%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET093-7 : TPTP v9.2.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:07:16 PM UTC 2026
% Result : Unsatisfiable 0.32s 1.62s
% Output : CNFRefutation 0.41s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_136)
% Comments :
%------------------------------------------------------------------------------
cnf(image,axiom,
range_of(restrict(X1,X2,universal_class)) = image(X1,X2),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',image) ).
cnf(range_of,axiom,
domain_of(inverse(X1)) = range_of(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',range_of) ).
cnf(restriction1,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',restriction1) ).
cnf(apply,axiom,
sum_class(image(X1,singleton(X2))) = apply(X1,X2),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',apply) ).
cnf(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',singleton_set) ).
cnf(sum_class_definition,axiom,
domain_of(restrict(element_relation,universal_class,X1)) = sum_class(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',sum_class_definition) ).
cnf(ordered_pair,axiom,
unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',ordered_pair) ).
cnf(power_class_definition,axiom,
complement(image(element_relation,complement(X1))) = power_class(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',power_class_definition) ).
cnf(inverse,axiom,
domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',inverse) ).
cnf(successor,axiom,
union(X1,singleton(X1)) = successor(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',successor) ).
cnf(homomorphism6,axiom,
( homomorphism(X3,X1,X2)
| ~ operation(X1)
| ~ operation(X2)
| ~ compatible(X3,X1,X2)
| apply(X2,ordered_pair(apply(X3,not_homomorphism1(X3,X1,X2)),apply(X3,not_homomorphism2(X3,X1,X2)))) != apply(X3,apply(X1,ordered_pair(not_homomorphism1(X3,X1,X2),not_homomorphism2(X3,X1,X2)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',homomorphism6) ).
cnf(homomorphism4,axiom,
( apply(X3,ordered_pair(apply(X1,X4),apply(X1,X5))) = apply(X1,apply(X2,ordered_pair(X4,X5)))
| ~ homomorphism(X1,X2,X3)
| ~ member(ordered_pair(X4,X5),domain_of(X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',homomorphism4) ).
cnf(compose3,axiom,
( member(ordered_pair(X4,X1),compose(X2,X3))
| ~ member(X1,image(X2,image(X3,singleton(X4))))
| ~ member(ordered_pair(X4,X1),cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',compose3) ).
cnf(compose2,axiom,
( member(X2,image(X3,image(X4,singleton(X1))))
| ~ member(ordered_pair(X1,X2),compose(X3,X4)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',compose2) ).
cnf(choice2,axiom,
( X1 = null_class
| member(apply(choice,X1),X1)
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',choice2) ).
cnf(flip3,axiom,
( member(ordered_pair(ordered_pair(X2,X1),X3),flip(X4))
| ~ member(ordered_pair(ordered_pair(X1,X2),X3),X4)
| ~ member(ordered_pair(ordered_pair(X2,X1),X3),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',flip3) ).
cnf(rotate3,axiom,
( member(ordered_pair(ordered_pair(X3,X1),X2),rotate(X4))
| ~ member(ordered_pair(ordered_pair(X1,X2),X3),X4)
| ~ member(ordered_pair(ordered_pair(X3,X1),X2),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',rotate3) ).
cnf(flip2,axiom,
( member(ordered_pair(ordered_pair(X2,X1),X3),X4)
| ~ member(ordered_pair(ordered_pair(X1,X2),X3),flip(X4)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',flip2) ).
cnf(rotate2,axiom,
( member(ordered_pair(ordered_pair(X2,X3),X1),X4)
| ~ member(ordered_pair(ordered_pair(X1,X2),X3),rotate(X4)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',rotate2) ).
cnf(power_class2,axiom,
( member(power_class(X1),universal_class)
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',power_class2) ).
cnf(homomorphism5,axiom,
( member(ordered_pair(not_homomorphism1(X3,X1,X2),not_homomorphism2(X3,X1,X2)),domain_of(X1))
| homomorphism(X3,X1,X2)
| ~ operation(X1)
| ~ operation(X2)
| ~ compatible(X3,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',homomorphism5) ).
cnf(inductive3,axiom,
( inductive(X1)
| ~ member(null_class,X1)
| ~ subclass(image(successor_relation,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',inductive3) ).
cnf(cantor_class,axiom,
intersection(domain_of(X1),diagonalise(compose(inverse(element_relation),X1))) = cantor(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cantor_class) ).
cnf(diagonalisation,axiom,
complement(domain_of(intersection(X1,identity_relation))) = diagonalise(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',diagonalisation) ).
cnf(replacement,axiom,
( member(image(X1,X2),universal_class)
| ~ function(X1)
| ~ member(X2,universal_class) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',replacement) ).
cnf(inductive2,axiom,
( subclass(image(successor_relation,X1),X1)
| ~ inductive(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',inductive2) ).
cnf(subset_relation,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('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',subset_relation) ).
cnf(successor_relation3,axiom,
( member(ordered_pair(X1,X2),successor_relation)
| successor(X1) != X2
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',successor_relation3) ).
cnf(union,axiom,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',union) ).
cnf(element_relation3,axiom,
( member(ordered_pair(X1,X2),element_relation)
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
| ~ member(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',element_relation3) ).
cnf(successor_relation2,axiom,
( successor(X1) = X2
| ~ member(ordered_pair(X1,X2),successor_relation) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',successor_relation2) ).
cnf(operation4,axiom,
( operation(X1)
| ~ 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))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',operation4) ).
cnf(compatible4,axiom,
( compatible(X1,X2,X3)
| ~ function(X1)
| domain_of(domain_of(X2)) != domain_of(X1)
| ~ subclass(range_of(X1),domain_of(domain_of(X3))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',compatible4) ).
cnf(corollary_1_to_unordered_pair,axiom,
( member(X1,unordered_pair(X1,X2))
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_1_to_unordered_pair) ).
cnf(corollary_2_to_unordered_pair,axiom,
( member(X2,unordered_pair(X1,X2))
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_2_to_unordered_pair) ).
cnf(right_cancellation,axiom,
( X1 = X3
| unordered_pair(X1,X2) != unordered_pair(X3,X2)
| ~ member(ordered_pair(X1,X3),cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_cancellation) ).
cnf(left_cancellation,axiom,
( X2 = X3
| unordered_pair(X1,X2) != unordered_pair(X1,X3)
| ~ member(ordered_pair(X2,X3),cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_cancellation) ).
cnf(function3,axiom,
( function(X1)
| ~ subclass(X1,cross_product(universal_class,universal_class))
| ~ subclass(compose(X1,inverse(X1)),identity_relation) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',function3) ).
cnf(corollary_to_unordered_pair_axiom3,axiom,
( ~ member(ordered_pair(X1,X2),cross_product(X3,X4))
| unordered_pair(X1,X2) != null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_to_unordered_pair_axiom3) ).
cnf(cartesian_product1,axiom,
( member(X1,X3)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product1) ).
cnf(cartesian_product2,axiom,
( member(X2,X4)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product2) ).
cnf(corollary_1_to_cartesian_product,axiom,
( member(X1,universal_class)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_1_to_cartesian_product) ).
cnf(corollary_2_to_cartesian_product,axiom,
( member(X2,universal_class)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_2_to_cartesian_product) ).
cnf(single_valued_class2,axiom,
( single_valued_class(X1)
| ~ subclass(compose(X1,inverse(X1)),identity_relation) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',single_valued_class2) ).
cnf(element_relation2,axiom,
( member(X1,X2)
| ~ member(ordered_pair(X1,X2),element_relation) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',element_relation2) ).
cnf(compatible3,axiom,
( subclass(range_of(X1),domain_of(domain_of(X3)))
| ~ compatible(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',compatible3) ).
cnf(cartesian_product3,axiom,
( member(ordered_pair(X1,X3),cross_product(X2,X4))
| ~ member(X1,X2)
| ~ member(X3,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product3) ).
cnf(cartesian_product4,axiom,
( ordered_pair(first(X1),second(X1)) = X1
| ~ member(X1,cross_product(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product4) ).
cnf(operation3,axiom,
( subclass(range_of(X1),domain_of(domain_of(X1)))
| ~ operation(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',operation3) ).
cnf(function2,axiom,
( subclass(compose(X1,inverse(X1)),identity_relation)
| ~ function(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',function2) ).
cnf(single_valued_class1,axiom,
( subclass(compose(X1,inverse(X1)),identity_relation)
| ~ single_valued_class(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',single_valued_class1) ).
cnf(one_to_one3,axiom,
( one_to_one(X1)
| ~ function(inverse(X1))
| ~ function(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',one_to_one3) ).
cnf(sum_class2,axiom,
( member(sum_class(X1),universal_class)
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',sum_class2) ).
cnf(domain1,axiom,
( restrict(X1,singleton(X2),universal_class) != null_class
| ~ member(X2,domain_of(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',domain1) ).
cnf(member_exists2,axiom,
( singleton(member_of(singleton(X1))) = singleton(X1)
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_exists2) ).
cnf(domain2,axiom,
( restrict(X2,singleton(X1),universal_class) = null_class
| member(X1,domain_of(X2))
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',domain2) ).
