,
! [X1,X2] :
( ( relation(X1)
& function(X1)
& relation(X2)
& function(X2) )
=> ( relation(relation_composition(X1,X2))
& function(relation_composition(X1,X2)) ) ),
c_0_41 ).
fof(c_0_175,plain,
! [X1,X2] :
( ( ~ empty(X1)
& ~ empty(X2) )
=> ~ empty(cartesian_product2(X1,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_42]) ).
fof(c_0_176,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X2,X1)) ),
inference(fof_simplification,[status(thm)],[c_0_43]) ).
fof(c_0_177,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X1,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_44]) ).
fof(c_0_178,plain,
! [X1,X2] : ~ empty(unordered_pair(X1,X2)),
inference(fof_simplification,[status(thm)],[c_0_45]) ).
fof(c_0_179,plain,
! [X1,X2] : ~ empty(ordered_pair(X1,X2)),
inference(fof_simplification,[status(thm)],[c_0_46]) ).
fof(c_0_180,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
c_0_47 ).
fof(c_0_181,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
c_0_48 ).
fof(c_0_182,plain,
! [X1,X2] :
( proper_subset(X1,X2)
=> ~ proper_subset(X2,X1) ),
inference(fof_simplification,[status(thm)],[c_0_49]) ).
fof(c_0_183,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[c_0_50]) ).
fof(c_0_184,axiom,
! [X1,X2] :
( ( empty(X1)
& relation(X2) )
=> ( empty(relation_composition(X1,X2))
& relation(relation_composition(X1,X2)) ) ),
c_0_51 ).
fof(c_0_185,axiom,
! [X1,X2] :
( ( relation(X1)
& function(X1) )
=> ( relation(relation_dom_restriction(X1,X2))
& function(relation_dom_restriction(X1,X2)) ) ),
c_0_52 ).
fof(c_0_186,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(set_union2(X1,X2)) ),
c_0_53 ).
fof(c_0_187,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(set_intersection2(X1,X2)) ),
c_0_54 ).
fof(c_0_188,axiom,
! [X1,X2] :
( ( relation(X1)
& relation_empty_yielding(X1) )
=> ( relation(relation_dom_restriction(X1,X2))
& relation_empty_yielding(relation_dom_restriction(X1,X2)) ) ),
c_0_55 ).
fof(c_0_189,axiom,
! [X1,X2] :
( ( empty(X1)
& relation(X2) )
=> ( empty(relation_composition(X2,X1))
& relation(relation_composition(X2,X1)) ) ),
c_0_56 ).
fof(c_0_190,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(relation_composition(X1,X2)) ),
c_0_57 ).
fof(c_0_191,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
c_0_58 ).
fof(c_0_192,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_59]) ).
fof(c_0_193,axiom,
! [X1,X2] :
( proper_subset(X1,X2)
<=> ( subset(X1,X2)
& X1 != X2 ) ),
c_0_60 ).
fof(c_0_194,axiom,
! [X1,X2] :
( relation(X2)
=> relation(relation_rng_restriction(X1,X2)) ),
c_0_61 ).
fof(c_0_195,axiom,
! [X1,X2] :
( relation(X1)
=> relation(relation_dom_restriction(X1,X2)) ),
c_0_62 ).
fof(c_0_196,axiom,
! [X1] :
( relation(X1)
=> relation_field(X1) = set_union2(relation_dom(X1),relation_rng(X1)) ),
c_0_63 ).
fof(c_0_197,axiom,
! [X1,X2] :
( in(X1,X2)
=> element(X1,X2) ),
c_0_64 ).
fof(c_0_198,axiom,
! [X1,X2] :
( disjoint(X1,X2)
=> disjoint(X2,X1) ),
c_0_65 ).
fof(c_0_199,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_intersection2(X1,X2) = empty_set ),
c_0_66 ).
fof(c_0_200,axiom,
! [X1] :
( ( relation(X1)
& function(X1)
& one_to_one(X1) )
=> ( relation(relation_inverse(X1))
& function(relation_inverse(X1)) ) ),
c_0_67 ).
fof(c_0_201,plain,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
inference(fof_simplification,[status(thm)],[c_0_68]) ).
fof(c_0_202,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
c_0_69 ).
fof(c_0_203,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> function_inverse(X1) = relation_inverse(X1) ) ),
c_0_70 ).
fof(c_0_204,plain,
! [X1] :
( ( ~ empty(X1)
& relation(X1) )
=> ~ empty(relation_rng(X1)) ),
inference(fof_simplification,[status(thm)],[c_0_71]) ).
fof(c_0_205,plain,
! [X1] :
( ( ~ empty(X1)
& relation(X1) )
=> ~ empty(relation_dom(X1)) ),
inference(fof_simplification,[status(thm)],[c_0_72]) ).
fof(c_0_206,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
c_0_73 ).
fof(c_0_207,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
c_0_74 ).
fof(c_0_208,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
c_0_75 ).
fof(c_0_209,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2) ),
c_0_76 ).
fof(c_0_210,axiom,
! [X1] : element(cast_to_subset(X1),powerset(X1)),
c_0_77 ).
fof(c_0_211,axiom,
! [X1] :
( ( relation(X1)
& empty(X1)
& function(X1) )
=> ( relation(X1)
& function(X1)
& one_to_one(X1) ) ),
c_0_78 ).
fof(c_0_212,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[c_0_79]) ).
fof(c_0_213,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( relation(function_inverse(X1))
& function(function_inverse(X1)) ) ),
c_0_80 ).
fof(c_0_214,plain,
! [X1,X2] : ~ proper_subset(X1,X1),
inference(fof_simplification,[status(thm)],[c_0_81]) ).
fof(c_0_215,axiom,
! [X1] :
? [X2] : element(X2,X1),
c_0_82 ).
fof(c_0_216,axiom,
! [X1] :
( relation(X1)
=> relation_inverse(relation_inverse(X1)) = X1 ),
c_0_83 ).
fof(c_0_217,axiom,
! [X1] :
( empty(X1)
=> ( empty(relation_rng(X1))
& relation(relation_rng(X1)) ) ),
c_0_84 ).
fof(c_0_218,axiom,
! [X1] :
( empty(X1)
=> ( empty(relation_dom(X1))
& relation(relation_dom(X1)) ) ),
c_0_85 ).
fof(c_0_219,axiom,
! [X1] :
( empty(X1)
=> ( empty(relation_inverse(X1))
& relation(relation_inverse(X1)) ) ),
c_0_86 ).
fof(c_0_220,axiom,
! [X1] :
( relation(X1)
=> relation(relation_inverse(X1)) ),
c_0_87 ).
fof(c_0_221,plain,
! [X1] : ~ empty(singleton(X1)),
inference(fof_simplification,[status(thm)],[c_0_88]) ).
fof(c_0_222,plain,
! [X1] : ~ empty(powerset(X1)),
inference(fof_simplification,[status(thm)],[c_0_89]) ).
fof(c_0_223,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
c_0_90 ).
fof(c_0_224,axiom,
! [X1,X2] : set_intersection2(X1,X1) = X1,
c_0_91 ).
fof(c_0_225,axiom,
! [X1,X2] : set_union2(X1,X1) = X1,
c_0_92 ).
fof(c_0_226,axiom,
! [X1,X2] : subset(X1,X1),
c_0_93 ).
fof(c_0_227,axiom,
! [X1] : set_difference(X1,empty_set) = X1,
c_0_94 ).
fof(c_0_228,axiom,
! [X1] : set_union2(X1,empty_set) = X1,
c_0_95 ).
fof(c_0_229,axiom,
! [X1] : set_difference(empty_set,X1) = empty_set,
c_0_96 ).
fof(c_0_230,axiom,
! [X1] : set_intersection2(X1,empty_set) = empty_set,
c_0_97 ).
fof(c_0_231,axiom,
! [X1] :
( empty(X1)
=> relation(X1) ),
c_0_98 ).
fof(c_0_232,axiom,
! [X1] :
( empty(X1)
=> function(X1) ),
c_0_99 ).
fof(c_0_233,axiom,
! [X1] :
( relation(identity_relation(X1))
& function(identity_relation(X1)) ),
c_0_100 ).
fof(c_0_234,axiom,
! [X1] : relation(identity_relation(X1)),
c_0_101 ).
fof(c_0_235,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
c_0_102 ).
fof(c_0_236,axiom,
! [X1] : cast_to_subset(X1) = X1,
c_0_103 ).
fof(c_0_237,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[c_0_104]) ).
fof(c_0_238,plain,
? [X1] :
( ~ empty(X1)
& relation(X1) ),
inference(fof_simplification,[status(thm)],[c_0_105]) ).
fof(c_0_239,axiom,
? [X1] :
( relation(X1)
& relation_empty_yielding(X1) ),
c_0_106 ).
fof(c_0_240,axiom,
? [X1] :
( relation(X1)
& function(X1)
& one_to_one(X1) ),
c_0_107 ).
fof(c_0_241,axiom,
? [X1] :
( relation(X1)
& empty(X1)
& function(X1) ),
c_0_108 ).
fof(c_0_242,axiom,
? [X1] : empty(X1),
c_0_109 ).
fof(c_0_243,axiom,
? [X1] :
( empty(X1)
& relation(X1) ),
c_0_110 ).
fof(c_0_244,axiom,
? [X1] :
( relation(X1)
& function(X1) ),
c_0_111 ).
fof(c_0_245,axiom,
( empty(empty_set)
& relation(empty_set) ),
c_0_112 ).
fof(c_0_246,axiom,
empty(empty_set),
c_0_113 ).
fof(c_0_247,axiom,
( empty(empty_set)
& relation(empty_set)
& relation_empty_yielding(empty_set) ),
c_0_114 ).
fof(c_0_248,axiom,
$true,
c_0_115 ).
fof(c_0_249,axiom,
$true,
c_0_116 ).
fof(c_0_250,axiom,
$true,
c_0_117 ).
fof(c_0_251,axiom,
$true,
c_0_118 ).
fof(c_0_252,axiom,
$true,
c_0_119 ).
fof(c_0_253,axiom,
$true,
c_0_120 ).
fof(c_0_254,axiom,
$true,
c_0_121 ).
fof(c_0_255,axiom,
$true,
c_0_122 ).
fof(c_0_256,axiom,
$true,
c_0_123 ).
fof(c_0_257,axiom,
$true,
c_0_124 ).
fof(c_0_258,axiom,
$true,
c_0_125 ).
fof(c_0_259,axiom,
$true,
c_0_126 ).
fof(c_0_260,axiom,
$true,
c_0_127 ).
fof(c_0_261,axiom,
$true,
c_0_128 ).
fof(c_0_262,axiom,
$true,
c_0_129 ).
fof(c_0_263,axiom,
$true,
c_0_130 ).
fof(c_0_264,axiom,
$true,
c_0_131 ).
fof(c_0_265,axiom,
$true,
c_0_132 ).
fof(c_0_266,plain,
! [X7,X8,X9,X10,X11,X13,X14,X15,X18] :
( ( in(ordered_pair(X10,esk49_5(X7,X8,X9,X10,X11)),X7)
| ~ in(ordered_pair(X10,X11),X9)
| X9 != relation_composition(X7,X8)
| ~ relation(X9)
| ~ relation(X8)
| ~ relation(X7) )
& ( in(ordered_pair(esk49_5(X7,X8,X9,X10,X11),X11),X8)
| ~ in(ordered_pair(X10,X11),X9)
| X9 != relation_composition(X7,X8)
| ~ relation(X9)
| ~ relation(X8)
| ~ relation(X7) )
& ( ~ in(ordered_pair(X13,X15),X7)
| ~ in(ordered_pair(X15,X14),X8)
| in(ordered_pair(X13,X14),X9)
| X9 != relation_composition(X7,X8)
| ~ relation(X9)
| ~ relation(X8)
| ~ relation(X7) )
& ( ~ in(ordered_pair(esk50_3(X7,X8,X9),esk51_3(X7,X8,X9)),X9)
| ~ in(ordered_pair(esk50_3(X7,X8,X9),X18),X7)
| ~ in(ordered_pair(X18,esk51_3(X7,X8,X9)),X8)
| X9 = relation_composition(X7,X8)
| ~ relation(X9)
| ~ relation(X8)
| ~ relation(X7) )
& ( in(ordered_pair(esk50_3(X7,X8,X9),esk52_3(X7,X8,X9)),X7)
| in(ordered_pair(esk50_3(X7,X8,X9),esk51_3(X7,X8,X9)),X9)
| X9 = relation_composition(X7,X8)
| ~ relation(X9)
| ~ relation(X8)
| ~ relation(X7) )
& ( in(ordered_pair(esk52_3(X7,X8,X9),esk51_3(X7,X8,X9)),X8)
| in(ordered_pair(esk50_3(X7,X8,X9),esk51_3(X7,X8,X9)),X9)
| X9 = relation_composition(X7,X8)
| ~ relation(X9)
| ~ relation(X8)
| ~ relation(X7) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_133])])])])])]) ).
fof(c_0_267,plain,
! [X6,X7,X8,X9,X10,X11,X12] :
( ( in(X10,X6)
| ~ in(ordered_pair(X9,X10),X8)
| X8 != relation_rng_restriction(X6,X7)
| ~ relation(X8)
| ~ relation(X7) )
& ( in(ordered_pair(X9,X10),X7)
| ~ in(ordered_pair(X9,X10),X8)
| X8 != relation_rng_restriction(X6,X7)
| ~ relation(X8)
| ~ relation(X7) )
& ( ~ in(X12,X6)
| ~ in(ordered_pair(X11,X12),X7)
| in(ordered_pair(X11,X12),X8)
| X8 != relation_rng_restriction(X6,X7)
| ~ relation(X8)
| ~ relation(X7) )
& ( ~ in(ordered_pair(esk5_3(X6,X7,X8),esk6_3(X6,X7,X8)),X8)
| ~ in(esk6_3(X6,X7,X8),X6)
| ~ in(ordered_pair(esk5_3(X6,X7,X8),esk6_3(X6,X7,X8)),X7)
| X8 = relation_rng_restriction(X6,X7)
| ~ relation(X8)
| ~ relation(X7) )
& ( in(esk6_3(X6,X7,X8),X6)
| in(ordered_pair(esk5_3(X6,X7,X8),esk6_3(X6,X7,X8)),X8)
| X8 = relation_rng_restriction(X6,X7)
| ~ relation(X8)
| ~ relation(X7) )
& ( in(ordered_pair(esk5_3(X6,X7,X8),esk6_3(X6,X7,X8)),X7)
| in(ordered_pair(esk5_3(X6,X7,X8),esk6_3(X6,X7,X8)),X8)
| X8 = relation_rng_restriction(X6,X7)
| ~ relation(X8)
| ~ relation(X7) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_134])])])])])]) ).
fof(c_0_268,plain,
! [X6,X7,X8,X9,X10,X11,X12] :
( ( in(X9,X7)
| ~ in(ordered_pair(X9,X10),X8)
| X8 != relation_dom_restriction(X6,X7)
| ~ relation(X8)
| ~ relation(X6) )
& ( in(ordered_pair(X9,X10),X6)
| ~ in(ordered_pair(X9,X10),X8)
| X8 != relation_dom_restriction(X6,X7)
| ~ relation(X8)
| ~ relation(X6) )
& ( ~ in(X11,X7)
| ~ in(ordered_pair(X11,X12),X6)
| in(ordered_pair(X11,X12),X8)
| X8 != relation_dom_restriction(X6,X7)
| ~ relation(X8)
| ~ relation(X6) )
& ( ~ in(ordered_pair(esk3_3(X6,X7,X8),esk4_3(X6,X7,X8)),X8)
| ~ in(esk3_3(X6,X7,X8),X7)
| ~ in(ordered_pair(esk3_3(X6,X7,X8),esk4_3(X6,X7,X8)),X6)
| X8 = relation_dom_restriction(X6,X7)
| ~ relation(X8)
| ~ relation(X6) )
& ( in(esk3_3(X6,X7,X8),X7)
| in(ordered_pair(esk3_3(X6,X7,X8),esk4_3(X6,X7,X8)),X8)
| X8 = relation_dom_restriction(X6,X7)
| ~ relation(X8)
| ~ relation(X6) )
& ( in(ordered_pair(esk3_3(X6,X7,X8),esk4_3(X6,X7,X8)),X6)
| in(ordered_pair(esk3_3(X6,X7,X8),esk4_3(X6,X7,X8)),X8)
| X8 = relation_dom_restriction(X6,X7)
| ~ relation(X8)
| ~ relation(X6) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_135])])])])])]) ).
fof(c_0_269,plain,
! [X6,X7,X8,X9,X11,X12,X13,X14,X16] :
( ( in(ordered_pair(X9,esk10_4(X6,X7,X8,X9)),X6)
| ~ in(X9,X8)
| X8 != relation_inverse_image(X6,X7)
| ~ relation(X6) )
& ( in(esk10_4(X6,X7,X8,X9),X7)
| ~ in(X9,X8)
| X8 != relation_inverse_image(X6,X7)
| ~ relation(X6) )
& ( ~ in(ordered_pair(X11,X12),X6)
| ~ in(X12,X7)
| in(X11,X8)
| X8 != relation_inverse_image(X6,X7)
| ~ relation(X6) )
& ( ~ in(esk11_3(X6,X13,X14),X14)
| ~ in(ordered_pair(esk11_3(X6,X13,X14),X16),X6)
| ~ in(X16,X13)
| X14 = relation_inverse_image(X6,X13)
| ~ relation(X6) )
& ( in(ordered_pair(esk11_3(X6,X13,X14),esk12_3(X6,X13,X14)),X6)
| in(esk11_3(X6,X13,X14),X14)
| X14 = relation_inverse_image(X6,X13)
| ~ relation(X6) )
& ( in(esk12_3(X6,X13,X14),X13)
| in(esk11_3(X6,X13,X14),X14)
| X14 = relation_inverse_image(X6,X13)
| ~ relation(X6) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_136])])])])])]) ).
fof(c_0_270,plain,
! [X6,X7,X8,X9,X11,X12,X13,X14,X16] :
( ( in(ordered_pair(esk7_4(X6,X7,X8,X9),X9),X6)
| ~ in(X9,X8)
| X8 != relation_image(X6,X7)
| ~ relation(X6) )
& ( in(esk7_4(X6,X7,X8,X9),X7)
| ~ in(X9,X8)
| X8 != relation_image(X6,X7)
| ~ relation(X6) )
& ( ~ in(ordered_pair(X12,X11),X6)
| ~ in(X12,X7)
| in(X11,X8)
| X8 != relation_image(X6,X7)
| ~ relation(X6) )
& ( ~ in(esk8_3(X6,X13,X14),X14)
| ~ in(ordered_pair(X16,esk8_3(X6,X13,X14)),X6)
| ~ in(X16,X13)
| X14 = relation_image(X6,X13)
| ~ relation(X6) )
& ( in(ordered_pair(esk9_3(X6,X13,X14),esk8_3(X6,X13,X14)),X6)
| in(esk8_3(X6,X13,X14),X14)
| X14 = relation_image(X6,X13)
| ~ relation(X6) )
& ( in(esk9_3(X6,X13,X14),X13)
| in(esk8_3(X6,X13,X14),X14)
| X14 = relation_image(X6,X13)
| ~ relation(X6) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_137])])])])])]) ).
fof(c_0_271,plain,
! [X7,X8,X9,X10,X13,X14,X15,X16,X17,X18,X20,X21] :
( ( in(esk26_4(X7,X8,X9,X10),X7)
| ~ in(X10,X9)
| X9 != cartesian_product2(X7,X8) )
& ( in(esk27_4(X7,X8,X9,X10),X8)
| ~ in(X10,X9)
| X9 != cartesian_product2(X7,X8) )
& ( X10 = ordered_pair(esk26_4(X7,X8,X9,X10),esk27_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(esk28_3(X16,X17,X18),X18)
| ~ in(X20,X16)
| ~ in(X21,X17)
| esk28_3(X16,X17,X18) != ordered_pair(X20,X21)
| X18 = cartesian_product2(X16,X17) )
& ( in(esk29_3(X16,X17,X18),X16)
| in(esk28_3(X16,X17,X18),X18)
| X18 = cartesian_product2(X16,X17) )
& ( in(esk30_3(X16,X17,X18),X17)
| in(esk28_3(X16,X17,X18),X18)
| X18 = cartesian_product2(X16,X17) )
& ( esk28_3(X16,X17,X18) = ordered_pair(esk29_3(X16,X17,X18),esk30_3(X16,X17,X18))
| in(esk28_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_138])])])])])]) ).
fof(c_0_272,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(esk53_3(X5,X6,X7),powerset(X5))
| X7 = complements_of_subsets(X5,X6)
| ~ element(X7,powerset(powerset(X5)))
| ~ element(X6,powerset(powerset(X5))) )
& ( ~ in(esk53_3(X5,X6,X7),X7)
| ~ in(subset_complement(X5,esk53_3(X5,X6,X7)),X6)
| X7 = complements_of_subsets(X5,X6)
| ~ element(X7,powerset(powerset(X5)))
| ~ element(X6,powerset(powerset(X5))) )
& ( in(esk53_3(X5,X6,X7),X7)
| in(subset_complement(X5,esk53_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_139])])])])]) ).
fof(c_0_273,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(esk34_3(X10,X11,X12),X12)
| ~ in(esk34_3(X10,X11,X12),X10)
| ~ in(esk34_3(X10,X11,X12),X11)
| X12 = set_intersection2(X10,X11) )
& ( in(esk34_3(X10,X11,X12),X10)
| in(esk34_3(X10,X11,X12),X12)
| X12 = set_intersection2(X10,X11) )
& ( in(esk34_3(X10,X11,X12),X11)
| in(esk34_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_140])])])])])]) ).
fof(c_0_274,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(esk41_3(X10,X11,X12),X12)
| ~ in(esk41_3(X10,X11,X12),X10)
| in(esk41_3(X10,X11,X12),X11)
| X12 = set_difference(X10,X11) )
& ( in(esk41_3(X10,X11,X12),X10)
| in(esk41_3(X10,X11,X12),X12)
| X12 = set_difference(X10,X11) )
& ( ~ in(esk41_3(X10,X11,X12),X11)
| in(esk41_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_141])])])])])]) ).
fof(c_0_275,plain,
! [X5,X6,X7,X8,X9,X10] :
( ( ~ in(ordered_pair(X7,X8),X6)
| in(ordered_pair(X8,X7),X5)
| X6 != relation_inverse(X5)
| ~ relation(X6)
| ~ relation(X5) )
& ( ~ in(ordered_pair(X10,X9),X5)
| in(ordered_pair(X9,X10),X6)
| X6 != relation_inverse(X5)
| ~ relation(X6)
| ~ relation(X5) )
& ( ~ in(ordered_pair(esk45_2(X5,X6),esk46_2(X5,X6)),X6)
| ~ in(ordered_pair(esk46_2(X5,X6),esk45_2(X5,X6)),X5)
| X6 = relation_inverse(X5)
| ~ relation(X6)
| ~ relation(X5) )
& ( in(ordered_pair(esk45_2(X5,X6),esk46_2(X5,X6)),X6)
| in(ordered_pair(esk46_2(X5,X6),esk45_2(X5,X6)),X5)
| X6 = relation_inverse(X5)
| ~ relation(X6)
| ~ relation(X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_142])])])])])]) ).
fof(c_0_276,plain,
! [X5,X6,X7,X8,X9,X10] :
( ( ~ in(ordered_pair(X7,X8),X5)
| in(ordered_pair(X7,X8),X6)
| X5 != X6
| ~ relation(X6)
| ~ relation(X5) )
& ( ~ in(ordered_pair(X9,X10),X6)
| in(ordered_pair(X9,X10),X5)
| X5 != X6
| ~ relation(X6)
| ~ relation(X5) )
& ( ~ in(ordered_pair(esk22_2(X5,X6),esk23_2(X5,X6)),X5)
| ~ in(ordered_pair(esk22_2(X5,X6),esk23_2(X5,X6)),X6)
| X5 = X6
| ~ relation(X6)
| ~ relation(X5) )
& ( in(ordered_pair(esk22_2(X5,X6),esk23_2(X5,X6)),X5)
| in(ordered_pair(esk22_2(X5,X6),esk23_2(X5,X6)),X6)
| X5 = X6
| ~ relation(X6)
| ~ relation(X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_143])])])])])]) ).
fof(c_0_277,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(esk25_3(X10,X11,X12),X10)
| ~ in(esk25_3(X10,X11,X12),X12)
| X12 = set_union2(X10,X11) )
& ( ~ in(esk25_3(X10,X11,X12),X11)
| ~ in(esk25_3(X10,X11,X12),X12)
| X12 = set_union2(X10,X11) )
& ( in(esk25_3(X10,X11,X12),X12)
| in(esk25_3(X10,X11,X12),X10)
| in(esk25_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_144])])])])])]) ).
fof(c_0_278,plain,
! [X5,X6,X7,X8,X9,X10] :
( ( in(X7,X5)
| ~ in(ordered_pair(X7,X8),X6)
| X6 != identity_relation(X5)
| ~ relation(X6) )
& ( X7 = X8
| ~ in(ordered_pair(X7,X8),X6)
| X6 != identity_relation(X5)
| ~ relation(X6) )
& ( ~ in(X9,X5)
| X9 != X10
| in(ordered_pair(X9,X10),X6)
| X6 != identity_relation(X5)
| ~ relation(X6) )
& ( ~ in(ordered_pair(esk1_2(X5,X6),esk2_2(X5,X6)),X6)
| ~ in(esk1_2(X5,X6),X5)
| esk1_2(X5,X6) != esk2_2(X5,X6)
| X6 = identity_relation(X5)
| ~ relation(X6) )
& ( in(esk1_2(X5,X6),X5)
| in(ordered_pair(esk1_2(X5,X6),esk2_2(X5,X6)),X6)
| X6 = identity_relation(X5)
| ~ relation(X6) )
& ( esk1_2(X5,X6) = esk2_2(X5,X6)
| in(ordered_pair(esk1_2(X5,X6),esk2_2(X5,X6)),X6)
| X6 = identity_relation(X5)
| ~ relation(X6) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_145])])])])])]) ).
fof(c_0_279,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) )
& ( esk24_3(X10,X11,X12) != X10
| ~ in(esk24_3(X10,X11,X12),X12)
| X12 = unordered_pair(X10,X11) )
& ( esk24_3(X10,X11,X12) != X11
| ~ in(esk24_3(X10,X11,X12),X12)
| X12 = unordered_pair(X10,X11) )
& ( in(esk24_3(X10,X11,X12),X12)
| esk24_3(X10,X11,X12) = X10
| esk24_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_146])])])])])]) ).
fof(c_0_280,plain,
! [X5,X6,X7,X9,X10,X11,X13] :
( ( ~ in(X7,X6)
| in(ordered_pair(esk42_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(esk43_2(X5,X11),X11)
| ~ in(ordered_pair(X13,esk43_2(X5,X11)),X5)
| X11 = relation_rng(X5)
| ~ relation(X5) )
& ( in(esk43_2(X5,X11),X11)
| in(ordered_pair(esk44_2(X5,X11),esk43_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_147])])])])])]) ).
fof(c_0_281,plain,
! [X5,X6,X7,X9,X10,X11,X13] :
( ( ~ in(X7,X6)
| in(ordered_pair(X7,esk35_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(esk36_2(X5,X11),X11)
| ~ in(ordered_pair(esk36_2(X5,X11),X13),X5)
| X11 = relation_dom(X5)
| ~ relation(X5) )
& ( in(esk36_2(X5,X11),X11)
| in(ordered_pair(esk36_2(X5,X11),esk37_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_148])])])])])]) ).
fof(c_0_282,plain,
! [X5,X6,X7,X8] :
( ( ~ subset(X5,X6)
| ~ in(ordered_pair(X7,X8),X5)
| in(ordered_pair(X7,X8),X6)
| ~ relation(X6)
| ~ relation(X5) )
& ( in(ordered_pair(esk31_2(X5,X6),esk32_2(X5,X6)),X5)
| subset(X5,X6)
| ~ relation(X6)
| ~ relation(X5) )
& ( ~ in(ordered_pair(esk31_2(X5,X6),esk32_2(X5,X6)),X6)
| subset(X5,X6)
| ~ relation(X6)
| ~ relation(X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_149])])])])]) ).
fof(c_0_283,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(esk16_3(X5,X6,X9),X5)
| in(X9,X6)
| X6 != set_meet(X5)
| X5 = empty_set )
& ( ~ in(X9,esk16_3(X5,X6,X9))
| in(X9,X6)
| X6 != set_meet(X5)
| X5 = empty_set )
& ( in(esk18_2(X5,X11),X5)
| ~ in(esk17_2(X5,X11),X11)
| X11 = set_meet(X5)
| X5 = empty_set )
& ( ~ in(esk17_2(X5,X11),esk18_2(X5,X11))
| ~ in(esk17_2(X5,X11),X11)
| X11 = set_meet(X5)
| X5 = empty_set )
& ( in(esk17_2(X5,X11),X11)
| ~ in(X14,X5)
| in(esk17_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_150])])])])])]) ).
fof(c_0_284,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_151])]) ).
fof(c_0_285,plain,
! [X5,X6,X7,X9,X10,X11,X12,X14] :
( ( in(X7,esk38_3(X5,X6,X7))
| ~ in(X7,X6)
| X6 != union(X5) )
& ( in(esk38_3(X5,X6,X7),X5)
| ~ in(X7,X6)
| X6 != union(X5) )
& ( ~ in(X9,X10)
| ~ in(X10,X5)
| in(X9,X6)
| X6 != union(X5) )
& ( ~ in(esk39_2(X11,X12),X12)
| ~ in(esk39_2(X11,X12),X14)
| ~ in(X14,X11)
| X12 = union(X11) )
& ( in(esk39_2(X11,X12),esk40_2(X11,X12))
| in(esk39_2(X11,X12),X12)
| X12 = union(X11) )
& ( in(esk40_2(X11,X12),X11)
| in(esk39_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_152])])])])])]) ).
fof(c_0_286,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_153])]) ).
fof(c_0_287,plain,
! [X4,X5,X6] :
( ( ~ one_to_one(X4)
| ~ in(X5,relation_dom(X4))
| ~ in(X6,relation_dom(X4))
| apply(X4,X5) != apply(X4,X6)
| X5 = X6
| ~ relation(X4)
| ~ function(X4) )
& ( in(esk47_1(X4),relation_dom(X4))
| one_to_one(X4)
| ~ relation(X4)
| ~ function(X4) )
& ( in(esk48_1(X4),relation_dom(X4))
| one_to_one(X4)
| ~ relation(X4)
| ~ function(X4) )
& ( apply(X4,esk47_1(X4)) = apply(X4,esk48_1(X4))
| one_to_one(X4)
| ~ relation(X4)
| ~ function(X4) )
& ( esk47_1(X4) != esk48_1(X4)
| one_to_one(X4)
| ~ relation(X4)
| ~ function(X4) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_154])])])])]) ).
fof(c_0_288,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(esk21_2(X8,X9),X9)
| ~ subset(esk21_2(X8,X9),X8)
| X9 = powerset(X8) )
& ( in(esk21_2(X8,X9),X9)
| subset(esk21_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_155])])])])])]) ).
fof(c_0_289,plain,
! [X4,X5] :
( ( ~ in(esk65_2(X4,X5),X4)
| ~ in(esk65_2(X4,X5),X5)
| X4 = X5 )
& ( in(esk65_2(X4,X5),X4)
| in(esk65_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_156])])])]) ).
fof(c_0_290,plain,
! [X4,X5,X6,X7,X8,X9,X10] :
( ( X6 != apply(X4,X5)
| in(ordered_pair(X5,X6),X4)
| ~ in(X5,relation_dom(X4))
| ~ relation(X4)
| ~ function(X4) )
& ( ~ in(ordered_pair(X5,X7),X4)
| X7 = apply(X4,X5)
| ~ in(X5,relation_dom(X4))
| ~ relation(X4)
| ~ function(X4) )
& ( X9 != apply(X4,X8)
| X9 = empty_set
| in(X8,relation_dom(X4))
| ~ relation(X4)
| ~ function(X4) )
& ( X10 != empty_set
| X10 = apply(X4,X8)
| in(X8,relation_dom(X4))
| ~ relation(X4)
| ~ function(X4) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_157])])])])]) ).
fof(c_0_291,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_158])]) ).
fof(c_0_292,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_159])]) ).
fof(c_0_293,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_160])]) ).
fof(c_0_294,plain,
! [X5,X6,X9,X11,X12] :
( ( ~ relation(X5)
| ~ in(X6,X5)
| X6 = ordered_pair(esk13_2(X5,X6),esk14_2(X5,X6)) )
& ( in(esk15_1(X9),X9)
| relation(X9) )
& ( esk15_1(X9) != ordered_pair(X11,X12)
| relation(X9) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_161])])])])])]) ).
fof(c_0_295,plain,
! [X6,X8,X9,X10,X12,X13] :
( in(X6,esk66_1(X6))
& ( ~ in(X8,esk66_1(X6))
| ~ subset(X9,X8)
| in(X9,esk66_1(X6)) )
& ( in(esk67_2(X6,X10),esk66_1(X6))
| ~ in(X10,esk66_1(X6)) )
& ( ~ subset(X12,X10)
| in(X12,esk67_2(X6,X10))
| ~ in(X10,esk66_1(X6)) )
& ( ~ subset(X13,esk66_1(X6))
| are_equipotent(X13,esk66_1(X6))
| in(X13,esk66_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_162])])])])]) ).
fof(c_0_296,plain,
! [X4,X5,X6,X7,X8,X9] :
( ( ~ in(X6,X5)
| X6 = X4
| X5 != singleton(X4) )
& ( X7 != X4
| in(X7,X5)
| X5 != singleton(X4) )
& ( ~ in(esk19_2(X8,X9),X9)
| esk19_2(X8,X9) != X8
| X9 = singleton(X8) )
& ( in(esk19_2(X8,X9),X9)
| esk19_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_163])])])])])]) ).
fof(c_0_297,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_164])]) ).
fof(c_0_298,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_165])]) ).
fof(c_0_299,plain,
! [X4,X5,X6,X7,X8] :
( ( ~ subset(X4,X5)
| ~ in(X6,X4)
| in(X6,X5) )
& ( in(esk33_2(X7,X8),X7)
| subset(X7,X8) )
& ( ~ in(esk33_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_166])])])])])]) ).
fof(c_0_300,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_167])]) ).
fof(c_0_301,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_168])]) ).
fof(c_0_302,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_169])]) ).
fof(c_0_303,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_170])]) ).
fof(c_0_304,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_171])])])]) ).
fof(c_0_305,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_172])]) ).
fof(c_0_306,plain,
! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
inference(variable_rename,[status(thm)],[c_0_173]) ).
fof(c_0_307,plain,
! [X3,X4] :
( ( relation(relation_composition(X3,X4))
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X4)
| ~ function(X4) )
& ( function(relation_composition(X3,X4))
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X4)
| ~ function(X4) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_174])])]) ).
fof(c_0_308,plain,
! [X3,X4] :
( empty(X3)
| empty(X4)
| ~ empty(cartesian_product2(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_175])]) ).
fof(c_0_309,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_176])])])]) ).
fof(c_0_310,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_177])])])]) ).
fof(c_0_311,plain,
! [X3,X4] : ~ empty(unordered_pair(X3,X4)),
inference(variable_rename,[status(thm)],[c_0_178]) ).
fof(c_0_312,plain,
! [X3,X4] : ~ empty(ordered_pair(X3,X4)),
inference(variable_rename,[status(thm)],[c_0_179]) ).
fof(c_0_313,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_180])])])])]) ).
fof(c_0_314,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_181])])])]) ).
fof(c_0_315,plain,
! [X3,X4] :
( ~ proper_subset(X3,X4)
| ~ proper_subset(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_182])]) ).
fof(c_0_316,plain,
! [X3,X4] :
( ~ in(X3,X4)
| ~ in(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_183])]) ).
fof(c_0_317,plain,
! [X3,X4] :
( ( empty(relation_composition(X3,X4))
| ~ empty(X3)
| ~ relation(X4) )
& ( relation(relation_composition(X3,X4))
| ~ empty(X3)
| ~ relation(X4) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_184])])]) ).
fof(c_0_318,plain,
! [X3,X4,X5] :
( ( relation(relation_dom_restriction(X3,X4))
| ~ relation(X3)
| ~ function(X3) )
& ( function(relation_dom_restriction(X3,X5))
| ~ relation(X3)
| ~ function(X3) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_185])])])])]) ).
fof(c_0_319,plain,
! [X3,X4] :
( ~ relation(X3)
| ~ relation(X4)
| relation(set_union2(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_186])]) ).
fof(c_0_320,plain,
! [X3,X4] :
( ~ relation(X3)
| ~ relation(X4)
| relation(set_intersection2(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_187])]) ).
fof(c_0_321,plain,
! [X3,X4,X5] :
( ( relation(relation_dom_restriction(X3,X4))
| ~ relation(X3)
| ~ relation_empty_yielding(X3) )
& ( relation_empty_yielding(relation_dom_restriction(X3,X5))
| ~ relation(X3)
| ~ relation_empty_yielding(X3) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_188])])])])]) ).
fof(c_0_322,plain,
! [X3,X4] :
( ( empty(relation_composition(X4,X3))
| ~ empty(X3)
| ~ relation(X4) )
& ( relation(relation_composition(X4,X3))
| ~ empty(X3)
| ~ relation(X4) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_189])])]) ).
fof(c_0_323,plain,
! [X3,X4] :
( ~ relation(X3)
| ~ relation(X4)
| relation(relation_composition(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_190])]) ).
fof(c_0_324,plain,
! [X3,X4] :
( ~ element(X3,X4)
| empty(X4)
| in(X3,X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_191])]) ).
fof(c_0_325,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_192])])])])]) ).
fof(c_0_326,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_193])])])])]) ).
fof(c_0_327,plain,
! [X3,X4] :
( ~ relation(X4)
| relation(relation_rng_restriction(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_194])]) ).
fof(c_0_328,plain,
! [X3,X4] :
( ~ relation(X3)
| relation(relation_dom_restriction(X3,X4)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_195])])])]) ).
fof(c_0_329,plain,
! [X2] :
( ~ relation(X2)
| relation_field(X2) = set_union2(relation_dom(X2),relation_rng(X2)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_196])]) ).
fof(c_0_330,plain,
! [X3,X4] :
( ~ in(X3,X4)
| element(X3,X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_197])]) ).
fof(c_0_331,plain,
! [X3,X4] :
( ~ disjoint(X3,X4)
| disjoint(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_198])]) ).
fof(c_0_332,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_199])])])]) ).
fof(c_0_333,plain,
! [X2] :
( ( relation(relation_inverse(X2))
| ~ relation(X2)
| ~ function(X2)
| ~ one_to_one(X2) )
& ( function(relation_inverse(X2))
| ~ relation(X2)
| ~ function(X2)
| ~ one_to_one(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_200])])]) ).
fof(c_0_334,plain,
! [X3] :
( ( element(esk57_1(X3),powerset(X3))
| empty(X3) )
& ( ~ empty(esk57_1(X3))
| empty(X3) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_201])])])]) ).
fof(c_0_335,plain,
! [X3,X4] :
( ~ in(X3,X4)
| ~ empty(X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_202])]) ).
fof(c_0_336,plain,
! [X2] :
( ~ relation(X2)
| ~ function(X2)
| ~ one_to_one(X2)
| function_inverse(X2) = relation_inverse(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_203])]) ).
fof(c_0_337,plain,
! [X2] :
( empty(X2)
| ~ relation(X2)
| ~ empty(relation_rng(X2)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_204])]) ).
fof(c_0_338,plain,
! [X2] :
( empty(X2)
| ~ relation(X2)
| ~ empty(relation_dom(X2)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_205])]) ).
fof(c_0_339,plain,
! [X3,X4] : set_intersection2(X3,X4) = set_intersection2(X4,X3),
inference(variable_rename,[status(thm)],[c_0_206]) ).
fof(c_0_340,plain,
! [X3,X4] : set_union2(X3,X4) = set_union2(X4,X3),
inference(variable_rename,[status(thm)],[c_0_207]) ).
fof(c_0_341,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[c_0_208]) ).
fof(c_0_342,plain,
! [X3] :
( element(esk61_1(X3),powerset(X3))
& empty(esk61_1(X3)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_209])]) ).
fof(c_0_343,plain,
! [X2] : element(cast_to_subset(X2),powerset(X2)),
inference(variable_rename,[status(thm)],[c_0_210]) ).
fof(c_0_344,plain,
! [X2] :
( ( relation(X2)
| ~ relation(X2)
| ~ empty(X2)
| ~ function(X2) )
& ( function(X2)
| ~ relation(X2)
| ~ empty(X2)
| ~ function(X2) )
& ( one_to_one(X2)
| ~ relation(X2)
| ~ empty(X2)
| ~ function(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_211])])]) ).
fof(c_0_345,plain,
! [X3,X4,X5] :
( ( X3 != empty_set
| ~ in(X4,X3) )
& ( in(esk20_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_212])])])])]) ).
fof(c_0_346,plain,
! [X2] :
( ( relation(function_inverse(X2))
| ~ relation(X2)
| ~ function(X2) )
& ( function(function_inverse(X2))
| ~ relation(X2)
| ~ function(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_213])])]) ).
fof(c_0_347,plain,
! [X3,X4] : ~ proper_subset(X3,X3),
inference(variable_rename,[status(thm)],[c_0_214]) ).
fof(c_0_348,plain,
! [X3] : element(esk54_1(X3),X3),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_215])]) ).
fof(c_0_349,plain,
! [X2] :
( ~ relation(X2)
| relation_inverse(relation_inverse(X2)) = X2 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_216])]) ).
fof(c_0_350,plain,
! [X2] :
( ( empty(relation_rng(X2))
| ~ empty(X2) )
& ( relation(relation_rng(X2))
| ~ empty(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_217])])]) ).
fof(c_0_351,plain,
! [X2] :
( ( empty(relation_dom(X2))
| ~ empty(X2) )
& ( relation(relation_dom(X2))
| ~ empty(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_218])])]) ).
fof(c_0_352,plain,
! [X2] :
( ( empty(relation_inverse(X2))
| ~ empty(X2) )
& ( relation(relation_inverse(X2))
| ~ empty(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_219])])]) ).
fof(c_0_353,plain,
! [X2] :
( ~ relation(X2)
| relation(relation_inverse(X2)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_220])]) ).
fof(c_0_354,plain,
! [X2] : ~ empty(singleton(X2)),
inference(variable_rename,[status(thm)],[c_0_221]) ).
fof(c_0_355,plain,
! [X2] : ~ empty(powerset(X2)),
inference(variable_rename,[status(thm)],[c_0_222]) ).
fof(c_0_356,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_223])])])]) ).
fof(c_0_357,plain,
! [X3,X4] : set_intersection2(X3,X3) = X3,
inference(variable_rename,[status(thm)],[c_0_224]) ).
fof(c_0_358,plain,
! [X3,X4] : set_union2(X3,X3) = X3,
inference(variable_rename,[status(thm)],[c_0_225]) ).
fof(c_0_359,plain,
! [X3,X4] : subset(X3,X3),
inference(variable_rename,[status(thm)],[c_0_226]) ).
fof(c_0_360,plain,
! [X2] : set_difference(X2,empty_set) = X2,
inference(variable_rename,[status(thm)],[c_0_227]) ).
fof(c_0_361,plain,
! [X2] : set_union2(X2,empty_set) = X2,
inference(variable_rename,[status(thm)],[c_0_228]) ).
fof(c_0_362,plain,
! [X2] : set_difference(empty_set,X2) = empty_set,
inference(variable_rename,[status(thm)],[c_0_229]) ).
fof(c_0_363,plain,
! [X2] : set_intersection2(X2,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[c_0_230]) ).
fof(c_0_364,plain,
! [X2] :
( ~ empty(X2)
| relation(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_231])]) ).
fof(c_0_365,plain,
! [X2] :
( ~ empty(X2)
| function(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_232])]) ).
fof(c_0_366,plain,
! [X2,X3] :
( relation(identity_relation(X2))
& function(identity_relation(X3)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_233])])]) ).
fof(c_0_367,plain,
! [X2] : relation(identity_relation(X2)),
inference(variable_rename,[status(thm)],[c_0_234]) ).
fof(c_0_368,plain,
! [X2] :
( ~ empty(X2)
| X2 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_235])]) ).
fof(c_0_369,plain,
! [X2] : cast_to_subset(X2) = X2,
inference(variable_rename,[status(thm)],[c_0_236]) ).
fof(c_0_370,plain,
~ empty(esk62_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_237])]) ).
fof(c_0_371,plain,
( ~ empty(esk60_0)
& relation(esk60_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_238])]) ).
fof(c_0_372,plain,
( relation(esk64_0)
& relation_empty_yielding(esk64_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_239])]) ).
fof(c_0_373,plain,
( relation(esk63_0)
& function(esk63_0)
& one_to_one(esk63_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_240])]) ).
fof(c_0_374,plain,
( relation(esk59_0)
& empty(esk59_0)
& function(esk59_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_241])]) ).
fof(c_0_375,plain,
empty(esk58_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_242])]) ).
fof(c_0_376,plain,
( empty(esk56_0)
& relation(esk56_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_243])]) ).
fof(c_0_377,plain,
( relation(esk55_0)
& function(esk55_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_244])]) ).
fof(c_0_378,axiom,
( empty(empty_set)
& relation(empty_set) ),
c_0_245 ).
fof(c_0_379,axiom,
empty(empty_set),
c_0_246 ).
fof(c_0_380,axiom,
( empty(empty_set)
& relation(empty_set)
& relation_empty_yielding(empty_set) ),
c_0_247 ).
fof(c_0_381,axiom,
$true,
c_0_248 ).
fof(c_0_382,axiom,
$true,
c_0_249 ).
fof(c_0_383,axiom,
$true,
c_0_250 ).
fof(c_0_384,axiom,
$true,
c_0_251 ).
fof(c_0_385,axiom,
$true,
c_0_252 ).
fof(c_0_386,axiom,
$true,
c_0_253 ).
fof(c_0_387,axiom,
$true,
c_0_254 ).
fof(c_0_388,axiom,
$true,
c_0_255 ).
fof(c_0_389,axiom,
$true,
c_0_256 ).
fof(c_0_390,axiom,
$true,
c_0_257 ).
fof(c_0_391,axiom,
$true,
c_0_258 ).
fof(c_0_392,axiom,
$true,
c_0_259 ).
fof(c_0_393,axiom,
$true,
c_0_260 ).
fof(c_0_394,axiom,
$true,
c_0_261 ).
fof(c_0_395,axiom,
$true,
c_0_262 ).
fof(c_0_396,axiom,
$true,
c_0_263 ).
fof(c_0_397,axiom,
$true,
c_0_264 ).
fof(c_0_398,axiom,
$true,
c_0_265 ).
cnf(c_0_399,plain,
( in(ordered_pair(X4,esk49_5(X1,X2,X3,X4,X5)),X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X4,X5),X3) ),
inference(split_conjunct,[status(thm)],[c_0_266]) ).
cnf(c_0_400,plain,
( in(ordered_pair(esk49_5(X1,X2,X3,X4,X5),X5),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X4,X5),X3) ),
inference(split_conjunct,[status(thm)],[c_0_266]) ).
cnf(c_0_401,plain,
( X2 = relation_rng_restriction(X3,X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(esk5_3(X3,X1,X2),esk6_3(X3,X1,X2)),X1)
| ~ in(esk6_3(X3,X1,X2),X3)
| ~ in(ordered_pair(esk5_3(X3,X1,X2),esk6_3(X3,X1,X2)),X2) ),
inference(split_conjunct,[status(thm)],[c_0_267]) ).
cnf(c_0_402,plain,
( X2 = relation_dom_restriction(X1,X3)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(esk3_3(X1,X3,X2),esk4_3(X1,X3,X2)),X1)
| ~ in(esk3_3(X1,X3,X2),X3)
| ~ in(ordered_pair(esk3_3(X1,X3,X2),esk4_3(X1,X3,X2)),X2) ),
inference(split_conjunct,[status(thm)],[c_0_268]) ).
cnf(c_0_403,plain,
( X3 = relation_composition(X1,X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3)
| ~ in(ordered_pair(X4,esk51_3(X1,X2,X3)),X2)
| ~ in(ordered_pair(esk50_3(X1,X2,X3),X4),X1)
| ~ in(ordered_pair(esk50_3(X1,X2,X3),esk51_3(X1,X2,X3)),X3) ),
inference(split_conjunct,[status(thm)],[c_0_266]) ).
cnf(c_0_404,plain,
( in(ordered_pair(X4,esk10_4(X1,X3,X2,X4)),X1)
| ~ relation(X1)
| X2 != relation_inverse_image(X1,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_269]) ).
cnf(c_0_405,plain,
( in(ordered_pair(esk7_4(X1,X3,X2,X4),X4),X1)
| ~ relation(X1)
| X2 != relation_image(X1,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_270]) ).
cnf(c_0_406,plain,
( X4 = ordered_pair(esk26_4(X2,X3,X1,X4),esk27_4(X2,X3,X1,X4))
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_271]) ).
cnf(c_0_407,plain,
( X3 = relation_composition(X1,X2)
| in(ordered_pair(esk50_3(X1,X2,X3),esk51_3(X1,X2,X3)),X3)
| in(ordered_pair(esk50_3(X1,X2,X3),esk52_3(X1,X2,X3)),X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_266]) ).
cnf(c_0_408,plain,
( X3 = relation_composition(X1,X2)
| in(ordered_pair(esk50_3(X1,X2,X3),esk51_3(X1,X2,X3)),X3)
| in(ordered_pair(esk52_3(X1,X2,X3),esk51_3(X1,X2,X3)),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_266]) ).
cnf(c_0_409,plain,
( X2 = relation_rng_restriction(X3,X1)
| in(ordered_pair(esk5_3(X3,X1,X2),esk6_3(X3,X1,X2)),X2)
| in(ordered_pair(esk5_3(X3,X1,X2),esk6_3(X3,X1,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_267]) ).
cnf(c_0_410,plain,
( X2 = relation_dom_restriction(X1,X3)
| in(ordered_pair(esk3_3(X1,X3,X2),esk4_3(X1,X3,X2)),X2)
| in(ordered_pair(esk3_3(X1,X3,X2),esk4_3(X1,X3,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_268]) ).
cnf(c_0_411,plain,
( X3 = complements_of_subsets(X2,X1)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2)))
| ~ in(subset_complement(X2,esk53_3(X2,X1,X3)),X1)
| ~ in(esk53_3(X2,X1,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_272]) ).
cnf(c_0_412,plain,
( X2 = relation_inverse_image(X1,X3)
| ~ relation(X1)
| ~ in(X4,X3)
| ~ in(ordered_pair(esk11_3(X1,X3,X2),X4),X1)
| ~ in(esk11_3(X1,X3,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_269]) ).
cnf(c_0_413,plain,
( X2 = relation_image(X1,X3)
| ~ relation(X1)
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk8_3(X1,X3,X2)),X1)
| ~ in(esk8_3(X1,X3,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_270]) ).
cnf(c_0_414,plain,
( X2 = relation_rng_restriction(X3,X1)
| in(ordered_pair(esk5_3(X3,X1,X2),esk6_3(X3,X1,X2)),X2)
| in(esk6_3(X3,X1,X2),X3)
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_267]) ).
cnf(c_0_415,plain,
( X2 = relation_dom_restriction(X1,X3)
| in(ordered_pair(esk3_3(X1,X3,X2),esk4_3(X1,X3,X2)),X2)
| in(esk3_3(X1,X3,X2),X3)
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_268]) ).
cnf(c_0_416,plain,
( X2 = relation_inverse_image(X1,X3)
| in(esk11_3(X1,X3,X2),X2)
| in(ordered_pair(esk11_3(X1,X3,X2),esk12_3(X1,X3,X2)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_269]) ).
cnf(c_0_417,plain,
( X2 = relation_image(X1,X3)
| in(esk8_3(X1,X3,X2),X2)
| in(ordered_pair(esk9_3(X1,X3,X2),esk8_3(X1,X3,X2)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_270]) ).
cnf(c_0_418,plain,
( X1 = set_intersection2(X2,X3)
| ~ in(esk34_3(X2,X3,X1),X3)
| ~ in(esk34_3(X2,X3,X1),X2)
| ~ in(esk34_3(X2,X3,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_273]) ).
cnf(c_0_419,plain,
( in(esk10_4(X1,X3,X2,X4),X3)
| ~ relation(X1)
| X2 != relation_inverse_image(X1,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_269]) ).
cnf(c_0_420,plain,
( in(esk7_4(X1,X3,X2,X4),X3)
| ~ relation(X1)
| X2 != relation_image(X1,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_270]) ).
cnf(c_0_421,plain,
( in(esk26_4(X2,X3,X1,X4),X2)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_271]) ).
cnf(c_0_422,plain,
( in(esk27_4(X2,X3,X1,X4),X3)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_271]) ).
cnf(c_0_423,plain,
( X1 = set_difference(X2,X3)
| in(esk41_3(X2,X3,X1),X3)
| ~ in(esk41_3(X2,X3,X1),X2)
| ~ in(esk41_3(X2,X3,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_274]) ).
cnf(c_0_424,plain,
( X3 = complements_of_subsets(X2,X1)
| in(subset_complement(X2,esk53_3(X2,X1,X3)),X1)
| in(esk53_3(X2,X1,X3),X3)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_272]) ).
cnf(c_0_425,plain,
( X2 = relation_inverse(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(esk46_2(X1,X2),esk45_2(X1,X2)),X1)
| ~ in(ordered_pair(esk45_2(X1,X2),esk46_2(X1,X2)),X2) ),
inference(split_conjunct,[status(thm)],[c_0_275]) ).
cnf(c_0_426,plain,
( X1 = X2
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(esk22_2(X1,X2),esk23_2(X1,X2)),X2)
| ~ in(ordered_pair(esk22_2(X1,X2),esk23_2(X1,X2)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_276]) ).
cnf(c_0_427,plain,
( X1 = cartesian_product2(X2,X3)
| in(esk28_3(X2,X3,X1),X1)
| esk28_3(X2,X3,X1) = ordered_pair(esk29_3(X2,X3,X1),esk30_3(X2,X3,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_271]) ).
cnf(c_0_428,plain,
( X1 = set_union2(X2,X3)
| ~ in(esk25_3(X2,X3,X1),X1)
| ~ in(esk25_3(X2,X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_277]) ).
cnf(c_0_429,plain,
( X1 = set_union2(X2,X3)
| ~ in(esk25_3(X2,X3,X1),X1)
| ~ in(esk25_3(X2,X3,X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_277]) ).
cnf(c_0_430,plain,
( X1 = set_union2(X2,X3)
| in(esk25_3(X2,X3,X1),X3)
| in(esk25_3(X2,X3,X1),X2)
| in(esk25_3(X2,X3,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_277]) ).
cnf(c_0_431,plain,
( X1 = cartesian_product2(X2,X3)
| esk28_3(X2,X3,X1) != ordered_pair(X4,X5)
| ~ in(X5,X3)
| ~ in(X4,X2)
| ~ in(esk28_3(X2,X3,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_271]) ).
cnf(c_0_432,plain,
( X1 = identity_relation(X2)
| ~ relation(X1)
| esk1_2(X2,X1) != esk2_2(X2,X1)
| ~ in(esk1_2(X2,X1),X2)
| ~ in(ordered_pair(esk1_2(X2,X1),esk2_2(X2,X1)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_278]) ).
