TSTP Solution File: SEU285+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU285+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n028.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 13:15:28 EDT 2022
% Result : Unknown 9.24s 9.45s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU285+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.11/0.32 % Computer : n028.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Wed Jul 27 07:41:03 EDT 2022
% 0.11/0.33 % CPUTime :
% 2.19/2.39 ----- Otter 3.3f, August 2004 -----
% 2.19/2.39 The process was started by sandbox on n028.cluster.edu,
% 2.19/2.39 Wed Jul 27 07:41:04 2022
% 2.19/2.39 The command was "./otter". The process ID is 1514.
% 2.19/2.39
% 2.19/2.39 set(prolog_style_variables).
% 2.19/2.39 set(auto).
% 2.19/2.39 dependent: set(auto1).
% 2.19/2.39 dependent: set(process_input).
% 2.19/2.39 dependent: clear(print_kept).
% 2.19/2.39 dependent: clear(print_new_demod).
% 2.19/2.39 dependent: clear(print_back_demod).
% 2.19/2.39 dependent: clear(print_back_sub).
% 2.19/2.39 dependent: set(control_memory).
% 2.19/2.39 dependent: assign(max_mem, 12000).
% 2.19/2.39 dependent: assign(pick_given_ratio, 4).
% 2.19/2.39 dependent: assign(stats_level, 1).
% 2.19/2.39 dependent: assign(max_seconds, 10800).
% 2.19/2.39 clear(print_given).
% 2.19/2.39
% 2.19/2.39 formula_list(usable).
% 2.19/2.39 all A (A=A).
% 2.19/2.39 all A B (in(A,B)-> -in(B,A)).
% 2.19/2.39 all A (empty(A)->function(A)).
% 2.19/2.39 all A (ordinal(A)->epsilon_transitive(A)&epsilon_connected(A)).
% 2.19/2.39 all A (relation(A)&empty(A)&function(A)->relation(A)&function(A)&one_to_one(A)).
% 2.19/2.39 all A (epsilon_transitive(A)&epsilon_connected(A)->ordinal(A)).
% 2.19/2.39 all A (empty(A)->epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)).
% 2.19/2.39 all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 2.19/2.39 all A B (set_union2(A,B)=set_union2(B,A)).
% 2.19/2.39 all A B (set_intersection2(A,B)=set_intersection2(B,A)).
% 2.19/2.39 all A B (ordinal(A)&ordinal(B)->ordinal_subset(A,B)|ordinal_subset(B,A)).
% 2.19/2.39 all A B (B=singleton(A)<-> (all C (in(C,B)<->C=A))).
% 2.19/2.39 all A B (relation(B)-> (B=inclusion_relation(A)<->relation_field(B)=A& (all C D (in(C,A)&in(D,A)-> (in(ordered_pair(C,D),B)<->subset(C,D)))))).
% 2.19/2.39 all A (epsilon_transitive(A)<-> (all B (in(B,A)->subset(B,A)))).
% 2.19/2.39 all A B (subset(A,B)<-> (all C (in(C,A)->in(C,B)))).
% 2.19/2.39 all A B (e_quipotent(A,B)<-> (exists C (relation(C)&function(C)&one_to_one(C)&relation_dom(C)=A&relation_rng(C)=B))).
% 2.19/2.39 all A (relation(A)&function(A)-> (all B (B=relation_rng(A)<-> (all C (in(C,B)<-> (exists D (in(D,relation_dom(A))&C=apply(A,D)))))))).
% 2.19/2.39 all A B (ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A))).
% 2.19/2.39 all A (relation(A)->relation_field(A)=set_union2(relation_dom(A),relation_rng(A))).
% 2.19/2.39 all A (relation(A)-> (all B (relation_restriction(A,B)=set_intersection2(A,cartesian_product2(B,B))))).
% 2.19/2.39 all A (relation(A)&function(A)-> (one_to_one(A)<-> (all B C (in(B,relation_dom(A))&in(C,relation_dom(A))&apply(A,B)=apply(A,C)->B=C)))).
% 2.19/2.39 $T.
% 2.19/2.39 $T.
% 2.19/2.39 $T.
% 2.19/2.39 all A relation(inclusion_relation(A)).
% 2.19/2.39 $T.
% 2.19/2.39 $T.
% 2.19/2.39 $T.
% 2.19/2.39 $T.
% 2.19/2.39 all A B (relation(A)->relation(relation_restriction(A,B))).
% 2.19/2.39 $T.
% 2.19/2.39 $T.
% 2.19/2.39 $T.
% 2.19/2.39 $T.
% 2.19/2.39 $T.
% 2.19/2.39 $T.
% 2.19/2.39 all A exists B element(B,A).
% 2.19/2.39 empty(empty_set).
% 2.19/2.39 all A B (-empty(ordered_pair(A,B))).
% 2.19/2.39 relation(empty_set).
% 2.19/2.39 relation_empty_yielding(empty_set).
% 2.19/2.39 function(empty_set).
% 2.19/2.39 one_to_one(empty_set).
% 2.19/2.39 empty(empty_set).
% 2.19/2.39 epsilon_transitive(empty_set).
% 2.19/2.39 epsilon_connected(empty_set).
% 2.19/2.39 ordinal(empty_set).
% 2.19/2.39 all A B (-empty(A)-> -empty(set_union2(A,B))).
% 2.19/2.39 all A B (-empty(A)-> -empty(set_union2(B,A))).
% 2.19/2.39 all A B (set_union2(A,A)=A).
% 2.19/2.39 all A B (set_intersection2(A,A)=A).
% 2.19/2.39 all A B (relation(B)-> -(well_ordering(B)&e_quipotent(A,relation_field(B))& (all C (relation(C)-> -well_orders(C,A))))).
% 2.19/2.39 exists A (relation(A)&function(A)).
