TSTP Solution File: SET101+1 by leanCoP---2.2
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- Process Solution
%------------------------------------------------------------------------------
% File : leanCoP---2.2
% Problem : SET101+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : leancop_casc.sh %s %d
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 02:51:25 EDT 2022
% Result : Theorem 13.96s 13.81s
% Output : Proof 13.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET101+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.11/0.12 % Command : leancop_casc.sh %s %d
% 0.12/0.33 % Computer : n020.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 Jul 11 07:14:43 EDT 2022
% 0.12/0.33 % CPUTime :
% 13.96/13.81 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.96/13.82 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.96/13.83
% 13.96/13.83 %-----------------------------------------------------
% 13.96/13.83 fof(singleton_member_of_ordered_pair, conjecture, ! [_80511, _80514] : member(singleton(_80511), ordered_pair(_80511, _80514)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', singleton_member_of_ordered_pair)).
% 13.96/13.83 fof(subclass_defn, axiom, ! [_80729, _80732] : (subclass(_80729, _80732) <=> ! [_80750] : (member(_80750, _80729) => member(_80750, _80732))), file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax', subclass_defn)).
% 13.96/13.83 fof(class_elements_are_sets, axiom, ! [_80933] : subclass(_80933, universal_class), file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax', class_elements_are_sets)).
% 13.96/13.83 fof(unordered_pair_defn, axiom, ! [_81045, _81048, _81051] : (member(_81045, unordered_pair(_81048, _81051)) <=> member(_81045, universal_class) & (_81045 = _81048 | _81045 = _81051)), file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax', unordered_pair_defn)).
% 13.96/13.83 fof(unordered_pair, axiom, ! [_81267, _81270] : member(unordered_pair(_81267, _81270), universal_class), file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax', unordered_pair)).
% 13.96/13.83 fof(singleton_set_defn, axiom, ! [_81401] : singleton(_81401) = unordered_pair(_81401, _81401), file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax', singleton_set_defn)).
% 13.96/13.83 fof(ordered_pair_defn, axiom, ! [_81529, _81532] : ordered_pair(_81529, _81532) = unordered_pair(singleton(_81529), unordered_pair(_81529, singleton(_81532))), file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax', ordered_pair_defn)).
% 13.96/13.83 fof(complement, axiom, ! [_81724, _81727] : (member(_81727, complement(_81724)) <=> member(_81727, universal_class) & ~ member(_81727, _81724)), file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax', complement)).
% 13.96/13.83 fof(union_defn, axiom, ! [_81928, _81931, _81934] : (member(_81934, union(_81928, _81931)) <=> member(_81934, _81928) | member(_81934, _81931)), file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax', union_defn)).
% 13.96/13.83
% 13.96/13.83 cnf(1, plain, [member(singleton(8 ^ []), ordered_pair(8 ^ [], 9 ^ []))], clausify(singleton_member_of_ordered_pair)).
% 13.96/13.83 cnf(2, plain, [-(_22605 = _22605)], theory(equality)).
% 13.96/13.83 cnf(3, plain, [_22758 = _22803, -(_22803 = _22758)], theory(equality)).
% 13.96/13.83 cnf(4, plain, [-(member(_24862, _24993)), member(_24795, _24928), _24795 = _24862, _24928 = _24993], theory(equality)).
% 13.96/13.83 cnf(5, plain, [-(subclass(_25476, _25607)), subclass(_25409, _25542), _25409 = _25476, _25542 = _25607], theory(equality)).
% 13.96/13.83 cnf(6, plain, [subclass(_36399, _36455), member(_36569, _36399), -(member(_36569, _36455))], clausify(subclass_defn)).
% 13.96/13.83 cnf(7, plain, [-(subclass(_36860, universal_class))], clausify(class_elements_are_sets)).
% 13.96/13.83 cnf(8, plain, [-(member(_37430, unordered_pair(_37495, _37559))), member(_37430, universal_class), _37430 = _37495], clausify(unordered_pair_defn)).
% 13.96/13.83 cnf(9, plain, [-(member(unordered_pair(_38035, _38077), universal_class))], clausify(unordered_pair)).
% 13.96/13.83 cnf(10, plain, [-(singleton(_38302) = unordered_pair(_38302, _38302))], clausify(singleton_set_defn)).
