TSTP Solution File: SEU098+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU098+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Jul 27 13:14:46 EDT 2022
% Result : Unknown 18.79s 18.94s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU098+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n011.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 07:29:40 EDT 2022
% 0.12/0.34 % CPUTime :
% 2.47/2.65 ----- Otter 3.3f, August 2004 -----
% 2.47/2.65 The process was started by sandbox2 on n011.cluster.edu,
% 2.47/2.65 Wed Jul 27 07:29:40 2022
% 2.47/2.65 The command was "./otter". The process ID is 6387.
% 2.47/2.65
% 2.47/2.65 set(prolog_style_variables).
% 2.47/2.65 set(auto).
% 2.47/2.65 dependent: set(auto1).
% 2.47/2.65 dependent: set(process_input).
% 2.47/2.65 dependent: clear(print_kept).
% 2.47/2.65 dependent: clear(print_new_demod).
% 2.47/2.65 dependent: clear(print_back_demod).
% 2.47/2.65 dependent: clear(print_back_sub).
% 2.47/2.65 dependent: set(control_memory).
% 2.47/2.65 dependent: assign(max_mem, 12000).
% 2.47/2.65 dependent: assign(pick_given_ratio, 4).
% 2.47/2.65 dependent: assign(stats_level, 1).
% 2.47/2.65 dependent: assign(max_seconds, 10800).
% 2.47/2.65 clear(print_given).
% 2.47/2.65
% 2.47/2.65 formula_list(usable).
% 2.47/2.65 all A (A=A).
% 2.47/2.65 all A B (in(A,B)-> -in(B,A)).
% 2.47/2.65 all A (ordinal(A)-> (all B (element(B,A)->epsilon_transitive(B)&epsilon_connected(B)&ordinal(B)))).
% 2.47/2.65 all A (empty(A)->finite(A)).
% 2.47/2.65 all A (empty(A)->function(A)).
% 2.47/2.65 all A (ordinal(A)->epsilon_transitive(A)&epsilon_connected(A)).
% 2.47/2.65 all A (empty(A)->relation(A)).
% 2.47/2.65 all A B C (element(C,powerset(cartesian_product2(A,B)))->relation(C)).
% 2.47/2.65 all A (empty(A)&ordinal(A)->epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)&natural(A)).
% 2.47/2.65 all A (finite(A)-> (all B (element(B,powerset(A))->finite(B)))).
% 2.47/2.65 all A (relation(A)&empty(A)&function(A)->relation(A)&function(A)&one_to_one(A)).
% 2.47/2.65 all A (epsilon_transitive(A)&epsilon_connected(A)->ordinal(A)).
% 2.47/2.65 all A (empty(A)->epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)).
% 2.47/2.65 all A (element(A,positive_rationals)-> (ordinal(A)->epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)&natural(A))).
% 2.47/2.65 all A B C D (function(C)&quasi_total(C,A,B)&relation_of2(C,A,B)->element(function_image(A,B,C,D),powerset(B))).
% 2.47/2.65 all A B (relation(first_projection(A,B))&function(first_projection(A,B))).
% 2.47/2.65 all A B (function(first_projection_as_func_of(A,B))&quasi_total(first_projection_as_func_of(A,B),cartesian_product2(A,B),A)&relation_of2_as_subset(first_projection_as_func_of(A,B),cartesian_product2(A,B),A)).
% 2.47/2.65 all A B C (relation_of2_as_subset(C,A,B)->element(C,powerset(cartesian_product2(A,B)))).
% 2.47/2.65 all A B exists C relation_of2(C,A,B).
% 2.47/2.65 all A exists B element(B,A).
% 2.47/2.65 all A B exists C relation_of2_as_subset(C,A,B).
% 2.47/2.65 empty(empty_set).
% 2.47/2.65 relation(empty_set).
% 2.47/2.65 relation_empty_yielding(empty_set).
% 2.47/2.65 all A B (relation(A)&function(A)&finite(B)->finite(relation_image(A,B))).
% 2.47/2.65 all A B (finite(A)&finite(B)->finite(cartesian_product2(A,B))).
% 2.47/2.65 all A (-empty(powerset(A))).
% 2.47/2.65 empty(empty_set).
% 2.47/2.65 relation(empty_set).
% 2.47/2.65 relation_empty_yielding(empty_set).
% 2.47/2.65 function(empty_set).
% 2.47/2.65 one_to_one(empty_set).
% 2.47/2.65 empty(empty_set).
% 2.47/2.65 epsilon_transitive(empty_set).
% 2.47/2.65 epsilon_connected(empty_set).
% 2.47/2.65 ordinal(empty_set).
% 2.47/2.65 empty(empty_set).
% 2.47/2.65 relation(empty_set).
% 2.47/2.65 all A B (-empty(A)& -empty(B)-> -empty(cartesian_product2(A,B))).
% 2.47/2.65 all A (relation(A)&function(A)&transfinite_se_quence(A)->epsilon_transitive(relation_dom(A))&epsilon_connected(relation_dom(A))&ordinal(relation_dom(A))).
% 2.47/2.65 all A (-empty(A)&relation(A)-> -empty(relation_dom(A))).
% 2.47/2.65 all A (relation(A)&relation_non_empty(A)&function(A)->with_non_empty_elements(relation_rng(A))).
% 2.47/2.65 all A (-empty(A)&relation(A)-> -empty(relation_rng(A))).
% 2.47/2.65 all A (empty(A)->empty(relation_dom(A))&relation(relation_dom(A))).
% 2.47/2.65 -empty(positive_rationals).
% 2.47/2.65 all A (empty(A)->empty(relation_rng(A))&relation(relation_rng(A))).
% 2.47/2.65 exists A (-empty(A)&epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)&natural(A)).
% 2.47/2.65 exists A (-empty(A)&finite(A)).
% 2.47/2.65 exists A (relation(A)&function(A)&function_yielding(A)).
