TSTP Solution File: SEU365+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU365+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n018.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 : Wed Jul 27 13:15:53 EDT 2022
% Result : Timeout 299.88s 300.07s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SEU365+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n018.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 : 300
% 0.12/0.33 % DateTime : Wed Jul 27 08:08:01 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.09/2.31 ----- Otter 3.3f, August 2004 -----
% 2.09/2.31 The process was started by sandbox on n018.cluster.edu,
% 2.09/2.31 Wed Jul 27 08:08:01 2022
% 2.09/2.31 The command was "./otter". The process ID is 25925.
% 2.09/2.31
% 2.09/2.31 set(prolog_style_variables).
% 2.09/2.31 set(auto).
% 2.09/2.31 dependent: set(auto1).
% 2.09/2.31 dependent: set(process_input).
% 2.09/2.31 dependent: clear(print_kept).
% 2.09/2.31 dependent: clear(print_new_demod).
% 2.09/2.31 dependent: clear(print_back_demod).
% 2.09/2.31 dependent: clear(print_back_sub).
% 2.09/2.31 dependent: set(control_memory).
% 2.09/2.31 dependent: assign(max_mem, 12000).
% 2.09/2.31 dependent: assign(pick_given_ratio, 4).
% 2.09/2.31 dependent: assign(stats_level, 1).
% 2.09/2.31 dependent: assign(max_seconds, 10800).
% 2.09/2.31 clear(print_given).
% 2.09/2.31
% 2.09/2.31 formula_list(usable).
% 2.09/2.31 all A (A=A).
% 2.09/2.31 -(all A B C (-empty_carrier(A)&transitive_relstr(A)&rel_str(A)&element(B,powerset(the_carrier(A)))&finite(C)&element(C,powerset(B))-> (finite(C)& (exists D (element(D,the_carrier(A))&in(D,B)&relstr_set_smaller(A,empty_set,D)))& (all E F (in(E,C)&subset(F,C)& (exists G (element(G,the_carrier(A))&in(G,B)&relstr_set_smaller(A,F,G)))-> (exists H (element(H,the_carrier(A))&in(H,B)&relstr_set_smaller(A,set_union2(F,singleton(E)),H)))))-> (exists I (element(I,the_carrier(A))&in(I,B)&relstr_set_smaller(A,C,I)))))).
% 2.09/2.31 $T.
% 2.09/2.31 exists A (one_sorted_str(A)& -empty_carrier(A)).
% 2.09/2.31 all A (-empty_carrier(A)&one_sorted_str(A)-> -empty(the_carrier(A))).
% 2.09/2.31 all A (-empty_carrier(A)&one_sorted_str(A)-> (exists B (element(B,powerset(the_carrier(A)))& -empty(B)))).
% 2.09/2.31 exists A (-empty(A)&finite(A)).
% 2.09/2.31 all A (empty(A)->finite(A)).
% 2.09/2.31 all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)&finite(B)))).
% 2.09/2.31 all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)&finite(B)))).
% 2.09/2.31 all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)))).
% 2.09/2.31 all A exists B (element(B,powerset(A))&empty(B)).
% 2.09/2.31 exists A empty(A).
% 2.09/2.31 exists A (-empty(A)).
% 2.09/2.31 all A B (-empty(A)-> -empty(set_union2(A,B))).
% 2.09/2.31 all A B (-empty(A)-> -empty(set_union2(B,A))).
% 2.09/2.31 all A B (set_union2(A,B)=set_union2(B,A)).
% 2.09/2.31 all A B (set_union2(A,A)=A).
% 2.09/2.31 all A B subset(A,A).
% 2.09/2.31 all A B (in(A,B)-> -in(B,A)).
% 2.09/2.31 $T.
% 2.09/2.31 $T.
% 2.09/2.31 $T.
% 2.09/2.31 $T.
% 2.09/2.31 all A (rel_str(A)->one_sorted_str(A)).
% 2.09/2.31 $T.
% 2.09/2.31 $T.
% 2.09/2.31 all A (-empty(singleton(A))&finite(singleton(A))).
% 2.09/2.31 all A (finite(A)-> (all B (element(B,powerset(A))->finite(B)))).
% 2.09/2.31 all A B (finite(A)&finite(B)->finite(set_union2(A,B))).
% 2.09/2.31 all A (-empty(powerset(A))).
% 2.09/2.31 all A (-empty(singleton(A))).
% 2.09/2.31 empty(empty_set).
% 2.09/2.31 all A B C (-empty_carrier(A)&transitive_relstr(A)&rel_str(A)&element(B,powerset(the_carrier(A)))&finite(C)&element(C,powerset(B))-> (exists D all E (in(E,D)<->in(E,powerset(C))& (exists F (F=E& (exists G (element(G,the_carrier(A))&in(G,B)&relstr_set_smaller(A,F,G)))))))).
% 2.09/2.31 all A (ordinal(A)-> (all B (element(B,A)->epsilon_transitive(B)&epsilon_connected(B)&ordinal(B)))).
% 2.09/2.31 all A (empty(A)->function(A)).
% 2.09/2.31 all A (ordinal(A)->epsilon_transitive(A)&epsilon_connected(A)).
% 2.09/2.31 all A (empty(A)->relation(A)).
% 2.09/2.31 all A (empty(A)&ordinal(A)->epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)&natural(A)).
% 2.09/2.31 all A (relation(A)&empty(A)&function(A)->relation(A)&function(A)&one_to_one(A)).
% 2.09/2.31 all A (epsilon_transitive(A)&epsilon_connected(A)->ordinal(A)).
% 2.09/2.31 all A (empty(A)->epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)).
% 2.09/2.31 all A B (A=B<->subset(A,B)&subset(B,A)).
% 2.09/2.31 all A B (subset(A,B)<-> (all C (in(C,A)->in(C,B)))).
% 2.09/2.31 all A B C (C=set_difference(A,B)<-> (all D (in(D,C)<->in(D,A)& -in(D,B)))).
