TSTP Solution File: SEU244+2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU244+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 14:35:28 EDT 2022
% Result : Theorem 69.21s 69.47s
% Output : Refutation 70.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU244+2 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n017.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 20 01:12:59 EDT 2022
% 0.12/0.33 % CPUTime :
% 69.21/69.47
% 69.21/69.47 SPASS V 3.9
% 69.21/69.47 SPASS beiseite: Proof found.
% 69.21/69.47 % SZS status Theorem
% 69.21/69.47 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 69.21/69.47 SPASS derived 27601 clauses, backtracked 3160 clauses, performed 11 splits and kept 13677 clauses.
% 69.21/69.47 SPASS allocated 126667 KBytes.
% 69.21/69.47 SPASS spent 0:01:09.10 on the problem.
% 69.21/69.47 0:00:00.04 for the input.
% 69.21/69.47 0:00:09.12 for the FLOTTER CNF translation.
% 69.21/69.47 0:00:00.69 for inferences.
% 69.21/69.47 0:00:00.97 for the backtracking.
% 69.21/69.47 0:0:57.38 for the reduction.
% 69.21/69.47
% 69.21/69.47
% 69.21/69.47 Here is a proof with depth 10, length 242 :
% 69.21/69.47 % SZS output start Refutation
% 69.21/69.47 1[0:Inp] || -> relation(skc13)*.
% 69.21/69.47 7[0:Inp] || -> relation_empty_yielding(empty_set)*.
% 69.21/69.47 8[0:Inp] || -> function(empty_set)*.
% 69.21/69.47 9[0:Inp] || -> one_to_one(empty_set)*.
% 69.21/69.47 11[0:Inp] || -> epsilon_transitive(empty_set)*.
% 69.21/69.47 12[0:Inp] || -> epsilon_connected(empty_set)*.
% 69.21/69.47 13[0:Inp] || -> ordinal(empty_set)*.
% 69.21/69.47 14[0:Inp] || -> empty(empty_set)*.
% 69.21/69.47 15[0:Inp] || -> relation(empty_set)*.
% 69.21/69.47 47[0:Inp] || -> relation(identity_relation(u))*.
% 69.21/69.47 48[0:Inp] || -> function(identity_relation(u))*.
% 69.21/69.47 59[0:Inp] || -> element(skf189(u),u)*.
% 69.21/69.47 66[0:Inp] || -> equal(relation_dom(empty_set),empty_set)**.
% 69.21/69.47 67[0:Inp] || -> equal(relation_rng(empty_set),empty_set)**.
% 69.21/69.47 72[0:Inp] empty(u) || -> relation(u)*.
% 69.21/69.47 77[0:Inp] || -> subset(skf153(u,v),v)*l.
% 69.21/69.47 84[0:Inp] || -> equal(set_union2(u,u),u)**.
% 69.21/69.47 90[0:Inp] || -> equal(set_union2(u,empty_set),u)**.
% 69.21/69.47 96[0:Inp] || -> equal(relation_dom(identity_relation(u)),u)**.
% 69.21/69.47 97[0:Inp] || -> equal(relation_rng(identity_relation(u)),u)**.
% 69.21/69.47 100[0:Inp] || -> well_ordering(skc13) well_orders(skc13,relation_field(skc13))*.
% 69.21/69.47 115[0:Inp] empty(u) || -> empty(relation_dom(u))*.
% 69.21/69.47 117[0:Inp] empty(u) || -> empty(relation_rng(u))*.
% 69.21/69.47 122[0:Inp] || -> ordinal(u) in(skf205(u),u)*.
% 69.21/69.47 124[0:Inp] empty(u) || -> equal(u,empty_set)*.
% 69.21/69.47 126[0:Inp] || -> equal(set_union2(u,v),set_union2(v,u))*.
% 69.21/69.47 143[0:Inp] || -> in(u,v) disjoint(singleton(u),v)*.
% 69.21/69.47 146[0:Inp] || subset(u,empty_set)* -> equal(u,empty_set).
% 69.21/69.47 147[0:Inp] empty(u) || in(v,u)* -> .
% 69.21/69.47 148[0:Inp] || well_ordering(skc13) well_orders(skc13,relation_field(skc13))* -> .
% 69.21/69.47 153[0:Inp] || in(u,v)* equal(v,empty_set) -> .
% 69.21/69.47 158[0:Inp] relation(u) well_ordering(u) || -> reflexive(u)*.
% 69.21/69.47 159[0:Inp] relation(u) well_ordering(u) || -> transitive(u)*.
% 69.21/69.47 160[0:Inp] relation(u) well_ordering(u) || -> antisymmetric(u)*.
% 69.21/69.47 161[0:Inp] relation(u) well_ordering(u) || -> connected(u)*.
% 69.21/69.47 162[0:Inp] relation(u) well_ordering(u) || -> well_founded_relation(u)*.
% 69.21/69.47 175[0:Inp] || -> disjoint(u,v) in(skf208(v,u),u)*.