% 2.19/2.39 exists A (epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)).
% 2.19/2.39 exists A empty(A).
% 2.19/2.39 exists A (relation(A)&empty(A)&function(A)).
% 2.19/2.39 exists A (relation(A)&function(A)&one_to_one(A)&empty(A)&epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)).
% 2.19/2.39 exists A (-empty(A)).
% 2.19/2.39 exists A (relation(A)&function(A)&one_to_one(A)).
% 2.19/2.39 exists A (-empty(A)&epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)).
% 2.19/2.39 exists A (relation(A)&relation_empty_yielding(A)&function(A)).
% 2.19/2.39 all A B (ordinal(A)&ordinal(B)-> (ordinal_subset(A,B)<->subset(A,B))).
% 2.19/2.39 all A B (e_quipotent(A,B)<->are_e_quipotent(A,B)).
% 2.19/2.39 all A B (ordinal(A)&ordinal(B)->ordinal_subset(A,A)).
% 2.19/2.39 all A B subset(A,A).
% 2.19/2.39 all A B e_quipotent(A,A).
% 2.19/2.39 all A exists B all C (in(C,B)<->in(C,A)&ordinal(C)).
% 2.19/2.39 all A exists B (relation(B)&function(B)&relation_dom(B)=A& (all C (in(C,A)->apply(B,C)=singleton(C)))).
% 2.19/2.39 all A B (e_quipotent(A,B)->e_quipotent(B,A)).
% 2.19/2.39 all A exists B (in(A,B)& (all C D (in(C,B)&subset(D,C)->in(D,B)))& (all C (in(C,B)->in(powerset(C),B)))& (all C (-(subset(C,B)& -are_e_quipotent(C,B)& -in(C,B))))).
% 2.19/2.39 all A (set_union2(A,empty_set)=A).
% 2.19/2.39 all A B (in(A,B)->element(A,B)).
% 2.19/2.39 all A B (ordinal(B)-> (in(A,B)->ordinal(A))).
% 2.19/2.39 all A B (relation(B)-> (well_orders(B,A)->relation_field(relation_restriction(B,A))=A&well_ordering(relation_restriction(B,A)))).
% 2.19/2.39 -(all A exists B (relation(B)&well_orders(B,A))).
% 2.19/2.39 all A (set_intersection2(A,empty_set)=empty_set).
% 2.19/2.39 all A B (element(A,B)->empty(B)|in(A,B)).
% 2.19/2.39 all A ((all B (in(B,A)->ordinal(B)&subset(B,A)))->ordinal(A)).
% 2.19/2.39 all A B (relation(B)-> (well_ordering(B)->well_ordering(relation_restriction(B,A)))).
% 2.19/2.39 all A B (relation(B)-> (well_ordering(B)&subset(A,relation_field(B))->relation_field(relation_restriction(B,A))=A)).
% 2.19/2.39 all A B (element(A,powerset(B))<->subset(A,B)).
% 2.19/2.39 all A B C (in(A,B)&element(B,powerset(C))->element(A,C)).
% 2.19/2.39 all A B C (-(in(A,B)&element(B,powerset(C))&empty(C))).
% 2.19/2.39 all A (empty(A)->A=empty_set).
% 2.19/2.39 all A B (subset(singleton(A),singleton(B))->A=B).
% 2.19/2.39 all A B (-(in(A,B)&empty(B))).
% 2.19/2.39 all A (ordinal(A)->well_ordering(inclusion_relation(A))).
% 2.19/2.39 all A B (-(empty(A)&A!=B&empty(B))).
% 2.19/2.39 end_of_list.
% 2.19/2.39
% 2.19/2.39 -------> usable clausifies to:
% 2.19/2.39
% 2.19/2.39 list(usable).
% 2.19/2.39 0 [] A=A.
% 2.19/2.39 0 [] -in(A,B)| -in(B,A).
% 2.19/2.39 0 [] -empty(A)|function(A).
% 2.19/2.39 0 [] -ordinal(A)|epsilon_transitive(A).
% 2.19/2.39 0 [] -ordinal(A)|epsilon_connected(A).
% 2.19/2.39 0 [] -relation(A)| -empty(A)| -function(A)|one_to_one(A).
% 2.19/2.39 0 [] -epsilon_transitive(A)| -epsilon_connected(A)|ordinal(A).
% 2.19/2.39 0 [] -empty(A)|epsilon_transitive(A).
% 2.19/2.39 0 [] -empty(A)|epsilon_connected(A).
% 2.19/2.39 0 [] -empty(A)|ordinal(A).
% 2.19/2.39 0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 2.19/2.39 0 [] set_union2(A,B)=set_union2(B,A).
% 2.19/2.39 0 [] set_intersection2(A,B)=set_intersection2(B,A).
% 2.19/2.39 0 [] -ordinal(A)| -ordinal(B)|ordinal_subset(A,B)|ordinal_subset(B,A).
% 2.19/2.39 0 [] B!=singleton(A)| -in(C,B)|C=A.
% 2.19/2.39 0 [] B!=singleton(A)|in(C,B)|C!=A.
% 2.19/2.39 0 [] B=singleton(A)|in($f1(A,B),B)|$f1(A,B)=A.
% 2.19/2.39 0 [] B=singleton(A)| -in($f1(A,B),B)|$f1(A,B)!=A.
% 2.19/2.39 0 [] -relation(B)|B!=inclusion_relation(A)|relation_field(B)=A.
% 2.19/2.39 0 [] -relation(B)|B!=inclusion_relation(A)| -in(C,A)| -in(D,A)| -in(ordered_pair(C,D),B)|subset(C,D).
% 2.19/2.39 0 [] -relation(B)|B!=inclusion_relation(A)| -in(C,A)| -in(D,A)|in(ordered_pair(C,D),B)| -subset(C,D).