% 2.09/2.31 $T.
% 2.09/2.31 all A exists B element(B,A).
% 2.09/2.31 all A B (finite(A)->finite(set_difference(A,B))).
% 2.09/2.31 empty(empty_set).
% 2.09/2.31 relation(empty_set).
% 2.09/2.31 relation_empty_yielding(empty_set).
% 2.09/2.31 relation(empty_set).
% 2.09/2.31 relation_empty_yielding(empty_set).
% 2.09/2.31 function(empty_set).
% 2.09/2.31 one_to_one(empty_set).
% 2.09/2.31 empty(empty_set).
% 2.09/2.31 epsilon_transitive(empty_set).
% 2.09/2.31 epsilon_connected(empty_set).
% 2.09/2.31 ordinal(empty_set).
% 2.09/2.31 all A B (relation(A)&relation(B)->relation(set_union2(A,B))).
% 2.09/2.31 all A B (relation(A)&relation(B)->relation(set_difference(A,B))).
% 2.09/2.31 empty(empty_set).
% 2.09/2.31 relation(empty_set).
% 2.09/2.31 exists A (-empty(A)&epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)&natural(A)).
% 2.09/2.31 exists A (relation(A)&function(A)).
% 2.09/2.31 exists A (epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)).
% 2.09/2.31 exists A (empty(A)&relation(A)).
% 2.09/2.31 all A exists B (element(B,powerset(A))&empty(B)&relation(B)&function(B)&one_to_one(B)&epsilon_transitive(B)&epsilon_connected(B)&ordinal(B)&natural(B)&finite(B)).
% 2.09/2.31 exists A (relation(A)&empty(A)&function(A)).
% 2.09/2.31 exists A (relation(A)&function(A)&one_to_one(A)&empty(A)&epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)).
% 2.09/2.31 exists A (-empty(A)&relation(A)).
% 2.09/2.31 exists A (relation(A)&function(A)&one_to_one(A)).
% 2.09/2.31 exists A (-empty(A)&epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)).
% 2.09/2.31 exists A (relation(A)&relation_empty_yielding(A)).
% 2.09/2.31 exists A (relation(A)&relation_empty_yielding(A)&function(A)).
% 2.09/2.31 all A (finite(A)-> (all B (element(B,powerset(powerset(A)))-> -(B!=empty_set& (all C (-(in(C,B)& (all D (in(D,B)&subset(C,D)->D=C))))))))).
% 2.09/2.31 all A (set_union2(A,empty_set)=A).
% 2.09/2.31 all A B (in(A,B)->element(A,B)).
% 2.09/2.31 all A B (element(A,B)->empty(B)|in(A,B)).
% 2.09/2.31 all A subset(empty_set,A).
% 2.09/2.31 all A B (set_difference(A,B)=empty_set<->subset(A,B)).
% 2.09/2.31 all A B (subset(singleton(A),B)<->in(A,B)).
% 2.09/2.31 all A (set_difference(A,empty_set)=A).
% 2.09/2.31 all A B (element(A,powerset(B))<->subset(A,B)).
% 2.09/2.31 all A (set_difference(empty_set,A)=empty_set).
% 2.09/2.31 all A B C (in(A,B)&element(B,powerset(C))->element(A,C)).
% 2.09/2.31 all A B C (-(in(A,B)&element(B,powerset(C))&empty(C))).
% 2.09/2.31 all A (empty(A)->A=empty_set).
% 2.09/2.31 all A B (-(in(A,B)&empty(B))).
% 2.09/2.31 all A B subset(A,set_union2(A,B)).
% 2.09/2.31 all A B (-(empty(A)&A!=B&empty(B))).
% 2.09/2.31 all A B C (subset(A,B)&subset(C,B)->subset(set_union2(A,C),B)).
% 2.09/2.31 end_of_list.
% 2.09/2.31
% 2.09/2.31 -------> usable clausifies to:
% 2.09/2.31
% 2.09/2.31 list(usable).
% 2.09/2.31 0 [] A=A.
% 2.09/2.31 0 [] -empty_carrier($c4).
% 2.09/2.31 0 [] transitive_relstr($c4).
% 2.09/2.31 0 [] rel_str($c4).
% 2.09/2.31 0 [] element($c3,powerset(the_carrier($c4))).
% 2.09/2.31 0 [] finite($c2).
% 2.09/2.31 0 [] element($c2,powerset($c3)).
% 2.09/2.31 0 [] element($c1,the_carrier($c4)).
% 2.09/2.31 0 [] in($c1,$c3).
% 2.09/2.31 0 [] relstr_set_smaller($c4,empty_set,$c1).
% 2.09/2.31 0 [] -in(E,$c2)| -subset(F,$c2)| -element(G,the_carrier($c4))| -in(G,$c3)| -relstr_set_smaller($c4,F,G)|element($f1(E,F),the_carrier($c4)).
% 2.09/2.31 0 [] -in(E,$c2)| -subset(F,$c2)| -element(G,the_carrier($c4))| -in(G,$c3)| -relstr_set_smaller($c4,F,G)|in($f1(E,F),$c3).
% 2.09/2.31 0 [] -in(E,$c2)| -subset(F,$c2)| -element(G,the_carrier($c4))| -in(G,$c3)| -relstr_set_smaller($c4,F,G)|relstr_set_smaller($c4,set_union2(F,singleton(E)),$f1(E,F)).
% 2.09/2.31 0 [] -element(I,the_carrier($c4))| -in(I,$c3)| -relstr_set_smaller($c4,$c2,I).
% 2.09/2.31 0 [] $T.
% 2.09/2.31 0 [] one_sorted_str($c5).
% 2.09/2.31 0 [] -empty_carrier($c5).
% 2.09/2.31 0 [] empty_carrier(A)| -one_sorted_str(A)| -empty(the_carrier(A)).
% 2.09/2.31 0 [] empty_carrier(A)| -one_sorted_str(A)|element($f2(A),powerset(the_carrier(A))).