cnf(one_to_one2,axiom,
( function(inverse(X1))
| ~ one_to_one(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',one_to_one2) ).
cnf(corollary_1_to_singletons_are_sets,axiom,
member(singleton(X1),unordered_pair(X2,singleton(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_1_to_singletons_are_sets) ).
cnf(identity_relation,axiom,
intersection(inverse(subset_relation),subset_relation) = identity_relation,
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',identity_relation) ).
cnf(member_exists1,axiom,
( member(member_of(singleton(X1)),universal_class)
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_exists1) ).
cnf(restriction2,axiom,
intersection(cross_product(X1,X2),X3) = restrict(X3,X1,X2),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',restriction2) ).
cnf(singleton_in_unordered_pair3,axiom,
( X3 = X1
| X3 = X2
| unordered_pair(X1,X2) != singleton(X3)
| ~ member(X3,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_in_unordered_pair3) ).
cnf(singleton_identified_by_element1,axiom,
( X1 = X2
| singleton(X1) != singleton(X2)
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_identified_by_element1) ).
cnf(singleton_identified_by_element2,axiom,
( X1 = X2
| singleton(X1) != singleton(X2)
| ~ member(X2,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_identified_by_element2) ).
cnf(singleton_in_unordered_pair1,axiom,
subclass(singleton(X1),unordered_pair(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_in_unordered_pair1) ).
cnf(singleton_in_unordered_pair2,axiom,
subclass(singleton(X1),unordered_pair(X2,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_in_unordered_pair2) ).
cnf(only_member_in_singleton,axiom,
( X1 = X2
| ~ member(X1,singleton(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',only_member_in_singleton) ).
cnf(set_in_its_singleton,axiom,
( member(X1,singleton(X1))
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_in_its_singleton) ).
cnf(member_of_singleton_is_unique,axiom,
( member_of(singleton(X1)) = X1
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_singleton_is_unique) ).
cnf(corollary_to_set_in_its_singleton,axiom,
( ~ member(X1,universal_class)
| singleton(X1) != null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_to_set_in_its_singleton) ).
cnf(unordered_pair_equals_singleton2,axiom,
( member(X1,universal_class)
| unordered_pair(X1,X2) = singleton(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_equals_singleton2) ).
cnf(unordered_pair_equals_singleton1,axiom,
( member(X1,universal_class)
| unordered_pair(X2,X1) = singleton(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_equals_singleton1) ).
cnf(singletons_are_sets,axiom,
member(singleton(X1),universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletons_are_sets) ).
cnf(member_of_non_singleton_unique2,axiom,
( singleton(member_of1(X1)) = X1
| member_of(X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_non_singleton_unique2) ).
cnf(member_exists4,axiom,
( singleton(member_of(X1)) = X1
| member_of(X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_exists4) ).
cnf(null_class_in_its_singleton,axiom,
member(null_class,singleton(null_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',null_class_in_its_singleton) ).
cnf(singleton_is_null_class,axiom,
( member(X1,universal_class)
| singleton(X1) = null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_is_null_class) ).
cnf(prove_corollary_2_to_singletons_are_sets_1,negated_conjecture,
singleton(member_of(x)) = x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_2_to_singletons_are_sets_1) ).
cnf(homomorphism3,axiom,
( compatible(X1,X2,X3)
| ~ homomorphism(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',homomorphism3) ).
cnf(equality4,axiom,
( X1 = X2
| ~ member(not_subclass_element(X1,X2),X2)
| ~ member(not_subclass_element(X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equality4) ).
cnf(equality3,axiom,
( X2 = X1
| member(not_subclass_element(X2,X1),X2)
| ~ member(not_subclass_element(X1,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equality3) ).
cnf(equality2,axiom,
( X1 = X2
| member(not_subclass_element(X2,X1),X2)
| ~ member(not_subclass_element(X1,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equality2) ).
cnf(compatible2,axiom,
( domain_of(domain_of(X2)) = domain_of(X1)
| ~ compatible(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',compatible2) ).
cnf(homomorphism1,axiom,
( operation(X2)
| ~ homomorphism(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',homomorphism1) ).
cnf(homomorphism2,axiom,
( operation(X3)
| ~ homomorphism(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',homomorphism2) ).
cnf(compatible1,axiom,
( function(X1)
| ~ compatible(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',compatible1) ).
cnf(unordered_pair_is_subset,axiom,
( subclass(unordered_pair(X1,X3),X2)
| ~ member(X1,X2)
| ~ member(X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_is_subset) ).
cnf(intersection3,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection3) ).
cnf(equality1,axiom,
( X1 = X2
| member(not_subclass_element(X1,X2),X1)
| member(not_subclass_element(X2,X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equality1) ).
cnf(flip1,axiom,
subclass(flip(X1),cross_product(cross_product(universal_class,universal_class),universal_class)),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',flip1) ).
cnf(rotate1,axiom,
subclass(rotate(X1),cross_product(cross_product(universal_class,universal_class),universal_class)),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',rotate1) ).
cnf(special_classes_lemma,axiom,
~ member(X1,intersection(complement(X2),X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',special_classes_lemma) ).
cnf(not_subclass_members2,axiom,
( subclass(X1,X2)
| ~ member(not_subclass_element(X1,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',not_subclass_members2) ).
cnf(intersection1,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection1) ).
cnf(intersection2,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection2) ).
cnf(unordered_pair_member,axiom,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair_member) ).
cnf(operation2,axiom,
( cross_product(domain_of(domain_of(X1)),domain_of(domain_of(X1))) = domain_of(X1)
| ~ operation(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',operation2) ).
cnf(unordered_pair2,axiom,
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair2) ).
cnf(unordered_pair3,axiom,
( member(X1,unordered_pair(X2,X1))
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair3) ).
cnf(compose1,axiom,
subclass(compose(X1,X2),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',compose1) ).
cnf(subclass_members,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',subclass_members) ).
cnf(transitivity_of_subclass,axiom,
( subclass(X1,X3)
| ~ subclass(X1,X2)
| ~ subclass(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_subclass) ).
cnf(complement2,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement2) ).
cnf(complement1,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement1) ).
cnf(not_subclass_members1,axiom,
( member(not_subclass_element(X1,X2),X1)
| subclass(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',not_subclass_members1) ).
cnf(subclass_implies_equal,axiom,
( X1 = X2
| ~ subclass(X1,X2)
| ~ subclass(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',subclass_implies_equal) ).
cnf(corollary_to_unordered_pair_axiom1,axiom,
( ~ member(X1,universal_class)
| unordered_pair(X1,X2) != null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_to_unordered_pair_axiom1) ).
cnf(corollary_to_unordered_pair_axiom2,axiom,
( ~ member(X1,universal_class)
| unordered_pair(X2,X1) != null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_to_unordered_pair_axiom2) ).
cnf(function1,axiom,
( subclass(X1,cross_product(universal_class,universal_class))
| ~ function(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',function1) ).
cnf(null_unordered_pair,axiom,
( unordered_pair(X1,X2) = null_class
| member(X1,universal_class)
| member(X2,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',null_unordered_pair) ).
cnf(null_class_is_unique,axiom,
( X1 = null_class
| member(not_subclass_element(X1,null_class),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',null_class_is_unique) ).
cnf(unordered_pairs_in_universal,axiom,
member(unordered_pair(X1,X2),universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pairs_in_universal) ).
cnf(successor_relation1,axiom,
subclass(successor_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',successor_relation1) ).
cnf(element_relation1,axiom,
subclass(element_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',element_relation1) ).
cnf(commutativity_of_unordered_pair,axiom,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_unordered_pair) ).
cnf(member_of_non_singleton_unique1,axiom,
( member(member_of1(X1),universal_class)
| member_of(X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_non_singleton_unique1) ).
cnf(member_exists3,axiom,
( member(member_of(X1),universal_class)
| member_of(X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_exists3) ).
cnf(regularity1,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity1) ).
cnf(regularity2,axiom,
( X1 = null_class
| intersection(X1,regular(X1)) = null_class ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity2) ).
cnf(corollary_of_null_class_is_subclass,axiom,
( X1 = null_class
| ~ subclass(X1,null_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_of_null_class_is_subclass) ).
cnf(existence_of_null_class,axiom,
~ member(X1,null_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_null_class) ).
cnf(inductive1,axiom,
( member(null_class,X1)
| ~ inductive(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',inductive1) ).
cnf(omega_is_inductive2,axiom,
( subclass(omega,X1)
| ~ inductive(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',omega_is_inductive2) ).
cnf(equal_implies_subclass1,axiom,
( subclass(X1,X2)
| X1 != X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',equal_implies_subclass1) ).
cnf(equal_implies_subclass2,axiom,
( subclass(X2,X1)
| X1 != X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',equal_implies_subclass2) ).
cnf(prove_corollary_2_to_singletons_are_sets_2,negated_conjecture,
~ member(x,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_2_to_singletons_are_sets_2) ).
cnf(subclass_is_reflexive,axiom,
subclass(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_is_reflexive) ).
cnf(null_class_is_subclass,axiom,
subclass(null_class,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',null_class_is_subclass) ).