% 2.19/2.39 0 [] -relation(B)|B=inclusion_relation(A)|relation_field(B)!=A|in($f3(A,B),A).
% 2.19/2.39 0 [] -relation(B)|B=inclusion_relation(A)|relation_field(B)!=A|in($f2(A,B),A).
% 2.19/2.39 0 [] -relation(B)|B=inclusion_relation(A)|relation_field(B)!=A|in(ordered_pair($f3(A,B),$f2(A,B)),B)|subset($f3(A,B),$f2(A,B)).
% 2.19/2.39 0 [] -relation(B)|B=inclusion_relation(A)|relation_field(B)!=A| -in(ordered_pair($f3(A,B),$f2(A,B)),B)| -subset($f3(A,B),$f2(A,B)).
% 2.19/2.39 0 [] -epsilon_transitive(A)| -in(B,A)|subset(B,A).
% 2.19/2.39 0 [] epsilon_transitive(A)|in($f4(A),A).
% 2.19/2.39 0 [] epsilon_transitive(A)| -subset($f4(A),A).
% 2.19/2.39 0 [] -subset(A,B)| -in(C,A)|in(C,B).
% 2.19/2.39 0 [] subset(A,B)|in($f5(A,B),A).
% 2.19/2.39 0 [] subset(A,B)| -in($f5(A,B),B).
% 2.19/2.39 0 [] -e_quipotent(A,B)|relation($f6(A,B)).
% 2.19/2.39 0 [] -e_quipotent(A,B)|function($f6(A,B)).
% 2.19/2.39 0 [] -e_quipotent(A,B)|one_to_one($f6(A,B)).
% 2.19/2.39 0 [] -e_quipotent(A,B)|relation_dom($f6(A,B))=A.
% 2.19/2.39 0 [] -e_quipotent(A,B)|relation_rng($f6(A,B))=B.
% 2.19/2.39 0 [] e_quipotent(A,B)| -relation(C)| -function(C)| -one_to_one(C)|relation_dom(C)!=A|relation_rng(C)!=B.
% 2.19/2.39 0 [] -relation(A)| -function(A)|B!=relation_rng(A)| -in(C,B)|in($f7(A,B,C),relation_dom(A)).
% 2.19/2.39 0 [] -relation(A)| -function(A)|B!=relation_rng(A)| -in(C,B)|C=apply(A,$f7(A,B,C)).
% 2.19/2.39 0 [] -relation(A)| -function(A)|B!=relation_rng(A)|in(C,B)| -in(D,relation_dom(A))|C!=apply(A,D).
% 2.19/2.39 0 [] -relation(A)| -function(A)|B=relation_rng(A)|in($f9(A,B),B)|in($f8(A,B),relation_dom(A)).
% 2.19/2.39 0 [] -relation(A)| -function(A)|B=relation_rng(A)|in($f9(A,B),B)|$f9(A,B)=apply(A,$f8(A,B)).
% 2.19/2.39 0 [] -relation(A)| -function(A)|B=relation_rng(A)| -in($f9(A,B),B)| -in(X1,relation_dom(A))|$f9(A,B)!=apply(A,X1).
% 2.19/2.39 0 [] ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A)).
% 2.19/2.39 0 [] -relation(A)|relation_field(A)=set_union2(relation_dom(A),relation_rng(A)).
% 2.19/2.39 0 [] -relation(A)|relation_restriction(A,B)=set_intersection2(A,cartesian_product2(B,B)).
% 2.19/2.39 0 [] -relation(A)| -function(A)| -one_to_one(A)| -in(B,relation_dom(A))| -in(C,relation_dom(A))|apply(A,B)!=apply(A,C)|B=C.
% 2.19/2.39 0 [] -relation(A)| -function(A)|one_to_one(A)|in($f11(A),relation_dom(A)).
% 2.19/2.39 0 [] -relation(A)| -function(A)|one_to_one(A)|in($f10(A),relation_dom(A)).
% 2.19/2.39 0 [] -relation(A)| -function(A)|one_to_one(A)|apply(A,$f11(A))=apply(A,$f10(A)).
% 2.22/2.39 0 [] -relation(A)| -function(A)|one_to_one(A)|$f11(A)!=$f10(A).
% 2.22/2.39 0 [] $T.
% 2.22/2.39 0 [] $T.
% 2.22/2.39 0 [] $T.
% 2.22/2.39 0 [] relation(inclusion_relation(A)).
% 2.22/2.39 0 [] $T.
% 2.22/2.39 0 [] $T.
% 2.22/2.39 0 [] $T.
% 2.22/2.39 0 [] $T.
% 2.22/2.39 0 [] -relation(A)|relation(relation_restriction(A,B)).
% 2.22/2.39 0 [] $T.
% 2.22/2.39 0 [] $T.
% 2.22/2.39 0 [] $T.
% 2.22/2.39 0 [] $T.
% 2.22/2.39 0 [] $T.
% 2.22/2.39 0 [] $T.
% 2.22/2.39 0 [] element($f12(A),A).
% 2.22/2.39 0 [] empty(empty_set).
% 2.22/2.39 0 [] -empty(ordered_pair(A,B)).
% 2.22/2.39 0 [] relation(empty_set).
% 2.22/2.39 0 [] relation_empty_yielding(empty_set).
% 2.22/2.39 0 [] function(empty_set).
% 2.22/2.39 0 [] one_to_one(empty_set).
% 2.22/2.39 0 [] empty(empty_set).
% 2.22/2.39 0 [] epsilon_transitive(empty_set).
% 2.22/2.39 0 [] epsilon_connected(empty_set).
% 2.22/2.39 0 [] ordinal(empty_set).
% 2.22/2.39 0 [] empty(A)| -empty(set_union2(A,B)).
% 2.22/2.39 0 [] empty(A)| -empty(set_union2(B,A)).
% 2.22/2.39 0 [] set_union2(A,A)=A.
