TSTP Solution File: SET074-7 by iProverMo---2.5-0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : SET074-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n014.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 02:09:55 EDT 2022
% Result : Unsatisfiable 151.01s 151.24s
% Output : CNFRefutation 151.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 123
% Syntax : Number of formulae : 844 ( 253 unt; 0 def)
% Number of atoms : 1741 ( 387 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 1692 ( 795 ~; 897 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 40 ( 40 usr; 10 con; 0-3 aty)
% Number of variables : 1663 ( 157 sgn 684 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
% Axioms transformation by autotheo
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0,axiom,
! [X10,X11,X12] :
( ~ operation(X12)
| ~ operation(X11)
| ~ compatible(X10,X12,X11)
| apply(X11,ordered_pair(apply(X10,not_homomorphism1(X10,X12,X11)),apply(X10,not_homomorphism2(X10,X12,X11)))) != apply(X10,apply(X12,ordered_pair(not_homomorphism1(X10,X12,X11),not_homomorphism2(X10,X12,X11))))
| homomorphism(X10,X12,X11) ),
file('<stdin>',homomorphism6) ).
fof(c_0_1,axiom,
! [X10,X11,X12] :
( ~ operation(X12)
| ~ operation(X11)
| ~ compatible(X10,X12,X11)
| member(ordered_pair(not_homomorphism1(X10,X12,X11),not_homomorphism2(X10,X12,X11)),domain_of(X12))
| homomorphism(X10,X12,X11) ),
file('<stdin>',homomorphism5) ).
fof(c_0_2,axiom,
! [X2,X7,X4,X3] :
( ~ member(ordered_pair(ordered_pair(X4,X3),X7),X2)
| ~ member(ordered_pair(ordered_pair(X3,X4),X7),cross_product(cross_product(universal_class,universal_class),universal_class))
| member(ordered_pair(ordered_pair(X3,X4),X7),flip(X2)) ),
file('<stdin>',flip3) ).
fof(c_0_3,axiom,
! [X2,X7,X4,X3] :
( ~ member(ordered_pair(ordered_pair(X4,X7),X3),X2)
| ~ member(ordered_pair(ordered_pair(X3,X4),X7),cross_product(cross_product(universal_class,universal_class),universal_class))
| member(ordered_pair(ordered_pair(X3,X4),X7),rotate(X2)) ),
file('<stdin>',rotate3) ).
fof(c_0_4,axiom,
! [X1,X10,X11,X12,X2] :
( ~ homomorphism(X10,X12,X11)
| ~ member(ordered_pair(X2,X1),domain_of(X12))
| apply(X11,ordered_pair(apply(X10,X2),apply(X10,X1))) = apply(X10,apply(X12,ordered_pair(X2,X1))) ),
file('<stdin>',homomorphism4) ).
fof(c_0_5,axiom,
! [X5,X8,X1,X6] :
( ~ member(X5,image(X8,image(X6,singleton(X1))))
| ~ member(ordered_pair(X1,X5),cross_product(universal_class,universal_class))
| member(ordered_pair(X1,X5),compose(X8,X6)) ),
file('<stdin>',compose3) ).
fof(c_0_6,axiom,
! [X5,X1,X2] : second(not_subclass_element(restrict(X5,singleton(X2),X1),null_class)) = range(X5,X2,X1),
file('<stdin>',range) ).
fof(c_0_7,axiom,
! [X5,X1,X2] : first(not_subclass_element(restrict(X5,X2,singleton(X1)),null_class)) = domain(X5,X2,X1),
file('<stdin>',domain) ).
fof(c_0_8,axiom,
intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))) = subset_relation,
file('<stdin>',subset_relation) ).
fof(c_0_9,axiom,
! [X2,X7,X4,X3] :
( ~ member(ordered_pair(ordered_pair(X3,X4),X7),flip(X2))
| member(ordered_pair(ordered_pair(X4,X3),X7),X2) ),
file('<stdin>',flip2) ).
fof(c_0_10,axiom,
! [X2,X7,X4,X3] :
( ~ member(ordered_pair(ordered_pair(X3,X4),X7),rotate(X2))
| member(ordered_pair(ordered_pair(X4,X7),X3),X2) ),
file('<stdin>',rotate2) ).
fof(c_0_11,axiom,
! [X5,X8,X1,X6] :
( ~ member(ordered_pair(X1,X5),compose(X8,X6))
| member(X5,image(X8,image(X6,singleton(X1)))) ),
file('<stdin>',compose2) ).
fof(c_0_12,axiom,
! [X1,X2] : intersection(complement(intersection(X2,X1)),complement(intersection(complement(X2),complement(X1)))) = symmetric_difference(X2,X1),
file('<stdin>',symmetric_difference) ).
fof(c_0_13,axiom,
! [X9] :
( ~ function(X9)
| cross_product(domain_of(domain_of(X9)),domain_of(domain_of(X9))) != domain_of(X9)
| ~ subclass(range_of(X9),domain_of(domain_of(X9)))
| operation(X9) ),
file('<stdin>',operation4) ).
fof(c_0_14,axiom,
! [X1,X2] :
( ~ member(ordered_pair(X2,X1),cross_product(universal_class,universal_class))
| ~ member(X2,X1)
| member(ordered_pair(X2,X1),element_relation) ),
file('<stdin>',element_relation3) ).
fof(c_0_15,axiom,
! [X10,X11,X12] :
( ~ function(X10)
| domain_of(domain_of(X12)) != domain_of(X10)
| ~ subclass(range_of(X10),domain_of(domain_of(X11)))
| compatible(X10,X12,X11) ),
file('<stdin>',compatible4) ).
fof(c_0_16,axiom,
! [X1,X2,X4,X3] :
( ~ member(ordered_pair(X2,X1),cross_product(X3,X4))
| member(X1,unordered_pair(X2,X1)) ),
file('<stdin>',corollary_2_to_unordered_pair) ).
fof(c_0_17,axiom,
! [X1,X2,X4,X3] :
( ~ member(ordered_pair(X2,X1),cross_product(X3,X4))
| member(X2,unordered_pair(X2,X1)) ),
file('<stdin>',corollary_1_to_unordered_pair) ).
fof(c_0_18,axiom,
! [X1,X2] :
( successor(X2) != X1
| ~ member(ordered_pair(X2,X1),cross_product(universal_class,universal_class))
| member(ordered_pair(X2,X1),successor_relation) ),
file('<stdin>',successor_relation3) ).
fof(c_0_19,axiom,
! [X5,X1,X2] :
( unordered_pair(X2,X5) != unordered_pair(X1,X5)
| ~ member(ordered_pair(X2,X1),cross_product(universal_class,universal_class))
| X2 = X1 ),
file('<stdin>',right_cancellation) ).
fof(c_0_20,axiom,
! [X5,X1,X2] :
( unordered_pair(X2,X1) != unordered_pair(X2,X5)
| ~ member(ordered_pair(X1,X5),cross_product(universal_class,universal_class))
| X1 = X5 ),
file('<stdin>',left_cancellation) ).
fof(c_0_21,axiom,
! [X10,X11,X12] :
( ~ homomorphism(X10,X12,X11)
| compatible(X10,X12,X11) ),
file('<stdin>',homomorphism3) ).
fof(c_0_22,axiom,
! [X9] :
( ~ subclass(X9,cross_product(universal_class,universal_class))
| ~ subclass(compose(X9,inverse(X9)),identity_relation)
| function(X9) ),
file('<stdin>',function3) ).
fof(c_0_23,axiom,
! [X1,X2] :
( ~ member(not_subclass_element(X2,X1),X1)
| ~ member(not_subclass_element(X1,X2),X2)
| X2 = X1 ),
file('<stdin>',equality4) ).
fof(c_0_24,axiom,
! [X5,X2] :
( restrict(X2,singleton(X5),universal_class) != null_class
| ~ member(X5,domain_of(X2)) ),
file('<stdin>',domain1) ).
fof(c_0_25,axiom,
! [X10,X11,X12] :
( ~ compatible(X10,X12,X11)
| subclass(range_of(X10),domain_of(domain_of(X11))) ),
file('<stdin>',compatible3) ).
fof(c_0_26,axiom,
! [X6,X2] : range_of(restrict(X6,X2,universal_class)) = image(X6,X2),
file('<stdin>',image) ).
fof(c_0_27,axiom,
! [X1,X2,X4,X3] :
( ~ member(ordered_pair(X3,X4),cross_product(X2,X1))
| member(X4,X1) ),
file('<stdin>',cartesian_product2) ).
fof(c_0_28,axiom,
! [X1,X2,X4,X3] :
( ~ member(ordered_pair(X3,X4),cross_product(X2,X1))
| member(X3,X2) ),
file('<stdin>',cartesian_product1) ).
fof(c_0_29,axiom,
! [X1,X2,X4,X3] :
( ~ member(ordered_pair(X3,X4),cross_product(X2,X1))
| member(X4,universal_class) ),
file('<stdin>',corollary_2_to_cartesian_product) ).
fof(c_0_30,axiom,
! [X1,X2,X4,X3] :
( ~ member(ordered_pair(X3,X4),cross_product(X2,X1))
| member(X3,universal_class) ),
file('<stdin>',corollary_1_to_cartesian_product) ).
fof(c_0_31,axiom,
! [X1,X2,X4,X3] :
( ~ member(X3,X2)
| ~ member(X4,X1)
| member(ordered_pair(X3,X4),cross_product(X2,X1)) ),
file('<stdin>',cartesian_product3) ).
fof(c_0_32,axiom,
! [X2] : domain_of(restrict(element_relation,universal_class,X2)) = sum_class(X2),
file('<stdin>',sum_class_definition) ).
fof(c_0_33,axiom,
! [X1,X2] :
( ~ member(not_subclass_element(X1,X2),X2)
| X2 = X1
| member(not_subclass_element(X2,X1),X2) ),
file('<stdin>',equality3) ).
fof(c_0_34,axiom,
! [X1,X2] :
( ~ member(not_subclass_element(X2,X1),X1)
| X2 = X1
| member(not_subclass_element(X1,X2),X1) ),
file('<stdin>',equality2) ).
fof(c_0_35,axiom,
! [X10,X11,X12] :
( ~ compatible(X10,X12,X11)
| domain_of(domain_of(X12)) = domain_of(X10) ),
file('<stdin>',compatible2) ).
fof(c_0_36,axiom,
! [X5,X2] :
( ~ member(X5,universal_class)
| restrict(X2,singleton(X5),universal_class) = null_class
| member(X5,domain_of(X2)) ),
file('<stdin>',domain2) ).
fof(c_0_37,axiom,
! [X2] : intersection(domain_of(X2),diagonalise(compose(inverse(element_relation),X2))) = cantor(X2),
file('<stdin>',cantor_class) ).
fof(c_0_38,axiom,
! [X1,X6,X2] : intersection(cross_product(X2,X1),X6) = restrict(X6,X2,X1),
file('<stdin>',restriction2) ).
fof(c_0_39,axiom,
! [X1,X6,X2] : intersection(X6,cross_product(X2,X1)) = restrict(X6,X2,X1),
file('<stdin>',restriction1) ).
fof(c_0_40,axiom,
! [X5,X1,X2] :
( ~ member(X5,cross_product(X2,X1))
| ordered_pair(first(X5),second(X5)) = X5 ),
file('<stdin>',cartesian_product4) ).
fof(c_0_41,axiom,
! [X10,X11,X12] :
( ~ homomorphism(X10,X12,X11)
| operation(X11) ),
file('<stdin>',homomorphism2) ).
fof(c_0_42,axiom,
! [X10,X11,X12] :
( ~ homomorphism(X10,X12,X11)
| operation(X12) ),
file('<stdin>',homomorphism1) ).
fof(c_0_43,axiom,
! [X10,X11,X12] :
( ~ compatible(X10,X12,X11)
| function(X10) ),
file('<stdin>',compatible1) ).
fof(c_0_44,axiom,
! [X5,X1,X2] :
( ~ member(X5,X2)
| ~ member(X5,X1)
| member(X5,intersection(X2,X1)) ),
file('<stdin>',intersection3) ).
fof(c_0_45,axiom,
! [X2] :
( ~ subclass(compose(X2,inverse(X2)),identity_relation)
| single_valued_class(X2) ),
file('<stdin>',single_valued_class2) ).
fof(c_0_46,axiom,
! [X2] :
( ~ member(null_class,X2)
| ~ subclass(image(successor_relation,X2),X2)
| inductive(X2) ),
file('<stdin>',inductive3) ).
fof(c_0_47,axiom,
! [X1,X2] :
( X2 = X1
| member(not_subclass_element(X2,X1),X2)
| member(not_subclass_element(X1,X2),X1) ),
file('<stdin>',equality1) ).
fof(c_0_48,axiom,
! [X2] : subclass(flip(X2),cross_product(cross_product(universal_class,universal_class),universal_class)),
file('<stdin>',flip1) ).
fof(c_0_49,axiom,
! [X2] : subclass(rotate(X2),cross_product(cross_product(universal_class,universal_class),universal_class)),
file('<stdin>',rotate1) ).
fof(c_0_50,axiom,
! [X1,X2] : ~ member(X1,intersection(complement(X2),X2)),
file('<stdin>',special_classes_lemma) ).
fof(c_0_51,axiom,
! [X5,X1,X2] :
( ~ member(X5,intersection(X2,X1))
| member(X5,X1) ),
file('<stdin>',intersection2) ).
fof(c_0_52,axiom,
! [X5,X1,X2] :
( ~ member(X5,intersection(X2,X1))
| member(X5,X2) ),
file('<stdin>',intersection1) ).
fof(c_0_53,axiom,
! [X1,X2] :
( ~ member(not_subclass_element(X2,X1),X1)
| subclass(X2,X1) ),
file('<stdin>',not_subclass_members2) ).
fof(c_0_54,axiom,
! [X1,X2] :
( ~ member(ordered_pair(X2,X1),element_relation)
| member(X2,X1) ),
file('<stdin>',element_relation2) ).
fof(c_0_55,axiom,
! [X1,X2] : unordered_pair(singleton(X2),unordered_pair(X2,singleton(X1))) = ordered_pair(X2,X1),
file('<stdin>',ordered_pair) ).
fof(c_0_56,axiom,
! [X1,X2] : complement(intersection(complement(X2),complement(X1))) = union(X2,X1),
file('<stdin>',union) ).
fof(c_0_57,axiom,
! [X1,X2,X3] :
( ~ member(X3,unordered_pair(X2,X1))
| X3 = X2
| X3 = X1 ),
file('<stdin>',unordered_pair_member) ).
fof(c_0_58,axiom,
! [X9,X2] :
( ~ function(X9)
| ~ member(X2,universal_class)
| member(image(X9,X2),universal_class) ),
file('<stdin>',replacement) ).
fof(c_0_59,axiom,
! [X1,X2] :
( ~ member(ordered_pair(X2,X1),successor_relation)
| successor(X2) = X1 ),
file('<stdin>',successor_relation2) ).
fof(c_0_60,axiom,
! [X9] :
( ~ operation(X9)
| cross_product(domain_of(domain_of(X9)),domain_of(domain_of(X9))) = domain_of(X9) ),
file('<stdin>',operation2) ).
fof(c_0_61,axiom,
! [X1,X2] :
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X2,X1)) ),
file('<stdin>',unordered_pair3) ).
fof(c_0_62,axiom,
! [X1,X2] :
( ~ member(X2,universal_class)
| member(X2,unordered_pair(X2,X1)) ),
file('<stdin>',unordered_pair2) ).
fof(c_0_63,axiom,
! [X6] : complement(domain_of(intersection(X6,identity_relation))) = diagonalise(X6),
file('<stdin>',diagonalisation) ).
fof(c_0_64,axiom,
! [X8,X6] : subclass(compose(X8,X6),cross_product(universal_class,universal_class)),
file('<stdin>',compose1) ).
fof(c_0_65,axiom,
! [X1] : domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
file('<stdin>',inverse) ).
fof(c_0_66,axiom,
! [X5,X1,X2] :
( ~ subclass(X2,X1)
| ~ subclass(X1,X5)
| subclass(X2,X5) ),
file('<stdin>',transitivity_of_subclass) ).
fof(c_0_67,axiom,
! [X1,X2,X3] :
( ~ subclass(X2,X1)
| ~ member(X3,X2)
| member(X3,X1) ),
file('<stdin>',subclass_members) ).
fof(c_0_68,axiom,
! [X1] :
( ~ member(X1,universal_class)
| X1 = null_class
| member(apply(choice,X1),X1) ),
file('<stdin>',choice2) ).
fof(c_0_69,axiom,
! [X9] :
( ~ function(X9)
| subclass(compose(X9,inverse(X9)),identity_relation) ),
file('<stdin>',function2) ).
fof(c_0_70,axiom,
! [X2] :
( ~ single_valued_class(X2)
| subclass(compose(X2,inverse(X2)),identity_relation) ),
file('<stdin>',single_valued_class1) ).
fof(c_0_71,axiom,
! [X1,X9] : sum_class(image(X9,singleton(X1))) = apply(X9,X1),
file('<stdin>',apply) ).
fof(c_0_72,axiom,
! [X5,X2] :
( ~ member(X5,universal_class)
| member(X5,complement(X2))
| member(X5,X2) ),
file('<stdin>',complement2) ).
fof(c_0_73,axiom,
! [X5,X2] :
( ~ member(X5,complement(X2))
| ~ member(X5,X2) ),
file('<stdin>',complement1) ).
fof(c_0_74,axiom,
! [X1,X2] :
( member(not_subclass_element(X2,X1),X2)
| subclass(X2,X1) ),
file('<stdin>',not_subclass_members1) ).
fof(c_0_75,axiom,
! [X1,X2] :
( ~ subclass(X2,X1)
| ~ subclass(X1,X2)
| X2 = X1 ),
file('<stdin>',subclass_implies_equal) ).
fof(c_0_76,axiom,
! [X1,X2] : subclass(singleton(X1),unordered_pair(X2,X1)),
file('<stdin>',singleton_in_unordered_pair2) ).
fof(c_0_77,axiom,
! [X1,X2] : subclass(singleton(X2),unordered_pair(X2,X1)),
file('<stdin>',singleton_in_unordered_pair1) ).
fof(c_0_78,axiom,
! [X9] :
( ~ operation(X9)
| subclass(range_of(X9),domain_of(domain_of(X9))) ),
file('<stdin>',operation3) ).
fof(c_0_79,axiom,
! [X2] :
( ~ inductive(X2)
| subclass(image(successor_relation,X2),X2) ),
file('<stdin>',inductive2) ).
fof(c_0_80,axiom,
! [X2] : complement(image(element_relation,complement(X2))) = power_class(X2),
file('<stdin>',power_class_definition) ).
fof(c_0_81,axiom,
! [X9] :
( ~ function(X9)
| subclass(X9,cross_product(universal_class,universal_class)) ),
file('<stdin>',function1) ).
fof(c_0_82,axiom,
! [X1,X2] :
( unordered_pair(X2,X1) = null_class
| member(X2,universal_class)
| member(X1,universal_class) ),
file('<stdin>',null_unordered_pair) ).
fof(c_0_83,axiom,
! [X3] :
( ~ member(X3,universal_class)
| member(power_class(X3),universal_class) ),
file('<stdin>',power_class2) ).
fof(c_0_84,axiom,
! [X2] :
( ~ member(X2,universal_class)
| member(sum_class(X2),universal_class) ),
file('<stdin>',sum_class2) ).
fof(c_0_85,axiom,
! [X5] :
( X5 = null_class
| member(not_subclass_element(X5,null_class),X5) ),
file('<stdin>',null_class_is_unique) ).
fof(c_0_86,axiom,
! [X1,X2] : member(unordered_pair(X2,X1),universal_class),
file('<stdin>',unordered_pairs_in_universal) ).
fof(c_0_87,axiom,
subclass(successor_relation,cross_product(universal_class,universal_class)),
file('<stdin>',successor_relation1) ).
fof(c_0_88,axiom,
subclass(element_relation,cross_product(universal_class,universal_class)),
file('<stdin>',element_relation1) ).
fof(c_0_89,axiom,
! [X1,X2] :
( member(X2,universal_class)
| unordered_pair(X2,X1) = singleton(X1) ),
file('<stdin>',unordered_pair_equals_singleton2) ).
fof(c_0_90,axiom,
! [X1,X2] :
( member(X1,universal_class)
| unordered_pair(X2,X1) = singleton(X2) ),
file('<stdin>',unordered_pair_equals_singleton1) ).
fof(c_0_91,axiom,
! [X9] :
( ~ function(inverse(X9))
| ~ function(X9)
| one_to_one(X9) ),
file('<stdin>',one_to_one3) ).
fof(c_0_92,axiom,
! [X1,X2] : unordered_pair(X2,X1) = unordered_pair(X1,X2),
file('<stdin>',commutativity_of_unordered_pair) ).
fof(c_0_93,axiom,
! [X2] : union(X2,singleton(X2)) = successor(X2),
file('<stdin>',successor) ).
fof(c_0_94,axiom,
! [X2] :
( X2 = null_class
| intersection(X2,regular(X2)) = null_class ),
file('<stdin>',regularity2) ).
fof(c_0_95,axiom,
! [X2] :
( X2 = null_class
| member(regular(X2),X2) ),
file('<stdin>',regularity1) ).
fof(c_0_96,axiom,
! [X2] :
( ~ subclass(X2,null_class)
| X2 = null_class ),
file('<stdin>',corollary_of_null_class_is_subclass) ).
fof(c_0_97,axiom,
! [X5] : ~ member(X5,null_class),
file('<stdin>',existence_of_null_class) ).
fof(c_0_98,axiom,
! [X1] :
( ~ inductive(X1)
| subclass(omega,X1) ),
file('<stdin>',omega_is_inductive2) ).
fof(c_0_99,axiom,
! [X2] :
( ~ inductive(X2)
| member(null_class,X2) ),
file('<stdin>',inductive1) ).
fof(c_0_100,axiom,
! [X2] : unordered_pair(X2,X2) = singleton(X2),
file('<stdin>',singleton_set) ).
fof(c_0_101,axiom,
! [X1,X2] :
( X2 != X1
| subclass(X1,X2) ),
file('<stdin>',equal_implies_subclass2) ).
fof(c_0_102,axiom,
! [X1,X2] :
( X2 != X1
| subclass(X2,X1) ),
file('<stdin>',equal_implies_subclass1) ).
fof(c_0_103,axiom,
! [X9] :
( ~ one_to_one(X9)
| function(inverse(X9)) ),
file('<stdin>',one_to_one2) ).
fof(c_0_104,axiom,
intersection(inverse(subset_relation),subset_relation) = identity_relation,
file('<stdin>',identity_relation) ).
fof(c_0_105,axiom,
! [X2] : subclass(X2,X2),
file('<stdin>',subclass_is_reflexive) ).
fof(c_0_106,axiom,
! [X5] : domain_of(inverse(X5)) = range_of(X5),
file('<stdin>',range_of) ).
fof(c_0_107,axiom,
! [X2] : subclass(null_class,X2),
file('<stdin>',null_class_is_subclass) ).
fof(c_0_108,axiom,
! [X2] : subclass(X2,universal_class),
file('<stdin>',class_elements_are_sets) ).
fof(c_0_109,axiom,
! [X9] :
( ~ operation(X9)
| function(X9) ),
file('<stdin>',operation1) ).
fof(c_0_110,axiom,
! [X9] :
( ~ one_to_one(X9)
| function(X9) ),
file('<stdin>',one_to_one1) ).
fof(c_0_111,axiom,
member(null_class,universal_class),
file('<stdin>',null_class_is_a_set) ).
fof(c_0_112,axiom,
member(omega,universal_class),
file('<stdin>',omega_in_universal) ).
fof(c_0_113,axiom,
function(choice),
file('<stdin>',choice1) ).
fof(c_0_114,axiom,
inductive(omega),
file('<stdin>',omega_is_inductive1) ).
fof(c_0_115,plain,
! [X10,X11,X12] :
( ~ operation(X12)
| ~ operation(X11)
| ~ compatible(X10,X12,X11)
| apply(X11,ordered_pair(apply(X10,not_homomorphism1(X10,X12,X11)),apply(X10,not_homomorphism2(X10,X12,X11)))) != apply(X10,apply(X12,ordered_pair(not_homomorphism1(X10,X12,X11),not_homomorphism2(X10,X12,X11))))
| homomorphism(X10,X12,X11) ),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_116,plain,
! [X10,X11,X12] :
( ~ operation(X12)
| ~ operation(X11)
| ~ compatible(X10,X12,X11)
| member(ordered_pair(not_homomorphism1(X10,X12,X11),not_homomorphism2(X10,X12,X11)),domain_of(X12))
| homomorphism(X10,X12,X11) ),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_117,plain,
! [X2,X7,X4,X3] :
( ~ member(ordered_pair(ordered_pair(X4,X3),X7),X2)
| ~ member(ordered_pair(ordered_pair(X3,X4),X7),cross_product(cross_product(universal_class,universal_class),universal_class))
| member(ordered_pair(ordered_pair(X3,X4),X7),flip(X2)) ),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_118,plain,
! [X2,X7,X4,X3] :
( ~ member(ordered_pair(ordered_pair(X4,X7),X3),X2)
| ~ member(ordered_pair(ordered_pair(X3,X4),X7),cross_product(cross_product(universal_class,universal_class),universal_class))
| member(ordered_pair(ordered_pair(X3,X4),X7),rotate(X2)) ),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_119,plain,
! [X1,X10,X11,X12,X2] :
( ~ homomorphism(X10,X12,X11)
| ~ member(ordered_pair(X2,X1),domain_of(X12))
| apply(X11,ordered_pair(apply(X10,X2),apply(X10,X1))) = apply(X10,apply(X12,ordered_pair(X2,X1))) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_120,plain,
! [X5,X8,X1,X6] :
( ~ member(X5,image(X8,image(X6,singleton(X1))))
| ~ member(ordered_pair(X1,X5),cross_product(universal_class,universal_class))
| member(ordered_pair(X1,X5),compose(X8,X6)) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_121,axiom,
! [X5,X1,X2] : second(not_subclass_element(restrict(X5,singleton(X2),X1),null_class)) = range(X5,X2,X1),
c_0_6 ).