cnf(c_0_433,plain,
( X1 = set_difference(X2,X3)
| in(esk41_3(X2,X3,X1),X1)
| ~ in(esk41_3(X2,X3,X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_274]) ).
cnf(c_0_434,plain,
( X2 = relation_inverse(X1)
| in(ordered_pair(esk46_2(X1,X2),esk45_2(X1,X2)),X1)
| in(ordered_pair(esk45_2(X1,X2),esk46_2(X1,X2)),X2)
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_275]) ).
cnf(c_0_435,plain,
( X1 = X2
| in(ordered_pair(esk22_2(X1,X2),esk23_2(X1,X2)),X2)
| in(ordered_pair(esk22_2(X1,X2),esk23_2(X1,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_276]) ).
cnf(c_0_436,plain,
( X1 = unordered_pair(X2,X3)
| ~ in(esk24_3(X2,X3,X1),X1)
| esk24_3(X2,X3,X1) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_279]) ).
cnf(c_0_437,plain,
( X1 = unordered_pair(X2,X3)
| ~ in(esk24_3(X2,X3,X1),X1)
| esk24_3(X2,X3,X1) != X3 ),
inference(split_conjunct,[status(thm)],[c_0_279]) ).
cnf(c_0_438,plain,
( in(ordered_pair(esk42_3(X1,X2,X3),X3),X1)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_280]) ).
cnf(c_0_439,plain,
( in(ordered_pair(X3,esk35_3(X1,X2,X3)),X1)
| ~ relation(X1)
| X2 != relation_dom(X1)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_281]) ).
cnf(c_0_440,plain,
( X2 = relation_inverse_image(X1,X3)
| in(esk11_3(X1,X3,X2),X2)
| in(esk12_3(X1,X3,X2),X3)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_269]) ).
cnf(c_0_441,plain,
( X2 = relation_image(X1,X3)
| in(esk8_3(X1,X3,X2),X2)
| in(esk9_3(X1,X3,X2),X3)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_270]) ).
cnf(c_0_442,plain,
( X1 = set_difference(X2,X3)
| in(esk41_3(X2,X3,X1),X1)
| in(esk41_3(X2,X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_274]) ).
cnf(c_0_443,plain,
( X1 = set_intersection2(X2,X3)
| in(esk34_3(X2,X3,X1),X1)
| in(esk34_3(X2,X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_273]) ).
cnf(c_0_444,plain,
( X1 = set_intersection2(X2,X3)
| in(esk34_3(X2,X3,X1),X1)
| in(esk34_3(X2,X3,X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_273]) ).
cnf(c_0_445,plain,
( X1 = cartesian_product2(X2,X3)
| in(esk28_3(X2,X3,X1),X1)
| in(esk29_3(X2,X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_271]) ).
cnf(c_0_446,plain,
( X1 = cartesian_product2(X2,X3)
| in(esk28_3(X2,X3,X1),X1)
| in(esk30_3(X2,X3,X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_271]) ).
cnf(c_0_447,plain,
( subset(X1,X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(esk31_2(X1,X2),esk32_2(X1,X2)),X2) ),
inference(split_conjunct,[status(thm)],[c_0_282]) ).
cnf(c_0_448,plain,
( X1 = unordered_pair(X2,X3)
| esk24_3(X2,X3,X1) = X3
| esk24_3(X2,X3,X1) = X2
| in(esk24_3(X2,X3,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_279]) ).
cnf(c_0_449,plain,
( X3 = complements_of_subsets(X2,X1)
| element(esk53_3(X2,X1,X3),powerset(X2))
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_272]) ).
cnf(c_0_450,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_272]) ).
cnf(c_0_451,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_272]) ).
cnf(c_0_452,plain,
( X2 = relation_rng(X1)
| ~ relation(X1)
| ~ in(ordered_pair(X3,esk43_2(X1,X2)),X1)
| ~ in(esk43_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_280]) ).
cnf(c_0_453,plain,
( X2 = relation_dom(X1)
| ~ relation(X1)
| ~ in(ordered_pair(esk36_2(X1,X2),X3),X1)
| ~ in(esk36_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_281]) ).
cnf(c_0_454,plain,
( X1 = empty_set
| in(X3,X2)
| X2 != set_meet(X1)
| ~ in(X3,esk16_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_283]) ).
cnf(c_0_455,plain,
( in(ordered_pair(X4,X5),X3)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X6,X5),X2)
| ~ in(ordered_pair(X4,X6),X1) ),
inference(split_conjunct,[status(thm)],[c_0_266]) ).
cnf(c_0_456,plain,
( X2 = relation_rng(X1)
| in(ordered_pair(esk44_2(X1,X2),esk43_2(X1,X2)),X1)
| in(esk43_2(X1,X2),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_280]) ).
cnf(c_0_457,plain,
( X2 = relation_dom(X1)
| in(ordered_pair(esk36_2(X1,X2),esk37_2(X1,X2)),X1)
| in(esk36_2(X1,X2),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_281]) ).
cnf(c_0_458,plain,
( X1 = identity_relation(X2)
| in(ordered_pair(esk1_2(X2,X1),esk2_2(X2,X1)),X1)
| in(esk1_2(X2,X1),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_278]) ).
cnf(c_0_459,plain,
( element(subset_difference(X1,X2,X3),powerset(X1))
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_284]) ).
cnf(c_0_460,plain,
( X1 = identity_relation(X2)
| in(ordered_pair(esk1_2(X2,X1),esk2_2(X2,X1)),X1)
| esk1_2(X2,X1) = esk2_2(X2,X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_278]) ).
cnf(c_0_461,plain,
( X1 = empty_set
| X2 = set_meet(X1)
| ~ in(esk17_2(X1,X2),X2)
| ~ in(esk17_2(X1,X2),esk18_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_283]) ).
cnf(c_0_462,plain,
( subset(X1,X2)
| in(ordered_pair(esk31_2(X1,X2),esk32_2(X1,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_282]) ).
cnf(c_0_463,plain,
( in(ordered_pair(X4,X5),X2)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_rng_restriction(X3,X1)
| ~ in(ordered_pair(X4,X5),X1)
| ~ in(X5,X3) ),
inference(split_conjunct,[status(thm)],[c_0_267]) ).
cnf(c_0_464,plain,
( in(ordered_pair(X4,X5),X2)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_dom_restriction(X1,X3)
| ~ in(ordered_pair(X4,X5),X1)
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_268]) ).
cnf(c_0_465,plain,
( X1 = union(X2)
| ~ in(X3,X2)
| ~ in(esk39_2(X2,X1),X3)
| ~ in(esk39_2(X2,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_285]) ).
cnf(c_0_466,plain,
( in(X3,esk38_3(X2,X1,X3))
| X1 != union(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_285]) ).
cnf(c_0_467,plain,
( in(esk38_3(X2,X1,X3),X2)
| X1 != union(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_285]) ).
cnf(c_0_468,plain,
( X1 = empty_set
| in(X3,X2)
| in(esk16_3(X1,X2,X3),X1)
| X2 != set_meet(X1) ),
inference(split_conjunct,[status(thm)],[c_0_283]) ).
cnf(c_0_469,plain,
( in(ordered_pair(X4,X5),X1)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_rng_restriction(X3,X1)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(split_conjunct,[status(thm)],[c_0_267]) ).
cnf(c_0_470,plain,
( in(ordered_pair(X4,X5),X1)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_dom_restriction(X1,X3)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(split_conjunct,[status(thm)],[c_0_268]) ).
cnf(c_0_471,plain,
( in(ordered_pair(X3,X4),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(X3,X4),X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_282]) ).
cnf(c_0_472,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_286]) ).
cnf(c_0_473,plain,
( X2 = X3
| ~ function(X1)
| ~ relation(X1)
| apply(X1,X2) != apply(X1,X3)
| ~ in(X3,relation_dom(X1))
| ~ in(X2,relation_dom(X1))
| ~ one_to_one(X1) ),
inference(split_conjunct,[status(thm)],[c_0_287]) ).
cnf(c_0_474,plain,
( X1 = powerset(X2)
| ~ subset(esk21_2(X2,X1),X2)
| ~ in(esk21_2(X2,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_288]) ).
cnf(c_0_475,plain,
( in(X4,X2)
| ~ relation(X1)
| X2 != relation_inverse_image(X1,X3)
| ~ in(X5,X3)
| ~ in(ordered_pair(X4,X5),X1) ),
inference(split_conjunct,[status(thm)],[c_0_269]) ).
cnf(c_0_476,plain,
( in(X4,X2)
| ~ relation(X1)
| X2 != relation_image(X1,X3)
| ~ in(X5,X3)
| ~ in(ordered_pair(X5,X4),X1) ),
inference(split_conjunct,[status(thm)],[c_0_270]) ).
cnf(c_0_477,plain,
( X1 = X2
| ~ in(esk65_2(X1,X2),X2)
| ~ in(esk65_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_289]) ).
cnf(c_0_478,plain,
( in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_inverse(X1)
| ~ in(ordered_pair(X4,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_275]) ).
cnf(c_0_479,plain,
( in(ordered_pair(X3,X4),X2)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_inverse(X1)
| ~ in(ordered_pair(X4,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_275]) ).
cnf(c_0_480,plain,
( X3 = apply(X1,X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_dom(X1))
| ~ in(ordered_pair(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_290]) ).
cnf(c_0_481,plain,
( in(ordered_pair(X3,X4),X2)
| ~ relation(X1)
| ~ relation(X2)
| X1 != X2
| ~ in(ordered_pair(X3,X4),X1) ),
inference(split_conjunct,[status(thm)],[c_0_276]) ).
cnf(c_0_482,plain,
( in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ relation(X2)
| X1 != X2
| ~ in(ordered_pair(X3,X4),X2) ),
inference(split_conjunct,[status(thm)],[c_0_276]) ).
cnf(c_0_483,plain,
( in(X5,X3)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_rng_restriction(X3,X1)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(split_conjunct,[status(thm)],[c_0_267]) ).
cnf(c_0_484,plain,
( in(X4,X3)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_dom_restriction(X1,X3)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(split_conjunct,[status(thm)],[c_0_268]) ).
cnf(c_0_485,plain,
( X1 = union(X2)
| in(esk39_2(X2,X1),X1)
| in(esk39_2(X2,X1),esk40_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_285]) ).
cnf(c_0_486,plain,
( in(ordered_pair(X2,X3),X1)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_dom(X1))
| X3 != apply(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_290]) ).
cnf(c_0_487,plain,
( X1 = empty_set
| X2 = set_meet(X1)
| in(esk18_2(X1,X2),X1)
| ~ in(esk17_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_283]) ).
cnf(c_0_488,plain,
( X1 = empty_set
| X2 = set_meet(X1)
| in(esk17_2(X1,X2),X3)
| in(esk17_2(X1,X2),X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_283]) ).
cnf(c_0_489,plain,
( element(complements_of_subsets(X1,X2),powerset(powerset(X1)))
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_291]) ).
cnf(c_0_490,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_271]) ).
cnf(c_0_491,plain,
( element(meet_of_subsets(X1,X2),powerset(X1))
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_292]) ).
cnf(c_0_492,plain,
( element(union_of_subsets(X1,X2),powerset(X1))
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_293]) ).
cnf(c_0_493,plain,
( X1 = ordered_pair(esk13_2(X2,X1),esk14_2(X2,X1))
| ~ in(X1,X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_294]) ).
cnf(c_0_494,plain,
( in(X3,esk67_2(X2,X1))
| ~ in(X1,esk66_1(X2))
| ~ subset(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_295]) ).
cnf(c_0_495,plain,
( in(X3,X2)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(ordered_pair(X4,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_280]) ).
cnf(c_0_496,plain,
( in(X3,X2)
| ~ relation(X1)
| X2 != relation_dom(X1)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(split_conjunct,[status(thm)],[c_0_281]) ).
cnf(c_0_497,plain,
( in(X3,X2)
| ~ relation(X1)
| X1 != identity_relation(X2)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(split_conjunct,[status(thm)],[c_0_278]) ).
cnf(c_0_498,plain,
( X1 = singleton(X2)
| esk19_2(X2,X1) != X2
| ~ in(esk19_2(X2,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_296]) ).
cnf(c_0_499,plain,
( complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_297]) ).
cnf(c_0_500,plain,
( X1 = union(X2)
| in(esk39_2(X2,X1),X1)
| in(esk40_2(X2,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_285]) ).
cnf(c_0_501,plain,
( X1 = powerset(X2)
| subset(esk21_2(X2,X1),X2)
| in(esk21_2(X2,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_288]) ).
cnf(c_0_502,plain,
( in(X4,X1)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_273]) ).
cnf(c_0_503,plain,
( X1 = X2
| in(esk65_2(X1,X2),X2)
| in(esk65_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_289]) ).
cnf(c_0_504,plain,
( in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| X1 != identity_relation(X2)
| X3 != X4
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_278]) ).
cnf(c_0_505,plain,
( X3 = X4
| ~ relation(X1)
| X1 != identity_relation(X2)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(split_conjunct,[status(thm)],[c_0_278]) ).
cnf(c_0_506,plain,
( in(esk67_2(X2,X1),esk66_1(X2))
| ~ in(X1,esk66_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_295]) ).
cnf(c_0_507,plain,
( element(subset_complement(X1,X2),powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_298]) ).
cnf(c_0_508,plain,
( subset(X1,X2)
| ~ in(esk33_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_299]) ).
cnf(c_0_509,plain,
( in(X1,esk66_1(X2))
| ~ subset(X1,X3)
| ~ in(X3,esk66_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_295]) ).
cnf(c_0_510,plain,
( in(X4,X1)
| in(X4,X3)
| X1 != set_difference(X2,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_274]) ).
cnf(c_0_511,plain,
( in(X4,X3)
| in(X4,X2)
| X1 != set_union2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_277]) ).
cnf(c_0_512,plain,
( in(X1,esk66_1(X2))
| are_equipotent(X1,esk66_1(X2))
| ~ subset(X1,esk66_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_295]) ).
cnf(c_0_513,plain,
( subset_complement(X1,subset_complement(X1,X2)) = X2
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_300]) ).
cnf(c_0_514,plain,
( X1 = empty_set
| in(X3,X4)
| X2 != set_meet(X1)
| ~ in(X4,X1)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_283]) ).
cnf(c_0_515,plain,
( meet_of_subsets(X1,X2) = set_meet(X2)
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_301]) ).
cnf(c_0_516,plain,
( union_of_subsets(X1,X2) = union(X2)
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_302]) ).
cnf(c_0_517,plain,
( element(X1,X2)
| ~ element(X3,powerset(X2))
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_303]) ).
cnf(c_0_518,plain,
( X1 != set_difference(X2,X3)
| ~ in(X4,X1)
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_274]) ).
cnf(c_0_519,plain,
( in(X3,X1)
| X1 != union(X2)
| ~ in(X4,X2)
| ~ in(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_285]) ).
cnf(c_0_520,plain,
( ~ empty(X1)
| ~ element(X2,powerset(X1))
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_304]) ).
cnf(c_0_521,plain,
( in(X4,X2)
| X1 != set_difference(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_274]) ).
cnf(c_0_522,plain,
( in(X4,X2)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_273]) ).
cnf(c_0_523,plain,
( in(X4,X3)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_273]) ).
cnf(c_0_524,plain,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_277]) ).
cnf(c_0_525,plain,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_277]) ).
cnf(c_0_526,plain,
( X1 = singleton(X2)
| esk19_2(X2,X1) = X2
| in(esk19_2(X2,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_296]) ).
cnf(c_0_527,plain,
( subset_complement(X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_305]) ).
cnf(c_0_528,plain,
( in(X2,relation_dom(X1))
| X3 = empty_set
| ~ function(X1)
| ~ relation(X1)
| X3 != apply(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_290]) ).
cnf(c_0_529,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_306]) ).
cnf(c_0_530,plain,
( in(X1,X2)
| ~ in(X1,X3)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_299]) ).
cnf(c_0_531,plain,
( one_to_one(X1)
| apply(X1,esk47_1(X1)) = apply(X1,esk48_1(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_287]) ).
cnf(c_0_532,plain,
( relation(relation_composition(X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_307]) ).
cnf(c_0_533,plain,
( function(relation_composition(X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_307]) ).
cnf(c_0_534,plain,
( empty(X2)
| empty(X1)
| ~ empty(cartesian_product2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_308]) ).
cnf(c_0_535,plain,
( subset(X1,X2)
| in(esk33_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_299]) ).
cnf(c_0_536,plain,
( in(X2,relation_dom(X1))
| X3 = apply(X1,X2)
| ~ function(X1)
| ~ relation(X1)
| X3 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_290]) ).
cnf(c_0_537,plain,
( empty(X2)
| ~ empty(set_union2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_309]) ).
cnf(c_0_538,plain,
( empty(X1)
| ~ empty(set_union2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_310]) ).
cnf(c_0_539,plain,
( X4 = X3
| X4 = X2
| X1 != unordered_pair(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_279]) ).
cnf(c_0_540,plain,
~ empty(unordered_pair(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_311]) ).
cnf(c_0_541,plain,
~ empty(ordered_pair(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_312]) ).
cnf(c_0_542,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_313]) ).
cnf(c_0_543,plain,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_314]) ).
cnf(c_0_544,plain,
( one_to_one(X1)
| in(esk47_1(X1),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_287]) ).
cnf(c_0_545,plain,
( one_to_one(X1)
| in(esk48_1(X1),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_287]) ).
cnf(c_0_546,plain,
( subset(X3,X2)
| X1 != powerset(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_288]) ).
cnf(c_0_547,plain,
( in(X3,X1)
| X1 != powerset(X2)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_288]) ).
cnf(c_0_548,plain,
( ~ proper_subset(X1,X2)
| ~ proper_subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_315]) ).
cnf(c_0_549,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_316]) ).
cnf(c_0_550,plain,
( empty(relation_composition(X2,X1))
| ~ relation(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_317]) ).
cnf(c_0_551,plain,
( relation(relation_composition(X2,X1))
| ~ relation(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_317]) ).
cnf(c_0_552,plain,
( relation(relation_dom_restriction(X1,X2))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_318]) ).
cnf(c_0_553,plain,
( function(relation_dom_restriction(X1,X2))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_318]) ).
cnf(c_0_554,plain,
( relation(set_union2(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_319]) ).
cnf(c_0_555,plain,
( relation(set_intersection2(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_320]) ).
cnf(c_0_556,plain,
( relation(relation_dom_restriction(X1,X2))
| ~ relation_empty_yielding(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_321]) ).
cnf(c_0_557,plain,
( relation_empty_yielding(relation_dom_restriction(X1,X2))
| ~ relation_empty_yielding(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_321]) ).
cnf(c_0_558,plain,
( empty(relation_composition(X1,X2))
| ~ relation(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_322]) ).
cnf(c_0_559,plain,
( relation(relation_composition(X1,X2))
| ~ relation(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_322]) ).
cnf(c_0_560,plain,
( relation(relation_composition(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_323]) ).
cnf(c_0_561,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_314]) ).
cnf(c_0_562,plain,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_279]) ).
cnf(c_0_563,plain,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_279]) ).
cnf(c_0_564,plain,
( in(X1,X2)
| empty(X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_324]) ).
cnf(c_0_565,plain,
( empty(X1)
| in(X2,X1)
| ~ element(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_325]) ).
cnf(c_0_566,plain,
( empty(X1)
| element(X2,X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_325]) ).
cnf(c_0_567,plain,
( proper_subset(X1,X2)
| X1 = X2
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_326]) ).
cnf(c_0_568,plain,
( relation(relation_rng_restriction(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_327]) ).
cnf(c_0_569,plain,
( relation(relation_dom_restriction(X1,X2))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_328]) ).
cnf(c_0_570,plain,
( relation_field(X1) = set_union2(relation_dom(X1),relation_rng(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_329]) ).
cnf(c_0_571,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_330]) ).
cnf(c_0_572,plain,
( disjoint(X1,X2)
| ~ disjoint(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_331]) ).
cnf(c_0_573,plain,
( subset(X1,X2)
| ~ proper_subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_326]) ).
cnf(c_0_574,plain,
( set_intersection2(X1,X2) = empty_set
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_332]) ).
cnf(c_0_575,plain,
( disjoint(X1,X2)
| set_intersection2(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_332]) ).
cnf(c_0_576,plain,
( empty(X2)
| ~ empty(X1)
| ~ element(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_325]) ).
cnf(c_0_577,plain,
( X3 = X2
| X1 != singleton(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_296]) ).
cnf(c_0_578,plain,
( relation(X1)
| esk15_1(X1) != ordered_pair(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_294]) ).
cnf(c_0_579,plain,
( relation(relation_inverse(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_333]) ).
cnf(c_0_580,plain,
( function(relation_inverse(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_333]) ).
cnf(c_0_581,plain,
( one_to_one(X1)
| ~ function(X1)
| ~ relation(X1)
| esk47_1(X1) != esk48_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_287]) ).
cnf(c_0_582,plain,
( empty(X1)
| element(esk57_1(X1),powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_334]) ).
cnf(c_0_583,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_335]) ).
cnf(c_0_584,plain,
( function_inverse(X1) = relation_inverse(X1)
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_336]) ).
cnf(c_0_585,plain,
( element(X2,X1)
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_325]) ).
cnf(c_0_586,plain,
( empty(X1)
| ~ empty(relation_rng(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_337]) ).
cnf(c_0_587,plain,
( empty(X1)
| ~ empty(relation_dom(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_338]) ).
cnf(c_0_588,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_339]) ).
cnf(c_0_589,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_340]) ).
cnf(c_0_590,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_341]) ).
cnf(c_0_591,plain,
element(esk61_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_342]) ).
cnf(c_0_592,plain,
element(cast_to_subset(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_343]) ).
cnf(c_0_593,plain,
( in(X3,X1)
| X1 != singleton(X2)
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_296]) ).
cnf(c_0_594,plain,
( ~ proper_subset(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_326]) ).
cnf(c_0_595,plain,
( relation(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_344]) ).
cnf(c_0_596,plain,
( function(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_344]) ).
cnf(c_0_597,plain,
( one_to_one(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_344]) ).
cnf(c_0_598,plain,
( ~ in(X1,X2)
| X2 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_345]) ).
cnf(c_0_599,plain,
( relation(X1)
| in(esk15_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_294]) ).
cnf(c_0_600,plain,
( relation(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_346]) ).
cnf(c_0_601,plain,
( function(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_346]) ).
cnf(c_0_602,plain,
~ proper_subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_347]) ).
cnf(c_0_603,plain,
( X1 = empty_set
| in(esk20_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_345]) ).
cnf(c_0_604,plain,
( empty(X1)
| ~ empty(esk57_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_334]) ).
cnf(c_0_605,plain,
in(X1,esk66_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_295]) ).
cnf(c_0_606,plain,
element(esk54_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_348]) ).
cnf(c_0_607,plain,
( relation_inverse(relation_inverse(X1)) = X1
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_349]) ).
cnf(c_0_608,plain,
( subset(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_313]) ).
cnf(c_0_609,plain,
( subset(X2,X1)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_313]) ).
cnf(c_0_610,plain,
( empty(relation_rng(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_350]) ).
cnf(c_0_611,plain,
( relation(relation_rng(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_350]) ).
cnf(c_0_612,plain,
( empty(relation_dom(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_351]) ).
cnf(c_0_613,plain,
( relation(relation_dom(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_351]) ).
cnf(c_0_614,plain,
( empty(relation_inverse(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_352]) ).
cnf(c_0_615,plain,
( relation(relation_inverse(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_352]) ).
cnf(c_0_616,plain,
( relation(relation_inverse(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_353]) ).
cnf(c_0_617,plain,
~ empty(singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_354]) ).
cnf(c_0_618,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_355]) ).
cnf(c_0_619,plain,
( X2 = X1
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_356]) ).
cnf(c_0_620,plain,
set_intersection2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_621,plain,
set_union2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_358]) ).
cnf(c_0_622,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_623,plain,
set_difference(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_360]) ).
cnf(c_0_624,plain,
set_union2(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_361]) ).
cnf(c_0_625,plain,
set_difference(empty_set,X1) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_362]) ).
cnf(c_0_626,plain,
set_intersection2(X1,empty_set) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_363]) ).
cnf(c_0_627,plain,
( X2 = empty_set
| X1 != empty_set
| X2 != set_meet(X1) ),
inference(split_conjunct,[status(thm)],[c_0_283]) ).
cnf(c_0_628,plain,
( relation(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_364]) ).
cnf(c_0_629,plain,
( function(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_365]) ).
cnf(c_0_630,plain,
empty(esk61_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_342]) ).
cnf(c_0_631,plain,
relation(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_366]) ).
cnf(c_0_632,plain,
function(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_366]) ).
cnf(c_0_633,plain,
relation(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_367]) ).
cnf(c_0_634,plain,
( X2 = set_meet(X1)
| X1 != empty_set
| X2 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_283]) ).
cnf(c_0_635,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_368]) ).
cnf(c_0_636,plain,
cast_to_subset(X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_369]) ).
cnf(c_0_637,plain,
~ empty(esk62_0),
inference(split_conjunct,[status(thm)],[c_0_370]) ).
cnf(c_0_638,plain,
~ empty(esk60_0),
inference(split_conjunct,[status(thm)],[c_0_371]) ).
cnf(c_0_639,plain,
relation(esk64_0),
inference(split_conjunct,[status(thm)],[c_0_372]) ).
cnf(c_0_640,plain,
relation_empty_yielding(esk64_0),
inference(split_conjunct,[status(thm)],[c_0_372]) ).
cnf(c_0_641,plain,
relation(esk63_0),
inference(split_conjunct,[status(thm)],[c_0_373]) ).
cnf(c_0_642,plain,
function(esk63_0),
inference(split_conjunct,[status(thm)],[c_0_373]) ).
cnf(c_0_643,plain,
one_to_one(esk63_0),
inference(split_conjunct,[status(thm)],[c_0_373]) ).
cnf(c_0_644,plain,
relation(esk60_0),
inference(split_conjunct,[status(thm)],[c_0_371]) ).
cnf(c_0_645,plain,
relation(esk59_0),
inference(split_conjunct,[status(thm)],[c_0_374]) ).
cnf(c_0_646,plain,
empty(esk59_0),
inference(split_conjunct,[status(thm)],[c_0_374]) ).
cnf(c_0_647,plain,
function(esk59_0),
inference(split_conjunct,[status(thm)],[c_0_374]) ).
cnf(c_0_648,plain,
empty(esk58_0),
inference(split_conjunct,[status(thm)],[c_0_375]) ).
cnf(c_0_649,plain,
empty(esk56_0),
inference(split_conjunct,[status(thm)],[c_0_376]) ).
cnf(c_0_650,plain,
relation(esk56_0),
inference(split_conjunct,[status(thm)],[c_0_376]) ).
cnf(c_0_651,plain,
relation(esk55_0),
inference(split_conjunct,[status(thm)],[c_0_377]) ).
cnf(c_0_652,plain,
function(esk55_0),
inference(split_conjunct,[status(thm)],[c_0_377]) ).
cnf(c_0_653,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[c_0_378]) ).
cnf(c_0_654,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[c_0_378]) ).
cnf(c_0_655,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[c_0_379]) ).
cnf(c_0_656,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[c_0_380]) ).
cnf(c_0_657,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[c_0_380]) ).
cnf(c_0_658,plain,
relation_empty_yielding(empty_set),
inference(split_conjunct,[status(thm)],[c_0_380]) ).
cnf(c_0_659,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_381]) ).
cnf(c_0_660,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_382]) ).
cnf(c_0_661,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_662,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_384]) ).
cnf(c_0_663,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_385]) ).
cnf(c_0_664,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_386]) ).
cnf(c_0_665,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_387]) ).
cnf(c_0_666,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_388]) ).
cnf(c_0_667,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_389]) ).
cnf(c_0_668,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_390]) ).
cnf(c_0_669,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_670,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_392]) ).
cnf(c_0_671,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_393]) ).
cnf(c_0_672,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_394]) ).
cnf(c_0_673,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_395]) ).
cnf(c_0_674,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_396]) ).
cnf(c_0_675,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_397]) ).
cnf(c_0_676,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_398]) ).
cnf(c_0_677,plain,
( in(ordered_pair(X4,esk49_5(X1,X2,X3,X4,X5)),X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X4,X5),X3) ),
c_0_399,
[final] ).
cnf(c_0_678,plain,
( in(ordered_pair(esk49_5(X1,X2,X3,X4,X5),X5),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X4,X5),X3) ),
c_0_400,
[final] ).
cnf(c_0_679,plain,
( X2 = relation_rng_restriction(X3,X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(esk5_3(X3,X1,X2),esk6_3(X3,X1,X2)),X1)
| ~ in(esk6_3(X3,X1,X2),X3)
| ~ in(ordered_pair(esk5_3(X3,X1,X2),esk6_3(X3,X1,X2)),X2) ),
c_0_401,
[final] ).
cnf(c_0_680,plain,
( X2 = relation_dom_restriction(X1,X3)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(esk3_3(X1,X3,X2),esk4_3(X1,X3,X2)),X1)
| ~ in(esk3_3(X1,X3,X2),X3)
| ~ in(ordered_pair(esk3_3(X1,X3,X2),esk4_3(X1,X3,X2)),X2) ),
c_0_402,
[final] ).
cnf(c_0_681,plain,
( X3 = relation_composition(X1,X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3)
| ~ in(ordered_pair(X4,esk51_3(X1,X2,X3)),X2)
| ~ in(ordered_pair(esk50_3(X1,X2,X3),X4),X1)
| ~ in(ordered_pair(esk50_3(X1,X2,X3),esk51_3(X1,X2,X3)),X3) ),
c_0_403,
[final] ).
cnf(c_0_682,plain,
( in(ordered_pair(X4,esk10_4(X1,X3,X2,X4)),X1)
| ~ relation(X1)
| X2 != relation_inverse_image(X1,X3)
| ~ in(X4,X2) ),
c_0_404,
[final] ).
cnf(c_0_683,plain,
( in(ordered_pair(esk7_4(X1,X3,X2,X4),X4),X1)
| ~ relation(X1)
| X2 != relation_image(X1,X3)
| ~ in(X4,X2) ),
c_0_405,
[final] ).
cnf(c_0_684,plain,
( ordered_pair(esk26_4(X2,X3,X1,X4),esk27_4(X2,X3,X1,X4)) = X4
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
c_0_406,
[final] ).
cnf(c_0_685,plain,
( X3 = relation_composition(X1,X2)
| in(ordered_pair(esk50_3(X1,X2,X3),esk51_3(X1,X2,X3)),X3)
| in(ordered_pair(esk50_3(X1,X2,X3),esk52_3(X1,X2,X3)),X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3) ),
c_0_407,
[final] ).
cnf(c_0_686,plain,
( X3 = relation_composition(X1,X2)
| in(ordered_pair(esk50_3(X1,X2,X3),esk51_3(X1,X2,X3)),X3)
| in(ordered_pair(esk52_3(X1,X2,X3),esk51_3(X1,X2,X3)),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3) ),
c_0_408,
[final] ).
cnf(c_0_687,plain,
( X2 = relation_rng_restriction(X3,X1)
| in(ordered_pair(esk5_3(X3,X1,X2),esk6_3(X3,X1,X2)),X2)
| in(ordered_pair(esk5_3(X3,X1,X2),esk6_3(X3,X1,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
c_0_409,
[final] ).
cnf(c_0_688,plain,
( X2 = relation_dom_restriction(X1,X3)
| in(ordered_pair(esk3_3(X1,X3,X2),esk4_3(X1,X3,X2)),X2)
| in(ordered_pair(esk3_3(X1,X3,X2),esk4_3(X1,X3,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
c_0_410,
[final] ).
cnf(c_0_689,plain,
( X3 = complements_of_subsets(X2,X1)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2)))
| ~ in(subset_complement(X2,esk53_3(X2,X1,X3)),X1)
| ~ in(esk53_3(X2,X1,X3),X3) ),
c_0_411,
[final] ).
cnf(c_0_690,plain,
( X2 = relation_inverse_image(X1,X3)
| ~ relation(X1)
| ~ in(X4,X3)
| ~ in(ordered_pair(esk11_3(X1,X3,X2),X4),X1)
| ~ in(esk11_3(X1,X3,X2),X2) ),
c_0_412,
[final] ).
cnf(c_0_691,plain,
( X2 = relation_image(X1,X3)
| ~ relation(X1)
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,esk8_3(X1,X3,X2)),X1)
| ~ in(esk8_3(X1,X3,X2),X2) ),
c_0_413,
[final] ).
cnf(c_0_692,plain,
( X2 = relation_rng_restriction(X3,X1)
| in(ordered_pair(esk5_3(X3,X1,X2),esk6_3(X3,X1,X2)),X2)
| in(esk6_3(X3,X1,X2),X3)
| ~ relation(X1)
| ~ relation(X2) ),
c_0_414,
[final] ).
cnf(c_0_693,plain,
( X2 = relation_dom_restriction(X1,X3)
| in(ordered_pair(esk3_3(X1,X3,X2),esk4_3(X1,X3,X2)),X2)
| in(esk3_3(X1,X3,X2),X3)
| ~ relation(X1)
| ~ relation(X2) ),
c_0_415,
[final] ).
cnf(c_0_694,plain,
( X2 = relation_inverse_image(X1,X3)
| in(esk11_3(X1,X3,X2),X2)
| in(ordered_pair(esk11_3(X1,X3,X2),esk12_3(X1,X3,X2)),X1)
| ~ relation(X1) ),
c_0_416,
[final] ).
cnf(c_0_695,plain,
( X2 = relation_image(X1,X3)
| in(esk8_3(X1,X3,X2),X2)
| in(ordered_pair(esk9_3(X1,X3,X2),esk8_3(X1,X3,X2)),X1)
| ~ relation(X1) ),
c_0_417,
[final] ).
cnf(c_0_696,plain,
( X1 = set_intersection2(X2,X3)
| ~ in(esk34_3(X2,X3,X1),X3)
| ~ in(esk34_3(X2,X3,X1),X2)
| ~ in(esk34_3(X2,X3,X1),X1) ),
c_0_418,
[final] ).
cnf(c_0_697,plain,
( in(esk10_4(X1,X3,X2,X4),X3)
| ~ relation(X1)
| X2 != relation_inverse_image(X1,X3)
| ~ in(X4,X2) ),
c_0_419,
[final] ).
cnf(c_0_698,plain,
( in(esk7_4(X1,X3,X2,X4),X3)
| ~ relation(X1)
| X2 != relation_image(X1,X3)
| ~ in(X4,X2) ),
c_0_420,
[final] ).
cnf(c_0_699,plain,
( in(esk26_4(X2,X3,X1,X4),X2)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
c_0_421,
[final] ).
cnf(c_0_700,plain,
( in(esk27_4(X2,X3,X1,X4),X3)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
c_0_422,
[final] ).
cnf(c_0_701,plain,
( X1 = set_difference(X2,X3)
| in(esk41_3(X2,X3,X1),X3)
| ~ in(esk41_3(X2,X3,X1),X2)
| ~ in(esk41_3(X2,X3,X1),X1) ),
c_0_423,
[final] ).
cnf(c_0_702,plain,
( X3 = complements_of_subsets(X2,X1)
| in(subset_complement(X2,esk53_3(X2,X1,X3)),X1)
| in(esk53_3(X2,X1,X3),X3)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2))) ),
c_0_424,
[final] ).
cnf(c_0_703,plain,
( X2 = relation_inverse(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(esk46_2(X1,X2),esk45_2(X1,X2)),X1)
| ~ in(ordered_pair(esk45_2(X1,X2),esk46_2(X1,X2)),X2) ),
c_0_425,
[final] ).
cnf(c_0_704,plain,
( X1 = X2
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(esk22_2(X1,X2),esk23_2(X1,X2)),X2)
| ~ in(ordered_pair(esk22_2(X1,X2),esk23_2(X1,X2)),X1) ),
c_0_426,
[final] ).
cnf(c_0_705,plain,
( X1 = cartesian_product2(X2,X3)
| in(esk28_3(X2,X3,X1),X1)
| ordered_pair(esk29_3(X2,X3,X1),esk30_3(X2,X3,X1)) = esk28_3(X2,X3,X1) ),
c_0_427,
[final] ).
cnf(c_0_706,plain,
( X1 = set_union2(X2,X3)
| ~ in(esk25_3(X2,X3,X1),X1)
| ~ in(esk25_3(X2,X3,X1),X2) ),
c_0_428,
[final] ).
cnf(c_0_707,plain,
( X1 = set_union2(X2,X3)
| ~ in(esk25_3(X2,X3,X1),X1)
| ~ in(esk25_3(X2,X3,X1),X3) ),
c_0_429,
[final] ).
cnf(c_0_708,plain,
( X1 = set_union2(X2,X3)
| in(esk25_3(X2,X3,X1),X3)
| in(esk25_3(X2,X3,X1),X2)
| in(esk25_3(X2,X3,X1),X1) ),
c_0_430,
[final] ).
cnf(c_0_709,plain,
( X1 = cartesian_product2(X2,X3)
| esk28_3(X2,X3,X1) != ordered_pair(X4,X5)
| ~ in(X5,X3)
| ~ in(X4,X2)
| ~ in(esk28_3(X2,X3,X1),X1) ),
c_0_431,
[final] ).
cnf(c_0_710,plain,
( X1 = identity_relation(X2)
| ~ relation(X1)
| esk2_2(X2,X1) != esk1_2(X2,X1)
| ~ in(esk1_2(X2,X1),X2)
| ~ in(ordered_pair(esk1_2(X2,X1),esk2_2(X2,X1)),X1) ),
c_0_432,
[final] ).
cnf(c_0_711,plain,
( X1 = set_difference(X2,X3)
| in(esk41_3(X2,X3,X1),X1)
| ~ in(esk41_3(X2,X3,X1),X3) ),
c_0_433,
[final] ).
cnf(c_0_712,plain,
( X2 = relation_inverse(X1)
| in(ordered_pair(esk46_2(X1,X2),esk45_2(X1,X2)),X1)
| in(ordered_pair(esk45_2(X1,X2),esk46_2(X1,X2)),X2)
| ~ relation(X1)
| ~ relation(X2) ),
c_0_434,
[final] ).
cnf(c_0_713,plain,
( X1 = X2
| in(ordered_pair(esk22_2(X1,X2),esk23_2(X1,X2)),X2)
| in(ordered_pair(esk22_2(X1,X2),esk23_2(X1,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
c_0_435,
[final] ).
cnf(c_0_714,plain,
( X1 = unordered_pair(X2,X3)
| ~ in(esk24_3(X2,X3,X1),X1)
| esk24_3(X2,X3,X1) != X2 ),
c_0_436,
[final] ).
cnf(c_0_715,plain,
( X1 = unordered_pair(X2,X3)
| ~ in(esk24_3(X2,X3,X1),X1)
| esk24_3(X2,X3,X1) != X3 ),
c_0_437,
[final] ).
cnf(c_0_716,plain,
( in(ordered_pair(esk42_3(X1,X2,X3),X3),X1)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(X3,X2) ),
c_0_438,
[final] ).
cnf(c_0_717,plain,
( in(ordered_pair(X3,esk35_3(X1,X2,X3)),X1)
| ~ relation(X1)
| X2 != relation_dom(X1)
| ~ in(X3,X2) ),
c_0_439,
[final] ).
cnf(c_0_718,plain,
( X2 = relation_inverse_image(X1,X3)
| in(esk11_3(X1,X3,X2),X2)
| in(esk12_3(X1,X3,X2),X3)
| ~ relation(X1) ),
c_0_440,
[final] ).
cnf(c_0_719,plain,
( X2 = relation_image(X1,X3)
| in(esk8_3(X1,X3,X2),X2)
| in(esk9_3(X1,X3,X2),X3)
| ~ relation(X1) ),
c_0_441,
[final] ).
cnf(c_0_720,plain,
( X1 = set_difference(X2,X3)
| in(esk41_3(X2,X3,X1),X1)
| in(esk41_3(X2,X3,X1),X2) ),
c_0_442,
[final] ).
cnf(c_0_721,plain,
( X1 = set_intersection2(X2,X3)
| in(esk34_3(X2,X3,X1),X1)
| in(esk34_3(X2,X3,X1),X2) ),
c_0_443,
[final] ).
cnf(c_0_722,plain,
( X1 = set_intersection2(X2,X3)
| in(esk34_3(X2,X3,X1),X1)
| in(esk34_3(X2,X3,X1),X3) ),
c_0_444,
[final] ).
cnf(c_0_723,plain,
( X1 = cartesian_product2(X2,X3)
| in(esk28_3(X2,X3,X1),X1)
| in(esk29_3(X2,X3,X1),X2) ),
c_0_445,
[final] ).
cnf(c_0_724,plain,
( X1 = cartesian_product2(X2,X3)
| in(esk28_3(X2,X3,X1),X1)
| in(esk30_3(X2,X3,X1),X3) ),
c_0_446,
[final] ).
cnf(c_0_725,plain,
( subset(X1,X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(esk31_2(X1,X2),esk32_2(X1,X2)),X2) ),
c_0_447,
[final] ).
cnf(c_0_726,plain,
( X1 = unordered_pair(X2,X3)
| esk24_3(X2,X3,X1) = X3
| esk24_3(X2,X3,X1) = X2
| in(esk24_3(X2,X3,X1),X1) ),
c_0_448,
[final] ).
cnf(c_0_727,plain,
( X3 = complements_of_subsets(X2,X1)
| element(esk53_3(X2,X1,X3),powerset(X2))
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2))) ),
c_0_449,
[final] ).
cnf(c_0_728,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_450,
[final] ).
cnf(c_0_729,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_451,
[final] ).
cnf(c_0_730,plain,
( X2 = relation_rng(X1)
| ~ relation(X1)
| ~ in(ordered_pair(X3,esk43_2(X1,X2)),X1)
| ~ in(esk43_2(X1,X2),X2) ),
c_0_452,
[final] ).
cnf(c_0_731,plain,
( X2 = relation_dom(X1)
| ~ relation(X1)
| ~ in(ordered_pair(esk36_2(X1,X2),X3),X1)
| ~ in(esk36_2(X1,X2),X2) ),
c_0_453,
[final] ).
cnf(c_0_732,plain,
( X1 = empty_set
| in(X3,X2)
| X2 != set_meet(X1)
| ~ in(X3,esk16_3(X1,X2,X3)) ),
c_0_454,
[final] ).
cnf(c_0_733,plain,
( in(ordered_pair(X4,X5),X3)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X6,X5),X2)
| ~ in(ordered_pair(X4,X6),X1) ),
c_0_455,
[final] ).
cnf(c_0_734,plain,
( X2 = relation_rng(X1)
| in(ordered_pair(esk44_2(X1,X2),esk43_2(X1,X2)),X1)
| in(esk43_2(X1,X2),X2)
| ~ relation(X1) ),
c_0_456,
[final] ).
cnf(c_0_735,plain,
( X2 = relation_dom(X1)
| in(ordered_pair(esk36_2(X1,X2),esk37_2(X1,X2)),X1)
| in(esk36_2(X1,X2),X2)
| ~ relation(X1) ),
c_0_457,
[final] ).
cnf(c_0_736,plain,
( X1 = identity_relation(X2)
| in(ordered_pair(esk1_2(X2,X1),esk2_2(X2,X1)),X1)
| in(esk1_2(X2,X1),X2)
| ~ relation(X1) ),
c_0_458,
[final] ).
cnf(c_0_737,plain,
( element(subset_difference(X1,X2,X3),powerset(X1))
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
c_0_459,
[final] ).
cnf(c_0_738,plain,
( X1 = identity_relation(X2)
| in(ordered_pair(esk1_2(X2,X1),esk2_2(X2,X1)),X1)
| esk2_2(X2,X1) = esk1_2(X2,X1)
| ~ relation(X1) ),
c_0_460,
[final] ).
cnf(c_0_739,plain,
( X1 = empty_set
| X2 = set_meet(X1)
| ~ in(esk17_2(X1,X2),X2)
| ~ in(esk17_2(X1,X2),esk18_2(X1,X2)) ),
c_0_461,
[final] ).
cnf(c_0_740,plain,
( subset(X1,X2)
| in(ordered_pair(esk31_2(X1,X2),esk32_2(X1,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
c_0_462,
[final] ).
cnf(c_0_741,plain,
( in(ordered_pair(X4,X5),X2)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_rng_restriction(X3,X1)
| ~ in(ordered_pair(X4,X5),X1)
| ~ in(X5,X3) ),
c_0_463,
[final] ).
cnf(c_0_742,plain,
( in(ordered_pair(X4,X5),X2)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_dom_restriction(X1,X3)
| ~ in(ordered_pair(X4,X5),X1)
| ~ in(X4,X3) ),
c_0_464,
[final] ).
cnf(c_0_743,plain,
( X1 = union(X2)
| ~ in(X3,X2)
| ~ in(esk39_2(X2,X1),X3)
| ~ in(esk39_2(X2,X1),X1) ),
c_0_465,
[final] ).
cnf(c_0_744,plain,
( in(X3,esk38_3(X2,X1,X3))
| X1 != union(X2)
| ~ in(X3,X1) ),
c_0_466,
[final] ).
cnf(c_0_745,plain,
( in(esk38_3(X2,X1,X3),X2)
| X1 != union(X2)
| ~ in(X3,X1) ),
c_0_467,
[final] ).
cnf(c_0_746,plain,
( X1 = empty_set
| in(X3,X2)
| in(esk16_3(X1,X2,X3),X1)
| X2 != set_meet(X1) ),
c_0_468,
[final] ).
cnf(c_0_747,plain,
( in(ordered_pair(X4,X5),X1)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_rng_restriction(X3,X1)
| ~ in(ordered_pair(X4,X5),X2) ),
c_0_469,
[final] ).
cnf(c_0_748,plain,
( in(ordered_pair(X4,X5),X1)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_dom_restriction(X1,X3)
| ~ in(ordered_pair(X4,X5),X2) ),
c_0_470,
[final] ).
cnf(c_0_749,plain,
( in(ordered_pair(X3,X4),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(X3,X4),X1)
| ~ subset(X1,X2) ),
c_0_471,
[final] ).
cnf(c_0_750,plain,
( subset_difference(X1,X2,X3) = set_difference(X2,X3)
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
c_0_472,
[final] ).
cnf(c_0_751,plain,
( X2 = X3
| ~ function(X1)
| ~ relation(X1)
| apply(X1,X2) != apply(X1,X3)
| ~ in(X3,relation_dom(X1))
| ~ in(X2,relation_dom(X1))
| ~ one_to_one(X1) ),
c_0_473,
[final] ).
cnf(c_0_752,plain,
( X1 = powerset(X2)
| ~ subset(esk21_2(X2,X1),X2)
| ~ in(esk21_2(X2,X1),X1) ),
c_0_474,
[final] ).
cnf(c_0_753,plain,
( in(X4,X2)
| ~ relation(X1)
| X2 != relation_inverse_image(X1,X3)
| ~ in(X5,X3)
| ~ in(ordered_pair(X4,X5),X1) ),
c_0_475,
[final] ).
cnf(c_0_754,plain,
( in(X4,X2)
| ~ relation(X1)
| X2 != relation_image(X1,X3)
| ~ in(X5,X3)
| ~ in(ordered_pair(X5,X4),X1) ),
c_0_476,
[final] ).
cnf(c_0_755,plain,
( X1 = X2
| ~ in(esk65_2(X1,X2),X2)
| ~ in(esk65_2(X1,X2),X1) ),
c_0_477,
[final] ).
cnf(c_0_756,plain,
( in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_inverse(X1)
| ~ in(ordered_pair(X4,X3),X2) ),
c_0_478,
[final] ).
cnf(c_0_757,plain,
( in(ordered_pair(X3,X4),X2)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_inverse(X1)
| ~ in(ordered_pair(X4,X3),X1) ),
c_0_479,
[final] ).
cnf(c_0_758,plain,
( X3 = apply(X1,X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_dom(X1))
| ~ in(ordered_pair(X2,X3),X1) ),
c_0_480,
[final] ).
cnf(c_0_759,plain,
( in(ordered_pair(X3,X4),X2)
| ~ relation(X1)
| ~ relation(X2)
| X1 != X2
| ~ in(ordered_pair(X3,X4),X1) ),
c_0_481,
[final] ).
cnf(c_0_760,plain,
( in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ relation(X2)
| X1 != X2
| ~ in(ordered_pair(X3,X4),X2) ),
c_0_482,
[final] ).
cnf(c_0_761,plain,
( in(X5,X3)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_rng_restriction(X3,X1)
| ~ in(ordered_pair(X4,X5),X2) ),
c_0_483,
[final] ).
cnf(c_0_762,plain,
( in(X4,X3)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_dom_restriction(X1,X3)
| ~ in(ordered_pair(X4,X5),X2) ),
c_0_484,
[final] ).
cnf(c_0_763,plain,
( X1 = union(X2)
| in(esk39_2(X2,X1),X1)
| in(esk39_2(X2,X1),esk40_2(X2,X1)) ),
c_0_485,
[final] ).
cnf(c_0_764,plain,
( in(ordered_pair(X2,X3),X1)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_dom(X1))
| X3 != apply(X1,X2) ),
c_0_486,
[final] ).
cnf(c_0_765,plain,
( X1 = empty_set
| X2 = set_meet(X1)
| in(esk18_2(X1,X2),X1)
| ~ in(esk17_2(X1,X2),X2) ),
c_0_487,
[final] ).
cnf(c_0_766,plain,
( X1 = empty_set
| X2 = set_meet(X1)
| in(esk17_2(X1,X2),X3)
| in(esk17_2(X1,X2),X2)
| ~ in(X3,X1) ),
c_0_488,
[final] ).
cnf(c_0_767,plain,
( element(complements_of_subsets(X1,X2),powerset(powerset(X1)))
| ~ element(X2,powerset(powerset(X1))) ),
c_0_489,
[final] ).
cnf(c_0_768,plain,
( in(X4,X1)
| X1 != cartesian_product2(X2,X3)
| X4 != ordered_pair(X5,X6)
| ~ in(X6,X3)
| ~ in(X5,X2) ),
c_0_490,
[final] ).
cnf(c_0_769,plain,
( element(meet_of_subsets(X1,X2),powerset(X1))
| ~ element(X2,powerset(powerset(X1))) ),
c_0_491,
[final] ).
cnf(c_0_770,plain,
( element(union_of_subsets(X1,X2),powerset(X1))
| ~ element(X2,powerset(powerset(X1))) ),
c_0_492,
[final] ).
cnf(c_0_771,plain,
( ordered_pair(esk13_2(X2,X1),esk14_2(X2,X1)) = X1
| ~ in(X1,X2)
| ~ relation(X2) ),
c_0_493,
[final] ).
cnf(c_0_772,plain,
( in(X3,esk67_2(X2,X1))
| ~ in(X1,esk66_1(X2))
| ~ subset(X3,X1) ),
c_0_494,
[final] ).
cnf(c_0_773,plain,
( in(X3,X2)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(ordered_pair(X4,X3),X1) ),
c_0_495,
[final] ).
cnf(c_0_774,plain,
( in(X3,X2)
| ~ relation(X1)
| X2 != relation_dom(X1)
| ~ in(ordered_pair(X3,X4),X1) ),
c_0_496,
[final] ).
cnf(c_0_775,plain,
( in(X3,X2)
| ~ relation(X1)
| X1 != identity_relation(X2)
| ~ in(ordered_pair(X3,X4),X1) ),
c_0_497,
[final] ).
cnf(c_0_776,plain,
( X1 = singleton(X2)
| esk19_2(X2,X1) != X2
| ~ in(esk19_2(X2,X1),X1) ),
c_0_498,
[final] ).
cnf(c_0_777,plain,
( complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2
| ~ element(X2,powerset(powerset(X1))) ),
c_0_499,
[final] ).
cnf(c_0_778,plain,
( X1 = union(X2)
| in(esk39_2(X2,X1),X1)
| in(esk40_2(X2,X1),X2) ),
c_0_500,
[final] ).
cnf(c_0_779,plain,
( X1 = powerset(X2)
| subset(esk21_2(X2,X1),X2)
| in(esk21_2(X2,X1),X1) ),
c_0_501,
[final] ).
cnf(c_0_780,plain,
( in(X4,X1)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X3)
| ~ in(X4,X2) ),
c_0_502,
[final] ).
cnf(c_0_781,plain,
( X1 = X2
| in(esk65_2(X1,X2),X2)
| in(esk65_2(X1,X2),X1) ),
c_0_503,
[final] ).
cnf(c_0_782,plain,
( in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| X1 != identity_relation(X2)
| X3 != X4
| ~ in(X3,X2) ),
c_0_504,
[final] ).
cnf(c_0_783,plain,
( X3 = X4
| ~ relation(X1)
| X1 != identity_relation(X2)
| ~ in(ordered_pair(X3,X4),X1) ),
c_0_505,
[final] ).
cnf(c_0_784,plain,
( in(esk67_2(X2,X1),esk66_1(X2))
| ~ in(X1,esk66_1(X2)) ),
c_0_506,
[final] ).
cnf(c_0_785,plain,
( element(subset_complement(X1,X2),powerset(X1))
| ~ element(X2,powerset(X1)) ),
c_0_507,
[final] ).
cnf(c_0_786,plain,
( subset(X1,X2)
| ~ in(esk33_2(X1,X2),X2) ),
c_0_508,
[final] ).
cnf(c_0_787,plain,
( in(X1,esk66_1(X2))
| ~ subset(X1,X3)
| ~ in(X3,esk66_1(X2)) ),
c_0_509,
[final] ).
cnf(c_0_788,plain,
( in(X4,X1)
| in(X4,X3)
| X1 != set_difference(X2,X3)
| ~ in(X4,X2) ),
c_0_510,
[final] ).
cnf(c_0_789,plain,
( in(X4,X3)
| in(X4,X2)
| X1 != set_union2(X2,X3)
| ~ in(X4,X1) ),
c_0_511,
[final] ).
cnf(c_0_790,plain,
( in(X1,esk66_1(X2))
| are_equipotent(X1,esk66_1(X2))
| ~ subset(X1,esk66_1(X2)) ),
c_0_512,
[final] ).
cnf(c_0_791,plain,
( subset_complement(X1,subset_complement(X1,X2)) = X2
| ~ element(X2,powerset(X1)) ),
c_0_513,
[final] ).
cnf(c_0_792,plain,
( X1 = empty_set
| in(X3,X4)
| X2 != set_meet(X1)
| ~ in(X4,X1)
| ~ in(X3,X2) ),
c_0_514,
[final] ).
cnf(c_0_793,plain,
( meet_of_subsets(X1,X2) = set_meet(X2)
| ~ element(X2,powerset(powerset(X1))) ),
c_0_515,
[final] ).
cnf(c_0_794,plain,
( union_of_subsets(X1,X2) = union(X2)
| ~ element(X2,powerset(powerset(X1))) ),
c_0_516,
[final] ).
cnf(c_0_795,plain,
( element(X1,X2)
| ~ element(X3,powerset(X2))
| ~ in(X1,X3) ),
c_0_517,
[final] ).
cnf(c_0_796,plain,
( X1 != set_difference(X2,X3)
| ~ in(X4,X1)
| ~ in(X4,X3) ),
c_0_518,
[final] ).