% 69.21/69.47 178[0:Inp] || in(u,v)*+ -> in(skf220(v),v)*.
% 69.21/69.47 187[0:Inp] || disjoint(u,v) -> equal(set_intersection2(u,v),empty_set)**.
% 69.21/69.47 199[0:Inp] || -> element(u,powerset(v)) in(skf198(v,u),u)*.
% 69.21/69.47 206[0:Inp] || element(u,v)* -> empty(v) in(u,v).
% 69.21/69.47 216[0:Inp] ordinal(u) || -> being_limit_ordinal(u) in(skf209(u),u)*.
% 69.21/69.47 226[0:Inp] relation(u) antisymmetric(u) || -> is_antisymmetric_in(u,relation_field(u))*.
% 69.21/69.47 227[0:Inp] relation(u) || is_antisymmetric_in(u,relation_field(u))* -> antisymmetric(u).
% 69.21/69.47 228[0:Inp] relation(u) connected(u) || -> is_connected_in(u,relation_field(u))*.
% 69.21/69.47 229[0:Inp] relation(u) || is_connected_in(u,relation_field(u))* -> connected(u).
% 69.21/69.47 230[0:Inp] relation(u) transitive(u) || -> is_transitive_in(u,relation_field(u))*.
% 69.21/69.47 231[0:Inp] relation(u) || is_transitive_in(u,relation_field(u))* -> transitive(u).
% 69.21/69.47 238[0:Inp] relation(u) || well_orders(u,v)* -> is_reflexive_in(u,v).
% 69.21/69.47 239[0:Inp] relation(u) || well_orders(u,v)* -> is_transitive_in(u,v).
% 69.21/69.47 240[0:Inp] relation(u) || well_orders(u,v)* -> is_antisymmetric_in(u,v).
% 69.21/69.47 241[0:Inp] relation(u) || well_orders(u,v)* -> is_connected_in(u,v).
% 69.21/69.47 242[0:Inp] relation(u) || well_orders(u,v)* -> is_well_founded_in(u,v).
% 69.21/69.47 244[0:Inp] relation(u) reflexive(u) || -> is_reflexive_in(u,relation_field(u))*.
% 69.21/69.47 245[0:Inp] relation(u) || is_reflexive_in(u,relation_field(u))* -> reflexive(u).
% 69.21/69.47 258[0:Inp] relation(u) || -> reflexive(u) in(skf190(u),relation_field(u))*.
% 69.21/69.47 261[0:Inp] relation(u) || -> connected(u) in(skf196(u),relation_field(u))*.
% 69.21/69.47 271[0:Inp] || in(u,set_intersection2(v,w))* disjoint(v,w) -> .
% 69.21/69.47 273[0:Inp] relation(u) well_founded_relation(u) || -> is_well_founded_in(u,relation_field(u))*.
% 69.21/69.47 274[0:Inp] relation(u) || is_well_founded_in(u,relation_field(u))* -> well_founded_relation(u).
% 69.21/69.47 281[0:Inp] relation(u) || -> is_reflexive_in(u,v)* in(skf129(v,w),v)*.
% 69.21/69.47 287[0:Inp] relation(u) || -> equal(set_union2(relation_dom(u),relation_rng(u)),relation_field(u))**.
% 69.21/69.47 288[0:Inp] relation(u) || -> is_connected_in(u,v)* in(skf175(v,w),v)*.
% 69.21/69.47 323[0:Inp] relation(u) || equal(skf153(u,v),empty_set)** -> is_well_founded_in(u,v).
% 69.21/69.47 330[0:Inp] relation(u) || -> transitive(u) in(ordered_pair(skf193(u),skf192(u)),u)*.
% 69.21/69.47 333[0:Inp] relation(u) || -> antisymmetric(u) in(ordered_pair(skf194(u),skf195(u)),u)*.
% 69.21/69.47 358[0:Inp] || element(u,powerset(powerset(v))) -> element(complements_of_subsets(v,u),powerset(powerset(v)))*.
% 69.21/69.47 359[0:Inp] || element(u,powerset(powerset(v))) -> equal(complements_of_subsets(v,complements_of_subsets(v,u)),u)**.
% 69.21/69.47 382[0:Inp] relation(u) || -> equal(u,empty_set) in(ordered_pair(skf217(u),skf216(u)),u)*.
% 69.21/69.47 411[0:Inp] relation(u) || -> is_antisymmetric_in(u,v) in(ordered_pair(skf160(v,u),skf159(v,u)),u)*.
% 69.21/69.47 413[0:Inp] relation(u) || -> is_transitive_in(u,v) in(ordered_pair(skf187(v,u),skf186(v,u)),u)*.
% 69.21/69.47 427[0:Inp] || element(u,powerset(powerset(v)))* equal(complements_of_subsets(v,u),empty_set) -> equal(u,empty_set).