fof(c_0_122,axiom,
! [X5,X1,X2] : first(not_subclass_element(restrict(X5,X2,singleton(X1)),null_class)) = domain(X5,X2,X1),
c_0_7 ).
fof(c_0_123,axiom,
intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))) = subset_relation,
c_0_8 ).
fof(c_0_124,plain,
! [X2,X7,X4,X3] :
( ~ member(ordered_pair(ordered_pair(X3,X4),X7),flip(X2))
| member(ordered_pair(ordered_pair(X4,X3),X7),X2) ),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_125,plain,
! [X2,X7,X4,X3] :
( ~ member(ordered_pair(ordered_pair(X3,X4),X7),rotate(X2))
| member(ordered_pair(ordered_pair(X4,X7),X3),X2) ),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_126,plain,
! [X5,X8,X1,X6] :
( ~ member(ordered_pair(X1,X5),compose(X8,X6))
| member(X5,image(X8,image(X6,singleton(X1)))) ),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_127,axiom,
! [X1,X2] : intersection(complement(intersection(X2,X1)),complement(intersection(complement(X2),complement(X1)))) = symmetric_difference(X2,X1),
c_0_12 ).
fof(c_0_128,plain,
! [X9] :
( ~ function(X9)
| cross_product(domain_of(domain_of(X9)),domain_of(domain_of(X9))) != domain_of(X9)
| ~ subclass(range_of(X9),domain_of(domain_of(X9)))
| operation(X9) ),
inference(fof_simplification,[status(thm)],[c_0_13]) ).
fof(c_0_129,plain,
! [X1,X2] :
( ~ member(ordered_pair(X2,X1),cross_product(universal_class,universal_class))
| ~ member(X2,X1)
| member(ordered_pair(X2,X1),element_relation) ),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_130,plain,
! [X10,X11,X12] :
( ~ function(X10)
| domain_of(domain_of(X12)) != domain_of(X10)
| ~ subclass(range_of(X10),domain_of(domain_of(X11)))
| compatible(X10,X12,X11) ),
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_131,plain,
! [X1,X2,X4,X3] :
( ~ member(ordered_pair(X2,X1),cross_product(X3,X4))
| member(X1,unordered_pair(X2,X1)) ),
inference(fof_simplification,[status(thm)],[c_0_16]) ).
fof(c_0_132,plain,
! [X1,X2,X4,X3] :
( ~ member(ordered_pair(X2,X1),cross_product(X3,X4))
| member(X2,unordered_pair(X2,X1)) ),
inference(fof_simplification,[status(thm)],[c_0_17]) ).
fof(c_0_133,plain,
! [X1,X2] :
( successor(X2) != X1
| ~ member(ordered_pair(X2,X1),cross_product(universal_class,universal_class))
| member(ordered_pair(X2,X1),successor_relation) ),
inference(fof_simplification,[status(thm)],[c_0_18]) ).
fof(c_0_134,plain,
! [X5,X1,X2] :
( unordered_pair(X2,X5) != unordered_pair(X1,X5)
| ~ member(ordered_pair(X2,X1),cross_product(universal_class,universal_class))
| X2 = X1 ),
inference(fof_simplification,[status(thm)],[c_0_19]) ).
fof(c_0_135,plain,
! [X5,X1,X2] :
( unordered_pair(X2,X1) != unordered_pair(X2,X5)
| ~ member(ordered_pair(X1,X5),cross_product(universal_class,universal_class))
| X1 = X5 ),
inference(fof_simplification,[status(thm)],[c_0_20]) ).
fof(c_0_136,plain,
! [X10,X11,X12] :
( ~ homomorphism(X10,X12,X11)
| compatible(X10,X12,X11) ),
inference(fof_simplification,[status(thm)],[c_0_21]) ).
fof(c_0_137,plain,
! [X9] :
( ~ subclass(X9,cross_product(universal_class,universal_class))
| ~ subclass(compose(X9,inverse(X9)),identity_relation)
| function(X9) ),
inference(fof_simplification,[status(thm)],[c_0_22]) ).
fof(c_0_138,plain,
! [X1,X2] :
( ~ member(not_subclass_element(X2,X1),X1)
| ~ member(not_subclass_element(X1,X2),X2)
| X2 = X1 ),
inference(fof_simplification,[status(thm)],[c_0_23]) ).
fof(c_0_139,plain,
! [X5,X2] :
( restrict(X2,singleton(X5),universal_class) != null_class
| ~ member(X5,domain_of(X2)) ),
inference(fof_simplification,[status(thm)],[c_0_24]) ).
fof(c_0_140,plain,
! [X10,X11,X12] :
( ~ compatible(X10,X12,X11)
| subclass(range_of(X10),domain_of(domain_of(X11))) ),
inference(fof_simplification,[status(thm)],[c_0_25]) ).
fof(c_0_141,axiom,
! [X6,X2] : range_of(restrict(X6,X2,universal_class)) = image(X6,X2),
c_0_26 ).
fof(c_0_142,plain,
! [X1,X2,X4,X3] :
( ~ member(ordered_pair(X3,X4),cross_product(X2,X1))
| member(X4,X1) ),
inference(fof_simplification,[status(thm)],[c_0_27]) ).
fof(c_0_143,plain,
! [X1,X2,X4,X3] :
( ~ member(ordered_pair(X3,X4),cross_product(X2,X1))
| member(X3,X2) ),
inference(fof_simplification,[status(thm)],[c_0_28]) ).
fof(c_0_144,plain,
! [X1,X2,X4,X3] :
( ~ member(ordered_pair(X3,X4),cross_product(X2,X1))
| member(X4,universal_class) ),
inference(fof_simplification,[status(thm)],[c_0_29]) ).
fof(c_0_145,plain,
! [X1,X2,X4,X3] :
( ~ member(ordered_pair(X3,X4),cross_product(X2,X1))
| member(X3,universal_class) ),
inference(fof_simplification,[status(thm)],[c_0_30]) ).
fof(c_0_146,plain,
! [X1,X2,X4,X3] :
( ~ member(X3,X2)
| ~ member(X4,X1)
| member(ordered_pair(X3,X4),cross_product(X2,X1)) ),
inference(fof_simplification,[status(thm)],[c_0_31]) ).
fof(c_0_147,axiom,
! [X2] : domain_of(restrict(element_relation,universal_class,X2)) = sum_class(X2),
c_0_32 ).
fof(c_0_148,plain,
! [X1,X2] :
( ~ member(not_subclass_element(X1,X2),X2)
| X2 = X1
| member(not_subclass_element(X2,X1),X2) ),
inference(fof_simplification,[status(thm)],[c_0_33]) ).
fof(c_0_149,plain,
! [X1,X2] :
( ~ member(not_subclass_element(X2,X1),X1)
| X2 = X1
| member(not_subclass_element(X1,X2),X1) ),
inference(fof_simplification,[status(thm)],[c_0_34]) ).
fof(c_0_150,plain,
! [X10,X11,X12] :
( ~ compatible(X10,X12,X11)
| domain_of(domain_of(X12)) = domain_of(X10) ),
inference(fof_simplification,[status(thm)],[c_0_35]) ).
fof(c_0_151,plain,
! [X5,X2] :
( ~ member(X5,universal_class)
| restrict(X2,singleton(X5),universal_class) = null_class
| member(X5,domain_of(X2)) ),
inference(fof_simplification,[status(thm)],[c_0_36]) ).
fof(c_0_152,axiom,
! [X2] : intersection(domain_of(X2),diagonalise(compose(inverse(element_relation),X2))) = cantor(X2),
c_0_37 ).
fof(c_0_153,axiom,
! [X1,X6,X2] : intersection(cross_product(X2,X1),X6) = restrict(X6,X2,X1),
c_0_38 ).
fof(c_0_154,axiom,
! [X1,X6,X2] : intersection(X6,cross_product(X2,X1)) = restrict(X6,X2,X1),
c_0_39 ).
fof(c_0_155,plain,
! [X5,X1,X2] :
( ~ member(X5,cross_product(X2,X1))
| ordered_pair(first(X5),second(X5)) = X5 ),
inference(fof_simplification,[status(thm)],[c_0_40]) ).
fof(c_0_156,plain,
! [X10,X11,X12] :
( ~ homomorphism(X10,X12,X11)
| operation(X11) ),
inference(fof_simplification,[status(thm)],[c_0_41]) ).
fof(c_0_157,plain,
! [X10,X11,X12] :
( ~ homomorphism(X10,X12,X11)
| operation(X12) ),
inference(fof_simplification,[status(thm)],[c_0_42]) ).
fof(c_0_158,plain,
! [X10,X11,X12] :
( ~ compatible(X10,X12,X11)
| function(X10) ),
inference(fof_simplification,[status(thm)],[c_0_43]) ).
fof(c_0_159,plain,
! [X5,X1,X2] :
( ~ member(X5,X2)
| ~ member(X5,X1)
| member(X5,intersection(X2,X1)) ),
inference(fof_simplification,[status(thm)],[c_0_44]) ).
fof(c_0_160,plain,
! [X2] :
( ~ subclass(compose(X2,inverse(X2)),identity_relation)
| single_valued_class(X2) ),
inference(fof_simplification,[status(thm)],[c_0_45]) ).
fof(c_0_161,plain,
! [X2] :
( ~ member(null_class,X2)
| ~ subclass(image(successor_relation,X2),X2)
| inductive(X2) ),
inference(fof_simplification,[status(thm)],[c_0_46]) ).
fof(c_0_162,axiom,
! [X1,X2] :
( X2 = X1
| member(not_subclass_element(X2,X1),X2)
| member(not_subclass_element(X1,X2),X1) ),
c_0_47 ).
fof(c_0_163,axiom,
! [X2] : subclass(flip(X2),cross_product(cross_product(universal_class,universal_class),universal_class)),
c_0_48 ).
fof(c_0_164,axiom,
! [X2] : subclass(rotate(X2),cross_product(cross_product(universal_class,universal_class),universal_class)),
c_0_49 ).
fof(c_0_165,plain,
! [X1,X2] : ~ member(X1,intersection(complement(X2),X2)),
inference(fof_simplification,[status(thm)],[c_0_50]) ).
fof(c_0_166,plain,
! [X5,X1,X2] :
( ~ member(X5,intersection(X2,X1))
| member(X5,X1) ),
inference(fof_simplification,[status(thm)],[c_0_51]) ).
fof(c_0_167,plain,
! [X5,X1,X2] :
( ~ member(X5,intersection(X2,X1))
| member(X5,X2) ),
inference(fof_simplification,[status(thm)],[c_0_52]) ).
fof(c_0_168,plain,
! [X1,X2] :
( ~ member(not_subclass_element(X2,X1),X1)
| subclass(X2,X1) ),
inference(fof_simplification,[status(thm)],[c_0_53]) ).
fof(c_0_169,plain,
! [X1,X2] :
( ~ member(ordered_pair(X2,X1),element_relation)
| member(X2,X1) ),
inference(fof_simplification,[status(thm)],[c_0_54]) ).
fof(c_0_170,axiom,
! [X1,X2] : unordered_pair(singleton(X2),unordered_pair(X2,singleton(X1))) = ordered_pair(X2,X1),
c_0_55 ).
fof(c_0_171,axiom,
! [X1,X2] : complement(intersection(complement(X2),complement(X1))) = union(X2,X1),
c_0_56 ).
fof(c_0_172,plain,
! [X1,X2,X3] :
( ~ member(X3,unordered_pair(X2,X1))
| X3 = X2
| X3 = X1 ),
inference(fof_simplification,[status(thm)],[c_0_57]) ).
fof(c_0_173,plain,
! [X9,X2] :
( ~ function(X9)
| ~ member(X2,universal_class)
| member(image(X9,X2),universal_class) ),
inference(fof_simplification,[status(thm)],[c_0_58]) ).
fof(c_0_174,plain,
! [X1,X2] :
( ~ member(ordered_pair(X2,X1),successor_relation)
| successor(X2) = X1 ),
inference(fof_simplification,[status(thm)],[c_0_59]) ).
fof(c_0_175,plain,
! [X9] :
( ~ operation(X9)
| cross_product(domain_of(domain_of(X9)),domain_of(domain_of(X9))) = domain_of(X9) ),
inference(fof_simplification,[status(thm)],[c_0_60]) ).
fof(c_0_176,plain,
! [X1,X2] :
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X2,X1)) ),
inference(fof_simplification,[status(thm)],[c_0_61]) ).
fof(c_0_177,plain,
! [X1,X2] :
( ~ member(X2,universal_class)
| member(X2,unordered_pair(X2,X1)) ),
inference(fof_simplification,[status(thm)],[c_0_62]) ).
fof(c_0_178,axiom,
! [X6] : complement(domain_of(intersection(X6,identity_relation))) = diagonalise(X6),
c_0_63 ).
fof(c_0_179,axiom,
! [X8,X6] : subclass(compose(X8,X6),cross_product(universal_class,universal_class)),
c_0_64 ).
fof(c_0_180,axiom,
! [X1] : domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
c_0_65 ).
fof(c_0_181,plain,
! [X5,X1,X2] :
( ~ subclass(X2,X1)
| ~ subclass(X1,X5)
| subclass(X2,X5) ),
inference(fof_simplification,[status(thm)],[c_0_66]) ).
fof(c_0_182,plain,
! [X1,X2,X3] :
( ~ subclass(X2,X1)
| ~ member(X3,X2)
| member(X3,X1) ),
inference(fof_simplification,[status(thm)],[c_0_67]) ).
fof(c_0_183,plain,
! [X1] :
( ~ member(X1,universal_class)
| X1 = null_class
| member(apply(choice,X1),X1) ),
inference(fof_simplification,[status(thm)],[c_0_68]) ).
fof(c_0_184,plain,
! [X9] :
( ~ function(X9)
| subclass(compose(X9,inverse(X9)),identity_relation) ),
inference(fof_simplification,[status(thm)],[c_0_69]) ).
fof(c_0_185,plain,
! [X2] :
( ~ single_valued_class(X2)
| subclass(compose(X2,inverse(X2)),identity_relation) ),
inference(fof_simplification,[status(thm)],[c_0_70]) ).
fof(c_0_186,axiom,
! [X1,X9] : sum_class(image(X9,singleton(X1))) = apply(X9,X1),
c_0_71 ).
fof(c_0_187,plain,
! [X5,X2] :
( ~ member(X5,universal_class)
| member(X5,complement(X2))
| member(X5,X2) ),
inference(fof_simplification,[status(thm)],[c_0_72]) ).
fof(c_0_188,plain,
! [X5,X2] :
( ~ member(X5,complement(X2))
| ~ member(X5,X2) ),
inference(fof_simplification,[status(thm)],[c_0_73]) ).
fof(c_0_189,axiom,
! [X1,X2] :
( member(not_subclass_element(X2,X1),X2)
| subclass(X2,X1) ),
c_0_74 ).
fof(c_0_190,plain,
! [X1,X2] :
( ~ subclass(X2,X1)
| ~ subclass(X1,X2)
| X2 = X1 ),
inference(fof_simplification,[status(thm)],[c_0_75]) ).
fof(c_0_191,axiom,
! [X1,X2] : subclass(singleton(X1),unordered_pair(X2,X1)),
c_0_76 ).
fof(c_0_192,axiom,
! [X1,X2] : subclass(singleton(X2),unordered_pair(X2,X1)),
c_0_77 ).
fof(c_0_193,plain,
! [X9] :
( ~ operation(X9)
| subclass(range_of(X9),domain_of(domain_of(X9))) ),
inference(fof_simplification,[status(thm)],[c_0_78]) ).
fof(c_0_194,plain,
! [X2] :
( ~ inductive(X2)
| subclass(image(successor_relation,X2),X2) ),
inference(fof_simplification,[status(thm)],[c_0_79]) ).
fof(c_0_195,axiom,
! [X2] : complement(image(element_relation,complement(X2))) = power_class(X2),
c_0_80 ).
fof(c_0_196,plain,
! [X9] :
( ~ function(X9)
| subclass(X9,cross_product(universal_class,universal_class)) ),
inference(fof_simplification,[status(thm)],[c_0_81]) ).
fof(c_0_197,axiom,
! [X1,X2] :
( unordered_pair(X2,X1) = null_class
| member(X2,universal_class)
| member(X1,universal_class) ),
c_0_82 ).
fof(c_0_198,plain,
! [X3] :
( ~ member(X3,universal_class)
| member(power_class(X3),universal_class) ),
inference(fof_simplification,[status(thm)],[c_0_83]) ).
fof(c_0_199,plain,
! [X2] :
( ~ member(X2,universal_class)
| member(sum_class(X2),universal_class) ),
inference(fof_simplification,[status(thm)],[c_0_84]) ).
fof(c_0_200,axiom,
! [X5] :
( X5 = null_class
| member(not_subclass_element(X5,null_class),X5) ),
c_0_85 ).
fof(c_0_201,axiom,
! [X1,X2] : member(unordered_pair(X2,X1),universal_class),
c_0_86 ).
fof(c_0_202,axiom,
subclass(successor_relation,cross_product(universal_class,universal_class)),
c_0_87 ).
fof(c_0_203,axiom,
subclass(element_relation,cross_product(universal_class,universal_class)),
c_0_88 ).
fof(c_0_204,axiom,
! [X1,X2] :
( member(X2,universal_class)
| unordered_pair(X2,X1) = singleton(X1) ),
c_0_89 ).
fof(c_0_205,axiom,
! [X1,X2] :
( member(X1,universal_class)
| unordered_pair(X2,X1) = singleton(X2) ),
c_0_90 ).
fof(c_0_206,plain,
! [X9] :
( ~ function(inverse(X9))
| ~ function(X9)
| one_to_one(X9) ),
inference(fof_simplification,[status(thm)],[c_0_91]) ).
fof(c_0_207,axiom,
! [X1,X2] : unordered_pair(X2,X1) = unordered_pair(X1,X2),
c_0_92 ).
fof(c_0_208,axiom,
! [X2] : union(X2,singleton(X2)) = successor(X2),
c_0_93 ).
fof(c_0_209,axiom,
! [X2] :
( X2 = null_class
| intersection(X2,regular(X2)) = null_class ),
c_0_94 ).
fof(c_0_210,axiom,
! [X2] :
( X2 = null_class
| member(regular(X2),X2) ),
c_0_95 ).
fof(c_0_211,plain,
! [X2] :
( ~ subclass(X2,null_class)
| X2 = null_class ),
inference(fof_simplification,[status(thm)],[c_0_96]) ).
fof(c_0_212,plain,
! [X5] : ~ member(X5,null_class),
inference(fof_simplification,[status(thm)],[c_0_97]) ).
fof(c_0_213,plain,
! [X1] :
( ~ inductive(X1)
| subclass(omega,X1) ),
inference(fof_simplification,[status(thm)],[c_0_98]) ).
fof(c_0_214,plain,
! [X2] :
( ~ inductive(X2)
| member(null_class,X2) ),
inference(fof_simplification,[status(thm)],[c_0_99]) ).
fof(c_0_215,axiom,
! [X2] : unordered_pair(X2,X2) = singleton(X2),
c_0_100 ).
fof(c_0_216,axiom,
! [X1,X2] :
( X2 != X1
| subclass(X1,X2) ),
c_0_101 ).
fof(c_0_217,axiom,
! [X1,X2] :
( X2 != X1
| subclass(X2,X1) ),
c_0_102 ).
fof(c_0_218,plain,
! [X9] :
( ~ one_to_one(X9)
| function(inverse(X9)) ),
inference(fof_simplification,[status(thm)],[c_0_103]) ).
fof(c_0_219,axiom,
intersection(inverse(subset_relation),subset_relation) = identity_relation,
c_0_104 ).
fof(c_0_220,axiom,
! [X2] : subclass(X2,X2),
c_0_105 ).
fof(c_0_221,axiom,
! [X5] : domain_of(inverse(X5)) = range_of(X5),
c_0_106 ).
fof(c_0_222,axiom,
! [X2] : subclass(null_class,X2),
c_0_107 ).
fof(c_0_223,axiom,
! [X2] : subclass(X2,universal_class),
c_0_108 ).
fof(c_0_224,plain,
! [X9] :
( ~ operation(X9)
| function(X9) ),
inference(fof_simplification,[status(thm)],[c_0_109]) ).
fof(c_0_225,plain,
! [X9] :
( ~ one_to_one(X9)
| function(X9) ),
inference(fof_simplification,[status(thm)],[c_0_110]) ).
fof(c_0_226,axiom,
member(null_class,universal_class),
c_0_111 ).
fof(c_0_227,axiom,
member(omega,universal_class),
c_0_112 ).
fof(c_0_228,axiom,
function(choice),
c_0_113 ).
fof(c_0_229,axiom,
inductive(omega),
c_0_114 ).
fof(c_0_230,plain,
! [X13,X14,X15] :
( ~ operation(X15)
| ~ operation(X14)
| ~ compatible(X13,X15,X14)
| apply(X14,ordered_pair(apply(X13,not_homomorphism1(X13,X15,X14)),apply(X13,not_homomorphism2(X13,X15,X14)))) != apply(X13,apply(X15,ordered_pair(not_homomorphism1(X13,X15,X14),not_homomorphism2(X13,X15,X14))))
| homomorphism(X13,X15,X14) ),
inference(variable_rename,[status(thm)],[c_0_115]) ).
fof(c_0_231,plain,
! [X13,X14,X15] :
( ~ operation(X15)
| ~ operation(X14)
| ~ compatible(X13,X15,X14)
| member(ordered_pair(not_homomorphism1(X13,X15,X14),not_homomorphism2(X13,X15,X14)),domain_of(X15))
| homomorphism(X13,X15,X14) ),
inference(variable_rename,[status(thm)],[c_0_116]) ).
fof(c_0_232,plain,
! [X8,X9,X10,X11] :
( ~ member(ordered_pair(ordered_pair(X10,X11),X9),X8)
| ~ member(ordered_pair(ordered_pair(X11,X10),X9),cross_product(cross_product(universal_class,universal_class),universal_class))
| member(ordered_pair(ordered_pair(X11,X10),X9),flip(X8)) ),
inference(variable_rename,[status(thm)],[c_0_117]) ).
fof(c_0_233,plain,
! [X8,X9,X10,X11] :
( ~ member(ordered_pair(ordered_pair(X10,X9),X11),X8)
| ~ member(ordered_pair(ordered_pair(X11,X10),X9),cross_product(cross_product(universal_class,universal_class),universal_class))
| member(ordered_pair(ordered_pair(X11,X10),X9),rotate(X8)) ),
inference(variable_rename,[status(thm)],[c_0_118]) ).
fof(c_0_234,plain,
! [X13,X14,X15,X16,X17] :
( ~ homomorphism(X14,X16,X15)
| ~ member(ordered_pair(X17,X13),domain_of(X16))
| apply(X15,ordered_pair(apply(X14,X17),apply(X14,X13))) = apply(X14,apply(X16,ordered_pair(X17,X13))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_119])])]) ).
fof(c_0_235,plain,
! [X9,X10,X11,X12] :
( ~ member(X9,image(X10,image(X12,singleton(X11))))
| ~ member(ordered_pair(X11,X9),cross_product(universal_class,universal_class))
| member(ordered_pair(X11,X9),compose(X10,X12)) ),
inference(variable_rename,[status(thm)],[c_0_120]) ).
fof(c_0_236,plain,
! [X6,X7,X8] : second(not_subclass_element(restrict(X6,singleton(X8),X7),null_class)) = range(X6,X8,X7),
inference(variable_rename,[status(thm)],[c_0_121]) ).
fof(c_0_237,plain,
! [X6,X7,X8] : first(not_subclass_element(restrict(X6,X8,singleton(X7)),null_class)) = domain(X6,X8,X7),
inference(variable_rename,[status(thm)],[c_0_122]) ).
fof(c_0_238,axiom,
intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))) = subset_relation,
c_0_123 ).
fof(c_0_239,plain,
! [X8,X9,X10,X11] :
( ~ member(ordered_pair(ordered_pair(X11,X10),X9),flip(X8))
| member(ordered_pair(ordered_pair(X10,X11),X9),X8) ),
inference(variable_rename,[status(thm)],[c_0_124]) ).
fof(c_0_240,plain,
! [X8,X9,X10,X11] :
( ~ member(ordered_pair(ordered_pair(X11,X10),X9),rotate(X8))
| member(ordered_pair(ordered_pair(X10,X9),X11),X8) ),
inference(variable_rename,[status(thm)],[c_0_125]) ).
fof(c_0_241,plain,
! [X9,X10,X11,X12] :
( ~ member(ordered_pair(X11,X9),compose(X10,X12))
| member(X9,image(X10,image(X12,singleton(X11)))) ),
inference(variable_rename,[status(thm)],[c_0_126]) ).