cnf(class_elements_are_sets,axiom,
subclass(X1,universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
cnf(operation1,axiom,
( function(X1)
| ~ operation(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',operation1) ).
cnf(one_to_one1,axiom,
( function(X1)
| ~ one_to_one(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',one_to_one1) ).
cnf(omega_in_universal,axiom,
member(omega,universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',omega_in_universal) ).
cnf(null_class_is_a_set,axiom,
member(null_class,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',null_class_is_a_set) ).
cnf(choice1,axiom,
function(choice),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',choice1) ).
cnf(omega_is_inductive1,axiom,
inductive(omega),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',omega_is_inductive1) ).
cnf(i_0_135,axiom,
range_of(restrict(X1,X2,universal_class)) = image(X1,X2),
image ).
cnf(i_0_136,axiom,
domain_of(inverse(X1)) = range_of(X1),
range_of ).
cnf(i_0_137,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
restriction1 ).
cnf(i_0_138,axiom,
sum_class(image(X1,singleton(X2))) = apply(X1,X2),
apply ).
cnf(i_0_139,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(i_0_140,axiom,
domain_of(restrict(element_relation,universal_class,X1)) = sum_class(X1),
sum_class_definition ).
cnf(i_0_141,axiom,
unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
ordered_pair ).
cnf(i_0_142,axiom,
complement(image(element_relation,complement(X1))) = power_class(X1),
power_class_definition ).
cnf(i_0_143,plain,
domain_of(inverse(intersection(X1,cross_product(X2,universal_class)))) = image(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_135,c_0_136]),c_0_137]) ).
cnf(i_0_144,axiom,
domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
inverse ).
cnf(i_0_145,axiom,
union(X1,singleton(X1)) = successor(X1),
successor ).
cnf(i_0_146,axiom,
( homomorphism(X3,X1,X2)
| ~ operation(X1)
| ~ operation(X2)
| ~ compatible(X3,X1,X2)
| apply(X2,ordered_pair(apply(X3,not_homomorphism1(X3,X1,X2)),apply(X3,not_homomorphism2(X3,X1,X2)))) != apply(X3,apply(X1,ordered_pair(not_homomorphism1(X3,X1,X2),not_homomorphism2(X3,X1,X2)))) ),
homomorphism6 ).
cnf(i_0_147,plain,
sum_class(image(X1,unordered_pair(X2,X2))) = apply(X1,X2),
inference(rw,[status(thm)],[i_0_138,c_0_139]) ).
cnf(i_0_148,plain,
domain_of(intersection(element_relation,cross_product(universal_class,X1))) = sum_class(X1),
inference(rw,[status(thm)],[i_0_140,c_0_137]) ).
cnf(i_0_149,plain,
unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))) = ordered_pair(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_141,c_0_139]),c_0_139]) ).
cnf(i_0_150,axiom,
( apply(X3,ordered_pair(apply(X1,X4),apply(X1,X5))) = apply(X1,apply(X2,ordered_pair(X4,X5)))
| ~ homomorphism(X1,X2,X3)
| ~ member(ordered_pair(X4,X5),domain_of(X2)) ),
homomorphism4 ).
cnf(i_0_151,axiom,
( member(ordered_pair(X4,X1),compose(X2,X3))
| ~ member(X1,image(X2,image(X3,singleton(X4))))
| ~ member(ordered_pair(X4,X1),cross_product(universal_class,universal_class)) ),
compose3 ).
cnf(i_0_152,axiom,
( member(X2,image(X3,image(X4,singleton(X1))))
| ~ member(ordered_pair(X1,X2),compose(X3,X4)) ),
compose2 ).
cnf(i_0_153,axiom,
( X1 = null_class
| member(apply(choice,X1),X1)
| ~ member(X1,universal_class) ),
choice2 ).
cnf(i_0_154,axiom,
( member(ordered_pair(ordered_pair(X2,X1),X3),flip(X4))
| ~ member(ordered_pair(ordered_pair(X1,X2),X3),X4)
| ~ member(ordered_pair(ordered_pair(X2,X1),X3),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
flip3 ).
cnf(i_0_155,axiom,
( member(ordered_pair(ordered_pair(X3,X1),X2),rotate(X4))
| ~ member(ordered_pair(ordered_pair(X1,X2),X3),X4)
| ~ member(ordered_pair(ordered_pair(X3,X1),X2),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
rotate3 ).
cnf(i_0_156,axiom,
( member(ordered_pair(ordered_pair(X2,X1),X3),X4)
| ~ member(ordered_pair(ordered_pair(X1,X2),X3),flip(X4)) ),
flip2 ).
cnf(i_0_157,axiom,
( member(ordered_pair(ordered_pair(X2,X3),X1),X4)
| ~ member(ordered_pair(ordered_pair(X1,X2),X3),rotate(X4)) ),
rotate2 ).
cnf(i_0_158,axiom,
( member(power_class(X1),universal_class)
| ~ member(X1,universal_class) ),
power_class2 ).
cnf(i_0_159,plain,
complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))) = power_class(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_142,c_0_143]),c_0_144]) ).
cnf(i_0_160,axiom,
( member(ordered_pair(not_homomorphism1(X3,X1,X2),not_homomorphism2(X3,X1,X2)),domain_of(X1))
| homomorphism(X3,X1,X2)
| ~ operation(X1)
| ~ operation(X2)
| ~ compatible(X3,X1,X2) ),
homomorphism5 ).
cnf(i_0_161,axiom,
( inductive(X1)
| ~ member(null_class,X1)
| ~ subclass(image(successor_relation,X1),X1) ),
inductive3 ).
cnf(i_0_162,axiom,
intersection(domain_of(X1),diagonalise(compose(inverse(element_relation),X1))) = cantor(X1),
cantor_class ).
cnf(i_0_163,axiom,
complement(domain_of(intersection(X1,identity_relation))) = diagonalise(X1),
diagonalisation ).
cnf(i_0_164,axiom,
( member(image(X1,X2),universal_class)
| ~ function(X1)
| ~ member(X2,universal_class) ),
replacement ).
cnf(i_0_165,axiom,
( subclass(image(successor_relation,X1),X1)
| ~ inductive(X1) ),
inductive2 ).
cnf(i_0_166,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,
subset_relation ).
cnf(i_0_167,axiom,
( member(ordered_pair(X1,X2),successor_relation)
| successor(X1) != X2
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class)) ),
successor_relation3 ).
cnf(i_0_168,plain,
union(X1,unordered_pair(X1,X1)) = successor(X1),
inference(rw,[status(thm)],[i_0_145,c_0_139]) ).
cnf(i_0_169,axiom,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
union ).
cnf(i_0_170,axiom,
( member(ordered_pair(X1,X2),element_relation)
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
| ~ member(X1,X2) ),
element_relation3 ).
cnf(i_0_171,axiom,
( successor(X1) = X2
| ~ member(ordered_pair(X1,X2),successor_relation) ),
successor_relation2 ).
cnf(i_0_172,axiom,
( operation(X1)
| ~ 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))) ),
operation4 ).
cnf(i_0_173,axiom,
( compatible(X1,X2,X3)
| ~ function(X1)
| domain_of(domain_of(X2)) != domain_of(X1)
| ~ subclass(range_of(X1),domain_of(domain_of(X3))) ),
compatible4 ).
cnf(i_0_174,axiom,
( member(X1,unordered_pair(X1,X2))
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
corollary_1_to_unordered_pair ).
cnf(i_0_175,axiom,
( member(X2,unordered_pair(X1,X2))
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
corollary_2_to_unordered_pair ).
cnf(i_0_176,axiom,
( X1 = X3
| unordered_pair(X1,X2) != unordered_pair(X3,X2)
| ~ member(ordered_pair(X1,X3),cross_product(universal_class,universal_class)) ),
right_cancellation ).
cnf(i_0_177,axiom,
( X2 = X3
| unordered_pair(X1,X2) != unordered_pair(X1,X3)
| ~ member(ordered_pair(X2,X3),cross_product(universal_class,universal_class)) ),
left_cancellation ).
cnf(i_0_178,axiom,
( function(X1)
| ~ subclass(X1,cross_product(universal_class,universal_class))
| ~ subclass(compose(X1,inverse(X1)),identity_relation) ),
function3 ).
cnf(i_0_179,axiom,
( ~ member(ordered_pair(X1,X2),cross_product(X3,X4))
| unordered_pair(X1,X2) != null_class ),
corollary_to_unordered_pair_axiom3 ).
cnf(i_0_180,axiom,
( member(X1,X3)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
cartesian_product1 ).
cnf(i_0_181,axiom,
( member(X2,X4)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
cartesian_product2 ).
cnf(i_0_182,axiom,
( member(X1,universal_class)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
corollary_1_to_cartesian_product ).
cnf(i_0_183,axiom,
( member(X2,universal_class)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
corollary_2_to_cartesian_product ).
cnf(i_0_184,axiom,
( single_valued_class(X1)
| ~ subclass(compose(X1,inverse(X1)),identity_relation) ),
single_valued_class2 ).