% 69.21/69.47 504[0:Inp] relation(u) well_founded_relation(u) connected(u) antisymmetric(u) transitive(u) reflexive(u) || -> well_ordering(u)*.
% 69.21/69.47 536[0:Inp] relation(u) || -> equal(u,identity_relation(v)) in(skf106(v,u),v) in(ordered_pair(skf106(v,u),skf107(v,u)),u)*.
% 69.21/69.47 577[0:Inp] relation(u) || is_reflexive_in(u,v) is_well_founded_in(u,v) is_connected_in(u,v) is_antisymmetric_in(u,v) is_transitive_in(u,v) -> well_orders(u,v)*.
% 69.21/69.47 623[0:Rew:187.1,271.0] || disjoint(u,v)*+ in(w,empty_set)* -> .
% 69.21/69.47 751[0:Res:1.0,536.0] || -> equal(identity_relation(u),skc13) in(skf106(u,skc13),u) in(ordered_pair(skf106(u,skc13),skf107(u,skc13)),skc13)*.
% 69.21/69.47 772[0:Res:1.0,504.5] well_founded_relation(skc13) connected(skc13) antisymmetric(skc13) transitive(skc13) reflexive(skc13) || -> well_ordering(skc13)*.
% 69.21/69.47 806[0:Res:1.0,411.0] || -> is_antisymmetric_in(skc13,u) in(ordered_pair(skf160(u,skc13),skf159(u,skc13)),skc13)*.
% 69.21/69.47 808[0:Res:1.0,413.0] || -> is_transitive_in(skc13,u) in(ordered_pair(skf187(u,skc13),skf186(u,skc13)),skc13)*.
% 69.21/69.47 841[0:Res:1.0,382.0] || -> equal(skc13,empty_set) in(ordered_pair(skf217(skc13),skf216(skc13)),skc13)*.
% 69.21/69.47 843[0:Res:1.0,323.0] || equal(skf153(skc13,u),empty_set)** -> is_well_founded_in(skc13,u).
% 69.21/69.47 845[0:Res:1.0,330.0] || -> transitive(skc13) in(ordered_pair(skf193(skc13),skf192(skc13)),skc13)*.
% 69.21/69.47 847[0:Res:1.0,333.0] || -> antisymmetric(skc13) in(ordered_pair(skf194(skc13),skf195(skc13)),skc13)*.
% 69.21/69.47 853[0:Res:1.0,281.0] || -> is_reflexive_in(skc13,u) in(skf129(u,v),u)*.
% 69.21/69.47 856[0:Res:1.0,287.0] || -> equal(set_union2(relation_dom(skc13),relation_rng(skc13)),relation_field(skc13))**.
% 69.21/69.47 857[0:Res:1.0,288.0] || -> is_connected_in(skc13,u) in(skf175(u,v),u)*.
% 69.21/69.47 866[0:Res:1.0,226.1] antisymmetric(skc13) || -> is_antisymmetric_in(skc13,relation_field(skc13))*.
% 69.21/69.47 867[0:Res:1.0,227.0] || is_antisymmetric_in(skc13,relation_field(skc13))* -> antisymmetric(skc13).
% 69.21/69.47 868[0:Res:1.0,228.1] connected(skc13) || -> is_connected_in(skc13,relation_field(skc13))*.
% 69.21/69.47 869[0:Res:1.0,229.0] || is_connected_in(skc13,relation_field(skc13))* -> connected(skc13).
% 69.21/69.47 870[0:Res:1.0,230.1] transitive(skc13) || -> is_transitive_in(skc13,relation_field(skc13))*.
% 69.21/69.47 871[0:Res:1.0,231.0] || is_transitive_in(skc13,relation_field(skc13))* -> transitive(skc13).
% 69.21/69.47 878[0:Res:1.0,244.1] reflexive(skc13) || -> is_reflexive_in(skc13,relation_field(skc13))*.
% 69.21/69.47 879[0:Res:1.0,245.0] || is_reflexive_in(skc13,relation_field(skc13))* -> reflexive(skc13).
% 69.21/69.47 888[0:Res:1.0,261.0] || -> connected(skc13) in(skf196(skc13),relation_field(skc13))*.
% 69.21/69.47 890[0:Res:1.0,273.1] well_founded_relation(skc13) || -> is_well_founded_in(skc13,relation_field(skc13))*.
% 69.21/69.47 891[0:Res:1.0,274.0] || is_well_founded_in(skc13,relation_field(skc13))* -> well_founded_relation(skc13).
% 69.21/69.47 898[0:Res:1.0,158.1] well_ordering(skc13) || -> reflexive(skc13)*.
% 69.21/69.47 899[0:Res:1.0,159.1] well_ordering(skc13) || -> transitive(skc13)*.
% 69.21/69.47 900[0:Res:1.0,160.1] well_ordering(skc13) || -> antisymmetric(skc13)*.
% 69.21/69.47 901[0:Res:1.0,161.1] well_ordering(skc13) || -> connected(skc13)*.