% 2.47/2.65 exists A (relation(A)&function(A)).
% 2.47/2.65 exists A (epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)).
% 2.47/2.65 exists A (epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)&being_limit_ordinal(A)).
% 2.47/2.65 exists A (empty(A)&relation(A)).
% 2.47/2.65 all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)))).
% 2.47/2.65 exists A empty(A).
% 2.47/2.65 exists A (element(A,positive_rationals)& -empty(A)&epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)).
% 2.47/2.65 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)).
% 2.47/2.65 exists A (relation(A)&empty(A)&function(A)).
% 2.47/2.65 exists A (relation(A)&function(A)&one_to_one(A)&empty(A)&epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)).
% 2.47/2.65 exists A (relation(A)&function(A)&transfinite_se_quence(A)&ordinal_yielding(A)).
% 2.47/2.65 exists A (-empty(A)&relation(A)).
% 2.47/2.65 all A exists B (element(B,powerset(A))&empty(B)).
% 2.47/2.65 exists A (-empty(A)).
% 2.47/2.65 exists A (element(A,positive_rationals)&empty(A)&epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)&natural(A)).
% 2.47/2.65 all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)&finite(B)))).
% 2.47/2.65 exists A (relation(A)&function(A)&one_to_one(A)).
% 2.47/2.65 exists A (-empty(A)&epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)).
% 2.47/2.65 exists A (relation(A)&relation_empty_yielding(A)).
% 2.47/2.65 all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)&finite(B)))).
% 2.47/2.65 exists A (relation(A)&relation_empty_yielding(A)&function(A)).
% 2.47/2.65 exists A (relation(A)&function(A)&transfinite_se_quence(A)).
% 2.47/2.65 exists A (relation(A)&relation_non_empty(A)&function(A)).
% 2.47/2.65 all A B C D (function(C)&quasi_total(C,A,B)&relation_of2(C,A,B)->function_image(A,B,C,D)=relation_image(C,D)).
% 2.47/2.65 all A B (first_projection_as_func_of(A,B)=first_projection(A,B)).
% 2.47/2.65 all A B C (relation_of2_as_subset(C,A,B)<->relation_of2(C,A,B)).
% 2.47/2.65 all A B subset(A,A).
% 2.47/2.65 all A (relation(A)&function(A)->function_image(cartesian_product2(relation_dom(A),relation_rng(A)),relation_dom(A),first_projection_as_func_of(relation_dom(A),relation_rng(A)),A)=relation_dom(A)).
% 2.47/2.65 all A B (subset(A,B)&finite(B)->finite(A)).
% 2.47/2.65 all A B (relation(B)&function(B)-> (finite(A)->finite(relation_image(B,A)))).
% 2.47/2.65 all A B (finite(A)&finite(B)->finite(cartesian_product2(A,B))).
% 2.47/2.65 all A B (in(A,B)->element(A,B)).
% 2.47/2.65 all A (relation(A)->subset(A,cartesian_product2(relation_dom(A),relation_rng(A)))).
% 2.47/2.65 all A (relation(A)&function(A)-> (finite(relation_dom(A))->finite(relation_rng(A)))).
% 2.47/2.65 -(all A (relation(A)&function(A)-> (finite(relation_dom(A))<->finite(A)))).
% 2.47/2.65 all A B (element(A,B)->empty(B)|in(A,B)).
% 2.47/2.65 all A B (element(A,powerset(B))<->subset(A,B)).
% 2.47/2.65 all A B C (in(A,B)&element(B,powerset(C))->element(A,C)).
% 2.47/2.65 all A B C (-(in(A,B)&element(B,powerset(C))&empty(C))).
% 2.47/2.65 all A (empty(A)->A=empty_set).
% 2.47/2.65 all A B (-(in(A,B)&empty(B))).
% 2.47/2.65 all A B (-(empty(A)&A!=B&empty(B))).
% 2.47/2.65 end_of_list.
% 2.47/2.65
% 2.47/2.65 -------> usable clausifies to:
% 2.47/2.65
% 2.47/2.65 list(usable).
% 2.47/2.65 0 [] A=A.
% 2.47/2.65 0 [] -in(A,B)| -in(B,A).
% 2.47/2.65 0 [] -ordinal(A)| -element(B,A)|epsilon_transitive(B).
% 2.47/2.65 0 [] -ordinal(A)| -element(B,A)|epsilon_connected(B).
% 2.47/2.65 0 [] -ordinal(A)| -element(B,A)|ordinal(B).
% 2.47/2.65 0 [] -empty(A)|finite(A).
% 2.47/2.65 0 [] -empty(A)|function(A).
% 2.47/2.65 0 [] -ordinal(A)|epsilon_transitive(A).
% 2.47/2.65 0 [] -ordinal(A)|epsilon_connected(A).
% 2.47/2.65 0 [] -empty(A)|relation(A).
% 2.47/2.65 0 [] -element(C,powerset(cartesian_product2(A,B)))|relation(C).
% 2.47/2.65 0 [] -empty(A)| -ordinal(A)|epsilon_transitive(A).
% 2.47/2.65 0 [] -empty(A)| -ordinal(A)|epsilon_connected(A).
% 2.47/2.65 0 [] -empty(A)| -ordinal(A)|natural(A).
% 2.47/2.65 0 [] -finite(A)| -element(B,powerset(A))|finite(B).
% 2.47/2.65 0 [] -relation(A)| -empty(A)| -function(A)|one_to_one(A).
% 2.47/2.65 0 [] -epsilon_transitive(A)| -epsilon_connected(A)|ordinal(A).
% 2.47/2.65 0 [] -empty(A)|epsilon_transitive(A).
% 2.47/2.65 0 [] -empty(A)|epsilon_connected(A).
% 2.47/2.65 0 [] -empty(A)|ordinal(A).
% 2.47/2.65 0 [] -element(A,positive_rationals)| -ordinal(A)|epsilon_transitive(A).
