TSTP Solution File: SEU096+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU096+1 : TPTP v8.1.0. Released v3.2.0.
% 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 13:14:46 EDT 2022
% Result : Theorem 2.04s 2.25s
% Output : Refutation 2.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 7
% Syntax : Number of clauses : 10 ( 8 unt; 0 nHn; 10 RR)
% Number of literals : 16 ( 2 equ; 7 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 4 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(18,axiom,
( ~ relation(A)
| ~ function(A)
| ~ finite(B)
| finite(relation_image(A,B)) ),
file('SEU096+1.p',unknown),
[] ).
cnf(33,axiom,
( ~ relation(A)
| ~ function(A)
| ~ subset(B,relation_rng(A))
| relation_image(A,relation_inverse_image(A,B)) = B ),
file('SEU096+1.p',unknown),
[] ).
cnf(35,axiom,
~ finite(dollar_c23),
file('SEU096+1.p',unknown),
[] ).
cnf(134,axiom,
relation(dollar_c22),
file('SEU096+1.p',unknown),
[] ).
cnf(135,axiom,
function(dollar_c22),
file('SEU096+1.p',unknown),
[] ).
cnf(136,axiom,
subset(dollar_c23,relation_rng(dollar_c22)),
file('SEU096+1.p',unknown),
[] ).
cnf(137,axiom,
finite(relation_inverse_image(dollar_c22,dollar_c23)),
file('SEU096+1.p',unknown),
[] ).
cnf(363,plain,
relation_image(dollar_c22,relation_inverse_image(dollar_c22,dollar_c23)) = dollar_c23,
inference(hyper,[status(thm)],[136,33,134,135]),
[iquote('hyper,136,33,134,135')] ).
cnf(371,plain,
finite(dollar_c23),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[137,18,134,135]),363]),
[iquote('hyper,137,18,134,135,demod,363')] ).
cnf(372,plain,
$false,
inference(binary,[status(thm)],[371,35]),
[iquote('binary,371.1,35.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU096+1 : TPTP v8.1.0. Released v3.2.0.
% 0.10/0.12 % 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 07:53:01 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.04/2.24 ----- Otter 3.3f, August 2004 -----
% 2.04/2.24 The process was started by sandbox on n018.cluster.edu,
% 2.04/2.24 Wed Jul 27 07:53:01 2022
% 2.04/2.24 The command was "./otter". The process ID is 27120.
% 2.04/2.24
% 2.04/2.24 set(prolog_style_variables).
% 2.04/2.24 set(auto).
% 2.04/2.24 dependent: set(auto1).
% 2.04/2.24 dependent: set(process_input).
% 2.04/2.24 dependent: clear(print_kept).
% 2.04/2.24 dependent: clear(print_new_demod).
% 2.04/2.24 dependent: clear(print_back_demod).
% 2.04/2.24 dependent: clear(print_back_sub).
% 2.04/2.24 dependent: set(control_memory).
% 2.04/2.24 dependent: assign(max_mem, 12000).
% 2.04/2.24 dependent: assign(pick_given_ratio, 4).
% 2.04/2.24 dependent: assign(stats_level, 1).
% 2.04/2.24 dependent: assign(max_seconds, 10800).
% 2.04/2.24 clear(print_given).
% 2.04/2.24
% 2.04/2.24 formula_list(usable).
% 2.04/2.24 all A (A=A).
% 2.04/2.24 all A B (in(A,B)-> -in(B,A)).
% 2.04/2.24 all A (ordinal(A)-> (all B (element(B,A)->epsilon_transitive(B)&epsilon_connected(B)&ordinal(B)))).
% 2.04/2.24 all A (empty(A)->finite(A)).
% 2.04/2.24 all A (empty(A)->function(A)).
% 2.04/2.24 all A (ordinal(A)->epsilon_transitive(A)&epsilon_connected(A)).
% 2.04/2.24 all A (empty(A)->relation(A)).
% 2.04/2.24 all A (empty(A)&ordinal(A)->epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)&natural(A)).
% 2.04/2.24 all A (finite(A)-> (all B (element(B,powerset(A))->finite(B)))).
% 2.04/2.24 all A (relation(A)&empty(A)&function(A)->relation(A)&function(A)&one_to_one(A)).
% 2.04/2.24 all A (epsilon_transitive(A)&epsilon_connected(A)->ordinal(A)).
% 2.04/2.24 all A (empty(A)->epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)).
% 2.04/2.24 all A (element(A,positive_rationals)-> (ordinal(A)->epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)&natural(A))).
% 2.04/2.24 all A exists B element(B,A).
% 2.04/2.24 empty(empty_set).
% 2.04/2.24 relation(empty_set).
% 2.04/2.24 relation_empty_yielding(empty_set).
% 2.04/2.24 all A B (relation(A)&function(A)&finite(B)->finite(relation_image(A,B))).