% 69.21/69.47 902[0:Res:1.0,162.1] well_ordering(skc13) || -> well_founded_relation(skc13)*.
% 69.21/69.47 1148[1:Spt:841.0] || -> equal(skc13,empty_set)**.
% 69.21/69.47 1155[1:Rew:1148.0,148.1] || well_ordering(skc13) well_orders(empty_set,relation_field(empty_set))* -> .
% 69.21/69.47 1156[1:Rew:1148.0,100.1] || -> well_ordering(skc13) well_orders(empty_set,relation_field(empty_set))*.
% 69.21/69.47 1180[1:Rew:1148.0,845.0] || -> transitive(empty_set) in(ordered_pair(skf193(skc13),skf192(skc13)),skc13)*.
% 69.21/69.47 1184[1:Rew:1148.0,847.0] || -> antisymmetric(empty_set) in(ordered_pair(skf194(skc13),skf195(skc13)),skc13)*.
% 69.21/69.47 1277[1:Rew:1148.0,856.0] || -> equal(set_union2(relation_dom(empty_set),relation_rng(empty_set)),relation_field(empty_set))**.
% 69.21/69.47 1294[1:Rew:1148.0,853.0] || -> is_reflexive_in(empty_set,u) in(skf129(u,v),u)*.
% 69.21/69.47 1296[1:Rew:1148.0,808.0] || -> is_transitive_in(empty_set,u) in(ordered_pair(skf187(u,skc13),skf186(u,skc13)),skc13)*.
% 69.21/69.47 1301[1:Rew:1148.0,806.0] || -> is_antisymmetric_in(empty_set,u) in(ordered_pair(skf160(u,skc13),skf159(u,skc13)),skc13)*.
% 69.21/69.47 1309[1:Rew:1148.0,857.0] || -> is_connected_in(empty_set,u) in(skf175(u,v),u)*.
% 69.21/69.47 1311[1:Rew:1148.0,843.1] || equal(skf153(skc13,u),empty_set)** -> is_well_founded_in(empty_set,u).
% 69.21/69.47 1376[1:Rew:1148.0,751.0] || -> equal(identity_relation(u),empty_set) in(skf106(u,skc13),u) in(ordered_pair(skf106(u,skc13),skf107(u,skc13)),skc13)*.
% 69.21/69.47 1497[1:Rew:1148.0,1156.0] || -> well_ordering(empty_set) well_orders(empty_set,relation_field(empty_set))*.
% 69.21/69.47 1520[1:Rew:1148.0,1155.0] || well_ordering(empty_set) well_orders(empty_set,relation_field(empty_set))* -> .
% 69.21/69.47 1522[1:Rew:84.0,1277.0,66.0,1277.0,67.0,1277.0] || -> equal(relation_field(empty_set),empty_set)**.
% 69.21/69.47 1523[1:Rew:1522.0,1520.1] || well_ordering(empty_set) well_orders(empty_set,empty_set)* -> .
% 69.21/69.47 1524[1:Rew:1522.0,1497.1] || -> well_ordering(empty_set) well_orders(empty_set,empty_set)*.
% 69.21/69.47 1538[1:Rew:1148.0,1180.1] || -> transitive(empty_set) in(ordered_pair(skf193(empty_set),skf192(empty_set)),empty_set)*.
% 69.21/69.47 1540[1:Rew:1148.0,1184.1] || -> antisymmetric(empty_set) in(ordered_pair(skf194(empty_set),skf195(empty_set)),empty_set)*.
% 69.21/69.47 1544[1:Rew:1148.0,1311.0] || equal(skf153(empty_set,u),empty_set)** -> is_well_founded_in(empty_set,u).
% 69.21/69.47 1566[1:Rew:1148.0,1296.1] || -> is_transitive_in(empty_set,u) in(ordered_pair(skf187(u,empty_set),skf186(u,empty_set)),empty_set)*.
% 69.21/69.47 1568[1:Rew:1148.0,1301.1] || -> is_antisymmetric_in(empty_set,u) in(ordered_pair(skf160(u,empty_set),skf159(u,empty_set)),empty_set)*.
% 69.21/69.47 1639[1:Rew:1148.0,1376.2,1148.0,1376.1] || -> equal(identity_relation(u),empty_set) in(skf106(u,empty_set),u) in(ordered_pair(skf106(u,empty_set),skf107(u,empty_set)),empty_set)*.
% 69.21/69.47 1825[2:Spt:1524.0] || -> well_ordering(empty_set)*.
% 69.21/69.47 1826[2:MRR:1523.0,1825.0] || well_orders(empty_set,empty_set)* -> .
% 69.21/69.47 1879[0:EmS:124.0,117.1] empty(u) || -> equal(relation_rng(u),empty_set)**.
% 69.21/69.47 1886[0:EmS:124.0,115.1] empty(u) || -> equal(relation_dom(u),empty_set)**.