% 2.47/2.65 0 [] -element(A,positive_rationals)| -ordinal(A)|epsilon_connected(A).
% 2.47/2.65 0 [] -element(A,positive_rationals)| -ordinal(A)|natural(A).
% 2.47/2.65 0 [] -function(C)| -quasi_total(C,A,B)| -relation_of2(C,A,B)|element(function_image(A,B,C,D),powerset(B)).
% 2.47/2.65 0 [] relation(first_projection(A,B)).
% 2.47/2.65 0 [] function(first_projection(A,B)).
% 2.47/2.65 0 [] function(first_projection_as_func_of(A,B)).
% 2.47/2.65 0 [] quasi_total(first_projection_as_func_of(A,B),cartesian_product2(A,B),A).
% 2.47/2.65 0 [] relation_of2_as_subset(first_projection_as_func_of(A,B),cartesian_product2(A,B),A).
% 2.47/2.65 0 [] -relation_of2_as_subset(C,A,B)|element(C,powerset(cartesian_product2(A,B))).
% 2.47/2.65 0 [] relation_of2($f1(A,B),A,B).
% 2.47/2.65 0 [] element($f2(A),A).
% 2.47/2.65 0 [] relation_of2_as_subset($f3(A,B),A,B).
% 2.47/2.65 0 [] empty(empty_set).
% 2.47/2.65 0 [] relation(empty_set).
% 2.47/2.65 0 [] relation_empty_yielding(empty_set).
% 2.47/2.65 0 [] -relation(A)| -function(A)| -finite(B)|finite(relation_image(A,B)).
% 2.47/2.65 0 [] -finite(A)| -finite(B)|finite(cartesian_product2(A,B)).
% 2.47/2.65 0 [] -empty(powerset(A)).
% 2.47/2.65 0 [] empty(empty_set).
% 2.47/2.65 0 [] relation(empty_set).
% 2.47/2.65 0 [] relation_empty_yielding(empty_set).
% 2.47/2.66 0 [] function(empty_set).
% 2.47/2.66 0 [] one_to_one(empty_set).
% 2.47/2.66 0 [] empty(empty_set).
% 2.47/2.66 0 [] epsilon_transitive(empty_set).
% 2.47/2.66 0 [] epsilon_connected(empty_set).
% 2.47/2.66 0 [] ordinal(empty_set).
% 2.47/2.66 0 [] empty(empty_set).
% 2.47/2.66 0 [] relation(empty_set).
% 2.47/2.66 0 [] empty(A)|empty(B)| -empty(cartesian_product2(A,B)).
% 2.47/2.66 0 [] -relation(A)| -function(A)| -transfinite_se_quence(A)|epsilon_transitive(relation_dom(A)).
% 2.47/2.66 0 [] -relation(A)| -function(A)| -transfinite_se_quence(A)|epsilon_connected(relation_dom(A)).
% 2.47/2.66 0 [] -relation(A)| -function(A)| -transfinite_se_quence(A)|ordinal(relation_dom(A)).
% 2.47/2.66 0 [] empty(A)| -relation(A)| -empty(relation_dom(A)).
% 2.47/2.66 0 [] -relation(A)| -relation_non_empty(A)| -function(A)|with_non_empty_elements(relation_rng(A)).
% 2.47/2.66 0 [] empty(A)| -relation(A)| -empty(relation_rng(A)).
% 2.47/2.66 0 [] -empty(A)|empty(relation_dom(A)).
% 2.47/2.66 0 [] -empty(A)|relation(relation_dom(A)).
% 2.47/2.66 0 [] -empty(positive_rationals).
% 2.47/2.66 0 [] -empty(A)|empty(relation_rng(A)).
% 2.47/2.66 0 [] -empty(A)|relation(relation_rng(A)).
% 2.47/2.66 0 [] -empty($c1).
% 2.47/2.66 0 [] epsilon_transitive($c1).
% 2.47/2.66 0 [] epsilon_connected($c1).
% 2.47/2.66 0 [] ordinal($c1).
% 2.47/2.66 0 [] natural($c1).
% 2.47/2.66 0 [] -empty($c2).
% 2.47/2.66 0 [] finite($c2).
% 2.47/2.66 0 [] relation($c3).
% 2.47/2.66 0 [] function($c3).
% 2.47/2.66 0 [] function_yielding($c3).
% 2.47/2.66 0 [] relation($c4).
% 2.47/2.66 0 [] function($c4).
% 2.47/2.66 0 [] epsilon_transitive($c5).
% 2.47/2.66 0 [] epsilon_connected($c5).
% 2.47/2.66 0 [] ordinal($c5).
% 2.47/2.66 0 [] epsilon_transitive($c6).
% 2.47/2.66 0 [] epsilon_connected($c6).
% 2.47/2.66 0 [] ordinal($c6).
% 2.47/2.66 0 [] being_limit_ordinal($c6).
% 2.47/2.66 0 [] empty($c7).
% 2.47/2.66 0 [] relation($c7).
% 2.47/2.66 0 [] empty(A)|element($f4(A),powerset(A)).
% 2.47/2.66 0 [] empty(A)| -empty($f4(A)).
% 2.47/2.66 0 [] empty($c8).
% 2.47/2.66 0 [] element($c9,positive_rationals).
% 2.47/2.66 0 [] -empty($c9).
% 2.47/2.66 0 [] epsilon_transitive($c9).
% 2.47/2.66 0 [] epsilon_connected($c9).
% 2.47/2.66 0 [] ordinal($c9).
% 2.47/2.66 0 [] element($f5(A),powerset(A)).
% 2.47/2.66 0 [] empty($f5(A)).
% 2.47/2.66 0 [] relation($f5(A)).
% 2.47/2.66 0 [] function($f5(A)).
% 2.47/2.66 0 [] one_to_one($f5(A)).
% 2.47/2.66 0 [] epsilon_transitive($f5(A)).