cnf(i_0_185,axiom,
( member(X1,X2)
| ~ member(ordered_pair(X1,X2),element_relation) ),
element_relation2 ).
cnf(i_0_186,axiom,
( subclass(range_of(X1),domain_of(domain_of(X3)))
| ~ compatible(X1,X2,X3) ),
compatible3 ).
cnf(i_0_187,axiom,
( member(ordered_pair(X1,X3),cross_product(X2,X4))
| ~ member(X1,X2)
| ~ member(X3,X4) ),
cartesian_product3 ).
cnf(i_0_188,axiom,
( ordered_pair(first(X1),second(X1)) = X1
| ~ member(X1,cross_product(X2,X3)) ),
cartesian_product4 ).
cnf(i_0_189,axiom,
( subclass(range_of(X1),domain_of(domain_of(X1)))
| ~ operation(X1) ),
operation3 ).
cnf(i_0_190,axiom,
( subclass(compose(X1,inverse(X1)),identity_relation)
| ~ function(X1) ),
function2 ).
cnf(i_0_191,axiom,
( subclass(compose(X1,inverse(X1)),identity_relation)
| ~ single_valued_class(X1) ),
single_valued_class1 ).
cnf(i_0_192,axiom,
( one_to_one(X1)
| ~ function(inverse(X1))
| ~ function(X1) ),
one_to_one3 ).
cnf(i_0_193,axiom,
( member(sum_class(X1),universal_class)
| ~ member(X1,universal_class) ),
sum_class2 ).
cnf(i_0_194,axiom,
( restrict(X1,singleton(X2),universal_class) != null_class
| ~ member(X2,domain_of(X1)) ),
domain1 ).
cnf(i_0_195,axiom,
( singleton(member_of(singleton(X1))) = singleton(X1)
| ~ member(X1,universal_class) ),
member_exists2 ).
cnf(i_0_196,axiom,
( restrict(X2,singleton(X1),universal_class) = null_class
| member(X1,domain_of(X2))
| ~ member(X1,universal_class) ),
domain2 ).
cnf(i_0_197,axiom,
( function(inverse(X1))
| ~ one_to_one(X1) ),
one_to_one2 ).
cnf(i_0_198,axiom,
member(singleton(X1),unordered_pair(X2,singleton(X1))),
corollary_1_to_singletons_are_sets ).
cnf(i_0_199,axiom,
intersection(inverse(subset_relation),subset_relation) = identity_relation,
identity_relation ).
cnf(i_0_200,axiom,
( member(member_of(singleton(X1)),universal_class)
| ~ member(X1,universal_class) ),
member_exists1 ).
cnf(i_0_201,axiom,
intersection(cross_product(X1,X2),X3) = restrict(X3,X1,X2),
restriction2 ).
cnf(i_0_202,axiom,
( X3 = X1
| X3 = X2
| unordered_pair(X1,X2) != singleton(X3)
| ~ member(X3,universal_class) ),
singleton_in_unordered_pair3 ).
cnf(i_0_203,axiom,
( X1 = X2
| singleton(X1) != singleton(X2)
| ~ member(X1,universal_class) ),
singleton_identified_by_element1 ).
cnf(i_0_204,axiom,
( X1 = X2
| singleton(X1) != singleton(X2)
| ~ member(X2,universal_class) ),
singleton_identified_by_element2 ).
cnf(i_0_205,axiom,
subclass(singleton(X1),unordered_pair(X1,X2)),
singleton_in_unordered_pair1 ).
cnf(i_0_206,axiom,
subclass(singleton(X1),unordered_pair(X2,X1)),
singleton_in_unordered_pair2 ).
cnf(i_0_207,axiom,
( X1 = X2
| ~ member(X1,singleton(X2)) ),
only_member_in_singleton ).
cnf(i_0_208,axiom,
( member(X1,singleton(X1))
| ~ member(X1,universal_class) ),
set_in_its_singleton ).
cnf(i_0_209,axiom,
( member_of(singleton(X1)) = X1
| ~ member(X1,universal_class) ),
member_of_singleton_is_unique ).
cnf(i_0_210,axiom,
( ~ member(X1,universal_class)
| singleton(X1) != null_class ),
corollary_to_set_in_its_singleton ).
cnf(i_0_211,axiom,
( member(X1,universal_class)
| unordered_pair(X1,X2) = singleton(X2) ),
unordered_pair_equals_singleton2 ).
cnf(i_0_212,axiom,
( member(X1,universal_class)
| unordered_pair(X2,X1) = singleton(X2) ),
unordered_pair_equals_singleton1 ).
cnf(i_0_213,axiom,
member(singleton(X1),universal_class),
singletons_are_sets ).
cnf(i_0_214,axiom,
( singleton(member_of1(X1)) = X1
| member_of(X1) = X1 ),
member_of_non_singleton_unique2 ).
cnf(i_0_215,axiom,
( singleton(member_of(X1)) = X1
| member_of(X1) = X1 ),
member_exists4 ).
cnf(i_0_216,axiom,
member(null_class,singleton(null_class)),
null_class_in_its_singleton ).
cnf(i_0_217,axiom,
( member(X1,universal_class)
| singleton(X1) = null_class ),
singleton_is_null_class ).
cnf(i_0_218,negated_conjecture,
singleton(member_of(x)) = x,
prove_corollary_2_to_singletons_are_sets_1 ).
cnf(i_0_219,plain,
( homomorphism(X3,X1,X2)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(not_homomorphism1(X3,X1,X2),not_homomorphism1(X3,X1,X2)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(not_homomorphism1(X3,X1,X2),not_homomorphism1(X3,X1,X2)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(not_homomorphism1(X3,X1,X2),not_homomorphism1(X3,X1,X2)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(not_homomorphism2(X3,X1,X2),not_homomorphism2(X3,X1,X2)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(not_homomorphism2(X3,X1,X2),not_homomorphism2(X3,X1,X2)),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(not_homomorphism1(X3,X1,X2),not_homomorphism1(X3,X1,X2)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(not_homomorphism1(X3,X1,X2),not_homomorphism1(X3,X1,X2)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(not_homomorphism1(X3,X1,X2),not_homomorphism1(X3,X1,X2)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(not_homomorphism2(X3,X1,X2),not_homomorphism2(X3,X1,X2)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(not_homomorphism2(X3,X1,X2),not_homomorphism2(X3,X1,X2)),universal_class)),universal_class))))))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X2),not_homomorphism1(X3,X1,X2)),unordered_pair(not_homomorphism1(X3,X1,X2),unordered_pair(not_homomorphism2(X3,X1,X2),not_homomorphism2(X3,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X2),not_homomorphism1(X3,X1,X2)),unordered_pair(not_homomorphism1(X3,X1,X2),unordered_pair(not_homomorphism2(X3,X1,X2),not_homomorphism2(X3,X1,X2))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X2),not_homomorphism1(X3,X1,X2)),unordered_pair(not_homomorphism1(X3,X1,X2),unordered_pair(not_homomorphism2(X3,X1,X2),not_homomorphism2(X3,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X2),not_homomorphism1(X3,X1,X2)),unordered_pair(not_homomorphism1(X3,X1,X2),unordered_pair(not_homomorphism2(X3,X1,X2),not_homomorphism2(X3,X1,X2))))),universal_class)),universal_class)))))))),universal_class)),universal_class)))))))
| ~ operation(X2)
| ~ operation(X1)
| ~ compatible(X3,X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_146,c_0_147]),c_0_147]),c_0_147]),c_0_147]),c_0_147]),c_0_143]),c_0_143]),c_0_143]),c_0_143]),c_0_143]),c_0_143]),c_0_143]),c_0_143]),c_0_144]),c_0_144]),c_0_144]),c_0_144]),c_0_144]),c_0_144]),c_0_144]),c_0_144]),c_0_148]),c_0_148]),c_0_148]),c_0_148]),c_0_148]),c_0_148]),c_0_148]),c_0_148]),c_0_149]),c_0_149]),c_0_149]),c_0_149]),c_0_149]),c_0_149]),
[final] ).
cnf(i_0_220,plain,
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X4,X4),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X4,X4),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X4,X4),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X5,X5),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X5,X5),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X4,X4),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X4,X4),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X4,X4),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X5,X5),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X5,X5),universal_class)),universal_class))))))))))),universal_class)),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(X5,X5))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(X5,X5)))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(X5,X5))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(X5,X5)))),universal_class)),universal_class)))))))),universal_class)),universal_class)))))))
| ~ homomorphism(X1,X2,X3)
| ~ member(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(X5,X5))),domain_of(X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_150,c_0_147]),c_0_147]),c_0_147]),c_0_147]),c_0_147]),c_0_143]),c_0_143]),c_0_143]),c_0_143]),c_0_143]),c_0_143]),c_0_143]),c_0_143]),c_0_144]),c_0_144]),c_0_144]),c_0_144]),c_0_144]),c_0_144]),c_0_144]),c_0_144]),c_0_148]),c_0_148]),c_0_148]),c_0_148]),c_0_148]),c_0_148]),c_0_148]),c_0_148]),c_0_149]),c_0_149]),c_0_149]),c_0_149]),c_0_149]),c_0_149]),c_0_149]),
[final] ).