cnf(c_0_797,plain,
( in(X3,X1)
| X1 != union(X2)
| ~ in(X4,X2)
| ~ in(X3,X4) ),
c_0_519,
[final] ).
cnf(c_0_798,plain,
( ~ empty(X1)
| ~ element(X2,powerset(X1))
| ~ in(X3,X2) ),
c_0_520,
[final] ).
cnf(c_0_799,plain,
( in(X4,X2)
| X1 != set_difference(X2,X3)
| ~ in(X4,X1) ),
c_0_521,
[final] ).
cnf(c_0_800,plain,
( in(X4,X2)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X1) ),
c_0_522,
[final] ).
cnf(c_0_801,plain,
( in(X4,X3)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X1) ),
c_0_523,
[final] ).
cnf(c_0_802,plain,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X2) ),
c_0_524,
[final] ).
cnf(c_0_803,plain,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X3) ),
c_0_525,
[final] ).
cnf(c_0_804,plain,
( X1 = singleton(X2)
| esk19_2(X2,X1) = X2
| in(esk19_2(X2,X1),X1) ),
c_0_526,
[final] ).
cnf(c_0_805,plain,
( subset_complement(X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X1)) ),
c_0_527,
[final] ).
cnf(c_0_806,plain,
( in(X2,relation_dom(X1))
| X3 = empty_set
| ~ function(X1)
| ~ relation(X1)
| X3 != apply(X1,X2) ),
c_0_528,
[final] ).
cnf(c_0_807,plain,
unordered_pair(unordered_pair(X1,X2),singleton(X1)) = ordered_pair(X1,X2),
c_0_529,
[final] ).
cnf(c_0_808,plain,
( in(X1,X2)
| ~ in(X1,X3)
| ~ subset(X3,X2) ),
c_0_530,
[final] ).
cnf(c_0_809,plain,
( one_to_one(X1)
| apply(X1,esk48_1(X1)) = apply(X1,esk47_1(X1))
| ~ function(X1)
| ~ relation(X1) ),
c_0_531,
[final] ).
cnf(c_0_810,plain,
( relation(relation_composition(X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2) ),
c_0_532,
[final] ).
cnf(c_0_811,plain,
( function(relation_composition(X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2) ),
c_0_533,
[final] ).
cnf(c_0_812,plain,
( empty(X2)
| empty(X1)
| ~ empty(cartesian_product2(X1,X2)) ),
c_0_534,
[final] ).
cnf(c_0_813,plain,
( subset(X1,X2)
| in(esk33_2(X1,X2),X1) ),
c_0_535,
[final] ).
cnf(c_0_814,plain,
( in(X2,relation_dom(X1))
| X3 = apply(X1,X2)
| ~ function(X1)
| ~ relation(X1)
| X3 != empty_set ),
c_0_536,
[final] ).
cnf(c_0_815,plain,
( empty(X2)
| ~ empty(set_union2(X1,X2)) ),
c_0_537,
[final] ).
cnf(c_0_816,plain,
( empty(X1)
| ~ empty(set_union2(X1,X2)) ),
c_0_538,
[final] ).
cnf(c_0_817,plain,
( X4 = X3
| X4 = X2
| X1 != unordered_pair(X2,X3)
| ~ in(X4,X1) ),
c_0_539,
[final] ).
cnf(c_0_818,plain,
~ empty(unordered_pair(X1,X2)),
c_0_540,
[final] ).
cnf(c_0_819,plain,
~ empty(ordered_pair(X1,X2)),
c_0_541,
[final] ).
cnf(c_0_820,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
c_0_542,
[final] ).
cnf(c_0_821,plain,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
c_0_543,
[final] ).
cnf(c_0_822,plain,
( one_to_one(X1)
| in(esk47_1(X1),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
c_0_544,
[final] ).
cnf(c_0_823,plain,
( one_to_one(X1)
| in(esk48_1(X1),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
c_0_545,
[final] ).
cnf(c_0_824,plain,
( subset(X3,X2)
| X1 != powerset(X2)
| ~ in(X3,X1) ),
c_0_546,
[final] ).
cnf(c_0_825,plain,
( in(X3,X1)
| X1 != powerset(X2)
| ~ subset(X3,X2) ),
c_0_547,
[final] ).
cnf(c_0_826,plain,
( ~ proper_subset(X1,X2)
| ~ proper_subset(X2,X1) ),
c_0_548,
[final] ).
cnf(c_0_827,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
c_0_549,
[final] ).
cnf(c_0_828,plain,
( empty(relation_composition(X2,X1))
| ~ relation(X1)
| ~ empty(X2) ),
c_0_550,
[final] ).
cnf(c_0_829,plain,
( relation(relation_composition(X2,X1))
| ~ relation(X1)
| ~ empty(X2) ),
c_0_551,
[final] ).
cnf(c_0_830,plain,
( relation(relation_dom_restriction(X1,X2))
| ~ function(X1)
| ~ relation(X1) ),
c_0_552,
[final] ).
cnf(c_0_831,plain,
( function(relation_dom_restriction(X1,X2))
| ~ function(X1)
| ~ relation(X1) ),
c_0_553,
[final] ).
cnf(c_0_832,plain,
( relation(set_union2(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
c_0_554,
[final] ).
cnf(c_0_833,plain,
( relation(set_intersection2(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
c_0_555,
[final] ).
cnf(c_0_834,plain,
( relation(relation_dom_restriction(X1,X2))
| ~ relation_empty_yielding(X1)
| ~ relation(X1) ),
c_0_556,
[final] ).
cnf(c_0_835,plain,
( relation_empty_yielding(relation_dom_restriction(X1,X2))
| ~ relation_empty_yielding(X1)
| ~ relation(X1) ),
c_0_557,
[final] ).
cnf(c_0_836,plain,
( empty(relation_composition(X1,X2))
| ~ relation(X1)
| ~ empty(X2) ),
c_0_558,
[final] ).
cnf(c_0_837,plain,
( relation(relation_composition(X1,X2))
| ~ relation(X1)
| ~ empty(X2) ),
c_0_559,
[final] ).
cnf(c_0_838,plain,
( relation(relation_composition(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
c_0_560,
[final] ).
cnf(c_0_839,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
c_0_561,
[final] ).
cnf(c_0_840,plain,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X2 ),
c_0_562,
[final] ).
cnf(c_0_841,plain,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X3 ),
c_0_563,
[final] ).
cnf(c_0_842,plain,
( in(X1,X2)
| empty(X2)
| ~ element(X1,X2) ),
c_0_564,
[final] ).
cnf(c_0_843,plain,
( empty(X1)
| in(X2,X1)
| ~ element(X2,X1) ),
c_0_565,
[final] ).
cnf(c_0_844,plain,
( empty(X1)
| element(X2,X1)
| ~ in(X2,X1) ),
c_0_566,
[final] ).
cnf(c_0_845,plain,
( proper_subset(X1,X2)
| X1 = X2
| ~ subset(X1,X2) ),
c_0_567,
[final] ).
cnf(c_0_846,plain,
( relation(relation_rng_restriction(X1,X2))
| ~ relation(X2) ),
c_0_568,
[final] ).
cnf(c_0_847,plain,
( relation(relation_dom_restriction(X1,X2))
| ~ relation(X1) ),
c_0_569,
[final] ).
cnf(c_0_848,plain,
( set_union2(relation_dom(X1),relation_rng(X1)) = relation_field(X1)
| ~ relation(X1) ),
c_0_570,
[final] ).
cnf(c_0_849,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
c_0_571,
[final] ).
cnf(c_0_850,plain,
( disjoint(X1,X2)
| ~ disjoint(X2,X1) ),
c_0_572,
[final] ).
cnf(c_0_851,plain,
( subset(X1,X2)
| ~ proper_subset(X1,X2) ),
c_0_573,
[final] ).
cnf(c_0_852,plain,
( set_intersection2(X1,X2) = empty_set
| ~ disjoint(X1,X2) ),
c_0_574,
[final] ).
cnf(c_0_853,plain,
( disjoint(X1,X2)
| set_intersection2(X1,X2) != empty_set ),
c_0_575,
[final] ).
cnf(c_0_854,plain,
( empty(X2)
| ~ empty(X1)
| ~ element(X2,X1) ),
c_0_576,
[final] ).
cnf(c_0_855,plain,
( X3 = X2
| X1 != singleton(X2)
| ~ in(X3,X1) ),
c_0_577,
[final] ).
cnf(c_0_856,plain,
( relation(X1)
| esk15_1(X1) != ordered_pair(X2,X3) ),
c_0_578,
[final] ).
cnf(c_0_857,plain,
( relation(relation_inverse(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
c_0_579,
[final] ).
cnf(c_0_858,plain,
( function(relation_inverse(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
c_0_580,
[final] ).
cnf(c_0_859,plain,
( one_to_one(X1)
| ~ function(X1)
| ~ relation(X1)
| esk48_1(X1) != esk47_1(X1) ),
c_0_581,
[final] ).
cnf(c_0_860,plain,
( empty(X1)
| element(esk57_1(X1),powerset(X1)) ),
c_0_582,
[final] ).
cnf(c_0_861,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
c_0_583,
[final] ).
cnf(c_0_862,plain,
( function_inverse(X1) = relation_inverse(X1)
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
c_0_584,
[final] ).
cnf(c_0_863,plain,
( element(X2,X1)
| ~ empty(X1)
| ~ empty(X2) ),
c_0_585,
[final] ).
cnf(c_0_864,plain,
( empty(X1)
| ~ empty(relation_rng(X1))
| ~ relation(X1) ),
c_0_586,
[final] ).
cnf(c_0_865,plain,
( empty(X1)
| ~ empty(relation_dom(X1))
| ~ relation(X1) ),
c_0_587,
[final] ).
cnf(c_0_866,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
c_0_588,
[final] ).
cnf(c_0_867,plain,
set_union2(X1,X2) = set_union2(X2,X1),
c_0_589,
[final] ).
cnf(c_0_868,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
c_0_590,
[final] ).
cnf(c_0_869,plain,
element(esk61_1(X1),powerset(X1)),
c_0_591,
[final] ).
cnf(c_0_870,plain,
element(cast_to_subset(X1),powerset(X1)),
c_0_592,
[final] ).
cnf(c_0_871,plain,
( in(X3,X1)
| X1 != singleton(X2)
| X3 != X2 ),
c_0_593,
[final] ).
cnf(c_0_872,plain,
( ~ proper_subset(X1,X2)
| X1 != X2 ),
c_0_594,
[final] ).
cnf(c_0_873,plain,
( relation(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
c_0_595,
[final] ).
cnf(c_0_874,plain,
( function(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
c_0_596,
[final] ).
cnf(c_0_875,plain,
( one_to_one(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
c_0_597,
[final] ).
cnf(c_0_876,plain,
( ~ in(X1,X2)
| X2 != empty_set ),
c_0_598,
[final] ).
cnf(c_0_877,plain,
( relation(X1)
| in(esk15_1(X1),X1) ),
c_0_599,
[final] ).
cnf(c_0_878,plain,
( relation(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
c_0_600,
[final] ).
cnf(c_0_879,plain,
( function(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
c_0_601,
[final] ).
cnf(c_0_880,plain,
~ proper_subset(X1,X1),
c_0_602,
[final] ).
cnf(c_0_881,plain,
( X1 = empty_set
| in(esk20_1(X1),X1) ),
c_0_603,
[final] ).
cnf(c_0_882,plain,
( empty(X1)
| ~ empty(esk57_1(X1)) ),
c_0_604,
[final] ).
cnf(c_0_883,plain,
in(X1,esk66_1(X1)),
c_0_605,
[final] ).
cnf(c_0_884,plain,
element(esk54_1(X1),X1),
c_0_606,
[final] ).
cnf(c_0_885,plain,
( relation_inverse(relation_inverse(X1)) = X1
| ~ relation(X1) ),
c_0_607,
[final] ).
cnf(c_0_886,plain,
( subset(X1,X2)
| X1 != X2 ),
c_0_608,
[final] ).
cnf(c_0_887,plain,
( subset(X2,X1)
| X1 != X2 ),
c_0_609,
[final] ).
cnf(c_0_888,plain,
( empty(relation_rng(X1))
| ~ empty(X1) ),
c_0_610,
[final] ).
cnf(c_0_889,plain,
( relation(relation_rng(X1))
| ~ empty(X1) ),
c_0_611,
[final] ).
cnf(c_0_890,plain,
( empty(relation_dom(X1))
| ~ empty(X1) ),
c_0_612,
[final] ).
cnf(c_0_891,plain,
( relation(relation_dom(X1))
| ~ empty(X1) ),
c_0_613,
[final] ).
cnf(c_0_892,plain,
( empty(relation_inverse(X1))
| ~ empty(X1) ),
c_0_614,
[final] ).
cnf(c_0_893,plain,
( relation(relation_inverse(X1))
| ~ empty(X1) ),
c_0_615,
[final] ).
cnf(c_0_894,plain,
( relation(relation_inverse(X1))
| ~ relation(X1) ),
c_0_616,
[final] ).
cnf(c_0_895,plain,
~ empty(singleton(X1)),
c_0_617,
[final] ).
cnf(c_0_896,plain,
~ empty(powerset(X1)),
c_0_618,
[final] ).
cnf(c_0_897,plain,
( X2 = X1
| ~ empty(X1)
| ~ empty(X2) ),
c_0_619,
[final] ).
cnf(c_0_898,plain,
set_intersection2(X1,X1) = X1,
c_0_620,
[final] ).
cnf(c_0_899,plain,
set_union2(X1,X1) = X1,
c_0_621,
[final] ).
cnf(c_0_900,plain,
subset(X1,X1),
c_0_622,
[final] ).
cnf(c_0_901,plain,
set_difference(X1,empty_set) = X1,
c_0_623,
[final] ).
cnf(c_0_902,plain,
set_union2(X1,empty_set) = X1,
c_0_624,
[final] ).
cnf(c_0_903,plain,
set_difference(empty_set,X1) = empty_set,
c_0_625,
[final] ).
cnf(c_0_904,plain,
set_intersection2(X1,empty_set) = empty_set,
c_0_626,
[final] ).
cnf(c_0_905,plain,
( X2 = empty_set
| X1 != empty_set
| X2 != set_meet(X1) ),
c_0_627,
[final] ).
cnf(c_0_906,plain,
( relation(X1)
| ~ empty(X1) ),
c_0_628,
[final] ).
cnf(c_0_907,plain,
( function(X1)
| ~ empty(X1) ),
c_0_629,
[final] ).
cnf(c_0_908,plain,
empty(esk61_1(X1)),
c_0_630,
[final] ).
cnf(c_0_909,plain,
relation(identity_relation(X1)),
c_0_631,
[final] ).
cnf(c_0_910,plain,
function(identity_relation(X1)),
c_0_632,
[final] ).
cnf(c_0_911,plain,
relation(identity_relation(X1)),
c_0_633,
[final] ).
cnf(c_0_912,plain,
( X2 = set_meet(X1)
| X1 != empty_set
| X2 != empty_set ),
c_0_634,
[final] ).
cnf(c_0_913,plain,
( X1 = empty_set
| ~ empty(X1) ),
c_0_635,
[final] ).
cnf(c_0_914,plain,
cast_to_subset(X1) = X1,
c_0_636,
[final] ).
cnf(c_0_915,plain,
~ empty(esk62_0),
c_0_637,
[final] ).
cnf(c_0_916,plain,
~ empty(esk60_0),
c_0_638,
[final] ).
cnf(c_0_917,plain,
relation(esk64_0),
c_0_639,
[final] ).
cnf(c_0_918,plain,
relation_empty_yielding(esk64_0),
c_0_640,
[final] ).
cnf(c_0_919,plain,
relation(esk63_0),
c_0_641,
[final] ).
cnf(c_0_920,plain,
function(esk63_0),
c_0_642,
[final] ).
cnf(c_0_921,plain,
one_to_one(esk63_0),
c_0_643,
[final] ).
cnf(c_0_922,plain,
relation(esk60_0),
c_0_644,
[final] ).
cnf(c_0_923,plain,
relation(esk59_0),
c_0_645,
[final] ).
cnf(c_0_924,plain,
empty(esk59_0),
c_0_646,
[final] ).
cnf(c_0_925,plain,
function(esk59_0),
c_0_647,
[final] ).
cnf(c_0_926,plain,
empty(esk58_0),
c_0_648,
[final] ).
cnf(c_0_927,plain,
empty(esk56_0),
c_0_649,
[final] ).
cnf(c_0_928,plain,
relation(esk56_0),
c_0_650,
[final] ).
cnf(c_0_929,plain,
relation(esk55_0),
c_0_651,
[final] ).
cnf(c_0_930,plain,
function(esk55_0),
c_0_652,
[final] ).
cnf(c_0_931,plain,
empty(empty_set),
c_0_653,
[final] ).
cnf(c_0_932,plain,
relation(empty_set),
c_0_654,
[final] ).
cnf(c_0_933,plain,
empty(empty_set),
c_0_655,
[final] ).
cnf(c_0_934,plain,
empty(empty_set),
c_0_656,
[final] ).
cnf(c_0_935,plain,
relation(empty_set),
c_0_657,
[final] ).
cnf(c_0_936,plain,
relation_empty_yielding(empty_set),
c_0_658,
[final] ).
cnf(c_0_937,plain,
$true,
c_0_659,
[final] ).
cnf(c_0_938,plain,
$true,
c_0_660,
[final] ).
cnf(c_0_939,plain,
$true,
c_0_661,
[final] ).
cnf(c_0_940,plain,
$true,
c_0_662,
[final] ).
cnf(c_0_941,plain,
$true,
c_0_663,
[final] ).
cnf(c_0_942,plain,
$true,
c_0_664,
[final] ).
cnf(c_0_943,plain,
$true,
c_0_665,
[final] ).
cnf(c_0_944,plain,
$true,
c_0_666,
[final] ).
cnf(c_0_945,plain,
$true,
c_0_667,
[final] ).
cnf(c_0_946,plain,
$true,
c_0_668,
[final] ).
cnf(c_0_947,plain,
$true,
c_0_669,
[final] ).
cnf(c_0_948,plain,
$true,
c_0_670,
[final] ).
cnf(c_0_949,plain,
$true,
c_0_671,
[final] ).
cnf(c_0_950,plain,
$true,
c_0_672,
[final] ).
cnf(c_0_951,plain,
$true,
c_0_673,
[final] ).
cnf(c_0_952,plain,
$true,
c_0_674,
[final] ).
cnf(c_0_953,plain,
$true,
c_0_675,
[final] ).
cnf(c_0_954,plain,
$true,
c_0_676,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_677_0,axiom,
( in(ordered_pair(X4,sk1_esk49_5(X1,X2,X3,X4,X5)),X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X4,X5),X3) ),
inference(literals_permutation,[status(thm)],[c_0_677]) ).
cnf(c_0_677_1,axiom,
( ~ relation(X1)
| in(ordered_pair(X4,sk1_esk49_5(X1,X2,X3,X4,X5)),X1)
| ~ relation(X2)
| ~ relation(X3)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X4,X5),X3) ),
inference(literals_permutation,[status(thm)],[c_0_677]) ).
cnf(c_0_677_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,sk1_esk49_5(X1,X2,X3,X4,X5)),X1)
| ~ relation(X3)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X4,X5),X3) ),
inference(literals_permutation,[status(thm)],[c_0_677]) ).
cnf(c_0_677_3,axiom,
( ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,sk1_esk49_5(X1,X2,X3,X4,X5)),X1)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X4,X5),X3) ),
inference(literals_permutation,[status(thm)],[c_0_677]) ).
cnf(c_0_677_4,axiom,
( X3 != relation_composition(X1,X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,sk1_esk49_5(X1,X2,X3,X4,X5)),X1)
| ~ in(ordered_pair(X4,X5),X3) ),
inference(literals_permutation,[status(thm)],[c_0_677]) ).
cnf(c_0_677_5,axiom,
( ~ in(ordered_pair(X4,X5),X3)
| X3 != relation_composition(X1,X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,sk1_esk49_5(X1,X2,X3,X4,X5)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_677]) ).
cnf(c_0_678_0,axiom,
( in(ordered_pair(sk1_esk49_5(X1,X2,X3,X4,X5),X5),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X4,X5),X3) ),
inference(literals_permutation,[status(thm)],[c_0_678]) ).
cnf(c_0_678_1,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk49_5(X1,X2,X3,X4,X5),X5),X2)
| ~ relation(X2)
| ~ relation(X3)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X4,X5),X3) ),
inference(literals_permutation,[status(thm)],[c_0_678]) ).
cnf(c_0_678_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk49_5(X1,X2,X3,X4,X5),X5),X2)
| ~ relation(X3)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X4,X5),X3) ),
inference(literals_permutation,[status(thm)],[c_0_678]) ).
cnf(c_0_678_3,axiom,
( ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk49_5(X1,X2,X3,X4,X5),X5),X2)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X4,X5),X3) ),
inference(literals_permutation,[status(thm)],[c_0_678]) ).
cnf(c_0_678_4,axiom,
( X3 != relation_composition(X1,X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk49_5(X1,X2,X3,X4,X5),X5),X2)
| ~ in(ordered_pair(X4,X5),X3) ),
inference(literals_permutation,[status(thm)],[c_0_678]) ).
cnf(c_0_678_5,axiom,
( ~ in(ordered_pair(X4,X5),X3)
| X3 != relation_composition(X1,X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk49_5(X1,X2,X3,X4,X5),X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_678]) ).
cnf(c_0_679_0,axiom,
( X2 = relation_rng_restriction(X3,X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(sk1_esk5_3(X3,X1,X2),sk1_esk6_3(X3,X1,X2)),X1)
| ~ in(sk1_esk6_3(X3,X1,X2),X3)
| ~ in(ordered_pair(sk1_esk5_3(X3,X1,X2),sk1_esk6_3(X3,X1,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_679]) ).
cnf(c_0_679_1,axiom,
( ~ relation(X1)
| X2 = relation_rng_restriction(X3,X1)
| ~ relation(X2)
| ~ in(ordered_pair(sk1_esk5_3(X3,X1,X2),sk1_esk6_3(X3,X1,X2)),X1)
| ~ in(sk1_esk6_3(X3,X1,X2),X3)
| ~ in(ordered_pair(sk1_esk5_3(X3,X1,X2),sk1_esk6_3(X3,X1,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_679]) ).
cnf(c_0_679_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| X2 = relation_rng_restriction(X3,X1)
| ~ in(ordered_pair(sk1_esk5_3(X3,X1,X2),sk1_esk6_3(X3,X1,X2)),X1)
| ~ in(sk1_esk6_3(X3,X1,X2),X3)
| ~ in(ordered_pair(sk1_esk5_3(X3,X1,X2),sk1_esk6_3(X3,X1,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_679]) ).
cnf(c_0_679_3,axiom,
( ~ in(ordered_pair(sk1_esk5_3(X3,X1,X2),sk1_esk6_3(X3,X1,X2)),X1)
| ~ relation(X2)
| ~ relation(X1)
| X2 = relation_rng_restriction(X3,X1)
| ~ in(sk1_esk6_3(X3,X1,X2),X3)
| ~ in(ordered_pair(sk1_esk5_3(X3,X1,X2),sk1_esk6_3(X3,X1,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_679]) ).
cnf(c_0_679_4,axiom,
( ~ in(sk1_esk6_3(X3,X1,X2),X3)
| ~ in(ordered_pair(sk1_esk5_3(X3,X1,X2),sk1_esk6_3(X3,X1,X2)),X1)
| ~ relation(X2)
| ~ relation(X1)
| X2 = relation_rng_restriction(X3,X1)
| ~ in(ordered_pair(sk1_esk5_3(X3,X1,X2),sk1_esk6_3(X3,X1,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_679]) ).
cnf(c_0_679_5,axiom,
( ~ in(ordered_pair(sk1_esk5_3(X3,X1,X2),sk1_esk6_3(X3,X1,X2)),X2)
| ~ in(sk1_esk6_3(X3,X1,X2),X3)
| ~ in(ordered_pair(sk1_esk5_3(X3,X1,X2),sk1_esk6_3(X3,X1,X2)),X1)
| ~ relation(X2)
| ~ relation(X1)
| X2 = relation_rng_restriction(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_679]) ).
cnf(c_0_680_0,axiom,
( X2 = relation_dom_restriction(X1,X3)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X1)
| ~ in(sk1_esk3_3(X1,X3,X2),X3)
| ~ in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_680]) ).
cnf(c_0_680_1,axiom,
( ~ relation(X1)
| X2 = relation_dom_restriction(X1,X3)
| ~ relation(X2)
| ~ in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X1)
| ~ in(sk1_esk3_3(X1,X3,X2),X3)
| ~ in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_680]) ).
cnf(c_0_680_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| X2 = relation_dom_restriction(X1,X3)
| ~ in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X1)
| ~ in(sk1_esk3_3(X1,X3,X2),X3)
| ~ in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_680]) ).
cnf(c_0_680_3,axiom,
( ~ in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X1)
| ~ relation(X2)
| ~ relation(X1)
| X2 = relation_dom_restriction(X1,X3)
| ~ in(sk1_esk3_3(X1,X3,X2),X3)
| ~ in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_680]) ).
cnf(c_0_680_4,axiom,
( ~ in(sk1_esk3_3(X1,X3,X2),X3)
| ~ in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X1)
| ~ relation(X2)
| ~ relation(X1)
| X2 = relation_dom_restriction(X1,X3)
| ~ in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_680]) ).
cnf(c_0_680_5,axiom,
( ~ in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X2)
| ~ in(sk1_esk3_3(X1,X3,X2),X3)
| ~ in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X1)
| ~ relation(X2)
| ~ relation(X1)
| X2 = relation_dom_restriction(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_680]) ).
cnf(c_0_681_0,axiom,
( X3 = relation_composition(X1,X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3)
| ~ in(ordered_pair(X4,sk1_esk51_3(X1,X2,X3)),X2)
| ~ in(ordered_pair(sk1_esk50_3(X1,X2,X3),X4),X1)
| ~ in(ordered_pair(sk1_esk50_3(X1,X2,X3),sk1_esk51_3(X1,X2,X3)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_681]) ).
cnf(c_0_681_1,axiom,
( ~ relation(X1)
| X3 = relation_composition(X1,X2)
| ~ relation(X2)
| ~ relation(X3)
| ~ in(ordered_pair(X4,sk1_esk51_3(X1,X2,X3)),X2)
| ~ in(ordered_pair(sk1_esk50_3(X1,X2,X3),X4),X1)
| ~ in(ordered_pair(sk1_esk50_3(X1,X2,X3),sk1_esk51_3(X1,X2,X3)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_681]) ).
cnf(c_0_681_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| X3 = relation_composition(X1,X2)
| ~ relation(X3)
| ~ in(ordered_pair(X4,sk1_esk51_3(X1,X2,X3)),X2)
| ~ in(ordered_pair(sk1_esk50_3(X1,X2,X3),X4),X1)
| ~ in(ordered_pair(sk1_esk50_3(X1,X2,X3),sk1_esk51_3(X1,X2,X3)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_681]) ).
cnf(c_0_681_3,axiom,
( ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| X3 = relation_composition(X1,X2)
| ~ in(ordered_pair(X4,sk1_esk51_3(X1,X2,X3)),X2)
| ~ in(ordered_pair(sk1_esk50_3(X1,X2,X3),X4),X1)
| ~ in(ordered_pair(sk1_esk50_3(X1,X2,X3),sk1_esk51_3(X1,X2,X3)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_681]) ).
cnf(c_0_681_4,axiom,
( ~ in(ordered_pair(X4,sk1_esk51_3(X1,X2,X3)),X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| X3 = relation_composition(X1,X2)
| ~ in(ordered_pair(sk1_esk50_3(X1,X2,X3),X4),X1)
| ~ in(ordered_pair(sk1_esk50_3(X1,X2,X3),sk1_esk51_3(X1,X2,X3)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_681]) ).
cnf(c_0_681_5,axiom,
( ~ in(ordered_pair(sk1_esk50_3(X1,X2,X3),X4),X1)
| ~ in(ordered_pair(X4,sk1_esk51_3(X1,X2,X3)),X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| X3 = relation_composition(X1,X2)
| ~ in(ordered_pair(sk1_esk50_3(X1,X2,X3),sk1_esk51_3(X1,X2,X3)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_681]) ).
cnf(c_0_681_6,axiom,
( ~ in(ordered_pair(sk1_esk50_3(X1,X2,X3),sk1_esk51_3(X1,X2,X3)),X3)
| ~ in(ordered_pair(sk1_esk50_3(X1,X2,X3),X4),X1)
| ~ in(ordered_pair(X4,sk1_esk51_3(X1,X2,X3)),X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| X3 = relation_composition(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_681]) ).
cnf(c_0_682_0,axiom,
( in(ordered_pair(X4,sk1_esk10_4(X1,X3,X2,X4)),X1)
| ~ relation(X1)
| X2 != relation_inverse_image(X1,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_682]) ).
cnf(c_0_682_1,axiom,
( ~ relation(X1)
| in(ordered_pair(X4,sk1_esk10_4(X1,X3,X2,X4)),X1)
| X2 != relation_inverse_image(X1,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_682]) ).
cnf(c_0_682_2,axiom,
( X2 != relation_inverse_image(X1,X3)
| ~ relation(X1)
| in(ordered_pair(X4,sk1_esk10_4(X1,X3,X2,X4)),X1)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_682]) ).
cnf(c_0_682_3,axiom,
( ~ in(X4,X2)
| X2 != relation_inverse_image(X1,X3)
| ~ relation(X1)
| in(ordered_pair(X4,sk1_esk10_4(X1,X3,X2,X4)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_682]) ).
cnf(c_0_683_0,axiom,
( in(ordered_pair(sk1_esk7_4(X1,X3,X2,X4),X4),X1)
| ~ relation(X1)
| X2 != relation_image(X1,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_683]) ).
cnf(c_0_683_1,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk7_4(X1,X3,X2,X4),X4),X1)
| X2 != relation_image(X1,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_683]) ).
cnf(c_0_683_2,axiom,
( X2 != relation_image(X1,X3)
| ~ relation(X1)
| in(ordered_pair(sk1_esk7_4(X1,X3,X2,X4),X4),X1)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_683]) ).
cnf(c_0_683_3,axiom,
( ~ in(X4,X2)
| X2 != relation_image(X1,X3)
| ~ relation(X1)
| in(ordered_pair(sk1_esk7_4(X1,X3,X2,X4),X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_683]) ).
cnf(c_0_684_0,axiom,
( ordered_pair(sk1_esk26_4(X2,X3,X1,X4),sk1_esk27_4(X2,X3,X1,X4)) = X4
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_684]) ).
cnf(c_0_684_1,axiom,
( X1 != cartesian_product2(X2,X3)
| ordered_pair(sk1_esk26_4(X2,X3,X1,X4),sk1_esk27_4(X2,X3,X1,X4)) = X4
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_684]) ).
cnf(c_0_684_2,axiom,
( ~ in(X4,X1)
| X1 != cartesian_product2(X2,X3)
| ordered_pair(sk1_esk26_4(X2,X3,X1,X4),sk1_esk27_4(X2,X3,X1,X4)) = X4 ),
inference(literals_permutation,[status(thm)],[c_0_684]) ).
cnf(c_0_685_0,axiom,
( X3 = relation_composition(X1,X2)
| in(ordered_pair(sk1_esk50_3(X1,X2,X3),sk1_esk51_3(X1,X2,X3)),X3)
| in(ordered_pair(sk1_esk50_3(X1,X2,X3),sk1_esk52_3(X1,X2,X3)),X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_685]) ).
cnf(c_0_685_1,axiom,
( in(ordered_pair(sk1_esk50_3(X1,X2,X3),sk1_esk51_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2)
| in(ordered_pair(sk1_esk50_3(X1,X2,X3),sk1_esk52_3(X1,X2,X3)),X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_685]) ).
cnf(c_0_685_2,axiom,
( in(ordered_pair(sk1_esk50_3(X1,X2,X3),sk1_esk52_3(X1,X2,X3)),X1)
| in(ordered_pair(sk1_esk50_3(X1,X2,X3),sk1_esk51_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_685]) ).
cnf(c_0_685_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk50_3(X1,X2,X3),sk1_esk52_3(X1,X2,X3)),X1)
| in(ordered_pair(sk1_esk50_3(X1,X2,X3),sk1_esk51_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2)
| ~ relation(X2)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_685]) ).
cnf(c_0_685_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk50_3(X1,X2,X3),sk1_esk52_3(X1,X2,X3)),X1)
| in(ordered_pair(sk1_esk50_3(X1,X2,X3),sk1_esk51_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_685]) ).
cnf(c_0_685_5,axiom,
( ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk50_3(X1,X2,X3),sk1_esk52_3(X1,X2,X3)),X1)
| in(ordered_pair(sk1_esk50_3(X1,X2,X3),sk1_esk51_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_685]) ).
cnf(c_0_686_0,axiom,
( X3 = relation_composition(X1,X2)
| in(ordered_pair(sk1_esk50_3(X1,X2,X3),sk1_esk51_3(X1,X2,X3)),X3)
| in(ordered_pair(sk1_esk52_3(X1,X2,X3),sk1_esk51_3(X1,X2,X3)),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_686]) ).
cnf(c_0_686_1,axiom,
( in(ordered_pair(sk1_esk50_3(X1,X2,X3),sk1_esk51_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2)
| in(ordered_pair(sk1_esk52_3(X1,X2,X3),sk1_esk51_3(X1,X2,X3)),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_686]) ).
cnf(c_0_686_2,axiom,
( in(ordered_pair(sk1_esk52_3(X1,X2,X3),sk1_esk51_3(X1,X2,X3)),X2)
| in(ordered_pair(sk1_esk50_3(X1,X2,X3),sk1_esk51_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_686]) ).
cnf(c_0_686_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk52_3(X1,X2,X3),sk1_esk51_3(X1,X2,X3)),X2)
| in(ordered_pair(sk1_esk50_3(X1,X2,X3),sk1_esk51_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2)
| ~ relation(X2)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_686]) ).
cnf(c_0_686_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk52_3(X1,X2,X3),sk1_esk51_3(X1,X2,X3)),X2)
| in(ordered_pair(sk1_esk50_3(X1,X2,X3),sk1_esk51_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2)
| ~ relation(X3) ),
inference(literals_permutation,[status(thm)],[c_0_686]) ).
cnf(c_0_686_5,axiom,
( ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk52_3(X1,X2,X3),sk1_esk51_3(X1,X2,X3)),X2)
| in(ordered_pair(sk1_esk50_3(X1,X2,X3),sk1_esk51_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_686]) ).
cnf(c_0_687_0,axiom,
( X2 = relation_rng_restriction(X3,X1)
| in(ordered_pair(sk1_esk5_3(X3,X1,X2),sk1_esk6_3(X3,X1,X2)),X2)
| in(ordered_pair(sk1_esk5_3(X3,X1,X2),sk1_esk6_3(X3,X1,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_687]) ).
cnf(c_0_687_1,axiom,
( in(ordered_pair(sk1_esk5_3(X3,X1,X2),sk1_esk6_3(X3,X1,X2)),X2)
| X2 = relation_rng_restriction(X3,X1)
| in(ordered_pair(sk1_esk5_3(X3,X1,X2),sk1_esk6_3(X3,X1,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_687]) ).
cnf(c_0_687_2,axiom,
( in(ordered_pair(sk1_esk5_3(X3,X1,X2),sk1_esk6_3(X3,X1,X2)),X1)
| in(ordered_pair(sk1_esk5_3(X3,X1,X2),sk1_esk6_3(X3,X1,X2)),X2)
| X2 = relation_rng_restriction(X3,X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_687]) ).
cnf(c_0_687_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk5_3(X3,X1,X2),sk1_esk6_3(X3,X1,X2)),X1)
| in(ordered_pair(sk1_esk5_3(X3,X1,X2),sk1_esk6_3(X3,X1,X2)),X2)
| X2 = relation_rng_restriction(X3,X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_687]) ).
cnf(c_0_687_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk5_3(X3,X1,X2),sk1_esk6_3(X3,X1,X2)),X1)
| in(ordered_pair(sk1_esk5_3(X3,X1,X2),sk1_esk6_3(X3,X1,X2)),X2)
| X2 = relation_rng_restriction(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_687]) ).
cnf(c_0_688_0,axiom,
( X2 = relation_dom_restriction(X1,X3)
| in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X2)
| in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_688]) ).
cnf(c_0_688_1,axiom,
( in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X2)
| X2 = relation_dom_restriction(X1,X3)
| in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_688]) ).
cnf(c_0_688_2,axiom,
( in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X1)
| in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X2)
| X2 = relation_dom_restriction(X1,X3)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_688]) ).
cnf(c_0_688_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X1)
| in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X2)
| X2 = relation_dom_restriction(X1,X3)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_688]) ).
cnf(c_0_688_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X1)
| in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X2)
| X2 = relation_dom_restriction(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_688]) ).
cnf(c_0_689_0,axiom,
( X3 = complements_of_subsets(X2,X1)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2)))
| ~ in(subset_complement(X2,sk1_esk53_3(X2,X1,X3)),X1)
| ~ in(sk1_esk53_3(X2,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_689]) ).
cnf(c_0_689_1,axiom,
( ~ element(X1,powerset(powerset(X2)))
| X3 = complements_of_subsets(X2,X1)
| ~ element(X3,powerset(powerset(X2)))
| ~ in(subset_complement(X2,sk1_esk53_3(X2,X1,X3)),X1)
| ~ in(sk1_esk53_3(X2,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_689]) ).
cnf(c_0_689_2,axiom,
( ~ element(X3,powerset(powerset(X2)))
| ~ element(X1,powerset(powerset(X2)))
| X3 = complements_of_subsets(X2,X1)
| ~ in(subset_complement(X2,sk1_esk53_3(X2,X1,X3)),X1)
| ~ in(sk1_esk53_3(X2,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_689]) ).
cnf(c_0_689_3,axiom,
( ~ in(subset_complement(X2,sk1_esk53_3(X2,X1,X3)),X1)
| ~ element(X3,powerset(powerset(X2)))
| ~ element(X1,powerset(powerset(X2)))
| X3 = complements_of_subsets(X2,X1)
| ~ in(sk1_esk53_3(X2,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_689]) ).
cnf(c_0_689_4,axiom,
( ~ in(sk1_esk53_3(X2,X1,X3),X3)
| ~ in(subset_complement(X2,sk1_esk53_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_689]) ).
cnf(c_0_690_0,axiom,
( X2 = relation_inverse_image(X1,X3)
| ~ relation(X1)
| ~ in(X4,X3)
| ~ in(ordered_pair(sk1_esk11_3(X1,X3,X2),X4),X1)
| ~ in(sk1_esk11_3(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_690]) ).
cnf(c_0_690_1,axiom,
( ~ relation(X1)
| X2 = relation_inverse_image(X1,X3)
| ~ in(X4,X3)
| ~ in(ordered_pair(sk1_esk11_3(X1,X3,X2),X4),X1)
| ~ in(sk1_esk11_3(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_690]) ).
cnf(c_0_690_2,axiom,
( ~ in(X4,X3)
| ~ relation(X1)
| X2 = relation_inverse_image(X1,X3)
| ~ in(ordered_pair(sk1_esk11_3(X1,X3,X2),X4),X1)
| ~ in(sk1_esk11_3(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_690]) ).
cnf(c_0_690_3,axiom,
( ~ in(ordered_pair(sk1_esk11_3(X1,X3,X2),X4),X1)
| ~ in(X4,X3)
| ~ relation(X1)
| X2 = relation_inverse_image(X1,X3)
| ~ in(sk1_esk11_3(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_690]) ).
cnf(c_0_690_4,axiom,
( ~ in(sk1_esk11_3(X1,X3,X2),X2)
| ~ in(ordered_pair(sk1_esk11_3(X1,X3,X2),X4),X1)
| ~ in(X4,X3)
| ~ relation(X1)
| X2 = relation_inverse_image(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_690]) ).
cnf(c_0_691_0,axiom,
( X2 = relation_image(X1,X3)
| ~ relation(X1)
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,sk1_esk8_3(X1,X3,X2)),X1)
| ~ in(sk1_esk8_3(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_691]) ).
cnf(c_0_691_1,axiom,
( ~ relation(X1)
| X2 = relation_image(X1,X3)
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,sk1_esk8_3(X1,X3,X2)),X1)
| ~ in(sk1_esk8_3(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_691]) ).
cnf(c_0_691_2,axiom,
( ~ in(X4,X3)
| ~ relation(X1)
| X2 = relation_image(X1,X3)
| ~ in(ordered_pair(X4,sk1_esk8_3(X1,X3,X2)),X1)
| ~ in(sk1_esk8_3(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_691]) ).
cnf(c_0_691_3,axiom,
( ~ in(ordered_pair(X4,sk1_esk8_3(X1,X3,X2)),X1)
| ~ in(X4,X3)
| ~ relation(X1)
| X2 = relation_image(X1,X3)
| ~ in(sk1_esk8_3(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_691]) ).
cnf(c_0_691_4,axiom,
( ~ in(sk1_esk8_3(X1,X3,X2),X2)
| ~ in(ordered_pair(X4,sk1_esk8_3(X1,X3,X2)),X1)
| ~ in(X4,X3)
| ~ relation(X1)
| X2 = relation_image(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_691]) ).
cnf(c_0_692_0,axiom,
( X2 = relation_rng_restriction(X3,X1)
| in(ordered_pair(sk1_esk5_3(X3,X1,X2),sk1_esk6_3(X3,X1,X2)),X2)
| in(sk1_esk6_3(X3,X1,X2),X3)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_692]) ).
cnf(c_0_692_1,axiom,
( in(ordered_pair(sk1_esk5_3(X3,X1,X2),sk1_esk6_3(X3,X1,X2)),X2)
| X2 = relation_rng_restriction(X3,X1)
| in(sk1_esk6_3(X3,X1,X2),X3)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_692]) ).
cnf(c_0_692_2,axiom,
( in(sk1_esk6_3(X3,X1,X2),X3)
| in(ordered_pair(sk1_esk5_3(X3,X1,X2),sk1_esk6_3(X3,X1,X2)),X2)
| X2 = relation_rng_restriction(X3,X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_692]) ).
cnf(c_0_692_3,axiom,
( ~ relation(X1)
| in(sk1_esk6_3(X3,X1,X2),X3)
| in(ordered_pair(sk1_esk5_3(X3,X1,X2),sk1_esk6_3(X3,X1,X2)),X2)
| X2 = relation_rng_restriction(X3,X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_692]) ).
cnf(c_0_692_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(sk1_esk6_3(X3,X1,X2),X3)
| in(ordered_pair(sk1_esk5_3(X3,X1,X2),sk1_esk6_3(X3,X1,X2)),X2)
| X2 = relation_rng_restriction(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_692]) ).
cnf(c_0_693_0,axiom,
( X2 = relation_dom_restriction(X1,X3)
| in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X2)
| in(sk1_esk3_3(X1,X3,X2),X3)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_693]) ).
cnf(c_0_693_1,axiom,
( in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X2)
| X2 = relation_dom_restriction(X1,X3)
| in(sk1_esk3_3(X1,X3,X2),X3)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_693]) ).
cnf(c_0_693_2,axiom,
( in(sk1_esk3_3(X1,X3,X2),X3)
| in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X2)
| X2 = relation_dom_restriction(X1,X3)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_693]) ).
cnf(c_0_693_3,axiom,
( ~ relation(X1)
| in(sk1_esk3_3(X1,X3,X2),X3)
| in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X2)
| X2 = relation_dom_restriction(X1,X3)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_693]) ).
cnf(c_0_693_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(sk1_esk3_3(X1,X3,X2),X3)
| in(ordered_pair(sk1_esk3_3(X1,X3,X2),sk1_esk4_3(X1,X3,X2)),X2)
| X2 = relation_dom_restriction(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_693]) ).
cnf(c_0_694_0,axiom,
( X2 = relation_inverse_image(X1,X3)
| in(sk1_esk11_3(X1,X3,X2),X2)
| in(ordered_pair(sk1_esk11_3(X1,X3,X2),sk1_esk12_3(X1,X3,X2)),X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_694]) ).
cnf(c_0_694_1,axiom,
( in(sk1_esk11_3(X1,X3,X2),X2)
| X2 = relation_inverse_image(X1,X3)
| in(ordered_pair(sk1_esk11_3(X1,X3,X2),sk1_esk12_3(X1,X3,X2)),X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_694]) ).
cnf(c_0_694_2,axiom,
( in(ordered_pair(sk1_esk11_3(X1,X3,X2),sk1_esk12_3(X1,X3,X2)),X1)
| in(sk1_esk11_3(X1,X3,X2),X2)
| X2 = relation_inverse_image(X1,X3)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_694]) ).
cnf(c_0_694_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk11_3(X1,X3,X2),sk1_esk12_3(X1,X3,X2)),X1)
| in(sk1_esk11_3(X1,X3,X2),X2)
| X2 = relation_inverse_image(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_694]) ).
cnf(c_0_695_0,axiom,
( X2 = relation_image(X1,X3)
| in(sk1_esk8_3(X1,X3,X2),X2)
| in(ordered_pair(sk1_esk9_3(X1,X3,X2),sk1_esk8_3(X1,X3,X2)),X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_695]) ).
cnf(c_0_695_1,axiom,
( in(sk1_esk8_3(X1,X3,X2),X2)
| X2 = relation_image(X1,X3)
| in(ordered_pair(sk1_esk9_3(X1,X3,X2),sk1_esk8_3(X1,X3,X2)),X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_695]) ).
cnf(c_0_695_2,axiom,
( in(ordered_pair(sk1_esk9_3(X1,X3,X2),sk1_esk8_3(X1,X3,X2)),X1)
| in(sk1_esk8_3(X1,X3,X2),X2)
| X2 = relation_image(X1,X3)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_695]) ).
cnf(c_0_695_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk9_3(X1,X3,X2),sk1_esk8_3(X1,X3,X2)),X1)
| in(sk1_esk8_3(X1,X3,X2),X2)
| X2 = relation_image(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_695]) ).
cnf(c_0_696_0,axiom,
( X1 = set_intersection2(X2,X3)
| ~ in(sk1_esk34_3(X2,X3,X1),X3)
| ~ in(sk1_esk34_3(X2,X3,X1),X2)
| ~ in(sk1_esk34_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_696]) ).
cnf(c_0_696_1,axiom,
( ~ in(sk1_esk34_3(X2,X3,X1),X3)
| X1 = set_intersection2(X2,X3)
| ~ in(sk1_esk34_3(X2,X3,X1),X2)
| ~ in(sk1_esk34_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_696]) ).
cnf(c_0_696_2,axiom,
( ~ in(sk1_esk34_3(X2,X3,X1),X2)
| ~ in(sk1_esk34_3(X2,X3,X1),X3)
| X1 = set_intersection2(X2,X3)
| ~ in(sk1_esk34_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_696]) ).
cnf(c_0_696_3,axiom,
( ~ in(sk1_esk34_3(X2,X3,X1),X1)
| ~ in(sk1_esk34_3(X2,X3,X1),X2)
| ~ in(sk1_esk34_3(X2,X3,X1),X3)
| X1 = set_intersection2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_696]) ).
cnf(c_0_697_0,axiom,
( in(sk1_esk10_4(X1,X3,X2,X4),X3)
| ~ relation(X1)
| X2 != relation_inverse_image(X1,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_697]) ).
cnf(c_0_697_1,axiom,
( ~ relation(X1)
| in(sk1_esk10_4(X1,X3,X2,X4),X3)
| X2 != relation_inverse_image(X1,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_697]) ).
cnf(c_0_697_2,axiom,
( X2 != relation_inverse_image(X1,X3)
| ~ relation(X1)
| in(sk1_esk10_4(X1,X3,X2,X4),X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_697]) ).
cnf(c_0_697_3,axiom,
( ~ in(X4,X2)
| X2 != relation_inverse_image(X1,X3)
| ~ relation(X1)
| in(sk1_esk10_4(X1,X3,X2,X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_697]) ).
cnf(c_0_698_0,axiom,
( in(sk1_esk7_4(X1,X3,X2,X4),X3)
| ~ relation(X1)
| X2 != relation_image(X1,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_698]) ).
cnf(c_0_698_1,axiom,
( ~ relation(X1)
| in(sk1_esk7_4(X1,X3,X2,X4),X3)
| X2 != relation_image(X1,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_698]) ).
cnf(c_0_698_2,axiom,
( X2 != relation_image(X1,X3)
| ~ relation(X1)
| in(sk1_esk7_4(X1,X3,X2,X4),X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_698]) ).
cnf(c_0_698_3,axiom,
( ~ in(X4,X2)
| X2 != relation_image(X1,X3)
| ~ relation(X1)
| in(sk1_esk7_4(X1,X3,X2,X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_698]) ).
cnf(c_0_699_0,axiom,
( in(sk1_esk26_4(X2,X3,X1,X4),X2)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_699]) ).
cnf(c_0_699_1,axiom,
( X1 != cartesian_product2(X2,X3)
| in(sk1_esk26_4(X2,X3,X1,X4),X2)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_699]) ).
cnf(c_0_699_2,axiom,
( ~ in(X4,X1)
| X1 != cartesian_product2(X2,X3)
| in(sk1_esk26_4(X2,X3,X1,X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_699]) ).
cnf(c_0_700_0,axiom,
( in(sk1_esk27_4(X2,X3,X1,X4),X3)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_700]) ).
cnf(c_0_700_1,axiom,
( X1 != cartesian_product2(X2,X3)
| in(sk1_esk27_4(X2,X3,X1,X4),X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_700]) ).
cnf(c_0_700_2,axiom,
( ~ in(X4,X1)
| X1 != cartesian_product2(X2,X3)
| in(sk1_esk27_4(X2,X3,X1,X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_700]) ).
cnf(c_0_701_0,axiom,
( X1 = set_difference(X2,X3)
| in(sk1_esk41_3(X2,X3,X1),X3)
| ~ in(sk1_esk41_3(X2,X3,X1),X2)
| ~ in(sk1_esk41_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_701]) ).
cnf(c_0_701_1,axiom,
( in(sk1_esk41_3(X2,X3,X1),X3)
| X1 = set_difference(X2,X3)
| ~ in(sk1_esk41_3(X2,X3,X1),X2)
| ~ in(sk1_esk41_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_701]) ).
cnf(c_0_701_2,axiom,
( ~ in(sk1_esk41_3(X2,X3,X1),X2)
| in(sk1_esk41_3(X2,X3,X1),X3)
| X1 = set_difference(X2,X3)
| ~ in(sk1_esk41_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_701]) ).
cnf(c_0_701_3,axiom,
( ~ in(sk1_esk41_3(X2,X3,X1),X1)
| ~ in(sk1_esk41_3(X2,X3,X1),X2)
| in(sk1_esk41_3(X2,X3,X1),X3)
| X1 = set_difference(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_701]) ).
cnf(c_0_702_0,axiom,
( X3 = complements_of_subsets(X2,X1)
| in(subset_complement(X2,sk1_esk53_3(X2,X1,X3)),X1)
| in(sk1_esk53_3(X2,X1,X3),X3)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_702]) ).
cnf(c_0_702_1,axiom,
( in(subset_complement(X2,sk1_esk53_3(X2,X1,X3)),X1)
| X3 = complements_of_subsets(X2,X1)
| in(sk1_esk53_3(X2,X1,X3),X3)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_702]) ).
cnf(c_0_702_2,axiom,
( in(sk1_esk53_3(X2,X1,X3),X3)
| in(subset_complement(X2,sk1_esk53_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_702]) ).
cnf(c_0_702_3,axiom,
( ~ element(X1,powerset(powerset(X2)))
| in(sk1_esk53_3(X2,X1,X3),X3)
| in(subset_complement(X2,sk1_esk53_3(X2,X1,X3)),X1)
| X3 = complements_of_subsets(X2,X1)
| ~ element(X3,powerset(powerset(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_702]) ).
cnf(c_0_702_4,axiom,
( ~ element(X3,powerset(powerset(X2)))
| ~ element(X1,powerset(powerset(X2)))
| in(sk1_esk53_3(X2,X1,X3),X3)
| in(subset_complement(X2,sk1_esk53_3(X2,X1,X3)),X1)
| X3 = complements_of_subsets(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_702]) ).
cnf(c_0_703_0,axiom,
( X2 = relation_inverse(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(sk1_esk46_2(X1,X2),sk1_esk45_2(X1,X2)),X1)
| ~ in(ordered_pair(sk1_esk45_2(X1,X2),sk1_esk46_2(X1,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_703]) ).
cnf(c_0_703_1,axiom,
( ~ relation(X1)
| X2 = relation_inverse(X1)
| ~ relation(X2)
| ~ in(ordered_pair(sk1_esk46_2(X1,X2),sk1_esk45_2(X1,X2)),X1)
| ~ in(ordered_pair(sk1_esk45_2(X1,X2),sk1_esk46_2(X1,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_703]) ).
cnf(c_0_703_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| X2 = relation_inverse(X1)
| ~ in(ordered_pair(sk1_esk46_2(X1,X2),sk1_esk45_2(X1,X2)),X1)
| ~ in(ordered_pair(sk1_esk45_2(X1,X2),sk1_esk46_2(X1,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_703]) ).
cnf(c_0_703_3,axiom,
( ~ in(ordered_pair(sk1_esk46_2(X1,X2),sk1_esk45_2(X1,X2)),X1)
| ~ relation(X2)
| ~ relation(X1)
| X2 = relation_inverse(X1)
| ~ in(ordered_pair(sk1_esk45_2(X1,X2),sk1_esk46_2(X1,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_703]) ).
cnf(c_0_703_4,axiom,
( ~ in(ordered_pair(sk1_esk45_2(X1,X2),sk1_esk46_2(X1,X2)),X2)
| ~ in(ordered_pair(sk1_esk46_2(X1,X2),sk1_esk45_2(X1,X2)),X1)
| ~ relation(X2)
| ~ relation(X1)
| X2 = relation_inverse(X1) ),
inference(literals_permutation,[status(thm)],[c_0_703]) ).
cnf(c_0_704_0,axiom,
( X1 = X2
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(sk1_esk22_2(X1,X2),sk1_esk23_2(X1,X2)),X2)
| ~ in(ordered_pair(sk1_esk22_2(X1,X2),sk1_esk23_2(X1,X2)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_704]) ).
cnf(c_0_704_1,axiom,
( ~ relation(X1)
| X1 = X2
| ~ relation(X2)
| ~ in(ordered_pair(sk1_esk22_2(X1,X2),sk1_esk23_2(X1,X2)),X2)
| ~ in(ordered_pair(sk1_esk22_2(X1,X2),sk1_esk23_2(X1,X2)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_704]) ).
cnf(c_0_704_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| X1 = X2
| ~ in(ordered_pair(sk1_esk22_2(X1,X2),sk1_esk23_2(X1,X2)),X2)
| ~ in(ordered_pair(sk1_esk22_2(X1,X2),sk1_esk23_2(X1,X2)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_704]) ).
cnf(c_0_704_3,axiom,
( ~ in(ordered_pair(sk1_esk22_2(X1,X2),sk1_esk23_2(X1,X2)),X2)
| ~ relation(X2)
| ~ relation(X1)
| X1 = X2
| ~ in(ordered_pair(sk1_esk22_2(X1,X2),sk1_esk23_2(X1,X2)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_704]) ).