% 2.09/2.31 0 [] empty_carrier(A)| -one_sorted_str(A)| -empty($f2(A)).
% 2.09/2.31 0 [] -empty($c6).
% 2.09/2.31 0 [] finite($c6).
% 2.09/2.31 0 [] -empty(A)|finite(A).
% 2.09/2.31 0 [] empty(A)|element($f3(A),powerset(A)).
% 2.09/2.31 0 [] empty(A)| -empty($f3(A)).
% 2.09/2.31 0 [] empty(A)|finite($f3(A)).
% 2.09/2.31 0 [] empty(A)|element($f4(A),powerset(A)).
% 2.09/2.31 0 [] empty(A)| -empty($f4(A)).
% 2.09/2.31 0 [] empty(A)|finite($f4(A)).
% 2.09/2.31 0 [] empty(A)|element($f5(A),powerset(A)).
% 2.09/2.31 0 [] empty(A)| -empty($f5(A)).
% 2.09/2.31 0 [] element($f6(A),powerset(A)).
% 2.09/2.31 0 [] empty($f6(A)).
% 2.09/2.31 0 [] empty($c7).
% 2.09/2.31 0 [] -empty($c8).
% 2.09/2.31 0 [] empty(A)| -empty(set_union2(A,B)).
% 2.09/2.31 0 [] empty(A)| -empty(set_union2(B,A)).
% 2.09/2.31 0 [] set_union2(A,B)=set_union2(B,A).
% 2.09/2.31 0 [] set_union2(A,A)=A.
% 2.09/2.31 0 [] subset(A,A).
% 2.09/2.31 0 [] -in(A,B)| -in(B,A).
% 2.09/2.31 0 [] $T.
% 2.09/2.31 0 [] $T.
% 2.09/2.31 0 [] $T.
% 2.09/2.31 0 [] $T.
% 2.09/2.31 0 [] -rel_str(A)|one_sorted_str(A).
% 2.09/2.31 0 [] $T.
% 2.09/2.31 0 [] $T.
% 2.09/2.31 0 [] -empty(singleton(A)).
% 2.09/2.31 0 [] finite(singleton(A)).
% 2.09/2.31 0 [] -finite(A)| -element(B,powerset(A))|finite(B).
% 2.09/2.31 0 [] -finite(A)| -finite(B)|finite(set_union2(A,B)).
% 2.09/2.31 0 [] -empty(powerset(A)).
% 2.09/2.31 0 [] -empty(singleton(A)).
% 2.09/2.31 0 [] empty(empty_set).
% 2.09/2.31 0 [] empty_carrier(A)| -transitive_relstr(A)| -rel_str(A)| -element(B,powerset(the_carrier(A)))| -finite(C)| -element(C,powerset(B))| -in(E,$f9(A,B,C))|in(E,powerset(C)).
% 2.09/2.31 0 [] empty_carrier(A)| -transitive_relstr(A)| -rel_str(A)| -element(B,powerset(the_carrier(A)))| -finite(C)| -element(C,powerset(B))| -in(E,$f9(A,B,C))|$f8(A,B,C,E)=E.
% 2.09/2.31 0 [] empty_carrier(A)| -transitive_relstr(A)| -rel_str(A)| -element(B,powerset(the_carrier(A)))| -finite(C)| -element(C,powerset(B))| -in(E,$f9(A,B,C))|element($f7(A,B,C,E),the_carrier(A)).
% 2.09/2.31 0 [] empty_carrier(A)| -transitive_relstr(A)| -rel_str(A)| -element(B,powerset(the_carrier(A)))| -finite(C)| -element(C,powerset(B))| -in(E,$f9(A,B,C))|in($f7(A,B,C,E),B).
% 2.09/2.31 0 [] empty_carrier(A)| -transitive_relstr(A)| -rel_str(A)| -element(B,powerset(the_carrier(A)))| -finite(C)| -element(C,powerset(B))| -in(E,$f9(A,B,C))|relstr_set_smaller(A,$f8(A,B,C,E),$f7(A,B,C,E)).
% 2.09/2.31 0 [] empty_carrier(A)| -transitive_relstr(A)| -rel_str(A)| -element(B,powerset(the_carrier(A)))| -finite(C)| -element(C,powerset(B))|in(E,$f9(A,B,C))| -in(E,powerset(C))|F!=E| -element(G,the_carrier(A))| -in(G,B)| -relstr_set_smaller(A,F,G).
% 2.09/2.31 0 [] -ordinal(A)| -element(B,A)|epsilon_transitive(B).
% 2.09/2.31 0 [] -ordinal(A)| -element(B,A)|epsilon_connected(B).
% 2.09/2.31 0 [] -ordinal(A)| -element(B,A)|ordinal(B).
% 2.09/2.31 0 [] -empty(A)|function(A).
% 2.09/2.31 0 [] -ordinal(A)|epsilon_transitive(A).
% 2.09/2.31 0 [] -ordinal(A)|epsilon_connected(A).
% 2.09/2.31 0 [] -empty(A)|relation(A).
% 2.09/2.31 0 [] -empty(A)| -ordinal(A)|epsilon_transitive(A).
% 2.09/2.31 0 [] -empty(A)| -ordinal(A)|epsilon_connected(A).
% 2.09/2.31 0 [] -empty(A)| -ordinal(A)|natural(A).
% 2.09/2.31 0 [] -relation(A)| -empty(A)| -function(A)|one_to_one(A).
% 2.09/2.31 0 [] -epsilon_transitive(A)| -epsilon_connected(A)|ordinal(A).
% 2.09/2.31 0 [] -empty(A)|epsilon_transitive(A).
% 2.09/2.31 0 [] -empty(A)|epsilon_connected(A).
% 2.09/2.31 0 [] -empty(A)|ordinal(A).
% 2.09/2.31 0 [] A!=B|subset(A,B).
% 2.09/2.31 0 [] A!=B|subset(B,A).
% 2.09/2.31 0 [] A=B| -subset(A,B)| -subset(B,A).
