TSTP Solution File: SET064+1 by ConnectPP---0.3.0
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%------------------------------------------------------------------------------
% File : ConnectPP---0.3.0
% Problem : SET064+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% Computer : n011.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 : Mon Mar 25 14:31:01 EDT 2024
% Result : Theorem 0.19s 0.51s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET064+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.03/0.13 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Mar 20 21:56:27 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.19/0.51 % SZS status Theorem for theBenchmark
% 0.19/0.51 % SZS output start Proof for theBenchmark
% 0.19/0.51
% 0.19/0.51 % Formula: subclass_defn ( axiom ) converted to clauses:
% 0.19/0.51 cnf(subclass_defn-1, axiom, ( ~subclass(_u6, _u4) | ~member(_u0, _u6) | member(_u0, _u4) )).
% 0.19/0.51 cnf(subclass_defn-2, axiom, ( subclass(_u7, _u5) | member(skolem1(_u7, _u5), _u7) )).
% 0.19/0.51 cnf(subclass_defn-3, axiom, ( subclass(_u7, _u5) | ~member(skolem1(_u7, _u5), _u5) )).
% 0.19/0.51
% 0.19/0.51 % Formula: class_elements_are_sets ( axiom ) converted to clauses:
% 0.19/0.51 cnf(class_elements_are_sets-1, axiom, ( subclass(_u8, universal_class) )).
% 0.19/0.51
% 0.19/0.51 % Formula: extensionality ( axiom ) converted to clauses:
% 0.19/0.51 cnf(extensionality-1, axiom, ( ( _u13 != _u11) | subclass(_u13, _u11) )).
% 0.19/0.51 cnf(extensionality-2, axiom, ( ( _u13 != _u11) | subclass(_u11, _u13) )).
% 0.19/0.51 cnf(extensionality-3, axiom, ( ~subclass(_u14, _u12) | ~subclass(_u12, _u14) | ( _u14 = _u12) )).
% 0.19/0.51
% 0.19/0.51 % Formula: unordered_pair_defn ( axiom ) converted to clauses:
% 0.19/0.51 cnf(unordered_pair_defn-1, axiom, ( ~member(_u22, unordered_pair(_u20, _u18)) | member(_u22, universal_class) )).
% 0.19/0.51 cnf(unordered_pair_defn-2, axiom, ( ~member(_u22, unordered_pair(_u20, _u18)) | ( _u22 = _u20) | ( _u22 = _u18) )).
% 0.19/0.51 cnf(unordered_pair_defn-3, axiom, ( member(_u23, unordered_pair(_u21, _u19)) | ~member(_u23, universal_class) | ( _u23 != _u21) )).
% 0.19/0.51 cnf(unordered_pair_defn-4, axiom, ( member(_u23, unordered_pair(_u21, _u19)) | ~member(_u23, universal_class) | ( _u23 != _u19) )).
% 0.19/0.51
% 0.19/0.51 % Formula: unordered_pair ( axiom ) converted to clauses:
% 0.19/0.51 cnf(unordered_pair-1, axiom, ( member(unordered_pair(_u25, _u24), universal_class) )).
% 0.19/0.51
% 0.19/0.51 % Formula: singleton_set_defn ( axiom ) converted to clauses:
% 0.19/0.51 cnf(singleton_set_defn-1, axiom, ( ( singleton(_u26) = unordered_pair(_u26, _u26)) )).
% 0.19/0.51
% 0.19/0.51 % Formula: ordered_pair_defn ( axiom ) converted to clauses:
% 0.19/0.51 cnf(ordered_pair_defn-1, axiom, ( ( ordered_pair(_u28, _u27) = unordered_pair(singleton(_u28), unordered_pair(_u28, singleton(_u27)))) )).
% 0.19/0.51
% 0.19/0.51 % Formula: cross_product_defn ( axiom ) converted to clauses:
% 0.19/0.51 cnf(cross_product_defn-1, axiom, ( ~member(ordered_pair(_u39, _u37), cross_product(_u35, _u33)) | member(_u39, _u35) )).
% 0.19/0.51 cnf(cross_product_defn-2, axiom, ( ~member(ordered_pair(_u39, _u37), cross_product(_u35, _u33)) | member(_u37, _u33) )).
% 0.19/0.51 cnf(cross_product_defn-3, axiom, ( ~member(_u40, _u36) | ~member(_u38, _u34) | member(ordered_pair(_u40, _u38), cross_product(_u36, _u34)) )).
% 0.19/0.51
% 0.19/0.51 % Formula: first_second ( axiom ) converted to clauses:
% 0.19/0.51 cnf(first_second-1, axiom, ( ~member(_u42, universal_class) | ~member(_u41, universal_class) | ( first(ordered_pair(_u42, _u41)) = _u42) )).
% 0.19/0.51 cnf(first_second-2, axiom, ( ~member(_u42, universal_class) | ~member(_u41, universal_class) | ( second(ordered_pair(_u42, _u41)) = _u41) )).
% 0.19/0.51
% 0.19/0.51 % Formula: cross_product ( axiom ) converted to clauses:
% 0.19/0.51 cnf(cross_product-1, axiom, ( ~member(_u43, cross_product(_u45, _u44)) | ( _u43 = ordered_pair(first(_u43), second(_u43))) )).