cnf(c_0_704_4,axiom,
( ~ in(ordered_pair(sk1_esk22_2(X1,X2),sk1_esk23_2(X1,X2)),X1)
| ~ in(ordered_pair(sk1_esk22_2(X1,X2),sk1_esk23_2(X1,X2)),X2)
| ~ relation(X2)
| ~ relation(X1)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_704]) ).
cnf(c_0_705_0,axiom,
( X1 = cartesian_product2(X2,X3)
| in(sk1_esk28_3(X2,X3,X1),X1)
| ordered_pair(sk1_esk29_3(X2,X3,X1),sk1_esk30_3(X2,X3,X1)) = sk1_esk28_3(X2,X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_705]) ).
cnf(c_0_705_1,axiom,
( in(sk1_esk28_3(X2,X3,X1),X1)
| X1 = cartesian_product2(X2,X3)
| ordered_pair(sk1_esk29_3(X2,X3,X1),sk1_esk30_3(X2,X3,X1)) = sk1_esk28_3(X2,X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_705]) ).
cnf(c_0_705_2,axiom,
( ordered_pair(sk1_esk29_3(X2,X3,X1),sk1_esk30_3(X2,X3,X1)) = sk1_esk28_3(X2,X3,X1)
| in(sk1_esk28_3(X2,X3,X1),X1)
| X1 = cartesian_product2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_705]) ).
cnf(c_0_706_0,axiom,
( X1 = set_union2(X2,X3)
| ~ in(sk1_esk25_3(X2,X3,X1),X1)
| ~ in(sk1_esk25_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_706]) ).
cnf(c_0_706_1,axiom,
( ~ in(sk1_esk25_3(X2,X3,X1),X1)
| X1 = set_union2(X2,X3)
| ~ in(sk1_esk25_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_706]) ).
cnf(c_0_706_2,axiom,
( ~ in(sk1_esk25_3(X2,X3,X1),X2)
| ~ in(sk1_esk25_3(X2,X3,X1),X1)
| X1 = set_union2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_706]) ).
cnf(c_0_707_0,axiom,
( X1 = set_union2(X2,X3)
| ~ in(sk1_esk25_3(X2,X3,X1),X1)
| ~ in(sk1_esk25_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_707]) ).
cnf(c_0_707_1,axiom,
( ~ in(sk1_esk25_3(X2,X3,X1),X1)
| X1 = set_union2(X2,X3)
| ~ in(sk1_esk25_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_707]) ).
cnf(c_0_707_2,axiom,
( ~ in(sk1_esk25_3(X2,X3,X1),X3)
| ~ in(sk1_esk25_3(X2,X3,X1),X1)
| X1 = set_union2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_707]) ).
cnf(c_0_708_0,axiom,
( X1 = set_union2(X2,X3)
| in(sk1_esk25_3(X2,X3,X1),X3)
| in(sk1_esk25_3(X2,X3,X1),X2)
| in(sk1_esk25_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_708]) ).
cnf(c_0_708_1,axiom,
( in(sk1_esk25_3(X2,X3,X1),X3)
| X1 = set_union2(X2,X3)
| in(sk1_esk25_3(X2,X3,X1),X2)
| in(sk1_esk25_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_708]) ).
cnf(c_0_708_2,axiom,
( in(sk1_esk25_3(X2,X3,X1),X2)
| in(sk1_esk25_3(X2,X3,X1),X3)
| X1 = set_union2(X2,X3)
| in(sk1_esk25_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_708]) ).
cnf(c_0_708_3,axiom,
( in(sk1_esk25_3(X2,X3,X1),X1)
| in(sk1_esk25_3(X2,X3,X1),X2)
| in(sk1_esk25_3(X2,X3,X1),X3)
| X1 = set_union2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_708]) ).
cnf(c_0_709_0,axiom,
( X1 = cartesian_product2(X2,X3)
| sk1_esk28_3(X2,X3,X1) != ordered_pair(X4,X5)
| ~ in(X5,X3)
| ~ in(X4,X2)
| ~ in(sk1_esk28_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_709]) ).
cnf(c_0_709_1,axiom,
( sk1_esk28_3(X2,X3,X1) != ordered_pair(X4,X5)
| X1 = cartesian_product2(X2,X3)
| ~ in(X5,X3)
| ~ in(X4,X2)
| ~ in(sk1_esk28_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_709]) ).
cnf(c_0_709_2,axiom,
( ~ in(X5,X3)
| sk1_esk28_3(X2,X3,X1) != ordered_pair(X4,X5)
| X1 = cartesian_product2(X2,X3)
| ~ in(X4,X2)
| ~ in(sk1_esk28_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_709]) ).
cnf(c_0_709_3,axiom,
( ~ in(X4,X2)
| ~ in(X5,X3)
| sk1_esk28_3(X2,X3,X1) != ordered_pair(X4,X5)
| X1 = cartesian_product2(X2,X3)
| ~ in(sk1_esk28_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_709]) ).
cnf(c_0_709_4,axiom,
( ~ in(sk1_esk28_3(X2,X3,X1),X1)
| ~ in(X4,X2)
| ~ in(X5,X3)
| sk1_esk28_3(X2,X3,X1) != ordered_pair(X4,X5)
| X1 = cartesian_product2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_709]) ).
cnf(c_0_710_0,axiom,
( X1 = identity_relation(X2)
| ~ relation(X1)
| sk1_esk2_2(X2,X1) != sk1_esk1_2(X2,X1)
| ~ in(sk1_esk1_2(X2,X1),X2)
| ~ in(ordered_pair(sk1_esk1_2(X2,X1),sk1_esk2_2(X2,X1)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_710]) ).
cnf(c_0_710_1,axiom,
( ~ relation(X1)
| X1 = identity_relation(X2)
| sk1_esk2_2(X2,X1) != sk1_esk1_2(X2,X1)
| ~ in(sk1_esk1_2(X2,X1),X2)
| ~ in(ordered_pair(sk1_esk1_2(X2,X1),sk1_esk2_2(X2,X1)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_710]) ).
cnf(c_0_710_2,axiom,
( sk1_esk2_2(X2,X1) != sk1_esk1_2(X2,X1)
| ~ relation(X1)
| X1 = identity_relation(X2)
| ~ in(sk1_esk1_2(X2,X1),X2)
| ~ in(ordered_pair(sk1_esk1_2(X2,X1),sk1_esk2_2(X2,X1)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_710]) ).
cnf(c_0_710_3,axiom,
( ~ in(sk1_esk1_2(X2,X1),X2)
| sk1_esk2_2(X2,X1) != sk1_esk1_2(X2,X1)
| ~ relation(X1)
| X1 = identity_relation(X2)
| ~ in(ordered_pair(sk1_esk1_2(X2,X1),sk1_esk2_2(X2,X1)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_710]) ).
cnf(c_0_710_4,axiom,
( ~ in(ordered_pair(sk1_esk1_2(X2,X1),sk1_esk2_2(X2,X1)),X1)
| ~ in(sk1_esk1_2(X2,X1),X2)
| sk1_esk2_2(X2,X1) != sk1_esk1_2(X2,X1)
| ~ relation(X1)
| X1 = identity_relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_710]) ).
cnf(c_0_711_0,axiom,
( X1 = set_difference(X2,X3)
| in(sk1_esk41_3(X2,X3,X1),X1)
| ~ in(sk1_esk41_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_711]) ).
cnf(c_0_711_1,axiom,
( in(sk1_esk41_3(X2,X3,X1),X1)
| X1 = set_difference(X2,X3)
| ~ in(sk1_esk41_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_711]) ).
cnf(c_0_711_2,axiom,
( ~ in(sk1_esk41_3(X2,X3,X1),X3)
| in(sk1_esk41_3(X2,X3,X1),X1)
| X1 = set_difference(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_711]) ).
cnf(c_0_712_0,axiom,
( X2 = relation_inverse(X1)
| in(ordered_pair(sk1_esk46_2(X1,X2),sk1_esk45_2(X1,X2)),X1)
| in(ordered_pair(sk1_esk45_2(X1,X2),sk1_esk46_2(X1,X2)),X2)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_712]) ).
cnf(c_0_712_1,axiom,
( in(ordered_pair(sk1_esk46_2(X1,X2),sk1_esk45_2(X1,X2)),X1)
| X2 = relation_inverse(X1)
| in(ordered_pair(sk1_esk45_2(X1,X2),sk1_esk46_2(X1,X2)),X2)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_712]) ).
cnf(c_0_712_2,axiom,
( in(ordered_pair(sk1_esk45_2(X1,X2),sk1_esk46_2(X1,X2)),X2)
| in(ordered_pair(sk1_esk46_2(X1,X2),sk1_esk45_2(X1,X2)),X1)
| X2 = relation_inverse(X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_712]) ).
cnf(c_0_712_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk45_2(X1,X2),sk1_esk46_2(X1,X2)),X2)
| in(ordered_pair(sk1_esk46_2(X1,X2),sk1_esk45_2(X1,X2)),X1)
| X2 = relation_inverse(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_712]) ).
cnf(c_0_712_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk45_2(X1,X2),sk1_esk46_2(X1,X2)),X2)
| in(ordered_pair(sk1_esk46_2(X1,X2),sk1_esk45_2(X1,X2)),X1)
| X2 = relation_inverse(X1) ),
inference(literals_permutation,[status(thm)],[c_0_712]) ).
cnf(c_0_713_0,axiom,
( X1 = X2
| in(ordered_pair(sk1_esk22_2(X1,X2),sk1_esk23_2(X1,X2)),X2)
| in(ordered_pair(sk1_esk22_2(X1,X2),sk1_esk23_2(X1,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_713]) ).
cnf(c_0_713_1,axiom,
( in(ordered_pair(sk1_esk22_2(X1,X2),sk1_esk23_2(X1,X2)),X2)
| X1 = X2
| in(ordered_pair(sk1_esk22_2(X1,X2),sk1_esk23_2(X1,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_713]) ).
cnf(c_0_713_2,axiom,
( in(ordered_pair(sk1_esk22_2(X1,X2),sk1_esk23_2(X1,X2)),X1)
| in(ordered_pair(sk1_esk22_2(X1,X2),sk1_esk23_2(X1,X2)),X2)
| X1 = X2
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_713]) ).
cnf(c_0_713_3,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk22_2(X1,X2),sk1_esk23_2(X1,X2)),X1)
| in(ordered_pair(sk1_esk22_2(X1,X2),sk1_esk23_2(X1,X2)),X2)
| X1 = X2
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_713]) ).
cnf(c_0_713_4,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk22_2(X1,X2),sk1_esk23_2(X1,X2)),X1)
| in(ordered_pair(sk1_esk22_2(X1,X2),sk1_esk23_2(X1,X2)),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_713]) ).
cnf(c_0_714_0,axiom,
( X1 = unordered_pair(X2,X3)
| ~ in(sk1_esk24_3(X2,X3,X1),X1)
| sk1_esk24_3(X2,X3,X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_714]) ).
cnf(c_0_714_1,axiom,
( ~ in(sk1_esk24_3(X2,X3,X1),X1)
| X1 = unordered_pair(X2,X3)
| sk1_esk24_3(X2,X3,X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_714]) ).
cnf(c_0_714_2,axiom,
( sk1_esk24_3(X2,X3,X1) != X2
| ~ in(sk1_esk24_3(X2,X3,X1),X1)
| X1 = unordered_pair(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_714]) ).
cnf(c_0_715_0,axiom,
( X1 = unordered_pair(X2,X3)
| ~ in(sk1_esk24_3(X2,X3,X1),X1)
| sk1_esk24_3(X2,X3,X1) != X3 ),
inference(literals_permutation,[status(thm)],[c_0_715]) ).
cnf(c_0_715_1,axiom,
( ~ in(sk1_esk24_3(X2,X3,X1),X1)
| X1 = unordered_pair(X2,X3)
| sk1_esk24_3(X2,X3,X1) != X3 ),
inference(literals_permutation,[status(thm)],[c_0_715]) ).
cnf(c_0_715_2,axiom,
( sk1_esk24_3(X2,X3,X1) != X3
| ~ in(sk1_esk24_3(X2,X3,X1),X1)
| X1 = unordered_pair(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_715]) ).
cnf(c_0_716_0,axiom,
( in(ordered_pair(sk1_esk42_3(X1,X2,X3),X3),X1)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_716]) ).
cnf(c_0_716_1,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk42_3(X1,X2,X3),X3),X1)
| X2 != relation_rng(X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_716]) ).
cnf(c_0_716_2,axiom,
( X2 != relation_rng(X1)
| ~ relation(X1)
| in(ordered_pair(sk1_esk42_3(X1,X2,X3),X3),X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_716]) ).
cnf(c_0_716_3,axiom,
( ~ in(X3,X2)
| X2 != relation_rng(X1)
| ~ relation(X1)
| in(ordered_pair(sk1_esk42_3(X1,X2,X3),X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_716]) ).
cnf(c_0_717_0,axiom,
( in(ordered_pair(X3,sk1_esk35_3(X1,X2,X3)),X1)
| ~ relation(X1)
| X2 != relation_dom(X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_717]) ).
cnf(c_0_717_1,axiom,
( ~ relation(X1)
| in(ordered_pair(X3,sk1_esk35_3(X1,X2,X3)),X1)
| X2 != relation_dom(X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_717]) ).
cnf(c_0_717_2,axiom,
( X2 != relation_dom(X1)
| ~ relation(X1)
| in(ordered_pair(X3,sk1_esk35_3(X1,X2,X3)),X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_717]) ).
cnf(c_0_717_3,axiom,
( ~ in(X3,X2)
| X2 != relation_dom(X1)
| ~ relation(X1)
| in(ordered_pair(X3,sk1_esk35_3(X1,X2,X3)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_717]) ).
cnf(c_0_718_0,axiom,
( X2 = relation_inverse_image(X1,X3)
| in(sk1_esk11_3(X1,X3,X2),X2)
| in(sk1_esk12_3(X1,X3,X2),X3)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_718]) ).
cnf(c_0_718_1,axiom,
( in(sk1_esk11_3(X1,X3,X2),X2)
| X2 = relation_inverse_image(X1,X3)
| in(sk1_esk12_3(X1,X3,X2),X3)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_718]) ).
cnf(c_0_718_2,axiom,
( in(sk1_esk12_3(X1,X3,X2),X3)
| in(sk1_esk11_3(X1,X3,X2),X2)
| X2 = relation_inverse_image(X1,X3)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_718]) ).
cnf(c_0_718_3,axiom,
( ~ relation(X1)
| in(sk1_esk12_3(X1,X3,X2),X3)
| in(sk1_esk11_3(X1,X3,X2),X2)
| X2 = relation_inverse_image(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_718]) ).
cnf(c_0_719_0,axiom,
( X2 = relation_image(X1,X3)
| in(sk1_esk8_3(X1,X3,X2),X2)
| in(sk1_esk9_3(X1,X3,X2),X3)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_719]) ).
cnf(c_0_719_1,axiom,
( in(sk1_esk8_3(X1,X3,X2),X2)
| X2 = relation_image(X1,X3)
| in(sk1_esk9_3(X1,X3,X2),X3)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_719]) ).
cnf(c_0_719_2,axiom,
( in(sk1_esk9_3(X1,X3,X2),X3)
| in(sk1_esk8_3(X1,X3,X2),X2)
| X2 = relation_image(X1,X3)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_719]) ).
cnf(c_0_719_3,axiom,
( ~ relation(X1)
| in(sk1_esk9_3(X1,X3,X2),X3)
| in(sk1_esk8_3(X1,X3,X2),X2)
| X2 = relation_image(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_719]) ).
cnf(c_0_720_0,axiom,
( X1 = set_difference(X2,X3)
| in(sk1_esk41_3(X2,X3,X1),X1)
| in(sk1_esk41_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_720]) ).
cnf(c_0_720_1,axiom,
( in(sk1_esk41_3(X2,X3,X1),X1)
| X1 = set_difference(X2,X3)
| in(sk1_esk41_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_720]) ).
cnf(c_0_720_2,axiom,
( in(sk1_esk41_3(X2,X3,X1),X2)
| in(sk1_esk41_3(X2,X3,X1),X1)
| X1 = set_difference(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_720]) ).
cnf(c_0_721_0,axiom,
( X1 = set_intersection2(X2,X3)
| in(sk1_esk34_3(X2,X3,X1),X1)
| in(sk1_esk34_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_721]) ).
cnf(c_0_721_1,axiom,
( in(sk1_esk34_3(X2,X3,X1),X1)
| X1 = set_intersection2(X2,X3)
| in(sk1_esk34_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_721]) ).
cnf(c_0_721_2,axiom,
( in(sk1_esk34_3(X2,X3,X1),X2)
| in(sk1_esk34_3(X2,X3,X1),X1)
| X1 = set_intersection2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_721]) ).
cnf(c_0_722_0,axiom,
( X1 = set_intersection2(X2,X3)
| in(sk1_esk34_3(X2,X3,X1),X1)
| in(sk1_esk34_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_722]) ).
cnf(c_0_722_1,axiom,
( in(sk1_esk34_3(X2,X3,X1),X1)
| X1 = set_intersection2(X2,X3)
| in(sk1_esk34_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_722]) ).
cnf(c_0_722_2,axiom,
( in(sk1_esk34_3(X2,X3,X1),X3)
| in(sk1_esk34_3(X2,X3,X1),X1)
| X1 = set_intersection2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_722]) ).
cnf(c_0_723_0,axiom,
( X1 = cartesian_product2(X2,X3)
| in(sk1_esk28_3(X2,X3,X1),X1)
| in(sk1_esk29_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_723]) ).
cnf(c_0_723_1,axiom,
( in(sk1_esk28_3(X2,X3,X1),X1)
| X1 = cartesian_product2(X2,X3)
| in(sk1_esk29_3(X2,X3,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_723]) ).
cnf(c_0_723_2,axiom,
( in(sk1_esk29_3(X2,X3,X1),X2)
| in(sk1_esk28_3(X2,X3,X1),X1)
| X1 = cartesian_product2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_723]) ).
cnf(c_0_724_0,axiom,
( X1 = cartesian_product2(X2,X3)
| in(sk1_esk28_3(X2,X3,X1),X1)
| in(sk1_esk30_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_724]) ).
cnf(c_0_724_1,axiom,
( in(sk1_esk28_3(X2,X3,X1),X1)
| X1 = cartesian_product2(X2,X3)
| in(sk1_esk30_3(X2,X3,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_724]) ).
cnf(c_0_724_2,axiom,
( in(sk1_esk30_3(X2,X3,X1),X3)
| in(sk1_esk28_3(X2,X3,X1),X1)
| X1 = cartesian_product2(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_724]) ).
cnf(c_0_725_0,axiom,
( subset(X1,X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(sk1_esk31_2(X1,X2),sk1_esk32_2(X1,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_725]) ).
cnf(c_0_725_1,axiom,
( ~ relation(X1)
| subset(X1,X2)
| ~ relation(X2)
| ~ in(ordered_pair(sk1_esk31_2(X1,X2),sk1_esk32_2(X1,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_725]) ).
cnf(c_0_725_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| subset(X1,X2)
| ~ in(ordered_pair(sk1_esk31_2(X1,X2),sk1_esk32_2(X1,X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_725]) ).
cnf(c_0_725_3,axiom,
( ~ in(ordered_pair(sk1_esk31_2(X1,X2),sk1_esk32_2(X1,X2)),X2)
| ~ relation(X2)
| ~ relation(X1)
| subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_725]) ).
cnf(c_0_726_0,axiom,
( X1 = unordered_pair(X2,X3)
| sk1_esk24_3(X2,X3,X1) = X3
| sk1_esk24_3(X2,X3,X1) = X2
| in(sk1_esk24_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_726]) ).
cnf(c_0_726_1,axiom,
( sk1_esk24_3(X2,X3,X1) = X3
| X1 = unordered_pair(X2,X3)
| sk1_esk24_3(X2,X3,X1) = X2
| in(sk1_esk24_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_726]) ).
cnf(c_0_726_2,axiom,
( sk1_esk24_3(X2,X3,X1) = X2
| sk1_esk24_3(X2,X3,X1) = X3
| X1 = unordered_pair(X2,X3)
| in(sk1_esk24_3(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_726]) ).
cnf(c_0_726_3,axiom,
( in(sk1_esk24_3(X2,X3,X1),X1)
| sk1_esk24_3(X2,X3,X1) = X2
| sk1_esk24_3(X2,X3,X1) = X3
| X1 = unordered_pair(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_726]) ).
cnf(c_0_727_0,axiom,
( X3 = complements_of_subsets(X2,X1)
| element(sk1_esk53_3(X2,X1,X3),powerset(X2))
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_727]) ).
cnf(c_0_727_1,axiom,
( element(sk1_esk53_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_727]) ).
cnf(c_0_727_2,axiom,
( ~ element(X1,powerset(powerset(X2)))
| element(sk1_esk53_3(X2,X1,X3),powerset(X2))
| X3 = complements_of_subsets(X2,X1)
| ~ element(X3,powerset(powerset(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_727]) ).
cnf(c_0_727_3,axiom,
( ~ element(X3,powerset(powerset(X2)))
| ~ element(X1,powerset(powerset(X2)))
| element(sk1_esk53_3(X2,X1,X3),powerset(X2))
| X3 = complements_of_subsets(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_727]) ).
cnf(c_0_728_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_728]) ).
cnf(c_0_728_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_728]) ).
cnf(c_0_728_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_728]) ).
cnf(c_0_728_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_728]) ).
cnf(c_0_728_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_728]) ).
cnf(c_0_728_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_728]) ).
cnf(c_0_729_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_729]) ).
cnf(c_0_729_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_729]) ).
cnf(c_0_729_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_729]) ).
cnf(c_0_729_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_729]) ).
cnf(c_0_729_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_729]) ).
cnf(c_0_729_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_729]) ).
cnf(c_0_730_0,axiom,
( X2 = relation_rng(X1)
| ~ relation(X1)
| ~ in(ordered_pair(X3,sk1_esk43_2(X1,X2)),X1)
| ~ in(sk1_esk43_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_730]) ).
cnf(c_0_730_1,axiom,
( ~ relation(X1)
| X2 = relation_rng(X1)
| ~ in(ordered_pair(X3,sk1_esk43_2(X1,X2)),X1)
| ~ in(sk1_esk43_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_730]) ).
cnf(c_0_730_2,axiom,
( ~ in(ordered_pair(X3,sk1_esk43_2(X1,X2)),X1)
| ~ relation(X1)
| X2 = relation_rng(X1)
| ~ in(sk1_esk43_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_730]) ).
cnf(c_0_730_3,axiom,
( ~ in(sk1_esk43_2(X1,X2),X2)
| ~ in(ordered_pair(X3,sk1_esk43_2(X1,X2)),X1)
| ~ relation(X1)
| X2 = relation_rng(X1) ),
inference(literals_permutation,[status(thm)],[c_0_730]) ).
cnf(c_0_731_0,axiom,
( X2 = relation_dom(X1)
| ~ relation(X1)
| ~ in(ordered_pair(sk1_esk36_2(X1,X2),X3),X1)
| ~ in(sk1_esk36_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_731]) ).
cnf(c_0_731_1,axiom,
( ~ relation(X1)
| X2 = relation_dom(X1)
| ~ in(ordered_pair(sk1_esk36_2(X1,X2),X3),X1)
| ~ in(sk1_esk36_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_731]) ).
cnf(c_0_731_2,axiom,
( ~ in(ordered_pair(sk1_esk36_2(X1,X2),X3),X1)
| ~ relation(X1)
| X2 = relation_dom(X1)
| ~ in(sk1_esk36_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_731]) ).
cnf(c_0_731_3,axiom,
( ~ in(sk1_esk36_2(X1,X2),X2)
| ~ in(ordered_pair(sk1_esk36_2(X1,X2),X3),X1)
| ~ relation(X1)
| X2 = relation_dom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_731]) ).
cnf(c_0_732_0,axiom,
( X1 = empty_set
| in(X3,X2)
| X2 != set_meet(X1)
| ~ in(X3,sk1_esk16_3(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_732]) ).
cnf(c_0_732_1,axiom,
( in(X3,X2)
| X1 = empty_set
| X2 != set_meet(X1)
| ~ in(X3,sk1_esk16_3(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_732]) ).
cnf(c_0_732_2,axiom,
( X2 != set_meet(X1)
| in(X3,X2)
| X1 = empty_set
| ~ in(X3,sk1_esk16_3(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_732]) ).
cnf(c_0_732_3,axiom,
( ~ in(X3,sk1_esk16_3(X1,X2,X3))
| X2 != set_meet(X1)
| in(X3,X2)
| X1 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_732]) ).
cnf(c_0_733_0,axiom,
( in(ordered_pair(X4,X5),X3)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X6,X5),X2)
| ~ in(ordered_pair(X4,X6),X1) ),
inference(literals_permutation,[status(thm)],[c_0_733]) ).
cnf(c_0_733_1,axiom,
( ~ relation(X1)
| in(ordered_pair(X4,X5),X3)
| ~ relation(X2)
| ~ relation(X3)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X6,X5),X2)
| ~ in(ordered_pair(X4,X6),X1) ),
inference(literals_permutation,[status(thm)],[c_0_733]) ).
cnf(c_0_733_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X3)
| ~ relation(X3)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X6,X5),X2)
| ~ in(ordered_pair(X4,X6),X1) ),
inference(literals_permutation,[status(thm)],[c_0_733]) ).
cnf(c_0_733_3,axiom,
( ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X3)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X6,X5),X2)
| ~ in(ordered_pair(X4,X6),X1) ),
inference(literals_permutation,[status(thm)],[c_0_733]) ).
cnf(c_0_733_4,axiom,
( X3 != relation_composition(X1,X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X3)
| ~ in(ordered_pair(X6,X5),X2)
| ~ in(ordered_pair(X4,X6),X1) ),
inference(literals_permutation,[status(thm)],[c_0_733]) ).
cnf(c_0_733_5,axiom,
( ~ in(ordered_pair(X6,X5),X2)
| X3 != relation_composition(X1,X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X3)
| ~ in(ordered_pair(X4,X6),X1) ),
inference(literals_permutation,[status(thm)],[c_0_733]) ).
cnf(c_0_733_6,axiom,
( ~ in(ordered_pair(X4,X6),X1)
| ~ in(ordered_pair(X6,X5),X2)
| X3 != relation_composition(X1,X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X3) ),
inference(literals_permutation,[status(thm)],[c_0_733]) ).
cnf(c_0_734_0,axiom,
( X2 = relation_rng(X1)
| in(ordered_pair(sk1_esk44_2(X1,X2),sk1_esk43_2(X1,X2)),X1)
| in(sk1_esk43_2(X1,X2),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_734]) ).
cnf(c_0_734_1,axiom,
( in(ordered_pair(sk1_esk44_2(X1,X2),sk1_esk43_2(X1,X2)),X1)
| X2 = relation_rng(X1)
| in(sk1_esk43_2(X1,X2),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_734]) ).
cnf(c_0_734_2,axiom,
( in(sk1_esk43_2(X1,X2),X2)
| in(ordered_pair(sk1_esk44_2(X1,X2),sk1_esk43_2(X1,X2)),X1)
| X2 = relation_rng(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_734]) ).
cnf(c_0_734_3,axiom,
( ~ relation(X1)
| in(sk1_esk43_2(X1,X2),X2)
| in(ordered_pair(sk1_esk44_2(X1,X2),sk1_esk43_2(X1,X2)),X1)
| X2 = relation_rng(X1) ),
inference(literals_permutation,[status(thm)],[c_0_734]) ).
cnf(c_0_735_0,axiom,
( X2 = relation_dom(X1)
| in(ordered_pair(sk1_esk36_2(X1,X2),sk1_esk37_2(X1,X2)),X1)
| in(sk1_esk36_2(X1,X2),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_735]) ).
cnf(c_0_735_1,axiom,
( in(ordered_pair(sk1_esk36_2(X1,X2),sk1_esk37_2(X1,X2)),X1)
| X2 = relation_dom(X1)
| in(sk1_esk36_2(X1,X2),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_735]) ).
cnf(c_0_735_2,axiom,
( in(sk1_esk36_2(X1,X2),X2)
| in(ordered_pair(sk1_esk36_2(X1,X2),sk1_esk37_2(X1,X2)),X1)
| X2 = relation_dom(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_735]) ).
cnf(c_0_735_3,axiom,
( ~ relation(X1)
| in(sk1_esk36_2(X1,X2),X2)
| in(ordered_pair(sk1_esk36_2(X1,X2),sk1_esk37_2(X1,X2)),X1)
| X2 = relation_dom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_735]) ).
cnf(c_0_736_0,axiom,
( X1 = identity_relation(X2)
| in(ordered_pair(sk1_esk1_2(X2,X1),sk1_esk2_2(X2,X1)),X1)
| in(sk1_esk1_2(X2,X1),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_736]) ).
cnf(c_0_736_1,axiom,
( in(ordered_pair(sk1_esk1_2(X2,X1),sk1_esk2_2(X2,X1)),X1)
| X1 = identity_relation(X2)
| in(sk1_esk1_2(X2,X1),X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_736]) ).
cnf(c_0_736_2,axiom,
( in(sk1_esk1_2(X2,X1),X2)
| in(ordered_pair(sk1_esk1_2(X2,X1),sk1_esk2_2(X2,X1)),X1)
| X1 = identity_relation(X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_736]) ).
cnf(c_0_736_3,axiom,
( ~ relation(X1)
| in(sk1_esk1_2(X2,X1),X2)
| in(ordered_pair(sk1_esk1_2(X2,X1),sk1_esk2_2(X2,X1)),X1)
| X1 = identity_relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_736]) ).
cnf(c_0_737_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_737]) ).
cnf(c_0_737_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_737]) ).
cnf(c_0_737_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_737]) ).
cnf(c_0_738_0,axiom,
( X1 = identity_relation(X2)
| in(ordered_pair(sk1_esk1_2(X2,X1),sk1_esk2_2(X2,X1)),X1)
| sk1_esk2_2(X2,X1) = sk1_esk1_2(X2,X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_738]) ).
cnf(c_0_738_1,axiom,
( in(ordered_pair(sk1_esk1_2(X2,X1),sk1_esk2_2(X2,X1)),X1)
| X1 = identity_relation(X2)
| sk1_esk2_2(X2,X1) = sk1_esk1_2(X2,X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_738]) ).
cnf(c_0_738_2,axiom,
( sk1_esk2_2(X2,X1) = sk1_esk1_2(X2,X1)
| in(ordered_pair(sk1_esk1_2(X2,X1),sk1_esk2_2(X2,X1)),X1)
| X1 = identity_relation(X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_738]) ).
cnf(c_0_738_3,axiom,
( ~ relation(X1)
| sk1_esk2_2(X2,X1) = sk1_esk1_2(X2,X1)
| in(ordered_pair(sk1_esk1_2(X2,X1),sk1_esk2_2(X2,X1)),X1)
| X1 = identity_relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_738]) ).
cnf(c_0_739_0,axiom,
( X1 = empty_set
| X2 = set_meet(X1)
| ~ in(sk1_esk17_2(X1,X2),X2)
| ~ in(sk1_esk17_2(X1,X2),sk1_esk18_2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_739]) ).
cnf(c_0_739_1,axiom,
( X2 = set_meet(X1)
| X1 = empty_set
| ~ in(sk1_esk17_2(X1,X2),X2)
| ~ in(sk1_esk17_2(X1,X2),sk1_esk18_2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_739]) ).
cnf(c_0_739_2,axiom,
( ~ in(sk1_esk17_2(X1,X2),X2)
| X2 = set_meet(X1)
| X1 = empty_set
| ~ in(sk1_esk17_2(X1,X2),sk1_esk18_2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_739]) ).
cnf(c_0_739_3,axiom,
( ~ in(sk1_esk17_2(X1,X2),sk1_esk18_2(X1,X2))
| ~ in(sk1_esk17_2(X1,X2),X2)
| X2 = set_meet(X1)
| X1 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_739]) ).
cnf(c_0_740_0,axiom,
( subset(X1,X2)
| in(ordered_pair(sk1_esk31_2(X1,X2),sk1_esk32_2(X1,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_740]) ).
cnf(c_0_740_1,axiom,
( in(ordered_pair(sk1_esk31_2(X1,X2),sk1_esk32_2(X1,X2)),X1)
| subset(X1,X2)
| ~ relation(X1)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_740]) ).
cnf(c_0_740_2,axiom,
( ~ relation(X1)
| in(ordered_pair(sk1_esk31_2(X1,X2),sk1_esk32_2(X1,X2)),X1)
| subset(X1,X2)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_740]) ).
cnf(c_0_740_3,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(sk1_esk31_2(X1,X2),sk1_esk32_2(X1,X2)),X1)
| subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_740]) ).
cnf(c_0_741_0,axiom,
( in(ordered_pair(X4,X5),X2)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_rng_restriction(X3,X1)
| ~ in(ordered_pair(X4,X5),X1)
| ~ in(X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_741]) ).
cnf(c_0_741_1,axiom,
( ~ relation(X1)
| in(ordered_pair(X4,X5),X2)
| ~ relation(X2)
| X2 != relation_rng_restriction(X3,X1)
| ~ in(ordered_pair(X4,X5),X1)
| ~ in(X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_741]) ).
cnf(c_0_741_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X2)
| X2 != relation_rng_restriction(X3,X1)
| ~ in(ordered_pair(X4,X5),X1)
| ~ in(X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_741]) ).
cnf(c_0_741_3,axiom,
( X2 != relation_rng_restriction(X3,X1)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X2)
| ~ in(ordered_pair(X4,X5),X1)
| ~ in(X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_741]) ).
cnf(c_0_741_4,axiom,
( ~ in(ordered_pair(X4,X5),X1)
| X2 != relation_rng_restriction(X3,X1)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X2)
| ~ in(X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_741]) ).
cnf(c_0_741_5,axiom,
( ~ in(X5,X3)
| ~ in(ordered_pair(X4,X5),X1)
| X2 != relation_rng_restriction(X3,X1)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_741]) ).
cnf(c_0_742_0,axiom,
( in(ordered_pair(X4,X5),X2)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_dom_restriction(X1,X3)
| ~ in(ordered_pair(X4,X5),X1)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_742]) ).
cnf(c_0_742_1,axiom,
( ~ relation(X1)
| in(ordered_pair(X4,X5),X2)
| ~ relation(X2)
| X2 != relation_dom_restriction(X1,X3)
| ~ in(ordered_pair(X4,X5),X1)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_742]) ).
cnf(c_0_742_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X2)
| X2 != relation_dom_restriction(X1,X3)
| ~ in(ordered_pair(X4,X5),X1)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_742]) ).
cnf(c_0_742_3,axiom,
( X2 != relation_dom_restriction(X1,X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X2)
| ~ in(ordered_pair(X4,X5),X1)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_742]) ).
cnf(c_0_742_4,axiom,
( ~ in(ordered_pair(X4,X5),X1)
| X2 != relation_dom_restriction(X1,X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X2)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_742]) ).
cnf(c_0_742_5,axiom,
( ~ in(X4,X3)
| ~ in(ordered_pair(X4,X5),X1)
| X2 != relation_dom_restriction(X1,X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_742]) ).
cnf(c_0_743_0,axiom,
( X1 = union(X2)
| ~ in(X3,X2)
| ~ in(sk1_esk39_2(X2,X1),X3)
| ~ in(sk1_esk39_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_743]) ).
cnf(c_0_743_1,axiom,
( ~ in(X3,X2)
| X1 = union(X2)
| ~ in(sk1_esk39_2(X2,X1),X3)
| ~ in(sk1_esk39_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_743]) ).
cnf(c_0_743_2,axiom,
( ~ in(sk1_esk39_2(X2,X1),X3)
| ~ in(X3,X2)
| X1 = union(X2)
| ~ in(sk1_esk39_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_743]) ).
cnf(c_0_743_3,axiom,
( ~ in(sk1_esk39_2(X2,X1),X1)
| ~ in(sk1_esk39_2(X2,X1),X3)
| ~ in(X3,X2)
| X1 = union(X2) ),
inference(literals_permutation,[status(thm)],[c_0_743]) ).
cnf(c_0_744_0,axiom,
( in(X3,sk1_esk38_3(X2,X1,X3))
| X1 != union(X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_744]) ).
cnf(c_0_744_1,axiom,
( X1 != union(X2)
| in(X3,sk1_esk38_3(X2,X1,X3))
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_744]) ).
cnf(c_0_744_2,axiom,
( ~ in(X3,X1)
| X1 != union(X2)
| in(X3,sk1_esk38_3(X2,X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_744]) ).
cnf(c_0_745_0,axiom,
( in(sk1_esk38_3(X2,X1,X3),X2)
| X1 != union(X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_745]) ).
cnf(c_0_745_1,axiom,
( X1 != union(X2)
| in(sk1_esk38_3(X2,X1,X3),X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_745]) ).
cnf(c_0_745_2,axiom,
( ~ in(X3,X1)
| X1 != union(X2)
| in(sk1_esk38_3(X2,X1,X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_745]) ).
cnf(c_0_746_0,axiom,
( X1 = empty_set
| in(X3,X2)
| in(sk1_esk16_3(X1,X2,X3),X1)
| X2 != set_meet(X1) ),
inference(literals_permutation,[status(thm)],[c_0_746]) ).
cnf(c_0_746_1,axiom,
( in(X3,X2)
| X1 = empty_set
| in(sk1_esk16_3(X1,X2,X3),X1)
| X2 != set_meet(X1) ),
inference(literals_permutation,[status(thm)],[c_0_746]) ).
cnf(c_0_746_2,axiom,
( in(sk1_esk16_3(X1,X2,X3),X1)
| in(X3,X2)
| X1 = empty_set
| X2 != set_meet(X1) ),
inference(literals_permutation,[status(thm)],[c_0_746]) ).
cnf(c_0_746_3,axiom,
( X2 != set_meet(X1)
| in(sk1_esk16_3(X1,X2,X3),X1)
| in(X3,X2)
| X1 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_746]) ).
cnf(c_0_747_0,axiom,
( in(ordered_pair(X4,X5),X1)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_rng_restriction(X3,X1)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_747]) ).
cnf(c_0_747_1,axiom,
( ~ relation(X1)
| in(ordered_pair(X4,X5),X1)
| ~ relation(X2)
| X2 != relation_rng_restriction(X3,X1)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_747]) ).
cnf(c_0_747_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X1)
| X2 != relation_rng_restriction(X3,X1)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_747]) ).
cnf(c_0_747_3,axiom,
( X2 != relation_rng_restriction(X3,X1)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X1)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_747]) ).
cnf(c_0_747_4,axiom,
( ~ in(ordered_pair(X4,X5),X2)
| X2 != relation_rng_restriction(X3,X1)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X1) ),
inference(literals_permutation,[status(thm)],[c_0_747]) ).
cnf(c_0_748_0,axiom,
( in(ordered_pair(X4,X5),X1)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_dom_restriction(X1,X3)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_748]) ).
cnf(c_0_748_1,axiom,
( ~ relation(X1)
| in(ordered_pair(X4,X5),X1)
| ~ relation(X2)
| X2 != relation_dom_restriction(X1,X3)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_748]) ).
cnf(c_0_748_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X1)
| X2 != relation_dom_restriction(X1,X3)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_748]) ).
cnf(c_0_748_3,axiom,
( X2 != relation_dom_restriction(X1,X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X1)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_748]) ).
cnf(c_0_748_4,axiom,
( ~ in(ordered_pair(X4,X5),X2)
| X2 != relation_dom_restriction(X1,X3)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X4,X5),X1) ),
inference(literals_permutation,[status(thm)],[c_0_748]) ).
cnf(c_0_749_0,axiom,
( in(ordered_pair(X3,X4),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(X3,X4),X1)
| ~ subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_749]) ).
cnf(c_0_749_1,axiom,
( ~ relation(X1)
| in(ordered_pair(X3,X4),X2)
| ~ relation(X2)
| ~ in(ordered_pair(X3,X4),X1)
| ~ subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_749]) ).
cnf(c_0_749_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X3,X4),X1)
| ~ subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_749]) ).
cnf(c_0_749_3,axiom,
( ~ in(ordered_pair(X3,X4),X1)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X2)
| ~ subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_749]) ).
cnf(c_0_749_4,axiom,
( ~ subset(X1,X2)
| ~ in(ordered_pair(X3,X4),X1)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_749]) ).
cnf(c_0_750_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_750]) ).
cnf(c_0_750_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_750]) ).
cnf(c_0_750_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_750]) ).
cnf(c_0_751_0,axiom,
( X2 = X3
| ~ function(X1)
| ~ relation(X1)
| apply(X1,X2) != apply(X1,X3)
| ~ in(X3,relation_dom(X1))
| ~ in(X2,relation_dom(X1))
| ~ one_to_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_751]) ).
cnf(c_0_751_1,axiom,
( ~ function(X1)
| X2 = X3
| ~ relation(X1)
| apply(X1,X2) != apply(X1,X3)
| ~ in(X3,relation_dom(X1))
| ~ in(X2,relation_dom(X1))
| ~ one_to_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_751]) ).
cnf(c_0_751_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| X2 = X3
| apply(X1,X2) != apply(X1,X3)
| ~ in(X3,relation_dom(X1))
| ~ in(X2,relation_dom(X1))
| ~ one_to_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_751]) ).
cnf(c_0_751_3,axiom,
( apply(X1,X2) != apply(X1,X3)
| ~ relation(X1)
| ~ function(X1)
| X2 = X3
| ~ in(X3,relation_dom(X1))
| ~ in(X2,relation_dom(X1))
| ~ one_to_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_751]) ).
cnf(c_0_751_4,axiom,
( ~ in(X3,relation_dom(X1))
| apply(X1,X2) != apply(X1,X3)
| ~ relation(X1)
| ~ function(X1)
| X2 = X3
| ~ in(X2,relation_dom(X1))
| ~ one_to_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_751]) ).
cnf(c_0_751_5,axiom,
( ~ in(X2,relation_dom(X1))
| ~ in(X3,relation_dom(X1))
| apply(X1,X2) != apply(X1,X3)
| ~ relation(X1)
| ~ function(X1)
| X2 = X3
| ~ one_to_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_751]) ).
cnf(c_0_751_6,axiom,
( ~ one_to_one(X1)
| ~ in(X2,relation_dom(X1))
| ~ in(X3,relation_dom(X1))
| apply(X1,X2) != apply(X1,X3)
| ~ relation(X1)
| ~ function(X1)
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_751]) ).
cnf(c_0_752_0,axiom,
( X1 = powerset(X2)
| ~ subset(sk1_esk21_2(X2,X1),X2)
| ~ in(sk1_esk21_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_752]) ).
cnf(c_0_752_1,axiom,
( ~ subset(sk1_esk21_2(X2,X1),X2)
| X1 = powerset(X2)
| ~ in(sk1_esk21_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_752]) ).
cnf(c_0_752_2,axiom,
( ~ in(sk1_esk21_2(X2,X1),X1)
| ~ subset(sk1_esk21_2(X2,X1),X2)
| X1 = powerset(X2) ),
inference(literals_permutation,[status(thm)],[c_0_752]) ).
cnf(c_0_753_0,axiom,
( in(X4,X2)
| ~ relation(X1)
| X2 != relation_inverse_image(X1,X3)
| ~ in(X5,X3)
| ~ in(ordered_pair(X4,X5),X1) ),
inference(literals_permutation,[status(thm)],[c_0_753]) ).
cnf(c_0_753_1,axiom,
( ~ relation(X1)
| in(X4,X2)
| X2 != relation_inverse_image(X1,X3)
| ~ in(X5,X3)
| ~ in(ordered_pair(X4,X5),X1) ),
inference(literals_permutation,[status(thm)],[c_0_753]) ).
cnf(c_0_753_2,axiom,
( X2 != relation_inverse_image(X1,X3)
| ~ relation(X1)
| in(X4,X2)
| ~ in(X5,X3)
| ~ in(ordered_pair(X4,X5),X1) ),
inference(literals_permutation,[status(thm)],[c_0_753]) ).
cnf(c_0_753_3,axiom,
( ~ in(X5,X3)
| X2 != relation_inverse_image(X1,X3)
| ~ relation(X1)
| in(X4,X2)
| ~ in(ordered_pair(X4,X5),X1) ),
inference(literals_permutation,[status(thm)],[c_0_753]) ).
cnf(c_0_753_4,axiom,
( ~ in(ordered_pair(X4,X5),X1)
| ~ in(X5,X3)
| X2 != relation_inverse_image(X1,X3)
| ~ relation(X1)
| in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_753]) ).
cnf(c_0_754_0,axiom,
( in(X4,X2)
| ~ relation(X1)
| X2 != relation_image(X1,X3)
| ~ in(X5,X3)
| ~ in(ordered_pair(X5,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_754]) ).
cnf(c_0_754_1,axiom,
( ~ relation(X1)
| in(X4,X2)
| X2 != relation_image(X1,X3)
| ~ in(X5,X3)
| ~ in(ordered_pair(X5,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_754]) ).
cnf(c_0_754_2,axiom,
( X2 != relation_image(X1,X3)
| ~ relation(X1)
| in(X4,X2)
| ~ in(X5,X3)
| ~ in(ordered_pair(X5,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_754]) ).
cnf(c_0_754_3,axiom,
( ~ in(X5,X3)
| X2 != relation_image(X1,X3)
| ~ relation(X1)
| in(X4,X2)
| ~ in(ordered_pair(X5,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_754]) ).
cnf(c_0_754_4,axiom,
( ~ in(ordered_pair(X5,X4),X1)
| ~ in(X5,X3)
| X2 != relation_image(X1,X3)
| ~ relation(X1)
| in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_754]) ).
cnf(c_0_755_0,axiom,
( X1 = X2
| ~ in(sk1_esk65_2(X1,X2),X2)
| ~ in(sk1_esk65_2(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_755]) ).
cnf(c_0_755_1,axiom,
( ~ in(sk1_esk65_2(X1,X2),X2)
| X1 = X2
| ~ in(sk1_esk65_2(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_755]) ).
cnf(c_0_755_2,axiom,
( ~ in(sk1_esk65_2(X1,X2),X1)
| ~ in(sk1_esk65_2(X1,X2),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_755]) ).
cnf(c_0_756_0,axiom,
( in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_inverse(X1)
| ~ in(ordered_pair(X4,X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_756]) ).
cnf(c_0_756_1,axiom,
( ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| ~ relation(X2)
| X2 != relation_inverse(X1)
| ~ in(ordered_pair(X4,X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_756]) ).
cnf(c_0_756_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| X2 != relation_inverse(X1)
| ~ in(ordered_pair(X4,X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_756]) ).
cnf(c_0_756_3,axiom,
( X2 != relation_inverse(X1)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| ~ in(ordered_pair(X4,X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_756]) ).
cnf(c_0_756_4,axiom,
( ~ in(ordered_pair(X4,X3),X2)
| X2 != relation_inverse(X1)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_756]) ).
cnf(c_0_757_0,axiom,
( in(ordered_pair(X3,X4),X2)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_inverse(X1)
| ~ in(ordered_pair(X4,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_757]) ).
cnf(c_0_757_1,axiom,
( ~ relation(X1)
| in(ordered_pair(X3,X4),X2)
| ~ relation(X2)
| X2 != relation_inverse(X1)
| ~ in(ordered_pair(X4,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_757]) ).
cnf(c_0_757_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X2)
| X2 != relation_inverse(X1)
| ~ in(ordered_pair(X4,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_757]) ).
cnf(c_0_757_3,axiom,
( X2 != relation_inverse(X1)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X4,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_757]) ).
cnf(c_0_757_4,axiom,
( ~ in(ordered_pair(X4,X3),X1)
| X2 != relation_inverse(X1)
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_757]) ).
cnf(c_0_758_0,axiom,
( X3 = apply(X1,X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_dom(X1))
| ~ in(ordered_pair(X2,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_758]) ).
cnf(c_0_758_1,axiom,
( ~ function(X1)
| X3 = apply(X1,X2)
| ~ relation(X1)
| ~ in(X2,relation_dom(X1))
| ~ in(ordered_pair(X2,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_758]) ).
cnf(c_0_758_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| X3 = apply(X1,X2)
| ~ in(X2,relation_dom(X1))
| ~ in(ordered_pair(X2,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_758]) ).
cnf(c_0_758_3,axiom,
( ~ in(X2,relation_dom(X1))
| ~ relation(X1)
| ~ function(X1)
| X3 = apply(X1,X2)
| ~ in(ordered_pair(X2,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_758]) ).
cnf(c_0_758_4,axiom,
( ~ in(ordered_pair(X2,X3),X1)
| ~ in(X2,relation_dom(X1))
| ~ relation(X1)
| ~ function(X1)
| X3 = apply(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_758]) ).
cnf(c_0_759_0,axiom,
( in(ordered_pair(X3,X4),X2)
| ~ relation(X1)
| ~ relation(X2)
| X1 != X2
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_759]) ).
cnf(c_0_759_1,axiom,
( ~ relation(X1)
| in(ordered_pair(X3,X4),X2)
| ~ relation(X2)
| X1 != X2
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_759]) ).
cnf(c_0_759_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X2)
| X1 != X2
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_759]) ).
cnf(c_0_759_3,axiom,
( X1 != X2
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_759]) ).
cnf(c_0_759_4,axiom,
( ~ in(ordered_pair(X3,X4),X1)
| X1 != X2
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_759]) ).
cnf(c_0_760_0,axiom,
( in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| ~ relation(X2)
| X1 != X2
| ~ in(ordered_pair(X3,X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_760]) ).
cnf(c_0_760_1,axiom,
( ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| ~ relation(X2)
| X1 != X2
| ~ in(ordered_pair(X3,X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_760]) ).
cnf(c_0_760_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| X1 != X2
| ~ in(ordered_pair(X3,X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_760]) ).
cnf(c_0_760_3,axiom,
( X1 != X2
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| ~ in(ordered_pair(X3,X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_760]) ).
cnf(c_0_760_4,axiom,
( ~ in(ordered_pair(X3,X4),X2)
| X1 != X2
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_760]) ).
cnf(c_0_761_0,axiom,
( in(X5,X3)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_rng_restriction(X3,X1)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_761]) ).
cnf(c_0_761_1,axiom,
( ~ relation(X1)
| in(X5,X3)
| ~ relation(X2)
| X2 != relation_rng_restriction(X3,X1)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_761]) ).
cnf(c_0_761_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(X5,X3)
| X2 != relation_rng_restriction(X3,X1)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_761]) ).
cnf(c_0_761_3,axiom,
( X2 != relation_rng_restriction(X3,X1)
| ~ relation(X2)
| ~ relation(X1)
| in(X5,X3)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_761]) ).
cnf(c_0_761_4,axiom,
( ~ in(ordered_pair(X4,X5),X2)
| X2 != relation_rng_restriction(X3,X1)
| ~ relation(X2)
| ~ relation(X1)
| in(X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_761]) ).
cnf(c_0_762_0,axiom,
( in(X4,X3)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_dom_restriction(X1,X3)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_762]) ).
cnf(c_0_762_1,axiom,
( ~ relation(X1)
| in(X4,X3)
| ~ relation(X2)
| X2 != relation_dom_restriction(X1,X3)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_762]) ).
cnf(c_0_762_2,axiom,
( ~ relation(X2)
| ~ relation(X1)
| in(X4,X3)
| X2 != relation_dom_restriction(X1,X3)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_762]) ).
cnf(c_0_762_3,axiom,
( X2 != relation_dom_restriction(X1,X3)
| ~ relation(X2)
| ~ relation(X1)
| in(X4,X3)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_762]) ).
cnf(c_0_762_4,axiom,
( ~ in(ordered_pair(X4,X5),X2)
| X2 != relation_dom_restriction(X1,X3)
| ~ relation(X2)
| ~ relation(X1)
| in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_762]) ).
cnf(c_0_763_0,axiom,
( X1 = union(X2)
| in(sk1_esk39_2(X2,X1),X1)
| in(sk1_esk39_2(X2,X1),sk1_esk40_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_763]) ).
cnf(c_0_763_1,axiom,
( in(sk1_esk39_2(X2,X1),X1)
| X1 = union(X2)
| in(sk1_esk39_2(X2,X1),sk1_esk40_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_763]) ).
cnf(c_0_763_2,axiom,
( in(sk1_esk39_2(X2,X1),sk1_esk40_2(X2,X1))
| in(sk1_esk39_2(X2,X1),X1)
| X1 = union(X2) ),
inference(literals_permutation,[status(thm)],[c_0_763]) ).
cnf(c_0_764_0,axiom,
( in(ordered_pair(X2,X3),X1)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_dom(X1))
| X3 != apply(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_764]) ).
cnf(c_0_764_1,axiom,
( ~ function(X1)
| in(ordered_pair(X2,X3),X1)
| ~ relation(X1)
| ~ in(X2,relation_dom(X1))
| X3 != apply(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_764]) ).
cnf(c_0_764_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(ordered_pair(X2,X3),X1)
| ~ in(X2,relation_dom(X1))
| X3 != apply(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_764]) ).
cnf(c_0_764_3,axiom,
( ~ in(X2,relation_dom(X1))
| ~ relation(X1)
| ~ function(X1)
| in(ordered_pair(X2,X3),X1)
| X3 != apply(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_764]) ).
cnf(c_0_764_4,axiom,
( X3 != apply(X1,X2)
| ~ in(X2,relation_dom(X1))
| ~ relation(X1)
| ~ function(X1)
| in(ordered_pair(X2,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_764]) ).
cnf(c_0_765_0,axiom,
( X1 = empty_set
| X2 = set_meet(X1)
| in(sk1_esk18_2(X1,X2),X1)
| ~ in(sk1_esk17_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_765]) ).
cnf(c_0_765_1,axiom,
( X2 = set_meet(X1)
| X1 = empty_set
| in(sk1_esk18_2(X1,X2),X1)
| ~ in(sk1_esk17_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_765]) ).
cnf(c_0_765_2,axiom,
( in(sk1_esk18_2(X1,X2),X1)
| X2 = set_meet(X1)
| X1 = empty_set
| ~ in(sk1_esk17_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_765]) ).
cnf(c_0_765_3,axiom,
( ~ in(sk1_esk17_2(X1,X2),X2)
| in(sk1_esk18_2(X1,X2),X1)
| X2 = set_meet(X1)
| X1 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_765]) ).
cnf(c_0_766_0,axiom,
( X1 = empty_set
| X2 = set_meet(X1)
| in(sk1_esk17_2(X1,X2),X3)
| in(sk1_esk17_2(X1,X2),X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_766]) ).
cnf(c_0_766_1,axiom,
( X2 = set_meet(X1)
| X1 = empty_set
| in(sk1_esk17_2(X1,X2),X3)
| in(sk1_esk17_2(X1,X2),X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_766]) ).
cnf(c_0_766_2,axiom,
( in(sk1_esk17_2(X1,X2),X3)
| X2 = set_meet(X1)
| X1 = empty_set
| in(sk1_esk17_2(X1,X2),X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_766]) ).
cnf(c_0_766_3,axiom,
( in(sk1_esk17_2(X1,X2),X2)
| in(sk1_esk17_2(X1,X2),X3)
| X2 = set_meet(X1)
| X1 = empty_set
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_766]) ).
cnf(c_0_766_4,axiom,
( ~ in(X3,X1)
| in(sk1_esk17_2(X1,X2),X2)
| in(sk1_esk17_2(X1,X2),X3)
| X2 = set_meet(X1)
| X1 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_766]) ).