cnf(i_0_221,plain,
( member(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(X1,X1))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X4,X4),universal_class)),universal_class)))),universal_class)),universal_class))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_151,c_0_139]),c_0_143]),c_0_143]),c_0_144]),c_0_144]),c_0_149]),c_0_149]),
[final] ).
cnf(i_0_222,plain,
( member(X2,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))),universal_class)),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),compose(X3,X4)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_152,c_0_139]),c_0_143]),c_0_143]),c_0_144]),c_0_144]),c_0_149]),
[final] ).
cnf(i_0_223,plain,
( X1 = null_class
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),X1)
| ~ member(X1,universal_class) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_153,c_0_147]),c_0_143]),c_0_144]),c_0_148]),
[final] ).
cnf(i_0_224,plain,
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),unordered_pair(X3,X3))),flip(X4))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),X4)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),unordered_pair(X3,X3))),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_154,c_0_149]),c_0_149]),c_0_149]),c_0_149]),c_0_149]),c_0_149]),
[final] ).
cnf(i_0_225,plain,
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(X4))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),X4)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X1,X1))),unordered_pair(X2,X2))),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_155,c_0_149]),c_0_149]),c_0_149]),c_0_149]),c_0_149]),c_0_149]),
[final] ).
cnf(i_0_226,plain,
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),unordered_pair(X3,X3))),X4)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),flip(X4)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_156,c_0_149]),c_0_149]),c_0_149]),c_0_149]),
[final] ).
cnf(i_0_227,plain,
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X1,X1))),X4)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),rotate(X4)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_157,c_0_149]),c_0_149]),c_0_149]),c_0_149]),
[final] ).
cnf(i_0_228,plain,
( member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),universal_class)
| ~ member(X1,universal_class) ),
inference(rw,[status(thm)],[i_0_158,c_0_159]),
[final] ).
cnf(i_0_229,plain,
( homomorphism(X3,X1,X2)
| member(unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X2),not_homomorphism1(X3,X1,X2)),unordered_pair(not_homomorphism1(X3,X1,X2),unordered_pair(not_homomorphism2(X3,X1,X2),not_homomorphism2(X3,X1,X2)))),domain_of(X1))
| ~ operation(X2)
| ~ operation(X1)
| ~ compatible(X3,X1,X2) ),
inference(rw,[status(thm)],[i_0_160,c_0_149]),
[final] ).
cnf(i_0_230,plain,
( inductive(X1)
| ~ member(null_class,X1)
| ~ subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X1,universal_class)),universal_class)))),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_161,c_0_143]),c_0_144]),
[final] ).
cnf(i_0_231,plain,
intersection(domain_of(X1),complement(domain_of(intersection(compose(domain_of(flip(cross_product(element_relation,universal_class))),X1),identity_relation)))) = cantor(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_162,c_0_163]),c_0_144]),
[final] ).
cnf(i_0_232,plain,
( member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X2,universal_class)),universal_class)))),universal_class)
| ~ function(X1)
| ~ member(X2,universal_class) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_164,c_0_143]),c_0_144]),
[final] ).
cnf(i_0_233,plain,
( subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X1,universal_class)),universal_class)))),X1)
| ~ inductive(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_165,c_0_143]),c_0_144]),
[final] ).
cnf(i_0_234,plain,
intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) = subset_relation,
inference(rw,[status(thm)],[i_0_166,c_0_144]),
[final] ).
cnf(i_0_235,plain,
( member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),successor_relation)
| complement(intersection(complement(X1),complement(unordered_pair(X1,X1)))) != X2
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_167,c_0_168]),c_0_169]),c_0_149]),c_0_149]),
[final] ).
cnf(i_0_236,plain,
( member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),element_relation)
| ~ member(X1,X2)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_170,c_0_149]),c_0_149]),
[final] ).
cnf(i_0_237,plain,
( complement(intersection(complement(X1),complement(unordered_pair(X1,X1)))) = X2
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),successor_relation) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_171,c_0_168]),c_0_169]),c_0_149]),
[final] ).
cnf(i_0_238,plain,
( operation(X1)
| cross_product(domain_of(domain_of(X1)),domain_of(domain_of(X1))) != domain_of(X1)
| ~ function(X1)
| ~ subclass(domain_of(domain_of(flip(cross_product(X1,universal_class)))),domain_of(domain_of(X1))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_172,c_0_136]),c_0_144]),
[final] ).
cnf(i_0_239,plain,
( compatible(X1,X2,X3)
| domain_of(domain_of(X2)) != domain_of(X1)
| ~ function(X1)
| ~ subclass(domain_of(domain_of(flip(cross_product(X1,universal_class)))),domain_of(domain_of(X3))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_173,c_0_136]),c_0_144]),
[final] ).
cnf(i_0_240,plain,
( member(X1,unordered_pair(X1,X2))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(X3,X4)) ),
inference(rw,[status(thm)],[i_0_174,c_0_149]),
[final] ).
cnf(i_0_241,plain,
( member(X2,unordered_pair(X1,X2))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(X3,X4)) ),
inference(rw,[status(thm)],[i_0_175,c_0_149]),
[final] ).
cnf(i_0_242,plain,
( X1 = X3
| unordered_pair(X1,X2) != unordered_pair(X3,X2)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X3,X3))),cross_product(universal_class,universal_class)) ),
inference(rw,[status(thm)],[i_0_176,c_0_149]),
[final] ).
cnf(i_0_243,plain,
( X2 = X3
| unordered_pair(X1,X2) != unordered_pair(X1,X3)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class)) ),
inference(rw,[status(thm)],[i_0_177,c_0_149]),
[final] ).
cnf(i_0_244,plain,
( function(X1)
| ~ subclass(X1,cross_product(universal_class,universal_class))
| ~ subclass(compose(X1,domain_of(flip(cross_product(X1,universal_class)))),identity_relation) ),
inference(rw,[status(thm)],[i_0_178,c_0_144]),
[final] ).
cnf(i_0_245,plain,
( unordered_pair(X1,X2) != null_class
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(X3,X4)) ),
inference(rw,[status(thm)],[i_0_179,c_0_149]),
[final] ).
cnf(i_0_246,plain,
( member(X1,X3)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(X3,X4)) ),
inference(rw,[status(thm)],[i_0_180,c_0_149]),
[final] ).
cnf(i_0_247,plain,
( member(X2,X4)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(X3,X4)) ),
inference(rw,[status(thm)],[i_0_181,c_0_149]),
[final] ).
cnf(i_0_248,plain,
( member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(X3,X4)) ),
inference(rw,[status(thm)],[i_0_182,c_0_149]),
[final] ).
cnf(i_0_249,plain,
( member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(X3,X4)) ),
inference(rw,[status(thm)],[i_0_183,c_0_149]),
[final] ).
cnf(i_0_250,plain,
( single_valued_class(X1)
| ~ subclass(compose(X1,domain_of(flip(cross_product(X1,universal_class)))),identity_relation) ),
inference(rw,[status(thm)],[i_0_184,c_0_144]),
[final] ).
cnf(i_0_251,plain,
( member(X1,X2)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),element_relation) ),
inference(rw,[status(thm)],[i_0_185,c_0_149]),
[final] ).
cnf(i_0_252,plain,
( subclass(domain_of(domain_of(flip(cross_product(X1,universal_class)))),domain_of(domain_of(X3)))
| ~ compatible(X1,X2,X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_186,c_0_136]),c_0_144]),
[final] ).
cnf(i_0_253,plain,
( member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X3,X3))),cross_product(X2,X4))
| ~ member(X3,X4)
| ~ member(X1,X2) ),
inference(rw,[status(thm)],[i_0_187,c_0_149]),
[final] ).
cnf(i_0_254,plain,
( unordered_pair(unordered_pair(first(X1),first(X1)),unordered_pair(first(X1),unordered_pair(second(X1),second(X1)))) = X1
| ~ member(X1,cross_product(X2,X3)) ),
inference(rw,[status(thm)],[i_0_188,c_0_149]),
[final] ).
cnf(i_0_255,plain,
( subclass(domain_of(domain_of(flip(cross_product(X1,universal_class)))),domain_of(domain_of(X1)))
| ~ operation(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_189,c_0_136]),c_0_144]),
[final] ).
cnf(i_0_256,plain,
( subclass(compose(X1,domain_of(flip(cross_product(X1,universal_class)))),identity_relation)
| ~ function(X1) ),
inference(rw,[status(thm)],[i_0_190,c_0_144]),
[final] ).
cnf(i_0_257,plain,
( subclass(compose(X1,domain_of(flip(cross_product(X1,universal_class)))),identity_relation)
| ~ single_valued_class(X1) ),
inference(rw,[status(thm)],[i_0_191,c_0_144]),
[final] ).
cnf(i_0_258,plain,
( one_to_one(X1)
| ~ function(X1)
| ~ function(domain_of(flip(cross_product(X1,universal_class)))) ),
inference(rw,[status(thm)],[i_0_192,c_0_144]),
[final] ).
cnf(i_0_259,plain,
( member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),universal_class)
| ~ member(X1,universal_class) ),
inference(rw,[status(thm)],[i_0_193,c_0_148]),
[final] ).