% 0.19/0.51
% 0.19/0.51 % Formula: element_relation_defn ( axiom ) converted to clauses:
% 0.19/0.51 cnf(element_relation_defn-1, axiom, ( ~member(ordered_pair(_u50, _u48), element_relation) | member(_u48, universal_class) )).
% 0.19/0.51 cnf(element_relation_defn-2, axiom, ( ~member(ordered_pair(_u50, _u48), element_relation) | member(_u50, _u48) )).
% 0.19/0.51 cnf(element_relation_defn-3, axiom, ( ~member(_u49, universal_class) | ~member(_u51, _u49) | member(ordered_pair(_u51, _u49), element_relation) )).
% 0.19/0.51
% 0.19/0.51 % Formula: element_relation ( axiom ) converted to clauses:
% 0.19/0.51 cnf(element_relation-1, axiom, ( subclass(element_relation, cross_product(universal_class, universal_class)) )).
% 0.19/0.51
% 0.19/0.51 % Formula: intersection ( axiom ) converted to clauses:
% 0.19/0.51 cnf(intersection-1, axiom, ( ~member(_u55, intersection(_u59, _u57)) | member(_u55, _u59) )).
% 0.19/0.51 cnf(intersection-2, axiom, ( ~member(_u55, intersection(_u59, _u57)) | member(_u55, _u57) )).
% 0.19/0.51 cnf(intersection-3, axiom, ( ~member(_u56, _u60) | ~member(_u56, _u58) | member(_u56, intersection(_u60, _u58)) )).
% 0.19/0.51
% 0.19/0.51 % Formula: complement ( axiom ) converted to clauses:
% 0.19/0.51 cnf(complement-1, axiom, ( ~member(_u63, complement(_u65)) | member(_u63, universal_class) )).
% 0.19/0.51 cnf(complement-2, axiom, ( ~member(_u63, complement(_u65)) | ~member(_u63, _u65) )).
% 0.19/0.51 cnf(complement-3, axiom, ( ~member(_u64, universal_class) | member(_u64, _u66) | member(_u64, complement(_u66)) )).
% 0.19/0.51
% 0.19/0.51 % Formula: restrict_defn ( axiom ) converted to clauses:
% 0.19/0.51 cnf(restrict_defn-1, axiom, ( ( restrict(_u68, _u69, _u67) = intersection(_u68, cross_product(_u69, _u67))) )).
% 0.19/0.51
% 0.19/0.51 % Formula: null_class_defn ( axiom ) converted to clauses:
% 0.19/0.51 cnf(null_class_defn-1, axiom, ( ~member(_u70, null_class) )).
% 0.19/0.51
% 0.19/0.51 % Formula: domain_of ( axiom ) converted to clauses:
% 0.19/0.51 cnf(domain_of-1, axiom, ( ~member(_u73, domain_of(_u75)) | member(_u73, universal_class) )).
% 0.19/0.51 cnf(domain_of-2, axiom, ( ~member(_u73, domain_of(_u75)) | ( restrict(_u75, singleton(_u73), universal_class) != null_class) )).
% 0.19/0.51 cnf(domain_of-3, axiom, ( ~member(_u74, universal_class) | ( restrict(_u76, singleton(_u74), universal_class) = null_class) | member(_u74, domain_of(_u76)) )).
% 0.19/0.51
% 0.19/0.51 % Formula: rotate_defn ( axiom ) converted to clauses:
% 0.19/0.51 cnf(rotate_defn-1, axiom, ( ~member(ordered_pair(ordered_pair(_u85, _u83), _u81), rotate(_u87)) | member(ordered_pair(ordered_pair(_u85, _u83), _u81), cross_product(cross_product(universal_class, universal_class), universal_class)) )).
% 0.19/0.51 cnf(rotate_defn-2, axiom, ( ~member(ordered_pair(ordered_pair(_u85, _u83), _u81), rotate(_u87)) | member(ordered_pair(ordered_pair(_u83, _u81), _u85), _u87) )).
% 0.19/0.51 cnf(rotate_defn-3, axiom, ( ~member(ordered_pair(ordered_pair(_u86, _u84), _u82), cross_product(cross_product(universal_class, universal_class), universal_class)) | ~member(ordered_pair(ordered_pair(_u84, _u82), _u86), _u88) | member(ordered_pair(ordered_pair(_u86, _u84), _u82), rotate(_u88)) )).
% 0.19/0.51
% 0.19/0.51 % Formula: rotate ( axiom ) converted to clauses:
% 0.19/0.51 cnf(rotate-1, axiom, ( subclass(rotate(_u89), cross_product(cross_product(universal_class, universal_class), universal_class)) )).
% 0.19/0.51
% 0.19/0.51 % Formula: flip_defn ( axiom ) converted to clauses:
% 0.19/0.51 cnf(flip_defn-1, axiom, ( ~member(ordered_pair(ordered_pair(_u100, _u98), _u96), flip(_u94)) | member(ordered_pair(ordered_pair(_u100, _u98), _u96), cross_product(cross_product(universal_class, universal_class), universal_class)) )).
% 0.19/0.51 cnf(flip_defn-2, axiom, ( ~member(ordered_pair(ordered_pair(_u100, _u98), _u96), flip(_u94)) | member(ordered_pair(ordered_pair(_u98, _u100), _u96), _u94) )).