fof(c_0_242,plain,
! [X3,X4] : intersection(complement(intersection(X4,X3)),complement(intersection(complement(X4),complement(X3)))) = symmetric_difference(X4,X3),
inference(variable_rename,[status(thm)],[c_0_127]) ).
fof(c_0_243,plain,
! [X10] :
( ~ function(X10)
| cross_product(domain_of(domain_of(X10)),domain_of(domain_of(X10))) != domain_of(X10)
| ~ subclass(range_of(X10),domain_of(domain_of(X10)))
| operation(X10) ),
inference(variable_rename,[status(thm)],[c_0_128]) ).
fof(c_0_244,plain,
! [X3,X4] :
( ~ member(ordered_pair(X4,X3),cross_product(universal_class,universal_class))
| ~ member(X4,X3)
| member(ordered_pair(X4,X3),element_relation) ),
inference(variable_rename,[status(thm)],[c_0_129]) ).
fof(c_0_245,plain,
! [X13,X14,X15] :
( ~ function(X13)
| domain_of(domain_of(X15)) != domain_of(X13)
| ~ subclass(range_of(X13),domain_of(domain_of(X14)))
| compatible(X13,X15,X14) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_130])])]) ).
fof(c_0_246,plain,
! [X5,X6,X7,X8] :
( ~ member(ordered_pair(X6,X5),cross_product(X8,X7))
| member(X5,unordered_pair(X6,X5)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_131])])]) ).
fof(c_0_247,plain,
! [X5,X6,X7,X8] :
( ~ member(ordered_pair(X6,X5),cross_product(X8,X7))
| member(X6,unordered_pair(X6,X5)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_132])])]) ).
fof(c_0_248,plain,
! [X3,X4] :
( successor(X4) != X3
| ~ member(ordered_pair(X4,X3),cross_product(universal_class,universal_class))
| member(ordered_pair(X4,X3),successor_relation) ),
inference(variable_rename,[status(thm)],[c_0_133]) ).
fof(c_0_249,plain,
! [X6,X7,X8] :
( unordered_pair(X8,X6) != unordered_pair(X7,X6)
| ~ member(ordered_pair(X8,X7),cross_product(universal_class,universal_class))
| X8 = X7 ),
inference(variable_rename,[status(thm)],[c_0_134]) ).
fof(c_0_250,plain,
! [X6,X7,X8] :
( unordered_pair(X8,X7) != unordered_pair(X8,X6)
| ~ member(ordered_pair(X7,X6),cross_product(universal_class,universal_class))
| X7 = X6 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_135])])]) ).
fof(c_0_251,plain,
! [X13,X14,X15] :
( ~ homomorphism(X13,X15,X14)
| compatible(X13,X15,X14) ),
inference(variable_rename,[status(thm)],[c_0_136]) ).
fof(c_0_252,plain,
! [X10] :
( ~ subclass(X10,cross_product(universal_class,universal_class))
| ~ subclass(compose(X10,inverse(X10)),identity_relation)
| function(X10) ),
inference(variable_rename,[status(thm)],[c_0_137]) ).
fof(c_0_253,plain,
! [X3,X4] :
( ~ member(not_subclass_element(X4,X3),X3)
| ~ member(not_subclass_element(X3,X4),X4)
| X4 = X3 ),
inference(variable_rename,[status(thm)],[c_0_138]) ).
fof(c_0_254,plain,
! [X6,X7] :
( restrict(X7,singleton(X6),universal_class) != null_class
| ~ member(X6,domain_of(X7)) ),
inference(variable_rename,[status(thm)],[c_0_139]) ).
fof(c_0_255,plain,
! [X13,X14,X15] :
( ~ compatible(X13,X15,X14)
| subclass(range_of(X13),domain_of(domain_of(X14))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_140])])]) ).
fof(c_0_256,plain,
! [X7,X8] : range_of(restrict(X7,X8,universal_class)) = image(X7,X8),
inference(variable_rename,[status(thm)],[c_0_141]) ).
fof(c_0_257,plain,
! [X5,X6,X7,X8] :
( ~ member(ordered_pair(X8,X7),cross_product(X6,X5))
| member(X7,X5) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_142])])]) ).
fof(c_0_258,plain,
! [X5,X6,X7,X8] :
( ~ member(ordered_pair(X8,X7),cross_product(X6,X5))
| member(X8,X6) ),
inference(variable_rename,[status(thm)],[c_0_143]) ).
fof(c_0_259,plain,
! [X5,X6,X7,X8] :
( ~ member(ordered_pair(X8,X7),cross_product(X6,X5))
| member(X7,universal_class) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_144])])]) ).
fof(c_0_260,plain,
! [X5,X6,X7,X8] :
( ~ member(ordered_pair(X8,X7),cross_product(X6,X5))
| member(X8,universal_class) ),
inference(variable_rename,[status(thm)],[c_0_145]) ).
fof(c_0_261,plain,
! [X5,X6,X7,X8] :
( ~ member(X8,X6)
| ~ member(X7,X5)
| member(ordered_pair(X8,X7),cross_product(X6,X5)) ),
inference(variable_rename,[status(thm)],[c_0_146]) ).
fof(c_0_262,plain,
! [X3] : domain_of(restrict(element_relation,universal_class,X3)) = sum_class(X3),
inference(variable_rename,[status(thm)],[c_0_147]) ).
fof(c_0_263,plain,
! [X3,X4] :
( ~ member(not_subclass_element(X3,X4),X4)
| X4 = X3
| member(not_subclass_element(X4,X3),X4) ),
inference(variable_rename,[status(thm)],[c_0_148]) ).
fof(c_0_264,plain,
! [X3,X4] :
( ~ member(not_subclass_element(X4,X3),X3)
| X4 = X3
| member(not_subclass_element(X3,X4),X3) ),
inference(variable_rename,[status(thm)],[c_0_149]) ).
fof(c_0_265,plain,
! [X13,X14,X15] :
( ~ compatible(X13,X15,X14)
| domain_of(domain_of(X15)) = domain_of(X13) ),
inference(variable_rename,[status(thm)],[c_0_150]) ).
fof(c_0_266,plain,
! [X6,X7] :
( ~ member(X6,universal_class)
| restrict(X7,singleton(X6),universal_class) = null_class
| member(X6,domain_of(X7)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_151])])]) ).
fof(c_0_267,plain,
! [X3] : intersection(domain_of(X3),diagonalise(compose(inverse(element_relation),X3))) = cantor(X3),
inference(variable_rename,[status(thm)],[c_0_152]) ).
fof(c_0_268,plain,
! [X7,X8,X9] : intersection(cross_product(X9,X7),X8) = restrict(X8,X9,X7),
inference(variable_rename,[status(thm)],[c_0_153]) ).
fof(c_0_269,plain,
! [X7,X8,X9] : intersection(X8,cross_product(X9,X7)) = restrict(X8,X9,X7),
inference(variable_rename,[status(thm)],[c_0_154]) ).
fof(c_0_270,plain,
! [X6,X7,X8] :
( ~ member(X6,cross_product(X8,X7))
| ordered_pair(first(X6),second(X6)) = X6 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_155])])]) ).
fof(c_0_271,plain,
! [X13,X14,X15] :
( ~ homomorphism(X13,X15,X14)
| operation(X14) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_156])])]) ).
fof(c_0_272,plain,
! [X13,X14,X15] :
( ~ homomorphism(X13,X15,X14)
| operation(X15) ),
inference(variable_rename,[status(thm)],[c_0_157]) ).
fof(c_0_273,plain,
! [X13,X14,X15] :
( ~ compatible(X13,X15,X14)
| function(X13) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_158])])]) ).
fof(c_0_274,plain,
! [X6,X7,X8] :
( ~ member(X6,X8)
| ~ member(X6,X7)
| member(X6,intersection(X8,X7)) ),
inference(variable_rename,[status(thm)],[c_0_159]) ).
fof(c_0_275,plain,
! [X3] :
( ~ subclass(compose(X3,inverse(X3)),identity_relation)
| single_valued_class(X3) ),
inference(variable_rename,[status(thm)],[c_0_160]) ).
fof(c_0_276,plain,
! [X3] :
( ~ member(null_class,X3)
| ~ subclass(image(successor_relation,X3),X3)
| inductive(X3) ),
inference(variable_rename,[status(thm)],[c_0_161]) ).
fof(c_0_277,plain,
! [X3,X4] :
( X4 = X3
| member(not_subclass_element(X4,X3),X4)
| member(not_subclass_element(X3,X4),X3) ),
inference(variable_rename,[status(thm)],[c_0_162]) ).
fof(c_0_278,plain,
! [X3] : subclass(flip(X3),cross_product(cross_product(universal_class,universal_class),universal_class)),
inference(variable_rename,[status(thm)],[c_0_163]) ).
fof(c_0_279,plain,
! [X3] : subclass(rotate(X3),cross_product(cross_product(universal_class,universal_class),universal_class)),
inference(variable_rename,[status(thm)],[c_0_164]) ).
fof(c_0_280,plain,
! [X3,X4] : ~ member(X3,intersection(complement(X4),X4)),
inference(variable_rename,[status(thm)],[c_0_165]) ).
fof(c_0_281,plain,
! [X6,X7,X8] :
( ~ member(X6,intersection(X8,X7))
| member(X6,X7) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_166])])]) ).
fof(c_0_282,plain,
! [X6,X7,X8] :
( ~ member(X6,intersection(X8,X7))
| member(X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_167]) ).
fof(c_0_283,plain,
! [X3,X4] :
( ~ member(not_subclass_element(X4,X3),X3)
| subclass(X4,X3) ),
inference(variable_rename,[status(thm)],[c_0_168]) ).
fof(c_0_284,plain,
! [X3,X4] :
( ~ member(ordered_pair(X4,X3),element_relation)
| member(X4,X3) ),
inference(variable_rename,[status(thm)],[c_0_169]) ).
fof(c_0_285,plain,
! [X3,X4] : unordered_pair(singleton(X4),unordered_pair(X4,singleton(X3))) = ordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[c_0_170]) ).
fof(c_0_286,plain,
! [X3,X4] : complement(intersection(complement(X4),complement(X3))) = union(X4,X3),
inference(variable_rename,[status(thm)],[c_0_171]) ).
fof(c_0_287,plain,
! [X4,X5,X6] :
( ~ member(X6,unordered_pair(X5,X4))
| X6 = X5
| X6 = X4 ),
inference(variable_rename,[status(thm)],[c_0_172]) ).
fof(c_0_288,plain,
! [X10,X11] :
( ~ function(X10)
| ~ member(X11,universal_class)
| member(image(X10,X11),universal_class) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_173])])]) ).
fof(c_0_289,plain,
! [X3,X4] :
( ~ member(ordered_pair(X4,X3),successor_relation)
| successor(X4) = X3 ),
inference(variable_rename,[status(thm)],[c_0_174]) ).
fof(c_0_290,plain,
! [X10] :
( ~ operation(X10)
| cross_product(domain_of(domain_of(X10)),domain_of(domain_of(X10))) = domain_of(X10) ),
inference(variable_rename,[status(thm)],[c_0_175]) ).
fof(c_0_291,plain,
! [X3,X4] :
( ~ member(X3,universal_class)
| member(X3,unordered_pair(X4,X3)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_176])])]) ).
fof(c_0_292,plain,
! [X3,X4] :
( ~ member(X4,universal_class)
| member(X4,unordered_pair(X4,X3)) ),
inference(variable_rename,[status(thm)],[c_0_177]) ).
fof(c_0_293,plain,
! [X7] : complement(domain_of(intersection(X7,identity_relation))) = diagonalise(X7),
inference(variable_rename,[status(thm)],[c_0_178]) ).
fof(c_0_294,plain,
! [X9,X10] : subclass(compose(X9,X10),cross_product(universal_class,universal_class)),
inference(variable_rename,[status(thm)],[c_0_179]) ).
fof(c_0_295,plain,
! [X2] : domain_of(flip(cross_product(X2,universal_class))) = inverse(X2),
inference(variable_rename,[status(thm)],[c_0_180]) ).
fof(c_0_296,plain,
! [X6,X7,X8] :
( ~ subclass(X8,X7)
| ~ subclass(X7,X6)
| subclass(X8,X6) ),
inference(variable_rename,[status(thm)],[c_0_181]) ).
fof(c_0_297,plain,
! [X4,X5,X6] :
( ~ subclass(X5,X4)
| ~ member(X6,X5)
| member(X6,X4) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_182])])]) ).
fof(c_0_298,plain,
! [X2] :
( ~ member(X2,universal_class)
| X2 = null_class
| member(apply(choice,X2),X2) ),
inference(variable_rename,[status(thm)],[c_0_183]) ).
fof(c_0_299,plain,
! [X10] :
( ~ function(X10)
| subclass(compose(X10,inverse(X10)),identity_relation) ),
inference(variable_rename,[status(thm)],[c_0_184]) ).
fof(c_0_300,plain,
! [X3] :
( ~ single_valued_class(X3)
| subclass(compose(X3,inverse(X3)),identity_relation) ),
inference(variable_rename,[status(thm)],[c_0_185]) ).
fof(c_0_301,plain,
! [X10,X11] : sum_class(image(X11,singleton(X10))) = apply(X11,X10),
inference(variable_rename,[status(thm)],[c_0_186]) ).
fof(c_0_302,plain,
! [X6,X7] :
( ~ member(X6,universal_class)
| member(X6,complement(X7))
| member(X6,X7) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_187])])]) ).
fof(c_0_303,plain,
! [X6,X7] :
( ~ member(X6,complement(X7))
| ~ member(X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_188]) ).
fof(c_0_304,plain,
! [X3,X4] :
( member(not_subclass_element(X4,X3),X4)
| subclass(X4,X3) ),
inference(variable_rename,[status(thm)],[c_0_189]) ).
fof(c_0_305,plain,
! [X3,X4] :
( ~ subclass(X4,X3)
| ~ subclass(X3,X4)
| X4 = X3 ),
inference(variable_rename,[status(thm)],[c_0_190]) ).
fof(c_0_306,plain,
! [X3,X4] : subclass(singleton(X3),unordered_pair(X4,X3)),
inference(variable_rename,[status(thm)],[c_0_191]) ).
fof(c_0_307,plain,
! [X3,X4] : subclass(singleton(X4),unordered_pair(X4,X3)),
inference(variable_rename,[status(thm)],[c_0_192]) ).
fof(c_0_308,plain,
! [X10] :
( ~ operation(X10)
| subclass(range_of(X10),domain_of(domain_of(X10))) ),
inference(variable_rename,[status(thm)],[c_0_193]) ).
fof(c_0_309,plain,
! [X3] :
( ~ inductive(X3)
| subclass(image(successor_relation,X3),X3) ),
inference(variable_rename,[status(thm)],[c_0_194]) ).
fof(c_0_310,plain,
! [X3] : complement(image(element_relation,complement(X3))) = power_class(X3),
inference(variable_rename,[status(thm)],[c_0_195]) ).
fof(c_0_311,plain,
! [X10] :
( ~ function(X10)
| subclass(X10,cross_product(universal_class,universal_class)) ),
inference(variable_rename,[status(thm)],[c_0_196]) ).
fof(c_0_312,plain,
! [X3,X4] :
( unordered_pair(X4,X3) = null_class
| member(X4,universal_class)
| member(X3,universal_class) ),
inference(variable_rename,[status(thm)],[c_0_197]) ).
fof(c_0_313,plain,
! [X4] :
( ~ member(X4,universal_class)
| member(power_class(X4),universal_class) ),
inference(variable_rename,[status(thm)],[c_0_198]) ).
fof(c_0_314,plain,
! [X3] :
( ~ member(X3,universal_class)
| member(sum_class(X3),universal_class) ),
inference(variable_rename,[status(thm)],[c_0_199]) ).
fof(c_0_315,plain,
! [X6] :
( X6 = null_class
| member(not_subclass_element(X6,null_class),X6) ),
inference(variable_rename,[status(thm)],[c_0_200]) ).
fof(c_0_316,plain,
! [X3,X4] : member(unordered_pair(X4,X3),universal_class),
inference(variable_rename,[status(thm)],[c_0_201]) ).
fof(c_0_317,axiom,
subclass(successor_relation,cross_product(universal_class,universal_class)),
c_0_202 ).
fof(c_0_318,axiom,
subclass(element_relation,cross_product(universal_class,universal_class)),
c_0_203 ).
fof(c_0_319,plain,
! [X3,X4] :
( member(X4,universal_class)
| unordered_pair(X4,X3) = singleton(X3) ),
inference(variable_rename,[status(thm)],[c_0_204]) ).
fof(c_0_320,plain,
! [X3,X4] :
( member(X3,universal_class)
| unordered_pair(X4,X3) = singleton(X4) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_205])])]) ).
fof(c_0_321,plain,
! [X10] :
( ~ function(inverse(X10))
| ~ function(X10)
| one_to_one(X10) ),
inference(variable_rename,[status(thm)],[c_0_206]) ).
fof(c_0_322,plain,
! [X3,X4] : unordered_pair(X4,X3) = unordered_pair(X3,X4),
inference(variable_rename,[status(thm)],[c_0_207]) ).
fof(c_0_323,plain,
! [X3] : union(X3,singleton(X3)) = successor(X3),
inference(variable_rename,[status(thm)],[c_0_208]) ).
fof(c_0_324,plain,
! [X3] :
( X3 = null_class
| intersection(X3,regular(X3)) = null_class ),
inference(variable_rename,[status(thm)],[c_0_209]) ).
fof(c_0_325,plain,
! [X3] :
( X3 = null_class
| member(regular(X3),X3) ),
inference(variable_rename,[status(thm)],[c_0_210]) ).
fof(c_0_326,plain,
! [X3] :
( ~ subclass(X3,null_class)
| X3 = null_class ),
inference(variable_rename,[status(thm)],[c_0_211]) ).
fof(c_0_327,plain,
! [X6] : ~ member(X6,null_class),
inference(variable_rename,[status(thm)],[c_0_212]) ).
fof(c_0_328,plain,
! [X2] :
( ~ inductive(X2)
| subclass(omega,X2) ),
inference(variable_rename,[status(thm)],[c_0_213]) ).
fof(c_0_329,plain,
! [X3] :
( ~ inductive(X3)
| member(null_class,X3) ),
inference(variable_rename,[status(thm)],[c_0_214]) ).
fof(c_0_330,plain,
! [X3] : unordered_pair(X3,X3) = singleton(X3),
inference(variable_rename,[status(thm)],[c_0_215]) ).
fof(c_0_331,plain,
! [X3,X4] :
( X4 != X3
| subclass(X3,X4) ),
inference(variable_rename,[status(thm)],[c_0_216]) ).
fof(c_0_332,plain,
! [X3,X4] :
( X4 != X3
| subclass(X4,X3) ),
inference(variable_rename,[status(thm)],[c_0_217]) ).
fof(c_0_333,plain,
! [X10] :
( ~ one_to_one(X10)
| function(inverse(X10)) ),
inference(variable_rename,[status(thm)],[c_0_218]) ).
fof(c_0_334,axiom,
intersection(inverse(subset_relation),subset_relation) = identity_relation,
c_0_219 ).
fof(c_0_335,plain,
! [X3] : subclass(X3,X3),
inference(variable_rename,[status(thm)],[c_0_220]) ).
fof(c_0_336,plain,
! [X6] : domain_of(inverse(X6)) = range_of(X6),
inference(variable_rename,[status(thm)],[c_0_221]) ).
fof(c_0_337,plain,
! [X3] : subclass(null_class,X3),
inference(variable_rename,[status(thm)],[c_0_222]) ).
fof(c_0_338,plain,
! [X3] : subclass(X3,universal_class),
inference(variable_rename,[status(thm)],[c_0_223]) ).
fof(c_0_339,plain,
! [X10] :
( ~ operation(X10)
| function(X10) ),
inference(variable_rename,[status(thm)],[c_0_224]) ).
fof(c_0_340,plain,
! [X10] :
( ~ one_to_one(X10)
| function(X10) ),
inference(variable_rename,[status(thm)],[c_0_225]) ).
fof(c_0_341,axiom,
member(null_class,universal_class),
c_0_226 ).
fof(c_0_342,axiom,
member(omega,universal_class),
c_0_227 ).
fof(c_0_343,axiom,
function(choice),
c_0_228 ).
fof(c_0_344,axiom,
inductive(omega),
c_0_229 ).
cnf(c_0_345,plain,
( homomorphism(X1,X2,X3)
| apply(X3,ordered_pair(apply(X1,not_homomorphism1(X1,X2,X3)),apply(X1,not_homomorphism2(X1,X2,X3)))) != apply(X1,apply(X2,ordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism2(X1,X2,X3))))
| ~ compatible(X1,X2,X3)
| ~ operation(X3)
| ~ operation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_230]) ).
cnf(c_0_346,plain,
( homomorphism(X1,X2,X3)
| member(ordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism2(X1,X2,X3)),domain_of(X2))
| ~ compatible(X1,X2,X3)
| ~ operation(X3)
| ~ operation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_231]) ).
cnf(c_0_347,plain,
( member(ordered_pair(ordered_pair(X1,X2),X3),flip(X4))
| ~ member(ordered_pair(ordered_pair(X1,X2),X3),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ member(ordered_pair(ordered_pair(X2,X1),X3),X4) ),
inference(split_conjunct,[status(thm)],[c_0_232]) ).
cnf(c_0_348,plain,
( member(ordered_pair(ordered_pair(X1,X2),X3),rotate(X4))
| ~ member(ordered_pair(ordered_pair(X1,X2),X3),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ member(ordered_pair(ordered_pair(X2,X3),X1),X4) ),
inference(split_conjunct,[status(thm)],[c_0_233]) ).
cnf(c_0_349,plain,
( apply(X1,ordered_pair(apply(X2,X3),apply(X2,X4))) = apply(X2,apply(X5,ordered_pair(X3,X4)))
| ~ member(ordered_pair(X3,X4),domain_of(X5))
| ~ homomorphism(X2,X5,X1) ),
inference(split_conjunct,[status(thm)],[c_0_234]) ).
cnf(c_0_350,plain,
( member(ordered_pair(X1,X2),compose(X3,X4))
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
| ~ member(X2,image(X3,image(X4,singleton(X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_235]) ).
cnf(c_0_351,plain,
second(not_subclass_element(restrict(X1,singleton(X2),X3),null_class)) = range(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_236]) ).
cnf(c_0_352,plain,
first(not_subclass_element(restrict(X1,X2,singleton(X3)),null_class)) = domain(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_237]) ).
cnf(c_0_353,plain,
intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))) = subset_relation,
inference(split_conjunct,[status(thm)],[c_0_238]) ).
cnf(c_0_354,plain,
( member(ordered_pair(ordered_pair(X1,X2),X3),X4)
| ~ member(ordered_pair(ordered_pair(X2,X1),X3),flip(X4)) ),
inference(split_conjunct,[status(thm)],[c_0_239]) ).
cnf(c_0_355,plain,
( member(ordered_pair(ordered_pair(X1,X2),X3),X4)
| ~ member(ordered_pair(ordered_pair(X3,X1),X2),rotate(X4)) ),
inference(split_conjunct,[status(thm)],[c_0_240]) ).
cnf(c_0_356,plain,
( member(X1,image(X2,image(X3,singleton(X4))))
| ~ member(ordered_pair(X4,X1),compose(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_241]) ).
cnf(c_0_357,plain,
intersection(complement(intersection(X1,X2)),complement(intersection(complement(X1),complement(X2)))) = symmetric_difference(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_242]) ).
cnf(c_0_358,plain,
( operation(X1)
| ~ subclass(range_of(X1),domain_of(domain_of(X1)))
| cross_product(domain_of(domain_of(X1)),domain_of(domain_of(X1))) != domain_of(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_243]) ).
cnf(c_0_359,plain,
( member(ordered_pair(X1,X2),element_relation)
| ~ member(X1,X2)
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class)) ),
inference(split_conjunct,[status(thm)],[c_0_244]) ).
cnf(c_0_360,plain,
( compatible(X1,X2,X3)
| ~ subclass(range_of(X1),domain_of(domain_of(X3)))
| domain_of(domain_of(X2)) != domain_of(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_245]) ).
cnf(c_0_361,plain,
( member(X1,unordered_pair(X2,X1))
| ~ member(ordered_pair(X2,X1),cross_product(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_246]) ).
cnf(c_0_362,plain,
( member(X1,unordered_pair(X1,X2))
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_247]) ).
cnf(c_0_363,plain,
( member(ordered_pair(X1,X2),successor_relation)
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
| successor(X1) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_248]) ).
cnf(c_0_364,plain,
( X1 = X2
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
| unordered_pair(X1,X3) != unordered_pair(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_249]) ).
cnf(c_0_365,plain,
( X1 = X2
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
| unordered_pair(X3,X1) != unordered_pair(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_250]) ).
cnf(c_0_366,plain,
( compatible(X1,X2,X3)
| ~ homomorphism(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_251]) ).
cnf(c_0_367,plain,
( function(X1)
| ~ subclass(compose(X1,inverse(X1)),identity_relation)
| ~ subclass(X1,cross_product(universal_class,universal_class)) ),
inference(split_conjunct,[status(thm)],[c_0_252]) ).
cnf(c_0_368,plain,
( X1 = X2
| ~ member(not_subclass_element(X2,X1),X1)
| ~ member(not_subclass_element(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_253]) ).