% 2.09/2.31 0 [] -subset(A,B)| -in(C,A)|in(C,B).
% 2.09/2.31 0 [] subset(A,B)|in($f10(A,B),A).
% 2.09/2.31 0 [] subset(A,B)| -in($f10(A,B),B).
% 2.09/2.31 0 [] C!=set_difference(A,B)| -in(D,C)|in(D,A).
% 2.09/2.31 0 [] C!=set_difference(A,B)| -in(D,C)| -in(D,B).
% 2.09/2.31 0 [] C!=set_difference(A,B)|in(D,C)| -in(D,A)|in(D,B).
% 2.09/2.31 0 [] C=set_difference(A,B)|in($f11(A,B,C),C)|in($f11(A,B,C),A).
% 2.09/2.31 0 [] C=set_difference(A,B)|in($f11(A,B,C),C)| -in($f11(A,B,C),B).
% 2.09/2.31 0 [] C=set_difference(A,B)| -in($f11(A,B,C),C)| -in($f11(A,B,C),A)|in($f11(A,B,C),B).
% 2.09/2.31 0 [] $T.
% 2.09/2.31 0 [] element($f12(A),A).
% 2.09/2.31 0 [] -finite(A)|finite(set_difference(A,B)).
% 2.09/2.31 0 [] empty(empty_set).
% 2.09/2.31 0 [] relation(empty_set).
% 2.09/2.31 0 [] relation_empty_yielding(empty_set).
% 2.09/2.31 0 [] relation(empty_set).
% 2.09/2.31 0 [] relation_empty_yielding(empty_set).
% 2.09/2.31 0 [] function(empty_set).
% 2.09/2.31 0 [] one_to_one(empty_set).
% 2.09/2.31 0 [] empty(empty_set).
% 2.09/2.31 0 [] epsilon_transitive(empty_set).
% 2.09/2.31 0 [] epsilon_connected(empty_set).
% 2.09/2.31 0 [] ordinal(empty_set).
% 2.09/2.31 0 [] -relation(A)| -relation(B)|relation(set_union2(A,B)).
% 2.09/2.31 0 [] -relation(A)| -relation(B)|relation(set_difference(A,B)).
% 2.09/2.31 0 [] empty(empty_set).
% 2.09/2.31 0 [] relation(empty_set).
% 2.09/2.31 0 [] -empty($c9).
% 2.09/2.31 0 [] epsilon_transitive($c9).
% 2.09/2.31 0 [] epsilon_connected($c9).
% 2.09/2.31 0 [] ordinal($c9).
% 2.09/2.31 0 [] natural($c9).
% 2.09/2.31 0 [] relation($c10).
% 2.09/2.31 0 [] function($c10).
% 2.09/2.31 0 [] epsilon_transitive($c11).
% 2.09/2.31 0 [] epsilon_connected($c11).
% 2.09/2.31 0 [] ordinal($c11).
% 2.09/2.31 0 [] empty($c12).
% 2.09/2.31 0 [] relation($c12).
% 2.09/2.31 0 [] element($f13(A),powerset(A)).
% 2.09/2.31 0 [] empty($f13(A)).
% 2.09/2.31 0 [] relation($f13(A)).
% 2.09/2.31 0 [] function($f13(A)).
% 2.09/2.31 0 [] one_to_one($f13(A)).
% 2.09/2.31 0 [] epsilon_transitive($f13(A)).
% 2.09/2.31 0 [] epsilon_connected($f13(A)).
% 2.09/2.31 0 [] ordinal($f13(A)).
% 2.09/2.31 0 [] natural($f13(A)).
% 2.09/2.31 0 [] finite($f13(A)).
% 2.09/2.31 0 [] relation($c13).
% 2.09/2.31 0 [] empty($c13).
% 2.09/2.31 0 [] function($c13).
% 2.09/2.31 0 [] relation($c14).
% 2.09/2.31 0 [] function($c14).
% 2.09/2.31 0 [] one_to_one($c14).
% 2.09/2.31 0 [] empty($c14).
% 2.09/2.31 0 [] epsilon_transitive($c14).
% 2.09/2.31 0 [] epsilon_connected($c14).
% 2.09/2.31 0 [] ordinal($c14).
% 2.09/2.31 0 [] -empty($c15).
% 2.09/2.31 0 [] relation($c15).
% 2.09/2.31 0 [] relation($c16).
% 2.09/2.31 0 [] function($c16).
% 2.09/2.31 0 [] one_to_one($c16).
% 2.09/2.31 0 [] -empty($c17).
% 2.09/2.31 0 [] epsilon_transitive($c17).
% 2.09/2.31 0 [] epsilon_connected($c17).
% 2.09/2.31 0 [] ordinal($c17).
% 2.09/2.31 0 [] relation($c18).
% 2.09/2.31 0 [] relation_empty_yielding($c18).
% 2.09/2.31 0 [] relation($c19).
% 2.09/2.31 0 [] relation_empty_yielding($c19).
% 2.09/2.31 0 [] function($c19).
% 2.09/2.31 0 [] -finite(A)| -element(B,powerset(powerset(A)))|B=empty_set|in($f14(A,B),B).
% 2.09/2.31 0 [] -finite(A)| -element(B,powerset(powerset(A)))|B=empty_set| -in(D,B)| -subset($f14(A,B),D)|D=$f14(A,B).
% 2.09/2.31 0 [] set_union2(A,empty_set)=A.
% 2.09/2.31 0 [] -in(A,B)|element(A,B).
% 2.09/2.31 0 [] -element(A,B)|empty(B)|in(A,B).
% 2.09/2.31 0 [] subset(empty_set,A).
% 2.09/2.31 0 [] set_difference(A,B)!=empty_set|subset(A,B).
% 2.09/2.31 0 [] set_difference(A,B)=empty_set| -subset(A,B).
% 2.09/2.31 0 [] -subset(singleton(A),B)|in(A,B).
% 2.09/2.31 0 [] subset(singleton(A),B)| -in(A,B).