% 0.19/0.51 cnf(flip_defn-3, axiom, ( ~member(ordered_pair(ordered_pair(_u101, _u99), _u97), cross_product(cross_product(universal_class, universal_class), universal_class)) | ~member(ordered_pair(ordered_pair(_u99, _u101), _u97), _u95) | member(ordered_pair(ordered_pair(_u101, _u99), _u97), flip(_u95)) )).
% 0.19/0.51
% 0.19/0.51 % Formula: flip ( axiom ) converted to clauses:
% 0.19/0.51 cnf(flip-1, axiom, ( subclass(flip(_u102), cross_product(cross_product(universal_class, universal_class), universal_class)) )).
% 0.19/0.51
% 0.19/0.51 % Formula: union_defn ( axiom ) converted to clauses:
% 0.19/0.51 cnf(union_defn-1, axiom, ( ~member(_u106, union(_u110, _u108)) | member(_u106, _u110) | member(_u106, _u108) )).
% 0.19/0.51 cnf(union_defn-2, axiom, ( member(_u107, union(_u111, _u109)) | ~member(_u107, _u111) )).
% 0.19/0.51 cnf(union_defn-3, axiom, ( member(_u107, union(_u111, _u109)) | ~member(_u107, _u109) )).
% 0.19/0.51
% 0.19/0.51 % Formula: successor_defn ( axiom ) converted to clauses:
% 0.19/0.51 cnf(successor_defn-1, axiom, ( ( successor(_u112) = union(_u112, singleton(_u112))) )).
% 0.19/0.51
% 0.19/0.51 % Formula: successor_relation_defn1 ( axiom ) converted to clauses:
% 0.19/0.51 cnf(successor_relation_defn1-1, axiom, ( subclass(successor_relation, cross_product(universal_class, universal_class)) )).
% 0.19/0.51
% 0.19/0.51 % Formula: successor_relation_defn2 ( axiom ) converted to clauses:
% 0.19/0.51 cnf(successor_relation_defn2-1, axiom, ( ~member(ordered_pair(_u117, _u115), successor_relation) | member(_u117, universal_class) )).
% 0.19/0.51 cnf(successor_relation_defn2-2, axiom, ( ~member(ordered_pair(_u117, _u115), successor_relation) | member(_u115, universal_class) )).
% 0.19/0.51 cnf(successor_relation_defn2-3, axiom, ( ~member(ordered_pair(_u117, _u115), successor_relation) | ( successor(_u117) = _u115) )).
% 0.19/0.51 cnf(successor_relation_defn2-4, axiom, ( ~member(_u118, universal_class) | ~member(_u116, universal_class) | ( successor(_u118) != _u116) | member(ordered_pair(_u118, _u116), successor_relation) )).
% 0.19/0.51
% 0.19/0.51 % Formula: inverse_defn ( axiom ) converted to clauses:
% 0.19/0.51 cnf(inverse_defn-1, axiom, ( ( inverse(_u119) = domain_of(flip(cross_product(_u119, universal_class)))) )).
% 0.19/0.51
% 0.19/0.51 % Formula: range_of_defn ( axiom ) converted to clauses:
% 0.19/0.51 cnf(range_of_defn-1, axiom, ( ( range_of(_u120) = domain_of(inverse(_u120))) )).
% 0.19/0.51
% 0.19/0.51 % Formula: image_defn ( axiom ) converted to clauses:
% 0.19/0.51 cnf(image_defn-1, axiom, ( ( image(_u121, _u122) = range_of(restrict(_u121, _u122, universal_class))) )).
% 0.19/0.51
% 0.19/0.51 % Formula: inductive_defn ( axiom ) converted to clauses:
% 0.19/0.51 cnf(inductive_defn-1, axiom, ( ~inductive(_u124) | member(null_class, _u124) )).
% 0.19/0.51 cnf(inductive_defn-2, axiom, ( ~inductive(_u124) | subclass(image(successor_relation, _u124), _u124) )).
% 0.19/0.51 cnf(inductive_defn-3, axiom, ( ~member(null_class, _u125) | ~subclass(image(successor_relation, _u125), _u125) | inductive(_u125) )).
% 0.19/0.51
% 0.19/0.51 % Formula: infinity ( axiom ) converted to clauses:
% 0.19/0.51 cnf(infinity-1, axiom, ( member(skolem2, universal_class) )).
% 0.19/0.51 cnf(infinity-2, axiom, ( inductive(skolem2) )).
% 0.19/0.51 cnf(infinity-3, axiom, ( ~inductive(_u126) | subclass(skolem2, _u126) )).
% 0.19/0.51
% 0.19/0.51 % Formula: sum_class_defn ( axiom ) converted to clauses:
% 0.19/0.51 cnf(sum_class_defn-1, axiom, ( ~member(_u134, sum_class(_u132)) | member(_u134, skolem3(_u134, _u132)) )).
% 0.19/0.51 cnf(sum_class_defn-2, axiom, ( ~member(_u134, sum_class(_u132)) | member(skolem3(_u134, _u132), _u132) )).
% 0.19/0.51 cnf(sum_class_defn-3, axiom, ( ~member(_u135, _u129) | ~member(_u129, _u133) | member(_u135, sum_class(_u133)) )).
% 0.19/0.51
% 0.19/0.51 % Formula: sum_class ( axiom ) converted to clauses:
% 0.19/0.51 cnf(sum_class-1, axiom, ( ~member(_u136, universal_class) | member(sum_class(_u136), universal_class) )).