% 2.47/2.66 0 [] epsilon_connected($f5(A)).
% 2.47/2.66 0 [] ordinal($f5(A)).
% 2.47/2.66 0 [] natural($f5(A)).
% 2.47/2.66 0 [] finite($f5(A)).
% 2.47/2.66 0 [] relation($c10).
% 2.47/2.66 0 [] empty($c10).
% 2.47/2.66 0 [] function($c10).
% 2.47/2.66 0 [] relation($c11).
% 2.47/2.66 0 [] function($c11).
% 2.47/2.66 0 [] one_to_one($c11).
% 2.47/2.66 0 [] empty($c11).
% 2.47/2.66 0 [] epsilon_transitive($c11).
% 2.47/2.66 0 [] epsilon_connected($c11).
% 2.47/2.66 0 [] ordinal($c11).
% 2.47/2.66 0 [] relation($c12).
% 2.47/2.66 0 [] function($c12).
% 2.47/2.66 0 [] transfinite_se_quence($c12).
% 2.47/2.66 0 [] ordinal_yielding($c12).
% 2.47/2.66 0 [] -empty($c13).
% 2.47/2.66 0 [] relation($c13).
% 2.47/2.66 0 [] element($f6(A),powerset(A)).
% 2.47/2.66 0 [] empty($f6(A)).
% 2.47/2.66 0 [] -empty($c14).
% 2.47/2.66 0 [] element($c15,positive_rationals).
% 2.47/2.66 0 [] empty($c15).
% 2.47/2.66 0 [] epsilon_transitive($c15).
% 2.47/2.66 0 [] epsilon_connected($c15).
% 2.47/2.66 0 [] ordinal($c15).
% 2.47/2.66 0 [] natural($c15).
% 2.47/2.66 0 [] empty(A)|element($f7(A),powerset(A)).
% 2.47/2.66 0 [] empty(A)| -empty($f7(A)).
% 2.47/2.66 0 [] empty(A)|finite($f7(A)).
% 2.47/2.66 0 [] relation($c16).
% 2.47/2.66 0 [] function($c16).
% 2.47/2.66 0 [] one_to_one($c16).
% 2.47/2.66 0 [] -empty($c17).
% 2.47/2.66 0 [] epsilon_transitive($c17).
% 2.47/2.66 0 [] epsilon_connected($c17).
% 2.47/2.66 0 [] ordinal($c17).
% 2.47/2.66 0 [] relation($c18).
% 2.47/2.66 0 [] relation_empty_yielding($c18).
% 2.47/2.66 0 [] empty(A)|element($f8(A),powerset(A)).
% 2.47/2.66 0 [] empty(A)| -empty($f8(A)).
% 2.47/2.66 0 [] empty(A)|finite($f8(A)).
% 2.47/2.66 0 [] relation($c19).
% 2.47/2.66 0 [] relation_empty_yielding($c19).
% 2.47/2.66 0 [] function($c19).
% 2.47/2.66 0 [] relation($c20).
% 2.47/2.66 0 [] function($c20).
% 2.47/2.66 0 [] transfinite_se_quence($c20).
% 2.47/2.66 0 [] relation($c21).
% 2.47/2.66 0 [] relation_non_empty($c21).
% 2.47/2.66 0 [] function($c21).
% 2.47/2.66 0 [] -function(C)| -quasi_total(C,A,B)| -relation_of2(C,A,B)|function_image(A,B,C,D)=relation_image(C,D).
% 2.47/2.66 0 [] first_projection_as_func_of(A,B)=first_projection(A,B).
% 2.47/2.66 0 [] -relation_of2_as_subset(C,A,B)|relation_of2(C,A,B).
% 2.47/2.66 0 [] relation_of2_as_subset(C,A,B)| -relation_of2(C,A,B).
% 2.47/2.66 0 [] subset(A,A).
% 2.47/2.66 0 [] -relation(A)| -function(A)|function_image(cartesian_product2(relation_dom(A),relation_rng(A)),relation_dom(A),first_projection_as_func_of(relation_dom(A),relation_rng(A)),A)=relation_dom(A).
% 2.47/2.66 0 [] -subset(A,B)| -finite(B)|finite(A).
% 2.47/2.66 0 [] -relation(B)| -function(B)| -finite(A)|finite(relation_image(B,A)).
% 2.47/2.66 0 [] -finite(A)| -finite(B)|finite(cartesian_product2(A,B)).
% 2.47/2.66 0 [] -in(A,B)|element(A,B).
% 2.47/2.66 0 [] -relation(A)|subset(A,cartesian_product2(relation_dom(A),relation_rng(A))).
% 2.47/2.66 0 [] -relation(A)| -function(A)| -finite(relation_dom(A))|finite(relation_rng(A)).
% 2.47/2.66 0 [] relation($c22).
% 2.47/2.66 0 [] function($c22).
% 2.47/2.66 0 [] finite(relation_dom($c22))|finite($c22).
% 2.47/2.66 0 [] -finite(relation_dom($c22))| -finite($c22).
% 2.47/2.66 0 [] -element(A,B)|empty(B)|in(A,B).
% 2.47/2.66 0 [] -element(A,powerset(B))|subset(A,B).
% 2.47/2.66 0 [] element(A,powerset(B))| -subset(A,B).
% 2.47/2.66 0 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 2.47/2.66 0 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 2.47/2.66 0 [] -empty(A)|A=empty_set.
% 2.47/2.66 0 [] -in(A,B)| -empty(B).
% 2.47/2.66 0 [] -empty(A)|A=B| -empty(B).
% 2.47/2.66 end_of_list.
% 2.47/2.66
% 2.47/2.66 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 2.47/2.66
% 2.47/2.66 This ia a non-Horn set with equality. The strategy will be
% 2.47/2.66 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.47/2.66 deletion, with positive clauses in sos and nonpositive
% 2.47/2.66 clauses in usable.