cnf(i_0_260,plain,
( intersection(X1,cross_product(unordered_pair(X2,X2),universal_class)) != null_class
| ~ member(X2,domain_of(X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_194,c_0_139]),c_0_137]),
[final] ).
cnf(i_0_261,plain,
( unordered_pair(member_of(unordered_pair(X1,X1)),member_of(unordered_pair(X1,X1))) = unordered_pair(X1,X1)
| ~ member(X1,universal_class) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_195,c_0_139]),c_0_139]),c_0_139]),
[final] ).
cnf(i_0_262,axiom,
( compatible(X1,X2,X3)
| ~ homomorphism(X1,X2,X3) ),
homomorphism3,
[final] ).
cnf(i_0_263,plain,
( intersection(X2,cross_product(unordered_pair(X1,X1),universal_class)) = null_class
| member(X1,domain_of(X2))
| ~ member(X1,universal_class) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_196,c_0_139]),c_0_137]),
[final] ).
cnf(i_0_264,axiom,
( X1 = X2
| ~ member(not_subclass_element(X1,X2),X2)
| ~ member(not_subclass_element(X2,X1),X1) ),
equality4,
[final] ).
cnf(i_0_265,plain,
( function(domain_of(flip(cross_product(X1,universal_class))))
| ~ one_to_one(X1) ),
inference(rw,[status(thm)],[i_0_197,c_0_144]),
[final] ).
cnf(i_0_266,plain,
member(unordered_pair(X1,X1),unordered_pair(X2,unordered_pair(X1,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_198,c_0_139]),c_0_139]),
[final] ).
cnf(i_0_267,plain,
intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation) = identity_relation,
inference(rw,[status(thm)],[i_0_199,c_0_144]),
[final] ).
cnf(i_0_268,axiom,
( X2 = X1
| member(not_subclass_element(X2,X1),X2)
| ~ member(not_subclass_element(X1,X2),X2) ),
equality3,
[final] ).
cnf(i_0_269,axiom,
( X1 = X2
| member(not_subclass_element(X2,X1),X2)
| ~ member(not_subclass_element(X1,X2),X2) ),
equality2,
[final] ).
cnf(i_0_270,axiom,
( domain_of(domain_of(X2)) = domain_of(X1)
| ~ compatible(X1,X2,X3) ),
compatible2,
[final] ).
cnf(i_0_271,plain,
( member(member_of(unordered_pair(X1,X1)),universal_class)
| ~ member(X1,universal_class) ),
inference(rw,[status(thm)],[i_0_200,c_0_139]),
[final] ).
cnf(i_0_272,axiom,
( operation(X2)
| ~ homomorphism(X1,X2,X3) ),
homomorphism1,
[final] ).
cnf(i_0_273,axiom,
( operation(X3)
| ~ homomorphism(X1,X2,X3) ),
homomorphism2,
[final] ).
cnf(i_0_274,axiom,
( function(X1)
| ~ compatible(X1,X2,X3) ),
compatible1,
[final] ).
cnf(i_0_275,axiom,
( subclass(unordered_pair(X1,X3),X2)
| ~ member(X1,X2)
| ~ member(X3,X2) ),
unordered_pair_is_subset,
[final] ).
cnf(i_0_276,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
intersection3,
[final] ).
cnf(i_0_277,axiom,
( X1 = X2
| member(not_subclass_element(X1,X2),X1)
| member(not_subclass_element(X2,X1),X2) ),
equality1,
[final] ).
cnf(i_0_278,axiom,
subclass(flip(X1),cross_product(cross_product(universal_class,universal_class),universal_class)),
flip1,
[final] ).
cnf(i_0_279,axiom,
subclass(rotate(X1),cross_product(cross_product(universal_class,universal_class),universal_class)),
rotate1,
[final] ).
cnf(i_0_280,axiom,
~ member(X1,intersection(complement(X2),X2)),
special_classes_lemma,
[final] ).
cnf(i_0_281,plain,
intersection(cross_product(X1,X2),X3) = intersection(X3,cross_product(X1,X2)),
inference(rw,[status(thm)],[i_0_201,c_0_137]),
[final] ).
cnf(i_0_282,axiom,
( subclass(X1,X2)
| ~ member(not_subclass_element(X1,X2),X2) ),
not_subclass_members2,
[final] ).
cnf(i_0_283,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
intersection1,
[final] ).
cnf(i_0_284,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
intersection2,
[final] ).
cnf(i_0_285,plain,
( X2 = X3
| X1 = X3
| unordered_pair(X1,X2) != unordered_pair(X3,X3)
| ~ member(X3,universal_class) ),
inference(rw,[status(thm)],[i_0_202,c_0_139]),
[final] ).
cnf(i_0_286,axiom,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
unordered_pair_member,
[final] ).
cnf(i_0_287,plain,
( X1 = X2
| unordered_pair(X1,X1) != unordered_pair(X2,X2)
| ~ member(X1,universal_class) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_203,c_0_139]),c_0_139]),
[final] ).
cnf(i_0_288,plain,
( X1 = X2
| unordered_pair(X1,X1) != unordered_pair(X2,X2)
| ~ member(X2,universal_class) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_204,c_0_139]),c_0_139]),
[final] ).
cnf(i_0_289,plain,
subclass(unordered_pair(X1,X1),unordered_pair(X1,X2)),
inference(rw,[status(thm)],[i_0_205,c_0_139]),
[final] ).
cnf(i_0_290,plain,
subclass(unordered_pair(X1,X1),unordered_pair(X2,X1)),
inference(rw,[status(thm)],[i_0_206,c_0_139]),
[final] ).
cnf(i_0_291,plain,
( X1 = X2
| ~ member(X1,unordered_pair(X2,X2)) ),
inference(rw,[status(thm)],[i_0_207,c_0_139]),
[final] ).
cnf(i_0_292,axiom,
( cross_product(domain_of(domain_of(X1)),domain_of(domain_of(X1))) = domain_of(X1)
| ~ operation(X1) ),
operation2,
[final] ).
cnf(i_0_293,plain,
( member(X1,unordered_pair(X1,X1))
| ~ member(X1,universal_class) ),
inference(rw,[status(thm)],[i_0_208,c_0_139]),
[final] ).
cnf(i_0_294,axiom,
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
unordered_pair2,
[final] ).
cnf(i_0_295,axiom,
( member(X1,unordered_pair(X2,X1))
| ~ member(X1,universal_class) ),
unordered_pair3,
[final] ).
cnf(i_0_296,axiom,
subclass(compose(X1,X2),cross_product(universal_class,universal_class)),
compose1,
[final] ).
cnf(i_0_297,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
subclass_members,
[final] ).
cnf(i_0_298,axiom,
( subclass(X1,X3)
| ~ subclass(X1,X2)
| ~ subclass(X2,X3) ),
transitivity_of_subclass,
[final] ).
cnf(i_0_299,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ member(X1,universal_class) ),
complement2,
[final] ).
cnf(i_0_300,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
complement1,
[final] ).
cnf(i_0_301,axiom,
( member(not_subclass_element(X1,X2),X1)
| subclass(X1,X2) ),
not_subclass_members1,
[final] ).
cnf(i_0_302,plain,
( member_of(unordered_pair(X1,X1)) = X1
| ~ member(X1,universal_class) ),
inference(rw,[status(thm)],[i_0_209,c_0_139]),
[final] ).
cnf(i_0_303,axiom,
( X1 = X2
| ~ subclass(X1,X2)
| ~ subclass(X2,X1) ),
subclass_implies_equal,
[final] ).
cnf(i_0_304,plain,
( unordered_pair(X1,X1) != null_class
| ~ member(X1,universal_class) ),
inference(rw,[status(thm)],[i_0_210,c_0_139]),
[final] ).
cnf(i_0_305,axiom,
( ~ member(X1,universal_class)
| unordered_pair(X1,X2) != null_class ),
corollary_to_unordered_pair_axiom1,
[final] ).
cnf(i_0_306,axiom,
( ~ member(X1,universal_class)
| unordered_pair(X2,X1) != null_class ),
corollary_to_unordered_pair_axiom2,
[final] ).
cnf(i_0_307,axiom,
( subclass(X1,cross_product(universal_class,universal_class))
| ~ function(X1) ),
function1,
[final] ).
cnf(i_0_308,plain,
( unordered_pair(X1,X2) = unordered_pair(X2,X2)
| member(X1,universal_class) ),
inference(rw,[status(thm)],[i_0_211,c_0_139]),
[final] ).
cnf(i_0_309,plain,
( unordered_pair(X2,X1) = unordered_pair(X2,X2)
| member(X1,universal_class) ),
inference(rw,[status(thm)],[i_0_212,c_0_139]),
[final] ).
cnf(i_0_310,axiom,
( unordered_pair(X1,X2) = null_class
| member(X1,universal_class)
| member(X2,universal_class) ),
null_unordered_pair,
[final] ).
cnf(i_0_311,axiom,
( X1 = null_class
| member(not_subclass_element(X1,null_class),X1) ),
null_class_is_unique,
[final] ).