% 2.22/2.39 0 [] set_intersection2(A,A)=A.
% 2.22/2.39 0 [] -relation(B)| -well_ordering(B)| -e_quipotent(A,relation_field(B))|relation($f13(A,B)).
% 2.22/2.39 0 [] -relation(B)| -well_ordering(B)| -e_quipotent(A,relation_field(B))|well_orders($f13(A,B),A).
% 2.22/2.39 0 [] relation($c1).
% 2.22/2.39 0 [] function($c1).
% 2.22/2.39 0 [] epsilon_transitive($c2).
% 2.22/2.39 0 [] epsilon_connected($c2).
% 2.22/2.39 0 [] ordinal($c2).
% 2.22/2.39 0 [] empty($c3).
% 2.22/2.39 0 [] relation($c4).
% 2.22/2.39 0 [] empty($c4).
% 2.22/2.39 0 [] function($c4).
% 2.22/2.39 0 [] relation($c5).
% 2.22/2.39 0 [] function($c5).
% 2.22/2.39 0 [] one_to_one($c5).
% 2.22/2.39 0 [] empty($c5).
% 2.22/2.39 0 [] epsilon_transitive($c5).
% 2.22/2.39 0 [] epsilon_connected($c5).
% 2.22/2.39 0 [] ordinal($c5).
% 2.22/2.39 0 [] -empty($c6).
% 2.22/2.39 0 [] relation($c7).
% 2.22/2.39 0 [] function($c7).
% 2.22/2.39 0 [] one_to_one($c7).
% 2.22/2.39 0 [] -empty($c8).
% 2.22/2.39 0 [] epsilon_transitive($c8).
% 2.22/2.39 0 [] epsilon_connected($c8).
% 2.22/2.39 0 [] ordinal($c8).
% 2.22/2.39 0 [] relation($c9).
% 2.22/2.39 0 [] relation_empty_yielding($c9).
% 2.22/2.39 0 [] function($c9).
% 2.22/2.39 0 [] -ordinal(A)| -ordinal(B)| -ordinal_subset(A,B)|subset(A,B).
% 2.22/2.39 0 [] -ordinal(A)| -ordinal(B)|ordinal_subset(A,B)| -subset(A,B).
% 2.22/2.39 0 [] -e_quipotent(A,B)|are_e_quipotent(A,B).
% 2.22/2.39 0 [] e_quipotent(A,B)| -are_e_quipotent(A,B).
% 2.22/2.39 0 [] -ordinal(A)| -ordinal(B)|ordinal_subset(A,A).
% 2.22/2.39 0 [] subset(A,A).
% 2.22/2.39 0 [] e_quipotent(A,A).
% 2.22/2.39 0 [] -in(C,$f14(A))|in(C,A).
% 2.22/2.39 0 [] -in(C,$f14(A))|ordinal(C).
% 2.22/2.39 0 [] in(C,$f14(A))| -in(C,A)| -ordinal(C).
% 2.22/2.39 0 [] relation($f15(A)).
% 2.22/2.39 0 [] function($f15(A)).
% 2.22/2.39 0 [] relation_dom($f15(A))=A.
% 2.22/2.39 0 [] -in(C,A)|apply($f15(A),C)=singleton(C).
% 2.22/2.39 0 [] -e_quipotent(A,B)|e_quipotent(B,A).
% 2.22/2.39 0 [] in(A,$f16(A)).
% 2.22/2.39 0 [] -in(C,$f16(A))| -subset(D,C)|in(D,$f16(A)).
% 2.22/2.39 0 [] -in(X2,$f16(A))|in(powerset(X2),$f16(A)).
% 2.22/2.39 0 [] -subset(X3,$f16(A))|are_e_quipotent(X3,$f16(A))|in(X3,$f16(A)).
% 2.22/2.39 0 [] set_union2(A,empty_set)=A.
% 2.22/2.39 0 [] -in(A,B)|element(A,B).
% 2.22/2.39 0 [] -ordinal(B)| -in(A,B)|ordinal(A).
% 2.22/2.39 0 [] -relation(B)| -well_orders(B,A)|relation_field(relation_restriction(B,A))=A.
% 2.22/2.39 0 [] -relation(B)| -well_orders(B,A)|well_ordering(relation_restriction(B,A)).
% 2.22/2.39 0 [] -relation(B)| -well_orders(B,$c10).
% 2.22/2.39 0 [] set_intersection2(A,empty_set)=empty_set.
% 2.22/2.39 0 [] -element(A,B)|empty(B)|in(A,B).
% 2.22/2.39 0 [] in($f17(A),A)|ordinal(A).
% 2.22/2.39 0 [] -ordinal($f17(A))| -subset($f17(A),A)|ordinal(A).
% 2.22/2.39 0 [] -relation(B)| -well_ordering(B)|well_ordering(relation_restriction(B,A)).
% 2.22/2.39 0 [] -relation(B)| -well_ordering(B)| -subset(A,relation_field(B))|relation_field(relation_restriction(B,A))=A.
% 2.22/2.39 0 [] -element(A,powerset(B))|subset(A,B).
% 2.22/2.39 0 [] element(A,powerset(B))| -subset(A,B).
% 2.22/2.39 0 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 2.22/2.39 0 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 2.22/2.39 0 [] -empty(A)|A=empty_set.
% 2.22/2.39 0 [] -subset(singleton(A),singleton(B))|A=B.
% 2.22/2.39 0 [] -in(A,B)| -empty(B).
% 2.22/2.39 0 [] -ordinal(A)|well_ordering(inclusion_relation(A)).
% 2.22/2.39 0 [] -empty(A)|A=B| -empty(B).
% 2.22/2.39 end_of_list.
% 2.22/2.39
% 2.22/2.39 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=7.