% 2.04/2.24 all A (-empty(powerset(A))).
% 2.04/2.24 empty(empty_set).
% 2.04/2.24 relation(empty_set).
% 2.04/2.24 relation_empty_yielding(empty_set).
% 2.04/2.24 function(empty_set).
% 2.04/2.24 one_to_one(empty_set).
% 2.04/2.24 empty(empty_set).
% 2.04/2.24 epsilon_transitive(empty_set).
% 2.04/2.24 epsilon_connected(empty_set).
% 2.04/2.24 ordinal(empty_set).
% 2.04/2.24 empty(empty_set).
% 2.04/2.24 relation(empty_set).
% 2.04/2.24 all A (relation(A)&relation_non_empty(A)&function(A)->with_non_empty_elements(relation_rng(A))).
% 2.04/2.24 all A (-empty(A)&relation(A)-> -empty(relation_rng(A))).
% 2.04/2.24 -empty(positive_rationals).
% 2.04/2.24 all A (empty(A)->empty(relation_rng(A))&relation(relation_rng(A))).
% 2.04/2.24 exists A (-empty(A)&epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)&natural(A)).
% 2.04/2.24 exists A (-empty(A)&finite(A)).
% 2.04/2.24 exists A (relation(A)&function(A)&function_yielding(A)).
% 2.04/2.24 exists A (relation(A)&function(A)).
% 2.04/2.24 exists A (epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)).
% 2.04/2.24 exists A (epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)&being_limit_ordinal(A)).
% 2.04/2.24 exists A (empty(A)&relation(A)).
% 2.04/2.24 all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)))).
% 2.04/2.24 exists A empty(A).
% 2.04/2.24 exists A (element(A,positive_rationals)& -empty(A)&epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)).
% 2.04/2.24 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)).
% 2.04/2.24 exists A (relation(A)&empty(A)&function(A)).
% 2.04/2.24 exists A (relation(A)&function(A)&one_to_one(A)&empty(A)&epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)).
% 2.04/2.24 exists A (relation(A)&function(A)&transfinite_se_quence(A)&ordinal_yielding(A)).
% 2.04/2.24 exists A (-empty(A)&relation(A)).
% 2.04/2.24 all A exists B (element(B,powerset(A))&empty(B)).
% 2.04/2.24 exists A (-empty(A)).
% 2.04/2.24 exists A (element(A,positive_rationals)&empty(A)&epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)&natural(A)).
% 2.04/2.24 all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)&finite(B)))).
% 2.04/2.24 exists A (relation(A)&function(A)&one_to_one(A)).
% 2.04/2.24 exists A (-empty(A)&epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)).
% 2.04/2.24 exists A (relation(A)&relation_empty_yielding(A)).
% 2.04/2.24 exists A (relation(A)&relation_empty_yielding(A)&function(A)).
% 2.04/2.24 exists A (relation(A)&function(A)&transfinite_se_quence(A)).
% 2.04/2.24 exists A (relation(A)&relation_non_empty(A)&function(A)).
% 2.04/2.24 all A B subset(A,A).
% 2.04/2.24 all A B (relation(B)&function(B)-> (subset(A,relation_rng(B))->relation_image(B,relation_inverse_image(B,A))=A)).
% 2.04/2.24 all A B (relation(B)&function(B)-> (finite(A)->finite(relation_image(B,A)))).
% 2.04/2.24 all A B (in(A,B)->element(A,B)).
% 2.04/2.24 -(all A B (relation(B)&function(B)-> (subset(A,relation_rng(B))&finite(relation_inverse_image(B,A))->finite(A)))).
% 2.04/2.24 all A B (element(A,B)->empty(B)|in(A,B)).
% 2.04/2.24 all A B (element(A,powerset(B))<->subset(A,B)).
% 2.04/2.24 all A B C (in(A,B)&element(B,powerset(C))->element(A,C)).
% 2.04/2.24 all A B C (-(in(A,B)&element(B,powerset(C))&empty(C))).
% 2.04/2.24 all A (empty(A)->A=empty_set).
% 2.04/2.24 all A B (-(in(A,B)&empty(B))).
% 2.04/2.24 all A B (-(empty(A)&A!=B&empty(B))).
% 2.04/2.24 end_of_list.
% 2.04/2.24
% 2.04/2.24 -------> usable clausifies to:
% 2.04/2.24
% 2.04/2.24 list(usable).
% 2.04/2.24 0 [] A=A.
% 2.04/2.24 0 [] -in(A,B)| -in(B,A).
% 2.04/2.24 0 [] -ordinal(A)| -element(B,A)|epsilon_transitive(B).
% 2.04/2.24 0 [] -ordinal(A)| -element(B,A)|epsilon_connected(B).