% 2.47/2.66
% 2.47/2.66 dependent: set(knuth_bendix).
% 2.47/2.66 dependent: set(anl_eq).
% 2.47/2.66 dependent: set(para_from).
% 2.47/2.66 dependent: set(para_into).
% 2.47/2.66 dependent: clear(para_from_right).
% 2.47/2.66 dependent: clear(para_into_right).
% 2.47/2.66 dependent: set(para_from_vars).
% 2.47/2.66 dependent: set(eq_units_both_ways).
% 2.47/2.66 dependent: set(dynamic_demod_all).
% 2.47/2.66 dependent: set(dynamic_demod).
% 2.47/2.66 dependent: set(order_eq).
% 2.47/2.66 dependent: set(back_demod).
% 2.47/2.66 dependent: set(lrpo).
% 2.47/2.66 dependent: set(hyper_res).
% 2.47/2.66 dependent: set(unit_deletion).
% 2.47/2.66 dependent: set(factor).
% 2.47/2.66
% 2.47/2.66 ------------> process usable:
% 2.47/2.66 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 2.47/2.66 ** KEPT (pick-wt=7): 2 [] -ordinal(A)| -element(B,A)|epsilon_transitive(B).
% 2.47/2.66 ** KEPT (pick-wt=7): 3 [] -ordinal(A)| -element(B,A)|epsilon_connected(B).
% 2.47/2.66 ** KEPT (pick-wt=7): 4 [] -ordinal(A)| -element(B,A)|ordinal(B).
% 2.47/2.66 ** KEPT (pick-wt=4): 5 [] -empty(A)|finite(A).
% 2.47/2.66 ** KEPT (pick-wt=4): 6 [] -empty(A)|function(A).
% 2.47/2.66 ** KEPT (pick-wt=4): 7 [] -ordinal(A)|epsilon_transitive(A).
% 2.47/2.66 ** KEPT (pick-wt=4): 8 [] -ordinal(A)|epsilon_connected(A).
% 2.47/2.66 ** KEPT (pick-wt=4): 9 [] -empty(A)|relation(A).
% 2.47/2.66 ** KEPT (pick-wt=8): 10 [] -element(A,powerset(cartesian_product2(B,C)))|relation(A).
% 2.47/2.66 Following clause subsumed by 7 during input processing: 0 [] -empty(A)| -ordinal(A)|epsilon_transitive(A).
% 2.47/2.66 Following clause subsumed by 8 during input processing: 0 [] -empty(A)| -ordinal(A)|epsilon_connected(A).
% 2.47/2.66 ** KEPT (pick-wt=6): 11 [] -empty(A)| -ordinal(A)|natural(A).
% 2.47/2.66 ** KEPT (pick-wt=8): 12 [] -finite(A)| -element(B,powerset(A))|finite(B).
% 2.47/2.66 ** KEPT (pick-wt=8): 13 [] -relation(A)| -empty(A)| -function(A)|one_to_one(A).
% 2.47/2.66 ** KEPT (pick-wt=6): 14 [] -epsilon_transitive(A)| -epsilon_connected(A)|ordinal(A).
% 2.47/2.66 ** KEPT (pick-wt=4): 15 [] -empty(A)|epsilon_transitive(A).
% 2.47/2.66 ** KEPT (pick-wt=4): 16 [] -empty(A)|epsilon_connected(A).
% 2.47/2.66 ** KEPT (pick-wt=4): 17 [] -empty(A)|ordinal(A).
% 2.47/2.66 Following clause subsumed by 7 during input processing: 0 [] -element(A,positive_rationals)| -ordinal(A)|epsilon_transitive(A).
% 2.47/2.66 Following clause subsumed by 8 during input processing: 0 [] -element(A,positive_rationals)| -ordinal(A)|epsilon_connected(A).
% 2.47/2.66 ** KEPT (pick-wt=7): 18 [] -element(A,positive_rationals)| -ordinal(A)|natural(A).
% 2.47/2.66 ** KEPT (pick-wt=18): 19 [] -function(A)| -quasi_total(A,B,C)| -relation_of2(A,B,C)|element(function_image(B,C,A,D),powerset(C)).
% 2.47/2.66 ** KEPT (pick-wt=10): 20 [] -relation_of2_as_subset(A,B,C)|element(A,powerset(cartesian_product2(B,C))).
% 2.47/2.66 ** KEPT (pick-wt=10): 21 [] -relation(A)| -function(A)| -finite(B)|finite(relation_image(A,B)).
% 2.47/2.66 ** KEPT (pick-wt=8): 22 [] -finite(A)| -finite(B)|finite(cartesian_product2(A,B)).
% 2.47/2.66 ** KEPT (pick-wt=3): 23 [] -empty(powerset(A)).
% 2.47/2.66 ** KEPT (pick-wt=8): 24 [] empty(A)|empty(B)| -empty(cartesian_product2(A,B)).
% 2.47/2.66 ** KEPT (pick-wt=9): 25 [] -relation(A)| -function(A)| -transfinite_se_quence(A)|epsilon_transitive(relation_dom(A)).
% 2.47/2.66 ** KEPT (pick-wt=9): 26 [] -relation(A)| -function(A)| -transfinite_se_quence(A)|epsilon_connected(relation_dom(A)).
% 2.47/2.66 ** KEPT (pick-wt=9): 27 [] -relation(A)| -function(A)| -transfinite_se_quence(A)|ordinal(relation_dom(A)).
% 2.47/2.66 ** KEPT (pick-wt=7): 28 [] empty(A)| -relation(A)| -empty(relation_dom(A)).
% 2.47/2.66 ** KEPT (pick-wt=9): 29 [] -relation(A)| -relation_non_empty(A)| -function(A)|with_non_empty_elements(relation_rng(A)).
% 2.47/2.66 ** KEPT (pick-wt=7): 30 [] empty(A)| -relation(A)| -empty(relation_rng(A)).