cnf(c_0_767_0,axiom,
( element(complements_of_subsets(X1,X2),powerset(powerset(X1)))
| ~ element(X2,powerset(powerset(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_767]) ).
cnf(c_0_767_1,axiom,
( ~ element(X2,powerset(powerset(X1)))
| element(complements_of_subsets(X1,X2),powerset(powerset(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_767]) ).
cnf(c_0_768_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_768]) ).
cnf(c_0_768_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_768]) ).
cnf(c_0_768_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_768]) ).
cnf(c_0_768_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_768]) ).
cnf(c_0_768_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_768]) ).
cnf(c_0_769_0,axiom,
( element(meet_of_subsets(X1,X2),powerset(X1))
| ~ element(X2,powerset(powerset(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_769]) ).
cnf(c_0_769_1,axiom,
( ~ element(X2,powerset(powerset(X1)))
| element(meet_of_subsets(X1,X2),powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_769]) ).
cnf(c_0_770_0,axiom,
( element(union_of_subsets(X1,X2),powerset(X1))
| ~ element(X2,powerset(powerset(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_770]) ).
cnf(c_0_770_1,axiom,
( ~ element(X2,powerset(powerset(X1)))
| element(union_of_subsets(X1,X2),powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_770]) ).
cnf(c_0_771_0,axiom,
( ordered_pair(sk1_esk13_2(X2,X1),sk1_esk14_2(X2,X1)) = X1
| ~ in(X1,X2)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_771]) ).
cnf(c_0_771_1,axiom,
( ~ in(X1,X2)
| ordered_pair(sk1_esk13_2(X2,X1),sk1_esk14_2(X2,X1)) = X1
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_771]) ).
cnf(c_0_771_2,axiom,
( ~ relation(X2)
| ~ in(X1,X2)
| ordered_pair(sk1_esk13_2(X2,X1),sk1_esk14_2(X2,X1)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_771]) ).
cnf(c_0_772_0,axiom,
( in(X3,sk1_esk67_2(X2,X1))
| ~ in(X1,sk1_esk66_1(X2))
| ~ subset(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_772]) ).
cnf(c_0_772_1,axiom,
( ~ in(X1,sk1_esk66_1(X2))
| in(X3,sk1_esk67_2(X2,X1))
| ~ subset(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_772]) ).
cnf(c_0_772_2,axiom,
( ~ subset(X3,X1)
| ~ in(X1,sk1_esk66_1(X2))
| in(X3,sk1_esk67_2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_772]) ).
cnf(c_0_773_0,axiom,
( in(X3,X2)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(ordered_pair(X4,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_773]) ).
cnf(c_0_773_1,axiom,
( ~ relation(X1)
| in(X3,X2)
| X2 != relation_rng(X1)
| ~ in(ordered_pair(X4,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_773]) ).
cnf(c_0_773_2,axiom,
( X2 != relation_rng(X1)
| ~ relation(X1)
| in(X3,X2)
| ~ in(ordered_pair(X4,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_773]) ).
cnf(c_0_773_3,axiom,
( ~ in(ordered_pair(X4,X3),X1)
| X2 != relation_rng(X1)
| ~ relation(X1)
| in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_773]) ).
cnf(c_0_774_0,axiom,
( in(X3,X2)
| ~ relation(X1)
| X2 != relation_dom(X1)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_774]) ).
cnf(c_0_774_1,axiom,
( ~ relation(X1)
| in(X3,X2)
| X2 != relation_dom(X1)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_774]) ).
cnf(c_0_774_2,axiom,
( X2 != relation_dom(X1)
| ~ relation(X1)
| in(X3,X2)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_774]) ).
cnf(c_0_774_3,axiom,
( ~ in(ordered_pair(X3,X4),X1)
| X2 != relation_dom(X1)
| ~ relation(X1)
| in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_774]) ).
cnf(c_0_775_0,axiom,
( in(X3,X2)
| ~ relation(X1)
| X1 != identity_relation(X2)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_775]) ).
cnf(c_0_775_1,axiom,
( ~ relation(X1)
| in(X3,X2)
| X1 != identity_relation(X2)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_775]) ).
cnf(c_0_775_2,axiom,
( X1 != identity_relation(X2)
| ~ relation(X1)
| in(X3,X2)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_775]) ).
cnf(c_0_775_3,axiom,
( ~ in(ordered_pair(X3,X4),X1)
| X1 != identity_relation(X2)
| ~ relation(X1)
| in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_775]) ).
cnf(c_0_776_0,axiom,
( X1 = singleton(X2)
| sk1_esk19_2(X2,X1) != X2
| ~ in(sk1_esk19_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_776]) ).
cnf(c_0_776_1,axiom,
( sk1_esk19_2(X2,X1) != X2
| X1 = singleton(X2)
| ~ in(sk1_esk19_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_776]) ).
cnf(c_0_776_2,axiom,
( ~ in(sk1_esk19_2(X2,X1),X1)
| sk1_esk19_2(X2,X1) != X2
| X1 = singleton(X2) ),
inference(literals_permutation,[status(thm)],[c_0_776]) ).
cnf(c_0_777_0,axiom,
( complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2
| ~ element(X2,powerset(powerset(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_777]) ).
cnf(c_0_777_1,axiom,
( ~ element(X2,powerset(powerset(X1)))
| complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_777]) ).
cnf(c_0_778_0,axiom,
( X1 = union(X2)
| in(sk1_esk39_2(X2,X1),X1)
| in(sk1_esk40_2(X2,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_778]) ).
cnf(c_0_778_1,axiom,
( in(sk1_esk39_2(X2,X1),X1)
| X1 = union(X2)
| in(sk1_esk40_2(X2,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_778]) ).
cnf(c_0_778_2,axiom,
( in(sk1_esk40_2(X2,X1),X2)
| in(sk1_esk39_2(X2,X1),X1)
| X1 = union(X2) ),
inference(literals_permutation,[status(thm)],[c_0_778]) ).
cnf(c_0_779_0,axiom,
( X1 = powerset(X2)
| subset(sk1_esk21_2(X2,X1),X2)
| in(sk1_esk21_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_779]) ).
cnf(c_0_779_1,axiom,
( subset(sk1_esk21_2(X2,X1),X2)
| X1 = powerset(X2)
| in(sk1_esk21_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_779]) ).
cnf(c_0_779_2,axiom,
( in(sk1_esk21_2(X2,X1),X1)
| subset(sk1_esk21_2(X2,X1),X2)
| X1 = powerset(X2) ),
inference(literals_permutation,[status(thm)],[c_0_779]) ).
cnf(c_0_780_0,axiom,
( in(X4,X1)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_780]) ).
cnf(c_0_780_1,axiom,
( X1 != set_intersection2(X2,X3)
| in(X4,X1)
| ~ in(X4,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_780]) ).
cnf(c_0_780_2,axiom,
( ~ in(X4,X3)
| X1 != set_intersection2(X2,X3)
| in(X4,X1)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_780]) ).
cnf(c_0_780_3,axiom,
( ~ in(X4,X2)
| ~ in(X4,X3)
| X1 != set_intersection2(X2,X3)
| in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_780]) ).
cnf(c_0_781_0,axiom,
( X1 = X2
| in(sk1_esk65_2(X1,X2),X2)
| in(sk1_esk65_2(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_781]) ).
cnf(c_0_781_1,axiom,
( in(sk1_esk65_2(X1,X2),X2)
| X1 = X2
| in(sk1_esk65_2(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_781]) ).
cnf(c_0_781_2,axiom,
( in(sk1_esk65_2(X1,X2),X1)
| in(sk1_esk65_2(X1,X2),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_781]) ).
cnf(c_0_782_0,axiom,
( in(ordered_pair(X3,X4),X1)
| ~ relation(X1)
| X1 != identity_relation(X2)
| X3 != X4
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_782]) ).
cnf(c_0_782_1,axiom,
( ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| X1 != identity_relation(X2)
| X3 != X4
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_782]) ).
cnf(c_0_782_2,axiom,
( X1 != identity_relation(X2)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| X3 != X4
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_782]) ).
cnf(c_0_782_3,axiom,
( X3 != X4
| X1 != identity_relation(X2)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_782]) ).
cnf(c_0_782_4,axiom,
( ~ in(X3,X2)
| X3 != X4
| X1 != identity_relation(X2)
| ~ relation(X1)
| in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_782]) ).
cnf(c_0_783_0,axiom,
( X3 = X4
| ~ relation(X1)
| X1 != identity_relation(X2)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_783]) ).
cnf(c_0_783_1,axiom,
( ~ relation(X1)
| X3 = X4
| X1 != identity_relation(X2)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_783]) ).
cnf(c_0_783_2,axiom,
( X1 != identity_relation(X2)
| ~ relation(X1)
| X3 = X4
| ~ in(ordered_pair(X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_783]) ).
cnf(c_0_783_3,axiom,
( ~ in(ordered_pair(X3,X4),X1)
| X1 != identity_relation(X2)
| ~ relation(X1)
| X3 = X4 ),
inference(literals_permutation,[status(thm)],[c_0_783]) ).
cnf(c_0_784_0,axiom,
( in(sk1_esk67_2(X2,X1),sk1_esk66_1(X2))
| ~ in(X1,sk1_esk66_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_784]) ).
cnf(c_0_784_1,axiom,
( ~ in(X1,sk1_esk66_1(X2))
| in(sk1_esk67_2(X2,X1),sk1_esk66_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_784]) ).
cnf(c_0_785_0,axiom,
( element(subset_complement(X1,X2),powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_785]) ).
cnf(c_0_785_1,axiom,
( ~ element(X2,powerset(X1))
| element(subset_complement(X1,X2),powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_785]) ).
cnf(c_0_786_0,axiom,
( subset(X1,X2)
| ~ in(sk1_esk33_2(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_786]) ).
cnf(c_0_786_1,axiom,
( ~ in(sk1_esk33_2(X1,X2),X2)
| subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_786]) ).
cnf(c_0_787_0,axiom,
( in(X1,sk1_esk66_1(X2))
| ~ subset(X1,X3)
| ~ in(X3,sk1_esk66_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_787]) ).
cnf(c_0_787_1,axiom,
( ~ subset(X1,X3)
| in(X1,sk1_esk66_1(X2))
| ~ in(X3,sk1_esk66_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_787]) ).
cnf(c_0_787_2,axiom,
( ~ in(X3,sk1_esk66_1(X2))
| ~ subset(X1,X3)
| in(X1,sk1_esk66_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_787]) ).
cnf(c_0_788_0,axiom,
( in(X4,X1)
| in(X4,X3)
| X1 != set_difference(X2,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_788]) ).
cnf(c_0_788_1,axiom,
( in(X4,X3)
| in(X4,X1)
| X1 != set_difference(X2,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_788]) ).
cnf(c_0_788_2,axiom,
( X1 != set_difference(X2,X3)
| in(X4,X3)
| in(X4,X1)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_788]) ).
cnf(c_0_788_3,axiom,
( ~ in(X4,X2)
| X1 != set_difference(X2,X3)
| in(X4,X3)
| in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_788]) ).
cnf(c_0_789_0,axiom,
( in(X4,X3)
| in(X4,X2)
| X1 != set_union2(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_789]) ).
cnf(c_0_789_1,axiom,
( in(X4,X2)
| in(X4,X3)
| X1 != set_union2(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_789]) ).
cnf(c_0_789_2,axiom,
( X1 != set_union2(X2,X3)
| in(X4,X2)
| in(X4,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_789]) ).
cnf(c_0_789_3,axiom,
( ~ in(X4,X1)
| X1 != set_union2(X2,X3)
| in(X4,X2)
| in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_789]) ).
cnf(c_0_790_0,axiom,
( in(X1,sk1_esk66_1(X2))
| are_equipotent(X1,sk1_esk66_1(X2))
| ~ subset(X1,sk1_esk66_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_790]) ).
cnf(c_0_790_1,axiom,
( are_equipotent(X1,sk1_esk66_1(X2))
| in(X1,sk1_esk66_1(X2))
| ~ subset(X1,sk1_esk66_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_790]) ).
cnf(c_0_790_2,axiom,
( ~ subset(X1,sk1_esk66_1(X2))
| are_equipotent(X1,sk1_esk66_1(X2))
| in(X1,sk1_esk66_1(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_790]) ).
cnf(c_0_791_0,axiom,
( subset_complement(X1,subset_complement(X1,X2)) = X2
| ~ element(X2,powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_791]) ).
cnf(c_0_791_1,axiom,
( ~ element(X2,powerset(X1))
| subset_complement(X1,subset_complement(X1,X2)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_791]) ).
cnf(c_0_792_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_792]) ).
cnf(c_0_792_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_792]) ).
cnf(c_0_792_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_792]) ).
cnf(c_0_792_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_792]) ).
cnf(c_0_792_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_792]) ).
cnf(c_0_793_0,axiom,
( meet_of_subsets(X1,X2) = set_meet(X2)
| ~ element(X2,powerset(powerset(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_793]) ).
cnf(c_0_793_1,axiom,
( ~ element(X2,powerset(powerset(X1)))
| meet_of_subsets(X1,X2) = set_meet(X2) ),
inference(literals_permutation,[status(thm)],[c_0_793]) ).
cnf(c_0_794_0,axiom,
( union_of_subsets(X1,X2) = union(X2)
| ~ element(X2,powerset(powerset(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_794]) ).
cnf(c_0_794_1,axiom,
( ~ element(X2,powerset(powerset(X1)))
| union_of_subsets(X1,X2) = union(X2) ),
inference(literals_permutation,[status(thm)],[c_0_794]) ).
cnf(c_0_795_0,axiom,
( element(X1,X2)
| ~ element(X3,powerset(X2))
| ~ in(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_795]) ).
cnf(c_0_795_1,axiom,
( ~ element(X3,powerset(X2))
| element(X1,X2)
| ~ in(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_795]) ).
cnf(c_0_795_2,axiom,
( ~ in(X1,X3)
| ~ element(X3,powerset(X2))
| element(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_795]) ).
cnf(c_0_796_0,axiom,
( X1 != set_difference(X2,X3)
| ~ in(X4,X1)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_796]) ).
cnf(c_0_796_1,axiom,
( ~ in(X4,X1)
| X1 != set_difference(X2,X3)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_796]) ).
cnf(c_0_796_2,axiom,
( ~ in(X4,X3)
| ~ in(X4,X1)
| X1 != set_difference(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_796]) ).
cnf(c_0_797_0,axiom,
( in(X3,X1)
| X1 != union(X2)
| ~ in(X4,X2)
| ~ in(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_797]) ).
cnf(c_0_797_1,axiom,
( X1 != union(X2)
| in(X3,X1)
| ~ in(X4,X2)
| ~ in(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_797]) ).
cnf(c_0_797_2,axiom,
( ~ in(X4,X2)
| X1 != union(X2)
| in(X3,X1)
| ~ in(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_797]) ).
cnf(c_0_797_3,axiom,
( ~ in(X3,X4)
| ~ in(X4,X2)
| X1 != union(X2)
| in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_797]) ).
cnf(c_0_798_0,axiom,
( ~ empty(X1)
| ~ element(X2,powerset(X1))
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_798]) ).
cnf(c_0_798_1,axiom,
( ~ element(X2,powerset(X1))
| ~ empty(X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_798]) ).
cnf(c_0_798_2,axiom,
( ~ in(X3,X2)
| ~ element(X2,powerset(X1))
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_798]) ).
cnf(c_0_799_0,axiom,
( in(X4,X2)
| X1 != set_difference(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_799]) ).
cnf(c_0_799_1,axiom,
( X1 != set_difference(X2,X3)
| in(X4,X2)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_799]) ).
cnf(c_0_799_2,axiom,
( ~ in(X4,X1)
| X1 != set_difference(X2,X3)
| in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_799]) ).
cnf(c_0_800_0,axiom,
( in(X4,X2)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_800]) ).
cnf(c_0_800_1,axiom,
( X1 != set_intersection2(X2,X3)
| in(X4,X2)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_800]) ).
cnf(c_0_800_2,axiom,
( ~ in(X4,X1)
| X1 != set_intersection2(X2,X3)
| in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_800]) ).
cnf(c_0_801_0,axiom,
( in(X4,X3)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_801]) ).
cnf(c_0_801_1,axiom,
( X1 != set_intersection2(X2,X3)
| in(X4,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_801]) ).
cnf(c_0_801_2,axiom,
( ~ in(X4,X1)
| X1 != set_intersection2(X2,X3)
| in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_801]) ).
cnf(c_0_802_0,axiom,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_802]) ).
cnf(c_0_802_1,axiom,
( X1 != set_union2(X2,X3)
| in(X4,X1)
| ~ in(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_802]) ).
cnf(c_0_802_2,axiom,
( ~ in(X4,X2)
| X1 != set_union2(X2,X3)
| in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_802]) ).
cnf(c_0_803_0,axiom,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_803]) ).
cnf(c_0_803_1,axiom,
( X1 != set_union2(X2,X3)
| in(X4,X1)
| ~ in(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_803]) ).
cnf(c_0_803_2,axiom,
( ~ in(X4,X3)
| X1 != set_union2(X2,X3)
| in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_803]) ).
cnf(c_0_804_0,axiom,
( X1 = singleton(X2)
| sk1_esk19_2(X2,X1) = X2
| in(sk1_esk19_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_804]) ).
cnf(c_0_804_1,axiom,
( sk1_esk19_2(X2,X1) = X2
| X1 = singleton(X2)
| in(sk1_esk19_2(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_804]) ).
cnf(c_0_804_2,axiom,
( in(sk1_esk19_2(X2,X1),X1)
| sk1_esk19_2(X2,X1) = X2
| X1 = singleton(X2) ),
inference(literals_permutation,[status(thm)],[c_0_804]) ).
cnf(c_0_805_0,axiom,
( subset_complement(X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_805]) ).
cnf(c_0_805_1,axiom,
( ~ element(X2,powerset(X1))
| subset_complement(X1,X2) = set_difference(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_805]) ).
cnf(c_0_806_0,axiom,
( in(X2,relation_dom(X1))
| X3 = empty_set
| ~ function(X1)
| ~ relation(X1)
| X3 != apply(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_806]) ).
cnf(c_0_806_1,axiom,
( X3 = empty_set
| in(X2,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| X3 != apply(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_806]) ).
cnf(c_0_806_2,axiom,
( ~ function(X1)
| X3 = empty_set
| in(X2,relation_dom(X1))
| ~ relation(X1)
| X3 != apply(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_806]) ).
cnf(c_0_806_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| X3 = empty_set
| in(X2,relation_dom(X1))
| X3 != apply(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_806]) ).
cnf(c_0_806_4,axiom,
( X3 != apply(X1,X2)
| ~ relation(X1)
| ~ function(X1)
| X3 = empty_set
| in(X2,relation_dom(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_806]) ).
cnf(c_0_808_0,axiom,
( in(X1,X2)
| ~ in(X1,X3)
| ~ subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_808]) ).
cnf(c_0_808_1,axiom,
( ~ in(X1,X3)
| in(X1,X2)
| ~ subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_808]) ).
cnf(c_0_808_2,axiom,
( ~ subset(X3,X2)
| ~ in(X1,X3)
| in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_808]) ).
cnf(c_0_809_0,axiom,
( one_to_one(X1)
| apply(X1,sk1_esk48_1(X1)) = apply(X1,sk1_esk47_1(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_809]) ).
cnf(c_0_809_1,axiom,
( apply(X1,sk1_esk48_1(X1)) = apply(X1,sk1_esk47_1(X1))
| one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_809]) ).
cnf(c_0_809_2,axiom,
( ~ function(X1)
| apply(X1,sk1_esk48_1(X1)) = apply(X1,sk1_esk47_1(X1))
| one_to_one(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_809]) ).
cnf(c_0_809_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| apply(X1,sk1_esk48_1(X1)) = apply(X1,sk1_esk47_1(X1))
| one_to_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_809]) ).
cnf(c_0_810_0,axiom,
( relation(relation_composition(X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_810]) ).
cnf(c_0_810_1,axiom,
( ~ function(X1)
| relation(relation_composition(X2,X1))
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_810]) ).
cnf(c_0_810_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| relation(relation_composition(X2,X1))
| ~ function(X2)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_810]) ).
cnf(c_0_810_3,axiom,
( ~ function(X2)
| ~ relation(X1)
| ~ function(X1)
| relation(relation_composition(X2,X1))
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_810]) ).
cnf(c_0_810_4,axiom,
( ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ function(X1)
| relation(relation_composition(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_810]) ).
cnf(c_0_811_0,axiom,
( function(relation_composition(X2,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_811]) ).
cnf(c_0_811_1,axiom,
( ~ function(X1)
| function(relation_composition(X2,X1))
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_811]) ).
cnf(c_0_811_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| function(relation_composition(X2,X1))
| ~ function(X2)
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_811]) ).
cnf(c_0_811_3,axiom,
( ~ function(X2)
| ~ relation(X1)
| ~ function(X1)
| function(relation_composition(X2,X1))
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_811]) ).
cnf(c_0_811_4,axiom,
( ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ function(X1)
| function(relation_composition(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_811]) ).
cnf(c_0_812_0,axiom,
( empty(X2)
| empty(X1)
| ~ empty(cartesian_product2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_812]) ).
cnf(c_0_812_1,axiom,
( empty(X1)
| empty(X2)
| ~ empty(cartesian_product2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_812]) ).
cnf(c_0_812_2,axiom,
( ~ empty(cartesian_product2(X1,X2))
| empty(X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_812]) ).
cnf(c_0_813_0,axiom,
( subset(X1,X2)
| in(sk1_esk33_2(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_813]) ).
cnf(c_0_813_1,axiom,
( in(sk1_esk33_2(X1,X2),X1)
| subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_813]) ).
cnf(c_0_814_0,axiom,
( in(X2,relation_dom(X1))
| X3 = apply(X1,X2)
| ~ function(X1)
| ~ relation(X1)
| X3 != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_814]) ).
cnf(c_0_814_1,axiom,
( X3 = apply(X1,X2)
| in(X2,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| X3 != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_814]) ).
cnf(c_0_814_2,axiom,
( ~ function(X1)
| X3 = apply(X1,X2)
| in(X2,relation_dom(X1))
| ~ relation(X1)
| X3 != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_814]) ).
cnf(c_0_814_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| X3 = apply(X1,X2)
| in(X2,relation_dom(X1))
| X3 != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_814]) ).
cnf(c_0_814_4,axiom,
( X3 != empty_set
| ~ relation(X1)
| ~ function(X1)
| X3 = apply(X1,X2)
| in(X2,relation_dom(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_814]) ).
cnf(c_0_815_0,axiom,
( empty(X2)
| ~ empty(set_union2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_815]) ).
cnf(c_0_815_1,axiom,
( ~ empty(set_union2(X1,X2))
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_815]) ).
cnf(c_0_816_0,axiom,
( empty(X1)
| ~ empty(set_union2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_816]) ).
cnf(c_0_816_1,axiom,
( ~ empty(set_union2(X1,X2))
| empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_816]) ).
cnf(c_0_817_0,axiom,
( X4 = X3
| X4 = X2
| X1 != unordered_pair(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_817]) ).
cnf(c_0_817_1,axiom,
( X4 = X2
| X4 = X3
| X1 != unordered_pair(X2,X3)
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_817]) ).
cnf(c_0_817_2,axiom,
( X1 != unordered_pair(X2,X3)
| X4 = X2
| X4 = X3
| ~ in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_817]) ).
cnf(c_0_817_3,axiom,
( ~ in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 = X2
| X4 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_817]) ).
cnf(c_0_820_0,axiom,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_820]) ).
cnf(c_0_820_1,axiom,
( ~ subset(X2,X1)
| X1 = X2
| ~ subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_820]) ).
cnf(c_0_820_2,axiom,
( ~ subset(X1,X2)
| ~ subset(X2,X1)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_820]) ).
cnf(c_0_821_0,axiom,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_821]) ).
cnf(c_0_821_1,axiom,
( ~ element(X1,powerset(X2))
| subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_821]) ).
cnf(c_0_822_0,axiom,
( one_to_one(X1)
| in(sk1_esk47_1(X1),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_822]) ).
cnf(c_0_822_1,axiom,
( in(sk1_esk47_1(X1),relation_dom(X1))
| one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_822]) ).
cnf(c_0_822_2,axiom,
( ~ function(X1)
| in(sk1_esk47_1(X1),relation_dom(X1))
| one_to_one(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_822]) ).
cnf(c_0_822_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(sk1_esk47_1(X1),relation_dom(X1))
| one_to_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_822]) ).
cnf(c_0_823_0,axiom,
( one_to_one(X1)
| in(sk1_esk48_1(X1),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_823]) ).
cnf(c_0_823_1,axiom,
( in(sk1_esk48_1(X1),relation_dom(X1))
| one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_823]) ).
cnf(c_0_823_2,axiom,
( ~ function(X1)
| in(sk1_esk48_1(X1),relation_dom(X1))
| one_to_one(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_823]) ).
cnf(c_0_823_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| in(sk1_esk48_1(X1),relation_dom(X1))
| one_to_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_823]) ).
cnf(c_0_824_0,axiom,
( subset(X3,X2)
| X1 != powerset(X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_824]) ).
cnf(c_0_824_1,axiom,
( X1 != powerset(X2)
| subset(X3,X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_824]) ).
cnf(c_0_824_2,axiom,
( ~ in(X3,X1)
| X1 != powerset(X2)
| subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_824]) ).
cnf(c_0_825_0,axiom,
( in(X3,X1)
| X1 != powerset(X2)
| ~ subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_825]) ).
cnf(c_0_825_1,axiom,
( X1 != powerset(X2)
| in(X3,X1)
| ~ subset(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_825]) ).
cnf(c_0_825_2,axiom,
( ~ subset(X3,X2)
| X1 != powerset(X2)
| in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_825]) ).
cnf(c_0_826_0,axiom,
( ~ proper_subset(X1,X2)
| ~ proper_subset(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_826]) ).
cnf(c_0_826_1,axiom,
( ~ proper_subset(X2,X1)
| ~ proper_subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_826]) ).
cnf(c_0_827_0,axiom,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_827]) ).
cnf(c_0_827_1,axiom,
( ~ in(X2,X1)
| ~ in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_827]) ).
cnf(c_0_828_0,axiom,
( empty(relation_composition(X2,X1))
| ~ relation(X1)
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_828]) ).
cnf(c_0_828_1,axiom,
( ~ relation(X1)
| empty(relation_composition(X2,X1))
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_828]) ).
cnf(c_0_828_2,axiom,
( ~ empty(X2)
| ~ relation(X1)
| empty(relation_composition(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_828]) ).
cnf(c_0_829_0,axiom,
( relation(relation_composition(X2,X1))
| ~ relation(X1)
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_829]) ).
cnf(c_0_829_1,axiom,
( ~ relation(X1)
| relation(relation_composition(X2,X1))
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_829]) ).
cnf(c_0_829_2,axiom,
( ~ empty(X2)
| ~ relation(X1)
| relation(relation_composition(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_829]) ).
cnf(c_0_830_0,axiom,
( relation(relation_dom_restriction(X1,X2))
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_830]) ).
cnf(c_0_830_1,axiom,
( ~ function(X1)
| relation(relation_dom_restriction(X1,X2))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_830]) ).
cnf(c_0_830_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| relation(relation_dom_restriction(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_830]) ).
cnf(c_0_831_0,axiom,
( function(relation_dom_restriction(X1,X2))
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_831]) ).
cnf(c_0_831_1,axiom,
( ~ function(X1)
| function(relation_dom_restriction(X1,X2))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_831]) ).
cnf(c_0_831_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| function(relation_dom_restriction(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_831]) ).
cnf(c_0_832_0,axiom,
( relation(set_union2(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_832]) ).
cnf(c_0_832_1,axiom,
( ~ relation(X2)
| relation(set_union2(X1,X2))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_832]) ).
cnf(c_0_832_2,axiom,
( ~ relation(X1)
| ~ relation(X2)
| relation(set_union2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_832]) ).
cnf(c_0_833_0,axiom,
( relation(set_intersection2(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_833]) ).
cnf(c_0_833_1,axiom,
( ~ relation(X2)
| relation(set_intersection2(X1,X2))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_833]) ).
cnf(c_0_833_2,axiom,
( ~ relation(X1)
| ~ relation(X2)
| relation(set_intersection2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_833]) ).
cnf(c_0_834_0,axiom,
( relation(relation_dom_restriction(X1,X2))
| ~ relation_empty_yielding(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_834]) ).
cnf(c_0_834_1,axiom,
( ~ relation_empty_yielding(X1)
| relation(relation_dom_restriction(X1,X2))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_834]) ).
cnf(c_0_834_2,axiom,
( ~ relation(X1)
| ~ relation_empty_yielding(X1)
| relation(relation_dom_restriction(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_834]) ).
cnf(c_0_835_0,axiom,
( relation_empty_yielding(relation_dom_restriction(X1,X2))
| ~ relation_empty_yielding(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_835]) ).
cnf(c_0_835_1,axiom,
( ~ relation_empty_yielding(X1)
| relation_empty_yielding(relation_dom_restriction(X1,X2))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_835]) ).
cnf(c_0_835_2,axiom,
( ~ relation(X1)
| ~ relation_empty_yielding(X1)
| relation_empty_yielding(relation_dom_restriction(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_835]) ).
cnf(c_0_836_0,axiom,
( empty(relation_composition(X1,X2))
| ~ relation(X1)
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_836]) ).
cnf(c_0_836_1,axiom,
( ~ relation(X1)
| empty(relation_composition(X1,X2))
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_836]) ).
cnf(c_0_836_2,axiom,
( ~ empty(X2)
| ~ relation(X1)
| empty(relation_composition(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_836]) ).
cnf(c_0_837_0,axiom,
( relation(relation_composition(X1,X2))
| ~ relation(X1)
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_837]) ).
cnf(c_0_837_1,axiom,
( ~ relation(X1)
| relation(relation_composition(X1,X2))
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_837]) ).
cnf(c_0_837_2,axiom,
( ~ empty(X2)
| ~ relation(X1)
| relation(relation_composition(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_837]) ).
cnf(c_0_838_0,axiom,
( relation(relation_composition(X1,X2))
| ~ relation(X2)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_838]) ).
cnf(c_0_838_1,axiom,
( ~ relation(X2)
| relation(relation_composition(X1,X2))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_838]) ).
cnf(c_0_838_2,axiom,
( ~ relation(X1)
| ~ relation(X2)
| relation(relation_composition(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_838]) ).
cnf(c_0_839_0,axiom,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_839]) ).
cnf(c_0_839_1,axiom,
( ~ subset(X1,X2)
| element(X1,powerset(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_839]) ).
cnf(c_0_840_0,axiom,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_840]) ).
cnf(c_0_840_1,axiom,
( X1 != unordered_pair(X2,X3)
| in(X4,X1)
| X4 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_840]) ).
cnf(c_0_840_2,axiom,
( X4 != X2
| X1 != unordered_pair(X2,X3)
| in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_840]) ).
cnf(c_0_841_0,axiom,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_841]) ).
cnf(c_0_841_1,axiom,
( X1 != unordered_pair(X2,X3)
| in(X4,X1)
| X4 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_841]) ).
cnf(c_0_841_2,axiom,
( X4 != X3
| X1 != unordered_pair(X2,X3)
| in(X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_841]) ).
cnf(c_0_842_0,axiom,
( in(X1,X2)
| empty(X2)
| ~ element(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_842]) ).
cnf(c_0_842_1,axiom,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_842]) ).
cnf(c_0_842_2,axiom,
( ~ element(X1,X2)
| empty(X2)
| in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_842]) ).
cnf(c_0_843_0,axiom,
( empty(X1)
| in(X2,X1)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_843]) ).
cnf(c_0_843_1,axiom,
( in(X2,X1)
| empty(X1)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_843]) ).
cnf(c_0_843_2,axiom,
( ~ element(X2,X1)
| in(X2,X1)
| empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_843]) ).
cnf(c_0_844_0,axiom,
( empty(X1)
| element(X2,X1)
| ~ in(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_844]) ).
cnf(c_0_844_1,axiom,
( element(X2,X1)
| empty(X1)
| ~ in(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_844]) ).
cnf(c_0_844_2,axiom,
( ~ in(X2,X1)
| element(X2,X1)
| empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_844]) ).
cnf(c_0_845_0,axiom,
( proper_subset(X1,X2)
| X1 = X2
| ~ subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_845]) ).
cnf(c_0_845_1,axiom,
( X1 = X2
| proper_subset(X1,X2)
| ~ subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_845]) ).
cnf(c_0_845_2,axiom,
( ~ subset(X1,X2)
| X1 = X2
| proper_subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_845]) ).
cnf(c_0_846_0,axiom,
( relation(relation_rng_restriction(X1,X2))
| ~ relation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_846]) ).
cnf(c_0_846_1,axiom,
( ~ relation(X2)
| relation(relation_rng_restriction(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_846]) ).
cnf(c_0_847_0,axiom,
( relation(relation_dom_restriction(X1,X2))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_847]) ).
cnf(c_0_847_1,axiom,
( ~ relation(X1)
| relation(relation_dom_restriction(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_847]) ).
cnf(c_0_848_0,axiom,
( set_union2(relation_dom(X1),relation_rng(X1)) = relation_field(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_848]) ).
cnf(c_0_848_1,axiom,
( ~ relation(X1)
| set_union2(relation_dom(X1),relation_rng(X1)) = relation_field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_848]) ).
cnf(c_0_849_0,axiom,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_849]) ).
cnf(c_0_849_1,axiom,
( ~ in(X1,X2)
| element(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_849]) ).
cnf(c_0_850_0,axiom,
( disjoint(X1,X2)
| ~ disjoint(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_850]) ).
cnf(c_0_850_1,axiom,
( ~ disjoint(X2,X1)
| disjoint(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_850]) ).
cnf(c_0_851_0,axiom,
( subset(X1,X2)
| ~ proper_subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_851]) ).
cnf(c_0_851_1,axiom,
( ~ proper_subset(X1,X2)
| subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_851]) ).
cnf(c_0_852_0,axiom,
( set_intersection2(X1,X2) = empty_set
| ~ disjoint(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_852]) ).
cnf(c_0_852_1,axiom,
( ~ disjoint(X1,X2)
| set_intersection2(X1,X2) = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_852]) ).
cnf(c_0_853_0,axiom,
( disjoint(X1,X2)
| set_intersection2(X1,X2) != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_853]) ).
cnf(c_0_853_1,axiom,
( set_intersection2(X1,X2) != empty_set
| disjoint(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_853]) ).
cnf(c_0_854_0,axiom,
( empty(X2)
| ~ empty(X1)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_854]) ).
cnf(c_0_854_1,axiom,
( ~ empty(X1)
| empty(X2)
| ~ element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_854]) ).
cnf(c_0_854_2,axiom,
( ~ element(X2,X1)
| ~ empty(X1)
| empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_854]) ).
cnf(c_0_855_0,axiom,
( X3 = X2
| X1 != singleton(X2)
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_855]) ).
cnf(c_0_855_1,axiom,
( X1 != singleton(X2)
| X3 = X2
| ~ in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_855]) ).
cnf(c_0_855_2,axiom,
( ~ in(X3,X1)
| X1 != singleton(X2)
| X3 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_855]) ).
cnf(c_0_856_0,axiom,
( relation(X1)
| sk1_esk15_1(X1) != ordered_pair(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_856]) ).
cnf(c_0_856_1,axiom,
( sk1_esk15_1(X1) != ordered_pair(X2,X3)
| relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_856]) ).
cnf(c_0_857_0,axiom,
( relation(relation_inverse(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_857]) ).
cnf(c_0_857_1,axiom,
( ~ one_to_one(X1)
| relation(relation_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_857]) ).
cnf(c_0_857_2,axiom,
( ~ function(X1)
| ~ one_to_one(X1)
| relation(relation_inverse(X1))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_857]) ).
cnf(c_0_857_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| ~ one_to_one(X1)
| relation(relation_inverse(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_857]) ).
cnf(c_0_858_0,axiom,
( function(relation_inverse(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_858]) ).
cnf(c_0_858_1,axiom,
( ~ one_to_one(X1)
| function(relation_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_858]) ).
cnf(c_0_858_2,axiom,
( ~ function(X1)
| ~ one_to_one(X1)
| function(relation_inverse(X1))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_858]) ).
cnf(c_0_858_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| ~ one_to_one(X1)
| function(relation_inverse(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_858]) ).
cnf(c_0_859_0,axiom,
( one_to_one(X1)
| ~ function(X1)
| ~ relation(X1)
| sk1_esk48_1(X1) != sk1_esk47_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_859]) ).
cnf(c_0_859_1,axiom,
( ~ function(X1)
| one_to_one(X1)
| ~ relation(X1)
| sk1_esk48_1(X1) != sk1_esk47_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_859]) ).
cnf(c_0_859_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| one_to_one(X1)
| sk1_esk48_1(X1) != sk1_esk47_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_859]) ).
cnf(c_0_859_3,axiom,
( sk1_esk48_1(X1) != sk1_esk47_1(X1)
| ~ relation(X1)
| ~ function(X1)
| one_to_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_859]) ).
cnf(c_0_860_0,axiom,
( empty(X1)
| element(sk1_esk57_1(X1),powerset(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_860]) ).
cnf(c_0_860_1,axiom,
( element(sk1_esk57_1(X1),powerset(X1))
| empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_860]) ).
cnf(c_0_861_0,axiom,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_861]) ).
cnf(c_0_861_1,axiom,
( ~ in(X2,X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_861]) ).
cnf(c_0_862_0,axiom,
( function_inverse(X1) = relation_inverse(X1)
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_862]) ).
cnf(c_0_862_1,axiom,
( ~ one_to_one(X1)
| function_inverse(X1) = relation_inverse(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_862]) ).
cnf(c_0_862_2,axiom,
( ~ function(X1)
| ~ one_to_one(X1)
| function_inverse(X1) = relation_inverse(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_862]) ).
cnf(c_0_862_3,axiom,
( ~ relation(X1)
| ~ function(X1)
| ~ one_to_one(X1)
| function_inverse(X1) = relation_inverse(X1) ),
inference(literals_permutation,[status(thm)],[c_0_862]) ).
cnf(c_0_863_0,axiom,
( element(X2,X1)
| ~ empty(X1)
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_863]) ).
cnf(c_0_863_1,axiom,
( ~ empty(X1)
| element(X2,X1)
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_863]) ).
cnf(c_0_863_2,axiom,
( ~ empty(X2)
| ~ empty(X1)
| element(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_863]) ).
cnf(c_0_864_0,axiom,
( empty(X1)
| ~ empty(relation_rng(X1))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_864]) ).
cnf(c_0_864_1,axiom,
( ~ empty(relation_rng(X1))
| empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_864]) ).
cnf(c_0_864_2,axiom,
( ~ relation(X1)
| ~ empty(relation_rng(X1))
| empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_864]) ).
cnf(c_0_865_0,axiom,
( empty(X1)
| ~ empty(relation_dom(X1))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_865]) ).
cnf(c_0_865_1,axiom,
( ~ empty(relation_dom(X1))
| empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_865]) ).
cnf(c_0_865_2,axiom,
( ~ relation(X1)
| ~ empty(relation_dom(X1))
| empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_865]) ).
cnf(c_0_871_0,axiom,
( in(X3,X1)
| X1 != singleton(X2)
| X3 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_871]) ).
cnf(c_0_871_1,axiom,
( X1 != singleton(X2)
| in(X3,X1)
| X3 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_871]) ).
cnf(c_0_871_2,axiom,
( X3 != X2
| X1 != singleton(X2)
| in(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_871]) ).
cnf(c_0_872_0,axiom,
( ~ proper_subset(X1,X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_872]) ).
cnf(c_0_872_1,axiom,
( X1 != X2
| ~ proper_subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_872]) ).
cnf(c_0_873_0,axiom,
( relation(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_873]) ).
cnf(c_0_873_1,axiom,
( ~ function(X1)
| relation(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_873]) ).
cnf(c_0_873_2,axiom,
( ~ empty(X1)
| ~ function(X1)
| relation(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_873]) ).
cnf(c_0_873_3,axiom,
( ~ relation(X1)
| ~ empty(X1)
| ~ function(X1)
| relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_873]) ).
cnf(c_0_874_0,axiom,
( function(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_874]) ).
cnf(c_0_874_1,axiom,
( ~ function(X1)
| function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_874]) ).
cnf(c_0_874_2,axiom,
( ~ empty(X1)
| ~ function(X1)
| function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_874]) ).
cnf(c_0_874_3,axiom,
( ~ relation(X1)
| ~ empty(X1)
| ~ function(X1)
| function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_874]) ).
cnf(c_0_875_0,axiom,
( one_to_one(X1)
| ~ function(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_875]) ).
cnf(c_0_875_1,axiom,
( ~ function(X1)
| one_to_one(X1)
| ~ empty(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_875]) ).
cnf(c_0_875_2,axiom,
( ~ empty(X1)
| ~ function(X1)
| one_to_one(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_875]) ).
cnf(c_0_875_3,axiom,
( ~ relation(X1)
| ~ empty(X1)
| ~ function(X1)
| one_to_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_875]) ).
cnf(c_0_876_0,axiom,
( ~ in(X1,X2)
| X2 != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_876]) ).
cnf(c_0_876_1,axiom,
( X2 != empty_set
| ~ in(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_876]) ).
cnf(c_0_877_0,axiom,
( relation(X1)
| in(sk1_esk15_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_877]) ).
cnf(c_0_877_1,axiom,
( in(sk1_esk15_1(X1),X1)
| relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_877]) ).
cnf(c_0_878_0,axiom,
( relation(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_878]) ).
cnf(c_0_878_1,axiom,
( ~ function(X1)
| relation(function_inverse(X1))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_878]) ).
cnf(c_0_878_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| relation(function_inverse(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_878]) ).
cnf(c_0_879_0,axiom,
( function(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_879]) ).
cnf(c_0_879_1,axiom,
( ~ function(X1)
| function(function_inverse(X1))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_879]) ).
cnf(c_0_879_2,axiom,
( ~ relation(X1)
| ~ function(X1)
| function(function_inverse(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_879]) ).
cnf(c_0_881_0,axiom,
( X1 = empty_set
| in(sk1_esk20_1(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_881]) ).
cnf(c_0_881_1,axiom,
( in(sk1_esk20_1(X1),X1)
| X1 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_881]) ).
cnf(c_0_882_0,axiom,
( empty(X1)
| ~ empty(sk1_esk57_1(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_882]) ).
cnf(c_0_882_1,axiom,
( ~ empty(sk1_esk57_1(X1))
| empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_882]) ).
cnf(c_0_885_0,axiom,
( relation_inverse(relation_inverse(X1)) = X1
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_885]) ).
cnf(c_0_885_1,axiom,
( ~ relation(X1)
| relation_inverse(relation_inverse(X1)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_885]) ).
cnf(c_0_886_0,axiom,
( subset(X1,X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_886]) ).
cnf(c_0_886_1,axiom,
( X1 != X2
| subset(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_886]) ).
cnf(c_0_887_0,axiom,
( subset(X2,X1)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_887]) ).
cnf(c_0_887_1,axiom,
( X1 != X2
| subset(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_887]) ).
cnf(c_0_888_0,axiom,
( empty(relation_rng(X1))
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_888]) ).
cnf(c_0_888_1,axiom,
( ~ empty(X1)
| empty(relation_rng(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_888]) ).
cnf(c_0_889_0,axiom,
( relation(relation_rng(X1))
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_889]) ).
cnf(c_0_889_1,axiom,
( ~ empty(X1)
| relation(relation_rng(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_889]) ).
cnf(c_0_890_0,axiom,
( empty(relation_dom(X1))
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_890]) ).
cnf(c_0_890_1,axiom,
( ~ empty(X1)
| empty(relation_dom(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_890]) ).
cnf(c_0_891_0,axiom,
( relation(relation_dom(X1))
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_891]) ).
cnf(c_0_891_1,axiom,
( ~ empty(X1)
| relation(relation_dom(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_891]) ).
cnf(c_0_892_0,axiom,
( empty(relation_inverse(X1))
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_892]) ).
cnf(c_0_892_1,axiom,
( ~ empty(X1)
| empty(relation_inverse(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_892]) ).
cnf(c_0_893_0,axiom,
( relation(relation_inverse(X1))
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_893]) ).
cnf(c_0_893_1,axiom,
( ~ empty(X1)
| relation(relation_inverse(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_893]) ).
cnf(c_0_894_0,axiom,
( relation(relation_inverse(X1))
| ~ relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_894]) ).
cnf(c_0_894_1,axiom,
( ~ relation(X1)
| relation(relation_inverse(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_894]) ).
cnf(c_0_897_0,axiom,
( X2 = X1
| ~ empty(X1)
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_897]) ).
cnf(c_0_897_1,axiom,
( ~ empty(X1)
| X2 = X1
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_897]) ).
cnf(c_0_897_2,axiom,
( ~ empty(X2)
| ~ empty(X1)
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_897]) ).
cnf(c_0_905_0,axiom,
( X2 = empty_set
| X1 != empty_set
| X2 != set_meet(X1) ),
inference(literals_permutation,[status(thm)],[c_0_905]) ).
cnf(c_0_905_1,axiom,
( X1 != empty_set
| X2 = empty_set
| X2 != set_meet(X1) ),
inference(literals_permutation,[status(thm)],[c_0_905]) ).
cnf(c_0_905_2,axiom,
( X2 != set_meet(X1)
| X1 != empty_set
| X2 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_905]) ).
cnf(c_0_906_0,axiom,
( relation(X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_906]) ).
cnf(c_0_906_1,axiom,
( ~ empty(X1)
| relation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_906]) ).
cnf(c_0_907_0,axiom,
( function(X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_907]) ).
cnf(c_0_907_1,axiom,
( ~ empty(X1)
| function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_907]) ).
cnf(c_0_912_0,axiom,
( X2 = set_meet(X1)
| X1 != empty_set
| X2 != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_912]) ).
cnf(c_0_912_1,axiom,
( X1 != empty_set
| X2 = set_meet(X1)
| X2 != empty_set ),
inference(literals_permutation,[status(thm)],[c_0_912]) ).
cnf(c_0_912_2,axiom,
( X2 != empty_set
| X1 != empty_set
| X2 = set_meet(X1) ),
inference(literals_permutation,[status(thm)],[c_0_912]) ).
cnf(c_0_913_0,axiom,
( X1 = empty_set
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_913]) ).
cnf(c_0_913_1,axiom,
( ~ empty(X1)
| X1 = empty_set ),
inference(literals_permutation,[status(thm)],[c_0_913]) ).
cnf(c_0_818_0,axiom,
~ empty(unordered_pair(X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_818]) ).
cnf(c_0_819_0,axiom,
~ empty(ordered_pair(X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_819]) ).
cnf(c_0_880_0,axiom,
~ proper_subset(X1,X1),
inference(literals_permutation,[status(thm)],[c_0_880]) ).
cnf(c_0_895_0,axiom,
~ empty(singleton(X1)),
inference(literals_permutation,[status(thm)],[c_0_895]) ).
cnf(c_0_896_0,axiom,
~ empty(powerset(X1)),
inference(literals_permutation,[status(thm)],[c_0_896]) ).
cnf(c_0_915_0,axiom,
~ empty(sk1_esk62_0),
inference(literals_permutation,[status(thm)],[c_0_915]) ).
cnf(c_0_916_0,axiom,
~ empty(sk1_esk60_0),
inference(literals_permutation,[status(thm)],[c_0_916]) ).
cnf(c_0_807_0,axiom,
unordered_pair(unordered_pair(X1,X2),singleton(X1)) = ordered_pair(X1,X2),
inference(literals_permutation,[status(thm)],[c_0_807]) ).
cnf(c_0_866_0,axiom,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(literals_permutation,[status(thm)],[c_0_866]) ).
cnf(c_0_867_0,axiom,
set_union2(X1,X2) = set_union2(X2,X1),
inference(literals_permutation,[status(thm)],[c_0_867]) ).
cnf(c_0_868_0,axiom,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(literals_permutation,[status(thm)],[c_0_868]) ).
cnf(c_0_869_0,axiom,
element(sk1_esk61_1(X1),powerset(X1)),
inference(literals_permutation,[status(thm)],[c_0_869]) ).
cnf(c_0_870_0,axiom,
element(cast_to_subset(X1),powerset(X1)),
inference(literals_permutation,[status(thm)],[c_0_870]) ).
cnf(c_0_883_0,axiom,
in(X1,sk1_esk66_1(X1)),
inference(literals_permutation,[status(thm)],[c_0_883]) ).
cnf(c_0_884_0,axiom,
element(sk1_esk54_1(X1),X1),
inference(literals_permutation,[status(thm)],[c_0_884]) ).
cnf(c_0_898_0,axiom,
set_intersection2(X1,X1) = X1,
inference(literals_permutation,[status(thm)],[c_0_898]) ).
cnf(c_0_899_0,axiom,
set_union2(X1,X1) = X1,
inference(literals_permutation,[status(thm)],[c_0_899]) ).
cnf(c_0_900_0,axiom,
subset(X1,X1),
inference(literals_permutation,[status(thm)],[c_0_900]) ).
cnf(c_0_901_0,axiom,
set_difference(X1,empty_set) = X1,
inference(literals_permutation,[status(thm)],[c_0_901]) ).
cnf(c_0_902_0,axiom,
set_union2(X1,empty_set) = X1,
inference(literals_permutation,[status(thm)],[c_0_902]) ).
cnf(c_0_903_0,axiom,
set_difference(empty_set,X1) = empty_set,
inference(literals_permutation,[status(thm)],[c_0_903]) ).
cnf(c_0_904_0,axiom,
set_intersection2(X1,empty_set) = empty_set,
inference(literals_permutation,[status(thm)],[c_0_904]) ).
cnf(c_0_908_0,axiom,
empty(sk1_esk61_1(X1)),
inference(literals_permutation,[status(thm)],[c_0_908]) ).
cnf(c_0_909_0,axiom,
relation(identity_relation(X1)),
inference(literals_permutation,[status(thm)],[c_0_909]) ).
cnf(c_0_910_0,axiom,
function(identity_relation(X1)),
inference(literals_permutation,[status(thm)],[c_0_910]) ).
cnf(c_0_911_0,axiom,
relation(identity_relation(X1)),
inference(literals_permutation,[status(thm)],[c_0_911]) ).
cnf(c_0_914_0,axiom,
cast_to_subset(X1) = X1,
inference(literals_permutation,[status(thm)],[c_0_914]) ).
cnf(c_0_917_0,axiom,
relation(sk1_esk64_0),
inference(literals_permutation,[status(thm)],[c_0_917]) ).
cnf(c_0_918_0,axiom,
relation_empty_yielding(sk1_esk64_0),
inference(literals_permutation,[status(thm)],[c_0_918]) ).
cnf(c_0_919_0,axiom,
relation(sk1_esk63_0),
inference(literals_permutation,[status(thm)],[c_0_919]) ).
cnf(c_0_920_0,axiom,
function(sk1_esk63_0),
inference(literals_permutation,[status(thm)],[c_0_920]) ).
cnf(c_0_921_0,axiom,
one_to_one(sk1_esk63_0),
inference(literals_permutation,[status(thm)],[c_0_921]) ).
cnf(c_0_922_0,axiom,
relation(sk1_esk60_0),
inference(literals_permutation,[status(thm)],[c_0_922]) ).
cnf(c_0_923_0,axiom,
relation(sk1_esk59_0),
inference(literals_permutation,[status(thm)],[c_0_923]) ).
cnf(c_0_924_0,axiom,
empty(sk1_esk59_0),
inference(literals_permutation,[status(thm)],[c_0_924]) ).
cnf(c_0_925_0,axiom,
function(sk1_esk59_0),
inference(literals_permutation,[status(thm)],[c_0_925]) ).
cnf(c_0_926_0,axiom,
empty(sk1_esk58_0),
inference(literals_permutation,[status(thm)],[c_0_926]) ).
cnf(c_0_927_0,axiom,
empty(sk1_esk56_0),
inference(literals_permutation,[status(thm)],[c_0_927]) ).
cnf(c_0_928_0,axiom,
relation(sk1_esk56_0),
inference(literals_permutation,[status(thm)],[c_0_928]) ).
cnf(c_0_929_0,axiom,
relation(sk1_esk55_0),
inference(literals_permutation,[status(thm)],[c_0_929]) ).
cnf(c_0_930_0,axiom,
function(sk1_esk55_0),
inference(literals_permutation,[status(thm)],[c_0_930]) ).
cnf(c_0_931_0,axiom,
empty(empty_set),
inference(literals_permutation,[status(thm)],[c_0_931]) ).
cnf(c_0_932_0,axiom,
relation(empty_set),
inference(literals_permutation,[status(thm)],[c_0_932]) ).
cnf(c_0_933_0,axiom,
empty(empty_set),
inference(literals_permutation,[status(thm)],[c_0_933]) ).
cnf(c_0_934_0,axiom,
empty(empty_set),
inference(literals_permutation,[status(thm)],[c_0_934]) ).
cnf(c_0_935_0,axiom,
relation(empty_set),
inference(literals_permutation,[status(thm)],[c_0_935]) ).
cnf(c_0_936_0,axiom,
relation_empty_yielding(empty_set),
inference(literals_permutation,[status(thm)],[c_0_936]) ).
cnf(c_0_937_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_937]) ).
cnf(c_0_938_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_938]) ).
cnf(c_0_939_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_939]) ).
cnf(c_0_940_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_940]) ).
cnf(c_0_941_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_941]) ).
cnf(c_0_942_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_942]) ).
cnf(c_0_943_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_943]) ).
cnf(c_0_944_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_944]) ).
cnf(c_0_945_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_945]) ).
cnf(c_0_946_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_946]) ).
cnf(c_0_947_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_947]) ).
cnf(c_0_948_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_948]) ).
cnf(c_0_949_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_949]) ).
cnf(c_0_950_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_950]) ).
cnf(c_0_951_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_951]) ).
cnf(c_0_952_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_952]) ).
cnf(c_0_953_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_953]) ).
cnf(c_0_954_0,axiom,
$true,
inference(literals_permutation,[status(thm)],[c_0_954]) ).