% 0.19/0.51
% 0.19/0.51 % Formula: power_class_defn ( axiom ) converted to clauses:
% 0.19/0.51 cnf(power_class_defn-1, axiom, ( ~member(_u141, power_class(_u139)) | member(_u141, universal_class) )).
% 0.19/0.51 cnf(power_class_defn-2, axiom, ( ~member(_u141, power_class(_u139)) | subclass(_u141, _u139) )).
% 0.19/0.51 cnf(power_class_defn-3, axiom, ( ~member(_u142, universal_class) | ~subclass(_u142, _u140) | member(_u142, power_class(_u140)) )).
% 0.19/0.51
% 0.19/0.51 % Formula: power_class ( axiom ) converted to clauses:
% 0.19/0.51 cnf(power_class-1, axiom, ( ~member(_u143, universal_class) | member(power_class(_u143), universal_class) )).
% 0.19/0.51
% 0.19/0.51 % Formula: compose_defn1 ( axiom ) converted to clauses:
% 0.19/0.51 cnf(compose_defn1-1, axiom, ( subclass(compose(_u144, _u145), cross_product(universal_class, universal_class)) )).
% 0.19/0.51
% 0.19/0.51 % Formula: compose_defn2 ( axiom ) converted to clauses:
% 0.19/0.51 cnf(compose_defn2-1, axiom, ( ~member(ordered_pair(_u152, _u150), compose(_u154, _u156)) | member(_u152, universal_class) )).
% 0.19/0.51 cnf(compose_defn2-2, axiom, ( ~member(ordered_pair(_u152, _u150), compose(_u154, _u156)) | member(_u150, image(_u154, image(_u156, singleton(_u152)))) )).
% 0.19/0.51 cnf(compose_defn2-3, axiom, ( ~member(_u153, universal_class) | ~member(_u151, image(_u155, image(_u157, singleton(_u153)))) | member(ordered_pair(_u153, _u151), compose(_u155, _u157)) )).
% 0.19/0.51
% 0.19/0.51 % Formula: identity_relation ( axiom ) converted to clauses:
% 0.19/0.51 cnf(identity_relation-1, axiom, ( ~member(_u161, identity_relation) | member(skolem4(_u161), universal_class) )).
% 0.19/0.51 cnf(identity_relation-2, axiom, ( ~member(_u161, identity_relation) | ( _u161 = ordered_pair(skolem4(_u161), skolem4(_u161))) )).
% 0.19/0.51 cnf(identity_relation-3, axiom, ( ~member(_u159, universal_class) | ( _u162 != ordered_pair(_u159, _u159)) | member(_u162, identity_relation) )).
% 0.19/0.51
% 0.19/0.51 % Formula: function_defn ( axiom ) converted to clauses:
% 0.19/0.51 cnf(function_defn-1, axiom, ( ~function(_u164) | subclass(_u164, cross_product(universal_class, universal_class)) )).
% 0.19/0.51 cnf(function_defn-2, axiom, ( ~function(_u164) | subclass(compose(_u164, inverse(_u164)), identity_relation) )).
% 0.19/0.51 cnf(function_defn-3, axiom, ( ~subclass(_u165, cross_product(universal_class, universal_class)) | ~subclass(compose(_u165, inverse(_u165)), identity_relation) | function(_u165) )).
% 0.19/0.51
% 0.19/0.51 % Formula: replacement ( axiom ) converted to clauses:
% 0.19/0.51 cnf(replacement-1, axiom, ( ~member(_u167, universal_class) | ~function(_u166) | member(image(_u166, _u167), universal_class) )).
% 0.19/0.51
% 0.19/0.51 % Formula: disjoint_defn ( axiom ) converted to clauses:
% 0.19/0.51 cnf(disjoint_defn-1, axiom, ( ~disjoint(_u174, _u172) | ~member(_u168, _u174) | ~member(_u168, _u172) )).
% 0.19/0.51 cnf(disjoint_defn-2, axiom, ( disjoint(_u175, _u173) | member(skolem5(_u175, _u173), _u175) )).
% 0.19/0.51 cnf(disjoint_defn-3, axiom, ( disjoint(_u175, _u173) | member(skolem5(_u175, _u173), _u173) )).
% 0.19/0.51
% 0.19/0.51 % Formula: regularity ( axiom ) converted to clauses:
% 0.19/0.51 cnf(regularity-1, axiom, ( ( _u177 = null_class) | member(skolem6(_u177), universal_class) )).
% 0.19/0.51 cnf(regularity-2, axiom, ( ( _u177 = null_class) | member(skolem6(_u177), _u177) )).
% 0.19/0.51 cnf(regularity-3, axiom, ( ( _u177 = null_class) | disjoint(skolem6(_u177), _u177) )).
% 0.19/0.51
% 0.19/0.51 % Formula: apply_defn ( axiom ) converted to clauses:
% 0.19/0.51 cnf(apply_defn-1, axiom, ( ( apply(_u179, _u178) = sum_class(image(_u179, singleton(_u178)))) )).
% 0.19/0.51
% 0.19/0.51 % Formula: choice ( axiom ) converted to clauses:
% 0.19/0.51 cnf(choice-1, axiom, ( function(skolem7) )).
% 0.19/0.51 cnf(choice-2, axiom, ( ~member(_u180, universal_class) | ( _u180 = null_class) | member(apply(skolem7, _u180), _u180) )).