cnf(c_0_369,plain,
( ~ member(X1,domain_of(X2))
| restrict(X2,singleton(X1),universal_class) != null_class ),
inference(split_conjunct,[status(thm)],[c_0_254]) ).
cnf(c_0_370,plain,
( subclass(range_of(X1),domain_of(domain_of(X2)))
| ~ compatible(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_255]) ).
cnf(c_0_371,plain,
range_of(restrict(X1,X2,universal_class)) = image(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_256]) ).
cnf(c_0_372,plain,
( member(X1,X2)
| ~ member(ordered_pair(X3,X1),cross_product(X4,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_257]) ).
cnf(c_0_373,plain,
( member(X1,X2)
| ~ member(ordered_pair(X1,X3),cross_product(X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_258]) ).
cnf(c_0_374,plain,
( member(X1,universal_class)
| ~ member(ordered_pair(X2,X1),cross_product(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_259]) ).
cnf(c_0_375,plain,
( member(X1,universal_class)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_260]) ).
cnf(c_0_376,plain,
( member(ordered_pair(X1,X2),cross_product(X3,X4))
| ~ member(X2,X4)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_261]) ).
cnf(c_0_377,plain,
domain_of(restrict(element_relation,universal_class,X1)) = sum_class(X1),
inference(split_conjunct,[status(thm)],[c_0_262]) ).
cnf(c_0_378,plain,
( member(not_subclass_element(X1,X2),X1)
| X1 = X2
| ~ member(not_subclass_element(X2,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_263]) ).
cnf(c_0_379,plain,
( member(not_subclass_element(X1,X2),X1)
| X2 = X1
| ~ member(not_subclass_element(X2,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_264]) ).
cnf(c_0_380,plain,
( domain_of(domain_of(X1)) = domain_of(X2)
| ~ compatible(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_265]) ).
cnf(c_0_381,plain,
( member(X1,domain_of(X2))
| restrict(X2,singleton(X1),universal_class) = null_class
| ~ member(X1,universal_class) ),
inference(split_conjunct,[status(thm)],[c_0_266]) ).
cnf(c_0_382,plain,
intersection(domain_of(X1),diagonalise(compose(inverse(element_relation),X1))) = cantor(X1),
inference(split_conjunct,[status(thm)],[c_0_267]) ).
cnf(c_0_383,plain,
intersection(cross_product(X1,X2),X3) = restrict(X3,X1,X2),
inference(split_conjunct,[status(thm)],[c_0_268]) ).
cnf(c_0_384,plain,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_269]) ).
cnf(c_0_385,plain,
( ordered_pair(first(X1),second(X1)) = X1
| ~ member(X1,cross_product(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_270]) ).
cnf(c_0_386,plain,
( operation(X1)
| ~ homomorphism(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_271]) ).
cnf(c_0_387,plain,
( operation(X1)
| ~ homomorphism(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_272]) ).
cnf(c_0_388,plain,
( function(X1)
| ~ compatible(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_273]) ).
cnf(c_0_389,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X3)
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_274]) ).
cnf(c_0_390,plain,
( single_valued_class(X1)
| ~ subclass(compose(X1,inverse(X1)),identity_relation) ),
inference(split_conjunct,[status(thm)],[c_0_275]) ).
cnf(c_0_391,plain,
( inductive(X1)
| ~ subclass(image(successor_relation,X1),X1)
| ~ member(null_class,X1) ),
inference(split_conjunct,[status(thm)],[c_0_276]) ).
cnf(c_0_392,plain,
( member(not_subclass_element(X1,X2),X1)
| member(not_subclass_element(X2,X1),X2)
| X2 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_277]) ).
cnf(c_0_393,plain,
subclass(flip(X1),cross_product(cross_product(universal_class,universal_class),universal_class)),
inference(split_conjunct,[status(thm)],[c_0_278]) ).
cnf(c_0_394,plain,
subclass(rotate(X1),cross_product(cross_product(universal_class,universal_class),universal_class)),
inference(split_conjunct,[status(thm)],[c_0_279]) ).
cnf(c_0_395,plain,
~ member(X1,intersection(complement(X2),X2)),
inference(split_conjunct,[status(thm)],[c_0_280]) ).
cnf(c_0_396,plain,
( member(X1,X2)
| ~ member(X1,intersection(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_281]) ).
cnf(c_0_397,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_282]) ).
cnf(c_0_398,plain,
( subclass(X1,X2)
| ~ member(not_subclass_element(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_283]) ).
cnf(c_0_399,plain,
( member(X1,X2)
| ~ member(ordered_pair(X1,X2),element_relation) ),
inference(split_conjunct,[status(thm)],[c_0_284]) ).
cnf(c_0_400,plain,
unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_285]) ).
cnf(c_0_401,plain,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_286]) ).
cnf(c_0_402,plain,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_287]) ).
cnf(c_0_403,plain,
( member(image(X1,X2),universal_class)
| ~ member(X2,universal_class)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_288]) ).
cnf(c_0_404,plain,
( successor(X1) = X2
| ~ member(ordered_pair(X1,X2),successor_relation) ),
inference(split_conjunct,[status(thm)],[c_0_289]) ).
cnf(c_0_405,plain,
( cross_product(domain_of(domain_of(X1)),domain_of(domain_of(X1))) = domain_of(X1)
| ~ operation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_290]) ).
cnf(c_0_406,plain,
( member(X1,unordered_pair(X2,X1))
| ~ member(X1,universal_class) ),
inference(split_conjunct,[status(thm)],[c_0_291]) ).
cnf(c_0_407,plain,
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
inference(split_conjunct,[status(thm)],[c_0_292]) ).
cnf(c_0_408,plain,
complement(domain_of(intersection(X1,identity_relation))) = diagonalise(X1),
inference(split_conjunct,[status(thm)],[c_0_293]) ).
cnf(c_0_409,plain,
subclass(compose(X1,X2),cross_product(universal_class,universal_class)),
inference(split_conjunct,[status(thm)],[c_0_294]) ).
cnf(c_0_410,plain,
domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
inference(split_conjunct,[status(thm)],[c_0_295]) ).
cnf(c_0_411,plain,
( subclass(X1,X2)
| ~ subclass(X3,X2)
| ~ subclass(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_296]) ).
cnf(c_0_412,plain,
( member(X1,X2)
| ~ member(X1,X3)
| ~ subclass(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_297]) ).
cnf(c_0_413,plain,
( member(apply(choice,X1),X1)
| X1 = null_class
| ~ member(X1,universal_class) ),
inference(split_conjunct,[status(thm)],[c_0_298]) ).
cnf(c_0_414,plain,
( subclass(compose(X1,inverse(X1)),identity_relation)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_299]) ).
cnf(c_0_415,plain,
( subclass(compose(X1,inverse(X1)),identity_relation)
| ~ single_valued_class(X1) ),
inference(split_conjunct,[status(thm)],[c_0_300]) ).
cnf(c_0_416,plain,
sum_class(image(X1,singleton(X2))) = apply(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_301]) ).
cnf(c_0_417,plain,
( member(X1,X2)
| member(X1,complement(X2))
| ~ member(X1,universal_class) ),
inference(split_conjunct,[status(thm)],[c_0_302]) ).
cnf(c_0_418,plain,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_303]) ).
cnf(c_0_419,plain,
( subclass(X1,X2)
| member(not_subclass_element(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_304]) ).
cnf(c_0_420,plain,
( X1 = X2
| ~ subclass(X2,X1)
| ~ subclass(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_305]) ).
cnf(c_0_421,plain,
subclass(singleton(X1),unordered_pair(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_306]) ).
cnf(c_0_422,plain,
subclass(singleton(X1),unordered_pair(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_307]) ).
cnf(c_0_423,plain,
( subclass(range_of(X1),domain_of(domain_of(X1)))
| ~ operation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_308]) ).
cnf(c_0_424,plain,
( subclass(image(successor_relation,X1),X1)
| ~ inductive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_309]) ).
cnf(c_0_425,plain,
complement(image(element_relation,complement(X1))) = power_class(X1),
inference(split_conjunct,[status(thm)],[c_0_310]) ).
cnf(c_0_426,plain,
( subclass(X1,cross_product(universal_class,universal_class))
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_311]) ).
cnf(c_0_427,plain,
( member(X1,universal_class)
| member(X2,universal_class)
| unordered_pair(X2,X1) = null_class ),
inference(split_conjunct,[status(thm)],[c_0_312]) ).
cnf(c_0_428,plain,
( member(power_class(X1),universal_class)
| ~ member(X1,universal_class) ),
inference(split_conjunct,[status(thm)],[c_0_313]) ).
cnf(c_0_429,plain,
( member(sum_class(X1),universal_class)
| ~ member(X1,universal_class) ),
inference(split_conjunct,[status(thm)],[c_0_314]) ).
cnf(c_0_430,plain,
( member(not_subclass_element(X1,null_class),X1)
| X1 = null_class ),
inference(split_conjunct,[status(thm)],[c_0_315]) ).
cnf(c_0_431,plain,
member(unordered_pair(X1,X2),universal_class),
inference(split_conjunct,[status(thm)],[c_0_316]) ).
cnf(c_0_432,plain,
subclass(successor_relation,cross_product(universal_class,universal_class)),
inference(split_conjunct,[status(thm)],[c_0_317]) ).
cnf(c_0_433,plain,
subclass(element_relation,cross_product(universal_class,universal_class)),
inference(split_conjunct,[status(thm)],[c_0_318]) ).
cnf(c_0_434,plain,
( unordered_pair(X1,X2) = singleton(X2)
| member(X1,universal_class) ),
inference(split_conjunct,[status(thm)],[c_0_319]) ).
cnf(c_0_435,plain,
( unordered_pair(X1,X2) = singleton(X1)
| member(X2,universal_class) ),
inference(split_conjunct,[status(thm)],[c_0_320]) ).
cnf(c_0_436,plain,
( one_to_one(X1)
| ~ function(X1)
| ~ function(inverse(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_321]) ).
cnf(c_0_437,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_322]) ).
cnf(c_0_438,plain,
union(X1,singleton(X1)) = successor(X1),
inference(split_conjunct,[status(thm)],[c_0_323]) ).
cnf(c_0_439,plain,
( intersection(X1,regular(X1)) = null_class
| X1 = null_class ),
inference(split_conjunct,[status(thm)],[c_0_324]) ).
cnf(c_0_440,plain,
( member(regular(X1),X1)
| X1 = null_class ),
inference(split_conjunct,[status(thm)],[c_0_325]) ).
cnf(c_0_441,plain,
( X1 = null_class
| ~ subclass(X1,null_class) ),
inference(split_conjunct,[status(thm)],[c_0_326]) ).
cnf(c_0_442,plain,
~ member(X1,null_class),
inference(split_conjunct,[status(thm)],[c_0_327]) ).
cnf(c_0_443,plain,
( subclass(omega,X1)
| ~ inductive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_328]) ).
cnf(c_0_444,plain,
( member(null_class,X1)
| ~ inductive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_329]) ).
cnf(c_0_445,plain,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[c_0_330]) ).
cnf(c_0_446,plain,
( subclass(X1,X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[c_0_331]) ).
cnf(c_0_447,plain,
( subclass(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_332]) ).
cnf(c_0_448,plain,
( function(inverse(X1))
| ~ one_to_one(X1) ),
inference(split_conjunct,[status(thm)],[c_0_333]) ).
cnf(c_0_449,plain,
intersection(inverse(subset_relation),subset_relation) = identity_relation,
inference(split_conjunct,[status(thm)],[c_0_334]) ).
cnf(c_0_450,plain,
subclass(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_335]) ).
cnf(c_0_451,plain,
domain_of(inverse(X1)) = range_of(X1),
inference(split_conjunct,[status(thm)],[c_0_336]) ).
cnf(c_0_452,plain,
subclass(null_class,X1),
inference(split_conjunct,[status(thm)],[c_0_337]) ).
cnf(c_0_453,plain,
subclass(X1,universal_class),
inference(split_conjunct,[status(thm)],[c_0_338]) ).
cnf(c_0_454,plain,
( function(X1)
| ~ operation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_339]) ).
cnf(c_0_455,plain,
( function(X1)
| ~ one_to_one(X1) ),
inference(split_conjunct,[status(thm)],[c_0_340]) ).
cnf(c_0_456,plain,
member(null_class,universal_class),
inference(split_conjunct,[status(thm)],[c_0_341]) ).
cnf(c_0_457,plain,
member(omega,universal_class),
inference(split_conjunct,[status(thm)],[c_0_342]) ).
cnf(c_0_458,plain,
function(choice),
inference(split_conjunct,[status(thm)],[c_0_343]) ).
cnf(c_0_459,plain,
inductive(omega),
inference(split_conjunct,[status(thm)],[c_0_344]) ).
cnf(c_0_460,plain,
( homomorphism(X1,X2,X3)
| apply(X3,ordered_pair(apply(X1,not_homomorphism1(X1,X2,X3)),apply(X1,not_homomorphism2(X1,X2,X3)))) != apply(X1,apply(X2,ordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism2(X1,X2,X3))))
| ~ compatible(X1,X2,X3)
| ~ operation(X3)
| ~ operation(X2) ),
c_0_345,
[final] ).
cnf(c_0_461,plain,
( homomorphism(X1,X2,X3)
| member(ordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism2(X1,X2,X3)),domain_of(X2))
| ~ compatible(X1,X2,X3)
| ~ operation(X3)
| ~ operation(X2) ),
c_0_346,
[final] ).
cnf(c_0_462,plain,
( member(ordered_pair(ordered_pair(X1,X2),X3),flip(X4))
| ~ member(ordered_pair(ordered_pair(X1,X2),X3),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ member(ordered_pair(ordered_pair(X2,X1),X3),X4) ),
c_0_347,
[final] ).
cnf(c_0_463,plain,
( member(ordered_pair(ordered_pair(X1,X2),X3),rotate(X4))
| ~ member(ordered_pair(ordered_pair(X1,X2),X3),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ member(ordered_pair(ordered_pair(X2,X3),X1),X4) ),
c_0_348,
[final] ).
cnf(c_0_464,plain,
( apply(X1,ordered_pair(apply(X2,X3),apply(X2,X4))) = apply(X2,apply(X5,ordered_pair(X3,X4)))
| ~ member(ordered_pair(X3,X4),domain_of(X5))
| ~ homomorphism(X2,X5,X1) ),
c_0_349,
[final] ).
cnf(c_0_465,plain,
( member(ordered_pair(X1,X2),compose(X3,X4))
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
| ~ member(X2,image(X3,image(X4,singleton(X1)))) ),
c_0_350,
[final] ).
cnf(c_0_466,plain,
second(not_subclass_element(restrict(X1,singleton(X2),X3),null_class)) = range(X1,X2,X3),
c_0_351,
[final] ).
cnf(c_0_467,plain,
first(not_subclass_element(restrict(X1,X2,singleton(X3)),null_class)) = domain(X1,X2,X3),
c_0_352,
[final] ).
cnf(c_0_468,plain,
intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))) = subset_relation,
c_0_353,
[final] ).
cnf(c_0_469,plain,
( member(ordered_pair(ordered_pair(X1,X2),X3),X4)
| ~ member(ordered_pair(ordered_pair(X2,X1),X3),flip(X4)) ),
c_0_354,
[final] ).
cnf(c_0_470,plain,
( member(ordered_pair(ordered_pair(X1,X2),X3),X4)
| ~ member(ordered_pair(ordered_pair(X3,X1),X2),rotate(X4)) ),
c_0_355,
[final] ).
cnf(c_0_471,plain,
( member(X1,image(X2,image(X3,singleton(X4))))
| ~ member(ordered_pair(X4,X1),compose(X2,X3)) ),
c_0_356,
[final] ).
cnf(c_0_472,plain,
intersection(complement(intersection(X1,X2)),complement(intersection(complement(X1),complement(X2)))) = symmetric_difference(X1,X2),
c_0_357,
[final] ).
cnf(c_0_473,plain,
( operation(X1)
| ~ subclass(range_of(X1),domain_of(domain_of(X1)))
| cross_product(domain_of(domain_of(X1)),domain_of(domain_of(X1))) != domain_of(X1)
| ~ function(X1) ),
c_0_358,
[final] ).
cnf(c_0_474,plain,
( member(ordered_pair(X1,X2),element_relation)
| ~ member(X1,X2)
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class)) ),
c_0_359,
[final] ).
cnf(c_0_475,plain,
( compatible(X1,X2,X3)
| ~ subclass(range_of(X1),domain_of(domain_of(X3)))
| domain_of(domain_of(X2)) != domain_of(X1)
| ~ function(X1) ),
c_0_360,
[final] ).
cnf(c_0_476,plain,
( member(X1,unordered_pair(X2,X1))
| ~ member(ordered_pair(X2,X1),cross_product(X3,X4)) ),
c_0_361,
[final] ).
cnf(c_0_477,plain,
( member(X1,unordered_pair(X1,X2))
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
c_0_362,
[final] ).
cnf(c_0_478,plain,
( member(ordered_pair(X1,X2),successor_relation)
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
| successor(X1) != X2 ),
c_0_363,
[final] ).
cnf(c_0_479,plain,
( X1 = X2
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
| unordered_pair(X1,X3) != unordered_pair(X2,X3) ),
c_0_364,
[final] ).
cnf(c_0_480,plain,
( X1 = X2
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
| unordered_pair(X3,X1) != unordered_pair(X3,X2) ),
c_0_365,
[final] ).
cnf(c_0_481,plain,
( compatible(X1,X2,X3)
| ~ homomorphism(X1,X2,X3) ),
c_0_366,
[final] ).
cnf(c_0_482,plain,
( function(X1)
| ~ subclass(compose(X1,inverse(X1)),identity_relation)
| ~ subclass(X1,cross_product(universal_class,universal_class)) ),
c_0_367,
[final] ).
cnf(c_0_483,plain,
( X1 = X2
| ~ member(not_subclass_element(X2,X1),X1)
| ~ member(not_subclass_element(X1,X2),X2) ),
c_0_368,
[final] ).
cnf(c_0_484,plain,
( ~ member(X1,domain_of(X2))
| restrict(X2,singleton(X1),universal_class) != null_class ),
c_0_369,
[final] ).
cnf(c_0_485,plain,
( subclass(range_of(X1),domain_of(domain_of(X2)))
| ~ compatible(X1,X3,X2) ),
c_0_370,
[final] ).
cnf(c_0_486,plain,
range_of(restrict(X1,X2,universal_class)) = image(X1,X2),
c_0_371,
[final] ).
cnf(c_0_487,plain,
( member(X1,X2)
| ~ member(ordered_pair(X3,X1),cross_product(X4,X2)) ),
c_0_372,
[final] ).
cnf(c_0_488,plain,
( member(X1,X2)
| ~ member(ordered_pair(X1,X3),cross_product(X2,X4)) ),
c_0_373,
[final] ).
cnf(c_0_489,plain,
( member(X1,universal_class)
| ~ member(ordered_pair(X2,X1),cross_product(X3,X4)) ),
c_0_374,
[final] ).
cnf(c_0_490,plain,
( member(X1,universal_class)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
c_0_375,
[final] ).
cnf(c_0_491,plain,
( member(ordered_pair(X1,X2),cross_product(X3,X4))
| ~ member(X2,X4)
| ~ member(X1,X3) ),
c_0_376,
[final] ).
cnf(c_0_492,plain,
domain_of(restrict(element_relation,universal_class,X1)) = sum_class(X1),
c_0_377,
[final] ).
cnf(c_0_493,plain,
( member(not_subclass_element(X1,X2),X1)
| X1 = X2
| ~ member(not_subclass_element(X2,X1),X1) ),
c_0_378,
[final] ).
cnf(c_0_494,plain,
( member(not_subclass_element(X1,X2),X1)
| X2 = X1
| ~ member(not_subclass_element(X2,X1),X1) ),
c_0_379,
[final] ).
cnf(c_0_495,plain,
( domain_of(domain_of(X1)) = domain_of(X2)
| ~ compatible(X2,X1,X3) ),
c_0_380,
[final] ).
cnf(c_0_496,plain,
( member(X1,domain_of(X2))
| restrict(X2,singleton(X1),universal_class) = null_class
| ~ member(X1,universal_class) ),
c_0_381,
[final] ).
cnf(c_0_497,plain,
intersection(domain_of(X1),diagonalise(compose(inverse(element_relation),X1))) = cantor(X1),
c_0_382,
[final] ).
cnf(c_0_498,plain,
intersection(cross_product(X1,X2),X3) = restrict(X3,X1,X2),
c_0_383,
[final] ).
cnf(c_0_499,plain,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
c_0_384,
[final] ).
cnf(c_0_500,plain,
( ordered_pair(first(X1),second(X1)) = X1
| ~ member(X1,cross_product(X2,X3)) ),
c_0_385,
[final] ).
cnf(c_0_501,plain,
( operation(X1)
| ~ homomorphism(X2,X3,X1) ),
c_0_386,
[final] ).
cnf(c_0_502,plain,
( operation(X1)
| ~ homomorphism(X2,X1,X3) ),
c_0_387,
[final] ).
cnf(c_0_503,plain,
( function(X1)
| ~ compatible(X1,X2,X3) ),
c_0_388,
[final] ).
cnf(c_0_504,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X3)
| ~ member(X1,X2) ),
c_0_389,
[final] ).
cnf(c_0_505,plain,
( single_valued_class(X1)
| ~ subclass(compose(X1,inverse(X1)),identity_relation) ),
c_0_390,
[final] ).
cnf(c_0_506,plain,
( inductive(X1)
| ~ subclass(image(successor_relation,X1),X1)
| ~ member(null_class,X1) ),
c_0_391,
[final] ).
cnf(c_0_507,plain,
( member(not_subclass_element(X1,X2),X1)
| member(not_subclass_element(X2,X1),X2)
| X2 = X1 ),
c_0_392,
[final] ).
cnf(c_0_508,plain,
subclass(flip(X1),cross_product(cross_product(universal_class,universal_class),universal_class)),
c_0_393,
[final] ).
cnf(c_0_509,plain,
subclass(rotate(X1),cross_product(cross_product(universal_class,universal_class),universal_class)),
c_0_394,
[final] ).
cnf(c_0_510,plain,
~ member(X1,intersection(complement(X2),X2)),
c_0_395,
[final] ).
cnf(c_0_511,plain,
( member(X1,X2)
| ~ member(X1,intersection(X3,X2)) ),
c_0_396,
[final] ).
cnf(c_0_512,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
c_0_397,
[final] ).
cnf(c_0_513,plain,
( subclass(X1,X2)
| ~ member(not_subclass_element(X1,X2),X2) ),
c_0_398,
[final] ).
cnf(c_0_514,plain,
( member(X1,X2)
| ~ member(ordered_pair(X1,X2),element_relation) ),
c_0_399,
[final] ).
cnf(c_0_515,plain,
unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
c_0_400,
[final] ).
cnf(c_0_516,plain,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
c_0_401,
[final] ).
cnf(c_0_517,plain,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X3,X2)) ),
c_0_402,
[final] ).
cnf(c_0_518,plain,
( member(image(X1,X2),universal_class)
| ~ member(X2,universal_class)
| ~ function(X1) ),
c_0_403,
[final] ).
cnf(c_0_519,plain,
( successor(X1) = X2
| ~ member(ordered_pair(X1,X2),successor_relation) ),
c_0_404,
[final] ).
cnf(c_0_520,plain,
( cross_product(domain_of(domain_of(X1)),domain_of(domain_of(X1))) = domain_of(X1)
| ~ operation(X1) ),
c_0_405,
[final] ).
cnf(c_0_521,plain,
( member(X1,unordered_pair(X2,X1))
| ~ member(X1,universal_class) ),
c_0_406,
[final] ).
cnf(c_0_522,plain,
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
c_0_407,
[final] ).
cnf(c_0_523,plain,
complement(domain_of(intersection(X1,identity_relation))) = diagonalise(X1),
c_0_408,
[final] ).
cnf(c_0_524,plain,
subclass(compose(X1,X2),cross_product(universal_class,universal_class)),
c_0_409,
[final] ).
cnf(c_0_525,plain,
domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
c_0_410,
[final] ).
cnf(c_0_526,plain,
( subclass(X1,X2)
| ~ subclass(X3,X2)
| ~ subclass(X1,X3) ),
c_0_411,
[final] ).
cnf(c_0_527,plain,
( member(X1,X2)
| ~ member(X1,X3)
| ~ subclass(X3,X2) ),
c_0_412,
[final] ).
cnf(c_0_528,plain,
( member(apply(choice,X1),X1)
| X1 = null_class
| ~ member(X1,universal_class) ),
c_0_413,
[final] ).
cnf(c_0_529,plain,
( subclass(compose(X1,inverse(X1)),identity_relation)
| ~ function(X1) ),
c_0_414,
[final] ).
cnf(c_0_530,plain,
( subclass(compose(X1,inverse(X1)),identity_relation)
| ~ single_valued_class(X1) ),
c_0_415,
[final] ).
cnf(c_0_531,plain,
sum_class(image(X1,singleton(X2))) = apply(X1,X2),
c_0_416,
[final] ).
cnf(c_0_532,plain,
( member(X1,X2)
| member(X1,complement(X2))
| ~ member(X1,universal_class) ),
c_0_417,
[final] ).
cnf(c_0_533,plain,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
c_0_418,
[final] ).
cnf(c_0_534,plain,
( subclass(X1,X2)
| member(not_subclass_element(X1,X2),X1) ),
c_0_419,
[final] ).