% 2.47/2.66 ** KEPT (pick-wt=5): 31 [] -empty(A)|empty(relation_dom(A)).
% 2.47/2.66 ** KEPT (pick-wt=5): 32 [] -empty(A)|relation(relation_dom(A)).
% 2.47/2.66 ** KEPT (pick-wt=2): 33 [] -empty(positive_rationals).
% 2.47/2.66 ** KEPT (pick-wt=5): 34 [] -empty(A)|empty(relation_rng(A)).
% 2.47/2.66 ** KEPT (pick-wt=5): 35 [] -empty(A)|relation(relation_rng(A)).
% 2.47/2.66 ** KEPT (pick-wt=2): 36 [] -empty($c1).
% 2.47/2.66 ** KEPT (pick-wt=2): 37 [] -empty($c2).
% 2.47/2.66 ** KEPT (pick-wt=5): 38 [] empty(A)| -empty($f4(A)).
% 2.47/2.66 ** KEPT (pick-wt=2): 39 [] -empty($c9).
% 2.47/2.66 ** KEPT (pick-wt=2): 40 [] -empty($c13).
% 2.47/2.66 ** KEPT (pick-wt=2): 41 [] -empty($c14).
% 2.47/2.66 ** KEPT (pick-wt=5): 42 [] empty(A)| -empty($f7(A)).
% 2.47/2.66 ** KEPT (pick-wt=2): 43 [] -empty($c17).
% 2.47/2.66 ** KEPT (pick-wt=5): 44 [] empty(A)| -empty($f8(A)).
% 2.47/2.66 ** KEPT (pick-wt=19): 45 [] -function(A)| -quasi_total(A,B,C)| -relation_of2(A,B,C)|function_image(B,C,A,D)=relation_image(A,D).
% 2.47/2.66 ** KEPT (pick-wt=8): 46 [] -relation_of2_as_subset(A,B,C)|relation_of2(A,B,C).
% 2.47/2.66 ** KEPT (pick-wt=8): 47 [] relation_of2_as_subset(A,B,C)| -relation_of2(A,B,C).
% 2.47/2.66 ** KEPT (pick-wt=21): 48 [] -relation(A)| -function(A)|function_image(cartesian_product2(relation_dom(A),relation_rng(A)),relation_dom(A),first_projection_as_func_of(relation_dom(A),relation_rng(A)),A)=relation_dom(A).
% 2.47/2.66 ** KEPT (pick-wt=7): 49 [] -subset(A,B)| -finite(B)|finite(A).
% 2.47/2.66 Following clause subsumed by 21 during input processing: 0 [] -relation(A)| -function(A)| -finite(B)|finite(relation_image(A,B)).
% 2.47/2.66 Following clause subsumed by 22 during input processing: 0 [] -finite(A)| -finite(B)|finite(cartesian_product2(A,B)).
% 2.47/2.66 ** KEPT (pick-wt=6): 50 [] -in(A,B)|element(A,B).
% 2.47/2.66 ** KEPT (pick-wt=9): 51 [] -relation(A)|subset(A,cartesian_product2(relation_dom(A),relation_rng(A))).
% 2.47/2.66 ** KEPT (pick-wt=10): 52 [] -relation(A)| -function(A)| -finite(relation_dom(A))|finite(relation_rng(A)).
% 2.47/2.66 ** KEPT (pick-wt=5): 53 [] -finite(relation_dom($c22))| -finite($c22).
% 2.47/2.66 ** KEPT (pick-wt=8): 54 [] -element(A,B)|empty(B)|in(A,B).
% 2.47/2.66 ** KEPT (pick-wt=7): 55 [] -element(A,powerset(B))|subset(A,B).
% 2.47/2.66 ** KEPT (pick-wt=7): 56 [] element(A,powerset(B))| -subset(A,B).
% 2.47/2.66 ** KEPT (pick-wt=10): 57 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 2.47/2.66 ** KEPT (pick-wt=9): 58 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 2.47/2.66 ** KEPT (pick-wt=5): 59 [] -empty(A)|A=empty_set.
% 2.47/2.66 ** KEPT (pick-wt=5): 60 [] -in(A,B)| -empty(B).
% 2.47/2.66 ** KEPT (pick-wt=7): 61 [] -empty(A)|A=B| -empty(B).
% 2.47/2.66
% 2.47/2.66 ------------> process sos:
% 2.47/2.66 ** KEPT (pick-wt=3): 66 [] A=A.
% 2.47/2.66 ** KEPT (pick-wt=4): 67 [] relation(first_projection(A,B)).
% 2.47/2.66 ** KEPT (pick-wt=4): 68 [] function(first_projection(A,B)).
% 2.47/2.66 ** KEPT (pick-wt=4): 69 [] function(first_projection_as_func_of(A,B)).
% 2.47/2.66 ** KEPT (pick-wt=8): 70 [] quasi_total(first_projection_as_func_of(A,B),cartesian_product2(A,B),A).
% 2.47/2.66 ** KEPT (pick-wt=8): 71 [] relation_of2_as_subset(first_projection_as_func_of(A,B),cartesian_product2(A,B),A).
% 2.47/2.66 ** KEPT (pick-wt=6): 72 [] relation_of2($f1(A,B),A,B).
% 2.47/2.66 ** KEPT (pick-wt=4): 73 [] element($f2(A),A).
% 2.47/2.66 ** KEPT (pick-wt=6): 74 [] relation_of2_as_subset($f3(A,B),A,B).
% 2.47/2.66 ** KEPT (pick-wt=2): 75 [] empty(empty_set).
% 2.47/2.66 ** KEPT (pick-wt=2): 76 [] relation(empty_set).
% 2.47/2.66 ** KEPT (pick-wt=2): 77 [] relation_empty_yielding(empty_set).
% 2.47/2.66 Following clause subsumed by 75 during input processing: 0 [] empty(empty_set).