% 0.19/0.51
% 0.19/0.51 % Formula: null_class_is_unique ( conjecture ) (definitionally) converted to clauses:
% 0.19/0.51 cnf(null_class_is_unique-1, negated_conjecture, ( ( skolem8 != null_class) )).
% 0.19/0.51 cnf(null_class_is_unique-2, negated_conjecture, ( ~member(_u182, skolem8) )).
% 0.19/0.51
% 0.19/0.51 % Problem matrix:
% 0.19/0.51 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 0.19/0.51 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 0.19/0.51 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 0.19/0.51 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( unordered_pair(__eqx_0, __eqx_1) = unordered_pair(__eqy_0, __eqy_1)) )).
% 0.19/0.51 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( singleton(__eqx_0) = singleton(__eqy_0)) )).
% 0.19/0.51 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( ordered_pair(__eqx_0, __eqx_1) = ordered_pair(__eqy_0, __eqy_1)) )).
% 0.19/0.51 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( cross_product(__eqx_0, __eqx_1) = cross_product(__eqy_0, __eqy_1)) )).
% 0.19/0.51 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( first(__eqx_0) = first(__eqy_0)) )).
% 0.19/0.51 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( second(__eqx_0) = second(__eqy_0)) )).
% 0.19/0.51 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( intersection(__eqx_0, __eqx_1) = intersection(__eqy_0, __eqy_1)) )).
% 0.19/0.51 cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ( complement(__eqx_0) = complement(__eqy_0)) )).
% 0.19/0.51 cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( restrict(__eqx_0, __eqx_1, __eqx_2) = restrict(__eqy_0, __eqy_1, __eqy_2)) )).
% 0.19/0.51 cnf(matrix-12, plain, ( ( __eqx_0 != __eqy_0) | ( domain_of(__eqx_0) = domain_of(__eqy_0)) )).
% 0.19/0.51 cnf(matrix-13, plain, ( ( __eqx_0 != __eqy_0) | ( rotate(__eqx_0) = rotate(__eqy_0)) )).
% 0.19/0.51 cnf(matrix-14, plain, ( ( __eqx_0 != __eqy_0) | ( flip(__eqx_0) = flip(__eqy_0)) )).
% 0.19/0.51 cnf(matrix-15, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( union(__eqx_0, __eqx_1) = union(__eqy_0, __eqy_1)) )).
% 0.19/0.51 cnf(matrix-16, plain, ( ( __eqx_0 != __eqy_0) | ( successor(__eqx_0) = successor(__eqy_0)) )).
% 0.19/0.51 cnf(matrix-17, plain, ( ( __eqx_0 != __eqy_0) | ( inverse(__eqx_0) = inverse(__eqy_0)) )).
% 0.19/0.51 cnf(matrix-18, plain, ( ( __eqx_0 != __eqy_0) | ( range_of(__eqx_0) = range_of(__eqy_0)) )).
% 0.19/0.51 cnf(matrix-19, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( image(__eqx_0, __eqx_1) = image(__eqy_0, __eqy_1)) )).
% 0.19/0.51 cnf(matrix-20, plain, ( ( __eqx_0 != __eqy_0) | ( sum_class(__eqx_0) = sum_class(__eqy_0)) )).
% 0.19/0.51 cnf(matrix-21, plain, ( ( __eqx_0 != __eqy_0) | ( power_class(__eqx_0) = power_class(__eqy_0)) )).
% 0.19/0.51 cnf(matrix-22, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( compose(__eqx_0, __eqx_1) = compose(__eqy_0, __eqy_1)) )).
% 0.19/0.51 cnf(matrix-23, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( apply(__eqx_0, __eqx_1) = apply(__eqy_0, __eqy_1)) )).
% 0.19/0.51 cnf(matrix-24, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem1(__eqx_0, __eqx_1) = skolem1(__eqy_0, __eqy_1)) )).
% 0.19/0.51 cnf(matrix-25, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem3(__eqx_0, __eqx_1) = skolem3(__eqy_0, __eqy_1)) )).
% 0.19/0.51 cnf(matrix-26, plain, ( ( __eqx_0 != __eqy_0) | ( skolem4(__eqx_0) = skolem4(__eqy_0)) )).
% 0.19/0.51 cnf(matrix-27, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem5(__eqx_0, __eqx_1) = skolem5(__eqy_0, __eqy_1)) )).
% 0.19/0.51 cnf(matrix-28, plain, ( ( __eqx_0 != __eqy_0) | ( skolem6(__eqx_0) = skolem6(__eqy_0)) )).
% 0.19/0.51 cnf(matrix-29, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~subclass(__eqx_0, __eqx_1) | subclass(__eqy_0, __eqy_1) )).
% 0.19/0.51 cnf(matrix-30, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~member(__eqx_0, __eqx_1) | member(__eqy_0, __eqy_1) )).
% 0.19/0.51 cnf(matrix-31, plain, ( ( __eqx_0 != __eqy_0) | ~inductive(__eqx_0) | inductive(__eqy_0) )).
% 0.19/0.51 cnf(matrix-32, plain, ( ( __eqx_0 != __eqy_0) | ~function(__eqx_0) | function(__eqy_0) )).
% 0.19/0.51 cnf(matrix-33, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~disjoint(__eqx_0, __eqx_1) | disjoint(__eqy_0, __eqy_1) )).