cnf(c_0_535,plain,
( X1 = X2
| ~ subclass(X2,X1)
| ~ subclass(X1,X2) ),
c_0_420,
[final] ).
cnf(c_0_536,plain,
subclass(singleton(X1),unordered_pair(X2,X1)),
c_0_421,
[final] ).
cnf(c_0_537,plain,
subclass(singleton(X1),unordered_pair(X1,X2)),
c_0_422,
[final] ).
cnf(c_0_538,plain,
( subclass(range_of(X1),domain_of(domain_of(X1)))
| ~ operation(X1) ),
c_0_423,
[final] ).
cnf(c_0_539,plain,
( subclass(image(successor_relation,X1),X1)
| ~ inductive(X1) ),
c_0_424,
[final] ).
cnf(c_0_540,plain,
complement(image(element_relation,complement(X1))) = power_class(X1),
c_0_425,
[final] ).
cnf(c_0_541,plain,
( subclass(X1,cross_product(universal_class,universal_class))
| ~ function(X1) ),
c_0_426,
[final] ).
cnf(c_0_542,plain,
( member(X1,universal_class)
| member(X2,universal_class)
| unordered_pair(X2,X1) = null_class ),
c_0_427,
[final] ).
cnf(c_0_543,plain,
( member(power_class(X1),universal_class)
| ~ member(X1,universal_class) ),
c_0_428,
[final] ).
cnf(c_0_544,plain,
( member(sum_class(X1),universal_class)
| ~ member(X1,universal_class) ),
c_0_429,
[final] ).
cnf(c_0_545,plain,
( member(not_subclass_element(X1,null_class),X1)
| X1 = null_class ),
c_0_430,
[final] ).
cnf(c_0_546,plain,
member(unordered_pair(X1,X2),universal_class),
c_0_431,
[final] ).
cnf(c_0_547,plain,
subclass(successor_relation,cross_product(universal_class,universal_class)),
c_0_432,
[final] ).
cnf(c_0_548,plain,
subclass(element_relation,cross_product(universal_class,universal_class)),
c_0_433,
[final] ).
cnf(c_0_549,plain,
( unordered_pair(X1,X2) = singleton(X2)
| member(X1,universal_class) ),
c_0_434,
[final] ).
cnf(c_0_550,plain,
( unordered_pair(X1,X2) = singleton(X1)
| member(X2,universal_class) ),
c_0_435,
[final] ).
cnf(c_0_551,plain,
( one_to_one(X1)
| ~ function(X1)
| ~ function(inverse(X1)) ),
c_0_436,
[final] ).
cnf(c_0_552,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
c_0_437,
[final] ).
cnf(c_0_553,plain,
union(X1,singleton(X1)) = successor(X1),
c_0_438,
[final] ).
cnf(c_0_554,plain,
( intersection(X1,regular(X1)) = null_class
| X1 = null_class ),
c_0_439,
[final] ).
cnf(c_0_555,plain,
( member(regular(X1),X1)
| X1 = null_class ),
c_0_440,
[final] ).
cnf(c_0_556,plain,
( X1 = null_class
| ~ subclass(X1,null_class) ),
c_0_441,
[final] ).
cnf(c_0_557,plain,
~ member(X1,null_class),
c_0_442,
[final] ).
cnf(c_0_558,plain,
( subclass(omega,X1)
| ~ inductive(X1) ),
c_0_443,
[final] ).
cnf(c_0_559,plain,
( member(null_class,X1)
| ~ inductive(X1) ),
c_0_444,
[final] ).
cnf(c_0_560,plain,
unordered_pair(X1,X1) = singleton(X1),
c_0_445,
[final] ).
cnf(c_0_561,plain,
( subclass(X1,X2)
| X2 != X1 ),
c_0_446,
[final] ).
cnf(c_0_562,plain,
( subclass(X1,X2)
| X1 != X2 ),
c_0_447,
[final] ).
cnf(c_0_563,plain,
( function(inverse(X1))
| ~ one_to_one(X1) ),
c_0_448,
[final] ).
cnf(c_0_564,plain,
intersection(inverse(subset_relation),subset_relation) = identity_relation,
c_0_449,
[final] ).
cnf(c_0_565,plain,
subclass(X1,X1),
c_0_450,
[final] ).
cnf(c_0_566,plain,
domain_of(inverse(X1)) = range_of(X1),
c_0_451,
[final] ).
cnf(c_0_567,plain,
subclass(null_class,X1),
c_0_452,
[final] ).
cnf(c_0_568,plain,
subclass(X1,universal_class),
c_0_453,
[final] ).
cnf(c_0_569,plain,
( function(X1)
| ~ operation(X1) ),
c_0_454,
[final] ).
cnf(c_0_570,plain,
( function(X1)
| ~ one_to_one(X1) ),
c_0_455,
[final] ).
cnf(c_0_571,plain,
member(null_class,universal_class),
c_0_456,
[final] ).
cnf(c_0_572,plain,
member(omega,universal_class),
c_0_457,
[final] ).
cnf(c_0_573,plain,
function(choice),
c_0_458,
[final] ).
cnf(c_0_574,plain,
inductive(omega),
c_0_459,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_460_0,axiom,
( homomorphism(X1,X2,X3)
| apply(X3,ordered_pair(apply(X1,not_homomorphism1(X1,X2,X3)),apply(X1,not_homomorphism2(X1,X2,X3)))) != apply(X1,apply(X2,ordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism2(X1,X2,X3))))
| ~ compatible(X1,X2,X3)
| ~ operation(X3)
| ~ operation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_460]) ).
cnf(c_0_460_1,axiom,
( apply(X3,ordered_pair(apply(X1,not_homomorphism1(X1,X2,X3)),apply(X1,not_homomorphism2(X1,X2,X3)))) != apply(X1,apply(X2,ordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism2(X1,X2,X3))))
| homomorphism(X1,X2,X3)
| ~ compatible(X1,X2,X3)
| ~ operation(X3)
| ~ operation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_460]) ).
cnf(c_0_460_2,axiom,
( ~ compatible(X1,X2,X3)
| apply(X3,ordered_pair(apply(X1,not_homomorphism1(X1,X2,X3)),apply(X1,not_homomorphism2(X1,X2,X3)))) != apply(X1,apply(X2,ordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism2(X1,X2,X3))))
| homomorphism(X1,X2,X3)
| ~ operation(X3)
| ~ operation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_460]) ).
cnf(c_0_460_3,axiom,
( ~ operation(X3)
| ~ compatible(X1,X2,X3)
| apply(X3,ordered_pair(apply(X1,not_homomorphism1(X1,X2,X3)),apply(X1,not_homomorphism2(X1,X2,X3)))) != apply(X1,apply(X2,ordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism2(X1,X2,X3))))
| homomorphism(X1,X2,X3)
| ~ operation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_460]) ).
cnf(c_0_460_4,axiom,
( ~ operation(X2)
| ~ operation(X3)
| ~ compatible(X1,X2,X3)
| apply(X3,ordered_pair(apply(X1,not_homomorphism1(X1,X2,X3)),apply(X1,not_homomorphism2(X1,X2,X3)))) != apply(X1,apply(X2,ordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism2(X1,X2,X3))))
| homomorphism(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_460]) ).
cnf(c_0_461_0,axiom,
( homomorphism(X1,X2,X3)
| member(ordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism2(X1,X2,X3)),domain_of(X2))
| ~ compatible(X1,X2,X3)
| ~ operation(X3)
| ~ operation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_461]) ).
cnf(c_0_461_1,axiom,
( member(ordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism2(X1,X2,X3)),domain_of(X2))
| homomorphism(X1,X2,X3)
| ~ compatible(X1,X2,X3)
| ~ operation(X3)
| ~ operation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_461]) ).
cnf(c_0_461_2,axiom,
( ~ compatible(X1,X2,X3)
| member(ordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism2(X1,X2,X3)),domain_of(X2))
| homomorphism(X1,X2,X3)
| ~ operation(X3)
| ~ operation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_461]) ).
cnf(c_0_461_3,axiom,
( ~ operation(X3)
| ~ compatible(X1,X2,X3)
| member(ordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism2(X1,X2,X3)),domain_of(X2))
| homomorphism(X1,X2,X3)
| ~ operation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_461]) ).
cnf(c_0_461_4,axiom,
( ~ operation(X2)
| ~ operation(X3)
| ~ compatible(X1,X2,X3)
| member(ordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism2(X1,X2,X3)),domain_of(X2))
| homomorphism(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_461]) ).
cnf(c_0_462_0,axiom,
( member(ordered_pair(ordered_pair(X1,X2),X3),flip(X4))
| ~ member(ordered_pair(ordered_pair(X1,X2),X3),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ member(ordered_pair(ordered_pair(X2,X1),X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_462]) ).
cnf(c_0_462_1,axiom,
( ~ member(ordered_pair(ordered_pair(X1,X2),X3),cross_product(cross_product(universal_class,universal_class),universal_class))
| member(ordered_pair(ordered_pair(X1,X2),X3),flip(X4))
| ~ member(ordered_pair(ordered_pair(X2,X1),X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_462]) ).
cnf(c_0_462_2,axiom,
( ~ member(ordered_pair(ordered_pair(X2,X1),X3),X4)
| ~ member(ordered_pair(ordered_pair(X1,X2),X3),cross_product(cross_product(universal_class,universal_class),universal_class))
| member(ordered_pair(ordered_pair(X1,X2),X3),flip(X4)) ),
inference(literals_permutation,[status(thm)],[c_0_462]) ).
cnf(c_0_463_0,axiom,
( member(ordered_pair(ordered_pair(X1,X2),X3),rotate(X4))
| ~ member(ordered_pair(ordered_pair(X1,X2),X3),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ member(ordered_pair(ordered_pair(X2,X3),X1),X4) ),
inference(literals_permutation,[status(thm)],[c_0_463]) ).
cnf(c_0_463_1,axiom,
( ~ member(ordered_pair(ordered_pair(X1,X2),X3),cross_product(cross_product(universal_class,universal_class),universal_class))
| member(ordered_pair(ordered_pair(X1,X2),X3),rotate(X4))
| ~ member(ordered_pair(ordered_pair(X2,X3),X1),X4) ),
inference(literals_permutation,[status(thm)],[c_0_463]) ).
cnf(c_0_463_2,axiom,
( ~ member(ordered_pair(ordered_pair(X2,X3),X1),X4)
| ~ member(ordered_pair(ordered_pair(X1,X2),X3),cross_product(cross_product(universal_class,universal_class),universal_class))
| member(ordered_pair(ordered_pair(X1,X2),X3),rotate(X4)) ),
inference(literals_permutation,[status(thm)],[c_0_463]) ).
cnf(c_0_464_0,axiom,
( apply(X1,ordered_pair(apply(X2,X3),apply(X2,X4))) = apply(X2,apply(X5,ordered_pair(X3,X4)))
| ~ member(ordered_pair(X3,X4),domain_of(X5))
| ~ homomorphism(X2,X5,X1) ),
inference(literals_permutation,[status(thm)],[c_0_464]) ).
cnf(c_0_464_1,axiom,
( ~ member(ordered_pair(X3,X4),domain_of(X5))
| apply(X1,ordered_pair(apply(X2,X3),apply(X2,X4))) = apply(X2,apply(X5,ordered_pair(X3,X4)))
| ~ homomorphism(X2,X5,X1) ),
inference(literals_permutation,[status(thm)],[c_0_464]) ).
cnf(c_0_464_2,axiom,
( ~ homomorphism(X2,X5,X1)
| ~ member(ordered_pair(X3,X4),domain_of(X5))
| apply(X1,ordered_pair(apply(X2,X3),apply(X2,X4))) = apply(X2,apply(X5,ordered_pair(X3,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_464]) ).
cnf(c_0_465_0,axiom,
( member(ordered_pair(X1,X2),compose(X3,X4))
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
| ~ member(X2,image(X3,image(X4,singleton(X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_465]) ).
cnf(c_0_465_1,axiom,
( ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
| member(ordered_pair(X1,X2),compose(X3,X4))
| ~ member(X2,image(X3,image(X4,singleton(X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_465]) ).
cnf(c_0_465_2,axiom,
( ~ member(X2,image(X3,image(X4,singleton(X1))))
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
| member(ordered_pair(X1,X2),compose(X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_465]) ).
cnf(c_0_469_0,axiom,
( member(ordered_pair(ordered_pair(X1,X2),X3),X4)
| ~ member(ordered_pair(ordered_pair(X2,X1),X3),flip(X4)) ),
inference(literals_permutation,[status(thm)],[c_0_469]) ).
cnf(c_0_469_1,axiom,
( ~ member(ordered_pair(ordered_pair(X2,X1),X3),flip(X4))
| member(ordered_pair(ordered_pair(X1,X2),X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_469]) ).
cnf(c_0_470_0,axiom,
( member(ordered_pair(ordered_pair(X1,X2),X3),X4)
| ~ member(ordered_pair(ordered_pair(X3,X1),X2),rotate(X4)) ),
inference(literals_permutation,[status(thm)],[c_0_470]) ).
cnf(c_0_470_1,axiom,
( ~ member(ordered_pair(ordered_pair(X3,X1),X2),rotate(X4))
| member(ordered_pair(ordered_pair(X1,X2),X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_470]) ).
cnf(c_0_471_0,axiom,
( member(X1,image(X2,image(X3,singleton(X4))))
| ~ member(ordered_pair(X4,X1),compose(X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_471]) ).
cnf(c_0_471_1,axiom,
( ~ member(ordered_pair(X4,X1),compose(X2,X3))
| member(X1,image(X2,image(X3,singleton(X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_471]) ).
cnf(c_0_473_0,axiom,
( operation(X1)
| ~ subclass(range_of(X1),domain_of(domain_of(X1)))
| cross_product(domain_of(domain_of(X1)),domain_of(domain_of(X1))) != domain_of(X1)
| ~ function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_473]) ).
cnf(c_0_473_1,axiom,
( ~ subclass(range_of(X1),domain_of(domain_of(X1)))
| operation(X1)
| cross_product(domain_of(domain_of(X1)),domain_of(domain_of(X1))) != domain_of(X1)
| ~ function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_473]) ).
cnf(c_0_473_2,axiom,
( cross_product(domain_of(domain_of(X1)),domain_of(domain_of(X1))) != domain_of(X1)
| ~ subclass(range_of(X1),domain_of(domain_of(X1)))
| operation(X1)
| ~ function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_473]) ).
cnf(c_0_473_3,axiom,
( ~ function(X1)
| cross_product(domain_of(domain_of(X1)),domain_of(domain_of(X1))) != domain_of(X1)
| ~ subclass(range_of(X1),domain_of(domain_of(X1)))
| operation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_473]) ).
cnf(c_0_474_0,axiom,
( member(ordered_pair(X1,X2),element_relation)
| ~ member(X1,X2)
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class)) ),
inference(literals_permutation,[status(thm)],[c_0_474]) ).
cnf(c_0_474_1,axiom,
( ~ member(X1,X2)
| member(ordered_pair(X1,X2),element_relation)
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class)) ),
inference(literals_permutation,[status(thm)],[c_0_474]) ).
cnf(c_0_474_2,axiom,
( ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
| ~ member(X1,X2)
| member(ordered_pair(X1,X2),element_relation) ),
inference(literals_permutation,[status(thm)],[c_0_474]) ).
cnf(c_0_475_0,axiom,
( compatible(X1,X2,X3)
| ~ subclass(range_of(X1),domain_of(domain_of(X3)))
| domain_of(domain_of(X2)) != domain_of(X1)
| ~ function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_475]) ).
cnf(c_0_475_1,axiom,
( ~ subclass(range_of(X1),domain_of(domain_of(X3)))
| compatible(X1,X2,X3)
| domain_of(domain_of(X2)) != domain_of(X1)
| ~ function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_475]) ).
cnf(c_0_475_2,axiom,
( domain_of(domain_of(X2)) != domain_of(X1)
| ~ subclass(range_of(X1),domain_of(domain_of(X3)))
| compatible(X1,X2,X3)
| ~ function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_475]) ).
cnf(c_0_475_3,axiom,
( ~ function(X1)
| domain_of(domain_of(X2)) != domain_of(X1)
| ~ subclass(range_of(X1),domain_of(domain_of(X3)))
| compatible(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_475]) ).
cnf(c_0_476_0,axiom,
( member(X1,unordered_pair(X2,X1))
| ~ member(ordered_pair(X2,X1),cross_product(X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_476]) ).
cnf(c_0_476_1,axiom,
( ~ member(ordered_pair(X2,X1),cross_product(X3,X4))
| member(X1,unordered_pair(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_476]) ).
cnf(c_0_477_0,axiom,
( member(X1,unordered_pair(X1,X2))
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_477]) ).
cnf(c_0_477_1,axiom,
( ~ member(ordered_pair(X1,X2),cross_product(X3,X4))
| member(X1,unordered_pair(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_477]) ).
cnf(c_0_478_0,axiom,
( member(ordered_pair(X1,X2),successor_relation)
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
| successor(X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_478]) ).
cnf(c_0_478_1,axiom,
( ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
| member(ordered_pair(X1,X2),successor_relation)
| successor(X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_478]) ).
cnf(c_0_478_2,axiom,
( successor(X1) != X2
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
| member(ordered_pair(X1,X2),successor_relation) ),
inference(literals_permutation,[status(thm)],[c_0_478]) ).
cnf(c_0_479_0,axiom,
( X1 = X2
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
| unordered_pair(X1,X3) != unordered_pair(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_479]) ).
cnf(c_0_479_1,axiom,
( ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
| X1 = X2
| unordered_pair(X1,X3) != unordered_pair(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_479]) ).
cnf(c_0_479_2,axiom,
( unordered_pair(X1,X3) != unordered_pair(X2,X3)
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_479]) ).
cnf(c_0_480_0,axiom,
( X1 = X2
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
| unordered_pair(X3,X1) != unordered_pair(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_480]) ).
cnf(c_0_480_1,axiom,
( ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
| X1 = X2
| unordered_pair(X3,X1) != unordered_pair(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_480]) ).
cnf(c_0_480_2,axiom,
( unordered_pair(X3,X1) != unordered_pair(X3,X2)
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_480]) ).
cnf(c_0_481_0,axiom,
( compatible(X1,X2,X3)
| ~ homomorphism(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_481]) ).
cnf(c_0_481_1,axiom,
( ~ homomorphism(X1,X2,X3)
| compatible(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_481]) ).
cnf(c_0_482_0,axiom,
( function(X1)
| ~ subclass(compose(X1,inverse(X1)),identity_relation)
| ~ subclass(X1,cross_product(universal_class,universal_class)) ),
inference(literals_permutation,[status(thm)],[c_0_482]) ).
cnf(c_0_482_1,axiom,
( ~ subclass(compose(X1,inverse(X1)),identity_relation)
| function(X1)
| ~ subclass(X1,cross_product(universal_class,universal_class)) ),
inference(literals_permutation,[status(thm)],[c_0_482]) ).
cnf(c_0_482_2,axiom,
( ~ subclass(X1,cross_product(universal_class,universal_class))
| ~ subclass(compose(X1,inverse(X1)),identity_relation)
| function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_482]) ).
cnf(c_0_483_0,axiom,
( X1 = X2
| ~ member(not_subclass_element(X2,X1),X1)
| ~ member(not_subclass_element(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_483]) ).
cnf(c_0_483_1,axiom,
( ~ member(not_subclass_element(X2,X1),X1)
| X1 = X2
| ~ member(not_subclass_element(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_483]) ).
cnf(c_0_483_2,axiom,
( ~ member(not_subclass_element(X1,X2),X2)
| ~ member(not_subclass_element(X2,X1),X1)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_483]) ).
cnf(c_0_484_0,axiom,
( ~ member(X1,domain_of(X2))
| restrict(X2,singleton(X1),universal_class) != null_class ),
inference(literals_permutation,[status(thm)],[c_0_484]) ).
cnf(c_0_484_1,axiom,
( restrict(X2,singleton(X1),universal_class) != null_class
| ~ member(X1,domain_of(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_484]) ).
cnf(c_0_485_0,axiom,
( subclass(range_of(X1),domain_of(domain_of(X2)))
| ~ compatible(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_485]) ).
cnf(c_0_485_1,axiom,
( ~ compatible(X1,X3,X2)
| subclass(range_of(X1),domain_of(domain_of(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_485]) ).
cnf(c_0_487_0,axiom,
( member(X1,X2)
| ~ member(ordered_pair(X3,X1),cross_product(X4,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_487]) ).
cnf(c_0_487_1,axiom,
( ~ member(ordered_pair(X3,X1),cross_product(X4,X2))
| member(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_487]) ).
cnf(c_0_488_0,axiom,
( member(X1,X2)
| ~ member(ordered_pair(X1,X3),cross_product(X2,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_488]) ).
cnf(c_0_488_1,axiom,
( ~ member(ordered_pair(X1,X3),cross_product(X2,X4))
| member(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_488]) ).
cnf(c_0_489_0,axiom,
( member(X1,universal_class)
| ~ member(ordered_pair(X2,X1),cross_product(X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_489]) ).
cnf(c_0_489_1,axiom,
( ~ member(ordered_pair(X2,X1),cross_product(X3,X4))
| member(X1,universal_class) ),
inference(literals_permutation,[status(thm)],[c_0_489]) ).
cnf(c_0_490_0,axiom,
( member(X1,universal_class)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_490]) ).
cnf(c_0_490_1,axiom,
( ~ member(ordered_pair(X1,X2),cross_product(X3,X4))
| member(X1,universal_class) ),
inference(literals_permutation,[status(thm)],[c_0_490]) ).
cnf(c_0_491_0,axiom,
( member(ordered_pair(X1,X2),cross_product(X3,X4))
| ~ member(X2,X4)
| ~ member(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_491]) ).
cnf(c_0_491_1,axiom,
( ~ member(X2,X4)
| member(ordered_pair(X1,X2),cross_product(X3,X4))
| ~ member(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_491]) ).
cnf(c_0_491_2,axiom,
( ~ member(X1,X3)
| ~ member(X2,X4)
| member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_491]) ).
cnf(c_0_493_0,axiom,
( member(not_subclass_element(X1,X2),X1)
| X1 = X2
| ~ member(not_subclass_element(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_493]) ).
cnf(c_0_493_1,axiom,
( X1 = X2
| member(not_subclass_element(X1,X2),X1)
| ~ member(not_subclass_element(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_493]) ).
cnf(c_0_493_2,axiom,
( ~ member(not_subclass_element(X2,X1),X1)
| X1 = X2
| member(not_subclass_element(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_493]) ).
cnf(c_0_494_0,axiom,
( member(not_subclass_element(X1,X2),X1)
| X2 = X1
| ~ member(not_subclass_element(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_494]) ).
cnf(c_0_494_1,axiom,
( X2 = X1
| member(not_subclass_element(X1,X2),X1)
| ~ member(not_subclass_element(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_494]) ).
cnf(c_0_494_2,axiom,
( ~ member(not_subclass_element(X2,X1),X1)
| X2 = X1
| member(not_subclass_element(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_494]) ).
cnf(c_0_495_0,axiom,
( domain_of(domain_of(X1)) = domain_of(X2)
| ~ compatible(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_495]) ).
cnf(c_0_495_1,axiom,
( ~ compatible(X2,X1,X3)
| domain_of(domain_of(X1)) = domain_of(X2) ),
inference(literals_permutation,[status(thm)],[c_0_495]) ).
cnf(c_0_496_0,axiom,
( member(X1,domain_of(X2))
| restrict(X2,singleton(X1),universal_class) = null_class
| ~ member(X1,universal_class) ),
inference(literals_permutation,[status(thm)],[c_0_496]) ).
cnf(c_0_496_1,axiom,
( restrict(X2,singleton(X1),universal_class) = null_class
| member(X1,domain_of(X2))
| ~ member(X1,universal_class) ),
inference(literals_permutation,[status(thm)],[c_0_496]) ).
cnf(c_0_496_2,axiom,
( ~ member(X1,universal_class)
| restrict(X2,singleton(X1),universal_class) = null_class
| member(X1,domain_of(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_496]) ).
cnf(c_0_500_0,axiom,
( ordered_pair(first(X1),second(X1)) = X1
| ~ member(X1,cross_product(X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_500]) ).
cnf(c_0_500_1,axiom,
( ~ member(X1,cross_product(X2,X3))
| ordered_pair(first(X1),second(X1)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_500]) ).
cnf(c_0_501_0,axiom,
( operation(X1)
| ~ homomorphism(X2,X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_501]) ).
cnf(c_0_501_1,axiom,
( ~ homomorphism(X2,X3,X1)
| operation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_501]) ).
cnf(c_0_502_0,axiom,
( operation(X1)
| ~ homomorphism(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_502]) ).
cnf(c_0_502_1,axiom,
( ~ homomorphism(X2,X1,X3)
| operation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_502]) ).
cnf(c_0_503_0,axiom,
( function(X1)
| ~ compatible(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_503]) ).
cnf(c_0_503_1,axiom,
( ~ compatible(X1,X2,X3)
| function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_503]) ).
cnf(c_0_504_0,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X3)
| ~ member(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_504]) ).
cnf(c_0_504_1,axiom,
( ~ member(X1,X3)
| member(X1,intersection(X2,X3))
| ~ member(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_504]) ).
cnf(c_0_504_2,axiom,
( ~ member(X1,X2)
| ~ member(X1,X3)
| member(X1,intersection(X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_504]) ).