% 2.47/2.66 Following clause subsumed by 76 during input processing: 0 [] relation(empty_set).
% 2.47/2.66 Following clause subsumed by 77 during input processing: 0 [] relation_empty_yielding(empty_set).
% 2.47/2.66 ** KEPT (pick-wt=2): 78 [] function(empty_set).
% 2.47/2.66 ** KEPT (pick-wt=2): 79 [] one_to_one(empty_set).
% 2.47/2.66 Following clause subsumed by 75 during input processing: 0 [] empty(empty_set).
% 2.47/2.66 ** KEPT (pick-wt=2): 80 [] epsilon_transitive(empty_set).
% 2.47/2.66 ** KEPT (pick-wt=2): 81 [] epsilon_connected(empty_set).
% 2.47/2.66 ** KEPT (pick-wt=2): 82 [] ordinal(empty_set).
% 2.47/2.66 Following clause subsumed by 75 during input processing: 0 [] empty(empty_set).
% 2.47/2.66 Following clause subsumed by 76 during input processing: 0 [] relation(empty_set).
% 2.47/2.66 ** KEPT (pick-wt=2): 83 [] epsilon_transitive($c1).
% 2.47/2.66 ** KEPT (pick-wt=2): 84 [] epsilon_connected($c1).
% 2.47/2.66 ** KEPT (pick-wt=2): 85 [] ordinal($c1).
% 2.47/2.66 ** KEPT (pick-wt=2): 86 [] natural($c1).
% 2.47/2.66 ** KEPT (pick-wt=2): 87 [] finite($c2).
% 2.47/2.66 ** KEPT (pick-wt=2): 88 [] relation($c3).
% 2.47/2.66 ** KEPT (pick-wt=2): 89 [] function($c3).
% 2.47/2.66 ** KEPT (pick-wt=2): 90 [] function_yielding($c3).
% 2.47/2.66 ** KEPT (pick-wt=2): 91 [] relation($c4).
% 2.47/2.66 ** KEPT (pick-wt=2): 92 [] function($c4).
% 2.47/2.66 ** KEPT (pick-wt=2): 93 [] epsilon_transitive($c5).
% 2.47/2.66 ** KEPT (pick-wt=2): 94 [] epsilon_connected($c5).
% 2.47/2.66 ** KEPT (pick-wt=2): 95 [] ordinal($c5).
% 2.47/2.66 ** KEPT (pick-wt=2): 96 [] epsilon_transitive($c6).
% 2.47/2.66 ** KEPT (pick-wt=2): 97 [] epsilon_connected($c6).
% 2.47/2.66 ** KEPT (pick-wt=2): 98 [] ordinal($c6).
% 2.47/2.66 ** KEPT (pick-wt=2): 99 [] being_limit_ordinal($c6).
% 2.47/2.66 ** KEPT (pick-wt=2): 100 [] empty($c7).
% 2.47/2.66 ** KEPT (pick-wt=2): 101 [] relation($c7).
% 2.47/2.66 ** KEPT (pick-wt=7): 102 [] empty(A)|element($f4(A),powerset(A)).
% 2.47/2.66 ** KEPT (pick-wt=2): 103 [] empty($c8).
% 2.47/2.66 ** KEPT (pick-wt=3): 104 [] element($c9,positive_rationals).
% 2.47/2.66 ** KEPT (pick-wt=2): 105 [] epsilon_transitive($c9).
% 2.47/2.66 ** KEPT (pick-wt=2): 106 [] epsilon_connected($c9).
% 2.47/2.66 ** KEPT (pick-wt=2): 107 [] ordinal($c9).
% 2.47/2.66 ** KEPT (pick-wt=5): 108 [] element($f5(A),powerset(A)).
% 2.47/2.66 ** KEPT (pick-wt=3): 109 [] empty($f5(A)).
% 2.47/2.66 ** KEPT (pick-wt=3): 110 [] relation($f5(A)).
% 2.47/2.66 ** KEPT (pick-wt=3): 111 [] function($f5(A)).
% 2.47/2.66 ** KEPT (pick-wt=3): 112 [] one_to_one($f5(A)).
% 2.47/2.66 ** KEPT (pick-wt=3): 113 [] epsilon_transitive($f5(A)).
% 2.47/2.66 ** KEPT (pick-wt=3): 114 [] epsilon_connected($f5(A)).
% 2.47/2.66 ** KEPT (pick-wt=3): 115 [] ordinal($f5(A)).
% 2.47/2.66 ** KEPT (pick-wt=3): 116 [] natural($f5(A)).
% 2.47/2.66 ** KEPT (pick-wt=3): 117 [] finite($f5(A)).
% 2.47/2.66 ** KEPT (pick-wt=2): 118 [] relation($c10).
% 2.47/2.66 ** KEPT (pick-wt=2): 119 [] empty($c10).
% 2.47/2.66 ** KEPT (pick-wt=2): 120 [] function($c10).
% 2.47/2.66 ** KEPT (pick-wt=2): 121 [] relation($c11).
% 2.47/2.66 ** KEPT (pick-wt=2): 122 [] function($c11).
% 2.47/2.66 ** KEPT (pick-wt=2): 123 [] one_to_one($c11).
% 2.47/2.66 ** KEPT (pick-wt=2): 124 [] empty($c11).
% 2.47/2.66 ** KEPT (pick-wt=2): 125 [] epsilon_transitive($c11).
% 2.47/2.66 ** KEPT (pick-wt=2): 126 [] epsilon_connected($c11).
% 2.47/2.66 ** KEPT (pick-wt=2): 127 [] ordinal($c11).
% 2.47/2.66 ** KEPT (pick-wt=2): 128 [] relation($c12).
% 2.47/2.66 ** KEPT (pick-wt=2): 129 [] function($c12).
% 2.47/2.66 ** KEPT (pick-wt=2): 130 [] transfinite_se_quence($c12).
% 2.47/2.66 ** KEPT (pick-wt=2): 131 [] ordinal_yielding($c12).