% 0.19/0.51 cnf(matrix-34, plain, ( ~subclass(_u6, _u4) | ~member(_u0, _u6) | member(_u0, _u4) )).
% 0.19/0.51 cnf(matrix-35, plain, ( subclass(_u7, _u5) | member(skolem1(_u7, _u5), _u7) )).
% 0.19/0.51 cnf(matrix-36, plain, ( subclass(_u7, _u5) | ~member(skolem1(_u7, _u5), _u5) )).
% 0.19/0.51 cnf(matrix-37, plain, ( subclass(_u8, universal_class) )).
% 0.19/0.51 cnf(matrix-38, plain, ( ( _u13 != _u11) | subclass(_u13, _u11) )).
% 0.19/0.51 cnf(matrix-39, plain, ( ( _u13 != _u11) | subclass(_u11, _u13) )).
% 0.19/0.51 cnf(matrix-40, plain, ( ~subclass(_u14, _u12) | ~subclass(_u12, _u14) | ( _u14 = _u12) )).
% 0.19/0.51 cnf(matrix-41, plain, ( ~member(_u22, unordered_pair(_u20, _u18)) | member(_u22, universal_class) )).
% 0.19/0.51 cnf(matrix-42, plain, ( ~member(_u22, unordered_pair(_u20, _u18)) | ( _u22 = _u20) | ( _u22 = _u18) )).
% 0.19/0.51 cnf(matrix-43, plain, ( member(_u23, unordered_pair(_u21, _u19)) | ~member(_u23, universal_class) | ( _u23 != _u21) )).
% 0.19/0.51 cnf(matrix-44, plain, ( member(_u23, unordered_pair(_u21, _u19)) | ~member(_u23, universal_class) | ( _u23 != _u19) )).
% 0.19/0.51 cnf(matrix-45, plain, ( member(unordered_pair(_u25, _u24), universal_class) )).
% 0.19/0.51 cnf(matrix-46, plain, ( ( singleton(_u26) = unordered_pair(_u26, _u26)) )).
% 0.19/0.51 cnf(matrix-47, plain, ( ( ordered_pair(_u28, _u27) = unordered_pair(singleton(_u28), unordered_pair(_u28, singleton(_u27)))) )).
% 0.19/0.51 cnf(matrix-48, plain, ( ~member(ordered_pair(_u39, _u37), cross_product(_u35, _u33)) | member(_u39, _u35) )).
% 0.19/0.51 cnf(matrix-49, plain, ( ~member(ordered_pair(_u39, _u37), cross_product(_u35, _u33)) | member(_u37, _u33) )).
% 0.19/0.51 cnf(matrix-50, plain, ( ~member(_u40, _u36) | ~member(_u38, _u34) | member(ordered_pair(_u40, _u38), cross_product(_u36, _u34)) )).
% 0.19/0.51 cnf(matrix-51, plain, ( ~member(_u42, universal_class) | ~member(_u41, universal_class) | ( first(ordered_pair(_u42, _u41)) = _u42) )).
% 0.19/0.51 cnf(matrix-52, plain, ( ~member(_u42, universal_class) | ~member(_u41, universal_class) | ( second(ordered_pair(_u42, _u41)) = _u41) )).
% 0.19/0.51 cnf(matrix-53, plain, ( ~member(_u43, cross_product(_u45, _u44)) | ( _u43 = ordered_pair(first(_u43), second(_u43))) )).
% 0.19/0.51 cnf(matrix-54, plain, ( ~member(ordered_pair(_u50, _u48), element_relation) | member(_u48, universal_class) )).
% 0.19/0.51 cnf(matrix-55, plain, ( ~member(ordered_pair(_u50, _u48), element_relation) | member(_u50, _u48) )).
% 0.19/0.51 cnf(matrix-56, plain, ( ~member(_u49, universal_class) | ~member(_u51, _u49) | member(ordered_pair(_u51, _u49), element_relation) )).
% 0.19/0.51 cnf(matrix-57, plain, ( subclass(element_relation, cross_product(universal_class, universal_class)) )).
% 0.19/0.51 cnf(matrix-58, plain, ( ~member(_u55, intersection(_u59, _u57)) | member(_u55, _u59) )).
% 0.19/0.51 cnf(matrix-59, plain, ( ~member(_u55, intersection(_u59, _u57)) | member(_u55, _u57) )).
% 0.19/0.51 cnf(matrix-60, plain, ( ~member(_u56, _u60) | ~member(_u56, _u58) | member(_u56, intersection(_u60, _u58)) )).
% 0.19/0.51 cnf(matrix-61, plain, ( ~member(_u63, complement(_u65)) | member(_u63, universal_class) )).
% 0.19/0.51 cnf(matrix-62, plain, ( ~member(_u63, complement(_u65)) | ~member(_u63, _u65) )).
% 0.19/0.51 cnf(matrix-63, plain, ( ~member(_u64, universal_class) | member(_u64, _u66) | member(_u64, complement(_u66)) )).
% 0.19/0.51 cnf(matrix-64, plain, ( ( restrict(_u68, _u69, _u67) = intersection(_u68, cross_product(_u69, _u67))) )).
% 0.19/0.51 cnf(matrix-65, plain, ( ~member(_u70, null_class) )).
% 0.19/0.51 cnf(matrix-66, plain, ( ~member(_u73, domain_of(_u75)) | member(_u73, universal_class) )).