% 2.22/2.39
% 2.22/2.39 This ia a non-Horn set with equality. The strategy will be
% 2.22/2.39 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.22/2.39 deletion, with positive clauses in sos and nonpositive
% 2.22/2.39 clauses in usable.
% 2.22/2.39
% 2.22/2.39 dependent: set(knuth_bendix).
% 2.22/2.39 dependent: set(anl_eq).
% 2.22/2.39 dependent: set(para_from).
% 2.22/2.39 dependent: set(para_into).
% 2.22/2.39 dependent: clear(para_from_right).
% 2.22/2.39 dependent: clear(para_into_right).
% 2.22/2.39 dependent: set(para_from_vars).
% 2.22/2.39 dependent: set(eq_units_both_ways).
% 2.22/2.39 dependent: set(dynamic_demod_all).
% 2.22/2.39 dependent: set(dynamic_demod).
% 2.22/2.39 dependent: set(order_eq).
% 2.22/2.39 dependent: set(back_demod).
% 2.22/2.39 dependent: set(lrpo).
% 2.22/2.39 dependent: set(hyper_res).
% 2.22/2.39 dependent: set(unit_deletion).
% 2.22/2.39 dependent: set(factor).
% 2.22/2.39
% 2.22/2.39 ------------> process usable:
% 2.22/2.39 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 2.22/2.39 ** KEPT (pick-wt=4): 2 [] -empty(A)|function(A).
% 2.22/2.39 ** KEPT (pick-wt=4): 3 [] -ordinal(A)|epsilon_transitive(A).
% 2.22/2.39 ** KEPT (pick-wt=4): 4 [] -ordinal(A)|epsilon_connected(A).
% 2.22/2.39 ** KEPT (pick-wt=8): 5 [] -relation(A)| -empty(A)| -function(A)|one_to_one(A).
% 2.22/2.39 ** KEPT (pick-wt=6): 6 [] -epsilon_transitive(A)| -epsilon_connected(A)|ordinal(A).
% 2.22/2.39 ** KEPT (pick-wt=4): 7 [] -empty(A)|epsilon_transitive(A).
% 2.22/2.39 ** KEPT (pick-wt=4): 8 [] -empty(A)|epsilon_connected(A).
% 2.22/2.39 ** KEPT (pick-wt=4): 9 [] -empty(A)|ordinal(A).
% 2.22/2.39 ** KEPT (pick-wt=10): 10 [] -ordinal(A)| -ordinal(B)|ordinal_subset(A,B)|ordinal_subset(B,A).
% 2.22/2.39 ** KEPT (pick-wt=10): 11 [] A!=singleton(B)| -in(C,A)|C=B.
% 2.22/2.39 ** KEPT (pick-wt=10): 12 [] A!=singleton(B)|in(C,A)|C!=B.
% 2.22/2.39 ** KEPT (pick-wt=14): 13 [] A=singleton(B)| -in($f1(B,A),A)|$f1(B,A)!=B.
% 2.22/2.39 ** KEPT (pick-wt=10): 14 [] -relation(A)|A!=inclusion_relation(B)|relation_field(A)=B.
% 2.22/2.39 ** KEPT (pick-wt=20): 15 [] -relation(A)|A!=inclusion_relation(B)| -in(C,B)| -in(D,B)| -in(ordered_pair(C,D),A)|subset(C,D).
% 2.22/2.39 ** KEPT (pick-wt=20): 16 [] -relation(A)|A!=inclusion_relation(B)| -in(C,B)| -in(D,B)|in(ordered_pair(C,D),A)| -subset(C,D).
% 2.22/2.39 ** KEPT (pick-wt=15): 17 [] -relation(A)|A=inclusion_relation(B)|relation_field(A)!=B|in($f3(B,A),B).
% 2.22/2.39 ** KEPT (pick-wt=15): 18 [] -relation(A)|A=inclusion_relation(B)|relation_field(A)!=B|in($f2(B,A),B).
% 2.22/2.39 ** KEPT (pick-wt=26): 19 [] -relation(A)|A=inclusion_relation(B)|relation_field(A)!=B|in(ordered_pair($f3(B,A),$f2(B,A)),A)|subset($f3(B,A),$f2(B,A)).
% 2.22/2.39 ** KEPT (pick-wt=26): 20 [] -relation(A)|A=inclusion_relation(B)|relation_field(A)!=B| -in(ordered_pair($f3(B,A),$f2(B,A)),A)| -subset($f3(B,A),$f2(B,A)).
% 2.22/2.39 ** KEPT (pick-wt=8): 21 [] -epsilon_transitive(A)| -in(B,A)|subset(B,A).
% 2.22/2.39 ** KEPT (pick-wt=6): 22 [] epsilon_transitive(A)| -subset($f4(A),A).
% 2.22/2.39 ** KEPT (pick-wt=9): 23 [] -subset(A,B)| -in(C,A)|in(C,B).
% 2.22/2.39 ** KEPT (pick-wt=8): 24 [] subset(A,B)| -in($f5(A,B),B).
% 2.22/2.39 ** KEPT (pick-wt=7): 25 [] -e_quipotent(A,B)|relation($f6(A,B)).
% 2.22/2.39 ** KEPT (pick-wt=7): 26 [] -e_quipotent(A,B)|function($f6(A,B)).
% 2.22/2.39 ** KEPT (pick-wt=7): 27 [] -e_quipotent(A,B)|one_to_one($f6(A,B)).
% 2.22/2.39 ** KEPT (pick-wt=9): 28 [] -e_quipotent(A,B)|relation_dom($f6(A,B))=A.
% 2.22/2.39 ** KEPT (pick-wt=9): 29 [] -e_quipotent(A,B)|relation_rng($f6(A,B))=B.
% 2.22/2.39 ** KEPT (pick-wt=17): 30 [] e_quipotent(A,B)| -relation(C)| -function(C)| -one_to_one(C)|relation_dom(C)!=A|relation_rng(C)!=B.