% 2.09/2.31 0 [] set_difference(A,empty_set)=A.
% 2.09/2.31 0 [] -element(A,powerset(B))|subset(A,B).
% 2.09/2.31 0 [] element(A,powerset(B))| -subset(A,B).
% 2.09/2.31 0 [] set_difference(empty_set,A)=empty_set.
% 2.09/2.31 0 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 2.09/2.31 0 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 2.09/2.31 0 [] -empty(A)|A=empty_set.
% 2.09/2.31 0 [] -in(A,B)| -empty(B).
% 2.09/2.31 0 [] subset(A,set_union2(A,B)).
% 2.09/2.31 0 [] -empty(A)|A=B| -empty(B).
% 2.09/2.31 0 [] -subset(A,B)| -subset(C,B)|subset(set_union2(A,C),B).
% 2.09/2.31 end_of_list.
% 2.09/2.31
% 2.09/2.31 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=12.
% 2.09/2.31
% 2.09/2.31 This ia a non-Horn set with equality. The strategy will be
% 2.09/2.31 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.09/2.31 deletion, with positive clauses in sos and nonpositive
% 2.09/2.31 clauses in usable.
% 2.09/2.31
% 2.09/2.31 dependent: set(knuth_bendix).
% 2.09/2.31 dependent: set(anl_eq).
% 2.09/2.31 dependent: set(para_from).
% 2.09/2.31 dependent: set(para_into).
% 2.09/2.31 dependent: clear(para_from_right).
% 2.09/2.31 dependent: clear(para_into_right).
% 2.09/2.31 dependent: set(para_from_vars).
% 2.09/2.31 dependent: set(eq_units_both_ways).
% 2.09/2.31 dependent: set(dynamic_demod_all).
% 2.09/2.31 dependent: set(dynamic_demod).
% 2.09/2.31 dependent: set(order_eq).
% 2.09/2.31 dependent: set(back_demod).
% 2.09/2.31 dependent: set(lrpo).
% 2.09/2.31 dependent: set(hyper_res).
% 2.09/2.31 dependent: set(unit_deletion).
% 2.09/2.31 dependent: set(factor).
% 2.09/2.31
% 2.09/2.31 ------------> process usable:
% 2.09/2.31 ** KEPT (pick-wt=2): 1 [] -empty_carrier($c4).
% 2.09/2.31 ** KEPT (pick-wt=23): 2 [] -in(A,$c2)| -subset(B,$c2)| -element(C,the_carrier($c4))| -in(C,$c3)| -relstr_set_smaller($c4,B,C)|element($f1(A,B),the_carrier($c4)).
% 2.09/2.31 ** KEPT (pick-wt=22): 3 [] -in(A,$c2)| -subset(B,$c2)| -element(C,the_carrier($c4))| -in(C,$c3)| -relstr_set_smaller($c4,B,C)|in($f1(A,B),$c3).
% 2.09/2.31 ** KEPT (pick-wt=26): 4 [] -in(A,$c2)| -subset(B,$c2)| -element(C,the_carrier($c4))| -in(C,$c3)| -relstr_set_smaller($c4,B,C)|relstr_set_smaller($c4,set_union2(B,singleton(A)),$f1(A,B)).
% 2.09/2.31 ** KEPT (pick-wt=11): 5 [] -element(A,the_carrier($c4))| -in(A,$c3)| -relstr_set_smaller($c4,$c2,A).
% 2.09/2.31 ** KEPT (pick-wt=2): 6 [] -empty_carrier($c5).
% 2.09/2.31 ** KEPT (pick-wt=7): 7 [] empty_carrier(A)| -one_sorted_str(A)| -empty(the_carrier(A)).
% 2.09/2.31 ** KEPT (pick-wt=10): 8 [] empty_carrier(A)| -one_sorted_str(A)|element($f2(A),powerset(the_carrier(A))).
% 2.09/2.31 ** KEPT (pick-wt=7): 9 [] empty_carrier(A)| -one_sorted_str(A)| -empty($f2(A)).
% 2.09/2.31 ** KEPT (pick-wt=2): 10 [] -empty($c6).
% 2.09/2.31 ** KEPT (pick-wt=4): 11 [] -empty(A)|finite(A).
% 2.09/2.31 ** KEPT (pick-wt=5): 12 [] empty(A)| -empty($f3(A)).
% 2.09/2.31 ** KEPT (pick-wt=5): 13 [] empty(A)| -empty($f4(A)).
% 2.09/2.31 ** KEPT (pick-wt=5): 14 [] empty(A)| -empty($f5(A)).
% 2.09/2.31 ** KEPT (pick-wt=2): 15 [] -empty($c8).
% 2.09/2.31 ** KEPT (pick-wt=6): 16 [] empty(A)| -empty(set_union2(A,B)).
% 2.09/2.31 ** KEPT (pick-wt=6): 17 [] empty(A)| -empty(set_union2(B,A)).
% 2.09/2.31 ** KEPT (pick-wt=6): 18 [] -in(A,B)| -in(B,A).
% 2.09/2.31 ** KEPT (pick-wt=4): 19 [] -rel_str(A)|one_sorted_str(A).
% 2.09/2.31 ** KEPT (pick-wt=3): 20 [] -empty(singleton(A)).
% 2.09/2.31 ** KEPT (pick-wt=8): 21 [] -finite(A)| -element(B,powerset(A))|finite(B).
% 2.09/2.31 ** KEPT (pick-wt=8): 22 [] -finite(A)| -finite(B)|finite(set_union2(A,B)).
% 2.09/2.31 ** KEPT (pick-wt=3): 23 [] -empty(powerset(A)).
% 2.09/2.31 Following clause subsumed by 20 during input processing: 0 [] -empty(singleton(A)).
% 2.09/2.31 ** KEPT (pick-wt=27): 24 [] empty_carrier(A)| -transitive_relstr(A)| -rel_str(A)| -element(B,powerset(the_carrier(A)))| -finite(C)| -element(C,powerset(B))| -in(D,$f9(A,B,C))|in(D,powerset(C)).