% 13.96/13.83 cnf(11, plain, [-(ordered_pair(_38534, _38586) = unordered_pair(singleton(_38534), unordered_pair(_38534, singleton(_38586))))], clausify(ordered_pair_defn)).
% 13.96/13.83 cnf(12, plain, [-(member(_41868, complement(_41813))), member(_41868, universal_class), -(member(_41868, _41813))], clausify(complement)).
% 13.96/13.83 cnf(13, plain, [-(member(_45973, union(_45856, _45915))), member(_45973, _45915)], clausify(union_defn)).
% 13.96/13.83 cnf(14, plain, [member(_45973, union(_45856, _45915)), -(member(_45973, _45856)), -(member(_45973, _45915))], clausify(union_defn)).
% 13.96/13.83
% 13.96/13.83 cnf('1',plain,[member(singleton(8 ^ []), ordered_pair(8 ^ [], 9 ^ []))],start(1)).
% 13.96/13.83 cnf('1.1',plain,[-(member(singleton(8 ^ []), ordered_pair(8 ^ [], 9 ^ []))), member(singleton(8 ^ []), union(ordered_pair(8 ^ [], 9 ^ []), unordered_pair(singleton(8 ^ []), unordered_pair(8 ^ [], singleton(9 ^ []))))), -(member(singleton(8 ^ []), unordered_pair(singleton(8 ^ []), unordered_pair(8 ^ [], singleton(9 ^ [])))))],extension(14,bind([[_45856, _45973, _45915], [ordered_pair(8 ^ [], 9 ^ []), singleton(8 ^ []), unordered_pair(singleton(8 ^ []), unordered_pair(8 ^ [], singleton(9 ^ [])))]]))).
% 13.96/13.83 cnf('1.1.1',plain,[-(member(singleton(8 ^ []), union(ordered_pair(8 ^ [], 9 ^ []), unordered_pair(singleton(8 ^ []), unordered_pair(8 ^ [], singleton(9 ^ [])))))), -(member(singleton(8 ^ []), complement(union(ordered_pair(8 ^ [], 9 ^ []), unordered_pair(singleton(8 ^ []), unordered_pair(8 ^ [], singleton(9 ^ []))))))), member(singleton(8 ^ []), universal_class)],extension(12,bind([[_41813, _41868], [union(ordered_pair(8 ^ [], 9 ^ []), unordered_pair(singleton(8 ^ []), unordered_pair(8 ^ [], singleton(9 ^ [])))), singleton(8 ^ [])]]))).
% 13.96/13.83 cnf('1.1.1.1',plain,[member(singleton(8 ^ []), complement(union(ordered_pair(8 ^ [], 9 ^ []), unordered_pair(singleton(8 ^ []), unordered_pair(8 ^ [], singleton(9 ^ [])))))), subclass(complement(union(ordered_pair(8 ^ [], 9 ^ []), unordered_pair(singleton(8 ^ []), unordered_pair(8 ^ [], singleton(9 ^ []))))), universal_class), -(member(singleton(8 ^ []), universal_class))],extension(6,bind([[_36399, _36569, _36455], [complement(union(ordered_pair(8 ^ [], 9 ^ []), unordered_pair(singleton(8 ^ []), unordered_pair(8 ^ [], singleton(9 ^ []))))), singleton(8 ^ []), universal_class]]))).
% 13.96/13.83 cnf('1.1.1.1.1',plain,[-(subclass(complement(union(ordered_pair(8 ^ [], 9 ^ []), unordered_pair(singleton(8 ^ []), unordered_pair(8 ^ [], singleton(9 ^ []))))), universal_class)), subclass(complement(union(ordered_pair(8 ^ [], 9 ^ []), unordered_pair(singleton(8 ^ []), unordered_pair(8 ^ [], singleton(9 ^ []))))), universal_class), complement(union(ordered_pair(8 ^ [], 9 ^ []), unordered_pair(singleton(8 ^ []), unordered_pair(8 ^ [], singleton(9 ^ []))))) = complement(union(ordered_pair(8 ^ [], 9 ^ []), unordered_pair(singleton(8 ^ []), unordered_pair(8 ^ [], singleton(9 ^ []))))), universal_class = universal_class],extension(5,bind([[_25409, _25476, _25542, _25607], [complement(union(ordered_pair(8 ^ [], 9 ^ []), unordered_pair(singleton(8 ^ []), unordered_pair(8 ^ [], singleton(9 ^ []))))), complement(union(ordered_pair(8 ^ [], 9 ^ []), unordered_pair(singleton(8 ^ []), unordered_pair(8 ^ [], singleton(9 ^ []))))), universal_class, universal_class]]))).