% 2.22/2.39 ** KEPT (pick-wt=18): 31 [] -relation(A)| -function(A)|B!=relation_rng(A)| -in(C,B)|in($f7(A,B,C),relation_dom(A)).
% 2.22/2.39 ** KEPT (pick-wt=19): 33 [copy,32,flip.5] -relation(A)| -function(A)|B!=relation_rng(A)| -in(C,B)|apply(A,$f7(A,B,C))=C.
% 2.22/2.39 ** KEPT (pick-wt=20): 34 [] -relation(A)| -function(A)|B!=relation_rng(A)|in(C,B)| -in(D,relation_dom(A))|C!=apply(A,D).
% 2.22/2.39 ** KEPT (pick-wt=19): 35 [] -relation(A)| -function(A)|B=relation_rng(A)|in($f9(A,B),B)|in($f8(A,B),relation_dom(A)).
% 2.22/2.39 ** KEPT (pick-wt=22): 37 [copy,36,flip.5] -relation(A)| -function(A)|B=relation_rng(A)|in($f9(A,B),B)|apply(A,$f8(A,B))=$f9(A,B).
% 2.22/2.39 ** KEPT (pick-wt=24): 38 [] -relation(A)| -function(A)|B=relation_rng(A)| -in($f9(A,B),B)| -in(C,relation_dom(A))|$f9(A,B)!=apply(A,C).
% 2.22/2.39 ** KEPT (pick-wt=10): 40 [copy,39,flip.2] -relation(A)|set_union2(relation_dom(A),relation_rng(A))=relation_field(A).
% 2.22/2.39 ** KEPT (pick-wt=11): 42 [copy,41,flip.2] -relation(A)|set_intersection2(A,cartesian_product2(B,B))=relation_restriction(A,B).
% 2.22/2.39 ** KEPT (pick-wt=24): 43 [] -relation(A)| -function(A)| -one_to_one(A)| -in(B,relation_dom(A))| -in(C,relation_dom(A))|apply(A,B)!=apply(A,C)|B=C.
% 2.22/2.39 ** KEPT (pick-wt=11): 44 [] -relation(A)| -function(A)|one_to_one(A)|in($f11(A),relation_dom(A)).
% 2.22/2.39 ** KEPT (pick-wt=11): 45 [] -relation(A)| -function(A)|one_to_one(A)|in($f10(A),relation_dom(A)).
% 2.22/2.39 ** KEPT (pick-wt=15): 46 [] -relation(A)| -function(A)|one_to_one(A)|apply(A,$f11(A))=apply(A,$f10(A)).
% 2.22/2.39 ** KEPT (pick-wt=11): 47 [] -relation(A)| -function(A)|one_to_one(A)|$f11(A)!=$f10(A).
% 2.22/2.39 ** KEPT (pick-wt=6): 48 [] -relation(A)|relation(relation_restriction(A,B)).
% 2.22/2.39 ** KEPT (pick-wt=4): 49 [] -empty(ordered_pair(A,B)).
% 2.22/2.39 ** KEPT (pick-wt=6): 50 [] empty(A)| -empty(set_union2(A,B)).
% 2.22/2.39 ** KEPT (pick-wt=6): 51 [] empty(A)| -empty(set_union2(B,A)).
% 2.22/2.39 ** KEPT (pick-wt=12): 52 [] -relation(A)| -well_ordering(A)| -e_quipotent(B,relation_field(A))|relation($f13(B,A)).
% 2.22/2.39 ** KEPT (pick-wt=13): 53 [] -relation(A)| -well_ordering(A)| -e_quipotent(B,relation_field(A))|well_orders($f13(B,A),B).
% 2.22/2.39 ** KEPT (pick-wt=2): 54 [] -empty($c6).
% 2.22/2.39 ** KEPT (pick-wt=2): 55 [] -empty($c8).
% 2.22/2.39 ** KEPT (pick-wt=10): 56 [] -ordinal(A)| -ordinal(B)| -ordinal_subset(A,B)|subset(A,B).
% 2.22/2.39 ** KEPT (pick-wt=10): 57 [] -ordinal(A)| -ordinal(B)|ordinal_subset(A,B)| -subset(A,B).
% 2.22/2.39 ** KEPT (pick-wt=6): 58 [] -e_quipotent(A,B)|are_e_quipotent(A,B).
% 2.22/2.39 ** KEPT (pick-wt=6): 59 [] e_quipotent(A,B)| -are_e_quipotent(A,B).
% 2.22/2.39 ** KEPT (pick-wt=5): 61 [copy,60,factor_simp] -ordinal(A)|ordinal_subset(A,A).
% 2.22/2.39 ** KEPT (pick-wt=7): 62 [] -in(A,$f14(B))|in(A,B).
% 2.22/2.39 ** KEPT (pick-wt=6): 63 [] -in(A,$f14(B))|ordinal(A).
% 2.22/2.39 ** KEPT (pick-wt=9): 64 [] in(A,$f14(B))| -in(A,B)| -ordinal(A).
% 2.22/2.39 ** KEPT (pick-wt=10): 65 [] -in(A,B)|apply($f15(B),A)=singleton(A).
% 2.22/2.39 ** KEPT (pick-wt=6): 66 [] -e_quipotent(A,B)|e_quipotent(B,A).
% 2.22/2.39 ** KEPT (pick-wt=11): 67 [] -in(A,$f16(B))| -subset(C,A)|in(C,$f16(B)).
% 2.22/2.39 ** KEPT (pick-wt=9): 68 [] -in(A,$f16(B))|in(powerset(A),$f16(B)).
% 2.22/2.39 ** KEPT (pick-wt=12): 69 [] -subset(A,$f16(B))|are_e_quipotent(A,$f16(B))|in(A,$f16(B)).