% 0.19/0.51 cnf(matrix-67, plain, ( ~member(_u73, domain_of(_u75)) | ( restrict(_u75, singleton(_u73), universal_class) != null_class) )).
% 0.19/0.51 cnf(matrix-68, plain, ( ~member(_u74, universal_class) | ( restrict(_u76, singleton(_u74), universal_class) = null_class) | member(_u74, domain_of(_u76)) )).
% 0.19/0.51 cnf(matrix-69, plain, ( ~member(ordered_pair(ordered_pair(_u85, _u83), _u81), rotate(_u87)) | member(ordered_pair(ordered_pair(_u85, _u83), _u81), cross_product(cross_product(universal_class, universal_class), universal_class)) )).
% 0.19/0.51 cnf(matrix-70, plain, ( ~member(ordered_pair(ordered_pair(_u85, _u83), _u81), rotate(_u87)) | member(ordered_pair(ordered_pair(_u83, _u81), _u85), _u87) )).
% 0.19/0.51 cnf(matrix-71, plain, ( ~member(ordered_pair(ordered_pair(_u86, _u84), _u82), cross_product(cross_product(universal_class, universal_class), universal_class)) | ~member(ordered_pair(ordered_pair(_u84, _u82), _u86), _u88) | member(ordered_pair(ordered_pair(_u86, _u84), _u82), rotate(_u88)) )).
% 0.19/0.51 cnf(matrix-72, plain, ( subclass(rotate(_u89), cross_product(cross_product(universal_class, universal_class), universal_class)) )).
% 0.19/0.51 cnf(matrix-73, plain, ( ~member(ordered_pair(ordered_pair(_u100, _u98), _u96), flip(_u94)) | member(ordered_pair(ordered_pair(_u100, _u98), _u96), cross_product(cross_product(universal_class, universal_class), universal_class)) )).
% 0.19/0.51 cnf(matrix-74, plain, ( ~member(ordered_pair(ordered_pair(_u100, _u98), _u96), flip(_u94)) | member(ordered_pair(ordered_pair(_u98, _u100), _u96), _u94) )).
% 0.19/0.51 cnf(matrix-75, plain, ( ~member(ordered_pair(ordered_pair(_u101, _u99), _u97), cross_product(cross_product(universal_class, universal_class), universal_class)) | ~member(ordered_pair(ordered_pair(_u99, _u101), _u97), _u95) | member(ordered_pair(ordered_pair(_u101, _u99), _u97), flip(_u95)) )).
% 0.19/0.51 cnf(matrix-76, plain, ( subclass(flip(_u102), cross_product(cross_product(universal_class, universal_class), universal_class)) )).
% 0.19/0.51 cnf(matrix-77, plain, ( ~member(_u106, union(_u110, _u108)) | member(_u106, _u110) | member(_u106, _u108) )).
% 0.19/0.51 cnf(matrix-78, plain, ( member(_u107, union(_u111, _u109)) | ~member(_u107, _u111) )).
% 0.19/0.51 cnf(matrix-79, plain, ( member(_u107, union(_u111, _u109)) | ~member(_u107, _u109) )).
% 0.19/0.51 cnf(matrix-80, plain, ( ( successor(_u112) = union(_u112, singleton(_u112))) )).
% 0.19/0.51 cnf(matrix-81, plain, ( subclass(successor_relation, cross_product(universal_class, universal_class)) )).
% 0.19/0.51 cnf(matrix-82, plain, ( ~member(ordered_pair(_u117, _u115), successor_relation) | member(_u117, universal_class) )).
% 0.19/0.51 cnf(matrix-83, plain, ( ~member(ordered_pair(_u117, _u115), successor_relation) | member(_u115, universal_class) )).
% 0.19/0.51 cnf(matrix-84, plain, ( ~member(ordered_pair(_u117, _u115), successor_relation) | ( successor(_u117) = _u115) )).
% 0.19/0.51 cnf(matrix-85, plain, ( ~member(_u118, universal_class) | ~member(_u116, universal_class) | ( successor(_u118) != _u116) | member(ordered_pair(_u118, _u116), successor_relation) )).
% 0.19/0.51 cnf(matrix-86, plain, ( ( inverse(_u119) = domain_of(flip(cross_product(_u119, universal_class)))) )).
% 0.19/0.51 cnf(matrix-87, plain, ( ( range_of(_u120) = domain_of(inverse(_u120))) )).
% 0.19/0.51 cnf(matrix-88, plain, ( ( image(_u121, _u122) = range_of(restrict(_u121, _u122, universal_class))) )).
% 0.19/0.51 cnf(matrix-89, plain, ( ~inductive(_u124) | member(null_class, _u124) )).
% 0.19/0.51 cnf(matrix-90, plain, ( ~inductive(_u124) | subclass(image(successor_relation, _u124), _u124) )).
% 0.19/0.51 cnf(matrix-91, plain, ( ~member(null_class, _u125) | ~subclass(image(successor_relation, _u125), _u125) | inductive(_u125) )).
% 0.19/0.51 cnf(matrix-92, plain, ( member(skolem2, universal_class) )).
% 0.19/0.51 cnf(matrix-93, plain, ( inductive(skolem2) )).
% 0.19/0.51 cnf(matrix-94, plain, ( ~inductive(_u126) | subclass(skolem2, _u126) )).