% 2.09/2.31 ** KEPT (pick-wt=30): 25 [] empty_carrier(A)| -transitive_relstr(A)| -rel_str(A)| -element(B,powerset(the_carrier(A)))| -finite(C)| -element(C,powerset(B))| -in(D,$f9(A,B,C))|$f8(A,B,C,D)=D.
% 2.09/2.31 ** KEPT (pick-wt=31): 26 [] empty_carrier(A)| -transitive_relstr(A)| -rel_str(A)| -element(B,powerset(the_carrier(A)))| -finite(C)| -element(C,powerset(B))| -in(D,$f9(A,B,C))|element($f7(A,B,C,D),the_carrier(A)).
% 2.09/2.31 ** KEPT (pick-wt=30): 27 [] empty_carrier(A)| -transitive_relstr(A)| -rel_str(A)| -element(B,powerset(the_carrier(A)))| -finite(C)| -element(C,powerset(B))| -in(D,$f9(A,B,C))|in($f7(A,B,C,D),B).
% 2.09/2.31 ** KEPT (pick-wt=35): 28 [] empty_carrier(A)| -transitive_relstr(A)| -rel_str(A)| -element(B,powerset(the_carrier(A)))| -finite(C)| -element(C,powerset(B))| -in(D,$f9(A,B,C))|relstr_set_smaller(A,$f8(A,B,C,D),$f7(A,B,C,D)).
% 2.09/2.31 ** KEPT (pick-wt=41): 29 [] empty_carrier(A)| -transitive_relstr(A)| -rel_str(A)| -element(B,powerset(the_carrier(A)))| -finite(C)| -element(C,powerset(B))|in(D,$f9(A,B,C))| -in(D,powerset(C))|E!=D| -element(F,the_carrier(A))| -in(F,B)| -relstr_set_smaller(A,E,F).
% 2.09/2.31 ** KEPT (pick-wt=7): 30 [] -ordinal(A)| -element(B,A)|epsilon_transitive(B).
% 2.09/2.31 ** KEPT (pick-wt=7): 31 [] -ordinal(A)| -element(B,A)|epsilon_connected(B).
% 2.09/2.31 ** KEPT (pick-wt=7): 32 [] -ordinal(A)| -element(B,A)|ordinal(B).
% 2.09/2.31 ** KEPT (pick-wt=4): 33 [] -empty(A)|function(A).
% 2.09/2.31 ** KEPT (pick-wt=4): 34 [] -ordinal(A)|epsilon_transitive(A).
% 2.09/2.31 ** KEPT (pick-wt=4): 35 [] -ordinal(A)|epsilon_connected(A).
% 2.09/2.31 ** KEPT (pick-wt=4): 36 [] -empty(A)|relation(A).
% 2.09/2.31 Following clause subsumed by 34 during input processing: 0 [] -empty(A)| -ordinal(A)|epsilon_transitive(A).
% 2.09/2.31 Following clause subsumed by 35 during input processing: 0 [] -empty(A)| -ordinal(A)|epsilon_connected(A).
% 2.09/2.31 ** KEPT (pick-wt=6): 37 [] -empty(A)| -ordinal(A)|natural(A).
% 2.09/2.31 ** KEPT (pick-wt=8): 38 [] -relation(A)| -empty(A)| -function(A)|one_to_one(A).
% 2.09/2.31 ** KEPT (pick-wt=6): 39 [] -epsilon_transitive(A)| -epsilon_connected(A)|ordinal(A).
% 2.09/2.31 ** KEPT (pick-wt=4): 40 [] -empty(A)|epsilon_transitive(A).
% 2.09/2.31 ** KEPT (pick-wt=4): 41 [] -empty(A)|epsilon_connected(A).
% 2.09/2.31 ** KEPT (pick-wt=4): 42 [] -empty(A)|ordinal(A).
% 2.09/2.31 ** KEPT (pick-wt=6): 43 [] A!=B|subset(A,B).
% 2.09/2.31 ** KEPT (pick-wt=6): 44 [] A!=B|subset(B,A).
% 2.09/2.31 ** KEPT (pick-wt=9): 45 [] A=B| -subset(A,B)| -subset(B,A).
% 2.09/2.31 ** KEPT (pick-wt=9): 46 [] -subset(A,B)| -in(C,A)|in(C,B).
% 2.09/2.31 ** KEPT (pick-wt=8): 47 [] subset(A,B)| -in($f10(A,B),B).
% 2.09/2.31 ** KEPT (pick-wt=11): 48 [] A!=set_difference(B,C)| -in(D,A)|in(D,B).
% 2.09/2.31 ** KEPT (pick-wt=11): 49 [] A!=set_difference(B,C)| -in(D,A)| -in(D,C).
% 2.09/2.31 ** KEPT (pick-wt=14): 50 [] A!=set_difference(B,C)|in(D,A)| -in(D,B)|in(D,C).
% 2.09/2.31 ** KEPT (pick-wt=17): 51 [] A=set_difference(B,C)|in($f11(B,C,A),A)| -in($f11(B,C,A),C).
% 2.09/2.31 ** KEPT (pick-wt=23): 52 [] A=set_difference(B,C)| -in($f11(B,C,A),A)| -in($f11(B,C,A),B)|in($f11(B,C,A),C).
% 2.09/2.31 ** KEPT (pick-wt=6): 53 [] -finite(A)|finite(set_difference(A,B)).
% 2.09/2.31 ** KEPT (pick-wt=8): 54 [] -relation(A)| -relation(B)|relation(set_union2(A,B)).
% 2.09/2.31 ** KEPT (pick-wt=8): 55 [] -relation(A)| -relation(B)|relation(set_difference(A,B)).
% 2.09/2.31 ** KEPT (pick-wt=2): 56 [] -empty($c9).
% 2.09/2.31 ** KEPT (pick-wt=2): 57 [] -empty($c15).
% 2.09/2.31 ** KEPT (pick-wt=2): 58 [] -empty($c17).