% 69.21/69.47 2044[0:SpR:126.0,90.0] || -> equal(set_union2(empty_set,u),u)**.
% 69.21/69.47 2287[0:Res:143.1,623.0] || in(u,empty_set)* -> in(v,w)*.
% 69.21/69.47 2297[1:MRR:1639.2,2287.0] || -> equal(identity_relation(u),empty_set) in(skf106(u,empty_set),u)*.
% 69.21/69.47 2512[0:Res:122.1,178.0] || -> ordinal(u) in(skf220(u),u)*.
% 69.21/69.47 2564[0:Res:175.1,147.1] empty(u) || -> disjoint(u,v)*.
% 69.21/69.47 2565[0:Res:2564.1,623.0] empty(u) || in(v,empty_set)* -> .
% 69.21/69.47 2585[0:EmS:2565.0,14.0] || in(u,empty_set)* -> .
% 69.21/69.47 2587[1:MRR:1538.1,2585.0] || -> transitive(empty_set)*.
% 69.21/69.47 2589[1:MRR:1540.1,2585.0] || -> antisymmetric(empty_set)*.
% 69.21/69.47 2595[1:MRR:1566.1,2585.0] || -> is_transitive_in(empty_set,u)*.
% 69.21/69.47 2597[1:MRR:1568.1,2585.0] || -> is_antisymmetric_in(empty_set,u)*.
% 69.21/69.47 2739[0:Res:216.2,178.0] ordinal(u) || -> being_limit_ordinal(u) in(skf220(u),u)*.
% 69.21/69.47 2745[0:MRR:2739.0,2512.0] || -> being_limit_ordinal(u) in(skf220(u),u)*.
% 69.21/69.47 2752[0:Res:2745.1,2585.0] || -> being_limit_ordinal(empty_set)*.
% 69.21/69.47 3045[0:Res:199.1,153.0] || equal(u,empty_set) -> element(u,powerset(v))*.
% 69.21/69.47 3083[1:Res:1294.1,2585.0] || -> is_reflexive_in(empty_set,empty_set)*.
% 69.21/69.47 3093[0:Res:59.0,206.0] || -> empty(u) in(skf189(u),u)*.
% 69.21/69.47 3180[0:Res:3093.1,153.0] || equal(u,empty_set) -> empty(u)*.
% 69.21/69.47 3478[1:Res:1309.1,2585.0] || -> is_connected_in(empty_set,empty_set)*.
% 69.21/69.47 3916[1:Res:2297.1,2585.0] || -> equal(identity_relation(empty_set),empty_set)**.
% 69.21/69.47 4706[0:SpR:97.0,287.1] relation(identity_relation(u)) || -> equal(set_union2(relation_dom(identity_relation(u)),u),relation_field(identity_relation(u)))**.
% 69.21/69.47 4707[0:SpR:1879.1,287.1] empty(u) relation(u) || -> equal(set_union2(relation_dom(u),empty_set),relation_field(u))**.
% 69.21/69.47 4719[0:Rew:84.0,4706.1,96.0,4706.1,126.0,4706.1] relation(identity_relation(u)) || -> equal(relation_field(identity_relation(u)),u)**.
% 69.21/69.47 4720[0:SSi:4719.0,48.0,47.0] || -> equal(relation_field(identity_relation(u)),u)**.
% 69.21/69.47 4721[0:Rew:1886.1,4707.2,2044.0,4707.2,126.0,4707.2] empty(u) relation(u) || -> equal(relation_field(u),empty_set)**.
% 69.21/69.47 4722[0:SSi:4721.1,72.1] empty(u) || -> equal(relation_field(u),empty_set)**.
% 69.21/69.47 4729[0:SpR:4720.0,273.2] relation(identity_relation(u)) well_founded_relation(identity_relation(u)) || -> is_well_founded_in(identity_relation(u),u)*.
% 69.21/69.47 4733[0:SpR:4720.0,258.2] relation(identity_relation(u)) || -> reflexive(identity_relation(u)) in(skf190(identity_relation(u)),u)*.
% 69.21/69.47 4734[0:SpR:4720.0,261.2] relation(identity_relation(u)) || -> connected(identity_relation(u)) in(skf196(identity_relation(u)),u)*.
% 69.21/69.47 4742[0:SpL:4720.0,274.1] relation(identity_relation(u)) || is_well_founded_in(identity_relation(u),u)* -> well_founded_relation(identity_relation(u)).
% 69.21/69.47 4754[0:SSi:4729.0,48.0,47.0] well_founded_relation(identity_relation(u)) || -> is_well_founded_in(identity_relation(u),u)*.
% 69.21/69.47 4758[0:SSi:4733.0,48.0,47.0] || -> reflexive(identity_relation(u)) in(skf190(identity_relation(u)),u)*.
% 69.21/69.47 4759[0:SSi:4734.0,48.0,47.0] || -> connected(identity_relation(u)) in(skf196(identity_relation(u)),u)*.