cnf(i_0_312,plain,
member(unordered_pair(X1,X1),universal_class),
inference(rw,[status(thm)],[i_0_213,c_0_139]),
[final] ).
cnf(i_0_313,axiom,
member(unordered_pair(X1,X2),universal_class),
unordered_pairs_in_universal,
[final] ).
cnf(i_0_314,plain,
( member_of(X1) = X1
| unordered_pair(member_of1(X1),member_of1(X1)) = X1 ),
inference(rw,[status(thm)],[i_0_214,c_0_139]),
[final] ).
cnf(i_0_315,plain,
( member_of(X1) = X1
| unordered_pair(member_of(X1),member_of(X1)) = X1 ),
inference(rw,[status(thm)],[i_0_215,c_0_139]),
[final] ).
cnf(i_0_316,plain,
member(null_class,unordered_pair(null_class,null_class)),
inference(rw,[status(thm)],[i_0_216,c_0_139]),
[final] ).
cnf(i_0_317,axiom,
subclass(successor_relation,cross_product(universal_class,universal_class)),
successor_relation1,
[final] ).
cnf(i_0_318,axiom,
subclass(element_relation,cross_product(universal_class,universal_class)),
element_relation1,
[final] ).
cnf(i_0_319,axiom,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
commutativity_of_unordered_pair,
[final] ).
cnf(i_0_320,plain,
( unordered_pair(X1,X1) = null_class
| member(X1,universal_class) ),
inference(rw,[status(thm)],[i_0_217,c_0_139]),
[final] ).
cnf(i_0_321,axiom,
( member(member_of1(X1),universal_class)
| member_of(X1) = X1 ),
member_of_non_singleton_unique1,
[final] ).
cnf(i_0_322,axiom,
( member(member_of(X1),universal_class)
| member_of(X1) = X1 ),
member_exists3,
[final] ).
cnf(i_0_323,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
regularity1,
[final] ).
cnf(i_0_324,axiom,
( X1 = null_class
| intersection(X1,regular(X1)) = null_class ),
regularity2,
[final] ).
cnf(i_0_325,axiom,
( X1 = null_class
| ~ subclass(X1,null_class) ),
corollary_of_null_class_is_subclass,
[final] ).
cnf(i_0_326,negated_conjecture,
unordered_pair(member_of(x),member_of(x)) = x,
inference(rw,[status(thm)],[i_0_218,c_0_139]),
[final] ).
cnf(i_0_327,axiom,
~ member(X1,null_class),
existence_of_null_class,
[final] ).
cnf(i_0_328,axiom,
( member(null_class,X1)
| ~ inductive(X1) ),
inductive1,
[final] ).
cnf(i_0_329,axiom,
( subclass(omega,X1)
| ~ inductive(X1) ),
omega_is_inductive2,
[final] ).
cnf(i_0_330,axiom,
( subclass(X1,X2)
| X1 != X2 ),
equal_implies_subclass1,
[final] ).
cnf(i_0_331,axiom,
( subclass(X2,X1)
| X1 != X2 ),
equal_implies_subclass2,
[final] ).
cnf(i_0_332,negated_conjecture,
~ member(x,universal_class),
prove_corollary_2_to_singletons_are_sets_2,
[final] ).
cnf(i_0_333,axiom,
subclass(X1,X1),
subclass_is_reflexive,
[final] ).
cnf(i_0_334,axiom,
subclass(null_class,X1),
null_class_is_subclass,
[final] ).
cnf(i_0_335,axiom,
subclass(X1,universal_class),
class_elements_are_sets,
[final] ).
cnf(i_0_336,axiom,
( function(X1)
| ~ operation(X1) ),
operation1,
[final] ).
cnf(i_0_337,axiom,
( function(X1)
| ~ one_to_one(X1) ),
one_to_one1,
[final] ).
cnf(i_0_338,axiom,
member(omega,universal_class),
omega_in_universal,
[final] ).
cnf(i_0_339,axiom,
member(null_class,universal_class),
null_class_is_a_set,
[final] ).
cnf(i_0_340,axiom,
function(choice),
choice1,
[final] ).
cnf(i_0_341,axiom,
inductive(omega),
omega_is_inductive1,
[final] ).
cnf(i_0_342,axiom,
X1 = X1 ).
cnf(i_0_343,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_344,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_345,axiom,
( X1 != X2
| domain_of(X1) = domain_of(X2) ) ).
cnf(i_0_346,axiom,
( X1 != X2
| complement(X1) = complement(X2) ) ).
cnf(i_0_347,axiom,
( X1 != X2
| cantor(X1) = cantor(X2) ) ).
cnf(i_0_348,axiom,
( X1 != X2
| member_of(X1) = member_of(X2) ) ).
cnf(i_0_349,axiom,
( X1 != X2
| intersection(X1,X3) = intersection(X2,X3) ) ).
cnf(i_0_350,axiom,
( X1 != X2
| intersection(X3,X1) = intersection(X3,X2) ) ).
cnf(i_0_351,axiom,
( X1 != X2
| cross_product(X1,X3) = cross_product(X2,X3) ) ).
cnf(i_0_352,axiom,
( X1 != X2
| cross_product(X3,X1) = cross_product(X3,X2) ) ).
cnf(i_0_353,axiom,
( X1 != X2
| unordered_pair(X1,X3) = unordered_pair(X2,X3) ) ).
cnf(i_0_354,axiom,
( X1 != X2
| unordered_pair(X3,X1) = unordered_pair(X3,X2) ) ).
cnf(i_0_355,axiom,
( X1 != X2
| ~ homomorphism(X1,X3,X4)
| homomorphism(X2,X3,X4) ) ).
cnf(i_0_356,axiom,
( X1 != X2
| ~ homomorphism(X3,X1,X4)
| homomorphism(X3,X2,X4) ) ).
cnf(i_0_357,axiom,
( X1 != X2
| ~ homomorphism(X3,X4,X1)
| homomorphism(X3,X4,X2) ) ).
cnf(i_0_358,axiom,
( X1 != X2
| ~ operation(X1)
| operation(X2) ) ).
cnf(i_0_359,axiom,
( X1 != X2
| ~ compatible(X1,X3,X4)
| compatible(X2,X3,X4) ) ).
cnf(i_0_360,axiom,
( X1 != X2
| ~ compatible(X3,X1,X4)
| compatible(X3,X2,X4) ) ).
cnf(i_0_361,axiom,
( X1 != X2
| ~ compatible(X3,X4,X1)
| compatible(X3,X4,X2) ) ).
cnf(i_0_362,axiom,
( X1 != X2
| ~ member(X1,X3)
| member(X2,X3) ) ).
cnf(i_0_363,axiom,
( X1 != X2
| ~ member(X3,X1)
| member(X3,X2) ) ).
cnf(i_0_364,axiom,
( X1 != X2
| ~ inductive(X1)
| inductive(X2) ) ).
cnf(i_0_365,axiom,
( X1 != X2
| ~ subclass(X1,X3)
| subclass(X2,X3) ) ).
cnf(i_0_366,axiom,
( X1 != X2
| ~ subclass(X3,X1)
| subclass(X3,X2) ) ).
cnf(i_0_367,axiom,
( X1 != X2
| ~ function(X1)
| function(X2) ) ).
cnf(i_0_368,axiom,
( X1 != X2
| ~ single_valued_class(X1)
| single_valued_class(X2) ) ).
cnf(i_0_369,axiom,
( X1 != X2
| ~ one_to_one(X1)
| one_to_one(X2) ) ).
cnf(i_0_342_001,axiom,
X1 = X1 ).
cnf(i_0_343_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_344_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_345_004,axiom,
( X1 != X2
| domain_of(X1) = domain_of(X2) ) ).
cnf(i_0_346_005,axiom,
( X1 != X2
| complement(X1) = complement(X2) ) ).
cnf(i_0_347_006,axiom,
( X1 != X2
| cantor(X1) = cantor(X2) ) ).
cnf(i_0_348_007,axiom,
( X1 != X2
| member_of(X1) = member_of(X2) ) ).
cnf(i_0_349_008,axiom,
( X1 != X2
| intersection(X1,X3) = intersection(X2,X3) ) ).
cnf(i_0_350_009,axiom,
( X1 != X2
| intersection(X3,X1) = intersection(X3,X2) ) ).
cnf(i_0_351_010,axiom,
( X1 != X2
| cross_product(X1,X3) = cross_product(X2,X3) ) ).
cnf(i_0_352_011,axiom,
( X1 != X2
| cross_product(X3,X1) = cross_product(X3,X2) ) ).
cnf(i_0_353_012,axiom,
( X1 != X2
| unordered_pair(X1,X3) = unordered_pair(X2,X3) ) ).
cnf(i_0_354_013,axiom,
( X1 != X2
| unordered_pair(X3,X1) = unordered_pair(X3,X2) ) ).
cnf(i_0_355_014,axiom,
( X1 != X2
| ~ homomorphism(X1,X3,X4)
| homomorphism(X2,X3,X4) ) ).
cnf(i_0_356_015,axiom,
( X1 != X2
| ~ homomorphism(X3,X1,X4)
| homomorphism(X3,X2,X4) ) ).