cnf(c_0_505_0,axiom,
( single_valued_class(X1)
| ~ subclass(compose(X1,inverse(X1)),identity_relation) ),
inference(literals_permutation,[status(thm)],[c_0_505]) ).
cnf(c_0_505_1,axiom,
( ~ subclass(compose(X1,inverse(X1)),identity_relation)
| single_valued_class(X1) ),
inference(literals_permutation,[status(thm)],[c_0_505]) ).
cnf(c_0_506_0,axiom,
( inductive(X1)
| ~ subclass(image(successor_relation,X1),X1)
| ~ member(null_class,X1) ),
inference(literals_permutation,[status(thm)],[c_0_506]) ).
cnf(c_0_506_1,axiom,
( ~ subclass(image(successor_relation,X1),X1)
| inductive(X1)
| ~ member(null_class,X1) ),
inference(literals_permutation,[status(thm)],[c_0_506]) ).
cnf(c_0_506_2,axiom,
( ~ member(null_class,X1)
| ~ subclass(image(successor_relation,X1),X1)
| inductive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_506]) ).
cnf(c_0_507_0,axiom,
( member(not_subclass_element(X1,X2),X1)
| member(not_subclass_element(X2,X1),X2)
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_507]) ).
cnf(c_0_507_1,axiom,
( member(not_subclass_element(X2,X1),X2)
| member(not_subclass_element(X1,X2),X1)
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_507]) ).
cnf(c_0_507_2,axiom,
( X2 = X1
| member(not_subclass_element(X2,X1),X2)
| member(not_subclass_element(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_507]) ).
cnf(c_0_511_0,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_511]) ).
cnf(c_0_511_1,axiom,
( ~ member(X1,intersection(X3,X2))
| member(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_511]) ).
cnf(c_0_512_0,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_512]) ).
cnf(c_0_512_1,axiom,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_512]) ).
cnf(c_0_513_0,axiom,
( subclass(X1,X2)
| ~ member(not_subclass_element(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_513]) ).
cnf(c_0_513_1,axiom,
( ~ member(not_subclass_element(X1,X2),X2)
| subclass(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_513]) ).
cnf(c_0_514_0,axiom,
( member(X1,X2)
| ~ member(ordered_pair(X1,X2),element_relation) ),
inference(literals_permutation,[status(thm)],[c_0_514]) ).
cnf(c_0_514_1,axiom,
( ~ member(ordered_pair(X1,X2),element_relation)
| member(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_514]) ).
cnf(c_0_517_0,axiom,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_517]) ).
cnf(c_0_517_1,axiom,
( X1 = X3
| X1 = X2
| ~ member(X1,unordered_pair(X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_517]) ).
cnf(c_0_517_2,axiom,
( ~ member(X1,unordered_pair(X3,X2))
| X1 = X3
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_517]) ).
cnf(c_0_518_0,axiom,
( member(image(X1,X2),universal_class)
| ~ member(X2,universal_class)
| ~ function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_518]) ).
cnf(c_0_518_1,axiom,
( ~ member(X2,universal_class)
| member(image(X1,X2),universal_class)
| ~ function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_518]) ).
cnf(c_0_518_2,axiom,
( ~ function(X1)
| ~ member(X2,universal_class)
| member(image(X1,X2),universal_class) ),
inference(literals_permutation,[status(thm)],[c_0_518]) ).
cnf(c_0_519_0,axiom,
( successor(X1) = X2
| ~ member(ordered_pair(X1,X2),successor_relation) ),
inference(literals_permutation,[status(thm)],[c_0_519]) ).
cnf(c_0_519_1,axiom,
( ~ member(ordered_pair(X1,X2),successor_relation)
| successor(X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_519]) ).
cnf(c_0_520_0,axiom,
( cross_product(domain_of(domain_of(X1)),domain_of(domain_of(X1))) = domain_of(X1)
| ~ operation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_520]) ).
cnf(c_0_520_1,axiom,
( ~ operation(X1)
| cross_product(domain_of(domain_of(X1)),domain_of(domain_of(X1))) = domain_of(X1) ),
inference(literals_permutation,[status(thm)],[c_0_520]) ).
cnf(c_0_521_0,axiom,
( member(X1,unordered_pair(X2,X1))
| ~ member(X1,universal_class) ),
inference(literals_permutation,[status(thm)],[c_0_521]) ).
cnf(c_0_521_1,axiom,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_521]) ).
cnf(c_0_522_0,axiom,
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
inference(literals_permutation,[status(thm)],[c_0_522]) ).
cnf(c_0_522_1,axiom,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_522]) ).
cnf(c_0_526_0,axiom,
( subclass(X1,X2)
| ~ subclass(X3,X2)
| ~ subclass(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_526]) ).
cnf(c_0_526_1,axiom,
( ~ subclass(X3,X2)
| subclass(X1,X2)
| ~ subclass(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_526]) ).
cnf(c_0_526_2,axiom,
( ~ subclass(X1,X3)
| ~ subclass(X3,X2)
| subclass(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_526]) ).
cnf(c_0_527_0,axiom,
( member(X1,X2)
| ~ member(X1,X3)
| ~ subclass(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_527]) ).
cnf(c_0_527_1,axiom,
( ~ member(X1,X3)
| member(X1,X2)
| ~ subclass(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_527]) ).
cnf(c_0_527_2,axiom,
( ~ subclass(X3,X2)
| ~ member(X1,X3)
| member(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_527]) ).
cnf(c_0_528_0,axiom,
( member(apply(choice,X1),X1)
| X1 = null_class
| ~ member(X1,universal_class) ),
inference(literals_permutation,[status(thm)],[c_0_528]) ).
cnf(c_0_528_1,axiom,
( X1 = null_class
| member(apply(choice,X1),X1)
| ~ member(X1,universal_class) ),
inference(literals_permutation,[status(thm)],[c_0_528]) ).
cnf(c_0_528_2,axiom,
( ~ member(X1,universal_class)
| X1 = null_class
| member(apply(choice,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_528]) ).
cnf(c_0_529_0,axiom,
( subclass(compose(X1,inverse(X1)),identity_relation)
| ~ function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_529]) ).
cnf(c_0_529_1,axiom,
( ~ function(X1)
| subclass(compose(X1,inverse(X1)),identity_relation) ),
inference(literals_permutation,[status(thm)],[c_0_529]) ).
cnf(c_0_530_0,axiom,
( subclass(compose(X1,inverse(X1)),identity_relation)
| ~ single_valued_class(X1) ),
inference(literals_permutation,[status(thm)],[c_0_530]) ).
cnf(c_0_530_1,axiom,
( ~ single_valued_class(X1)
| subclass(compose(X1,inverse(X1)),identity_relation) ),
inference(literals_permutation,[status(thm)],[c_0_530]) ).
cnf(c_0_532_0,axiom,
( member(X1,X2)
| member(X1,complement(X2))
| ~ member(X1,universal_class) ),
inference(literals_permutation,[status(thm)],[c_0_532]) ).
cnf(c_0_532_1,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ member(X1,universal_class) ),
inference(literals_permutation,[status(thm)],[c_0_532]) ).
cnf(c_0_532_2,axiom,
( ~ member(X1,universal_class)
| member(X1,complement(X2))
| member(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_532]) ).
cnf(c_0_533_0,axiom,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_533]) ).
cnf(c_0_533_1,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_533]) ).
cnf(c_0_534_0,axiom,
( subclass(X1,X2)
| member(not_subclass_element(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_534]) ).
cnf(c_0_534_1,axiom,
( member(not_subclass_element(X1,X2),X1)
| subclass(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_534]) ).
cnf(c_0_535_0,axiom,
( X1 = X2
| ~ subclass(X2,X1)
| ~ subclass(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_535]) ).
cnf(c_0_535_1,axiom,
( ~ subclass(X2,X1)
| X1 = X2
| ~ subclass(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_535]) ).
cnf(c_0_535_2,axiom,
( ~ subclass(X1,X2)
| ~ subclass(X2,X1)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_535]) ).
cnf(c_0_538_0,axiom,
( subclass(range_of(X1),domain_of(domain_of(X1)))
| ~ operation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_538]) ).
cnf(c_0_538_1,axiom,
( ~ operation(X1)
| subclass(range_of(X1),domain_of(domain_of(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_538]) ).
cnf(c_0_539_0,axiom,
( subclass(image(successor_relation,X1),X1)
| ~ inductive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_539]) ).
cnf(c_0_539_1,axiom,
( ~ inductive(X1)
| subclass(image(successor_relation,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_539]) ).
cnf(c_0_541_0,axiom,
( subclass(X1,cross_product(universal_class,universal_class))
| ~ function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_541]) ).
cnf(c_0_541_1,axiom,
( ~ function(X1)
| subclass(X1,cross_product(universal_class,universal_class)) ),
inference(literals_permutation,[status(thm)],[c_0_541]) ).
cnf(c_0_542_0,axiom,
( member(X1,universal_class)
| member(X2,universal_class)
| unordered_pair(X2,X1) = null_class ),
inference(literals_permutation,[status(thm)],[c_0_542]) ).
cnf(c_0_542_1,axiom,
( member(X2,universal_class)
| member(X1,universal_class)
| unordered_pair(X2,X1) = null_class ),
inference(literals_permutation,[status(thm)],[c_0_542]) ).
cnf(c_0_542_2,axiom,
( unordered_pair(X2,X1) = null_class
| member(X2,universal_class)
| member(X1,universal_class) ),
inference(literals_permutation,[status(thm)],[c_0_542]) ).
cnf(c_0_543_0,axiom,
( member(power_class(X1),universal_class)
| ~ member(X1,universal_class) ),
inference(literals_permutation,[status(thm)],[c_0_543]) ).
cnf(c_0_543_1,axiom,
( ~ member(X1,universal_class)
| member(power_class(X1),universal_class) ),
inference(literals_permutation,[status(thm)],[c_0_543]) ).
cnf(c_0_544_0,axiom,
( member(sum_class(X1),universal_class)
| ~ member(X1,universal_class) ),
inference(literals_permutation,[status(thm)],[c_0_544]) ).
cnf(c_0_544_1,axiom,
( ~ member(X1,universal_class)
| member(sum_class(X1),universal_class) ),
inference(literals_permutation,[status(thm)],[c_0_544]) ).
cnf(c_0_545_0,axiom,
( member(not_subclass_element(X1,null_class),X1)
| X1 = null_class ),
inference(literals_permutation,[status(thm)],[c_0_545]) ).
cnf(c_0_545_1,axiom,
( X1 = null_class
| member(not_subclass_element(X1,null_class),X1) ),
inference(literals_permutation,[status(thm)],[c_0_545]) ).
cnf(c_0_549_0,axiom,
( unordered_pair(X1,X2) = singleton(X2)
| member(X1,universal_class) ),
inference(literals_permutation,[status(thm)],[c_0_549]) ).
cnf(c_0_549_1,axiom,
( member(X1,universal_class)
| unordered_pair(X1,X2) = singleton(X2) ),
inference(literals_permutation,[status(thm)],[c_0_549]) ).
cnf(c_0_550_0,axiom,
( unordered_pair(X1,X2) = singleton(X1)
| member(X2,universal_class) ),
inference(literals_permutation,[status(thm)],[c_0_550]) ).
cnf(c_0_550_1,axiom,
( member(X2,universal_class)
| unordered_pair(X1,X2) = singleton(X1) ),
inference(literals_permutation,[status(thm)],[c_0_550]) ).
cnf(c_0_551_0,axiom,
( one_to_one(X1)
| ~ function(X1)
| ~ function(inverse(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_551]) ).
cnf(c_0_551_1,axiom,
( ~ function(X1)
| one_to_one(X1)
| ~ function(inverse(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_551]) ).
cnf(c_0_551_2,axiom,
( ~ function(inverse(X1))
| ~ function(X1)
| one_to_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_551]) ).
cnf(c_0_554_0,axiom,
( intersection(X1,regular(X1)) = null_class
| X1 = null_class ),
inference(literals_permutation,[status(thm)],[c_0_554]) ).
cnf(c_0_554_1,axiom,
( X1 = null_class
| intersection(X1,regular(X1)) = null_class ),
inference(literals_permutation,[status(thm)],[c_0_554]) ).
cnf(c_0_555_0,axiom,
( member(regular(X1),X1)
| X1 = null_class ),
inference(literals_permutation,[status(thm)],[c_0_555]) ).
cnf(c_0_555_1,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_555]) ).
cnf(c_0_556_0,axiom,
( X1 = null_class
| ~ subclass(X1,null_class) ),
inference(literals_permutation,[status(thm)],[c_0_556]) ).
cnf(c_0_556_1,axiom,
( ~ subclass(X1,null_class)
| X1 = null_class ),
inference(literals_permutation,[status(thm)],[c_0_556]) ).
cnf(c_0_558_0,axiom,
( subclass(omega,X1)
| ~ inductive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_558]) ).
cnf(c_0_558_1,axiom,
( ~ inductive(X1)
| subclass(omega,X1) ),
inference(literals_permutation,[status(thm)],[c_0_558]) ).
cnf(c_0_559_0,axiom,
( member(null_class,X1)
| ~ inductive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_559]) ).
cnf(c_0_559_1,axiom,
( ~ inductive(X1)
| member(null_class,X1) ),
inference(literals_permutation,[status(thm)],[c_0_559]) ).
cnf(c_0_561_0,axiom,
( subclass(X1,X2)
| X2 != X1 ),
inference(literals_permutation,[status(thm)],[c_0_561]) ).
cnf(c_0_561_1,axiom,
( X2 != X1
| subclass(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_561]) ).
cnf(c_0_562_0,axiom,
( subclass(X1,X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_562]) ).
cnf(c_0_562_1,axiom,
( X1 != X2
| subclass(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_562]) ).
cnf(c_0_563_0,axiom,
( function(inverse(X1))
| ~ one_to_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_563]) ).
cnf(c_0_563_1,axiom,
( ~ one_to_one(X1)
| function(inverse(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_563]) ).
cnf(c_0_569_0,axiom,
( function(X1)
| ~ operation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_569]) ).
cnf(c_0_569_1,axiom,
( ~ operation(X1)
| function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_569]) ).
cnf(c_0_570_0,axiom,
( function(X1)
| ~ one_to_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_570]) ).
cnf(c_0_570_1,axiom,
( ~ one_to_one(X1)
| function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_570]) ).
cnf(c_0_510_0,axiom,
~ member(X1,intersection(complement(X2),X2)),
inference(literals_permutation,[status(thm)],[c_0_510]) ).
cnf(c_0_557_0,axiom,
~ member(X1,null_class),
inference(literals_permutation,[status(thm)],[c_0_557]) ).
cnf(c_0_466_0,axiom,
second(not_subclass_element(restrict(X1,singleton(X2),X3),null_class)) = range(X1,X2,X3),
inference(literals_permutation,[status(thm)],[c_0_466]) ).
cnf(c_0_467_0,axiom,
first(not_subclass_element(restrict(X1,X2,singleton(X3)),null_class)) = domain(X1,X2,X3),
inference(literals_permutation,[status(thm)],[c_0_467]) ).
cnf(c_0_468_0,axiom,
intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))) = subset_relation,
inference(literals_permutation,[status(thm)],[c_0_468]) ).
cnf(c_0_472_0,axiom,
intersection(complement(intersection(X1,X2)),complement(intersection(complement(X1),complement(X2)))) = symmetric_difference(X1,X2),
inference(literals_permutation,[status(thm)],[c_0_472]) ).
cnf(c_0_486_0,axiom,
range_of(restrict(X1,X2,universal_class)) = image(X1,X2),
inference(literals_permutation,[status(thm)],[c_0_486]) ).
cnf(c_0_492_0,axiom,
domain_of(restrict(element_relation,universal_class,X1)) = sum_class(X1),
inference(literals_permutation,[status(thm)],[c_0_492]) ).
cnf(c_0_497_0,axiom,
intersection(domain_of(X1),diagonalise(compose(inverse(element_relation),X1))) = cantor(X1),
inference(literals_permutation,[status(thm)],[c_0_497]) ).
cnf(c_0_498_0,axiom,
intersection(cross_product(X1,X2),X3) = restrict(X3,X1,X2),
inference(literals_permutation,[status(thm)],[c_0_498]) ).
cnf(c_0_499_0,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
inference(literals_permutation,[status(thm)],[c_0_499]) ).
cnf(c_0_508_0,axiom,
subclass(flip(X1),cross_product(cross_product(universal_class,universal_class),universal_class)),
inference(literals_permutation,[status(thm)],[c_0_508]) ).
cnf(c_0_509_0,axiom,
subclass(rotate(X1),cross_product(cross_product(universal_class,universal_class),universal_class)),
inference(literals_permutation,[status(thm)],[c_0_509]) ).
cnf(c_0_515_0,axiom,
unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
inference(literals_permutation,[status(thm)],[c_0_515]) ).
cnf(c_0_516_0,axiom,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
inference(literals_permutation,[status(thm)],[c_0_516]) ).
cnf(c_0_523_0,axiom,
complement(domain_of(intersection(X1,identity_relation))) = diagonalise(X1),
inference(literals_permutation,[status(thm)],[c_0_523]) ).
cnf(c_0_524_0,axiom,
subclass(compose(X1,X2),cross_product(universal_class,universal_class)),
inference(literals_permutation,[status(thm)],[c_0_524]) ).
cnf(c_0_525_0,axiom,
domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
inference(literals_permutation,[status(thm)],[c_0_525]) ).
cnf(c_0_531_0,axiom,
sum_class(image(X1,singleton(X2))) = apply(X1,X2),
inference(literals_permutation,[status(thm)],[c_0_531]) ).
cnf(c_0_536_0,axiom,
subclass(singleton(X1),unordered_pair(X2,X1)),
inference(literals_permutation,[status(thm)],[c_0_536]) ).
cnf(c_0_537_0,axiom,
subclass(singleton(X1),unordered_pair(X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_537]) ).
cnf(c_0_540_0,axiom,
complement(image(element_relation,complement(X1))) = power_class(X1),
inference(literals_permutation,[status(thm)],[c_0_540]) ).
cnf(c_0_546_0,axiom,
member(unordered_pair(X1,X2),universal_class),
inference(literals_permutation,[status(thm)],[c_0_546]) ).
cnf(c_0_547_0,axiom,
subclass(successor_relation,cross_product(universal_class,universal_class)),
inference(literals_permutation,[status(thm)],[c_0_547]) ).
cnf(c_0_548_0,axiom,
subclass(element_relation,cross_product(universal_class,universal_class)),
inference(literals_permutation,[status(thm)],[c_0_548]) ).
cnf(c_0_552_0,axiom,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(literals_permutation,[status(thm)],[c_0_552]) ).
cnf(c_0_553_0,axiom,
union(X1,singleton(X1)) = successor(X1),
inference(literals_permutation,[status(thm)],[c_0_553]) ).
cnf(c_0_560_0,axiom,
unordered_pair(X1,X1) = singleton(X1),
inference(literals_permutation,[status(thm)],[c_0_560]) ).
cnf(c_0_564_0,axiom,
intersection(inverse(subset_relation),subset_relation) = identity_relation,
inference(literals_permutation,[status(thm)],[c_0_564]) ).
cnf(c_0_565_0,axiom,
subclass(X1,X1),
inference(literals_permutation,[status(thm)],[c_0_565]) ).
cnf(c_0_566_0,axiom,
domain_of(inverse(X1)) = range_of(X1),
inference(literals_permutation,[status(thm)],[c_0_566]) ).
cnf(c_0_567_0,axiom,
subclass(null_class,X1),
inference(literals_permutation,[status(thm)],[c_0_567]) ).
cnf(c_0_568_0,axiom,
subclass(X1,universal_class),
inference(literals_permutation,[status(thm)],[c_0_568]) ).
cnf(c_0_571_0,axiom,
member(null_class,universal_class),
inference(literals_permutation,[status(thm)],[c_0_571]) ).
cnf(c_0_572_0,axiom,
member(omega,universal_class),
inference(literals_permutation,[status(thm)],[c_0_572]) ).
cnf(c_0_573_0,axiom,
function(choice),
inference(literals_permutation,[status(thm)],[c_0_573]) ).
cnf(c_0_574_0,axiom,
inductive(omega),
inference(literals_permutation,[status(thm)],[c_0_574]) ).
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_001,negated_conjecture,
unordered_pair(x,y) = null_class,
file('<stdin>',prove_corollary_to_unordered_pair_axiom2_2) ).
fof(c_0_1_002,negated_conjecture,
member(y,universal_class),
file('<stdin>',prove_corollary_to_unordered_pair_axiom2_1) ).
fof(c_0_2_003,negated_conjecture,
unordered_pair(x,y) = null_class,
c_0_0 ).
fof(c_0_3_004,negated_conjecture,
member(y,universal_class),
c_0_1 ).
fof(c_0_4_005,negated_conjecture,
unordered_pair(x,y) = null_class,
c_0_2 ).
fof(c_0_5_006,negated_conjecture,
member(y,universal_class),
c_0_3 ).
cnf(c_0_6_007,negated_conjecture,
unordered_pair(x,y) = null_class,
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7_008,negated_conjecture,
member(y,universal_class),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8_009,negated_conjecture,
unordered_pair(x,y) = null_class,
c_0_6,
[final] ).
cnf(c_0_9_010,negated_conjecture,
member(y,universal_class),
c_0_7,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_229,negated_conjecture,
unordered_pair(x,y) = null_class,
file('/export/starexec/sandbox/tmp/iprover_modulo_37633d.p',c_0_8) ).
cnf(c_321,negated_conjecture,
unordered_pair(x,y) = null_class,
inference(copy,[status(esa)],[c_229]) ).
cnf(c_329,negated_conjecture,
unordered_pair(x,y) = null_class,
inference(copy,[status(esa)],[c_321]) ).
cnf(c_332,negated_conjecture,
unordered_pair(x,y) = null_class,
inference(copy,[status(esa)],[c_329]) ).
cnf(c_333,negated_conjecture,
unordered_pair(x,y) = null_class,
inference(copy,[status(esa)],[c_332]) ).
cnf(c_1005,negated_conjecture,
unordered_pair(x,y) = null_class,
inference(copy,[status(esa)],[c_333]) ).
cnf(c_43,plain,
( subclass(X0,X1)
| X0 != X1 ),
file('/export/starexec/sandbox/tmp/iprover_modulo_37633d.p',c_0_562_1) ).
cnf(c_633,plain,
( subclass(X0,X1)
| X0 != X1 ),
inference(copy,[status(esa)],[c_43]) ).
cnf(c_1035,plain,
subclass(unordered_pair(x,y),null_class),
inference(resolution,[status(thm)],[c_1005,c_633]) ).
cnf(c_1036,plain,
subclass(unordered_pair(x,y),null_class),
inference(rewriting,[status(thm)],[c_1035]) ).
cnf(c_96,plain,
( member(X0,X1)
| ~ member(X0,X2)
| ~ subclass(X2,X1) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_37633d.p',c_0_527_2) ).
cnf(c_739,plain,
( member(X0,X1)
| ~ member(X0,X2)
| ~ subclass(X2,X1) ),
inference(copy,[status(esa)],[c_96]) ).
cnf(c_1119,plain,
( member(X0,null_class)
| ~ member(X0,unordered_pair(x,y)) ),
inference(resolution,[status(thm)],[c_1036,c_739]) ).
cnf(c_1120,plain,
( member(X0,null_class)
| ~ member(X0,unordered_pair(x,y)) ),
inference(rewriting,[status(thm)],[c_1119]) ).
cnf(c_35,plain,
~ member(X0,null_class),
file('/export/starexec/sandbox/tmp/iprover_modulo_37633d.p',c_0_557_0) ).
cnf(c_617,plain,
~ member(X0,null_class),
inference(copy,[status(esa)],[c_35]) ).
cnf(c_1403,plain,
~ member(X0,unordered_pair(x,y)),
inference(forward_subsumption_resolution,[status(thm)],[c_1120,c_617]) ).
cnf(c_1404,plain,
~ member(X0,unordered_pair(x,y)),
inference(rewriting,[status(thm)],[c_1403]) ).
cnf(c_230,negated_conjecture,
member(y,universal_class),
file('/export/starexec/sandbox/tmp/iprover_modulo_37633d.p',c_0_9) ).
cnf(c_323,negated_conjecture,
member(y,universal_class),
inference(copy,[status(esa)],[c_230]) ).
cnf(c_330,negated_conjecture,
member(y,universal_class),
inference(copy,[status(esa)],[c_323]) ).
cnf(c_331,negated_conjecture,
member(y,universal_class),
inference(copy,[status(esa)],[c_330]) ).
cnf(c_334,negated_conjecture,
member(y,universal_class),
inference(copy,[status(esa)],[c_331]) ).
cnf(c_1007,plain,
member(y,universal_class),
inference(copy,[status(esa)],[c_334]) ).
cnf(c_104,plain,
( member(X0,unordered_pair(X1,X0))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_37633d.p',c_0_521_1) ).
cnf(c_755,plain,
( member(X0,unordered_pair(X1,X0))
| ~ member(X0,universal_class) ),
inference(copy,[status(esa)],[c_104]) ).
cnf(c_756,plain,
( ~ member(X0,universal_class)
| member(X0,unordered_pair(X1,X0)) ),
inference(rewriting,[status(thm)],[c_755]) ).
cnf(c_1012,plain,
member(y,unordered_pair(X0,y)),
inference(resolution,[status(thm)],[c_1007,c_756]) ).
cnf(c_1023,plain,
member(y,unordered_pair(X0,y)),
inference(rewriting,[status(thm)],[c_1012]) ).
cnf(c_1412,plain,
$false,
inference(resolution,[status(thm)],[c_1404,c_1023]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET074-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.12/0.14 % Command : iprover_modulo %s %d
% 0.14/0.35 % Computer : n014.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sun Jul 10 11:43:05 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % Running in mono-core mode
% 0.22/0.44 % Orienting using strategy Equiv(ClausalAll)
% 0.22/0.44 % Orientation found
% 0.22/0.44 % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format " --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_0c1ff8.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_37633d.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_055f30 | grep -v "SZS"
% 0.22/0.46
% 0.22/0.46 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.22/0.46
% 0.22/0.46 %
% 0.22/0.46 % ------ iProver source info
% 0.22/0.46
% 0.22/0.46 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.22/0.46 % git: non_committed_changes: true
% 0.22/0.46 % git: last_make_outside_of_git: true
% 0.22/0.46
% 0.22/0.46 %
% 0.22/0.46 % ------ Input Options
% 0.22/0.46
% 0.22/0.46 % --out_options all
% 0.22/0.46 % --tptp_safe_out true
% 0.22/0.46 % --problem_path ""
% 0.22/0.46 % --include_path ""
% 0.22/0.46 % --clausifier .//eprover
% 0.22/0.46 % --clausifier_options --tstp-format
% 0.22/0.46 % --stdin false
% 0.22/0.46 % --dbg_backtrace false
% 0.22/0.46 % --dbg_dump_prop_clauses false
% 0.22/0.46 % --dbg_dump_prop_clauses_file -
% 0.22/0.46 % --dbg_out_stat false
% 0.22/0.46
% 0.22/0.46 % ------ General Options
% 0.22/0.46
% 0.22/0.46 % --fof false
% 0.22/0.46 % --time_out_real 150.