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_001,lemma,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( X2 = relation_dom_restriction(X3,X1)
<=> ( relation_dom(X2) = set_intersection2(relation_dom(X3),X1)
& ! [X4] :
( in(X4,relation_dom(X2))
=> apply(X2,X4) = apply(X3,X4) ) ) ) ) ),
file('<stdin>',t68_funct_1) ).
fof(c_0_1_002,lemma,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( X2 = function_inverse(X1)
<=> ( relation_dom(X2) = relation_rng(X1)
& ! [X3,X4] :
( ( ( in(X3,relation_rng(X1))
& X4 = apply(X2,X3) )
=> ( in(X4,relation_dom(X1))
& X3 = apply(X1,X4) ) )
& ( ( in(X4,relation_dom(X1))
& X3 = apply(X1,X4) )
=> ( in(X3,relation_rng(X1))
& X4 = apply(X2,X3) ) ) ) ) ) ) ) ),
file('<stdin>',t54_funct_1) ).
fof(c_0_2_003,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_inverse_image(X3,X2))
<=> ? [X4] :
( in(X4,relation_rng(X3))
& in(ordered_pair(X1,X4),X3)
& in(X4,X2) ) ) ),
file('<stdin>',t166_relat_1) ).
fof(c_0_3_004,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_image(X3,X2))
<=> ? [X4] :
( in(X4,relation_dom(X3))
& in(ordered_pair(X4,X1),X3)
& in(X4,X2) ) ) ),
file('<stdin>',t143_relat_1) ).
fof(c_0_4_005,lemma,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X1,relation_dom(relation_composition(X3,X2)))
=> apply(relation_composition(X3,X2),X1) = apply(X2,apply(X3,X1)) ) ) ),
file('<stdin>',t22_funct_1) ).
fof(c_0_5_006,lemma,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X1,relation_dom(relation_composition(X3,X2)))
<=> ( in(X1,relation_dom(X3))
& in(apply(X3,X1),relation_dom(X2)) ) ) ) ),
file('<stdin>',t21_funct_1) ).
fof(c_0_6_007,lemma,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X2,relation_dom(relation_dom_restriction(X3,X1)))
=> apply(relation_dom_restriction(X3,X1),X2) = apply(X3,X2) ) ),
file('<stdin>',t70_funct_1) ).
fof(c_0_7_008,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_8_009,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_9_010,lemma,
! [X1,X2,X3,X4] :
( relation(X4)
=> ( in(ordered_pair(X1,X2),relation_composition(identity_relation(X3),X4))
<=> ( in(X1,X3)
& in(ordered_pair(X1,X2),X4) ) ) ),
file('<stdin>',t74_relat_1) ).
fof(c_0_10_011,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_11_012,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_dom(relation_dom_restriction(X3,X2)))
<=> ( in(X1,X2)
& in(X1,relation_dom(X3)) ) ) ),
file('<stdin>',t86_relat_1) ).
fof(c_0_12_013,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_rng(relation_rng_restriction(X2,X3)))
<=> ( in(X1,X2)
& in(X1,relation_rng(X3)) ) ) ),
file('<stdin>',t115_relat_1) ).
fof(c_0_13_014,lemma,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X1,relation_dom(X2))
=> apply(relation_composition(X2,X3),X1) = apply(X3,apply(X2,X1)) ) ) ),
file('<stdin>',t23_funct_1) ).
fof(c_0_14_015,conjecture,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X2,relation_dom(relation_dom_restriction(X3,X1)))
<=> ( in(X2,relation_dom(X3))
& in(X2,X1) ) ) ),
file('<stdin>',l82_funct_1) ).
fof(c_0_15_016,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_16_017,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_17_018,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_18_019,lemma,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( X2 = identity_relation(X1)
<=> ( relation_dom(X2) = X1
& ! [X3] :
( in(X3,X1)
=> apply(X2,X3) = X3 ) ) ) ),
file('<stdin>',t34_funct_1) ).
fof(c_0_19_020,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_20_021,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_21_022,lemma,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(ordered_pair(X1,X2),X3)
<=> ( in(X1,relation_dom(X3))
& X2 = apply(X3,X1) ) ) ),
file('<stdin>',t8_funct_1) ).
fof(c_0_22_023,lemma,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( ( one_to_one(X2)
& in(X1,relation_rng(X2)) )
=> ( X1 = apply(X2,apply(function_inverse(X2),X1))
& X1 = apply(relation_composition(function_inverse(X2),X2),X1) ) ) ),
file('<stdin>',t57_funct_1) ).
fof(c_0_23_024,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( subset(X1,X2)
=> subset(relation_inverse_image(X3,X1),relation_inverse_image(X3,X2)) ) ),
file('<stdin>',t178_relat_1) ).
fof(c_0_24_025,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> subset(relation_rng(relation_composition(X1,X2)),relation_rng(X2)) ) ),
file('<stdin>',t45_relat_1) ).
fof(c_0_25_026,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> subset(relation_dom(relation_composition(X1,X2)),relation_dom(X1)) ) ),
file('<stdin>',t44_relat_1) ).
fof(c_0_26_027,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X1,X2),X3)
=> ( in(X1,relation_field(X3))
& in(X2,relation_field(X3)) ) ) ),
file('<stdin>',t30_relat_1) ).
fof(c_0_27_028,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X1,X2),X3)
=> ( in(X1,relation_dom(X3))
& in(X2,relation_rng(X3)) ) ) ),
file('<stdin>',t20_relat_1) ).
fof(c_0_28_029,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( subset(relation_dom(X1),relation_rng(X2))
=> relation_rng(relation_composition(X2,X1)) = relation_rng(X1) ) ) ),
file('<stdin>',t47_relat_1) ).
fof(c_0_29_030,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( subset(relation_rng(X1),relation_dom(X2))
=> relation_dom(relation_composition(X1,X2)) = relation_dom(X1) ) ) ),
file('<stdin>',t46_relat_1) ).
fof(c_0_30_031,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_31_032,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_difference(X1,X3),set_difference(X2,X3)) ),
file('<stdin>',t33_xboole_1) ).
fof(c_0_32_033,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_intersection2(X1,X3),set_intersection2(X2,X3)) ),
file('<stdin>',t26_xboole_1) ).
fof(c_0_33_034,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_34_035,lemma,
! [X1,X2,X3] :
( relation(X3)
=> relation_dom_restriction(relation_rng_restriction(X1,X3),X2) = relation_rng_restriction(X1,relation_dom_restriction(X3,X2)) ),
file('<stdin>',t140_relat_1) ).
fof(c_0_35_036,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_36_037,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X3,X2) )
=> subset(set_union2(X1,X3),X2) ),
file('<stdin>',t8_xboole_1) ).
fof(c_0_37_038,lemma,
! [X1,X2,X3] :
( subset(unordered_pair(X1,X2),X3)
<=> ( in(X1,X3)
& in(X2,X3) ) ),
file('<stdin>',t38_zfmisc_1) ).
fof(c_0_38_039,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X1,X3) )
=> subset(X1,set_intersection2(X2,X3)) ),
file('<stdin>',t19_xboole_1) ).
fof(c_0_39_040,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_rng(relation_dom_restriction(X2,X1)),relation_rng(X2)) ),
file('<stdin>',t99_relat_1) ).
fof(c_0_40_041,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_rng(relation_rng_restriction(X1,X2)),relation_rng(X2)) ),
file('<stdin>',t118_relat_1) ).
fof(c_0_41_042,lemma,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
=> in(X3,X2) )
=> element(X1,powerset(X2)) ),
file('<stdin>',l71_subset_1) ).
fof(c_0_42_043,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_rng(relation_rng_restriction(X1,X2)),X1) ),
file('<stdin>',t116_relat_1) ).
fof(c_0_43_044,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_44_045,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_45_046,lemma,
! [X1] :
( relation(X1)
=> ( ! [X2,X3] : ~ in(ordered_pair(X2,X3),X1)
=> X1 = empty_set ) ),
file('<stdin>',t56_relat_1) ).
fof(c_0_46_047,lemma,
! [X1,X2] :
( relation(X2)
=> relation_image(X2,X1) = relation_image(X2,set_intersection2(relation_dom(X2),X1)) ),
file('<stdin>',t145_relat_1) ).
fof(c_0_47_048,lemma,
! [X1] :
( relation(X1)
=> subset(X1,cartesian_product2(relation_dom(X1),relation_rng(X1))) ),
file('<stdin>',t21_relat_1) ).
fof(c_0_48_049,lemma,
! [X1,X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( in(X3,X2)
=> in(X3,X1) ) ),
file('<stdin>',l3_subset_1) ).
fof(c_0_49_050,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_50_051,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> relation_rng(relation_composition(X1,X2)) = relation_image(X2,relation_rng(X1)) ) ),
file('<stdin>',t160_relat_1) ).
fof(c_0_51_052,lemma,
! [X1,X2] :
( subset(X1,X2)
=> X2 = set_union2(X1,set_difference(X2,X1)) ),
file('<stdin>',t45_xboole_1) ).
fof(c_0_52_053,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( subset(X1,X2)
=> ( subset(relation_dom(X1),relation_dom(X2))
& subset(relation_rng(X1),relation_rng(X2)) ) ) ) ),
file('<stdin>',t25_relat_1) ).
fof(c_0_53_054,lemma,
! [X1,X2] :
( relation(X2)
=> ~ ( X1 != empty_set
& subset(X1,relation_rng(X2))
& relation_inverse_image(X2,X1) = empty_set ) ),
file('<stdin>',t174_relat_1) ).
fof(c_0_54_055,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& disjoint(X2,X3) )
=> disjoint(X1,X3) ),
file('<stdin>',t63_xboole_1) ).
fof(c_0_55_056,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ),
file('<stdin>',t1_xboole_1) ).
fof(c_0_56_057,lemma,
! [X1,X2] :
( relation(X2)
=> relation_dom(relation_dom_restriction(X2,X1)) = set_intersection2(relation_dom(X2),X1) ),
file('<stdin>',t90_relat_1) ).
fof(c_0_57_058,lemma,
! [X1,X2] :
( relation(X2)
=> relation_rng(relation_rng_restriction(X1,X2)) = set_intersection2(relation_rng(X2),X1) ),
file('<stdin>',t119_relat_1) ).
fof(c_0_58_059,lemma,
! [X1,X2] :
( set_difference(X1,singleton(X2)) = X1
<=> ~ in(X2,X1) ),
file('<stdin>',t65_zfmisc_1) ).
fof(c_0_59_060,lemma,
! [X1,X2] :
~ ( disjoint(singleton(X1),X2)
& in(X1,X2) ),
file('<stdin>',l25_zfmisc_1) ).
fof(c_0_60_061,lemma,
! [X1,X2] : set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
file('<stdin>',t48_xboole_1) ).
fof(c_0_61_062,lemma,
! [X1,X2] : set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
file('<stdin>',t40_xboole_1) ).
fof(c_0_62_063,lemma,
! [X1,X2] : set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
file('<stdin>',t39_xboole_1) ).
fof(c_0_63_064,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_inverse_image(X2,X1),relation_dom(X2)) ),
file('<stdin>',t167_relat_1) ).
fof(c_0_64_065,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_image(X2,X1),relation_rng(X2)) ),
file('<stdin>',t144_relat_1) ).
fof(c_0_65_066,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_66_067,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_dom_restriction(X2,X1),X2) ),
file('<stdin>',t88_relat_1) ).
fof(c_0_67_068,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_rng_restriction(X1,X2),X2) ),
file('<stdin>',t117_relat_1) ).
fof(c_0_68_069,lemma,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
file('<stdin>',t37_zfmisc_1) ).
fof(c_0_69_070,lemma,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
file('<stdin>',l2_zfmisc_1) ).
fof(c_0_70_071,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_71_072,lemma,
! [X1,X2] :
~ ( subset(X1,X2)
& proper_subset(X2,X1) ),
file('<stdin>',t60_xboole_1) ).
fof(c_0_72_073,lemma,
! [X1,X2] :
( subset(singleton(X1),singleton(X2))
=> X1 = X2 ),
file('<stdin>',t6_zfmisc_1) ).
fof(c_0_73_074,lemma,
! [X1,X2] :
( in(X1,X2)
=> set_union2(singleton(X1),X2) = X2 ),
file('<stdin>',t46_zfmisc_1) ).
fof(c_0_74_075,lemma,
! [X1,X2] :
( in(X2,X1)
=> apply(identity_relation(X1),X2) = X2 ),
file('<stdin>',t35_funct_1) ).
fof(c_0_75_076,lemma,
! [X1,X2] :
( in(X1,X2)
=> set_union2(singleton(X1),X2) = X2 ),
file('<stdin>',l23_zfmisc_1) ).
fof(c_0_76_077,lemma,
! [X1,X2] :
( in(X1,X2)
=> subset(X1,union(X2)) ),
file('<stdin>',t92_zfmisc_1) ).
fof(c_0_77_078,lemma,
! [X1,X2] :
( in(X1,X2)
=> subset(X1,union(X2)) ),
file('<stdin>',l50_zfmisc_1) ).
fof(c_0_78_079,lemma,
! [X1,X2] :
( relation(X2)
=> relation_dom_restriction(X2,X1) = relation_composition(identity_relation(X1),X2) ),
file('<stdin>',t94_relat_1) ).
fof(c_0_79_080,lemma,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
file('<stdin>',t7_xboole_1) ).
fof(c_0_80_081,lemma,
! [X1,X2] : subset(set_difference(X1,X2),X1),
file('<stdin>',t36_xboole_1) ).
fof(c_0_81_082,lemma,
! [X1,X2] : subset(set_intersection2(X1,X2),X1),
file('<stdin>',t17_xboole_1) ).
fof(c_0_82_083,lemma,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
file('<stdin>',t39_zfmisc_1) ).
fof(c_0_83_084,lemma,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
file('<stdin>',l4_zfmisc_1) ).
fof(c_0_84_085,lemma,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_difference(X1,X2) = X1 ),
file('<stdin>',t83_xboole_1) ).
fof(c_0_85_086,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_intersection2(X1,X2) = X1 ),
file('<stdin>',t28_xboole_1) ).
fof(c_0_86_087,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_union2(X1,X2) = X2 ),
file('<stdin>',t12_xboole_1) ).
fof(c_0_87_088,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('<stdin>',t37_xboole_1) ).
fof(c_0_88_089,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('<stdin>',l32_xboole_1) ).
fof(c_0_89_090,lemma,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> ( relation_rng(X1) = relation_dom(function_inverse(X1))
& relation_dom(X1) = relation_rng(function_inverse(X1)) ) ) ),
file('<stdin>',t55_funct_1) ).
fof(c_0_90_091,lemma,
! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
file('<stdin>',l28_zfmisc_1) ).
fof(c_0_91_092,lemma,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> one_to_one(function_inverse(X1)) ) ),
file('<stdin>',t62_funct_1) ).
fof(c_0_92_093,lemma,
! [X1] :
( relation(X1)
=> relation_image(X1,relation_dom(X1)) = relation_rng(X1) ),
file('<stdin>',t146_relat_1) ).
fof(c_0_93_094,lemma,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X2 = X3 ),
file('<stdin>',t9_zfmisc_1) ).
fof(c_0_94_095,lemma,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X1 = X2 ),
file('<stdin>',t8_zfmisc_1) ).
fof(c_0_95_096,lemma,
! [X1] :
( subset(X1,empty_set)
=> X1 = empty_set ),
file('<stdin>',t3_xboole_1) ).
fof(c_0_96_097,lemma,
! [X1] :
( relation(X1)
=> ( relation_rng(X1) = relation_dom(relation_inverse(X1))
& relation_dom(X1) = relation_rng(relation_inverse(X1)) ) ),
file('<stdin>',t37_relat_1) ).
fof(c_0_97_098,lemma,
! [X1] :
( relation(X1)
=> ( relation_dom(X1) = empty_set
<=> relation_rng(X1) = empty_set ) ),
file('<stdin>',t65_relat_1) ).
fof(c_0_98_099,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('<stdin>',t69_enumset1) ).
fof(c_0_99_100,lemma,
! [X1] :
( relation(X1)
=> ( ( relation_dom(X1) = empty_set
| relation_rng(X1) = empty_set )
=> X1 = empty_set ) ),
file('<stdin>',t64_relat_1) ).
fof(c_0_100_101,lemma,
! [X1] : subset(empty_set,X1),
file('<stdin>',t2_xboole_1) ).
fof(c_0_101_102,lemma,
! [X1] : union(powerset(X1)) = X1,
file('<stdin>',t99_zfmisc_1) ).
fof(c_0_102_103,lemma,
! [X1] :
( relation_dom(identity_relation(X1)) = X1
& relation_rng(identity_relation(X1)) = X1 ),
file('<stdin>',t71_relat_1) ).
fof(c_0_103_104,lemma,
! [X1] : singleton(X1) != empty_set,
file('<stdin>',l1_zfmisc_1) ).
fof(c_0_104_105,lemma,
powerset(empty_set) = singleton(empty_set),
file('<stdin>',t1_zfmisc_1) ).
fof(c_0_105_106,lemma,
( relation_dom(empty_set) = empty_set
& relation_rng(empty_set) = empty_set ),
file('<stdin>',t60_relat_1) ).
fof(c_0_106_107,lemma,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( X2 = relation_dom_restriction(X3,X1)
<=> ( relation_dom(X2) = set_intersection2(relation_dom(X3),X1)
& ! [X4] :
( in(X4,relation_dom(X2))
=> apply(X2,X4) = apply(X3,X4) ) ) ) ) ),
c_0_0 ).
fof(c_0_107_108,lemma,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( X2 = function_inverse(X1)
<=> ( relation_dom(X2) = relation_rng(X1)
& ! [X3,X4] :
( ( ( in(X3,relation_rng(X1))
& X4 = apply(X2,X3) )
=> ( in(X4,relation_dom(X1))
& X3 = apply(X1,X4) ) )
& ( ( in(X4,relation_dom(X1))
& X3 = apply(X1,X4) )
=> ( in(X3,relation_rng(X1))
& X4 = apply(X2,X3) ) ) ) ) ) ) ) ),
c_0_1 ).
fof(c_0_108_109,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_inverse_image(X3,X2))
<=> ? [X4] :
( in(X4,relation_rng(X3))
& in(ordered_pair(X1,X4),X3)
& in(X4,X2) ) ) ),
c_0_2 ).
fof(c_0_109_110,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_image(X3,X2))
<=> ? [X4] :
( in(X4,relation_dom(X3))
& in(ordered_pair(X4,X1),X3)
& in(X4,X2) ) ) ),
c_0_3 ).
fof(c_0_110_111,lemma,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X1,relation_dom(relation_composition(X3,X2)))
=> apply(relation_composition(X3,X2),X1) = apply(X2,apply(X3,X1)) ) ) ),
c_0_4 ).
fof(c_0_111_112,lemma,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X1,relation_dom(relation_composition(X3,X2)))
<=> ( in(X1,relation_dom(X3))
& in(apply(X3,X1),relation_dom(X2)) ) ) ) ),
c_0_5 ).
fof(c_0_112_113,lemma,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X2,relation_dom(relation_dom_restriction(X3,X1)))
=> apply(relation_dom_restriction(X3,X1),X2) = apply(X3,X2) ) ),
c_0_6 ).
fof(c_0_113_114,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_7 ).
fof(c_0_114_115,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_8 ).
fof(c_0_115_116,lemma,
! [X1,X2,X3,X4] :
( relation(X4)
=> ( in(ordered_pair(X1,X2),relation_composition(identity_relation(X3),X4))
<=> ( in(X1,X3)
& in(ordered_pair(X1,X2),X4) ) ) ),
c_0_9 ).
fof(c_0_116_117,lemma,
! [X1,X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( element(X3,powerset(X1))
=> ( disjoint(X2,X3)
<=> subset(X2,subset_complement(X1,X3)) ) ) ),
c_0_10 ).
fof(c_0_117_118,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_dom(relation_dom_restriction(X3,X2)))
<=> ( in(X1,X2)
& in(X1,relation_dom(X3)) ) ) ),
c_0_11 ).
fof(c_0_118_119,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_rng(relation_rng_restriction(X2,X3)))
<=> ( in(X1,X2)
& in(X1,relation_rng(X3)) ) ) ),
c_0_12 ).
fof(c_0_119_120,lemma,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X1,relation_dom(X2))
=> apply(relation_composition(X2,X3),X1) = apply(X3,apply(X2,X1)) ) ) ),
c_0_13 ).
fof(c_0_120_121,negated_conjecture,
~ ! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X2,relation_dom(relation_dom_restriction(X3,X1)))
<=> ( in(X2,relation_dom(X3))
& in(X2,X1) ) ) ),
inference(assume_negation,[status(cth)],[c_0_14]) ).
fof(c_0_121_122,lemma,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X1,X3)
& in(X2,X4) ) ),
c_0_15 ).
fof(c_0_122_123,lemma,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X1,X3)
& in(X2,X4) ) ),
c_0_16 ).
fof(c_0_123_124,lemma,
! [X1,X2,X3] :
( element(X3,powerset(X1))
=> ~ ( in(X2,subset_complement(X1,X3))
& in(X2,X3) ) ),
c_0_17 ).
fof(c_0_124_125,lemma,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( X2 = identity_relation(X1)
<=> ( relation_dom(X2) = X1
& ! [X3] :
( in(X3,X1)
=> apply(X2,X3) = X3 ) ) ) ),
c_0_18 ).
fof(c_0_125_126,lemma,
! [X1,X2,X3,X4] :
( ( subset(X1,X2)
& subset(X3,X4) )
=> subset(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) ),
c_0_19 ).
fof(c_0_126_127,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_20]) ).
fof(c_0_127_128,lemma,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(ordered_pair(X1,X2),X3)
<=> ( in(X1,relation_dom(X3))
& X2 = apply(X3,X1) ) ) ),
c_0_21 ).
fof(c_0_128_129,lemma,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( ( one_to_one(X2)
& in(X1,relation_rng(X2)) )
=> ( X1 = apply(X2,apply(function_inverse(X2),X1))
& X1 = apply(relation_composition(function_inverse(X2),X2),X1) ) ) ),
c_0_22 ).
fof(c_0_129_130,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( subset(X1,X2)
=> subset(relation_inverse_image(X3,X1),relation_inverse_image(X3,X2)) ) ),
c_0_23 ).
fof(c_0_130_131,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> subset(relation_rng(relation_composition(X1,X2)),relation_rng(X2)) ) ),
c_0_24 ).
fof(c_0_131_132,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> subset(relation_dom(relation_composition(X1,X2)),relation_dom(X1)) ) ),
c_0_25 ).
fof(c_0_132_133,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X1,X2),X3)
=> ( in(X1,relation_field(X3))
& in(X2,relation_field(X3)) ) ) ),
c_0_26 ).
fof(c_0_133_134,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X1,X2),X3)
=> ( in(X1,relation_dom(X3))
& in(X2,relation_rng(X3)) ) ) ),
c_0_27 ).
fof(c_0_134_135,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( subset(relation_dom(X1),relation_rng(X2))
=> relation_rng(relation_composition(X2,X1)) = relation_rng(X1) ) ) ),
c_0_28 ).
fof(c_0_135_136,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( subset(relation_rng(X1),relation_dom(X2))
=> relation_dom(relation_composition(X1,X2)) = relation_dom(X1) ) ) ),
c_0_29 ).
fof(c_0_136_137,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> ( in(X3,X1)
| subset(X1,set_difference(X2,singleton(X3))) ) ),
c_0_30 ).
fof(c_0_137_138,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_difference(X1,X3),set_difference(X2,X3)) ),
c_0_31 ).
fof(c_0_138_139,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_intersection2(X1,X3),set_intersection2(X2,X3)) ),
c_0_32 ).
fof(c_0_139_140,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_33 ).
fof(c_0_140_141,lemma,
! [X1,X2,X3] :
( relation(X3)
=> relation_dom_restriction(relation_rng_restriction(X1,X3),X2) = relation_rng_restriction(X1,relation_dom_restriction(X3,X2)) ),
c_0_34 ).
fof(c_0_141_142,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_35]) ).
fof(c_0_142_143,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X3,X2) )
=> subset(set_union2(X1,X3),X2) ),
c_0_36 ).
fof(c_0_143_144,lemma,
! [X1,X2,X3] :
( subset(unordered_pair(X1,X2),X3)
<=> ( in(X1,X3)
& in(X2,X3) ) ),
c_0_37 ).
fof(c_0_144_145,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X1,X3) )
=> subset(X1,set_intersection2(X2,X3)) ),
c_0_38 ).
fof(c_0_145_146,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_rng(relation_dom_restriction(X2,X1)),relation_rng(X2)) ),
c_0_39 ).
fof(c_0_146_147,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_rng(relation_rng_restriction(X1,X2)),relation_rng(X2)) ),
c_0_40 ).
fof(c_0_147_148,lemma,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
=> in(X3,X2) )
=> element(X1,powerset(X2)) ),
c_0_41 ).
fof(c_0_148_149,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_rng(relation_rng_restriction(X1,X2)),X1) ),
c_0_42 ).
fof(c_0_149_150,lemma,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ~ ( X2 != empty_set
& complements_of_subsets(X1,X2) = empty_set ) ),
c_0_43 ).
fof(c_0_150_151,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_44]) ).
fof(c_0_151_152,lemma,
! [X1] :
( relation(X1)
=> ( ! [X2,X3] : ~ in(ordered_pair(X2,X3),X1)
=> X1 = empty_set ) ),
inference(fof_simplification,[status(thm)],[c_0_45]) ).
fof(c_0_152_153,lemma,
! [X1,X2] :
( relation(X2)
=> relation_image(X2,X1) = relation_image(X2,set_intersection2(relation_dom(X2),X1)) ),
c_0_46 ).
fof(c_0_153_154,lemma,
! [X1] :
( relation(X1)
=> subset(X1,cartesian_product2(relation_dom(X1),relation_rng(X1))) ),
c_0_47 ).
fof(c_0_154_155,lemma,
! [X1,X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( in(X3,X2)
=> in(X3,X1) ) ),
c_0_48 ).
fof(c_0_155_156,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_49]) ).
fof(c_0_156_157,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> relation_rng(relation_composition(X1,X2)) = relation_image(X2,relation_rng(X1)) ) ),
c_0_50 ).
fof(c_0_157_158,lemma,
! [X1,X2] :
( subset(X1,X2)
=> X2 = set_union2(X1,set_difference(X2,X1)) ),
c_0_51 ).
fof(c_0_158_159,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( subset(X1,X2)
=> ( subset(relation_dom(X1),relation_dom(X2))
& subset(relation_rng(X1),relation_rng(X2)) ) ) ) ),
c_0_52 ).
fof(c_0_159_160,lemma,
! [X1,X2] :
( relation(X2)
=> ~ ( X1 != empty_set
& subset(X1,relation_rng(X2))
& relation_inverse_image(X2,X1) = empty_set ) ),
c_0_53 ).
fof(c_0_160_161,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& disjoint(X2,X3) )
=> disjoint(X1,X3) ),
c_0_54 ).
fof(c_0_161_162,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ),
c_0_55 ).
fof(c_0_162_163,lemma,
! [X1,X2] :
( relation(X2)
=> relation_dom(relation_dom_restriction(X2,X1)) = set_intersection2(relation_dom(X2),X1) ),
c_0_56 ).
fof(c_0_163_164,lemma,
! [X1,X2] :
( relation(X2)
=> relation_rng(relation_rng_restriction(X1,X2)) = set_intersection2(relation_rng(X2),X1) ),
c_0_57 ).
fof(c_0_164_165,lemma,
! [X1,X2] :
( set_difference(X1,singleton(X2)) = X1
<=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[c_0_58]) ).
fof(c_0_165_166,lemma,
! [X1,X2] :
~ ( disjoint(singleton(X1),X2)
& in(X1,X2) ),
c_0_59 ).
fof(c_0_166_167,lemma,
! [X1,X2] : set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
c_0_60 ).
fof(c_0_167_168,lemma,
! [X1,X2] : set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
c_0_61 ).
fof(c_0_168_169,lemma,
! [X1,X2] : set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
c_0_62 ).
fof(c_0_169_170,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_inverse_image(X2,X1),relation_dom(X2)) ),
c_0_63 ).
fof(c_0_170_171,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_image(X2,X1),relation_rng(X2)) ),
c_0_64 ).
fof(c_0_171_172,lemma,
! [X1,X2,X3,X4] :
~ ( unordered_pair(X1,X2) = unordered_pair(X3,X4)
& X1 != X3
& X1 != X4 ),
c_0_65 ).
fof(c_0_172_173,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_dom_restriction(X2,X1),X2) ),
c_0_66 ).
fof(c_0_173_174,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_rng_restriction(X1,X2),X2) ),
c_0_67 ).
fof(c_0_174_175,lemma,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
c_0_68 ).
fof(c_0_175_176,lemma,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
c_0_69 ).
fof(c_0_176_177,lemma,
! [X1,X2,X3,X4] :
( ordered_pair(X1,X2) = ordered_pair(X3,X4)
=> ( X1 = X3
& X2 = X4 ) ),
c_0_70 ).
fof(c_0_177_178,lemma,
! [X1,X2] :
~ ( subset(X1,X2)
& proper_subset(X2,X1) ),
c_0_71 ).
fof(c_0_178_179,lemma,
! [X1,X2] :
( subset(singleton(X1),singleton(X2))
=> X1 = X2 ),
c_0_72 ).
fof(c_0_179_180,lemma,
! [X1,X2] :
( in(X1,X2)
=> set_union2(singleton(X1),X2) = X2 ),
c_0_73 ).
fof(c_0_180_181,lemma,
! [X1,X2] :
( in(X2,X1)
=> apply(identity_relation(X1),X2) = X2 ),
c_0_74 ).
fof(c_0_181_182,lemma,
! [X1,X2] :
( in(X1,X2)
=> set_union2(singleton(X1),X2) = X2 ),
c_0_75 ).
fof(c_0_182_183,lemma,
! [X1,X2] :
( in(X1,X2)
=> subset(X1,union(X2)) ),
c_0_76 ).
fof(c_0_183_184,lemma,
! [X1,X2] :
( in(X1,X2)
=> subset(X1,union(X2)) ),
c_0_77 ).
fof(c_0_184_185,lemma,
! [X1,X2] :
( relation(X2)
=> relation_dom_restriction(X2,X1) = relation_composition(identity_relation(X1),X2) ),
c_0_78 ).
fof(c_0_185_186,lemma,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
c_0_79 ).
fof(c_0_186_187,lemma,
! [X1,X2] : subset(set_difference(X1,X2),X1),
c_0_80 ).
fof(c_0_187_188,lemma,
! [X1,X2] : subset(set_intersection2(X1,X2),X1),
c_0_81 ).
fof(c_0_188_189,lemma,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
c_0_82 ).
fof(c_0_189_190,lemma,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
c_0_83 ).
fof(c_0_190_191,lemma,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_difference(X1,X2) = X1 ),
c_0_84 ).
fof(c_0_191_192,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_intersection2(X1,X2) = X1 ),
c_0_85 ).
fof(c_0_192_193,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_union2(X1,X2) = X2 ),
c_0_86 ).
fof(c_0_193_194,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
c_0_87 ).
fof(c_0_194_195,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
c_0_88 ).
fof(c_0_195_196,lemma,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> ( relation_rng(X1) = relation_dom(function_inverse(X1))
& relation_dom(X1) = relation_rng(function_inverse(X1)) ) ) ),
c_0_89 ).
fof(c_0_196_197,lemma,
! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
inference(fof_simplification,[status(thm)],[c_0_90]) ).
fof(c_0_197_198,lemma,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> one_to_one(function_inverse(X1)) ) ),
c_0_91 ).
fof(c_0_198_199,lemma,
! [X1] :
( relation(X1)
=> relation_image(X1,relation_dom(X1)) = relation_rng(X1) ),
c_0_92 ).
fof(c_0_199_200,lemma,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X2 = X3 ),
c_0_93 ).
fof(c_0_200_201,lemma,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X1 = X2 ),
c_0_94 ).
fof(c_0_201_202,lemma,
! [X1] :
( subset(X1,empty_set)
=> X1 = empty_set ),
c_0_95 ).
fof(c_0_202_203,lemma,
! [X1] :
( relation(X1)
=> ( relation_rng(X1) = relation_dom(relation_inverse(X1))
& relation_dom(X1) = relation_rng(relation_inverse(X1)) ) ),
c_0_96 ).
fof(c_0_203_204,lemma,
! [X1] :
( relation(X1)
=> ( relation_dom(X1) = empty_set
<=> relation_rng(X1) = empty_set ) ),
c_0_97 ).
fof(c_0_204_205,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
c_0_98 ).
fof(c_0_205_206,lemma,
! [X1] :
( relation(X1)
=> ( ( relation_dom(X1) = empty_set
| relation_rng(X1) = empty_set )
=> X1 = empty_set ) ),
c_0_99 ).
fof(c_0_206_207,lemma,
! [X1] : subset(empty_set,X1),
c_0_100 ).
fof(c_0_207_208,lemma,
! [X1] : union(powerset(X1)) = X1,
c_0_101 ).
fof(c_0_208_209,lemma,
! [X1] :
( relation_dom(identity_relation(X1)) = X1
& relation_rng(identity_relation(X1)) = X1 ),
c_0_102 ).
fof(c_0_209_210,lemma,
! [X1] : singleton(X1) != empty_set,
c_0_103 ).
fof(c_0_210_211,lemma,
powerset(empty_set) = singleton(empty_set),
c_0_104 ).
fof(c_0_211_212,lemma,
( relation_dom(empty_set) = empty_set
& relation_rng(empty_set) = empty_set ),
c_0_105 ).
fof(c_0_212_213,lemma,
! [X5,X6,X7,X8] :
( ( relation_dom(X6) = set_intersection2(relation_dom(X7),X5)
| X6 != relation_dom_restriction(X7,X5)
| ~ relation(X7)
| ~ function(X7)
| ~ relation(X6)
| ~ function(X6) )
& ( ~ in(X8,relation_dom(X6))
| apply(X6,X8) = apply(X7,X8)
| X6 != relation_dom_restriction(X7,X5)
| ~ relation(X7)
| ~ function(X7)
| ~ relation(X6)
| ~ function(X6) )
& ( in(esk17_3(X5,X6,X7),relation_dom(X6))
| relation_dom(X6) != set_intersection2(relation_dom(X7),X5)
| X6 = relation_dom_restriction(X7,X5)
| ~ relation(X7)
| ~ function(X7)
| ~ relation(X6)
| ~ function(X6) )
& ( apply(X6,esk17_3(X5,X6,X7)) != apply(X7,esk17_3(X5,X6,X7))
| relation_dom(X6) != set_intersection2(relation_dom(X7),X5)
| X6 = relation_dom_restriction(X7,X5)
| ~ relation(X7)
| ~ function(X7)
| ~ relation(X6)
| ~ function(X6) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_106])])])])]) ).
fof(c_0_213_214,lemma,
! [X5,X6,X7,X8,X9,X10] :
( ( relation_dom(X6) = relation_rng(X5)
| X6 != function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( in(X8,relation_dom(X5))
| ~ in(X7,relation_rng(X5))
| X8 != apply(X6,X7)
| X6 != function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( X7 = apply(X5,X8)
| ~ in(X7,relation_rng(X5))
| X8 != apply(X6,X7)
| X6 != function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( in(X9,relation_rng(X5))
| ~ in(X10,relation_dom(X5))
| X9 != apply(X5,X10)
| X6 != function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( X10 = apply(X6,X9)
| ~ in(X10,relation_dom(X5))
| X9 != apply(X5,X10)
| X6 != function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( in(esk14_2(X5,X6),relation_dom(X5))
| in(esk11_2(X5,X6),relation_rng(X5))
| relation_dom(X6) != relation_rng(X5)
| X6 = function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( esk13_2(X5,X6) = apply(X5,esk14_2(X5,X6))
| in(esk11_2(X5,X6),relation_rng(X5))
| relation_dom(X6) != relation_rng(X5)
| X6 = function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( ~ in(esk13_2(X5,X6),relation_rng(X5))
| esk14_2(X5,X6) != apply(X6,esk13_2(X5,X6))
| in(esk11_2(X5,X6),relation_rng(X5))
| relation_dom(X6) != relation_rng(X5)
| X6 = function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( in(esk14_2(X5,X6),relation_dom(X5))
| esk12_2(X5,X6) = apply(X6,esk11_2(X5,X6))
| relation_dom(X6) != relation_rng(X5)
| X6 = function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( esk13_2(X5,X6) = apply(X5,esk14_2(X5,X6))
| esk12_2(X5,X6) = apply(X6,esk11_2(X5,X6))
| relation_dom(X6) != relation_rng(X5)
| X6 = function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( ~ in(esk13_2(X5,X6),relation_rng(X5))
| esk14_2(X5,X6) != apply(X6,esk13_2(X5,X6))
| esk12_2(X5,X6) = apply(X6,esk11_2(X5,X6))
| relation_dom(X6) != relation_rng(X5)
| X6 = function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( in(esk14_2(X5,X6),relation_dom(X5))
| ~ in(esk12_2(X5,X6),relation_dom(X5))
| esk11_2(X5,X6) != apply(X5,esk12_2(X5,X6))
| relation_dom(X6) != relation_rng(X5)
| X6 = function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( esk13_2(X5,X6) = apply(X5,esk14_2(X5,X6))
| ~ in(esk12_2(X5,X6),relation_dom(X5))
| esk11_2(X5,X6) != apply(X5,esk12_2(X5,X6))
| relation_dom(X6) != relation_rng(X5)
| X6 = function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( ~ in(esk13_2(X5,X6),relation_rng(X5))
| esk14_2(X5,X6) != apply(X6,esk13_2(X5,X6))
| ~ in(esk12_2(X5,X6),relation_dom(X5))
| esk11_2(X5,X6) != apply(X5,esk12_2(X5,X6))
| relation_dom(X6) != relation_rng(X5)
| X6 = function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_107])])])])])]) ).
fof(c_0_214_215,lemma,
! [X5,X6,X7,X9] :
( ( in(esk7_3(X5,X6,X7),relation_rng(X7))
| ~ in(X5,relation_inverse_image(X7,X6))
| ~ relation(X7) )
& ( in(ordered_pair(X5,esk7_3(X5,X6,X7)),X7)
| ~ in(X5,relation_inverse_image(X7,X6))
| ~ relation(X7) )
& ( in(esk7_3(X5,X6,X7),X6)
| ~ in(X5,relation_inverse_image(X7,X6))
| ~ relation(X7) )
& ( ~ in(X9,relation_rng(X7))
| ~ in(ordered_pair(X5,X9),X7)
| ~ in(X9,X6)
| in(X5,relation_inverse_image(X7,X6))
| ~ relation(X7) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_108])])])])]) ).
fof(c_0_215_216,lemma,
! [X5,X6,X7,X9] :
( ( in(esk6_3(X5,X6,X7),relation_dom(X7))
| ~ in(X5,relation_image(X7,X6))
| ~ relation(X7) )
& ( in(ordered_pair(esk6_3(X5,X6,X7),X5),X7)
| ~ in(X5,relation_image(X7,X6))
| ~ relation(X7) )
& ( in(esk6_3(X5,X6,X7),X6)
| ~ in(X5,relation_image(X7,X6))
| ~ relation(X7) )
& ( ~ in(X9,relation_dom(X7))
| ~ in(ordered_pair(X9,X5),X7)
| ~ in(X9,X6)
| in(X5,relation_image(X7,X6))
| ~ relation(X7) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_109])])])])]) ).
fof(c_0_216_217,lemma,
! [X4,X5,X6] :
( ~ relation(X5)
| ~ function(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ in(X4,relation_dom(relation_composition(X6,X5)))
| apply(relation_composition(X6,X5),X4) = apply(X5,apply(X6,X4)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_110])])]) ).
fof(c_0_217_218,lemma,
! [X4,X5,X6] :
( ( in(X4,relation_dom(X6))
| ~ in(X4,relation_dom(relation_composition(X6,X5)))
| ~ relation(X6)
| ~ function(X6)
| ~ relation(X5)
| ~ function(X5) )
& ( in(apply(X6,X4),relation_dom(X5))
| ~ in(X4,relation_dom(relation_composition(X6,X5)))
| ~ relation(X6)
| ~ function(X6)
| ~ relation(X5)
| ~ function(X5) )
& ( ~ in(X4,relation_dom(X6))
| ~ in(apply(X6,X4),relation_dom(X5))
| in(X4,relation_dom(relation_composition(X6,X5)))
| ~ relation(X6)
| ~ function(X6)
| ~ relation(X5)
| ~ function(X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_111])])])]) ).
fof(c_0_218_219,lemma,
! [X4,X5,X6] :
( ~ relation(X6)
| ~ function(X6)
| ~ in(X5,relation_dom(relation_dom_restriction(X6,X4)))
| apply(relation_dom_restriction(X6,X4),X5) = apply(X6,X5) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_112])]) ).
fof(c_0_219_220,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_113])]) ).
fof(c_0_220_221,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_114])]) ).
fof(c_0_221_222,lemma,
! [X5,X6,X7,X8] :
( ( in(X5,X7)
| ~ in(ordered_pair(X5,X6),relation_composition(identity_relation(X7),X8))
| ~ relation(X8) )
& ( in(ordered_pair(X5,X6),X8)
| ~ in(ordered_pair(X5,X6),relation_composition(identity_relation(X7),X8))
| ~ relation(X8) )
& ( ~ in(X5,X7)
| ~ in(ordered_pair(X5,X6),X8)
| in(ordered_pair(X5,X6),relation_composition(identity_relation(X7),X8))
| ~ relation(X8) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_115])])]) ).
fof(c_0_222_223,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_116])])])]) ).
fof(c_0_223_224,lemma,
! [X4,X5,X6] :
( ( in(X4,X5)
| ~ in(X4,relation_dom(relation_dom_restriction(X6,X5)))
| ~ relation(X6) )
& ( in(X4,relation_dom(X6))
| ~ in(X4,relation_dom(relation_dom_restriction(X6,X5)))
| ~ relation(X6) )
& ( ~ in(X4,X5)
| ~ in(X4,relation_dom(X6))
| in(X4,relation_dom(relation_dom_restriction(X6,X5)))
| ~ relation(X6) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_117])])]) ).
fof(c_0_224_225,lemma,
! [X4,X5,X6] :
( ( in(X4,X5)
| ~ in(X4,relation_rng(relation_rng_restriction(X5,X6)))
| ~ relation(X6) )
& ( in(X4,relation_rng(X6))
| ~ in(X4,relation_rng(relation_rng_restriction(X5,X6)))
| ~ relation(X6) )
& ( ~ in(X4,X5)
| ~ in(X4,relation_rng(X6))
| in(X4,relation_rng(relation_rng_restriction(X5,X6)))
| ~ relation(X6) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_118])])]) ).
fof(c_0_225_226,lemma,
! [X4,X5,X6] :
( ~ relation(X5)
| ~ function(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ in(X4,relation_dom(X5))
| apply(relation_composition(X5,X6),X4) = apply(X6,apply(X5,X4)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_119])])]) ).
fof(c_0_226_227,negated_conjecture,
( relation(esk4_0)
& function(esk4_0)
& ( ~ in(esk3_0,relation_dom(relation_dom_restriction(esk4_0,esk2_0)))
| ~ in(esk3_0,relation_dom(esk4_0))
| ~ in(esk3_0,esk2_0) )
& ( in(esk3_0,relation_dom(esk4_0))
| in(esk3_0,relation_dom(relation_dom_restriction(esk4_0,esk2_0))) )
& ( in(esk3_0,esk2_0)
| in(esk3_0,relation_dom(relation_dom_restriction(esk4_0,esk2_0))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_120])])])]) ).
fof(c_0_227_228,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_121])])])])]) ).
fof(c_0_228_229,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_122])])])])]) ).
fof(c_0_229_230,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_123])]) ).
fof(c_0_230_231,lemma,
! [X4,X5,X6] :
( ( relation_dom(X5) = X4
| X5 != identity_relation(X4)
| ~ relation(X5)
| ~ function(X5) )
& ( ~ in(X6,X4)
| apply(X5,X6) = X6
| X5 != identity_relation(X4)
| ~ relation(X5)
| ~ function(X5) )
& ( in(esk8_2(X4,X5),X4)
| relation_dom(X5) != X4
| X5 = identity_relation(X4)
| ~ relation(X5)
| ~ function(X5) )
& ( apply(X5,esk8_2(X4,X5)) != esk8_2(X4,X5)
| relation_dom(X5) != X4
| X5 = identity_relation(X4)
| ~ relation(X5)
| ~ function(X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_124])])])])]) ).
fof(c_0_231_232,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_125])]) ).
fof(c_0_232_233,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_126])])]) ).
fof(c_0_233_234,lemma,
! [X4,X5,X6] :
( ( in(X4,relation_dom(X6))
| ~ in(ordered_pair(X4,X5),X6)
| ~ relation(X6)
| ~ function(X6) )
& ( X5 = apply(X6,X4)
| ~ in(ordered_pair(X4,X5),X6)
| ~ relation(X6)
| ~ function(X6) )
& ( ~ in(X4,relation_dom(X6))
| X5 != apply(X6,X4)
| in(ordered_pair(X4,X5),X6)
| ~ relation(X6)
| ~ function(X6) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_127])])]) ).
fof(c_0_234_235,lemma,
! [X3,X4] :
( ( X3 = apply(X4,apply(function_inverse(X4),X3))
| ~ one_to_one(X4)
| ~ in(X3,relation_rng(X4))
| ~ relation(X4)
| ~ function(X4) )
& ( X3 = apply(relation_composition(function_inverse(X4),X4),X3)
| ~ one_to_one(X4)
| ~ in(X3,relation_rng(X4))
| ~ relation(X4)
| ~ function(X4) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_128])])]) ).
fof(c_0_235_236,lemma,
! [X4,X5,X6] :
( ~ relation(X6)
| ~ subset(X4,X5)
| subset(relation_inverse_image(X6,X4),relation_inverse_image(X6,X5)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_129])]) ).
fof(c_0_236_237,lemma,
! [X3,X4] :
( ~ relation(X3)
| ~ relation(X4)
| subset(relation_rng(relation_composition(X3,X4)),relation_rng(X4)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_130])])]) ).
fof(c_0_237_238,lemma,
! [X3,X4] :
( ~ relation(X3)
| ~ relation(X4)
| subset(relation_dom(relation_composition(X3,X4)),relation_dom(X3)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_131])])]) ).
fof(c_0_238_239,lemma,
! [X4,X5,X6] :
( ( in(X4,relation_field(X6))
| ~ in(ordered_pair(X4,X5),X6)
| ~ relation(X6) )
& ( in(X5,relation_field(X6))
| ~ in(ordered_pair(X4,X5),X6)
| ~ relation(X6) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_132])])]) ).
fof(c_0_239_240,lemma,
! [X4,X5,X6] :
( ( in(X4,relation_dom(X6))
| ~ in(ordered_pair(X4,X5),X6)
| ~ relation(X6) )
& ( in(X5,relation_rng(X6))
| ~ in(ordered_pair(X4,X5),X6)
| ~ relation(X6) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_133])])]) ).
fof(c_0_240_241,lemma,
! [X3,X4] :
( ~ relation(X3)
| ~ relation(X4)
| ~ subset(relation_dom(X3),relation_rng(X4))
| relation_rng(relation_composition(X4,X3)) = relation_rng(X3) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_134])])]) ).
fof(c_0_241_242,lemma,
! [X3,X4] :
( ~ relation(X3)
| ~ relation(X4)
| ~ subset(relation_rng(X3),relation_dom(X4))
| relation_dom(relation_composition(X3,X4)) = relation_dom(X3) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_135])])]) ).
fof(c_0_242_243,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_136])])])]) ).
fof(c_0_243_244,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_137])])])]) ).
fof(c_0_244_245,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_138])])])]) ).
fof(c_0_245_246,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_139])])])])]) ).
fof(c_0_246_247,lemma,
! [X4,X5,X6] :
( ~ relation(X6)
| relation_dom_restriction(relation_rng_restriction(X4,X6),X5) = relation_rng_restriction(X4,relation_dom_restriction(X6,X5)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_140])]) ).
fof(c_0_247_248,lemma,
! [X4,X5,X7,X8,X9] :
( ( disjoint(X4,X5)
| in(esk10_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_141])])])])]) ).
fof(c_0_248_249,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_142])]) ).
fof(c_0_249_250,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_143])])])])]) ).
fof(c_0_250_251,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_144])]) ).
fof(c_0_251_252,lemma,
! [X3,X4] :
( ~ relation(X4)
| subset(relation_rng(relation_dom_restriction(X4,X3)),relation_rng(X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_145])]) ).
fof(c_0_252_253,lemma,
! [X3,X4] :
( ~ relation(X4)
| subset(relation_rng(relation_rng_restriction(X3,X4)),relation_rng(X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_146])]) ).
fof(c_0_253_254,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_147])])])]) ).
fof(c_0_254_255,lemma,
! [X3,X4] :
( ~ relation(X4)
| subset(relation_rng(relation_rng_restriction(X3,X4)),X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_148])]) ).
fof(c_0_255_256,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_149])]) ).
fof(c_0_256_257,lemma,
! [X5,X7,X8,X9,X10] :
( in(X5,esk5_1(X5))
& ( ~ in(X7,esk5_1(X5))
| ~ subset(X8,X7)
| in(X8,esk5_1(X5)) )
& ( ~ in(X9,esk5_1(X5))
| in(powerset(X9),esk5_1(X5)) )
& ( ~ subset(X10,esk5_1(X5))
| are_equipotent(X10,esk5_1(X5))
| in(X10,esk5_1(X5)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_150])])])]) ).
fof(c_0_257_258,lemma,
! [X4] :
( ~ relation(X4)
| in(ordered_pair(esk15_1(X4),esk16_1(X4)),X4)
| X4 = empty_set ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_151])])]) ).
fof(c_0_258_259,lemma,
! [X3,X4] :
( ~ relation(X4)
| relation_image(X4,X3) = relation_image(X4,set_intersection2(relation_dom(X4),X3)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_152])]) ).
fof(c_0_259_260,lemma,
! [X2] :
( ~ relation(X2)
| subset(X2,cartesian_product2(relation_dom(X2),relation_rng(X2))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_153])]) ).
fof(c_0_260_261,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_154])])]) ).
fof(c_0_261_262,lemma,
! [X4,X5,X7,X8,X9] :
( ( in(esk9_2(X4,X5),X4)
| disjoint(X4,X5) )
& ( in(esk9_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_155])])])])])]) ).
fof(c_0_262_263,lemma,
! [X3,X4] :
( ~ relation(X3)
| ~ relation(X4)
| relation_rng(relation_composition(X3,X4)) = relation_image(X4,relation_rng(X3)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_156])])]) ).
fof(c_0_263_264,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_157])]) ).
fof(c_0_264_265,lemma,
! [X3,X4] :
( ( subset(relation_dom(X3),relation_dom(X4))
| ~ subset(X3,X4)
| ~ relation(X4)
| ~ relation(X3) )
& ( subset(relation_rng(X3),relation_rng(X4))
| ~ subset(X3,X4)
| ~ relation(X4)
| ~ relation(X3) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_158])])])]) ).
fof(c_0_265_266,lemma,
! [X3,X4] :
( ~ relation(X4)
| X3 = empty_set
| ~ subset(X3,relation_rng(X4))
| relation_inverse_image(X4,X3) != empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_159])]) ).
fof(c_0_266_267,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_160])]) ).
fof(c_0_267_268,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_161])]) ).
fof(c_0_268_269,lemma,
! [X3,X4] :
( ~ relation(X4)
| relation_dom(relation_dom_restriction(X4,X3)) = set_intersection2(relation_dom(X4),X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_162])]) ).
fof(c_0_269_270,lemma,
! [X3,X4] :
( ~ relation(X4)
| relation_rng(relation_rng_restriction(X3,X4)) = set_intersection2(relation_rng(X4),X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_163])]) ).
fof(c_0_270_271,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_164])])])]) ).
fof(c_0_271_272,lemma,
! [X3,X4] :
( ~ disjoint(singleton(X3),X4)
| ~ in(X3,X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_165])]) ).
fof(c_0_272_273,lemma,
! [X3,X4] : set_difference(X3,set_difference(X3,X4)) = set_intersection2(X3,X4),
inference(variable_rename,[status(thm)],[c_0_166]) ).
fof(c_0_273_274,lemma,
! [X3,X4] : set_difference(set_union2(X3,X4),X4) = set_difference(X3,X4),
inference(variable_rename,[status(thm)],[c_0_167]) ).
fof(c_0_274_275,lemma,
! [X3,X4] : set_union2(X3,set_difference(X4,X3)) = set_union2(X3,X4),
inference(variable_rename,[status(thm)],[c_0_168]) ).
fof(c_0_275_276,lemma,
! [X3,X4] :
( ~ relation(X4)
| subset(relation_inverse_image(X4,X3),relation_dom(X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_169])]) ).
fof(c_0_276_277,lemma,
! [X3,X4] :
( ~ relation(X4)
| subset(relation_image(X4,X3),relation_rng(X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_170])]) ).
fof(c_0_277_278,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_171])]) ).
fof(c_0_278_279,lemma,
! [X3,X4] :
( ~ relation(X4)
| subset(relation_dom_restriction(X4,X3),X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_172])]) ).
fof(c_0_279_280,lemma,
! [X3,X4] :
( ~ relation(X4)
| subset(relation_rng_restriction(X3,X4),X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_173])]) ).
fof(c_0_280_281,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_174])])])]) ).
fof(c_0_281_282,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_175])])])]) ).
fof(c_0_282_283,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_176])])]) ).
fof(c_0_283_284,lemma,
! [X3,X4] :
( ~ subset(X3,X4)
| ~ proper_subset(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_177])]) ).
fof(c_0_284_285,lemma,
! [X3,X4] :
( ~ subset(singleton(X3),singleton(X4))
| X3 = X4 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_178])]) ).
fof(c_0_285_286,lemma,
! [X3,X4] :
( ~ in(X3,X4)
| set_union2(singleton(X3),X4) = X4 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_179])]) ).
fof(c_0_286_287,lemma,
! [X3,X4] :
( ~ in(X4,X3)
| apply(identity_relation(X3),X4) = X4 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_180])]) ).
fof(c_0_287_288,lemma,
! [X3,X4] :
( ~ in(X3,X4)
| set_union2(singleton(X3),X4) = X4 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_181])]) ).
fof(c_0_288_289,lemma,
! [X3,X4] :
( ~ in(X3,X4)
| subset(X3,union(X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_182])]) ).
fof(c_0_289_290,lemma,
! [X3,X4] :
( ~ in(X3,X4)
| subset(X3,union(X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_183])]) ).
fof(c_0_290_291,lemma,
! [X3,X4] :
( ~ relation(X4)
| relation_dom_restriction(X4,X3) = relation_composition(identity_relation(X3),X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_184])]) ).
fof(c_0_291_292,lemma,
! [X3,X4] : subset(X3,set_union2(X3,X4)),
inference(variable_rename,[status(thm)],[c_0_185]) ).
fof(c_0_292_293,lemma,
! [X3,X4] : subset(set_difference(X3,X4),X3),
inference(variable_rename,[status(thm)],[c_0_186]) ).
fof(c_0_293_294,lemma,
! [X3,X4] : subset(set_intersection2(X3,X4),X3),
inference(variable_rename,[status(thm)],[c_0_187]) ).
fof(c_0_294_295,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_188])])])])]) ).
fof(c_0_295_296,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_189])])])])]) ).
fof(c_0_296_297,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_190])])])]) ).
fof(c_0_297_298,lemma,
! [X3,X4] :
( ~ subset(X3,X4)
| set_intersection2(X3,X4) = X3 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_191])]) ).
fof(c_0_298_299,lemma,
! [X3,X4] :
( ~ subset(X3,X4)
| set_union2(X3,X4) = X4 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_192])]) ).
fof(c_0_299_300,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_193])])])]) ).
fof(c_0_300_301,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_194])])])]) ).
fof(c_0_301_302,lemma,
! [X2] :
( ( relation_rng(X2) = relation_dom(function_inverse(X2))
| ~ one_to_one(X2)
| ~ relation(X2)
| ~ function(X2) )
& ( relation_dom(X2) = relation_rng(function_inverse(X2))
| ~ one_to_one(X2)
| ~ relation(X2)
| ~ function(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_195])])]) ).
fof(c_0_302_303,lemma,
! [X3,X4] :
( in(X3,X4)
| disjoint(singleton(X3),X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_196])]) ).