cnf(i_0_357_016,axiom,
( X1 != X2
| ~ homomorphism(X3,X4,X1)
| homomorphism(X3,X4,X2) ) ).
cnf(i_0_358_017,axiom,
( X1 != X2
| ~ operation(X1)
| operation(X2) ) ).
cnf(i_0_359_018,axiom,
( X1 != X2
| ~ compatible(X1,X3,X4)
| compatible(X2,X3,X4) ) ).
cnf(i_0_360_019,axiom,
( X1 != X2
| ~ compatible(X3,X1,X4)
| compatible(X3,X2,X4) ) ).
cnf(i_0_361_020,axiom,
( X1 != X2
| ~ compatible(X3,X4,X1)
| compatible(X3,X4,X2) ) ).
cnf(i_0_362_021,axiom,
( X1 != X2
| ~ member(X1,X3)
| member(X2,X3) ) ).
cnf(i_0_363_022,axiom,
( X1 != X2
| ~ member(X3,X1)
| member(X3,X2) ) ).
cnf(i_0_364_023,axiom,
( X1 != X2
| ~ inductive(X1)
| inductive(X2) ) ).
cnf(i_0_365_024,axiom,
( X1 != X2
| ~ subclass(X1,X3)
| subclass(X2,X3) ) ).
cnf(i_0_366_025,axiom,
( X1 != X2
| ~ subclass(X3,X1)
| subclass(X3,X2) ) ).
cnf(i_0_367_026,axiom,
( X1 != X2
| ~ function(X1)
| function(X2) ) ).
cnf(i_0_368_027,axiom,
( X1 != X2
| ~ single_valued_class(X1)
| single_valued_class(X2) ) ).
cnf(i_0_369_028,axiom,
( X1 != X2
| ~ one_to_one(X1)
| one_to_one(X2) ) ).
cnf(i_0_370,plain,
( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(complement(intersection(complement(X1),complement(unordered_pair(X1,X1)))),complement(intersection(complement(X1),complement(unordered_pair(X1,X1))))))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(complement(intersection(complement(X1),complement(unordered_pair(X1,X1)))),complement(intersection(complement(X1),complement(unordered_pair(X1,X1))))))),successor_relation) ),
inference(equality_inference,[],[235]) ).
cnf(i_0_371,plain,
( ~ function(domain_of(X1))
| compatible(domain_of(X1),X1,X2)
| ~ subclass(domain_of(domain_of(flip(cross_product(domain_of(X1),universal_class)))),domain_of(domain_of(X2))) ),
inference(equality_inference,[],[239]) ).
cnf(i_0_372,plain,
( X1 = X1
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ),
inference(equality_inference,[],[242]) ).
cnf(i_0_373,plain,
( X1 = X1
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ),
inference(equality_inference,[],[243]) ).
cnf(i_0_374,plain,
( X1 = X1
| X1 = X1
| ~ member(X1,universal_class) ),
inference(equality_inference,[],[285]) ).
cnf(i_0_375,plain,
( X1 = X1
| ~ member(X1,universal_class) ),
inference(equality_inference,[],[287]) ).
cnf(i_0_376,plain,
( X1 = X1
| ~ member(X1,universal_class) ),
inference(equality_inference,[],[288]) ).
cnf(i_0_377,plain,
subclass(X1,X1),
inference(equality_inference,[],[330]) ).
cnf(i_0_378,plain,
subclass(X1,X1),
inference(equality_inference,[],[331]) ).
cnf(i_0_379,plain,
subclass(unordered_pair(member_of(x),member_of(x)),x),
inference(scs_inference,[],[i_0_326,i_0_330]) ).
cnf(i_0_380,plain,
( X1 != X2
| subclass(X1,X2) ),
inference(rename_variables,[],[i_0_330]) ).
cnf(i_0_381,plain,
subclass(x,unordered_pair(member_of(x),member_of(x))),
inference(scs_inference,[],[i_0_326,i_0_330,i_0_331]) ).
cnf(i_0_382,plain,
( X1 != X2
| subclass(X2,X1) ),
inference(rename_variables,[],[i_0_331]) ).
cnf(i_0_383,plain,
x = unordered_pair(member_of(x),member_of(x)),
inference(scs_inference,[],[i_0_326,i_0_330,i_0_331,i_0_343]) ).
cnf(i_0_384,plain,
member(omega,unordered_pair(omega,X1)),
inference(scs_inference,[],[i_0_326,i_0_338,i_0_330,i_0_331,i_0_343,i_0_294]) ).
cnf(i_0_385,plain,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X1,X2)) ),
inference(rename_variables,[],[i_0_294]) ).
cnf(i_0_386,plain,
member(omega,unordered_pair(X1,omega)),
inference(scs_inference,[],[i_0_326,i_0_338,i_0_330,i_0_331,i_0_343,i_0_294,i_0_295]) ).
cnf(i_0_387,plain,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X2,X1)) ),
inference(rename_variables,[],[i_0_295]) ).
cnf(i_0_388,plain,
subclass(intersection(complement(X1),X1),X2),
inference(scs_inference,[],[i_0_326,i_0_338,i_0_280,i_0_330,i_0_331,i_0_343,i_0_294,i_0_295,i_0_301]) ).
cnf(i_0_389,plain,
~ member(X1,intersection(complement(X2),X2)),
inference(rename_variables,[],[i_0_280]) ).
cnf(i_0_390,plain,
( member(not_subclass_element(X1,X2),X1)
| subclass(X1,X2) ),
inference(rename_variables,[],[i_0_301]) ).
cnf(i_0_391,plain,
unordered_pair(x,X1) = unordered_pair(X1,X1),
inference(scs_inference,[],[i_0_326,i_0_332,i_0_338,i_0_280,i_0_330,i_0_331,i_0_343,i_0_294,i_0_295,i_0_301,i_0_308]) ).
cnf(i_0_392,plain,
( member(X1,universal_class)
| unordered_pair(X1,X2) = unordered_pair(X2,X2) ),
inference(rename_variables,[],[i_0_308]) ).
cnf(i_0_393,plain,
unordered_pair(X1,x) = unordered_pair(X1,X1),
inference(scs_inference,[],[i_0_326,i_0_332,i_0_338,i_0_280,i_0_330,i_0_331,i_0_343,i_0_294,i_0_295,i_0_301,i_0_308,i_0_309]) ).
cnf(i_0_394,plain,
( member(X1,universal_class)
| unordered_pair(X2,X1) = unordered_pair(X2,X2) ),
inference(rename_variables,[],[i_0_309]) ).
cnf(i_0_395,plain,
intersection(complement(X1),X1) = null_class,
inference(scs_inference,[],[i_0_326,i_0_332,i_0_338,i_0_280,i_0_389,i_0_330,i_0_331,i_0_343,i_0_294,i_0_295,i_0_301,i_0_308,i_0_309,i_0_311]) ).
cnf(i_0_396,plain,
~ member(X1,intersection(complement(X2),X2)),
inference(rename_variables,[],[i_0_280]) ).
cnf(i_0_397,plain,
( member(not_subclass_element(X1,null_class),X1)
| X1 = null_class ),
inference(rename_variables,[],[i_0_311]) ).
cnf(i_0_398,plain,
~ inductive(null_class),
inference(scs_inference,[],[i_0_326,i_0_332,i_0_327,i_0_338,i_0_280,i_0_389,i_0_330,i_0_331,i_0_343,i_0_294,i_0_295,i_0_301,i_0_308,i_0_309,i_0_311,i_0_328]) ).
cnf(i_0_399,plain,
~ member(X1,null_class),
inference(rename_variables,[],[i_0_327]) ).
cnf(i_0_400,plain,
( member(null_class,X1)
| ~ inductive(X1) ),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_401,plain,
intersection(cross_product(X1,X2),complement(cross_product(X1,X2))) = null_class,
inference(scs_inference,[],[i_0_326,i_0_332,i_0_327,i_0_338,i_0_281,i_0_280,i_0_389,i_0_330,i_0_331,i_0_343,i_0_294,i_0_295,i_0_301,i_0_308,i_0_309,i_0_311,i_0_328,i_0_344]) ).
cnf(i_0_402,plain,
intersection(cross_product(X1,X2),X3) = intersection(X3,cross_product(X1,X2)),
inference(rename_variables,[],[i_0_281]) ).
cnf(i_0_403,plain,
$false,
inference(scs_inference,[],[i_0_326,i_0_332,i_0_327,i_0_338,i_0_313,i_0_281,i_0_280,i_0_389,i_0_330,i_0_331,i_0_343,i_0_294,i_0_295,i_0_301,i_0_308,i_0_309,i_0_311,i_0_328,i_0_344,i_0_362]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET093-7 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n029.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 02:10:30 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 0.32/1.62 % Version : CSE_E---1.7
% 0.32/1.62 % Problem : theBenchmark.p
% 0.32/1.62 % SZS status Unsatisfiable for theBenchmark.p
% 0.32/1.62 % SZS output start CNFRefutation
% See solution above
% 0.41/1.71 % Total time : 1.273s
%------------------------------------------------------------------------------