% 0.22/0.46 % --time_out_prep_mult 0.2
% 0.22/0.46 % --time_out_virtual -1.
% 0.22/0.46 % --schedule none
% 0.22/0.46 % --ground_splitting input
% 0.22/0.46 % --splitting_nvd 16
% 0.22/0.46 % --non_eq_to_eq false
% 0.22/0.46 % --prep_gs_sim true
% 0.22/0.46 % --prep_unflatten false
% 0.22/0.46 % --prep_res_sim true
% 0.22/0.46 % --prep_upred true
% 0.22/0.46 % --res_sim_input true
% 0.22/0.46 % --clause_weak_htbl true
% 0.22/0.46 % --gc_record_bc_elim false
% 0.22/0.46 % --symbol_type_check false
% 0.22/0.46 % --clausify_out false
% 0.22/0.46 % --large_theory_mode false
% 0.22/0.46 % --prep_sem_filter none
% 0.22/0.46 % --prep_sem_filter_out false
% 0.22/0.46 % --preprocessed_out false
% 0.22/0.46 % --sub_typing false
% 0.22/0.46 % --brand_transform false
% 0.22/0.46 % --pure_diseq_elim true
% 0.22/0.46 % --min_unsat_core false
% 0.22/0.46 % --pred_elim true
% 0.22/0.46 % --add_important_lit false
% 0.22/0.46 % --soft_assumptions false
% 0.22/0.46 % --reset_solvers false
% 0.22/0.46 % --bc_imp_inh []
% 0.22/0.46 % --conj_cone_tolerance 1.5
% 0.22/0.46 % --prolific_symb_bound 500
% 0.22/0.46 % --lt_threshold 2000
% 0.22/0.46
% 0.22/0.46 % ------ SAT Options
% 0.22/0.46
% 0.22/0.46 % --sat_mode false
% 0.22/0.46 % --sat_fm_restart_options ""
% 0.22/0.46 % --sat_gr_def false
% 0.22/0.46 % --sat_epr_types true
% 0.22/0.46 % --sat_non_cyclic_types false
% 0.22/0.46 % --sat_finite_models false
% 0.22/0.46 % --sat_fm_lemmas false
% 0.22/0.46 % --sat_fm_prep false
% 0.22/0.46 % --sat_fm_uc_incr true
% 0.22/0.46 % --sat_out_model small
% 0.22/0.46 % --sat_out_clauses false
% 0.22/0.46
% 0.22/0.46 % ------ QBF Options
% 0.22/0.46
% 0.22/0.46 % --qbf_mode false
% 0.22/0.46 % --qbf_elim_univ true
% 0.22/0.46 % --qbf_sk_in true
% 0.22/0.46 % --qbf_pred_elim true
% 0.22/0.46 % --qbf_split 32
% 0.22/0.46
% 0.22/0.46 % ------ BMC1 Options
% 0.22/0.46
% 0.22/0.46 % --bmc1_incremental false
% 0.22/0.46 % --bmc1_axioms reachable_all
% 0.22/0.46 % --bmc1_min_bound 0
% 0.22/0.46 % --bmc1_max_bound -1
% 0.22/0.46 % --bmc1_max_bound_default -1
% 0.22/0.46 % --bmc1_symbol_reachability true
% 0.22/0.46 % --bmc1_property_lemmas false
% 0.22/0.46 % --bmc1_k_induction false
% 0.22/0.46 % --bmc1_non_equiv_states false
% 0.22/0.46 % --bmc1_deadlock false
% 0.22/0.46 % --bmc1_ucm false
% 0.22/0.46 % --bmc1_add_unsat_core none
% 0.22/0.46 % --bmc1_unsat_core_children false
% 0.22/0.46 % --bmc1_unsat_core_extrapolate_axioms false
% 0.22/0.46 % --bmc1_out_stat full
% 0.22/0.46 % --bmc1_ground_init false
% 0.22/0.46 % --bmc1_pre_inst_next_state false
% 0.22/0.46 % --bmc1_pre_inst_state false
% 0.22/0.46 % --bmc1_pre_inst_reach_state false
% 0.22/0.46 % --bmc1_out_unsat_core false
% 0.22/0.46 % --bmc1_aig_witness_out false
% 0.22/0.46 % --bmc1_verbose false
% 0.22/0.46 % --bmc1_dump_clauses_tptp false
% 0.92/1.29 % --bmc1_dump_unsat_core_tptp false
% 0.92/1.29 % --bmc1_dump_file -
% 0.92/1.29 % --bmc1_ucm_expand_uc_limit 128
% 0.92/1.29 % --bmc1_ucm_n_expand_iterations 6
% 0.92/1.29 % --bmc1_ucm_extend_mode 1
% 0.92/1.29 % --bmc1_ucm_init_mode 2
% 0.92/1.29 % --bmc1_ucm_cone_mode none
% 0.92/1.29 % --bmc1_ucm_reduced_relation_type 0
% 0.92/1.29 % --bmc1_ucm_relax_model 4
% 0.92/1.29 % --bmc1_ucm_full_tr_after_sat true
% 0.92/1.29 % --bmc1_ucm_expand_neg_assumptions false
% 0.92/1.29 % --bmc1_ucm_layered_model none
% 0.92/1.29 % --bmc1_ucm_max_lemma_size 10
% 0.92/1.29
% 0.92/1.29 % ------ AIG Options
% 0.92/1.29
% 0.92/1.29 % --aig_mode false
% 0.92/1.29
% 0.92/1.29 % ------ Instantiation Options
% 0.92/1.29
% 0.92/1.29 % --instantiation_flag true
% 0.92/1.29 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.92/1.29 % --inst_solver_per_active 750
% 0.92/1.29 % --inst_solver_calls_frac 0.5
% 0.92/1.29 % --inst_passive_queue_type priority_queues
% 0.92/1.29 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.92/1.29 % --inst_passive_queues_freq [25;2]
% 0.92/1.29 % --inst_dismatching true
% 0.92/1.29 % --inst_eager_unprocessed_to_passive true
% 0.92/1.29 % --inst_prop_sim_given true
% 0.92/1.29 % --inst_prop_sim_new false
% 0.92/1.29 % --inst_orphan_elimination true
% 0.92/1.29 % --inst_learning_loop_flag true
% 0.92/1.29 % --inst_learning_start 3000
% 0.92/1.29 % --inst_learning_factor 2
% 0.92/1.29 % --inst_start_prop_sim_after_learn 3
% 0.92/1.29 % --inst_sel_renew solver
% 0.92/1.29 % --inst_lit_activity_flag true
% 0.92/1.29 % --inst_out_proof true
% 0.92/1.29
% 0.92/1.29 % ------ Resolution Options
% 0.92/1.29
% 0.92/1.29 % --resolution_flag true
% 0.92/1.29 % --res_lit_sel kbo_max
% 0.92/1.29 % --res_to_prop_solver none
% 0.92/1.29 % --res_prop_simpl_new false
% 0.92/1.29 % --res_prop_simpl_given false
% 0.92/1.29 % --res_passive_queue_type priority_queues
% 0.92/1.29 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.92/1.29 % --res_passive_queues_freq [15;5]
% 0.92/1.29 % --res_forward_subs full
% 0.92/1.29 % --res_backward_subs full
% 0.92/1.29 % --res_forward_subs_resolution true
% 0.92/1.29 % --res_backward_subs_resolution true
% 0.92/1.29 % --res_orphan_elimination false
% 0.92/1.29 % --res_time_limit 1000.
% 0.92/1.29 % --res_out_proof true
% 0.92/1.29 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_0c1ff8.s
% 0.92/1.29 % --modulo true
% 0.92/1.29
% 0.92/1.29 % ------ Combination Options
% 0.92/1.29
% 0.92/1.29 % --comb_res_mult 1000
% 0.92/1.29 % --comb_inst_mult 300
% 0.92/1.29 % ------
% 0.92/1.29
% 0.92/1.29 % ------ Parsing...% successful
% 0.92/1.29
% 0.92/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e pe_s pe_e snvd_s sp: 0 0s snvd_e %
% 0.92/1.29
% 0.92/1.29 % ------ Proving...
% 0.92/1.29 % ------ Problem Properties
% 0.92/1.29
% 0.92/1.29 %
% 0.92/1.29 % EPR false
% 0.92/1.29 % Horn false
% 0.92/1.29 % Has equality true
% 0.92/1.29
% 0.92/1.29 % % ------ Input Options Time Limit: Unbounded
% 0.92/1.29
% 0.92/1.29
% 0.92/1.29 Compiling...
% 0.92/1.29 Loading plugin: done.
% 0.92/1.29 Compiling...
% 0.92/1.29 Loading plugin: done.
% 0.92/1.29 Compiling...
% 0.92/1.29 Loading plugin: done.
% 0.92/1.29 Compiling...
% 0.92/1.29 Loading plugin: done.
% 0.92/1.29 Compiling...
% 0.92/1.29 Loading plugin: done.
% 0.92/1.29 Compiling...
% 0.92/1.29 Loading plugin: done.
% 0.92/1.29 % % ------ Current options:
% 0.92/1.29
% 0.92/1.29 % ------ Input Options
% 0.92/1.29
% 0.92/1.29 % --out_options all
% 0.92/1.29 % --tptp_safe_out true
% 0.92/1.29 % --problem_path ""
% 0.92/1.29 % --include_path ""
% 0.92/1.29 % --clausifier .//eprover
% 0.92/1.29 % --clausifier_options --tstp-format
% 0.92/1.29 % --stdin false
% 0.92/1.29 % --dbg_backtrace false
% 0.92/1.29 % --dbg_dump_prop_clauses false
% 0.92/1.29 % --dbg_dump_prop_clauses_file -
% 0.92/1.29 % --dbg_out_stat false
% 0.92/1.29
% 0.92/1.29 % ------ General Options
% 0.92/1.29
% 0.92/1.29 % --fof false
% 0.92/1.29 % --time_out_real 150.
% 0.92/1.29 % --time_out_prep_mult 0.2
% 0.92/1.29 % --time_out_virtual -1.
% 0.92/1.29 % --schedule none
% 0.92/1.29 % --ground_splitting input
% 0.92/1.29 % --splitting_nvd 16
% 0.92/1.29 % --non_eq_to_eq false
% 0.92/1.29 % --prep_gs_sim true
% 0.92/1.29 % --prep_unflatten false
% 0.92/1.29 % --prep_res_sim true
% 0.92/1.29 % --prep_upred true
% 0.92/1.29 % --res_sim_input true
% 0.92/1.29 % --clause_weak_htbl true
% 0.92/1.29 % --gc_record_bc_elim false
% 0.92/1.29 % --symbol_type_check false
% 0.92/1.29 % --clausify_out false
% 0.92/1.29 % --large_theory_mode false
% 0.92/1.29 % --prep_sem_filter none
% 0.92/1.29 % --prep_sem_filter_out false
% 0.92/1.29 % --preprocessed_out false
% 0.92/1.29 % --sub_typing false
% 0.92/1.29 % --brand_transform false
% 0.92/1.29 % --pure_diseq_elim true
% 0.92/1.29 % --min_unsat_core false
% 0.92/1.29 % --pred_elim true
% 0.92/1.29 % --add_important_lit false
% 0.92/1.29 % --soft_assumptions false
% 0.92/1.29 % --reset_solvers false
% 0.92/1.29 % --bc_imp_inh []
% 0.92/1.29 % --conj_cone_tolerance 1.5
% 0.92/1.29 % --prolific_symb_bound 500
% 0.92/1.29 % --lt_threshold 2000
% 0.92/1.29
% 0.92/1.29 % ------ SAT Options
% 0.92/1.29
% 0.92/1.29 % --sat_mode false
% 0.92/1.29 % --sat_fm_restart_options ""
% 0.92/1.29 % --sat_gr_def false
% 0.92/1.29 % --sat_epr_types true
% 0.92/1.29 % --sat_non_cyclic_types false
% 0.92/1.29 % --sat_finite_models false
% 0.92/1.29 % --sat_fm_lemmas false
% 0.92/1.29 % --sat_fm_prep false
% 0.92/1.29 % --sat_fm_uc_incr true
% 0.92/1.29 % --sat_out_model small
% 0.92/1.29 % --sat_out_clauses false
% 0.92/1.29
% 0.92/1.29 % ------ QBF Options
% 0.92/1.29
% 0.92/1.29 % --qbf_mode false
% 0.92/1.29 % --qbf_elim_univ true
% 0.92/1.29 % --qbf_sk_in true
% 0.92/1.29 % --qbf_pred_elim true
% 0.92/1.29 % --qbf_split 32
% 0.92/1.29
% 0.92/1.29 % ------ BMC1 Options
% 0.92/1.29
% 0.92/1.29 % --bmc1_incremental false
% 0.92/1.29 % --bmc1_axioms reachable_all
% 0.92/1.29 % --bmc1_min_bound 0
% 0.92/1.29 % --bmc1_max_bound -1
% 0.92/1.29 % --bmc1_max_bound_default -1
% 0.92/1.29 % --bmc1_symbol_reachability true
% 0.92/1.29 % --bmc1_property_lemmas false
% 0.92/1.29 % --bmc1_k_induction false
% 0.92/1.29 % --bmc1_non_equiv_states false
% 0.92/1.29 % --bmc1_deadlock false
% 0.92/1.29 % --bmc1_ucm false
% 0.92/1.29 % --bmc1_add_unsat_core none
% 0.92/1.29 % --bmc1_unsat_core_children false
% 0.92/1.29 % --bmc1_unsat_core_extrapolate_axioms false
% 0.92/1.29 % --bmc1_out_stat full
% 0.92/1.29 % --bmc1_ground_init false
% 0.92/1.29 % --bmc1_pre_inst_next_state false
% 0.92/1.29 % --bmc1_pre_inst_state false
% 0.92/1.29 % --bmc1_pre_inst_reach_state false
% 0.92/1.29 % --bmc1_out_unsat_core false
% 0.92/1.29 % --bmc1_aig_witness_out false
% 0.92/1.29 % --bmc1_verbose false
% 0.92/1.29 % --bmc1_dump_clauses_tptp false
% 0.92/1.29 % --bmc1_dump_unsat_core_tptp false
% 0.92/1.29 % --bmc1_dump_file -
% 0.92/1.29 % --bmc1_ucm_expand_uc_limit 128
% 0.92/1.29 % --bmc1_ucm_n_expand_iterations 6
% 0.92/1.29 % --bmc1_ucm_extend_mode 1
% 0.92/1.29 % --bmc1_ucm_init_mode 2
% 0.92/1.29 % --bmc1_ucm_cone_mode none
% 0.92/1.29 % --bmc1_ucm_reduced_relation_type 0
% 0.92/1.29 % --bmc1_ucm_relax_model 4
% 0.92/1.29 % --bmc1_ucm_full_tr_after_sat true
% 0.92/1.29 % --bmc1_ucm_expand_neg_assumptions false
% 0.92/1.29 % --bmc1_ucm_layered_model none
% 0.92/1.29 % --bmc1_ucm_max_lemma_size 10
% 0.92/1.29
% 0.92/1.29 % ------ AIG Options
% 0.92/1.29
% 0.92/1.29 % --aig_mode false
% 0.92/1.29
% 0.92/1.29 % ------ Instantiation Options
% 0.92/1.29
% 0.92/1.29 % --instantiation_flag true
% 0.92/1.29 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.92/1.29 % --inst_solver_per_active 750
% 0.92/1.29 % --inst_solver_calls_frac 0.5
% 0.92/1.29 % --inst_passive_queue_type priority_queues
% 0.92/1.29 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 150.23/150.46 % --inst_passive_queues_freq [25;2]
% 150.23/150.46 % --inst_dismatching true
% 150.23/150.46 % --inst_eager_unprocessed_to_passive true
% 150.23/150.46 % --inst_prop_sim_given true
% 150.23/150.46 % --inst_prop_sim_new false
% 150.23/150.46 % --inst_orphan_elimination true
% 150.23/150.46 % --inst_learning_loop_flag true
% 150.23/150.46 % --inst_learning_start 3000
% 150.23/150.46 % --inst_learning_factor 2
% 150.23/150.46 % --inst_start_prop_sim_after_learn 3
% 150.23/150.46 % --inst_sel_renew solver
% 150.23/150.46 % --inst_lit_activity_flag true
% 150.23/150.46 % --inst_out_proof true
% 150.23/150.46
% 150.23/150.46 % ------ Resolution Options
% 150.23/150.46
% 150.23/150.46 % --resolution_flag true
% 150.23/150.46 % --res_lit_sel kbo_max
% 150.23/150.46 % --res_to_prop_solver none
% 150.23/150.46 % --res_prop_simpl_new false
% 150.23/150.46 % --res_prop_simpl_given false
% 150.23/150.46 % --res_passive_queue_type priority_queues
% 150.23/150.46 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 150.23/150.46 % --res_passive_queues_freq [15;5]
% 150.23/150.46 % --res_forward_subs full
% 150.23/150.46 % --res_backward_subs full
% 150.23/150.46 % --res_forward_subs_resolution true
% 150.23/150.46 % --res_backward_subs_resolution true
% 150.23/150.46 % --res_orphan_elimination false
% 150.23/150.46 % --res_time_limit 1000.
% 150.23/150.46 % --res_out_proof true
% 150.23/150.46 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_0c1ff8.s
% 150.23/150.46 % --modulo true
% 150.23/150.46
% 150.23/150.46 % ------ Combination Options
% 150.23/150.46
% 150.23/150.46 % --comb_res_mult 1000
% 150.23/150.46 % --comb_inst_mult 300
% 150.23/150.46 % ------
% 150.23/150.46
% 150.23/150.46
% 150.23/150.46
% 150.23/150.46 % ------ Proving...
% 150.23/150.46 %
% 150.23/150.46
% 150.23/150.46
% 150.23/150.46 % Time Out Real
% 150.23/150.46
% 150.23/150.46 % ------ Statistics
% 150.23/150.46
% 150.23/150.46 % ------ General
% 150.23/150.46
% 150.23/150.46 % num_of_input_clauses: 231
% 150.23/150.46 % num_of_input_neg_conjectures: 2
% 150.23/150.46 % num_of_splits: 0
% 150.23/150.46 % num_of_split_atoms: 0
% 150.23/150.46 % num_of_sem_filtered_clauses: 0
% 150.23/150.46 % num_of_subtypes: 0
% 150.23/150.46 % monotx_restored_types: 0
% 150.23/150.46 % sat_num_of_epr_types: 0
% 150.23/150.46 % sat_num_of_non_cyclic_types: 0
% 150.23/150.46 % sat_guarded_non_collapsed_types: 0
% 150.23/150.46 % is_epr: 0
% 150.23/150.46 % is_horn: 0
% 150.23/150.46 % has_eq: 1
% 150.23/150.46 % num_pure_diseq_elim: 0
% 150.23/150.46 % simp_replaced_by: 0
% 150.23/150.46 % res_preprocessed: 4
% 150.23/150.46 % prep_upred: 0
% 150.23/150.46 % prep_unflattend: 0
% 150.23/150.46 % pred_elim_cands: 0
% 150.23/150.46 % pred_elim: 0
% 150.23/150.46 % pred_elim_cl: 0
% 150.23/150.46 % pred_elim_cycles: 0
% 150.23/150.46 % forced_gc_time: 0
% 150.23/150.46 % gc_basic_clause_elim: 0
% 150.23/150.46 % parsing_time: 0.01
% 150.23/150.46 % sem_filter_time: 0.
% 150.23/150.46 % pred_elim_time: 0.
% 150.23/150.46 % out_proof_time: 0.
% 150.23/150.46 % monotx_time: 0.
% 150.23/150.46 % subtype_inf_time: 0.
% 150.23/150.46 % unif_index_cands_time: 2.64
% 150.23/150.46 % unif_index_add_time: 0.129
% 150.23/150.46 % total_time: 150.018
% 150.23/150.46 % num_of_symbols: 74
% 150.23/150.46 % num_of_terms: 649128
% 150.23/150.46
% 150.23/150.46 % ------ Propositional Solver
% 150.23/150.46
% 150.23/150.46 % prop_solver_calls: 36
% 150.23/150.46 % prop_fast_solver_calls: 6
% 150.23/150.46 % prop_num_of_clauses: 40429
% 150.23/150.46 % prop_preprocess_simplified: 55930
% 150.23/150.46 % prop_fo_subsumed: 0
% 150.23/150.46 % prop_solver_time: 0.03
% 150.23/150.46 % prop_fast_solver_time: 0.
% 150.23/150.46 % prop_unsat_core_time: 0.
% 150.23/150.46
% 150.23/150.46 % ------ QBF
% 150.23/150.46
% 150.23/150.46 % qbf_q_res: 0
% 150.23/150.46 % qbf_num_tautologies: 0
% 150.23/150.46 % qbf_prep_cycles: 0
% 150.23/150.46
% 150.23/150.46 % ------ BMC1
% 150.23/150.46
% 150.23/150.46 % bmc1_current_bound: -1
% 150.23/150.46 % bmc1_last_solved_bound: -1
% 150.23/150.46 % bmc1_unsat_core_size: -1
% 150.23/150.46 % bmc1_unsat_core_parents_size: -1
% 150.23/150.46 % bmc1_merge_next_fun: 0
% 150.23/150.46 % bmc1_unsat_core_clauses_time: 0.
% 150.23/150.46
% 150.23/150.46 % ------ Instantiation
% 150.23/150.47
% 150.23/150.47 % inst_num_of_clauses: 20987
% 150.23/150.47 % inst_num_in_passive: 15144
% 150.23/150.47 % inst_num_in_active: 4961
% 150.23/150.47 % inst_num_in_unprocessed: 876
% 150.23/150.47 % inst_num_of_loops: 5699
% 150.23/150.47 % inst_num_of_learning_restarts: 1
% 150.23/150.47 % inst_num_moves_active_passive: 731
% 150.23/150.47 % inst_lit_activity: 2769
% 150.23/150.47 % inst_lit_activity_moves: 3
% 150.23/150.47 % inst_num_tautologies: 6
% 150.23/150.47 % inst_num_prop_implied: 0
% 150.23/150.47 % inst_num_existing_simplified: 0
% 150.23/150.47 % inst_num_eq_res_simplified: 0
% 150.23/150.47 % inst_num_child_elim: 0
% 150.23/150.47 % inst_num_of_dismatching_blockings: 130998
% 150.23/150.47 % inst_num_of_non_proper_insts: 39427
% 150.23/150.47 % inst_num_of_duplicates: 36507
% 150.23/150.47 % inst_inst_num_from_inst_to_res: 0
% 150.23/150.47 % inst_dismatching_checking_time: 2.979
% 150.23/150.47
% 150.23/150.47 % ------ Resolution
% 150.23/150.47
% 150.23/150.47 % res_num_of_clauses: 189043
% 150.23/150.47 % res_num_in_passive: 175543
% 150.23/150.47 % res_num_in_active: 14361
% 150.23/150.47 % res_num_of_loops: 29246
% 150.23/150.47 % res_forward_subset_subsumed: 2331447
% 150.23/150.47 % res_backward_subset_subsumed: 1235
% 150.23/150.47 % res_forward_subsumed: 14960
% 150.23/150.47 % res_backward_subsumed: 24
% 150.23/150.47 % res_forward_subsumption_resolution: 448
% 150.23/150.47 % res_backward_subsumption_resolution: 0
% 150.23/150.47 % res_clause_to_clause_subsumption: 179514
% 150.23/150.47 % res_orphan_elimination: 0
% 150.23/150.47 % res_tautology_del: 0
% 150.23/150.47 % res_num_eq_res_simplified: 0
% 150.23/150.47 % res_num_sel_changes: 0
% 150.23/150.47 % res_moves_from_active_to_pass: 0
% 150.23/150.47
% 150.23/150.47 % Status Unknown
% 150.30/150.53 % Orienting using strategy ClausalAll
% 150.30/150.53 % Orientation found
% 150.30/150.53 % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format " --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_0c1ff8.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_37633d.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_d918fe | grep -v "SZS"
% 150.30/150.54
% 150.30/150.54 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 150.30/150.54
% 150.30/150.54 %
% 150.30/150.54 % ------ iProver source info
% 150.30/150.54
% 150.30/150.54 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 150.30/150.54 % git: non_committed_changes: true
% 150.30/150.54 % git: last_make_outside_of_git: true
% 150.30/150.54
% 150.30/150.54 %
% 150.30/150.54 % ------ Input Options
% 150.30/150.54
% 150.30/150.54 % --out_options all
% 150.30/150.54 % --tptp_safe_out true
% 150.30/150.54 % --problem_path ""
% 150.30/150.54 % --include_path ""
% 150.30/150.54 % --clausifier .//eprover
% 150.30/150.54 % --clausifier_options --tstp-format
% 150.30/150.54 % --stdin false
% 150.30/150.54 % --dbg_backtrace false
% 150.30/150.54 % --dbg_dump_prop_clauses false
% 150.30/150.54 % --dbg_dump_prop_clauses_file -
% 150.30/150.54 % --dbg_out_stat false
% 150.30/150.54
% 150.30/150.54 % ------ General Options
% 150.30/150.54
% 150.30/150.54 % --fof false
% 150.30/150.54 % --time_out_real 150.