% 2.09/2.31 ** KEPT (pick-wt=15): 59 [] -finite(A)| -element(B,powerset(powerset(A)))|B=empty_set|in($f14(A,B),B).
% 2.09/2.31 ** KEPT (pick-wt=23): 60 [] -finite(A)| -element(B,powerset(powerset(A)))|B=empty_set| -in(C,B)| -subset($f14(A,B),C)|C=$f14(A,B).
% 2.09/2.31 ** KEPT (pick-wt=6): 61 [] -in(A,B)|element(A,B).
% 2.09/2.31 ** KEPT (pick-wt=8): 62 [] -element(A,B)|empty(B)|in(A,B).
% 2.09/2.31 ** KEPT (pick-wt=8): 63 [] set_difference(A,B)!=empty_set|subset(A,B).
% 2.09/2.31 ** KEPT (pick-wt=8): 64 [] set_difference(A,B)=empty_set| -subset(A,B).
% 2.09/2.31 ** KEPT (pick-wt=7): 65 [] -subset(singleton(A),B)|in(A,B).
% 2.09/2.31 ** KEPT (pick-wt=7): 66 [] subset(singleton(A),B)| -in(A,B).
% 2.09/2.31 ** KEPT (pick-wt=7): 67 [] -element(A,powerset(B))|subset(A,B).
% 2.09/2.31 ** KEPT (pick-wt=7): 68 [] element(A,powerset(B))| -subset(A,B).
% 2.09/2.31 ** KEPT (pick-wt=10): 69 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 2.09/2.31 ** KEPT (pick-wt=9): 70 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 2.09/2.31 ** KEPT (pick-wt=5): 71 [] -empty(A)|A=empty_set.
% 2.09/2.31 ** KEPT (pick-wt=5): 72 [] -in(A,B)| -empty(B).
% 2.09/2.31 ** KEPT (pick-wt=7): 73 [] -empty(A)|A=B| -empty(B).
% 2.09/2.31 ** KEPT (pick-wt=11): 74 [] -subset(A,B)| -subset(C,B)|subset(set_union2(A,C),B).
% 2.09/2.31
% 2.09/2.31 ------------> process sos:
% 2.09/2.31 ** KEPT (pick-wt=3): 92 [] A=A.
% 2.09/2.31 ** KEPT (pick-wt=2): 93 [] transitive_relstr($c4).
% 2.09/2.31 ** KEPT (pick-wt=2): 94 [] rel_str($c4).
% 2.09/2.31 ** KEPT (pick-wt=5): 95 [] element($c3,powerset(the_carrier($c4))).
% 2.09/2.31 ** KEPT (pick-wt=2): 96 [] finite($c2).
% 2.09/2.31 ** KEPT (pick-wt=4): 97 [] element($c2,powerset($c3)).
% 2.09/2.31 ** KEPT (pick-wt=4): 98 [] element($c1,the_carrier($c4)).
% 2.09/2.31 ** KEPT (pick-wt=3): 99 [] in($c1,$c3).
% 2.09/2.31 ** KEPT (pick-wt=4): 100 [] relstr_set_smaller($c4,empty_set,$c1).
% 2.09/2.31 ** KEPT (pick-wt=2): 101 [] one_sorted_str($c5).
% 2.09/2.31 ** KEPT (pick-wt=2): 102 [] finite($c6).
% 2.09/2.31 ** KEPT (pick-wt=7): 103 [] empty(A)|element($f3(A),powerset(A)).
% 2.09/2.31 ** KEPT (pick-wt=5): 104 [] empty(A)|finite($f3(A)).
% 2.09/2.31 ** KEPT (pick-wt=7): 105 [] empty(A)|element($f4(A),powerset(A)).
% 2.09/2.31 ** KEPT (pick-wt=5): 106 [] empty(A)|finite($f4(A)).
% 2.09/2.31 ** KEPT (pick-wt=7): 107 [] empty(A)|element($f5(A),powerset(A)).
% 2.09/2.31 ** KEPT (pick-wt=5): 108 [] element($f6(A),powerset(A)).
% 2.09/2.31 ** KEPT (pick-wt=3): 109 [] empty($f6(A)).
% 2.09/2.31 ** KEPT (pick-wt=2): 110 [] empty($c7).
% 2.09/2.31 ** KEPT (pick-wt=7): 111 [] set_union2(A,B)=set_union2(B,A).
% 2.09/2.31 ** KEPT (pick-wt=5): 112 [] set_union2(A,A)=A.
% 2.09/2.31 ---> New Demodulator: 113 [new_demod,112] set_union2(A,A)=A.
% 2.09/2.31 ** KEPT (pick-wt=3): 114 [] subset(A,A).
% 2.09/2.31 ** KEPT (pick-wt=3): 115 [] finite(singleton(A)).
% 2.09/2.31 ** KEPT (pick-wt=2): 116 [] empty(empty_set).
% 2.09/2.31 ** KEPT (pick-wt=8): 117 [] subset(A,B)|in($f10(A,B),A).
% 2.09/2.31 ** KEPT (pick-wt=17): 118 [] A=set_difference(B,C)|in($f11(B,C,A),A)|in($f11(B,C,A),B).
% 2.09/2.31 ** KEPT (pick-wt=4): 119 [] element($f12(A),A).
% 2.09/2.31 Following clause subsumed by 116 during input processing: 0 [] empty(empty_set).
% 2.09/2.31 ** KEPT (pick-wt=2): 120 [] relation(empty_set).
% 2.09/2.31 ** KEPT (pick-wt=2): 121 [] relation_empty_yielding(empty_set).
% 2.09/2.31 Following clause subsumed by 120 during input processing: 0 [] relation(empty_set).
% 2.09/2.31 Following clause subsumed by 121 during input processing: 0 [] relation_empty_yielding(empty_set).
% 2.09/2.31 ** KEPT (pick-wt=2): 122 [] function(empty_set).
% 2.09/2.31 ** KEPT (pick-wt=2): 123 [] one_to_one(empty_set).