% 0.19/0.51 cnf(matrix-95, plain, ( ~member(_u134, sum_class(_u132)) | member(_u134, skolem3(_u134, _u132)) )).
% 0.19/0.51 cnf(matrix-96, plain, ( ~member(_u134, sum_class(_u132)) | member(skolem3(_u134, _u132), _u132) )).
% 0.19/0.51 cnf(matrix-97, plain, ( ~member(_u135, _u129) | ~member(_u129, _u133) | member(_u135, sum_class(_u133)) )).
% 0.19/0.51 cnf(matrix-98, plain, ( ~member(_u136, universal_class) | member(sum_class(_u136), universal_class) )).
% 0.19/0.51 cnf(matrix-99, plain, ( ~member(_u141, power_class(_u139)) | member(_u141, universal_class) )).
% 0.19/0.51 cnf(matrix-100, plain, ( ~member(_u141, power_class(_u139)) | subclass(_u141, _u139) )).
% 0.19/0.51 cnf(matrix-101, plain, ( ~member(_u142, universal_class) | ~subclass(_u142, _u140) | member(_u142, power_class(_u140)) )).
% 0.19/0.51 cnf(matrix-102, plain, ( ~member(_u143, universal_class) | member(power_class(_u143), universal_class) )).
% 0.19/0.51 cnf(matrix-103, plain, ( subclass(compose(_u144, _u145), cross_product(universal_class, universal_class)) )).
% 0.19/0.51 cnf(matrix-104, plain, ( ~member(ordered_pair(_u152, _u150), compose(_u154, _u156)) | member(_u152, universal_class) )).
% 0.19/0.51 cnf(matrix-105, plain, ( ~member(ordered_pair(_u152, _u150), compose(_u154, _u156)) | member(_u150, image(_u154, image(_u156, singleton(_u152)))) )).
% 0.19/0.51 cnf(matrix-106, plain, ( ~member(_u153, universal_class) | ~member(_u151, image(_u155, image(_u157, singleton(_u153)))) | member(ordered_pair(_u153, _u151), compose(_u155, _u157)) )).
% 0.19/0.51 cnf(matrix-107, plain, ( ~member(_u161, identity_relation) | member(skolem4(_u161), universal_class) )).
% 0.19/0.51 cnf(matrix-108, plain, ( ~member(_u161, identity_relation) | ( _u161 = ordered_pair(skolem4(_u161), skolem4(_u161))) )).
% 0.19/0.51 cnf(matrix-109, plain, ( ~member(_u159, universal_class) | ( _u162 != ordered_pair(_u159, _u159)) | member(_u162, identity_relation) )).
% 0.19/0.51 cnf(matrix-110, plain, ( ~function(_u164) | subclass(_u164, cross_product(universal_class, universal_class)) )).
% 0.19/0.51 cnf(matrix-111, plain, ( ~function(_u164) | subclass(compose(_u164, inverse(_u164)), identity_relation) )).
% 0.19/0.51 cnf(matrix-112, plain, ( ~subclass(_u165, cross_product(universal_class, universal_class)) | ~subclass(compose(_u165, inverse(_u165)), identity_relation) | function(_u165) )).
% 0.19/0.51 cnf(matrix-113, plain, ( ~member(_u167, universal_class) | ~function(_u166) | member(image(_u166, _u167), universal_class) )).
% 0.19/0.51 cnf(matrix-114, plain, ( ~disjoint(_u174, _u172) | ~member(_u168, _u174) | ~member(_u168, _u172) )).
% 0.19/0.51 cnf(matrix-115, plain, ( disjoint(_u175, _u173) | member(skolem5(_u175, _u173), _u175) )).
% 0.19/0.51 cnf(matrix-116, plain, ( disjoint(_u175, _u173) | member(skolem5(_u175, _u173), _u173) )).
% 0.19/0.51 cnf(matrix-117, plain, ( ( _u177 = null_class) | member(skolem6(_u177), universal_class) )).
% 0.19/0.51 cnf(matrix-118, plain, ( ( _u177 = null_class) | member(skolem6(_u177), _u177) )).
% 0.19/0.51 cnf(matrix-119, plain, ( ( _u177 = null_class) | disjoint(skolem6(_u177), _u177) )).
% 0.19/0.51 cnf(matrix-120, plain, ( ( apply(_u179, _u178) = sum_class(image(_u179, singleton(_u178)))) )).
% 0.19/0.51 cnf(matrix-121, plain, ( function(skolem7) )).
% 0.19/0.51 cnf(matrix-122, plain, ( ~member(_u180, universal_class) | ( _u180 = null_class) | member(apply(skolem7, _u180), _u180) )).
% 0.19/0.51 cnf(matrix-123, plain, ( ( skolem8 != null_class) )).
% 0.19/0.51 cnf(matrix-124, plain, ( ~member(_u182, skolem8) )).
% 0.19/0.51
% 0.19/0.51 % Proof stack:
% 0.19/0.51 cnf(proof-stack, plain,
% 0.19/0.51 proof_stack(
% 0.19/0.51 start(123),
% 0.19/0.51 left_branch(0, 118, 0, 2),
% 0.19/0.51 left_branch(0, 124, 0, 3),
% 0.19/0.51 right_branch(3),
% 0.19/0.51 right_branch(2)
% 0.19/0.51 )).
% 0.19/0.51 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------