% 69.21/69.47 4762[0:SSi:4742.0,48.0,47.0] || is_well_founded_in(identity_relation(u),u)* -> well_founded_relation(identity_relation(u)).
% 69.21/69.47 4798[0:SpL:4722.1,274.1] empty(u) relation(u) || is_well_founded_in(u,empty_set)* -> well_founded_relation(u).
% 69.21/69.47 4815[0:SSi:4798.1,72.1] empty(u) || is_well_founded_in(u,empty_set)* -> well_founded_relation(u).
% 69.21/69.47 4982[0:Res:4758.1,2585.0] || -> reflexive(identity_relation(empty_set))*.
% 69.21/69.47 4987[1:Rew:3916.0,4982.0] || -> reflexive(empty_set)*.
% 69.21/69.47 5014[0:Res:4759.1,2585.0] || -> connected(identity_relation(empty_set))*.
% 69.21/69.47 5019[1:Rew:3916.0,5014.0] || -> connected(empty_set)*.
% 69.21/69.47 5565[0:Res:77.0,146.0] || -> equal(skf153(u,empty_set),empty_set)**.
% 69.21/69.47 5576[1:SpL:5565.0,1544.0] || equal(empty_set,empty_set) -> is_well_founded_in(empty_set,empty_set)*.
% 69.21/69.47 5577[1:Obv:5576.0] || -> is_well_founded_in(empty_set,empty_set)*.
% 69.21/69.47 7607[0:SpL:5565.0,323.1] relation(u) || equal(empty_set,empty_set) -> is_well_founded_in(u,empty_set)*.
% 69.21/69.47 7609[0:Obv:7607.1] relation(u) || -> is_well_founded_in(u,empty_set)*.
% 69.21/69.47 7611[0:Res:7609.1,4815.1] relation(u) empty(u) || -> well_founded_relation(u)*.
% 69.21/69.47 7614[0:SSi:7611.0,72.1] empty(u) || -> well_founded_relation(u)*.
% 69.21/69.47 7616[0:SoR:4754.0,7614.1] empty(identity_relation(u)) || -> is_well_founded_in(identity_relation(u),u)*.
% 69.21/69.47 7654[0:SoR:7616.0,3180.1] || equal(identity_relation(u),empty_set) -> is_well_founded_in(identity_relation(u),u)*.
% 69.21/69.47 11332[0:Res:7654.1,4762.0] || equal(identity_relation(u),empty_set) -> well_founded_relation(identity_relation(u))*.
% 69.21/69.47 13758[0:Res:358.1,427.0] || element(u,powerset(powerset(v))) equal(complements_of_subsets(v,complements_of_subsets(v,u)),empty_set)** -> equal(complements_of_subsets(v,u),empty_set).
% 69.21/69.47 13761[0:Rew:359.1,13758.1] || element(u,powerset(powerset(v)))* equal(u,empty_set) -> equal(complements_of_subsets(v,u),empty_set).
% 69.21/69.47 13762[0:MRR:13761.0,3045.1] || equal(u,empty_set) -> equal(complements_of_subsets(v,u),empty_set)**.
% 69.21/69.47 20720[0:SpR:13762.1,359.1] || equal(u,empty_set) element(u,powerset(powerset(v)))* -> equal(complements_of_subsets(v,empty_set),u).
% 69.21/69.47 20727[0:MRR:20720.1,3045.1] || equal(u,empty_set) -> equal(complements_of_subsets(v,empty_set),u)*.
% 69.21/69.47 22070[0:SpR:20727.1,11332.1] || equal(identity_relation(u),empty_set)** equal(identity_relation(u),empty_set)** -> well_founded_relation(complements_of_subsets(v,empty_set))*.
% 70.12/70.41 23801[0:Obv:22070.0] || equal(identity_relation(u),empty_set)**+ -> well_founded_relation(complements_of_subsets(v,empty_set))*.
% 70.12/70.41 24310[1:SpL:3916.0,23801.0] || equal(empty_set,empty_set) -> well_founded_relation(complements_of_subsets(u,empty_set))*.
% 70.12/70.41 24311[1:Obv:24310.0] || -> well_founded_relation(complements_of_subsets(u,empty_set))*.
% 70.12/70.41 24317[1:SpR:13762.1,24311.0] || equal(empty_set,empty_set) -> well_founded_relation(empty_set)*.
% 70.12/70.41 24319[1:Obv:24317.0] || -> well_founded_relation(empty_set)*.
% 70.12/70.41 33212[2:Res:577.6,1826.0] relation(empty_set) || is_reflexive_in(empty_set,empty_set) is_well_founded_in(empty_set,empty_set)* is_connected_in(empty_set,empty_set) is_antisymmetric_in(empty_set,empty_set) is_transitive_in(empty_set,empty_set) -> .