% 13.96/13.83 cnf('1.1.1.1.1.1',plain,[-(subclass(complement(union(ordered_pair(8 ^ [], 9 ^ []), unordered_pair(singleton(8 ^ []), unordered_pair(8 ^ [], singleton(9 ^ []))))), universal_class))],extension(7,bind([[_36860], [complement(union(ordered_pair(8 ^ [], 9 ^ []), unordered_pair(singleton(8 ^ []), unordered_pair(8 ^ [], singleton(9 ^ [])))))]]))).
% 13.96/13.83 cnf('1.1.1.1.1.2',plain,[-(complement(union(ordered_pair(8 ^ [], 9 ^ []), unordered_pair(singleton(8 ^ []), unordered_pair(8 ^ [], singleton(9 ^ []))))) = complement(union(ordered_pair(8 ^ [], 9 ^ []), unordered_pair(singleton(8 ^ []), unordered_pair(8 ^ [], singleton(9 ^ []))))))],extension(2,bind([[_22605], [complement(union(ordered_pair(8 ^ [], 9 ^ []), unordered_pair(singleton(8 ^ []), unordered_pair(8 ^ [], singleton(9 ^ [])))))]]))).
% 13.96/13.83 cnf('1.1.1.1.1.3',plain,[-(universal_class = universal_class)],extension(2,bind([[_22605], [universal_class]]))).
% 13.96/13.83 cnf('1.1.1.1.2',plain,[member(singleton(8 ^ []), universal_class), -(member(singleton(8 ^ []), unordered_pair(singleton(8 ^ []), unordered_pair(8 ^ [], singleton(9 ^ []))))), singleton(8 ^ []) = singleton(8 ^ [])],extension(8,bind([[_37559, _37430, _37495], [unordered_pair(8 ^ [], singleton(9 ^ [])), singleton(8 ^ []), singleton(8 ^ [])]]))).
% 13.96/13.83 cnf('1.1.1.1.2.1',plain,[member(singleton(8 ^ []), unordered_pair(singleton(8 ^ []), unordered_pair(8 ^ [], singleton(9 ^ [])))), -(member(singleton(8 ^ []), union(ordered_pair(8 ^ [], 9 ^ []), unordered_pair(singleton(8 ^ []), unordered_pair(8 ^ [], singleton(9 ^ []))))))],extension(13,bind([[_45973, _45856, _45915], [singleton(8 ^ []), ordered_pair(8 ^ [], 9 ^ []), unordered_pair(singleton(8 ^ []), unordered_pair(8 ^ [], singleton(9 ^ [])))]]))).
% 13.96/13.83 cnf('1.1.1.1.2.1.1',plain,[member(singleton(8 ^ []), union(ordered_pair(8 ^ [], 9 ^ []), unordered_pair(singleton(8 ^ []), unordered_pair(8 ^ [], singleton(9 ^ [])))))],reduction('1.1')).
% 13.96/13.83 cnf('1.1.1.1.2.2',plain,[-(singleton(8 ^ []) = singleton(8 ^ []))],extension(2,bind([[_22605], [singleton(8 ^ [])]]))).
% 13.96/13.83 cnf('1.1.1.2',plain,[-(member(singleton(8 ^ []), universal_class)), member(unordered_pair(8 ^ [], 8 ^ []), universal_class), unordered_pair(8 ^ [], 8 ^ []) = singleton(8 ^ []), universal_class = universal_class],extension(4,bind([[_24795, _24862, _24928, _24993], [unordered_pair(8 ^ [], 8 ^ []), singleton(8 ^ []), universal_class, universal_class]]))).