% 2.09/2.31 Following clause subsumed by 116 during input processing: 0 [] empty(empty_set).
% 2.09/2.31 ** KEPT (pick-wt=2): 124 [] epsilon_transitive(empty_set).
% 2.09/2.31 ** KEPT (pick-wt=2): 125 [] epsilon_connected(empty_set).
% 2.09/2.31 ** KEPT (pick-wt=2): 126 [] ordinal(empty_set).
% 2.09/2.31 Following clause subsumed by 116 during input processing: 0 [] empty(empty_set).
% 2.09/2.31 Following clause subsumed by 120 during input processing: 0 [] relation(empty_set).
% 2.09/2.31 ** KEPT (pick-wt=2): 127 [] epsilon_transitive($c9).
% 2.09/2.31 ** KEPT (pick-wt=2): 128 [] epsilon_connected($c9).
% 2.09/2.31 ** KEPT (pick-wt=2): 129 [] ordinal($c9).
% 2.09/2.31 ** KEPT (pick-wt=2): 130 [] natural($c9).
% 2.09/2.31 ** KEPT (pick-wt=2): 131 [] relation($c10).
% 2.09/2.31 ** KEPT (pick-wt=2): 132 [] function($c10).
% 2.09/2.31 ** KEPT (pick-wt=2): 133 [] epsilon_transitive($c11).
% 2.09/2.31 ** KEPT (pick-wt=2): 134 [] epsilon_connected($c11).
% 2.09/2.31 ** KEPT (pick-wt=2): 135 [] ordinal($c11).
% 2.09/2.31 ** KEPT (pick-wt=2): 136 [] empty($c12).
% 2.09/2.31 ** KEPT (pick-wt=2): 137 [] relation($c12).
% 2.09/2.31 ** KEPT (pick-wt=5): 138 [] element($f13(A),powerset(A)).
% 2.09/2.31 ** KEPT (pick-wt=3): 139 [] empty($f13(A)).
% 2.09/2.31 ** KEPT (pick-wt=3): 140 [] relation($f13(A)).
% 2.09/2.31 ** KEPT (pick-wt=3): 141 [] function($f13(A)).
% 2.09/2.31 ** KEPT (pick-wt=3): 142 [] one_to_one($f13(A)).
% 2.09/2.31 ** KEPT (pick-wt=3): 143 [] epsilon_transitive($f13(A)).
% 2.09/2.31 ** KEPT (pick-wt=3): 144 [] epsilon_connected($f13(A)).
% 2.09/2.31 ** KEPT (pick-wt=3): 145 [] ordinal($f13(A)).
% 2.09/2.31 ** KEPT (pick-wt=3): 146 [] natural($f13(A)).
% 2.09/2.31 ** KEPT (pick-wt=3): 147 [] finite($f13(A)).
% 2.09/2.31 ** KEPT (pick-wt=2): 148 [] relation($c13).
% 2.09/2.31 ** KEPT (pick-wt=2): 149 [] empty($c13).
% 2.09/2.31 ** KEPT (pick-wt=2): 150 [] function($c13).
% 2.09/2.31 ** KEPT (pick-wt=2): 151 [] relation($c14).
% 2.09/2.31 ** KEPT (pick-wt=2): 152 [] function($c14).
% 2.09/2.31 ** KEPT (pick-wt=2): 153 [] one_to_one($c14).
% 2.09/2.31 ** KEPT (pick-wt=2): 154 [] empty($c14).
% 2.09/2.31 ** KEPT (pick-wt=2): 155 [] epsilon_transitive($c14).
% 2.09/2.31 ** KEPT (pick-wt=2): 156 [] epsilon_connected($c14).
% 2.09/2.31 ** KEPT (pick-wt=2): 157 [] ordinal($c14).
% 2.09/2.31 ** KEPT (pick-wt=2): 158 [] relation($c15).
% 2.09/2.31 ** KEPT (pick-wt=2): 159 [] relation($c16).
% 2.09/2.31 ** KEPT (pick-wt=2): 160 [] function($c16).
% 2.09/2.31 ** KEPT (pick-wt=2): 161 [] one_to_one($c16).
% 2.09/2.31 ** KEPT (pick-wt=2): 162 [] epsilon_transitive($c17).
% 2.09/2.31 ** KEPT (pick-wt=2): 163 [] epsilon_connected($c17).
% 2.09/2.31 ** KEPT (pick-wt=2): 164 [] ordinal($c17).
% 2.09/2.31 ** KEPT (pick-wt=2): 165 [] relation($c18).
% 2.09/2.31 ** KEPT (pick-wt=2): 166 [] relation_empty_yielding($c18).
% 2.09/2.31 ** KEPT (pick-wt=2): 167 [] relation($c19).
% 2.09/2.31 ** KEPT (pick-wt=2): 168 [] relation_empty_yielding($c19).
% 2.09/2.31 ** KEPT (pick-wt=2): 169 [] function($c19).
% 2.09/2.31 ** KEPT (pick-wt=5): 170 [] set_union2(A,empty_set)=A.
% 2.09/2.31 ---> New Demodulator: 171 [new_demod,170] set_union2(A,empty_set)=A.
% 2.09/2.31 ** KEPT (pick-wt=3): 172 [] subset(empty_set,A).
% 2.09/2.31 ** KEPT (pick-wt=5): 173 [] set_difference(A,empty_set)=A.
% 2.09/2.31 ---> New Demodulator: 174 [new_demod,173] set_difference(A,empty_set)=A.
% 2.09/2.31 ** KEPT (pick-wt=5): 175 [] set_difference(empty_set,A)=empty_set.
% 2.09/2.31 ---> New Demodulator: 176 [new_demod,175] set_difference(empty_set,A)=empty_set.
% 2.09/2.31 ** KEPT (pick-wt=5): 177 [] subset(A,set_union2(A,B))Alarm clock
% 299.88/300.07 Otter interrupted
% 299.88/300.07 PROOF NOT FOUND
%------------------------------------------------------------------------------