% 150.30/150.54 % --time_out_prep_mult 0.2
% 150.30/150.54 % --time_out_virtual -1.
% 150.30/150.54 % --schedule none
% 150.30/150.54 % --ground_splitting input
% 150.30/150.54 % --splitting_nvd 16
% 150.30/150.54 % --non_eq_to_eq false
% 150.30/150.54 % --prep_gs_sim true
% 150.30/150.54 % --prep_unflatten false
% 150.30/150.54 % --prep_res_sim true
% 150.30/150.54 % --prep_upred true
% 150.30/150.54 % --res_sim_input true
% 150.30/150.54 % --clause_weak_htbl true
% 150.30/150.54 % --gc_record_bc_elim false
% 150.30/150.54 % --symbol_type_check false
% 150.30/150.54 % --clausify_out false
% 150.30/150.54 % --large_theory_mode false
% 150.30/150.54 % --prep_sem_filter none
% 150.30/150.54 % --prep_sem_filter_out false
% 150.30/150.54 % --preprocessed_out false
% 150.30/150.54 % --sub_typing false
% 150.30/150.54 % --brand_transform false
% 150.30/150.54 % --pure_diseq_elim true
% 150.30/150.54 % --min_unsat_core false
% 150.30/150.54 % --pred_elim true
% 150.30/150.54 % --add_important_lit false
% 150.30/150.54 % --soft_assumptions false
% 150.30/150.55 % --reset_solvers false
% 150.30/150.55 % --bc_imp_inh []
% 150.30/150.55 % --conj_cone_tolerance 1.5
% 150.30/150.55 % --prolific_symb_bound 500
% 150.30/150.55 % --lt_threshold 2000
% 150.30/150.55
% 150.30/150.55 % ------ SAT Options
% 150.30/150.55
% 150.30/150.55 % --sat_mode false
% 150.30/150.55 % --sat_fm_restart_options ""
% 150.30/150.55 % --sat_gr_def false
% 150.30/150.55 % --sat_epr_types true
% 150.30/150.55 % --sat_non_cyclic_types false
% 150.30/150.55 % --sat_finite_models false
% 150.30/150.55 % --sat_fm_lemmas false
% 150.30/150.55 % --sat_fm_prep false
% 150.30/150.55 % --sat_fm_uc_incr true
% 150.30/150.55 % --sat_out_model small
% 150.30/150.55 % --sat_out_clauses false
% 150.30/150.55
% 150.30/150.55 % ------ QBF Options
% 150.30/150.55
% 150.30/150.55 % --qbf_mode false
% 150.30/150.55 % --qbf_elim_univ true
% 150.30/150.55 % --qbf_sk_in true
% 150.30/150.55 % --qbf_pred_elim true
% 150.30/150.55 % --qbf_split 32
% 150.30/150.55
% 150.30/150.55 % ------ BMC1 Options
% 150.30/150.55
% 150.30/150.55 % --bmc1_incremental false
% 150.30/150.55 % --bmc1_axioms reachable_all
% 150.30/150.55 % --bmc1_min_bound 0
% 150.30/150.55 % --bmc1_max_bound -1
% 150.30/150.55 % --bmc1_max_bound_default -1
% 150.30/150.55 % --bmc1_symbol_reachability true
% 150.30/150.55 % --bmc1_property_lemmas false
% 150.30/150.55 % --bmc1_k_induction false
% 150.30/150.55 % --bmc1_non_equiv_states false
% 150.30/150.55 % --bmc1_deadlock false
% 150.30/150.55 % --bmc1_ucm false
% 150.30/150.55 % --bmc1_add_unsat_core none
% 150.30/150.55 % --bmc1_unsat_core_children false
% 150.30/150.55 % --bmc1_unsat_core_extrapolate_axioms false
% 150.30/150.55 % --bmc1_out_stat full
% 150.30/150.55 % --bmc1_ground_init false
% 150.30/150.55 % --bmc1_pre_inst_next_state false
% 150.30/150.55 % --bmc1_pre_inst_state false
% 150.30/150.55 % --bmc1_pre_inst_reach_state false
% 150.30/150.55 % --bmc1_out_unsat_core false
% 150.30/150.55 % --bmc1_aig_witness_out false
% 150.30/150.55 % --bmc1_verbose false
% 150.30/150.55 % --bmc1_dump_clauses_tptp false
% 151.01/151.23 % --bmc1_dump_unsat_core_tptp false
% 151.01/151.23 % --bmc1_dump_file -
% 151.01/151.23 % --bmc1_ucm_expand_uc_limit 128
% 151.01/151.23 % --bmc1_ucm_n_expand_iterations 6
% 151.01/151.23 % --bmc1_ucm_extend_mode 1
% 151.01/151.23 % --bmc1_ucm_init_mode 2
% 151.01/151.23 % --bmc1_ucm_cone_mode none
% 151.01/151.23 % --bmc1_ucm_reduced_relation_type 0
% 151.01/151.23 % --bmc1_ucm_relax_model 4
% 151.01/151.23 % --bmc1_ucm_full_tr_after_sat true
% 151.01/151.23 % --bmc1_ucm_expand_neg_assumptions false
% 151.01/151.23 % --bmc1_ucm_layered_model none
% 151.01/151.23 % --bmc1_ucm_max_lemma_size 10
% 151.01/151.23
% 151.01/151.23 % ------ AIG Options
% 151.01/151.23
% 151.01/151.23 % --aig_mode false
% 151.01/151.23
% 151.01/151.23 % ------ Instantiation Options
% 151.01/151.23
% 151.01/151.23 % --instantiation_flag true
% 151.01/151.23 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 151.01/151.23 % --inst_solver_per_active 750
% 151.01/151.23 % --inst_solver_calls_frac 0.5
% 151.01/151.23 % --inst_passive_queue_type priority_queues
% 151.01/151.23 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 151.01/151.23 % --inst_passive_queues_freq [25;2]
% 151.01/151.23 % --inst_dismatching true
% 151.01/151.23 % --inst_eager_unprocessed_to_passive true
% 151.01/151.23 % --inst_prop_sim_given true
% 151.01/151.23 % --inst_prop_sim_new false
% 151.01/151.23 % --inst_orphan_elimination true
% 151.01/151.23 % --inst_learning_loop_flag true
% 151.01/151.23 % --inst_learning_start 3000
% 151.01/151.23 % --inst_learning_factor 2
% 151.01/151.23 % --inst_start_prop_sim_after_learn 3
% 151.01/151.23 % --inst_sel_renew solver
% 151.01/151.23 % --inst_lit_activity_flag true
% 151.01/151.23 % --inst_out_proof true
% 151.01/151.23
% 151.01/151.23 % ------ Resolution Options
% 151.01/151.23
% 151.01/151.23 % --resolution_flag true
% 151.01/151.23 % --res_lit_sel kbo_max
% 151.01/151.23 % --res_to_prop_solver none
% 151.01/151.23 % --res_prop_simpl_new false
% 151.01/151.23 % --res_prop_simpl_given false
% 151.01/151.23 % --res_passive_queue_type priority_queues
% 151.01/151.23 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 151.01/151.23 % --res_passive_queues_freq [15;5]
% 151.01/151.23 % --res_forward_subs full
% 151.01/151.23 % --res_backward_subs full
% 151.01/151.23 % --res_forward_subs_resolution true
% 151.01/151.23 % --res_backward_subs_resolution true
% 151.01/151.23 % --res_orphan_elimination false
% 151.01/151.23 % --res_time_limit 1000.
% 151.01/151.23 % --res_out_proof true
% 151.01/151.23 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_0c1ff8.s
% 151.01/151.23 % --modulo true
% 151.01/151.23
% 151.01/151.23 % ------ Combination Options
% 151.01/151.23
% 151.01/151.23 % --comb_res_mult 1000
% 151.01/151.23 % --comb_inst_mult 300
% 151.01/151.23 % ------
% 151.01/151.23
% 151.01/151.23 % ------ Parsing...% successful
% 151.01/151.23
% 151.01/151.23 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e pe_s pe_e snvd_s sp: 0 0s snvd_e %
% 151.01/151.23
% 151.01/151.23 % ------ Proving...
% 151.01/151.23 % ------ Problem Properties
% 151.01/151.23
% 151.01/151.23 %
% 151.01/151.23 % EPR false
% 151.01/151.23 % Horn false
% 151.01/151.23 % Has equality true
% 151.01/151.23
% 151.01/151.23 % % ------ Input Options Time Limit: Unbounded
% 151.01/151.23
% 151.01/151.23
% 151.01/151.23 Compiling...
% 151.01/151.23 Loading plugin: done.
% 151.01/151.23 Compiling...
% 151.01/151.23 Loading plugin: done.
% 151.01/151.23 Compiling...
% 151.01/151.23 Loading plugin: done.
% 151.01/151.23 Compiling...
% 151.01/151.23 Loading plugin: done.
% 151.01/151.23 Compiling...
% 151.01/151.23 Loading plugin: done.
% 151.01/151.23 Compiling...
% 151.01/151.23 Loading plugin: done.
% 151.01/151.23 % % ------ Current options:
% 151.01/151.23
% 151.01/151.23 % ------ Input Options
% 151.01/151.23
% 151.01/151.23 % --out_options all
% 151.01/151.23 % --tptp_safe_out true
% 151.01/151.23 % --problem_path ""
% 151.01/151.23 % --include_path ""
% 151.01/151.23 % --clausifier .//eprover
% 151.01/151.23 % --clausifier_options --tstp-format
% 151.01/151.23 % --stdin false
% 151.01/151.23 % --dbg_backtrace false
% 151.01/151.23 % --dbg_dump_prop_clauses false
% 151.01/151.23 % --dbg_dump_prop_clauses_file -
% 151.01/151.23 % --dbg_out_stat false
% 151.01/151.23
% 151.01/151.23 % ------ General Options
% 151.01/151.23
% 151.01/151.23 % --fof false
% 151.01/151.23 % --time_out_real 150.
% 151.01/151.23 % --time_out_prep_mult 0.2
% 151.01/151.23 % --time_out_virtual -1.
% 151.01/151.23 % --schedule none
% 151.01/151.23 % --ground_splitting input
% 151.01/151.23 % --splitting_nvd 16
% 151.01/151.23 % --non_eq_to_eq false
% 151.01/151.23 % --prep_gs_sim true
% 151.01/151.23 % --prep_unflatten false
% 151.01/151.23 % --prep_res_sim true
% 151.01/151.23 % --prep_upred true
% 151.01/151.23 % --res_sim_input true
% 151.01/151.23 % --clause_weak_htbl true
% 151.01/151.23 % --gc_record_bc_elim false
% 151.01/151.23 % --symbol_type_check false
% 151.01/151.23 % --clausify_out false
% 151.01/151.23 % --large_theory_mode false
% 151.01/151.23 % --prep_sem_filter none
% 151.01/151.23 % --prep_sem_filter_out false
% 151.01/151.23 % --preprocessed_out false
% 151.01/151.23 % --sub_typing false
% 151.01/151.23 % --brand_transform false
% 151.01/151.23 % --pure_diseq_elim true
% 151.01/151.23 % --min_unsat_core false
% 151.01/151.23 % --pred_elim true
% 151.01/151.23 % --add_important_lit false
% 151.01/151.23 % --soft_assumptions false
% 151.01/151.23 % --reset_solvers false
% 151.01/151.23 % --bc_imp_inh []
% 151.01/151.23 % --conj_cone_tolerance 1.5
% 151.01/151.23 % --prolific_symb_bound 500
% 151.01/151.23 % --lt_threshold 2000
% 151.01/151.23
% 151.01/151.23 % ------ SAT Options
% 151.01/151.23
% 151.01/151.23 % --sat_mode false
% 151.01/151.23 % --sat_fm_restart_options ""
% 151.01/151.23 % --sat_gr_def false
% 151.01/151.23 % --sat_epr_types true
% 151.01/151.23 % --sat_non_cyclic_types false
% 151.01/151.23 % --sat_finite_models false
% 151.01/151.23 % --sat_fm_lemmas false
% 151.01/151.23 % --sat_fm_prep false
% 151.01/151.23 % --sat_fm_uc_incr true
% 151.01/151.23 % --sat_out_model small
% 151.01/151.23 % --sat_out_clauses false
% 151.01/151.23
% 151.01/151.23 % ------ QBF Options
% 151.01/151.23
% 151.01/151.23 % --qbf_mode false
% 151.01/151.23 % --qbf_elim_univ true
% 151.01/151.23 % --qbf_sk_in true
% 151.01/151.23 % --qbf_pred_elim true
% 151.01/151.23 % --qbf_split 32
% 151.01/151.23
% 151.01/151.23 % ------ BMC1 Options
% 151.01/151.23
% 151.01/151.23 % --bmc1_incremental false
% 151.01/151.23 % --bmc1_axioms reachable_all
% 151.01/151.23 % --bmc1_min_bound 0
% 151.01/151.23 % --bmc1_max_bound -1
% 151.01/151.23 % --bmc1_max_bound_default -1
% 151.01/151.23 % --bmc1_symbol_reachability true
% 151.01/151.23 % --bmc1_property_lemmas false
% 151.01/151.23 % --bmc1_k_induction false
% 151.01/151.23 % --bmc1_non_equiv_states false
% 151.01/151.23 % --bmc1_deadlock false
% 151.01/151.23 % --bmc1_ucm false
% 151.01/151.23 % --bmc1_add_unsat_core none
% 151.01/151.23 % --bmc1_unsat_core_children false
% 151.01/151.23 % --bmc1_unsat_core_extrapolate_axioms false
% 151.01/151.23 % --bmc1_out_stat full
% 151.01/151.23 % --bmc1_ground_init false
% 151.01/151.23 % --bmc1_pre_inst_next_state false
% 151.01/151.23 % --bmc1_pre_inst_state false
% 151.01/151.23 % --bmc1_pre_inst_reach_state false
% 151.01/151.23 % --bmc1_out_unsat_core false
% 151.01/151.23 % --bmc1_aig_witness_out false
% 151.01/151.23 % --bmc1_verbose false
% 151.01/151.23 % --bmc1_dump_clauses_tptp false
% 151.01/151.23 % --bmc1_dump_unsat_core_tptp false
% 151.01/151.23 % --bmc1_dump_file -
% 151.01/151.23 % --bmc1_ucm_expand_uc_limit 128
% 151.01/151.23 % --bmc1_ucm_n_expand_iterations 6
% 151.01/151.23 % --bmc1_ucm_extend_mode 1
% 151.01/151.23 % --bmc1_ucm_init_mode 2
% 151.01/151.23 % --bmc1_ucm_cone_mode none
% 151.01/151.23 % --bmc1_ucm_reduced_relation_type 0
% 151.01/151.23 % --bmc1_ucm_relax_model 4
% 151.01/151.23 % --bmc1_ucm_full_tr_after_sat true
% 151.01/151.23 % --bmc1_ucm_expand_neg_assumptions false
% 151.01/151.23 % --bmc1_ucm_layered_model none
% 151.01/151.23 % --bmc1_ucm_max_lemma_size 10
% 151.01/151.23
% 151.01/151.23 % ------ AIG Options
% 151.01/151.23
% 151.01/151.23 % --aig_mode false
% 151.01/151.23
% 151.01/151.23 % ------ Instantiation Options
% 151.01/151.23
% 151.01/151.23 % --instantiation_flag true
% 151.01/151.23 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 151.01/151.23 % --inst_solver_per_active 750
% 151.01/151.23 % --inst_solver_calls_frac 0.5
% 151.01/151.23 % --inst_passive_queue_type priority_queues
% 151.01/151.23 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 151.01/151.24 % --inst_passive_queues_freq [25;2]
% 151.01/151.24 % --inst_dismatching true
% 151.01/151.24 % --inst_eager_unprocessed_to_passive true
% 151.01/151.24 % --inst_prop_sim_given true
% 151.01/151.24 % --inst_prop_sim_new false
% 151.01/151.24 % --inst_orphan_elimination true
% 151.01/151.24 % --inst_learning_loop_flag true
% 151.01/151.24 % --inst_learning_start 3000
% 151.01/151.24 % --inst_learning_factor 2
% 151.01/151.24 % --inst_start_prop_sim_after_learn 3
% 151.01/151.24 % --inst_sel_renew solver
% 151.01/151.24 % --inst_lit_activity_flag true
% 151.01/151.24 % --inst_out_proof true
% 151.01/151.24
% 151.01/151.24 % ------ Resolution Options
% 151.01/151.24
% 151.01/151.24 % --resolution_flag true
% 151.01/151.24 % --res_lit_sel kbo_max
% 151.01/151.24 % --res_to_prop_solver none
% 151.01/151.24 % --res_prop_simpl_new false
% 151.01/151.24 % --res_prop_simpl_given false
% 151.01/151.24 % --res_passive_queue_type priority_queues
% 151.01/151.24 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 151.01/151.24 % --res_passive_queues_freq [15;5]
% 151.01/151.24 % --res_forward_subs full
% 151.01/151.24 % --res_backward_subs full
% 151.01/151.24 % --res_forward_subs_resolution true
% 151.01/151.24 % --res_backward_subs_resolution true
% 151.01/151.24 % --res_orphan_elimination false
% 151.01/151.24 % --res_time_limit 1000.
% 151.01/151.24 % --res_out_proof true
% 151.01/151.24 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_0c1ff8.s
% 151.01/151.24 % --modulo true
% 151.01/151.24
% 151.01/151.24 % ------ Combination Options
% 151.01/151.24
% 151.01/151.24 % --comb_res_mult 1000
% 151.01/151.24 % --comb_inst_mult 300
% 151.01/151.24 % ------
% 151.01/151.24
% 151.01/151.24
% 151.01/151.24
% 151.01/151.24 % ------ Proving...
% 151.01/151.24 %
% 151.01/151.24
% 151.01/151.24
% 151.01/151.24 % Resolution empty clause
% 151.01/151.24
% 151.01/151.24 % ------ Statistics
% 151.01/151.24
% 151.01/151.24 % ------ General
% 151.01/151.24
% 151.01/151.24 % num_of_input_clauses: 231
% 151.01/151.24 % num_of_input_neg_conjectures: 2
% 151.01/151.24 % num_of_splits: 0
% 151.01/151.24 % num_of_split_atoms: 0
% 151.01/151.24 % num_of_sem_filtered_clauses: 0
% 151.01/151.24 % num_of_subtypes: 0
% 151.01/151.24 % monotx_restored_types: 0
% 151.01/151.24 % sat_num_of_epr_types: 0
% 151.01/151.24 % sat_num_of_non_cyclic_types: 0
% 151.01/151.24 % sat_guarded_non_collapsed_types: 0
% 151.01/151.24 % is_epr: 0
% 151.01/151.24 % is_horn: 0
% 151.01/151.24 % has_eq: 1
% 151.01/151.24 % num_pure_diseq_elim: 0
% 151.01/151.24 % simp_replaced_by: 0
% 151.01/151.24 % res_preprocessed: 4
% 151.01/151.24 % prep_upred: 0
% 151.01/151.24 % prep_unflattend: 0
% 151.01/151.24 % pred_elim_cands: 0
% 151.01/151.24 % pred_elim: 0
% 151.01/151.24 % pred_elim_cl: 0
% 151.01/151.24 % pred_elim_cycles: 0
% 151.01/151.24 % forced_gc_time: 0
% 151.01/151.24 % gc_basic_clause_elim: 0
% 151.01/151.24 % parsing_time: 0.005
% 151.01/151.24 % sem_filter_time: 0.
% 151.01/151.24 % pred_elim_time: 0.
% 151.01/151.24 % out_proof_time: 0.001
% 151.01/151.24 % monotx_time: 0.
% 151.01/151.24 % subtype_inf_time: 0.
% 151.01/151.24 % unif_index_cands_time: 0.
% 151.01/151.24 % unif_index_add_time: 0.
% 151.01/151.24 % total_time: 0.7
% 151.01/151.24 % num_of_symbols: 74
% 151.01/151.24 % num_of_terms: 1078
% 151.01/151.24
% 151.01/151.24 % ------ Propositional Solver
% 151.01/151.24
% 151.01/151.24 % prop_solver_calls: 1
% 151.01/151.24 % prop_fast_solver_calls: 6
% 151.01/151.24 % prop_num_of_clauses: 240
% 151.01/151.24 % prop_preprocess_simplified: 680
% 151.01/151.24 % prop_fo_subsumed: 0
% 151.01/151.24 % prop_solver_time: 0.
% 151.01/151.24 % prop_fast_solver_time: 0.
% 151.01/151.24 % prop_unsat_core_time: 0.
% 151.01/151.24
% 151.01/151.24 % ------ QBF
% 151.01/151.24
% 151.01/151.24 % qbf_q_res: 0
% 151.01/151.24 % qbf_num_tautologies: 0
% 151.01/151.24 % qbf_prep_cycles: 0
% 151.01/151.24
% 151.01/151.24 % ------ BMC1
% 151.01/151.24
% 151.01/151.24 % bmc1_current_bound: -1
% 151.01/151.24 % bmc1_last_solved_bound: -1
% 151.01/151.24 % bmc1_unsat_core_size: -1
% 151.01/151.24 % bmc1_unsat_core_parents_size: -1
% 151.01/151.24 % bmc1_merge_next_fun: 0
% 151.01/151.24 % bmc1_unsat_core_clauses_time: 0.
% 151.01/151.24
% 151.01/151.24 % ------ Instantiation
% 151.01/151.24
% 151.01/151.24 % inst_num_of_clauses: 231
% 151.01/151.24 % inst_num_in_passive: 0
% 151.01/151.24 % inst_num_in_active: 0
% 151.01/151.24 % inst_num_in_unprocessed: 231
% 151.01/151.24 % inst_num_of_loops: 0
% 151.01/151.24 % inst_num_of_learning_restarts: 0
% 151.01/151.24 % inst_num_moves_active_passive: 0
% 151.01/151.24 % inst_lit_activity: 0
% 151.01/151.24 % inst_lit_activity_moves: 0
% 151.01/151.24 % inst_num_tautologies: 0
% 151.01/151.24 % inst_num_prop_implied: 0
% 151.01/151.24 % inst_num_existing_simplified: 0
% 151.01/151.24 % inst_num_eq_res_simplified: 0
% 151.01/151.24 % inst_num_child_elim: 0
% 151.01/151.24 % inst_num_of_dismatching_blockings: 0
% 151.01/151.24 % inst_num_of_non_proper_insts: 0
% 151.01/151.24 % inst_num_of_duplicates: 0
% 151.01/151.24 % inst_inst_num_from_inst_to_res: 0
% 151.01/151.24 % inst_dismatching_checking_time: 0.
% 151.01/151.24
% 151.01/151.24 % ------ Resolution
% 151.01/151.24
% 151.01/151.24 % res_num_of_clauses: 404
% 151.01/151.24 % res_num_in_passive: 126
% 151.01/151.24 % res_num_in_active: 134
% 151.01/151.24 % res_num_of_loops: 27
% 151.01/151.24 % res_forward_subset_subsumed: 110
% 151.01/151.24 % res_backward_subset_subsumed: 0
% 151.01/151.24 % res_forward_subsumed: 2
% 151.01/151.24 % res_backward_subsumed: 0
% 151.01/151.24 % res_forward_subsumption_resolution: 1
% 151.01/151.24 % res_backward_subsumption_resolution: 0
% 151.01/151.24 % res_clause_to_clause_subsumption: 14
% 151.01/151.24 % res_orphan_elimination: 0
% 151.01/151.24 % res_tautology_del: 6
% 151.01/151.24 % res_num_eq_res_simplified: 0
% 151.01/151.24 % res_num_sel_changes: 0
% 151.01/151.24 % res_moves_from_active_to_pass: 0
% 151.01/151.24
% 151.01/151.24 % Status Unsatisfiable
% 151.01/151.24 % SZS status Unsatisfiable
% 151.01/151.24 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------