% 13.96/13.83 cnf('1.1.1.2.1',plain,[-(member(unordered_pair(8 ^ [], 8 ^ []), universal_class)), member(unordered_pair(8 ^ [], 8 ^ []), universal_class), unordered_pair(8 ^ [], 8 ^ []) = unordered_pair(8 ^ [], 8 ^ []), universal_class = universal_class],extension(4,bind([[_24795, _24862, _24928, _24993], [unordered_pair(8 ^ [], 8 ^ []), unordered_pair(8 ^ [], 8 ^ []), universal_class, universal_class]]))).
% 13.96/13.83 cnf('1.1.1.2.1.1',plain,[-(member(unordered_pair(8 ^ [], 8 ^ []), universal_class))],extension(9,bind([[_38035, _38077], [8 ^ [], 8 ^ []]]))).
% 13.96/13.83 cnf('1.1.1.2.1.2',plain,[-(unordered_pair(8 ^ [], 8 ^ []) = unordered_pair(8 ^ [], 8 ^ []))],extension(2,bind([[_22605], [unordered_pair(8 ^ [], 8 ^ [])]]))).
% 13.96/13.83 cnf('1.1.1.2.1.3',plain,[-(universal_class = universal_class)],extension(2,bind([[_22605], [universal_class]]))).
% 13.96/13.83 cnf('1.1.1.2.2',plain,[-(unordered_pair(8 ^ [], 8 ^ []) = singleton(8 ^ [])), singleton(8 ^ []) = unordered_pair(8 ^ [], 8 ^ [])],extension(3,bind([[_22758, _22803], [singleton(8 ^ []), unordered_pair(8 ^ [], 8 ^ [])]]))).
% 13.96/13.83 cnf('1.1.1.2.2.1',plain,[-(singleton(8 ^ []) = unordered_pair(8 ^ [], 8 ^ []))],extension(10,bind([[_38302], [8 ^ []]]))).
% 13.96/13.83 cnf('1.1.1.2.3',plain,[-(universal_class = universal_class)],extension(2,bind([[_22605], [universal_class]]))).
% 13.96/13.83 cnf('1.1.2',plain,[member(singleton(8 ^ []), unordered_pair(singleton(8 ^ []), unordered_pair(8 ^ [], singleton(9 ^ [])))), -(member(singleton(8 ^ []), ordered_pair(8 ^ [], 9 ^ []))), singleton(8 ^ []) = singleton(8 ^ []), unordered_pair(singleton(8 ^ []), unordered_pair(8 ^ [], singleton(9 ^ []))) = ordered_pair(8 ^ [], 9 ^ [])],extension(4,bind([[_24795, _24862, _24928, _24993], [singleton(8 ^ []), singleton(8 ^ []), unordered_pair(singleton(8 ^ []), unordered_pair(8 ^ [], singleton(9 ^ []))), ordered_pair(8 ^ [], 9 ^ [])]]))).
% 13.96/13.83 cnf('1.1.2.1',plain,[member(singleton(8 ^ []), ordered_pair(8 ^ [], 9 ^ []))],extension(1)).
% 13.96/13.83 cnf('1.1.2.2',plain,[-(singleton(8 ^ []) = singleton(8 ^ []))],extension(2,bind([[_22605], [singleton(8 ^ [])]]))).
% 13.96/13.83 cnf('1.1.2.3',plain,[-(unordered_pair(singleton(8 ^ []), unordered_pair(8 ^ [], singleton(9 ^ []))) = ordered_pair(8 ^ [], 9 ^ [])), ordered_pair(8 ^ [], 9 ^ []) = unordered_pair(singleton(8 ^ []), unordered_pair(8 ^ [], singleton(9 ^ [])))],extension(3,bind([[_22758, _22803], [ordered_pair(8 ^ [], 9 ^ []), unordered_pair(singleton(8 ^ []), unordered_pair(8 ^ [], singleton(9 ^ [])))]]))).
% 13.96/13.83 cnf('1.1.2.3.1',plain,[-(ordered_pair(8 ^ [], 9 ^ []) = unordered_pair(singleton(8 ^ []), unordered_pair(8 ^ [], singleton(9 ^ []))))],extension(11,bind([[_38534, _38586], [8 ^ [], 9 ^ []]]))).
% 13.96/13.83 %-----------------------------------------------------
% 13.96/13.83
% 13.96/13.83 % SZS output end Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------