% 2.22/2.39 ** KEPT (pick-wt=6): 70 [] -in(A,B)|element(A,B).
% 2.22/2.39 ** KEPT (pick-wt=7): 71 [] -ordinal(A)| -in(B,A)|ordinal(B).
% 2.22/2.39 ** KEPT (pick-wt=11): 72 [] -relation(A)| -well_orders(A,B)|relation_field(relation_restriction(A,B))=B.
% 2.22/2.39 ** KEPT (pick-wt=9): 73 [] -relation(A)| -well_orders(A,B)|well_ordering(relation_restriction(A,B)).
% 2.22/2.39 ** KEPT (pick-wt=5): 74 [] -relation(A)| -well_orders(A,$c10).
% 2.22/2.39 ** KEPT (pick-wt=8): 75 [] -element(A,B)|empty(B)|in(A,B).
% 2.22/2.39 ** KEPT (pick-wt=9): 76 [] -ordinal($f17(A))| -subset($f17(A),A)|ordinal(A).
% 2.22/2.39 ** KEPT (pick-wt=8): 77 [] -relation(A)| -well_ordering(A)|well_ordering(relation_restriction(A,B)).
% 2.22/2.39 ** KEPT (pick-wt=14): 78 [] -relation(A)| -well_ordering(A)| -subset(B,relation_field(A))|relation_field(relation_restriction(A,B))=B.
% 2.22/2.39 ** KEPT (pick-wt=7): 79 [] -element(A,powerset(B))|subset(A,B).
% 2.22/2.39 ** KEPT (pick-wt=7): 80 [] element(A,powerset(B))| -subset(A,B).
% 2.22/2.39 ** KEPT (pick-wt=10): 81 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 2.22/2.39 ** KEPT (pick-wt=9): 82 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 2.22/2.39 ** KEPT (pick-wt=5): 83 [] -empty(A)|A=empty_set.
% 2.22/2.39 ** KEPT (pick-wt=8): 84 [] -subset(singleton(A),singleton(B))|A=B.
% 2.22/2.39 ** KEPT (pick-wt=5): 85 [] -in(A,B)| -empty(B).
% 2.22/2.39 ** KEPT (pick-wt=5): 86 [] -ordinal(A)|well_ordering(inclusion_relation(A)).
% 2.22/2.39 ** KEPT (pick-wt=7): 87 [] -empty(A)|A=B| -empty(B).
% 2.22/2.39
% 2.22/2.39 ------------> process sos:
% 2.22/2.39 ** KEPT (pick-wt=3): 95 [] A=A.
% 2.22/2.39 ** KEPT (pick-wt=7): 96 [] unordered_pair(A,B)=unordered_pair(B,A).
% 2.22/2.39 ** KEPT (pick-wt=7): 97 [] set_union2(A,B)=set_union2(B,A).
% 2.22/2.39 ** KEPT (pick-wt=7): 98 [] set_intersection2(A,B)=set_intersection2(B,A).
% 2.22/2.39 ** KEPT (pick-wt=14): 99 [] A=singleton(B)|in($f1(B,A),A)|$f1(B,A)=B.
% 2.22/2.39 ** KEPT (pick-wt=6): 100 [] epsilon_transitive(A)|in($f4(A),A).
% 2.22/2.39 ** KEPT (pick-wt=8): 101 [] subset(A,B)|in($f5(A,B),A).
% 2.22/2.39 ** KEPT (pick-wt=10): 103 [copy,102,flip.1] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 2.22/2.39 ---> New Demodulator: 104 [new_demod,103] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 2.22/2.39 ** KEPT (pick-wt=3): 105 [] relation(inclusion_relation(A)).
% 2.22/2.39 ** KEPT (pick-wt=4): 106 [] element($f12(A),A).
% 2.22/2.39 ** KEPT (pick-wt=2): 107 [] empty(empty_set).
% 2.22/2.39 ** KEPT (pick-wt=2): 108 [] relation(empty_set).
% 2.22/2.39 ** KEPT (pick-wt=2): 109 [] relation_empty_yielding(empty_set).
% 2.22/2.39 ** KEPT (pick-wt=2): 110 [] function(empty_set).
% 2.22/2.39 ** KEPT (pick-wt=2): 111 [] one_to_one(empty_set).
% 2.22/2.39 Following clause subsumed by 107 during input processing: 0 [] empty(empty_set).
% 2.22/2.39 ** KEPT (pick-wt=2): 112 [] epsilon_transitive(empty_set).
% 2.22/2.39 ** KEPT (pick-wt=2): 113 [] epsilon_connected(empty_set).
% 2.22/2.39 ** KEPT (pick-wt=2): 114 [] ordinal(empty_set).
% 2.22/2.39 ** KEPT (pick-wt=5): 115 [] set_union2(A,A)=A.
% 2.22/2.39 ---> New Demodulator: 116 [new_demod,115] set_union2(A,A)=A.
% 9.24/9.45 ** KEPT (pick-wt=5): 117 [] set_intersection2(A,A)=A.
% 9.24/9.45 ---> New Demodulator: 118 [new_demod,117] set_intersection2(A,A)=A.
% 9.24/9.45 ** KEPT (pick-wt=2): 119 [] relation($c1).
% 9.24/9.45 ** KEPT (pick-wt=2): 120 [] function($c1).
% 9.24/9.45 ** KEPT (pick-wt=2): 121 [] epsilon_transitive($c2).
% 9.24/9.45 ** KEPT (pick-wt=2): 122 [] epsilon_connected($c2).
% 9.24/9.45 ** KEPT (pick-wt=2): 123 [] ordinal($c2).
% 9.24/9.45 ** KEPT (pick-wt=2): 124 [] empty($c3).
% 9.24/9.45 ** KEPT (pick-wt=2): 125 [] relation($c4).