% 70.12/70.41 33335[2:SSi:33212.0,7.0,11.0,12.0,13.0,9.0,14.0,8.0,15.0,1825.0,2587.0,2589.0] || is_reflexive_in(empty_set,empty_set) is_well_founded_in(empty_set,empty_set)* is_connected_in(empty_set,empty_set) is_antisymmetric_in(empty_set,empty_set) is_transitive_in(empty_set,empty_set) -> .
% 70.12/70.41 33336[2:MRR:33335.0,33335.3,33335.4,3083.0,2597.0,2595.0] || is_well_founded_in(empty_set,empty_set)* is_connected_in(empty_set,empty_set) -> .
% 70.12/70.41 33337[2:MRR:33336.0,33336.1,5577.0,3478.0] || -> .
% 70.12/70.41 33338[2:Spt:33337.0,1524.0,1825.0] || well_ordering(empty_set)* -> .
% 70.12/70.41 33339[2:Spt:33337.0,1524.1] || -> well_orders(empty_set,empty_set)*.
% 70.12/70.41 33387[2:Res:504.6,33338.0] relation(empty_set) well_founded_relation(empty_set) connected(empty_set) antisymmetric(empty_set) transitive(empty_set) reflexive(empty_set) || -> .
% 70.12/70.41 33388[2:SSi:33387.5,33387.4,33387.3,33387.2,33387.1,33387.0,7.0,11.0,12.0,13.0,9.0,14.0,8.0,15.0,2587.0,2589.0,2752.0,5019.0,24319.0,4987.0,7.0,11.0,12.0,13.0,9.0,14.0,8.0,15.0,2587.0,2589.0,2752.0,5019.0,24319.0,4987.0,7.0,11.0,12.0,13.0,9.0,14.0,8.0,15.0,2587.0,2589.0,2752.0,5019.0,24319.0,4987.0,7.0,11.0,12.0,13.0,9.0,14.0,8.0,15.0,2587.0,2589.0,2752.0,5019.0,24319.0,4987.0,7.0,11.0,12.0,13.0,9.0,14.0,8.0,15.0,2587.0,2589.0,2752.0,5019.0,24319.0,4987.0,7.0,11.0,12.0,13.0,9.0,14.0,8.0,15.0,2587.0,2589.0,2752.0,5019.0,24319.0,4987.0] || -> .
% 70.12/70.41 33389[1:Spt:33388.0,841.0,1148.0] || equal(skc13,empty_set)** -> .
% 70.12/70.41 33390[1:Spt:33388.0,841.1] || -> in(ordered_pair(skf217(skc13),skf216(skc13)),skc13)*.
% 70.12/70.41 34473[2:Spt:888.0] || -> connected(skc13)*.
% 70.12/70.41 34474[2:MRR:868.0,34473.0] || -> is_connected_in(skc13,relation_field(skc13))*.
% 70.12/70.41 34475[2:MRR:772.1,34473.0] well_founded_relation(skc13) antisymmetric(skc13) transitive(skc13) reflexive(skc13) || -> well_ordering(skc13)*.
% 70.12/70.41 34477[3:Spt:100.0] || -> well_ordering(skc13)*.
% 70.12/70.41 34478[3:MRR:902.0,34477.0] || -> well_founded_relation(skc13)*.
% 70.12/70.41 34479[3:MRR:900.0,34477.0] || -> antisymmetric(skc13)*.
% 70.12/70.41 34480[3:MRR:899.0,34477.0] || -> transitive(skc13)*.
% 70.12/70.41 34481[3:MRR:898.0,34477.0] || -> reflexive(skc13)*.
% 70.12/70.41 34482[3:MRR:148.0,34477.0] || well_orders(skc13,relation_field(skc13))* -> .
% 70.12/70.41 34483[3:MRR:890.0,34478.0] || -> is_well_founded_in(skc13,relation_field(skc13))*.
% 70.12/70.41 34486[3:MRR:866.0,34479.0] || -> is_antisymmetric_in(skc13,relation_field(skc13))*.
% 70.12/70.41 34488[3:MRR:870.0,34480.0] || -> is_transitive_in(skc13,relation_field(skc13))*.
% 70.12/70.41 34490[3:MRR:878.0,34481.0] || -> is_reflexive_in(skc13,relation_field(skc13))*.
% 70.12/70.41 34498[3:Res:577.6,34482.0] relation(skc13) || is_reflexive_in(skc13,relation_field(skc13)) is_well_founded_in(skc13,relation_field(skc13))* is_connected_in(skc13,relation_field(skc13)) is_antisymmetric_in(skc13,relation_field(skc13)) is_transitive_in(skc13,relation_field(skc13)) -> .
% 70.12/70.41 34499[3:SSi:34498.0,34473.0,34477.0,1.0,34478.0,34479.0,34480.0] || is_reflexive_in(skc13,relation_field(skc13)) is_well_founded_in(skc13,relation_field(skc13))* is_connected_in(skc13,relation_field(skc13)) is_antisymmetric_in(skc13,relation_field(skc13)) is_transitive_in(skc13,relation_field(skc13)) -> .