fof(c_0_303_304,lemma,
! [X2] :
( ~ relation(X2)
| ~ function(X2)
| ~ one_to_one(X2)
| one_to_one(function_inverse(X2)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_197])]) ).
fof(c_0_304_305,lemma,
! [X2] :
( ~ relation(X2)
| relation_image(X2,relation_dom(X2)) = relation_rng(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_198])]) ).
fof(c_0_305_306,lemma,
! [X4,X5,X6] :
( singleton(X4) != unordered_pair(X5,X6)
| X5 = X6 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_199])]) ).
fof(c_0_306_307,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_200])])])]) ).
fof(c_0_307_308,lemma,
! [X2] :
( ~ subset(X2,empty_set)
| X2 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_201])]) ).
fof(c_0_308_309,lemma,
! [X2] :
( ( relation_rng(X2) = relation_dom(relation_inverse(X2))
| ~ relation(X2) )
& ( relation_dom(X2) = relation_rng(relation_inverse(X2))
| ~ relation(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_202])])]) ).
fof(c_0_309_310,lemma,
! [X2] :
( ( relation_dom(X2) != empty_set
| relation_rng(X2) = empty_set
| ~ relation(X2) )
& ( relation_rng(X2) != empty_set
| relation_dom(X2) = empty_set
| ~ relation(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_203])])]) ).
fof(c_0_310_311,lemma,
! [X2] : unordered_pair(X2,X2) = singleton(X2),
inference(variable_rename,[status(thm)],[c_0_204]) ).
fof(c_0_311_312,lemma,
! [X2] :
( ( relation_dom(X2) != empty_set
| X2 = empty_set
| ~ relation(X2) )
& ( relation_rng(X2) != empty_set
| X2 = empty_set
| ~ relation(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_205])])]) ).
fof(c_0_312_313,lemma,
! [X2] : subset(empty_set,X2),
inference(variable_rename,[status(thm)],[c_0_206]) ).
fof(c_0_313_314,lemma,
! [X2] : union(powerset(X2)) = X2,
inference(variable_rename,[status(thm)],[c_0_207]) ).
fof(c_0_314_315,lemma,
! [X2,X3] :
( relation_dom(identity_relation(X2)) = X2
& relation_rng(identity_relation(X3)) = X3 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_208])])]) ).
fof(c_0_315_316,lemma,
! [X2] : singleton(X2) != empty_set,
inference(variable_rename,[status(thm)],[c_0_209]) ).
fof(c_0_316_317,lemma,
powerset(empty_set) = singleton(empty_set),
c_0_210 ).
fof(c_0_317_318,lemma,
( relation_dom(empty_set) = empty_set
& relation_rng(empty_set) = empty_set ),
c_0_211 ).
cnf(c_0_318_319,lemma,
( X1 = relation_dom_restriction(X2,X3)
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X1) != set_intersection2(relation_dom(X2),X3)
| apply(X1,esk17_3(X3,X1,X2)) != apply(X2,esk17_3(X3,X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_212]) ).
cnf(c_0_319_320,lemma,
( X2 = function_inverse(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != relation_rng(X1)
| esk11_2(X1,X2) != apply(X1,esk12_2(X1,X2))
| ~ in(esk12_2(X1,X2),relation_dom(X1))
| esk14_2(X1,X2) != apply(X2,esk13_2(X1,X2))
| ~ in(esk13_2(X1,X2),relation_rng(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_213]) ).
cnf(c_0_320_321,lemma,
( in(ordered_pair(X2,esk7_3(X2,X3,X1)),X1)
| ~ relation(X1)
| ~ in(X2,relation_inverse_image(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_214]) ).
cnf(c_0_321_322,lemma,
( in(ordered_pair(esk6_3(X2,X3,X1),X2),X1)
| ~ relation(X1)
| ~ in(X2,relation_image(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_215]) ).
cnf(c_0_322_323,lemma,
( X2 = function_inverse(X1)
| esk12_2(X1,X2) = apply(X2,esk11_2(X1,X2))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != relation_rng(X1)
| esk14_2(X1,X2) != apply(X2,esk13_2(X1,X2))
| ~ in(esk13_2(X1,X2),relation_rng(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_213]) ).
cnf(c_0_323_324,lemma,
( X2 = function_inverse(X1)
| esk13_2(X1,X2) = apply(X1,esk14_2(X1,X2))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != relation_rng(X1)
| esk11_2(X1,X2) != apply(X1,esk12_2(X1,X2))
| ~ in(esk12_2(X1,X2),relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_213]) ).
cnf(c_0_324_325,lemma,
( X2 = function_inverse(X1)
| in(esk11_2(X1,X2),relation_rng(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != relation_rng(X1)
| esk14_2(X1,X2) != apply(X2,esk13_2(X1,X2))
| ~ in(esk13_2(X1,X2),relation_rng(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_213]) ).
cnf(c_0_325_326,lemma,
( X2 = function_inverse(X1)
| in(esk14_2(X1,X2),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != relation_rng(X1)
| esk11_2(X1,X2) != apply(X1,esk12_2(X1,X2))
| ~ in(esk12_2(X1,X2),relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_213]) ).
cnf(c_0_326_327,lemma,
( apply(relation_composition(X1,X2),X3) = apply(X2,apply(X1,X3))
| ~ in(X3,relation_dom(relation_composition(X1,X2)))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_216]) ).
cnf(c_0_327_328,lemma,
( X1 = relation_dom_restriction(X2,X3)
| in(esk17_3(X3,X1,X2),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X1) != set_intersection2(relation_dom(X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_212]) ).
cnf(c_0_328_329,lemma,
( in(X3,relation_dom(relation_composition(X2,X1)))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ in(apply(X2,X3),relation_dom(X1))
| ~ in(X3,relation_dom(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_217]) ).
cnf(c_0_329_330,lemma,
( in(esk7_3(X2,X3,X1),relation_rng(X1))
| ~ relation(X1)
| ~ in(X2,relation_inverse_image(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_214]) ).
cnf(c_0_330_331,lemma,
( in(esk6_3(X2,X3,X1),relation_dom(X1))
| ~ relation(X1)
| ~ in(X2,relation_image(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_215]) ).
cnf(c_0_331_332,lemma,
( in(esk7_3(X2,X3,X1),X3)
| ~ relation(X1)
| ~ in(X2,relation_inverse_image(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_214]) ).
cnf(c_0_332_333,lemma,
( in(esk6_3(X2,X3,X1),X3)
| ~ relation(X1)
| ~ in(X2,relation_image(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_215]) ).
cnf(c_0_333_334,lemma,
( in(apply(X2,X3),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ in(X3,relation_dom(relation_composition(X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_217]) ).
cnf(c_0_334_335,lemma,
( apply(relation_dom_restriction(X1,X2),X3) = apply(X1,X3)
| ~ in(X3,relation_dom(relation_dom_restriction(X1,X2)))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_218]) ).
cnf(c_0_335_336,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_219]) ).
cnf(c_0_336_337,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_220]) ).
cnf(c_0_337_338,lemma,
( in(ordered_pair(X2,X3),relation_composition(identity_relation(X4),X1))
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1)
| ~ in(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_221]) ).
cnf(c_0_338_339,lemma,
( in(ordered_pair(X2,X3),X1)
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),relation_composition(identity_relation(X4),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_221]) ).
cnf(c_0_339_340,lemma,
( in(X2,relation_inverse_image(X1,X3))
| ~ relation(X1)
| ~ in(X4,X3)
| ~ in(ordered_pair(X2,X4),X1)
| ~ in(X4,relation_rng(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_214]) ).
cnf(c_0_340_341,lemma,
( in(X2,relation_image(X1,X3))
| ~ relation(X1)
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,X2),X1)
| ~ in(X4,relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_215]) ).
cnf(c_0_341_342,lemma,
( in(X3,relation_dom(X2))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ in(X3,relation_dom(relation_composition(X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_217]) ).
cnf(c_0_342_343,lemma,
( X2 = function_inverse(X1)
| esk12_2(X1,X2) = apply(X2,esk11_2(X1,X2))
| esk13_2(X1,X2) = apply(X1,esk14_2(X1,X2))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != relation_rng(X1) ),
inference(split_conjunct,[status(thm)],[c_0_213]) ).
cnf(c_0_343_344,lemma,
( X2 = function_inverse(X1)
| in(esk11_2(X1,X2),relation_rng(X1))
| esk13_2(X1,X2) = apply(X1,esk14_2(X1,X2))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != relation_rng(X1) ),
inference(split_conjunct,[status(thm)],[c_0_213]) ).
cnf(c_0_344_345,lemma,
( X2 = function_inverse(X1)
| esk12_2(X1,X2) = apply(X2,esk11_2(X1,X2))
| in(esk14_2(X1,X2),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != relation_rng(X1) ),
inference(split_conjunct,[status(thm)],[c_0_213]) ).
cnf(c_0_345_346,lemma,
( X2 = function_inverse(X1)
| in(esk11_2(X1,X2),relation_rng(X1))
| in(esk14_2(X1,X2),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != relation_rng(X1) ),
inference(split_conjunct,[status(thm)],[c_0_213]) ).
cnf(c_0_346_347,lemma,
( in(X2,X4)
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),relation_composition(identity_relation(X4),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_221]) ).
cnf(c_0_347_348,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_222]) ).
cnf(c_0_348_349,lemma,
( in(X2,relation_dom(X1))
| ~ relation(X1)
| ~ in(X2,relation_dom(relation_dom_restriction(X1,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_223]) ).
cnf(c_0_349_350,lemma,
( in(X2,relation_rng(X1))
| ~ relation(X1)
| ~ in(X2,relation_rng(relation_rng_restriction(X3,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_224]) ).
cnf(c_0_350_351,lemma,
( apply(relation_composition(X1,X2),X3) = apply(X2,apply(X1,X3))
| ~ in(X3,relation_dom(X1))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_225]) ).
cnf(c_0_351_352,lemma,
( in(X2,X3)
| ~ relation(X1)
| ~ in(X2,relation_dom(relation_dom_restriction(X1,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_223]) ).
cnf(c_0_352_353,lemma,
( in(X2,X3)
| ~ relation(X1)
| ~ in(X2,relation_rng(relation_rng_restriction(X3,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_224]) ).
cnf(c_0_353_354,negated_conjecture,
( ~ in(esk3_0,esk2_0)
| ~ in(esk3_0,relation_dom(esk4_0))
| ~ in(esk3_0,relation_dom(relation_dom_restriction(esk4_0,esk2_0))) ),
inference(split_conjunct,[status(thm)],[c_0_226]) ).
cnf(c_0_354_355,lemma,
( in(X2,relation_dom(relation_dom_restriction(X1,X3)))
| ~ relation(X1)
| ~ in(X2,relation_dom(X1))
| ~ in(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_223]) ).
cnf(c_0_355_356,lemma,
( in(X2,relation_rng(relation_rng_restriction(X3,X1)))
| ~ relation(X1)
| ~ in(X2,relation_rng(X1))
| ~ in(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_224]) ).
cnf(c_0_356_357,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_222]) ).
cnf(c_0_357_358,lemma,
( in(X3,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| X2 != function_inverse(X1)
| X3 != apply(X2,X4)
| ~ in(X4,relation_rng(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_213]) ).
cnf(c_0_358_359,lemma,
( in(X3,relation_rng(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| X2 != function_inverse(X1)
| X3 != apply(X1,X4)
| ~ in(X4,relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_213]) ).
cnf(c_0_359_360,lemma,
( in(X1,X3)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_227]) ).
cnf(c_0_360_361,lemma,
( in(X2,X4)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_227]) ).
cnf(c_0_361_362,lemma,
( in(X1,X3)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_228]) ).
cnf(c_0_362_363,lemma,
( in(X2,X4)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_228]) ).
cnf(c_0_363_364,lemma,
( ~ in(X1,X2)
| ~ in(X1,subset_complement(X3,X2))
| ~ element(X2,powerset(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_229]) ).
cnf(c_0_364_365,lemma,
( X4 = apply(X1,X3)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| X2 != function_inverse(X1)
| X3 != apply(X2,X4)
| ~ in(X4,relation_rng(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_213]) ).
cnf(c_0_365_366,lemma,
( X4 = apply(X2,X3)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| X2 != function_inverse(X1)
| X3 != apply(X1,X4)
| ~ in(X4,relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_213]) ).
cnf(c_0_366_367,lemma,
( apply(X1,X4) = apply(X2,X4)
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| X1 != relation_dom_restriction(X2,X3)
| ~ in(X4,relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_212]) ).
cnf(c_0_367_368,lemma,
( X1 = identity_relation(X2)
| ~ function(X1)
| ~ relation(X1)
| relation_dom(X1) != X2
| apply(X1,esk8_2(X2,X1)) != esk8_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_230]) ).
cnf(c_0_368_369,lemma,
( subset(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
| ~ subset(X2,X4)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_231]) ).
cnf(c_0_369_370,lemma,
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_227]) ).
cnf(c_0_370_371,lemma,
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_228]) ).
cnf(c_0_371_372,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_232]) ).
cnf(c_0_372_373,lemma,
( in(ordered_pair(X2,X3),X1)
| ~ function(X1)
| ~ relation(X1)
| X3 != apply(X1,X2)
| ~ in(X2,relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_233]) ).
cnf(c_0_373_374,lemma,
( X2 = apply(X1,apply(function_inverse(X1),X2))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_rng(X1))
| ~ one_to_one(X1) ),
inference(split_conjunct,[status(thm)],[c_0_234]) ).
cnf(c_0_374_375,lemma,
( X2 = apply(relation_composition(function_inverse(X1),X1),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_rng(X1))
| ~ one_to_one(X1) ),
inference(split_conjunct,[status(thm)],[c_0_234]) ).
cnf(c_0_375_376,lemma,
( in(X2,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_233]) ).
cnf(c_0_376_377,lemma,
( subset(relation_inverse_image(X1,X2),relation_inverse_image(X1,X3))
| ~ subset(X2,X3)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_235]) ).
cnf(c_0_377_378,lemma,
( X3 = apply(X1,X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_233]) ).
cnf(c_0_378_379,lemma,
( subset(relation_rng(relation_composition(X1,X2)),relation_rng(X2))
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_236]) ).
cnf(c_0_379_380,lemma,
( subset(relation_dom(relation_composition(X1,X2)),relation_dom(X1))
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_237]) ).
cnf(c_0_380_381,lemma,
( in(X2,relation_field(X1))
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_238]) ).
cnf(c_0_381_382,lemma,
( in(X3,relation_field(X1))
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_238]) ).
cnf(c_0_382_383,lemma,
( in(X2,relation_dom(X1))
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_239]) ).
cnf(c_0_383_384,lemma,
( in(X3,relation_rng(X1))
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_239]) ).
cnf(c_0_384_385,lemma,
( relation_rng(relation_composition(X1,X2)) = relation_rng(X2)
| ~ subset(relation_dom(X2),relation_rng(X1))
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_240]) ).
cnf(c_0_385_386,lemma,
( relation_dom(relation_composition(X1,X2)) = relation_dom(X1)
| ~ subset(relation_rng(X1),relation_dom(X2))
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_241]) ).
cnf(c_0_386_387,lemma,
( subset(X1,set_difference(X2,singleton(X3)))
| in(X3,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_242]) ).
cnf(c_0_387_388,lemma,
( subset(set_difference(X1,X2),set_difference(X3,X2))
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_243]) ).
cnf(c_0_388_389,lemma,
( subset(set_intersection2(X1,X2),set_intersection2(X3,X2))
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_244]) ).
cnf(c_0_389_390,lemma,
( subset(cartesian_product2(X1,X3),cartesian_product2(X2,X3))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_245]) ).
cnf(c_0_390_391,lemma,
( subset(cartesian_product2(X3,X1),cartesian_product2(X3,X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_245]) ).
cnf(c_0_391_392,lemma,
( relation_dom_restriction(relation_rng_restriction(X1,X2),X3) = relation_rng_restriction(X1,relation_dom_restriction(X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_246]) ).
cnf(c_0_392_393,lemma,
( ~ disjoint(X1,X2)
| ~ in(X3,set_intersection2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_247]) ).
cnf(c_0_393_394,lemma,
( subset(set_union2(X1,X2),X3)
| ~ subset(X2,X3)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_248]) ).
cnf(c_0_394_395,lemma,
( subset(unordered_pair(X1,X2),X3)
| ~ in(X2,X3)
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_249]) ).
cnf(c_0_395_396,lemma,
( subset(X1,set_intersection2(X2,X3))
| ~ subset(X1,X3)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_250]) ).
cnf(c_0_396_397,lemma,
( subset(relation_rng(relation_dom_restriction(X1,X2)),relation_rng(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_251]) ).
cnf(c_0_397_398,lemma,
( subset(relation_rng(relation_rng_restriction(X1,X2)),relation_rng(X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_252]) ).
cnf(c_0_398_399,lemma,
( element(X1,powerset(X2))
| ~ in(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_253]) ).
cnf(c_0_399_400,lemma,
( in(esk10_2(X1,X2),set_intersection2(X1,X2))
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_247]) ).
cnf(c_0_400_401,lemma,
( subset(relation_rng(relation_rng_restriction(X1,X2)),X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_254]) ).
cnf(c_0_401_402,lemma,
( in(X1,X3)
| ~ subset(unordered_pair(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_249]) ).
cnf(c_0_402_403,lemma,
( in(X2,X3)
| ~ subset(unordered_pair(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_249]) ).
cnf(c_0_403_404,lemma,
( relation_dom(X1) = set_intersection2(relation_dom(X2),X3)
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| X1 != relation_dom_restriction(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_212]) ).
cnf(c_0_404_405,lemma,
( X2 = empty_set
| complements_of_subsets(X1,X2) != empty_set
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_255]) ).
cnf(c_0_405_406,lemma,
( in(X1,esk5_1(X2))
| ~ subset(X1,X3)
| ~ in(X3,esk5_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_256]) ).
cnf(c_0_406_407,negated_conjecture,
( in(esk3_0,relation_dom(relation_dom_restriction(esk4_0,esk2_0)))
| in(esk3_0,relation_dom(esk4_0)) ),
inference(split_conjunct,[status(thm)],[c_0_226]) ).
cnf(c_0_407_408,lemma,
( X1 = empty_set
| in(ordered_pair(esk15_1(X1),esk16_1(X1)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_257]) ).
cnf(c_0_408_409,lemma,
( relation_image(X1,X2) = relation_image(X1,set_intersection2(relation_dom(X1),X2))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_258]) ).
cnf(c_0_409_410,lemma,
( in(X1,esk5_1(X2))
| are_equipotent(X1,esk5_1(X2))
| ~ subset(X1,esk5_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_256]) ).
cnf(c_0_410_411,lemma,
( subset(X1,cartesian_product2(relation_dom(X1),relation_rng(X1)))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_259]) ).
cnf(c_0_411_412,negated_conjecture,
( in(esk3_0,relation_dom(relation_dom_restriction(esk4_0,esk2_0)))
| in(esk3_0,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_226]) ).
cnf(c_0_412_413,lemma,
( in(X1,X2)
| ~ in(X1,X3)
| ~ element(X3,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_260]) ).
cnf(c_0_413_414,lemma,
( X1 = identity_relation(X2)
| in(esk8_2(X2,X1),X2)
| ~ function(X1)
| ~ relation(X1)
| relation_dom(X1) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_230]) ).
cnf(c_0_414_415,lemma,
( ~ disjoint(X1,X2)
| ~ in(X3,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_261]) ).
cnf(c_0_415_416,lemma,
( relation_rng(relation_composition(X1,X2)) = relation_image(X2,relation_rng(X1))
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_262]) ).
cnf(c_0_416_417,lemma,
( X1 = set_union2(X2,set_difference(X1,X2))
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_263]) ).
cnf(c_0_417_418,lemma,
( subset(relation_dom(X1),relation_dom(X2))
| ~ relation(X1)
| ~ relation(X2)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_264]) ).
cnf(c_0_418_419,lemma,
( subset(relation_rng(X1),relation_rng(X2))
| ~ relation(X1)
| ~ relation(X2)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_264]) ).
cnf(c_0_419_420,lemma,
( X2 = empty_set
| relation_inverse_image(X1,X2) != empty_set
| ~ subset(X2,relation_rng(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_265]) ).
cnf(c_0_420_421,lemma,
( element(X1,powerset(X2))
| in(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_253]) ).
cnf(c_0_421_422,lemma,
( apply(X1,X3) = X3
| ~ function(X1)
| ~ relation(X1)
| X1 != identity_relation(X2)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_230]) ).
cnf(c_0_422_423,lemma,
( disjoint(X1,X2)
| ~ disjoint(X3,X2)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_266]) ).
cnf(c_0_423_424,lemma,
( subset(X1,X2)
| ~ subset(X3,X2)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_267]) ).
cnf(c_0_424_425,lemma,
( in(powerset(X1),esk5_1(X2))
| ~ in(X1,esk5_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_256]) ).
cnf(c_0_425_426,lemma,
( relation_dom(relation_dom_restriction(X1,X2)) = set_intersection2(relation_dom(X1),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_268]) ).
cnf(c_0_426_427,lemma,
( relation_rng(relation_rng_restriction(X1,X2)) = set_intersection2(relation_rng(X2),X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_269]) ).
cnf(c_0_427_428,lemma,
( ~ in(X1,X2)
| set_difference(X2,singleton(X1)) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_270]) ).
cnf(c_0_428_429,lemma,
( ~ in(X1,X2)
| ~ disjoint(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_271]) ).
cnf(c_0_429_430,lemma,
( disjoint(X1,X2)
| in(esk9_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_261]) ).
cnf(c_0_430_431,lemma,
( disjoint(X1,X2)
| in(esk9_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_261]) ).
cnf(c_0_431_432,lemma,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_272]) ).
cnf(c_0_432_433,lemma,
set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_273]) ).
cnf(c_0_433_434,lemma,
set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_274]) ).
cnf(c_0_434_435,lemma,
( subset(relation_inverse_image(X1,X2),relation_dom(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_275]) ).
cnf(c_0_435_436,lemma,
( subset(relation_image(X1,X2),relation_rng(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_276]) ).
cnf(c_0_436_437,lemma,
( relation_dom(X2) = relation_rng(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| X2 != function_inverse(X1) ),
inference(split_conjunct,[status(thm)],[c_0_213]) ).
cnf(c_0_437_438,lemma,
( X1 = X2
| X1 = X3
| unordered_pair(X1,X4) != unordered_pair(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_277]) ).
cnf(c_0_438_439,lemma,
( subset(relation_dom_restriction(X1,X2),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_278]) ).
cnf(c_0_439_440,lemma,
( subset(relation_rng_restriction(X1,X2),X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_279]) ).
cnf(c_0_440_441,lemma,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_280]) ).
cnf(c_0_441_442,lemma,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_281]) ).
cnf(c_0_442_443,lemma,
( X1 = X3
| ordered_pair(X1,X2) != ordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_282]) ).
cnf(c_0_443_444,lemma,
( X2 = X4
| ordered_pair(X1,X2) != ordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_282]) ).
cnf(c_0_444_445,lemma,
( ~ proper_subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_283]) ).
cnf(c_0_445_446,lemma,
( X1 = X2
| ~ subset(singleton(X1),singleton(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_284]) ).
cnf(c_0_446_447,lemma,
( set_union2(singleton(X1),X2) = X2
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_285]) ).
cnf(c_0_447_448,lemma,
( apply(identity_relation(X1),X2) = X2
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_286]) ).
cnf(c_0_448_449,lemma,
( set_union2(singleton(X1),X2) = X2
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_287]) ).
cnf(c_0_449_450,lemma,
( subset(X1,union(X2))
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_288]) ).
cnf(c_0_450_451,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_280]) ).
cnf(c_0_451_452,lemma,
( subset(X1,union(X2))
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_289]) ).
cnf(c_0_452_453,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_281]) ).
cnf(c_0_453_454,lemma,
( relation_dom_restriction(X1,X2) = relation_composition(identity_relation(X2),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_290]) ).
cnf(c_0_454_455,lemma,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_291]) ).
cnf(c_0_455_456,lemma,
subset(set_difference(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_292]) ).
cnf(c_0_456_457,lemma,
subset(set_intersection2(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_293]) ).
cnf(c_0_457_458,lemma,
( X1 = singleton(X2)
| X1 = empty_set
| ~ subset(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_294]) ).
cnf(c_0_458_459,lemma,
( X1 = singleton(X2)
| X1 = empty_set
| ~ subset(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_295]) ).
cnf(c_0_459_460,lemma,
( disjoint(X1,X2)
| set_difference(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_296]) ).
cnf(c_0_460_461,lemma,
( set_difference(X1,X2) = X1
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_296]) ).
cnf(c_0_461_462,lemma,
( set_intersection2(X1,X2) = X1
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_297]) ).
cnf(c_0_462_463,lemma,
( set_union2(X1,X2) = X2
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_298]) ).
cnf(c_0_463_464,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_299]) ).
cnf(c_0_464_465,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_299]) ).
cnf(c_0_465_466,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_300]) ).
cnf(c_0_466_467,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_300]) ).
cnf(c_0_467_468,lemma,
( relation_rng(X1) = relation_dom(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1) ),
inference(split_conjunct,[status(thm)],[c_0_301]) ).
cnf(c_0_468_469,lemma,
( relation_dom(X1) = relation_rng(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1) ),
inference(split_conjunct,[status(thm)],[c_0_301]) ).
cnf(c_0_469_470,lemma,
( set_difference(X1,singleton(X2)) = X1
| in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_270]) ).
cnf(c_0_470_471,lemma,
( disjoint(singleton(X1),X2)
| in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_302]) ).
cnf(c_0_471_472,lemma,
( one_to_one(function_inverse(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_303]) ).
cnf(c_0_472_473,lemma,
( relation_image(X1,relation_dom(X1)) = relation_rng(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_304]) ).
cnf(c_0_473_474,lemma,
( X1 = X2
| singleton(X3) != unordered_pair(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_305]) ).
cnf(c_0_474_475,lemma,
( X1 = X2
| singleton(X1) != unordered_pair(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_306]) ).
cnf(c_0_475_476,lemma,
( subset(X1,singleton(X2))
| X1 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[c_0_294]) ).
cnf(c_0_476_477,lemma,
( subset(X1,singleton(X2))
| X1 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[c_0_295]) ).
cnf(c_0_477_478,lemma,
( relation_dom(X1) = X2
| ~ function(X1)
| ~ relation(X1)
| X1 != identity_relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_230]) ).
cnf(c_0_478_479,lemma,
( subset(X1,singleton(X2))
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_294]) ).
cnf(c_0_479_480,lemma,
( subset(X1,singleton(X2))
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_295]) ).
cnf(c_0_480_481,lemma,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
inference(split_conjunct,[status(thm)],[c_0_307]) ).
cnf(c_0_481_482,lemma,
( relation_rng(X1) = relation_dom(relation_inverse(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_308]) ).
cnf(c_0_482_483,lemma,
( relation_dom(X1) = relation_rng(relation_inverse(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_308]) ).
cnf(c_0_483_484,lemma,
in(X1,esk5_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_256]) ).
cnf(c_0_484_485,lemma,
( relation_rng(X1) = empty_set
| ~ relation(X1)
| relation_dom(X1) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_309]) ).
cnf(c_0_485_486,lemma,
( relation_dom(X1) = empty_set
| ~ relation(X1)
| relation_rng(X1) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_309]) ).
cnf(c_0_486_487,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[c_0_310]) ).
cnf(c_0_487_488,lemma,
( X1 = empty_set
| ~ relation(X1)
| relation_dom(X1) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_311]) ).
cnf(c_0_488_489,lemma,
( X1 = empty_set
| ~ relation(X1)
| relation_rng(X1) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_311]) ).
cnf(c_0_489_490,lemma,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[c_0_312]) ).
cnf(c_0_490_491,lemma,
union(powerset(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_313]) ).
cnf(c_0_491_492,lemma,
relation_dom(identity_relation(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_314]) ).
cnf(c_0_492_493,lemma,
relation_rng(identity_relation(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_314]) ).
cnf(c_0_493_494,lemma,
singleton(X1) != empty_set,
inference(split_conjunct,[status(thm)],[c_0_315]) ).
cnf(c_0_494_495,lemma,
powerset(empty_set) = singleton(empty_set),
inference(split_conjunct,[status(thm)],[c_0_316]) ).
cnf(c_0_495_496,lemma,
relation_dom(empty_set) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_317]) ).
cnf(c_0_496_497,lemma,
relation_rng(empty_set) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_317]) ).
cnf(c_0_497_498,negated_conjecture,
relation(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_226]) ).
cnf(c_0_498_499,negated_conjecture,
function(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_226]) ).
cnf(c_0_499_500,lemma,
( X1 = relation_dom_restriction(X2,X3)
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X1) != set_intersection2(relation_dom(X2),X3)
| apply(X1,esk17_3(X3,X1,X2)) != apply(X2,esk17_3(X3,X1,X2)) ),
c_0_318,
[final] ).
cnf(c_0_500_501,lemma,
( X2 = function_inverse(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != relation_rng(X1)
| apply(X1,esk12_2(X1,X2)) != esk11_2(X1,X2)
| ~ in(esk12_2(X1,X2),relation_dom(X1))
| apply(X2,esk13_2(X1,X2)) != esk14_2(X1,X2)
| ~ in(esk13_2(X1,X2),relation_rng(X1)) ),
c_0_319,
[final] ).
cnf(c_0_501_502,lemma,
( in(ordered_pair(X2,esk7_3(X2,X3,X1)),X1)
| ~ relation(X1)
| ~ in(X2,relation_inverse_image(X1,X3)) ),
c_0_320,
[final] ).
cnf(c_0_502_503,lemma,
( in(ordered_pair(esk6_3(X2,X3,X1),X2),X1)
| ~ relation(X1)
| ~ in(X2,relation_image(X1,X3)) ),
c_0_321,
[final] ).
cnf(c_0_503_504,lemma,
( X2 = function_inverse(X1)
| apply(X2,esk11_2(X1,X2)) = esk12_2(X1,X2)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != relation_rng(X1)
| apply(X2,esk13_2(X1,X2)) != esk14_2(X1,X2)
| ~ in(esk13_2(X1,X2),relation_rng(X1)) ),
c_0_322,
[final] ).
cnf(c_0_504_505,lemma,
( X2 = function_inverse(X1)
| apply(X1,esk14_2(X1,X2)) = esk13_2(X1,X2)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != relation_rng(X1)
| apply(X1,esk12_2(X1,X2)) != esk11_2(X1,X2)
| ~ in(esk12_2(X1,X2),relation_dom(X1)) ),
c_0_323,
[final] ).
cnf(c_0_505_506,lemma,
( X2 = function_inverse(X1)
| in(esk11_2(X1,X2),relation_rng(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != relation_rng(X1)
| apply(X2,esk13_2(X1,X2)) != esk14_2(X1,X2)
| ~ in(esk13_2(X1,X2),relation_rng(X1)) ),
c_0_324,
[final] ).
cnf(c_0_506_507,lemma,
( X2 = function_inverse(X1)
| in(esk14_2(X1,X2),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != relation_rng(X1)
| apply(X1,esk12_2(X1,X2)) != esk11_2(X1,X2)
| ~ in(esk12_2(X1,X2),relation_dom(X1)) ),
c_0_325,
[final] ).
cnf(c_0_507_508,lemma,
( apply(relation_composition(X1,X2),X3) = apply(X2,apply(X1,X3))
| ~ in(X3,relation_dom(relation_composition(X1,X2)))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2) ),
c_0_326,
[final] ).
cnf(c_0_508_509,lemma,
( X1 = relation_dom_restriction(X2,X3)
| in(esk17_3(X3,X1,X2),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X1) != set_intersection2(relation_dom(X2),X3) ),
c_0_327,
[final] ).
cnf(c_0_509_510,lemma,
( in(X3,relation_dom(relation_composition(X2,X1)))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ in(apply(X2,X3),relation_dom(X1))
| ~ in(X3,relation_dom(X2)) ),
c_0_328,
[final] ).
cnf(c_0_510_511,lemma,
( in(esk7_3(X2,X3,X1),relation_rng(X1))
| ~ relation(X1)
| ~ in(X2,relation_inverse_image(X1,X3)) ),
c_0_329,
[final] ).
cnf(c_0_511_512,lemma,
( in(esk6_3(X2,X3,X1),relation_dom(X1))
| ~ relation(X1)
| ~ in(X2,relation_image(X1,X3)) ),
c_0_330,
[final] ).
cnf(c_0_512_513,lemma,
( in(esk7_3(X2,X3,X1),X3)
| ~ relation(X1)
| ~ in(X2,relation_inverse_image(X1,X3)) ),
c_0_331,
[final] ).
cnf(c_0_513_514,lemma,
( in(esk6_3(X2,X3,X1),X3)
| ~ relation(X1)
| ~ in(X2,relation_image(X1,X3)) ),
c_0_332,
[final] ).
cnf(c_0_514_515,lemma,
( in(apply(X2,X3),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ in(X3,relation_dom(relation_composition(X2,X1))) ),
c_0_333,
[final] ).
cnf(c_0_515_516,lemma,
( apply(relation_dom_restriction(X1,X2),X3) = apply(X1,X3)
| ~ in(X3,relation_dom(relation_dom_restriction(X1,X2)))
| ~ function(X1)
| ~ relation(X1) ),
c_0_334,
[final] ).
cnf(c_0_516_517,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_335,
[final] ).
cnf(c_0_517_518,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_336,
[final] ).
cnf(c_0_518_519,lemma,
( in(ordered_pair(X2,X3),relation_composition(identity_relation(X4),X1))
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1)
| ~ in(X2,X4) ),
c_0_337,
[final] ).
cnf(c_0_519_520,lemma,
( in(ordered_pair(X2,X3),X1)
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),relation_composition(identity_relation(X4),X1)) ),
c_0_338,
[final] ).
cnf(c_0_520_521,lemma,
( in(X2,relation_inverse_image(X1,X3))
| ~ relation(X1)
| ~ in(X4,X3)
| ~ in(ordered_pair(X2,X4),X1)
| ~ in(X4,relation_rng(X1)) ),
c_0_339,
[final] ).
cnf(c_0_521_522,lemma,
( in(X2,relation_image(X1,X3))
| ~ relation(X1)
| ~ in(X4,X3)
| ~ in(ordered_pair(X4,X2),X1)
| ~ in(X4,relation_dom(X1)) ),
c_0_340,
[final] ).
cnf(c_0_522_523,lemma,
( in(X3,relation_dom(X2))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ in(X3,relation_dom(relation_composition(X2,X1))) ),
c_0_341,
[final] ).
cnf(c_0_523_524,lemma,
( X2 = function_inverse(X1)
| apply(X2,esk11_2(X1,X2)) = esk12_2(X1,X2)
| apply(X1,esk14_2(X1,X2)) = esk13_2(X1,X2)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != relation_rng(X1) ),
c_0_342,
[final] ).
cnf(c_0_524_525,lemma,
( X2 = function_inverse(X1)
| in(esk11_2(X1,X2),relation_rng(X1))
| apply(X1,esk14_2(X1,X2)) = esk13_2(X1,X2)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != relation_rng(X1) ),
c_0_343,
[final] ).
cnf(c_0_525_526,lemma,
( X2 = function_inverse(X1)
| apply(X2,esk11_2(X1,X2)) = esk12_2(X1,X2)
| in(esk14_2(X1,X2),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != relation_rng(X1) ),
c_0_344,
[final] ).
cnf(c_0_526_527,lemma,
( X2 = function_inverse(X1)
| in(esk11_2(X1,X2),relation_rng(X1))
| in(esk14_2(X1,X2),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X2) != relation_rng(X1) ),
c_0_345,
[final] ).
cnf(c_0_527_528,lemma,
( in(X2,X4)
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),relation_composition(identity_relation(X4),X1)) ),
c_0_346,
[final] ).
cnf(c_0_528_529,lemma,
( disjoint(X1,X3)
| ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2))
| ~ subset(X1,subset_complement(X2,X3)) ),
c_0_347,
[final] ).
cnf(c_0_529_530,lemma,
( in(X2,relation_dom(X1))
| ~ relation(X1)
| ~ in(X2,relation_dom(relation_dom_restriction(X1,X3))) ),
c_0_348,
[final] ).
cnf(c_0_530_531,lemma,
( in(X2,relation_rng(X1))
| ~ relation(X1)
| ~ in(X2,relation_rng(relation_rng_restriction(X3,X1))) ),
c_0_349,
[final] ).
cnf(c_0_531_532,lemma,
( apply(relation_composition(X1,X2),X3) = apply(X2,apply(X1,X3))
| ~ in(X3,relation_dom(X1))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
c_0_350,
[final] ).
cnf(c_0_532_533,lemma,
( in(X2,X3)
| ~ relation(X1)
| ~ in(X2,relation_dom(relation_dom_restriction(X1,X3))) ),
c_0_351,
[final] ).
cnf(c_0_533_534,lemma,
( in(X2,X3)
| ~ relation(X1)
| ~ in(X2,relation_rng(relation_rng_restriction(X3,X1))) ),
c_0_352,
[final] ).
cnf(c_0_534_535,negated_conjecture,
( ~ in(esk3_0,esk2_0)
| ~ in(esk3_0,relation_dom(esk4_0))
| ~ in(esk3_0,relation_dom(relation_dom_restriction(esk4_0,esk2_0))) ),
c_0_353,
[final] ).
cnf(c_0_535_536,lemma,
( in(X2,relation_dom(relation_dom_restriction(X1,X3)))
| ~ relation(X1)
| ~ in(X2,relation_dom(X1))
| ~ in(X2,X3) ),
c_0_354,
[final] ).
cnf(c_0_536_537,lemma,
( in(X2,relation_rng(relation_rng_restriction(X3,X1)))
| ~ relation(X1)
| ~ in(X2,relation_rng(X1))
| ~ in(X2,X3) ),
c_0_355,
[final] ).
cnf(c_0_537_538,lemma,
( subset(X1,subset_complement(X2,X3))
| ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2))
| ~ disjoint(X1,X3) ),
c_0_356,
[final] ).
cnf(c_0_538_539,lemma,
( in(X3,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| X2 != function_inverse(X1)
| X3 != apply(X2,X4)
| ~ in(X4,relation_rng(X1)) ),
c_0_357,
[final] ).
cnf(c_0_539_540,lemma,
( in(X3,relation_rng(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| X2 != function_inverse(X1)
| X3 != apply(X1,X4)
| ~ in(X4,relation_dom(X1)) ),
c_0_358,
[final] ).
cnf(c_0_540_541,lemma,
( in(X1,X3)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
c_0_359,
[final] ).
cnf(c_0_541_542,lemma,
( in(X2,X4)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
c_0_360,
[final] ).
cnf(c_0_542_543,lemma,
( in(X1,X3)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
c_0_361,
[final] ).
cnf(c_0_543_544,lemma,
( in(X2,X4)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
c_0_362,
[final] ).
cnf(c_0_544_545,lemma,
( ~ in(X1,X2)
| ~ in(X1,subset_complement(X3,X2))
| ~ element(X2,powerset(X3)) ),
c_0_363,
[final] ).
cnf(c_0_545_546,lemma,
( X4 = apply(X1,X3)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| X2 != function_inverse(X1)
| X3 != apply(X2,X4)
| ~ in(X4,relation_rng(X1)) ),
c_0_364,
[final] ).
cnf(c_0_546_547,lemma,
( X4 = apply(X2,X3)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| X2 != function_inverse(X1)
| X3 != apply(X1,X4)
| ~ in(X4,relation_dom(X1)) ),
c_0_365,
[final] ).
cnf(c_0_547_548,lemma,
( apply(X1,X4) = apply(X2,X4)
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| X1 != relation_dom_restriction(X2,X3)
| ~ in(X4,relation_dom(X1)) ),
c_0_366,
[final] ).
cnf(c_0_548_549,lemma,
( X1 = identity_relation(X2)
| ~ function(X1)
| ~ relation(X1)
| relation_dom(X1) != X2
| apply(X1,esk8_2(X2,X1)) != esk8_2(X2,X1) ),
c_0_367,
[final] ).
cnf(c_0_549_550,lemma,
( subset(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
| ~ subset(X2,X4)
| ~ subset(X1,X3) ),
c_0_368,
[final] ).
cnf(c_0_550_551,lemma,
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
c_0_369,
[final] ).
cnf(c_0_551_552,lemma,
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
c_0_370,
[final] ).
cnf(c_0_552_553,lemma,
( in(X1,subset_complement(X2,X3))
| in(X1,X3)
| X2 = empty_set
| ~ element(X1,X2)
| ~ element(X3,powerset(X2)) ),
c_0_371,
[final] ).
cnf(c_0_553_554,lemma,
( in(ordered_pair(X2,X3),X1)
| ~ function(X1)
| ~ relation(X1)
| X3 != apply(X1,X2)
| ~ in(X2,relation_dom(X1)) ),
c_0_372,
[final] ).
cnf(c_0_554_555,lemma,
( apply(X1,apply(function_inverse(X1),X2)) = X2
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_rng(X1))
| ~ one_to_one(X1) ),
c_0_373,
[final] ).
cnf(c_0_555_556,lemma,
( apply(relation_composition(function_inverse(X1),X1),X2) = X2
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_rng(X1))
| ~ one_to_one(X1) ),
c_0_374,
[final] ).
cnf(c_0_556_557,lemma,
( in(X2,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
c_0_375,
[final] ).
cnf(c_0_557_558,lemma,
( subset(relation_inverse_image(X1,X2),relation_inverse_image(X1,X3))
| ~ subset(X2,X3)
| ~ relation(X1) ),
c_0_376,
[final] ).
cnf(c_0_558_559,lemma,
( X3 = apply(X1,X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
c_0_377,
[final] ).
cnf(c_0_559_560,lemma,
( subset(relation_rng(relation_composition(X1,X2)),relation_rng(X2))
| ~ relation(X2)
| ~ relation(X1) ),
c_0_378,
[final] ).
cnf(c_0_560_561,lemma,
( subset(relation_dom(relation_composition(X1,X2)),relation_dom(X1))
| ~ relation(X2)
| ~ relation(X1) ),
c_0_379,
[final] ).
cnf(c_0_561_562,lemma,
( in(X2,relation_field(X1))
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
c_0_380,
[final] ).
cnf(c_0_562_563,lemma,
( in(X3,relation_field(X1))
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
c_0_381,
[final] ).
cnf(c_0_563_564,lemma,
( in(X2,relation_dom(X1))
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
c_0_382,
[final] ).
cnf(c_0_564_565,lemma,
( in(X3,relation_rng(X1))
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
c_0_383,
[final] ).
cnf(c_0_565_566,lemma,
( relation_rng(relation_composition(X1,X2)) = relation_rng(X2)
| ~ subset(relation_dom(X2),relation_rng(X1))
| ~ relation(X1)
| ~ relation(X2) ),
c_0_384,
[final] ).
cnf(c_0_566_567,lemma,
( relation_dom(relation_composition(X1,X2)) = relation_dom(X1)
| ~ subset(relation_rng(X1),relation_dom(X2))
| ~ relation(X2)
| ~ relation(X1) ),
c_0_385,
[final] ).
cnf(c_0_567_568,lemma,
( subset(X1,set_difference(X2,singleton(X3)))
| in(X3,X1)
| ~ subset(X1,X2) ),
c_0_386,
[final] ).
cnf(c_0_568_569,lemma,
( subset(set_difference(X1,X2),set_difference(X3,X2))
| ~ subset(X1,X3) ),
c_0_387,
[final] ).
cnf(c_0_569_570,lemma,
( subset(set_intersection2(X1,X2),set_intersection2(X3,X2))
| ~ subset(X1,X3) ),
c_0_388,
[final] ).
cnf(c_0_570_571,lemma,
( subset(cartesian_product2(X1,X3),cartesian_product2(X2,X3))
| ~ subset(X1,X2) ),
c_0_389,
[final] ).
cnf(c_0_571_572,lemma,
( subset(cartesian_product2(X3,X1),cartesian_product2(X3,X2))
| ~ subset(X1,X2) ),
c_0_390,
[final] ).
cnf(c_0_572_573,lemma,
( relation_rng_restriction(X1,relation_dom_restriction(X2,X3)) = relation_dom_restriction(relation_rng_restriction(X1,X2),X3)
| ~ relation(X2) ),
c_0_391,
[final] ).
cnf(c_0_573_574,lemma,
( ~ disjoint(X1,X2)
| ~ in(X3,set_intersection2(X1,X2)) ),
c_0_392,
[final] ).
cnf(c_0_574_575,lemma,
( subset(set_union2(X1,X2),X3)
| ~ subset(X2,X3)
| ~ subset(X1,X3) ),
c_0_393,
[final] ).
cnf(c_0_575_576,lemma,
( subset(unordered_pair(X1,X2),X3)
| ~ in(X2,X3)
| ~ in(X1,X3) ),
c_0_394,
[final] ).
cnf(c_0_576_577,lemma,
( subset(X1,set_intersection2(X2,X3))
| ~ subset(X1,X3)
| ~ subset(X1,X2) ),
c_0_395,
[final] ).
cnf(c_0_577_578,lemma,
( subset(relation_rng(relation_dom_restriction(X1,X2)),relation_rng(X1))
| ~ relation(X1) ),
c_0_396,
[final] ).
cnf(c_0_578_579,lemma,
( subset(relation_rng(relation_rng_restriction(X1,X2)),relation_rng(X2))
| ~ relation(X2) ),
c_0_397,
[final] ).
cnf(c_0_579_580,lemma,
( element(X1,powerset(X2))
| ~ in(esk1_2(X1,X2),X2) ),
c_0_398,
[final] ).
cnf(c_0_580_581,lemma,
( in(esk10_2(X1,X2),set_intersection2(X1,X2))
| disjoint(X1,X2) ),
c_0_399,
[final] ).
cnf(c_0_581_582,lemma,
( subset(relation_rng(relation_rng_restriction(X1,X2)),X1)
| ~ relation(X2) ),
c_0_400,
[final] ).
cnf(c_0_582_583,lemma,
( in(X1,X3)
| ~ subset(unordered_pair(X1,X2),X3) ),
c_0_401,
[final] ).
cnf(c_0_583_584,lemma,
( in(X2,X3)
| ~ subset(unordered_pair(X1,X2),X3) ),
c_0_402,
[final] ).
cnf(c_0_584_585,lemma,
( relation_dom(X1) = set_intersection2(relation_dom(X2),X3)
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| X1 != relation_dom_restriction(X2,X3) ),
c_0_403,
[final] ).
cnf(c_0_585_586,lemma,
( X2 = empty_set
| complements_of_subsets(X1,X2) != empty_set
| ~ element(X2,powerset(powerset(X1))) ),
c_0_404,
[final] ).
cnf(c_0_586_587,lemma,
( in(X1,esk5_1(X2))
| ~ subset(X1,X3)
| ~ in(X3,esk5_1(X2)) ),
c_0_405,
[final] ).
cnf(c_0_587_588,negated_conjecture,
( in(esk3_0,relation_dom(relation_dom_restriction(esk4_0,esk2_0)))
| in(esk3_0,relation_dom(esk4_0)) ),
c_0_406,
[final] ).
cnf(c_0_588_589,lemma,
( X1 = empty_set
| in(ordered_pair(esk15_1(X1),esk16_1(X1)),X1)
| ~ relation(X1) ),
c_0_407,
[final] ).
cnf(c_0_589_590,lemma,
( relation_image(X1,set_intersection2(relation_dom(X1),X2)) = relation_image(X1,X2)
| ~ relation(X1) ),
c_0_408,
[final] ).
cnf(c_0_590_591,lemma,
( in(X1,esk5_1(X2))
| are_equipotent(X1,esk5_1(X2))
| ~ subset(X1,esk5_1(X2)) ),
c_0_409,
[final] ).
cnf(c_0_591_592,lemma,
( subset(X1,cartesian_product2(relation_dom(X1),relation_rng(X1)))
| ~ relation(X1) ),
c_0_410,
[final] ).
cnf(c_0_592_593,negated_conjecture,
( in(esk3_0,relation_dom(relation_dom_restriction(esk4_0,esk2_0)))
| in(esk3_0,esk2_0) ),
c_0_411,
[final] ).
cnf(c_0_593_594,lemma,
( in(X1,X2)
| ~ in(X1,X3)
| ~ element(X3,powerset(X2)) ),
c_0_412,
[final] ).
cnf(c_0_594_595,lemma,
( X1 = identity_relation(X2)
| in(esk8_2(X2,X1),X2)
| ~ function(X1)
| ~ relation(X1)
| relation_dom(X1) != X2 ),
c_0_413,
[final] ).
cnf(c_0_595_596,lemma,
( ~ disjoint(X1,X2)
| ~ in(X3,X2)
| ~ in(X3,X1) ),
c_0_414,
[final] ).
cnf(c_0_596_597,lemma,
( relation_rng(relation_composition(X1,X2)) = relation_image(X2,relation_rng(X1))
| ~ relation(X2)
| ~ relation(X1) ),
c_0_415,
[final] ).
cnf(c_0_597_598,lemma,
( set_union2(X2,set_difference(X1,X2)) = X1
| ~ subset(X2,X1) ),
c_0_416,
[final] ).
cnf(c_0_598_599,lemma,
( subset(relation_dom(X1),relation_dom(X2))
| ~ relation(X1)
| ~ relation(X2)
| ~ subset(X1,X2) ),
c_0_417,
[final] ).
cnf(c_0_599_600,lemma,
( subset(relation_rng(X1),relation_rng(X2))
| ~ relation(X1)
| ~ relation(X2)
| ~ subset(X1,X2) ),
c_0_418,
[final] ).
cnf(c_0_600_601,lemma,
( X2 = empty_set
| relation_inverse_image(X1,X2) != empty_set
| ~ subset(X2,relation_rng(X1))
| ~ relation(X1) ),
c_0_419,
[final] ).
cnf(c_0_601_602,lemma,
( element(X1,powerset(X2))
| in(esk1_2(X1,X2),X1) ),
c_0_420,
[final] ).
cnf(c_0_602_603,lemma,
( apply(X1,X3) = X3
| ~ function(X1)
| ~ relation(X1)
| X1 != identity_relation(X2)
| ~ in(X3,X2) ),
c_0_421,
[final] ).
cnf(c_0_603_604,lemma,
( disjoint(X1,X2)
| ~ disjoint(X3,X2)
| ~ subset(X1,X3) ),
c_0_422,
[final] ).
cnf(c_0_604_605,lemma,
( subset(X1,X2)
| ~ subset(X3,X2)
| ~ subset(X1,X3) ),
c_0_423,
[final] ).
cnf(c_0_605_606,lemma,
( in(powerset(X1),esk5_1(X2))
| ~ in(X1,esk5_1(X2)) ),
c_0_424,
[final] ).
cnf(c_0_606_607,lemma,
( relation_dom(relation_dom_restriction(X1,X2)) = set_intersection2(relation_dom(X1),X2)
| ~ relation(X1) ),
c_0_425,
[final] ).
cnf(c_0_607_608,lemma,
( relation_rng(relation_rng_restriction(X1,X2)) = set_intersection2(relation_rng(X2),X1)
| ~ relation(X2) ),
c_0_426,
[final] ).
cnf(c_0_608_609,lemma,
( ~ in(X1,X2)
| set_difference(X2,singleton(X1)) != X2 ),
c_0_427,
[final] ).
cnf(c_0_609_610,lemma,
( ~ in(X1,X2)
| ~ disjoint(singleton(X1),X2) ),
c_0_428,
[final] ).
cnf(c_0_610_611,lemma,
( disjoint(X1,X2)
| in(esk9_2(X1,X2),X1) ),
c_0_429,
[final] ).
cnf(c_0_611_612,lemma,
( disjoint(X1,X2)
| in(esk9_2(X1,X2),X2) ),
c_0_430,
[final] ).
cnf(c_0_612_613,lemma,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
c_0_431,
[final] ).
cnf(c_0_613_614,lemma,
set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
c_0_432,
[final] ).
cnf(c_0_614_615,lemma,
set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
c_0_433,
[final] ).
cnf(c_0_615_616,lemma,
( subset(relation_inverse_image(X1,X2),relation_dom(X1))
| ~ relation(X1) ),
c_0_434,
[final] ).
cnf(c_0_616_617,lemma,
( subset(relation_image(X1,X2),relation_rng(X1))
| ~ relation(X1) ),
c_0_435,
[final] ).
cnf(c_0_617_618,lemma,
( relation_dom(X2) = relation_rng(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| X2 != function_inverse(X1) ),
c_0_436,
[final] ).
cnf(c_0_618_619,lemma,
( X1 = X2
| X1 = X3
| unordered_pair(X1,X4) != unordered_pair(X3,X2) ),
c_0_437,
[final] ).
cnf(c_0_619_620,lemma,
( subset(relation_dom_restriction(X1,X2),X1)
| ~ relation(X1) ),
c_0_438,
[final] ).
cnf(c_0_620_621,lemma,
( subset(relation_rng_restriction(X1,X2),X2)
| ~ relation(X2) ),
c_0_439,
[final] ).
cnf(c_0_621_622,lemma,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
c_0_440,
[final] ).
cnf(c_0_622_623,lemma,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
c_0_441,
[final] ).
cnf(c_0_623_624,lemma,
( X1 = X3
| ordered_pair(X1,X2) != ordered_pair(X3,X4) ),
c_0_442,
[final] ).
cnf(c_0_624_625,lemma,
( X2 = X4
| ordered_pair(X1,X2) != ordered_pair(X3,X4) ),
c_0_443,
[final] ).
cnf(c_0_625_626,lemma,
( ~ proper_subset(X1,X2)
| ~ subset(X2,X1) ),
c_0_444,
[final] ).
cnf(c_0_626_627,lemma,
( X1 = X2
| ~ subset(singleton(X1),singleton(X2)) ),
c_0_445,
[final] ).
cnf(c_0_627_628,lemma,
( set_union2(singleton(X1),X2) = X2
| ~ in(X1,X2) ),
c_0_446,
[final] ).
cnf(c_0_628_629,lemma,
( apply(identity_relation(X1),X2) = X2
| ~ in(X2,X1) ),
c_0_447,
[final] ).
cnf(c_0_629_630,lemma,
( set_union2(singleton(X1),X2) = X2
| ~ in(X1,X2) ),
c_0_448,
[final] ).
cnf(c_0_630_631,lemma,
( subset(X1,union(X2))
| ~ in(X1,X2) ),
c_0_449,
[final] ).
cnf(c_0_631_632,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
c_0_450,
[final] ).
cnf(c_0_632_633,lemma,
( subset(X1,union(X2))
| ~ in(X1,X2) ),
c_0_451,
[final] ).
cnf(c_0_633_634,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
c_0_452,
[final] ).
cnf(c_0_634_635,lemma,
( relation_composition(identity_relation(X2),X1) = relation_dom_restriction(X1,X2)
| ~ relation(X1) ),
c_0_453,
[final] ).
cnf(c_0_635_636,lemma,
subset(X1,set_union2(X1,X2)),
c_0_454,
[final] ).
cnf(c_0_636_637,lemma,
subset(set_difference(X1,X2),X1),
c_0_455,
[final] ).
cnf(c_0_637_638,lemma,
subset(set_intersection2(X1,X2),X1),
c_0_456,
[final] ).
cnf(c_0_638_639,lemma,
( X1 = singleton(X2)
| X1 = empty_set
| ~ subset(X1,singleton(X2)) ),
c_0_457,
[final] ).