% 9.24/9.45 ** KEPT (pick-wt=2): 126 [] empty($c4).
% 9.24/9.45 ** KEPT (pick-wt=2): 127 [] function($c4).
% 9.24/9.45 ** KEPT (pick-wt=2): 128 [] relation($c5).
% 9.24/9.45 ** KEPT (pick-wt=2): 129 [] function($c5).
% 9.24/9.45 ** KEPT (pick-wt=2): 130 [] one_to_one($c5).
% 9.24/9.45 ** KEPT (pick-wt=2): 131 [] empty($c5).
% 9.24/9.45 ** KEPT (pick-wt=2): 132 [] epsilon_transitive($c5).
% 9.24/9.45 ** KEPT (pick-wt=2): 133 [] epsilon_connected($c5).
% 9.24/9.45 ** KEPT (pick-wt=2): 134 [] ordinal($c5).
% 9.24/9.45 ** KEPT (pick-wt=2): 135 [] relation($c7).
% 9.24/9.45 ** KEPT (pick-wt=2): 136 [] function($c7).
% 9.24/9.45 ** KEPT (pick-wt=2): 137 [] one_to_one($c7).
% 9.24/9.45 ** KEPT (pick-wt=2): 138 [] epsilon_transitive($c8).
% 9.24/9.45 ** KEPT (pick-wt=2): 139 [] epsilon_connected($c8).
% 9.24/9.45 ** KEPT (pick-wt=2): 140 [] ordinal($c8).
% 9.24/9.45 ** KEPT (pick-wt=2): 141 [] relation($c9).
% 9.24/9.45 ** KEPT (pick-wt=2): 142 [] relation_empty_yielding($c9).
% 9.24/9.45 ** KEPT (pick-wt=2): 143 [] function($c9).
% 9.24/9.45 ** KEPT (pick-wt=3): 144 [] subset(A,A).
% 9.24/9.45 ** KEPT (pick-wt=3): 145 [] e_quipotent(A,A).
% 9.24/9.45 ** KEPT (pick-wt=3): 146 [] relation($f15(A)).
% 9.24/9.45 ** KEPT (pick-wt=3): 147 [] function($f15(A)).
% 9.24/9.45 ** KEPT (pick-wt=5): 148 [] relation_dom($f15(A))=A.
% 9.24/9.45 ---> New Demodulator: 149 [new_demod,148] relation_dom($f15(A))=A.
% 9.24/9.45 ** KEPT (pick-wt=4): 150 [] in(A,$f16(A)).
% 9.24/9.45 ** KEPT (pick-wt=5): 151 [] set_union2(A,empty_set)=A.
% 9.24/9.45 ---> New Demodulator: 152 [new_demod,151] set_union2(A,empty_set)=A.
% 9.24/9.45 ** KEPT (pick-wt=5): 153 [] set_intersection2(A,empty_set)=empty_set.
% 9.24/9.45 ---> New Demodulator: 154 [new_demod,153] set_intersection2(A,empty_set)=empty_set.
% 9.24/9.45 ** KEPT (pick-wt=6): 155 [] in($f17(A),A)|ordinal(A).
% 9.24/9.45 Following clause subsumed by 95 during input processing: 0 [copy,95,flip.1] A=A.
% 9.24/9.45 95 back subsumes 94.
% 9.24/9.45 95 back subsumes 92.
% 9.24/9.45 Following clause subsumed by 96 during input processing: 0 [copy,96,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 9.24/9.45 Following clause subsumed by 97 during input processing: 0 [copy,97,flip.1] set_union2(A,B)=set_union2(B,A).
% 9.24/9.45 Following clause subsumed by 98 during input processing: 0 [copy,98,flip.1] set_intersection2(A,B)=set_intersection2(B,A).
% 9.24/9.45 >>>> Starting back demodulation with 104.
% 9.24/9.45 >>>> Starting back demodulation with 116.
% 9.24/9.45 >>>> Starting back demodulation with 118.
% 9.24/9.45 144 back subsumes 93.
% 9.24/9.45 144 back subsumes 89.
% 9.24/9.45 >>>> Starting back demodulation with 149.
% 9.24/9.45 >>>> Starting back demodulation with 152.
% 9.24/9.45 >>>> Starting back demodulation with 154.
% 9.24/9.45
% 9.24/9.45 ======= end of input processing =======
% 9.24/9.45
% 9.24/9.45 =========== start of search ===========
% 9.24/9.45
% 9.24/9.45
% 9.24/9.45 Resetting weight limit to 2.
% 9.24/9.45
% 9.24/9.45
% 9.24/9.45 Resetting weight limit to 2.
% 9.24/9.45
% 9.24/9.45 sos_size=418
% 9.24/9.45
% 9.24/9.45 Search stopped because sos empty.
% 9.24/9.45
% 9.24/9.45
% 9.24/9.45 Search stopped because sos empty.
% 9.24/9.45
% 9.24/9.45 ============ end of search ============
% 9.24/9.45
% 9.24/9.45 -------------- statistics -------------
% 9.24/9.45 clauses given 441
% 9.24/9.45 clauses generated 330465
% 9.24/9.45 clauses kept 645
% 9.24/9.45 clauses forward subsumed 226
% 9.24/9.45 clauses back subsumed 5
% 9.24/9.45 Kbytes malloced 7812
% 9.24/9.45
% 9.24/9.45 ----------- times (seconds) -----------
% 9.24/9.45 user CPU time 7.07 (0 hr, 0 min, 7 sec)
% 9.24/9.45 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 9.24/9.45 wall-clock time 9 (0 hr, 0 min, 9 sec)
% 9.24/9.45
% 9.24/9.45 Process 1514 finished Wed Jul 27 07:41:13 2022
% 9.24/9.45 Otter interrupted
% 9.24/9.45 PROOF NOT FOUND
%------------------------------------------------------------------------------