% 70.12/70.41 34500[3:MRR:34499.0,34499.1,34499.2,34499.3,34499.4,34490.0,34483.0,34474.0,34486.0,34488.0] || -> .
% 70.12/70.41 34501[3:Spt:34500.0,100.0,34477.0] || well_ordering(skc13)* -> .
% 70.12/70.41 34502[3:Spt:34500.0,100.1] || -> well_orders(skc13,relation_field(skc13))*.
% 70.12/70.41 34503[3:MRR:34475.4,34501.0] well_founded_relation(skc13) antisymmetric(skc13) transitive(skc13) reflexive(skc13) || -> .
% 70.12/70.41 34505[3:Res:34502.0,239.1] relation(skc13) || -> is_transitive_in(skc13,relation_field(skc13))*.
% 70.12/70.41 34506[3:Res:34502.0,240.1] relation(skc13) || -> is_antisymmetric_in(skc13,relation_field(skc13))*.
% 70.12/70.41 34508[3:Res:34502.0,242.1] relation(skc13) || -> is_well_founded_in(skc13,relation_field(skc13))*.
% 70.12/70.41 34509[3:Res:34502.0,238.1] relation(skc13) || -> is_reflexive_in(skc13,relation_field(skc13))*.
% 70.12/70.41 34510[3:SSi:34505.0,34473.0,1.0] || -> is_transitive_in(skc13,relation_field(skc13))*.
% 70.12/70.41 34511[3:MRR:871.0,34510.0] || -> transitive(skc13)*.
% 70.12/70.41 34512[3:MRR:34503.2,34511.0] well_founded_relation(skc13) antisymmetric(skc13) reflexive(skc13) || -> .
% 70.12/70.41 34514[3:SSi:34506.0,34473.0,1.0] || -> is_antisymmetric_in(skc13,relation_field(skc13))*.
% 70.12/70.41 34515[3:MRR:867.0,34514.0] || -> antisymmetric(skc13)*.
% 70.12/70.41 34517[3:SSi:34508.0,34473.0,1.0] || -> is_well_founded_in(skc13,relation_field(skc13))*.
% 70.12/70.41 34518[3:MRR:891.0,34517.0] || -> well_founded_relation(skc13)*.
% 70.12/70.41 34521[3:SSi:34509.0,34473.0,1.0] || -> is_reflexive_in(skc13,relation_field(skc13))*.
% 70.12/70.41 34522[3:MRR:879.0,34521.0] || -> reflexive(skc13)*.
% 70.12/70.41 34524[3:MRR:34512.0,34512.1,34512.2,34518.0,34515.0,34522.0] || -> .
% 70.12/70.41 34530[2:Spt:34524.0,888.0,34473.0] || connected(skc13)* -> .
% 70.12/70.41 34531[2:Spt:34524.0,888.1] || -> in(skf196(skc13),relation_field(skc13))*.
% 70.12/70.41 34532[2:MRR:901.1,34530.0] well_ordering(skc13) || -> .
% 70.12/70.41 34533[2:MRR:100.0,34532.0] || -> well_orders(skc13,relation_field(skc13))*.
% 70.12/70.41 34535[2:MRR:869.1,34530.0] || is_connected_in(skc13,relation_field(skc13))* -> .
% 70.12/70.41 34589[2:Res:34533.0,241.1] relation(skc13) || -> is_connected_in(skc13,relation_field(skc13))*.
% 70.12/70.41 34641[2:SSi:34589.0,1.0] || -> is_connected_in(skc13,relation_field(skc13))*.
% 70.12/70.41 34642[2:MRR:34641.0,34535.0] || -> .
% 70.12/70.41 % SZS output end Refutation
% 70.12/70.41 Formulae used in the proof : t8_wellord1 fc2_ordinal1 fc4_relat_1 fc2_funct_1 existence_m1_subset_1 t60_relat_1 cc1_relat_1 d3_wellord1 t2_xboole_1 idempotence_k2_xboole_0 t1_boole t71_relat_1 fc7_relat_1 fc8_relat_1 t31_ordinal1 t6_boole commutativity_k2_xboole_0 l28_zfmisc_1 t3_xboole_1 t7_boole d1_xboole_0 d4_wellord1 t3_xboole_0 t7_tarski d7_xboole_0 l71_subset_1 t2_subset t41_ordinal1 rc3_ordinal1 d12_relat_2 d14_relat_2 d16_relat_2 d5_wellord1 d9_relat_2 l1_wellord1 l4_wellord1 t4_xboole_0 t5_wellord1 d1_relat_2 d6_relat_1 d6_relat_2 l2_wellord1 l3_wellord1 l1_zfmisc_1 dt_k7_setfam_1 involutiveness_k7_setfam_1 t56_relat_1 d4_relat_2 d8_relat_2 t46_setfam_1 d10_relat_1
% 70.12/70.41
%------------------------------------------------------------------------------