cnf(c_0_639_640,lemma,
( X1 = singleton(X2)
| X1 = empty_set
| ~ subset(X1,singleton(X2)) ),
c_0_458,
[final] ).
cnf(c_0_640_641,lemma,
( disjoint(X1,X2)
| set_difference(X1,X2) != X1 ),
c_0_459,
[final] ).
cnf(c_0_641_642,lemma,
( set_difference(X1,X2) = X1
| ~ disjoint(X1,X2) ),
c_0_460,
[final] ).
cnf(c_0_642_643,lemma,
( set_intersection2(X1,X2) = X1
| ~ subset(X1,X2) ),
c_0_461,
[final] ).
cnf(c_0_643_644,lemma,
( set_union2(X1,X2) = X2
| ~ subset(X1,X2) ),
c_0_462,
[final] ).
cnf(c_0_644_645,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
c_0_463,
[final] ).
cnf(c_0_645_646,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
c_0_464,
[final] ).
cnf(c_0_646_647,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
c_0_465,
[final] ).
cnf(c_0_647_648,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
c_0_466,
[final] ).
cnf(c_0_648_649,lemma,
( relation_dom(function_inverse(X1)) = relation_rng(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1) ),
c_0_467,
[final] ).
cnf(c_0_649_650,lemma,
( relation_rng(function_inverse(X1)) = relation_dom(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1) ),
c_0_468,
[final] ).
cnf(c_0_650_651,lemma,
( set_difference(X1,singleton(X2)) = X1
| in(X2,X1) ),
c_0_469,
[final] ).
cnf(c_0_651_652,lemma,
( disjoint(singleton(X1),X2)
| in(X1,X2) ),
c_0_470,
[final] ).
cnf(c_0_652_653,lemma,
( one_to_one(function_inverse(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
c_0_471,
[final] ).
cnf(c_0_653_654,lemma,
( relation_image(X1,relation_dom(X1)) = relation_rng(X1)
| ~ relation(X1) ),
c_0_472,
[final] ).
cnf(c_0_654_655,lemma,
( X1 = X2
| singleton(X3) != unordered_pair(X1,X2) ),
c_0_473,
[final] ).
cnf(c_0_655_656,lemma,
( X1 = X2
| singleton(X1) != unordered_pair(X2,X3) ),
c_0_474,
[final] ).
cnf(c_0_656_657,lemma,
( subset(X1,singleton(X2))
| X1 != singleton(X2) ),
c_0_475,
[final] ).
cnf(c_0_657_658,lemma,
( subset(X1,singleton(X2))
| X1 != singleton(X2) ),
c_0_476,
[final] ).
cnf(c_0_658_659,lemma,
( relation_dom(X1) = X2
| ~ function(X1)
| ~ relation(X1)
| X1 != identity_relation(X2) ),
c_0_477,
[final] ).
cnf(c_0_659_660,lemma,
( subset(X1,singleton(X2))
| X1 != empty_set ),
c_0_478,
[final] ).
cnf(c_0_660_661,lemma,
( subset(X1,singleton(X2))
| X1 != empty_set ),
c_0_479,
[final] ).
cnf(c_0_661_662,lemma,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
c_0_480,
[final] ).
cnf(c_0_662_663,lemma,
( relation_dom(relation_inverse(X1)) = relation_rng(X1)
| ~ relation(X1) ),
c_0_481,
[final] ).
cnf(c_0_663_664,lemma,
( relation_rng(relation_inverse(X1)) = relation_dom(X1)
| ~ relation(X1) ),
c_0_482,
[final] ).
cnf(c_0_664_665,lemma,
in(X1,esk5_1(X1)),
c_0_483,
[final] ).
cnf(c_0_665_666,lemma,
( relation_rng(X1) = empty_set
| ~ relation(X1)
| relation_dom(X1) != empty_set ),
c_0_484,
[final] ).
cnf(c_0_666_667,lemma,
( relation_dom(X1) = empty_set
| ~ relation(X1)
| relation_rng(X1) != empty_set ),
c_0_485,
[final] ).
cnf(c_0_667_668,lemma,
unordered_pair(X1,X1) = singleton(X1),
c_0_486,
[final] ).
cnf(c_0_668_669,lemma,
( X1 = empty_set
| ~ relation(X1)
| relation_dom(X1) != empty_set ),
c_0_487,
[final] ).
cnf(c_0_669_670,lemma,
( X1 = empty_set
| ~ relation(X1)
| relation_rng(X1) != empty_set ),
c_0_488,
[final] ).
cnf(c_0_670_671,lemma,
subset(empty_set,X1),
c_0_489,
[final] ).
cnf(c_0_671_672,lemma,
union(powerset(X1)) = X1,
c_0_490,
[final] ).
cnf(c_0_672_673,lemma,
relation_dom(identity_relation(X1)) = X1,
c_0_491,
[final] ).
cnf(c_0_673_674,lemma,
relation_rng(identity_relation(X1)) = X1,
c_0_492,
[final] ).
cnf(c_0_674_675,lemma,
singleton(X1) != empty_set,
c_0_493,
[final] ).
cnf(c_0_675_676,lemma,
powerset(empty_set) = singleton(empty_set),
c_0_494,
[final] ).
cnf(c_0_676_677,lemma,
relation_dom(empty_set) = empty_set,
c_0_495,
[final] ).
cnf(c_0_677_678,lemma,
relation_rng(empty_set) = empty_set,
c_0_496,
[final] ).
cnf(c_0_678_679,negated_conjecture,
relation(esk4_0),
c_0_497,
[final] ).
cnf(c_0_679_680,negated_conjecture,
function(esk4_0),
c_0_498,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_852,plain,
( ~ relation(X0)
| in(X1,relation_dom(relation_dom_restriction(X0,X2)))
| ~ in(X1,relation_dom(X0))
| ~ in(X1,X2) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_7ad96c.p',c_0_535) ).
cnf(c_1384,plain,
( ~ relation(X0)
| in(X1,relation_dom(relation_dom_restriction(X0,X2)))
| ~ in(X1,relation_dom(X0))
| ~ in(X1,X2) ),
inference(copy,[status(esa)],[c_852]) ).
cnf(c_1720,plain,
( ~ relation(X0)
| in(X1,relation_dom(relation_dom_restriction(X0,X2)))
| ~ in(X1,relation_dom(X0))
| ~ in(X1,X2) ),
inference(copy,[status(esa)],[c_1384]) ).
cnf(c_1991,plain,
( ~ relation(X0)
| in(X1,relation_dom(relation_dom_restriction(X0,X2)))
| ~ in(X1,relation_dom(X0))
| ~ in(X1,X2) ),
inference(copy,[status(esa)],[c_1720]) ).
cnf(c_2060,plain,
( ~ relation(X0)
| in(X1,relation_dom(relation_dom_restriction(X0,X2)))
| ~ in(X1,relation_dom(X0))
| ~ in(X1,X2) ),
inference(copy,[status(esa)],[c_1991]) ).
cnf(c_3044,plain,
( ~ relation(X0)
| in(X1,relation_dom(relation_dom_restriction(X0,X2)))
| ~ in(X1,relation_dom(X0))
| ~ in(X1,X2) ),
inference(copy,[status(esa)],[c_2060]) ).
cnf(c_186852,plain,
( ~ relation(X0)
| in(sk2_esk3_0,relation_dom(relation_dom_restriction(X0,sk2_esk2_0)))
| ~ in(sk2_esk3_0,relation_dom(X0))
| ~ in(sk2_esk3_0,sk2_esk2_0) ),
inference(instantiation,[status(thm)],[c_3044]) ).
cnf(c_392558,plain,
( ~ relation(sk2_esk4_0)
| in(sk2_esk3_0,relation_dom(relation_dom_restriction(sk2_esk4_0,sk2_esk2_0)))
| ~ in(sk2_esk3_0,relation_dom(sk2_esk4_0))
| ~ in(sk2_esk3_0,sk2_esk2_0) ),
inference(instantiation,[status(thm)],[c_186852]) ).
cnf(c_849,plain,
( ~ relation(X0)
| ~ in(X1,relation_dom(relation_dom_restriction(X0,X2)))
| in(X1,X2) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_7ad96c.p',c_0_532) ).
cnf(c_1380,plain,
( ~ relation(X0)
| ~ in(X1,relation_dom(relation_dom_restriction(X0,X2)))
| in(X1,X2) ),
inference(copy,[status(esa)],[c_849]) ).
cnf(c_1717,plain,
( ~ relation(X0)
| ~ in(X1,relation_dom(relation_dom_restriction(X0,X2)))
| in(X1,X2) ),
inference(copy,[status(esa)],[c_1380]) ).
cnf(c_1994,plain,
( ~ relation(X0)
| ~ in(X1,relation_dom(relation_dom_restriction(X0,X2)))
| in(X1,X2) ),
inference(copy,[status(esa)],[c_1717]) ).
cnf(c_2057,plain,
( ~ relation(X0)
| ~ in(X1,relation_dom(relation_dom_restriction(X0,X2)))
| in(X1,X2) ),
inference(copy,[status(esa)],[c_1994]) ).
cnf(c_3041,plain,
( ~ relation(X0)
| ~ in(X1,relation_dom(relation_dom_restriction(X0,X2)))
| in(X1,X2) ),
inference(copy,[status(esa)],[c_2057]) ).
cnf(c_74315,plain,
( ~ relation(sk2_esk4_0)
| ~ in(sk2_esk3_0,relation_dom(relation_dom_restriction(sk2_esk4_0,sk2_esk2_0)))
| in(sk2_esk3_0,sk2_esk2_0) ),
inference(instantiation,[status(thm)],[c_3041]) ).
cnf(c_846,plain,
( ~ relation(X0)
| ~ in(X1,relation_dom(relation_dom_restriction(X0,X2)))
| in(X1,relation_dom(X0)) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_7ad96c.p',c_0_529) ).
cnf(c_1374,plain,
( ~ relation(X0)
| ~ in(X1,relation_dom(relation_dom_restriction(X0,X2)))
| in(X1,relation_dom(X0)) ),
inference(copy,[status(esa)],[c_846]) ).
cnf(c_1714,plain,
( ~ relation(X0)
| ~ in(X1,relation_dom(relation_dom_restriction(X0,X2)))
| in(X1,relation_dom(X0)) ),
inference(copy,[status(esa)],[c_1374]) ).
cnf(c_1997,plain,
( ~ relation(X0)
| ~ in(X1,relation_dom(relation_dom_restriction(X0,X2)))
| in(X1,relation_dom(X0)) ),
inference(copy,[status(esa)],[c_1714]) ).
cnf(c_2054,plain,
( ~ relation(X0)
| ~ in(X1,relation_dom(relation_dom_restriction(X0,X2)))
| in(X1,relation_dom(X0)) ),
inference(copy,[status(esa)],[c_1997]) ).
cnf(c_3038,plain,
( ~ relation(X0)
| ~ in(X1,relation_dom(relation_dom_restriction(X0,X2)))
| in(X1,relation_dom(X0)) ),
inference(copy,[status(esa)],[c_2054]) ).
cnf(c_74314,plain,
( ~ relation(sk2_esk4_0)
| ~ in(sk2_esk3_0,relation_dom(relation_dom_restriction(sk2_esk4_0,sk2_esk2_0)))
| in(sk2_esk3_0,relation_dom(sk2_esk4_0)) ),
inference(instantiation,[status(thm)],[c_3038]) ).
cnf(c_851,negated_conjecture,
( ~ in(sk2_esk3_0,relation_dom(relation_dom_restriction(sk2_esk4_0,sk2_esk2_0)))
| ~ in(sk2_esk3_0,relation_dom(sk2_esk4_0))
| ~ in(sk2_esk3_0,sk2_esk2_0) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_7ad96c.p',c_0_534) ).
cnf(c_904,negated_conjecture,
( in(sk2_esk3_0,relation_dom(relation_dom_restriction(sk2_esk4_0,sk2_esk2_0)))
| in(sk2_esk3_0,relation_dom(sk2_esk4_0)) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_7ad96c.p',c_0_587) ).
cnf(c_909,negated_conjecture,
( in(sk2_esk3_0,relation_dom(relation_dom_restriction(sk2_esk4_0,sk2_esk2_0)))
| in(sk2_esk3_0,sk2_esk2_0) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_7ad96c.p',c_0_592) ).
cnf(c_995,negated_conjecture,
relation(sk2_esk4_0),
file('/export/starexec/sandbox/tmp/iprover_modulo_7ad96c.p',c_0_678) ).
cnf(contradiction,plain,
$false,
inference(minisat,[status(thm)],[c_392558,c_74315,c_74314,c_851,c_904,c_909,c_995]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU224+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.14 % Command : iprover_modulo %s %d
% 0.14/0.36 % Computer : n009.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Sun Jun 19 12:23:52 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.37 % Running in mono-core mode
% 0.22/0.49 % Orienting using strategy Equiv(ClausalAll)
% 0.22/0.49 % FOF problem with conjecture
% 0.22/0.49 % 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_cc0343.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_7ad96c.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_4076a4 | grep -v "SZS"
% 0.22/0.52
% 0.22/0.52 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.22/0.52
% 0.22/0.52 %
% 0.22/0.52 % ------ iProver source info
% 0.22/0.52
% 0.22/0.52 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.22/0.52 % git: non_committed_changes: true
% 0.22/0.52 % git: last_make_outside_of_git: true
% 0.22/0.52
% 0.22/0.52 %
% 0.22/0.52 % ------ Input Options
% 0.22/0.52
% 0.22/0.52 % --out_options all
% 0.22/0.52 % --tptp_safe_out true
% 0.22/0.52 % --problem_path ""
% 0.22/0.52 % --include_path ""
% 0.22/0.52 % --clausifier .//eprover
% 0.22/0.52 % --clausifier_options --tstp-format
% 0.22/0.52 % --stdin false
% 0.22/0.52 % --dbg_backtrace false
% 0.22/0.52 % --dbg_dump_prop_clauses false
% 0.22/0.52 % --dbg_dump_prop_clauses_file -
% 0.22/0.52 % --dbg_out_stat false
% 0.22/0.52
% 0.22/0.52 % ------ General Options
% 0.22/0.52
% 0.22/0.52 % --fof false
% 0.22/0.52 % --time_out_real 150.
% 0.22/0.52 % --time_out_prep_mult 0.2
% 0.22/0.52 % --time_out_virtual -1.
% 0.22/0.52 % --schedule none
% 0.22/0.52 % --ground_splitting input
% 0.22/0.52 % --splitting_nvd 16
% 0.22/0.52 % --non_eq_to_eq false
% 0.22/0.52 % --prep_gs_sim true
% 0.22/0.52 % --prep_unflatten false
% 0.22/0.52 % --prep_res_sim true
% 0.22/0.52 % --prep_upred true
% 0.22/0.52 % --res_sim_input true
% 0.22/0.52 % --clause_weak_htbl true
% 0.22/0.52 % --gc_record_bc_elim false
% 0.22/0.52 % --symbol_type_check false
% 0.22/0.52 % --clausify_out false
% 0.22/0.52 % --large_theory_mode false
% 0.22/0.52 % --prep_sem_filter none
% 0.22/0.52 % --prep_sem_filter_out false
% 0.22/0.52 % --preprocessed_out false
% 0.22/0.52 % --sub_typing false
% 0.22/0.52 % --brand_transform false
% 0.22/0.52 % --pure_diseq_elim true
% 0.22/0.52 % --min_unsat_core false
% 0.22/0.52 % --pred_elim true
% 0.22/0.52 % --add_important_lit false
% 0.22/0.52 % --soft_assumptions false
% 0.22/0.52 % --reset_solvers false
% 0.22/0.52 % --bc_imp_inh []
% 0.22/0.52 % --conj_cone_tolerance 1.5
% 0.22/0.52 % --prolific_symb_bound 500
% 0.22/0.52 % --lt_threshold 2000
% 0.22/0.52
% 0.22/0.52 % ------ SAT Options
% 0.22/0.52
% 0.22/0.52 % --sat_mode false
% 0.22/0.52 % --sat_fm_restart_options ""
% 0.22/0.52 % --sat_gr_def false
% 0.22/0.52 % --sat_epr_types true
% 0.22/0.52 % --sat_non_cyclic_types false
% 0.22/0.52 % --sat_finite_models false
% 0.22/0.52 % --sat_fm_lemmas false
% 0.22/0.52 % --sat_fm_prep false
% 0.22/0.52 % --sat_fm_uc_incr true
% 0.22/0.52 % --sat_out_model small
% 0.22/0.52 % --sat_out_clauses false
% 0.22/0.52
% 0.22/0.52 % ------ QBF Options
% 0.22/0.52
% 0.22/0.52 % --qbf_mode false
% 0.22/0.52 % --qbf_elim_univ true
% 0.22/0.52 % --qbf_sk_in true
% 0.22/0.52 % --qbf_pred_elim true
% 0.22/0.52 % --qbf_split 32
% 0.22/0.52
% 0.22/0.52 % ------ BMC1 Options
% 0.22/0.52
% 0.22/0.52 % --bmc1_incremental false
% 0.22/0.52 % --bmc1_axioms reachable_all
% 0.22/0.52 % --bmc1_min_bound 0
% 0.22/0.52 % --bmc1_max_bound -1
% 0.22/0.52 % --bmc1_max_bound_default -1
% 0.22/0.52 % --bmc1_symbol_reachability true
% 0.22/0.52 % --bmc1_property_lemmas false
% 0.22/0.52 % --bmc1_k_induction false
% 0.22/0.52 % --bmc1_non_equiv_states false
% 0.22/0.52 % --bmc1_deadlock false
% 0.22/0.52 % --bmc1_ucm false
% 0.22/0.52 % --bmc1_add_unsat_core none
% 0.22/0.52 % --bmc1_unsat_core_children false
% 0.22/0.52 % --bmc1_unsat_core_extrapolate_axioms false
% 0.22/0.52 % --bmc1_out_stat full
% 0.22/0.52 % --bmc1_ground_init false
% 0.22/0.52 % --bmc1_pre_inst_next_state false
% 0.22/0.52 % --bmc1_pre_inst_state false
% 0.22/0.52 % --bmc1_pre_inst_reach_state false
% 0.22/0.52 % --bmc1_out_unsat_core false
% 0.22/0.52 % --bmc1_aig_witness_out false
% 0.22/0.52 % --bmc1_verbose false
% 0.22/0.52 % --bmc1_dump_clauses_tptp false
% 0.35/0.52 % --bmc1_dump_unsat_core_tptp false
% 0.35/0.52 % --bmc1_dump_file -
% 0.35/0.52 % --bmc1_ucm_expand_uc_limit 128
% 0.35/0.52 % --bmc1_ucm_n_expand_iterations 6
% 0.35/0.52 % --bmc1_ucm_extend_mode 1
% 0.35/0.52 % --bmc1_ucm_init_mode 2
% 0.35/0.52 % --bmc1_ucm_cone_mode none
% 0.35/0.52 % --bmc1_ucm_reduced_relation_type 0
% 0.35/0.52 % --bmc1_ucm_relax_model 4
% 0.35/0.52 % --bmc1_ucm_full_tr_after_sat true
% 0.35/0.52 % --bmc1_ucm_expand_neg_assumptions false
% 0.35/0.52 % --bmc1_ucm_layered_model none
% 0.35/0.52 % --bmc1_ucm_max_lemma_size 10
% 0.35/0.52
% 0.35/0.52 % ------ AIG Options
% 0.35/0.52
% 0.35/0.52 % --aig_mode false
% 0.35/0.52
% 0.35/0.52 % ------ Instantiation Options
% 0.35/0.52
% 0.35/0.52 % --instantiation_flag true
% 0.35/0.52 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.35/0.52 % --inst_solver_per_active 750
% 0.35/0.52 % --inst_solver_calls_frac 0.5
% 0.35/0.52 % --inst_passive_queue_type priority_queues
% 0.35/0.52 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.35/0.52 % --inst_passive_queues_freq [25;2]
% 0.35/0.52 % --inst_dismatching true
% 0.35/0.52 % --inst_eager_unprocessed_to_passive true
% 0.35/0.52 % --inst_prop_sim_given true
% 0.35/0.52 % --inst_prop_sim_new false
% 0.35/0.52 % --inst_orphan_elimination true
% 0.35/0.52 % --inst_learning_loop_flag true
% 0.35/0.52 % --inst_learning_start 3000
% 0.35/0.52 % --inst_learning_factor 2
% 0.35/0.52 % --inst_start_prop_sim_after_learn 3
% 0.35/0.52 % --inst_sel_renew solver
% 0.35/0.52 % --inst_lit_activity_flag true
% 0.35/0.52 % --inst_out_proof true
% 0.35/0.52
% 0.35/0.52 % ------ Resolution Options
% 0.35/0.52
% 0.35/0.52 % --resolution_flag true
% 0.35/0.52 % --res_lit_sel kbo_max
% 0.35/0.52 % --res_to_prop_solver none
% 0.35/0.52 % --res_prop_simpl_new false
% 0.35/0.52 % --res_prop_simpl_given false
% 0.35/0.52 % --res_passive_queue_type priority_queues
% 0.35/0.52 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.35/0.52 % --res_passive_queues_freq [15;5]
% 0.35/0.52 % --res_forward_subs full
% 0.35/0.52 % --res_backward_subs full
% 0.35/0.52 % --res_forward_subs_resolution true
% 0.35/0.52 % --res_backward_subs_resolution true
% 0.35/0.52 % --res_orphan_elimination false
% 0.35/0.52 % --res_time_limit 1000.
% 0.35/0.52 % --res_out_proof true
% 0.35/0.52 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_cc0343.s
% 0.35/0.52 % --modulo true
% 0.35/0.52
% 0.35/0.52 % ------ Combination Options
% 0.35/0.52
% 0.35/0.52 % --comb_res_mult 1000
% 0.35/0.52 % --comb_inst_mult 300
% 0.35/0.52 % ------
% 0.35/0.52
% 0.35/0.52 % ------ Parsing...%
% 0.35/0.52
% 0.35/0.52
% 0.35/0.52 % ------ Statistics
% 0.35/0.52
% 0.35/0.52 % ------ General
% 0.35/0.52
% 0.35/0.52 % num_of_input_clauses: 256
% 0.35/0.52 % num_of_input_neg_conjectures: 0
% 0.35/0.52 % num_of_splits: 0
% 0.35/0.52 % num_of_split_atoms: 0
% 0.35/0.52 % num_of_sem_filtered_clauses: 0
% 0.35/0.52 % num_of_subtypes: 0
% 0.35/0.52 % monotx_restored_types: 0
% 0.35/0.52 % sat_num_of_epr_types: 0
% 0.35/0.52 % sat_num_of_non_cyclic_types: 0
% 0.35/0.52 % sat_guarded_non_collapsed_types: 0
% 0.35/0.52 % is_epr: 0
% 0.35/0.52 % is_horn: 0
% 0.35/0.52 % has_eq: 0
% 0.35/0.52 % num_pure_diseq_elim: 0
% 0.35/0.52 % simp_replaced_by: 0
% 0.35/0.52 % res_preprocessed: 0
% 0.35/0.52 % prep_upred: 0
% 0.35/0.52 % prep_unflattend: 0
% 0.35/0.52 % pred_elim_cands: 0
% 0.35/0.52 % pred_elim: 0
% 0.35/0.52 % pred_elim_cl: 0
% 0.35/0.52 % pred_elim_cycles: 0
% 0.35/0.52 % forced_gc_time: 0
% 0.35/0.52 % gc_basic_clause_elim: 0
% 0.35/0.52 % parsing_time: 0.
% 0.35/0.52 % sem_filter_time: 0.
% 0.35/0.52 % pred_elim_time: 0.
% 0.35/0.52 % out_proof_time: 0.
% 0.35/0.52 % monotx_time: 0.
% 0.35/0.52 % subtype_inf_time: 0.
% 0.35/0.52 % unif_index_cands_time: 0.
% 0.35/0.52 % uFatal error: exception Failure("Parse error in: /export/starexec/sandbox/tmp/iprover_modulo_7ad96c.p line: 259 near token: '!='")
% 0.35/0.53 nif_index_add_time: 0.
% 0.35/0.53 % total_time: 0.025
% 0.35/0.53 % num_of_symbols: 81
% 0.35/0.53 % num_of_terms: 448
% 0.35/0.53
% 0.35/0.53 % ------ Propositional Solver
% 0.35/0.53
% 0.35/0.53 % prop_solver_calls: 0
% 0.35/0.53 % prop_fast_solver_calls: 0
% 0.35/0.53 % prop_num_of_clauses: 0
% 0.35/0.53 % prop_preprocess_simplified: 0
% 0.35/0.53 % prop_fo_subsumed: 0
% 0.35/0.53 % prop_solver_time: 0.
% 0.35/0.53 % prop_fast_solver_time: 0.
% 0.35/0.53 % prop_unsat_core_time: 0.
% 0.35/0.53
% 0.35/0.53 % ------ QBF
% 0.35/0.53
% 0.35/0.53 % qbf_q_res: 0
% 0.35/0.53 % qbf_num_tautologies: 0
% 0.35/0.53 % qbf_prep_cycles: 0
% 0.35/0.53
% 0.35/0.53 % ------ BMC1
% 0.35/0.53
% 0.35/0.53 % bmc1_current_bound: -1
% 0.35/0.53 % bmc1_last_solved_bound: -1
% 0.35/0.53 % bmc1_unsat_core_size: -1
% 0.35/0.53 % bmc1_unsat_core_parents_size: -1
% 0.35/0.53 % bmc1_merge_next_fun: 0
% 0.35/0.53 % bmc1_unsat_core_clauses_time: 0.
% 0.35/0.53
% 0.35/0.53 % ------ Instantiation
% 0.35/0.53
% 0.35/0.53 % inst_num_of_clauses: undef
% 0.35/0.53 % inst_num_in_passive: undef
% 0.35/0.53 % inst_num_in_active: 0
% 0.35/0.53 % inst_num_in_unprocessed: 0
% 0.35/0.53 % inst_num_of_loops: 0
% 0.35/0.53 % inst_num_of_learning_restarts: 0
% 0.35/0.53 % inst_num_moves_active_passive: 0
% 0.35/0.53 % inst_lit_activity: 0
% 0.35/0.53 % inst_lit_activity_moves: 0
% 0.35/0.53 % inst_num_tautologies: 0
% 0.35/0.53 % inst_num_prop_implied: 0
% 0.35/0.53 % inst_num_existing_simplified: 0
% 0.35/0.53 % inst_num_eq_res_simplified: 0
% 0.35/0.53 % inst_num_child_elim: 0
% 0.35/0.53 % inst_num_of_dismatching_blockings: 0
% 0.35/0.53 % inst_num_of_non_proper_insts: 0
% 0.35/0.53 % inst_num_of_duplicates: 0
% 0.35/0.53 % inst_inst_num_from_inst_to_res: 0
% 0.35/0.53 % inst_dismatching_checking_time: 0.
% 0.35/0.53
% 0.35/0.53 % ------ Resolution
% 0.35/0.53
% 0.35/0.53 % res_num_of_clauses: undef
% 0.35/0.53 % res_num_in_passive: undef
% 0.35/0.53 % res_num_in_active: 0
% 0.35/0.53 % res_num_of_loops: 0
% 0.35/0.53 % res_forward_subset_subsumed: 0
% 0.35/0.53 % res_backward_subset_subsumed: 0
% 0.35/0.53 % res_forward_subsumed: 0
% 0.35/0.53 % res_backward_subsumed: 0
% 0.35/0.53 % res_forward_subsumption_resolution: 0
% 0.35/0.53 % res_backward_subsumption_resolution: 0
% 0.35/0.53 % res_clause_to_clause_subsumption: 0
% 0.35/0.53 % res_orphan_elimination: 0
% 0.35/0.53 % res_tautology_del: 0
% 0.35/0.53 % res_num_eq_res_simplified: 0
% 0.35/0.53 % res_num_sel_changes: 0
% 0.35/0.53 % res_moves_from_active_to_pass: 0
% 0.35/0.53
% 0.35/0.53 % Status Unknown
% 0.38/0.63 % Orienting using strategy ClausalAll
% 0.38/0.63 % FOF problem with conjecture
% 0.38/0.63 % 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_cc0343.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_7ad96c.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_3c2a0f | grep -v "SZS"
% 0.48/0.66
% 0.48/0.66 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.48/0.66
% 0.48/0.66 %
% 0.48/0.66 % ------ iProver source info
% 0.48/0.66
% 0.48/0.66 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.48/0.66 % git: non_committed_changes: true
% 0.48/0.66 % git: last_make_outside_of_git: true
% 0.48/0.66
% 0.48/0.66 %
% 0.48/0.66 % ------ Input Options
% 0.48/0.66
% 0.48/0.66 % --out_options all
% 0.48/0.66 % --tptp_safe_out true
% 0.48/0.66 % --problem_path ""
% 0.48/0.66 % --include_path ""
% 0.48/0.66 % --clausifier .//eprover
% 0.48/0.66 % --clausifier_options --tstp-format
% 0.48/0.66 % --stdin false
% 0.48/0.66 % --dbg_backtrace false
% 0.48/0.66 % --dbg_dump_prop_clauses false
% 0.48/0.66 % --dbg_dump_prop_clauses_file -
% 0.48/0.66 % --dbg_out_stat false
% 0.48/0.66
% 0.48/0.66 % ------ General Options
% 0.48/0.66
% 0.48/0.66 % --fof false
% 0.48/0.66 % --time_out_real 150.
% 0.48/0.66 % --time_out_prep_mult 0.2
% 0.48/0.66 % --time_out_virtual -1.
% 0.48/0.66 % --schedule none
% 0.48/0.66 % --ground_splitting input
% 0.48/0.66 % --splitting_nvd 16
% 0.48/0.66 % --non_eq_to_eq false
% 0.48/0.66 % --prep_gs_sim true
% 0.48/0.66 % --prep_unflatten false
% 0.48/0.66 % --prep_res_sim true
% 0.48/0.66 % --prep_upred true
% 0.48/0.66 % --res_sim_input true
% 0.48/0.66 % --clause_weak_htbl true
% 0.48/0.66 % --gc_record_bc_elim false
% 0.48/0.66 % --symbol_type_check false
% 0.48/0.66 % --clausify_out false
% 0.48/0.66 % --large_theory_mode false
% 0.48/0.66 % --prep_sem_filter none
% 0.48/0.66 % --prep_sem_filter_out false
% 0.48/0.66 % --preprocessed_out false
% 0.48/0.66 % --sub_typing false
% 0.48/0.66 % --brand_transform false
% 0.48/0.66 % --pure_diseq_elim true
% 0.48/0.66 % --min_unsat_core false
% 0.48/0.66 % --pred_elim true
% 0.48/0.66 % --add_important_lit false
% 0.48/0.66 % --soft_assumptions false
% 0.48/0.66 % --reset_solvers false
% 0.48/0.66 % --bc_imp_inh []
% 0.48/0.66 % --conj_cone_tolerance 1.5
% 0.48/0.66 % --prolific_symb_bound 500
% 0.48/0.66 % --lt_threshold 2000
% 0.48/0.66
% 0.48/0.66 % ------ SAT Options
% 0.48/0.66
% 0.48/0.66 % --sat_mode false
% 0.48/0.66 % --sat_fm_restart_options ""
% 0.48/0.66 % --sat_gr_def false
% 0.48/0.66 % --sat_epr_types true
% 0.48/0.66 % --sat_non_cyclic_types false
% 0.48/0.66 % --sat_finite_models false
% 0.48/0.66 % --sat_fm_lemmas false
% 0.48/0.66 % --sat_fm_prep false
% 0.48/0.66 % --sat_fm_uc_incr true
% 0.48/0.66 % --sat_out_model small
% 0.48/0.66 % --sat_out_clauses false
% 0.48/0.66
% 0.48/0.66 % ------ QBF Options
% 0.48/0.66
% 0.48/0.66 % --qbf_mode false
% 0.48/0.66 % --qbf_elim_univ true
% 0.48/0.66 % --qbf_sk_in true
% 0.48/0.66 % --qbf_pred_elim true
% 0.48/0.66 % --qbf_split 32
% 0.48/0.66
% 0.48/0.66 % ------ BMC1 Options
% 0.48/0.66
% 0.48/0.66 % --bmc1_incremental false
% 0.48/0.66 % --bmc1_axioms reachable_all
% 0.48/0.66 % --bmc1_min_bound 0
% 0.48/0.66 % --bmc1_max_bound -1
% 0.48/0.66 % --bmc1_max_bound_default -1
% 0.48/0.66 % --bmc1_symbol_reachability true
% 0.48/0.66 % --bmc1_property_lemmas false
% 0.48/0.66 % --bmc1_k_induction false
% 0.48/0.66 % --bmc1_non_equiv_states false
% 0.48/0.66 % --bmc1_deadlock false
% 0.48/0.66 % --bmc1_ucm false
% 0.48/0.66 % --bmc1_add_unsat_core none
% 0.48/0.66 % --bmc1_unsat_core_children false
% 0.48/0.66 % --bmc1_unsat_core_extrapolate_axioms false
% 0.48/0.66 % --bmc1_out_stat full
% 0.48/0.66 % --bmc1_ground_init false
% 0.48/0.66 % --bmc1_pre_inst_next_state false
% 0.48/0.66 % --bmc1_pre_inst_state false
% 0.48/0.66 % --bmc1_pre_inst_reach_state false
% 0.48/0.66 % --bmc1_out_unsat_core false
% 0.48/0.66 % --bmc1_aig_witness_out false
% 0.48/0.66 % --bmc1_verbose false
% 0.48/0.66 % --bmc1_dump_clauses_tptp false
% 0.90/1.20 % --bmc1_dump_unsat_core_tptp false
% 0.90/1.20 % --bmc1_dump_file -
% 0.90/1.20 % --bmc1_ucm_expand_uc_limit 128
% 0.90/1.20 % --bmc1_ucm_n_expand_iterations 6
% 0.90/1.20 % --bmc1_ucm_extend_mode 1
% 0.90/1.20 % --bmc1_ucm_init_mode 2
% 0.90/1.20 % --bmc1_ucm_cone_mode none
% 0.90/1.20 % --bmc1_ucm_reduced_relation_type 0
% 0.90/1.20 % --bmc1_ucm_relax_model 4
% 0.90/1.20 % --bmc1_ucm_full_tr_after_sat true
% 0.90/1.20 % --bmc1_ucm_expand_neg_assumptions false
% 0.90/1.20 % --bmc1_ucm_layered_model none
% 0.90/1.20 % --bmc1_ucm_max_lemma_size 10
% 0.90/1.20
% 0.90/1.20 % ------ AIG Options
% 0.90/1.20
% 0.90/1.20 % --aig_mode false
% 0.90/1.20
% 0.90/1.20 % ------ Instantiation Options
% 0.90/1.20
% 0.90/1.20 % --instantiation_flag true
% 0.90/1.20 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.90/1.20 % --inst_solver_per_active 750
% 0.90/1.20 % --inst_solver_calls_frac 0.5
% 0.90/1.20 % --inst_passive_queue_type priority_queues
% 0.90/1.20 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.90/1.20 % --inst_passive_queues_freq [25;2]
% 0.90/1.20 % --inst_dismatching true
% 0.90/1.20 % --inst_eager_unprocessed_to_passive true
% 0.90/1.20 % --inst_prop_sim_given true
% 0.90/1.20 % --inst_prop_sim_new false
% 0.90/1.20 % --inst_orphan_elimination true
% 0.90/1.20 % --inst_learning_loop_flag true
% 0.90/1.20 % --inst_learning_start 3000
% 0.90/1.20 % --inst_learning_factor 2
% 0.90/1.20 % --inst_start_prop_sim_after_learn 3
% 0.90/1.20 % --inst_sel_renew solver
% 0.90/1.20 % --inst_lit_activity_flag true
% 0.90/1.20 % --inst_out_proof true
% 0.90/1.20
% 0.90/1.20 % ------ Resolution Options
% 0.90/1.20
% 0.90/1.20 % --resolution_flag true
% 0.90/1.20 % --res_lit_sel kbo_max
% 0.90/1.20 % --res_to_prop_solver none
% 0.90/1.20 % --res_prop_simpl_new false
% 0.90/1.20 % --res_prop_simpl_given false
% 0.90/1.20 % --res_passive_queue_type priority_queues
% 0.90/1.20 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.90/1.20 % --res_passive_queues_freq [15;5]
% 0.90/1.20 % --res_forward_subs full
% 0.90/1.20 % --res_backward_subs full
% 0.90/1.20 % --res_forward_subs_resolution true
% 0.90/1.20 % --res_backward_subs_resolution true
% 0.90/1.20 % --res_orphan_elimination false
% 0.90/1.20 % --res_time_limit 1000.
% 0.90/1.20 % --res_out_proof true
% 0.90/1.20 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_cc0343.s
% 0.90/1.20 % --modulo true
% 0.90/1.20
% 0.90/1.20 % ------ Combination Options
% 0.90/1.20
% 0.90/1.20 % --comb_res_mult 1000
% 0.90/1.20 % --comb_inst_mult 300
% 0.90/1.20 % ------
% 0.90/1.20
% 0.90/1.20 % ------ Parsing...% successful
% 0.90/1.20
% 0.90/1.20 % ------ 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 %
% 0.90/1.20
% 0.90/1.20 % ------ Proving...
% 0.90/1.20 % ------ Problem Properties
% 0.90/1.20
% 0.90/1.20 %
% 0.90/1.20 % EPR false
% 0.90/1.20 % Horn false
% 0.90/1.20 % Has equality true
% 0.90/1.20
% 0.90/1.20 % % ------ Input Options Time Limit: Unbounded
% 0.90/1.20
% 0.90/1.20
% 0.90/1.20 Compiling...
% 0.90/1.20 Loading plugin: done.
% 0.90/1.20 Compiling...
% 0.90/1.20 Loading plugin: done.
% 0.90/1.20 Compiling...
% 0.90/1.20 Loading plugin: done.
% 0.90/1.20 Compiling...
% 0.90/1.20 Loading plugin: done.
% 0.90/1.20 % warning: Clause {~(relation(X0));~(function(X0));in(ordered_pair(X1,X2),X0);~(in(X1,relation_dom(X0)));~(equality_sorted($i,X2,apply(X0,X1)))} has no selected literals
% 0.90/1.20 cnf(c_2075,plain,
% 0.90/1.20 ( ~ relation(X0)
% 0.90/1.20 | ~ function(X0)
% 0.90/1.20 | in(ordered_pair(X1,X2),X0)
% 0.90/1.20 | ~ in(X1,relation_dom(X0))
% 0.90/1.20 | X2 != apply(X0,X1) ),
% 0.90/1.20 inference(copy,[status(esa)],[c_1976]) ).
% 0.90/1.20
% 0.90/1.20 cnf(c_1976,plain,
% 0.90/1.20 ( ~ relation(X0)
% 0.90/1.20 | ~ function(X0)
% 0.90/1.20 | in(ordered_pair(X1,X2),X0)
% 0.90/1.20 | ~ in(X1,relation_dom(X0))
% 0.90/1.20 | X2 != apply(X0,X1) ),
% 0.90/1.20 inference(copy,[status(esa)],[c_1735]) ).
% 0.90/1.20
% 0.90/1.20 cnf(c_1735,plain,
% 0.90/1.20 ( ~ relation(X0)
% 0.90/1.20 | ~ function(X0)
% 0.90/1.20 | in(ordered_pair(X1,X2),X0)
% 0.90/1.20 | ~ in(X1,relation_dom(X0))
% 0.90/1.20 | X2 != apply(X0,X1) ),
% 0.90/1.20 inference(copy,[status(esa)],[c_1420]) ).
% 0.90/1.20
% 0.90/1.20 cnf(c_1420,plain,
% 0.90/1.20 ( ~ relation(X0)
% 0.90/1.20 | ~ function(X0)
% 0.90/1.20 | in(ordered_pair(X1,X2),X0)
% 0.90/1.20 | ~ in(X1,relation_dom(X0))
% 0.90/1.20 | X2 != apply(X0,X1) ),
% 0.90/1.20 inference(copy,[status(esa)],[c_870]) ).
% 0.90/1.20
% 0.90/1.20 cnf(c_870,plain,
% 0.90/1.20 ( ~ relation(X0)
% 0.90/1.20 | ~ function(X0)
% 0.90/1.20 | in(ordered_pair(X1,X2),X0)
% 0.90/1.20 | ~ in(X1,relation_dom(X0))
% 0.90/1.20 | X2 != apply(X0,X1) ),
% 0.90/1.20 file('/export/starexec/sandbox/tmp/iprover_modulo_7ad96c.p', c_0_553) ).
% 0.90/1.20
% 0.90/1.20 % % ------ Current options:
% 0.90/1.20
% 0.90/1.20 % ------ Input Options
% 0.90/1.20
% 0.90/1.20 % --out_options all
% 0.90/1.20 % --tptp_safe_out true
% 0.90/1.20 % --problem_path ""
% 0.90/1.20 % --include_path ""
% 0.90/1.20 % --clausifier .//eprover
% 0.90/1.20 % --clausifier_options --tstp-format
% 0.90/1.20 % --stdin false
% 0.90/1.20 % --dbg_backtrace false
% 0.90/1.20 % --dbg_dump_prop_clauses false
% 0.90/1.20 % --dbg_dump_prop_clauses_file -
% 0.90/1.20 % --dbg_out_stat false
% 0.90/1.20
% 0.90/1.20 % ------ General Options
% 0.90/1.20
% 0.90/1.20 % --fof false
% 0.90/1.20 % --time_out_real 150.
% 0.90/1.20 % --time_out_prep_mult 0.2
% 0.90/1.20 % --time_out_virtual -1.
% 0.90/1.20 % --schedule none
% 0.90/1.20 % --ground_splitting input
% 0.90/1.20 % --splitting_nvd 16
% 0.90/1.20 % --non_eq_to_eq false
% 0.90/1.20 % --prep_gs_sim true
% 0.90/1.20 % --prep_unflatten false
% 0.90/1.20 % --prep_res_sim true
% 0.90/1.20 % --prep_upred true
% 0.90/1.20 % --res_sim_input true
% 0.90/1.20 % --clause_weak_htbl true
% 0.90/1.20 % --gc_record_bc_elim false
% 0.90/1.20 % --symbol_type_check false
% 0.90/1.20 % --clausify_out false
% 0.90/1.20 % --large_theory_mode false
% 0.90/1.20 % --prep_sem_filter none
% 0.90/1.20 % --prep_sem_filter_out false
% 0.90/1.20 % --preprocessed_out false
% 0.90/1.20 % --sub_typing false
% 0.90/1.20 % --brand_transform false
% 0.90/1.20 % --pure_diseq_elim true
% 0.90/1.20 % --min_unsat_core false
% 0.90/1.20 % --pred_elim true
% 0.90/1.20 % --add_important_lit false
% 0.90/1.20 % --soft_assumptions false
% 0.90/1.20 % --reset_solvers false
% 0.90/1.20 % --bc_imp_inh []
% 0.90/1.20 % --conj_cone_tolerance 1.5
% 0.90/1.20 % --prolific_symb_bound 500
% 0.90/1.20 % --lt_threshold 2000
% 0.90/1.20
% 0.90/1.20 % ------ SAT Options
% 0.90/1.20
% 0.90/1.20 % --sat_mode false
% 0.90/1.20 % --sat_fm_restart_options ""
% 0.90/1.20 % --sat_gr_def false
% 0.90/1.20 % --sat_epr_types true
% 0.90/1.20 % --sat_non_cyclic_types false
% 0.90/1.20 % --sat_finite_models false
% 0.90/1.20 % --sat_fm_lemmas false
% 0.90/1.20 % --sat_fm_prep false
% 0.90/1.20 % --sat_fm_uc_incr true
% 0.90/1.20 % --sat_out_model small
% 0.90/1.20 % --sat_out_clauses false
% 0.90/1.20
% 0.90/1.20 % ------ QBF Options
% 0.90/1.20
% 0.90/1.20 % --qbf_mode false
% 0.90/1.20 % --qbf_elim_univ true
% 0.90/1.20 % --qbf_sk_in true
% 0.90/1.20 % --qbf_pred_elim true
% 0.90/1.20 % --qbf_split 32
% 0.90/1.20
% 0.90/1.20 % ------ BMC1 Options
% 0.90/1.20
% 0.90/1.20 % --bmc1_incremental false
% 0.90/1.20 % --bmc1_axioms reachable_all
% 0.90/1.20 % --bmc1_min_bound 0
% 0.90/1.20 % --bmc1_max_bound -1
% 0.90/1.20 % --bmc1_max_bound_default -1
% 0.90/1.20 % --bmc1_symbol_reachability true
% 0.90/1.20 % --bmc1_property_lemmas false
% 0.90/1.20 % --bmc1_k_induction false
% 0.90/1.20 % --bmc1_non_equiv_states false
% 0.90/1.20 % --bmc1_deadlock false
% 0.90/1.20 % --bmc1_ucm false
% 0.90/1.20 % --bmc1_add_unsat_core none
% 0.90/1.20 % --bmc1_unsat_core_children false
% 0.90/1.20 % --bmc1_unsat_core_extrapolate_axioms false
% 0.90/1.20 % --bmc1_out_stat full
% 0.90/1.20 % --bmc1_ground_init false
% 0.90/1.20 % --bmc1_pre_inst_next_state false
% 0.90/1.20 % --bmc1_pre_inst_state false
% 0.90/1.20 % --bmc1_pre_inst_reach_state false
% 0.90/1.20 % --bmc1_out_unsat_core false
% 10.93/11.13 % --bmc1_aig_witness_out false
% 10.93/11.13 % --bmc1_verbose false
% 10.93/11.13 % --bmc1_dump_clauses_tptp false
% 10.93/11.13 % --bmc1_dump_unsat_core_tptp false
% 10.93/11.13 % --bmc1_dump_file -
% 10.93/11.13 % --bmc1_ucm_expand_uc_limit 128
% 10.93/11.13 % --bmc1_ucm_n_expand_iterations 6
% 10.93/11.13 % --bmc1_ucm_extend_mode 1
% 10.93/11.13 % --bmc1_ucm_init_mode 2
% 10.93/11.13 % --bmc1_ucm_cone_mode none
% 10.93/11.13 % --bmc1_ucm_reduced_relation_type 0
% 10.93/11.13 % --bmc1_ucm_relax_model 4
% 10.93/11.13 % --bmc1_ucm_full_tr_after_sat true
% 10.93/11.13 % --bmc1_ucm_expand_neg_assumptions false
% 10.93/11.13 % --bmc1_ucm_layered_model none
% 10.93/11.13 % --bmc1_ucm_max_lemma_size 10
% 10.93/11.13
% 10.93/11.13 % ------ AIG Options
% 10.93/11.13
% 10.93/11.13 % --aig_mode false
% 10.93/11.13
% 10.93/11.13 % ------ Instantiation Options
% 10.93/11.13
% 10.93/11.13 % --instantiation_flag true
% 10.93/11.13 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 10.93/11.13 % --inst_solver_per_active 750
% 10.93/11.13 % --inst_solver_calls_frac 0.5
% 10.93/11.13 % --inst_passive_queue_type priority_queues
% 10.93/11.13 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 10.93/11.13 % --inst_passive_queues_freq [25;2]
% 10.93/11.13 % --inst_dismatching true
% 10.93/11.13 % --inst_eager_unprocessed_to_passive true
% 10.93/11.13 % --inst_prop_sim_given true
% 10.93/11.13 % --inst_prop_sim_new false
% 10.93/11.13 % --inst_orphan_elimination true
% 10.93/11.13 % --inst_learning_loop_flag true
% 10.93/11.13 % --inst_learning_start 3000
% 10.93/11.13 % --inst_learning_factor 2
% 10.93/11.13 % --inst_start_prop_sim_after_learn 3
% 10.93/11.13 % --inst_sel_renew solver
% 10.93/11.13 % --inst_lit_activity_flag true
% 10.93/11.13 % --inst_out_proof true
% 10.93/11.13
% 10.93/11.13 % ------ Resolution Options
% 10.93/11.13
% 10.93/11.13 % --resolution_flag true
% 10.93/11.13 % --res_lit_sel kbo_max
% 10.93/11.13 % --res_to_prop_solver none
% 10.93/11.13 % --res_prop_simpl_new false
% 10.93/11.13 % --res_prop_simpl_given false
% 10.93/11.13 % --res_passive_queue_type priority_queues
% 10.93/11.13 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 10.93/11.13 % --res_passive_queues_freq [15;5]
% 10.93/11.13 % --res_forward_subs full
% 10.93/11.13 % --res_backward_subs full
% 10.93/11.13 % --res_forward_subs_resolution true
% 10.93/11.13 % --res_backward_subs_resolution true
% 10.93/11.13 % --res_orphan_elimination false
% 10.93/11.13 % --res_time_limit 1000.
% 10.93/11.13 % --res_out_proof true
% 10.93/11.13 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_cc0343.s
% 10.93/11.13 % --modulo true
% 10.93/11.13
% 10.93/11.13 % ------ Combination Options
% 10.93/11.13
% 10.93/11.13 % --comb_res_mult 1000
% 10.93/11.13 % --comb_inst_mult 300
% 10.93/11.13 % ------
% 10.93/11.13
% 10.93/11.13
% 10.93/11.13
% 10.93/11.13 % ------ Proving...
% 10.93/11.13 %
% 10.93/11.13
% 10.93/11.13
% 10.93/11.13 % ------ Statistics
% 10.93/11.13
% 10.93/11.13 % ------ General
% 10.93/11.13
% 10.93/11.13 % num_of_input_clauses: 997
% 10.93/11.13 % num_of_input_neg_conjectures: 5
% 10.93/11.13 % num_of_splits: 0
% 10.93/11.13 % num_of_split_atoms: 0
% 10.93/11.13 % num_of_sem_filtered_clauses: 0
% 10.93/11.13 % num_of_subtypes: 0
% 10.93/11.13 % monotx_restored_types: 0
% 10.93/11.13 % sat_num_of_epr_types: 0
% 10.93/11.13 % sat_num_of_non_cyclic_types: 0
% 10.93/11.13 % sat_guarded_non_collapsed_types: 0
% 10.93/11.13 % is_epr: 0
% 10.93/11.13 % is_horn: 0
% 10.93/11.13 % has_eq: 1
% 10.93/11.13 % num_pure_diseq_elim: 0
% 10.93/11.13 % simp_replaced_by: 0
% 10.93/11.13 % res_preprocessed: 186
% 10.93/11.13 % prep_upred: 0
% 10.93/11.13 % prep_unflattend: 0
% 10.93/11.13 % pred_elim_cands: 6
% 10.93/11.13 % pred_elim: 2
% 10.93/11.13 % pred_elim_cl: 2
% 10.93/11.13 % pred_elim_cycles: 3
% 10.93/11.13 % forced_gc_time: 0
% 10.93/11.13 % gc_basic_clause_elim: 0
% 10.93/11.13 % parsing_time: 0.049
% 10.93/11.13 % sem_filter_time: 0.
% 10.93/11.13 % pred_elim_time: 0.002
% 10.93/11.13 % out_proof_time: 0.001
% 10.93/11.13 % monotx_time: 0.
% 10.93/11.13 % subtype_inf_time: 0.
% 10.93/11.13 % unif_index_cands_time: 0.076
% 10.93/11.13 % unif_index_add_time: 0.01
% 10.93/11.13 % total_time: 10.488
% 10.93/11.13 % num_of_symbols: 149
% 10.93/11.13 % num_of_terms: 314251
% 10.93/11.13
% 10.93/11.13 % ------ Propositional Solver
% 10.93/11.13
% 10.93/11.13 % prop_solver_calls: 6
% 10.93/11.13 % prop_fast_solver_calls: 1174
% 10.93/11.13 % prop_num_of_clauses: 4806
% 10.93/11.13 % prop_preprocess_simplified: 11435
% 10.93/11.13 % prop_fo_subsumed: 3
% 10.93/11.13 % prop_solver_time: 0.001
% 10.93/11.13 % prop_fast_solver_time: 0.001
% 10.93/11.13 % prop_unsat_core_time: 0.
% 10.93/11.13
% 10.93/11.13 % ------ QBF
% 10.93/11.13
% 10.93/11.13 % qbf_q_res: 0
% 10.93/11.13 % qbf_num_tautologies: 0
% 10.93/11.13 % qbf_prep_cycles: 0
% 10.93/11.13
% 10.93/11.13 % ------ BMC1
% 10.93/11.13
% 10.93/11.13 % bmc1_current_bound: -1
% 10.93/11.13 % bmc1_last_solved_bound: -1
% 10.93/11.13 % bmc1_unsat_core_size: -1
% 10.93/11.13 % bmc1_unsat_core_parents_size: -1
% 10.93/11.13 % bmc1_merge_next_fun: 0
% 10.93/11.13 % bmc1_unsat_core_clauses_time: 0.
% 10.93/11.13
% 10.93/11.13 % ------ Instantiation
% 10.93/11.13
% 10.93/11.13 % inst_num_of_clauses: 3269
% 10.93/11.13 % inst_num_in_passive: 1459
% 10.93/11.13 % inst_num_in_active: 700
% 10.93/11.13 % inst_num_in_unprocessed: 1102
% 10.93/11.13 % inst_num_of_loops: 730
% 10.93/11.13 % inst_num_of_learning_restarts: 0
% 10.93/11.13 % inst_num_moves_active_passive: 20
% 10.93/11.13 % inst_lit_activity: 669
% 10.93/11.13 % inst_lit_activity_moves: 0
% 10.93/11.13 % inst_num_tautologies: 8
% 10.93/11.13 % inst_num_prop_implied: 0
% 10.93/11.13 % inst_num_existing_simplified: 0
% 10.93/11.13 % inst_num_eq_res_simplified: 0
% 10.93/11.13 % inst_num_child_elim: 0
% 10.93/11.13 % inst_num_of_dismatching_blockings: 1194
% 10.93/11.13 % inst_num_of_non_proper_insts: 1735
% 10.93/11.13 % inst_num_of_duplicates: 2570
% 10.93/11.13 % inst_inst_num_from_inst_to_res: 0
% 10.93/11.13 % inst_dismatching_checking_time: 0.005
% 10.93/11.13
% 10.93/11.13 % ------ Resolution
% 10.93/11.13
% 10.93/11.13 % res_num_of_clauses: 175896
% 10.93/11.13 % res_num_in_passive: 173244
% 10.93/11.13 % res_num_in_active: 2416
% 10.93/11.13 % res_num_of_loops: 3000
% 10.93/11.13 % res_forward_subset_subsumed: 6878
% 10.93/11.13 % res_backward_subset_subsumed: 490
% 10.93/11.13 % res_forward_subsumed: 603
% 10.93/11.13 % res_backward_subsumed: 75
% 10.93/11.13 % res_forward_subsumption_resolution: 314
% 10.93/11.13 % res_backward_subsumption_resolution: 89
% 10.93/11.13 % res_clause_to_clause_subsumption: 24624
% 10.93/11.13 % res_orphan_elimination: 0
% 10.93/11.13 % res_tautology_del: 252
% 10.93/11.13 % res_num_eq_res_simplified: 0
% 10.93/11.13 % res_num_sel_changes: 0
% 10.93/11.13 % res_moves_from_active_to_pass: 0
% 10.93/11.13
% 10.93/11.13 % Status Unsatisfiable
% 10.93/11.13 % SZS status Theorem
% 10.93/11.13 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------