% 2.47/2.66 ** KEPT (pick-wt=2): 132 [] relation($c13).
% 2.47/2.66 ** KEPT (pick-wt=5): 133 [] element($f6(A),powerset(A)).
% 2.47/2.66 ** KEPT (pick-wt=3): 134 [] empty($f6(A)).
% 2.47/2.66 ** KEPT (pick-wt=3): 135 [] element($c15,positive_rationals).
% 2.47/2.66 ** KEPT (pick-wt=2): 136 [] empty($c15).
% 2.47/2.66 ** KEPT (pick-wt=2): 137 [] epsilon_transitive($c15).
% 2.47/2.66 ** KEPT (pick-wt=2): 138 [] epsilon_connected($c15).
% 2.47/2.66 ** KEPT (pick-wt=2): 139 [] ordinal($c15).
% 2.47/2.66 ** KEPT (pick-wt=2): 140 [] natural($c15).
% 2.47/2.66 ** KEPT (pick-wt=7): 141 [] empty(A)|element($f7(A),powerset(A)).
% 2.47/2.66 ** KEPT (pick-wt=5): 142 [] empty(A)|finite($f7(A)).
% 2.47/2.66 ** KEPT (pick-wt=2): 143 [] relation($c16).
% 2.47/2.66 ** KEPT (pick-wt=2): 144 [] function($c16).
% 2.47/2.66 ** KEPT (pick-wt=2): 145 [] one_to_one($c16).
% 2.47/2.66 ** KEPT (pick-wt=2): 146 [] epsilon_transitive($c17).
% 2.47/2.66 ** KEPT (pick-wt=2): 147 [] epsilon_connected($c17).
% 2.47/2.66 ** KEPT (pick-wt=2): 148 [] ordinal($c17).
% 2.47/2.66 ** KEPT (pick-wt=2): 149 [] relation($c18).
% 2.47/2.66 ** KEPT (pick-wt=2): 150 [] relation_empty_yielding($c18).
% 2.47/2.66 ** KEPT (pick-wt=7): 151 [] empty(A)|element($f8(A),powerset(A)).
% 2.47/2.66 ** KEPT (pick-wt=5): 152 [] empty(A)|finite($f8(A)).
% 2.47/2.66 ** KEPT (pick-wt=2): 153 [] relation($c19).
% 2.47/2.66 ** KEPT (pick-wt=2): 154 [] relation_empty_yielding($c19).
% 2.47/2.66 ** KEPT (pick-wt=2): 155 [] function($c19).
% 2.47/2.66 ** KEPT (pick-wt=2): 156 [] relation($c20).
% 2.47/2.66 ** KEPT (pick-wt=2): 157 [] function($c20).
% 2.47/2.66 ** KEPT (pick-wt=2): 158 [] transfinite_se_quence($c20).
% 2.47/2.66 ** KEPT (pick-wt=2): 159 [] relation($c21).
% 2.47/2.66 ** KEPT (pick-wt=2): 160 [] relation_non_empty($c21).
% 2.47/2.66 ** KEPT (pick-wt=2): 161 [] function($c21).
% 2.47/2.66 ** KEPT (pick-wt=7): 162 [] first_projection_as_func_of(A,B)=first_projection(A,B).
% 2.47/2.66 ---> New Demodulator: 163 [new_demod,162] first_projection_as_func_of(A,B)=first_projection(A,B).
% 2.47/2.66 ** KEPT (pick-wt=3): 164 [] subset(A,A).
% 2.47/2.66 ** KEPT (pick-wt=2): 165 [] relation($c22).
% 2.47/2.66 ** KEPT (pick-wt=2): 166 [] function($c22).
% 2.47/2.66 ** KEPT (pick-wt=5): 167 [] finite(relation_dom($c22))|finite($c22).
% 2.47/2.66 Following clause subsumed by 66 during input processing: 0 [copy,66,flip.1] A=A.
% 2.47/2.66 66 back subsumes 65.
% 2.47/2.66 >>>> Starting back demodulation with 163.
% 2.47/2.66 >> back demodulating 71 with 163.
% 18.79/18.93 >> back demodulating 70 with 163.
% 18.79/18.93 >> back demodulating 69 with 163.
% 18.79/18.93 >> back demodulating 48 with 163.
% 18.79/18.93
% 18.79/18.93 ======= end of input processing =======
% 18.79/18.93
% 18.79/18.93 =========== start of search ===========
% 18.79/18.93
% 18.79/18.93
% 18.79/18.93 Resetting weight limit to 4.
% 18.79/18.93
% 18.79/18.93
% 18.79/18.93 Resetting weight limit to 4.
% 18.79/18.93
% 18.79/18.93 sos_size=677
% 18.79/18.93
% 18.79/18.93 Search stopped because sos empty.
% 18.79/18.93
% 18.79/18.93
% 18.79/18.93 Search stopped because sos empty.
% 18.79/18.93
% 18.79/18.93 ============ end of search ============
% 18.79/18.93
% 18.79/18.93 -------------- statistics -------------
% 18.79/18.93 clauses given 886
% 18.79/18.93 clauses generated 2475287
% 18.79/18.93 clauses kept 1044
% 18.79/18.93 clauses forward subsumed 1710
% 18.79/18.93 clauses back subsumed 58
% 18.79/18.93 Kbytes malloced 6835
% 18.79/18.93
% 18.79/18.93 ----------- times (seconds) -----------
% 18.79/18.93 user CPU time 16.28 (0 hr, 0 min, 16 sec)
% 18.79/18.93 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 18.79/18.93 wall-clock time 19 (0 hr, 0 min, 19 sec)
% 18.79/18.93
% 18.79/18.93 Process 6387 finished Wed Jul 27 07:29:59 2022
% 18.79/18.93 Otter interrupted
% 18.79/18.93 PROOF NOT FOUND
%------------------------------------------------------------------------------