% 2.04/2.24 0 [] -ordinal(A)| -element(B,A)|ordinal(B).
% 2.04/2.24 0 [] -empty(A)|finite(A).
% 2.04/2.24 0 [] -empty(A)|function(A).
% 2.04/2.24 0 [] -ordinal(A)|epsilon_transitive(A).
% 2.04/2.24 0 [] -ordinal(A)|epsilon_connected(A).
% 2.04/2.24 0 [] -empty(A)|relation(A).
% 2.04/2.24 0 [] -empty(A)| -ordinal(A)|epsilon_transitive(A).
% 2.04/2.24 0 [] -empty(A)| -ordinal(A)|epsilon_connected(A).
% 2.04/2.24 0 [] -empty(A)| -ordinal(A)|natural(A).
% 2.04/2.24 0 [] -finite(A)| -element(B,powerset(A))|finite(B).
% 2.04/2.24 0 [] -relation(A)| -empty(A)| -function(A)|one_to_one(A).
% 2.04/2.24 0 [] -epsilon_transitive(A)| -epsilon_connected(A)|ordinal(A).
% 2.04/2.24 0 [] -empty(A)|epsilon_transitive(A).
% 2.04/2.24 0 [] -empty(A)|epsilon_connected(A).
% 2.04/2.24 0 [] -empty(A)|ordinal(A).
% 2.04/2.24 0 [] -element(A,positive_rationals)| -ordinal(A)|epsilon_transitive(A).
% 2.04/2.24 0 [] -element(A,positive_rationals)| -ordinal(A)|epsilon_connected(A).
% 2.04/2.24 0 [] -element(A,positive_rationals)| -ordinal(A)|natural(A).
% 2.04/2.24 0 [] element($f1(A),A).
% 2.04/2.24 0 [] empty(empty_set).
% 2.04/2.24 0 [] relation(empty_set).
% 2.04/2.24 0 [] relation_empty_yielding(empty_set).
% 2.04/2.24 0 [] -relation(A)| -function(A)| -finite(B)|finite(relation_image(A,B)).
% 2.04/2.24 0 [] -empty(powerset(A)).
% 2.04/2.24 0 [] empty(empty_set).
% 2.04/2.24 0 [] relation(empty_set).
% 2.04/2.24 0 [] relation_empty_yielding(empty_set).
% 2.04/2.24 0 [] function(empty_set).
% 2.04/2.24 0 [] one_to_one(empty_set).
% 2.04/2.24 0 [] empty(empty_set).
% 2.04/2.24 0 [] epsilon_transitive(empty_set).
% 2.04/2.24 0 [] epsilon_connected(empty_set).
% 2.04/2.24 0 [] ordinal(empty_set).
% 2.04/2.24 0 [] empty(empty_set).
% 2.04/2.24 0 [] relation(empty_set).
% 2.04/2.24 0 [] -relation(A)| -relation_non_empty(A)| -function(A)|with_non_empty_elements(relation_rng(A)).
% 2.04/2.24 0 [] empty(A)| -relation(A)| -empty(relation_rng(A)).
% 2.04/2.24 0 [] -empty(positive_rationals).
% 2.04/2.24 0 [] -empty(A)|empty(relation_rng(A)).
% 2.04/2.24 0 [] -empty(A)|relation(relation_rng(A)).
% 2.04/2.24 0 [] -empty($c1).
% 2.04/2.24 0 [] epsilon_transitive($c1).
% 2.04/2.24 0 [] epsilon_connected($c1).
% 2.04/2.24 0 [] ordinal($c1).
% 2.04/2.24 0 [] natural($c1).
% 2.04/2.24 0 [] -empty($c2).
% 2.04/2.24 0 [] finite($c2).
% 2.04/2.24 0 [] relation($c3).
% 2.04/2.24 0 [] function($c3).
% 2.04/2.24 0 [] function_yielding($c3).
% 2.04/2.24 0 [] relation($c4).
% 2.04/2.24 0 [] function($c4).
% 2.04/2.24 0 [] epsilon_transitive($c5).
% 2.04/2.24 0 [] epsilon_connected($c5).
% 2.04/2.24 0 [] ordinal($c5).
% 2.04/2.24 0 [] epsilon_transitive($c6).
% 2.04/2.24 0 [] epsilon_connected($c6).
% 2.04/2.24 0 [] ordinal($c6).
% 2.04/2.24 0 [] being_limit_ordinal($c6).
% 2.04/2.24 0 [] empty($c7).
% 2.04/2.24 0 [] relation($c7).
% 2.04/2.24 0 [] empty(A)|element($f2(A),powerset(A)).
% 2.04/2.24 0 [] empty(A)| -empty($f2(A)).
% 2.04/2.24 0 [] empty($c8).
% 2.04/2.24 0 [] element($c9,positive_rationals).
% 2.04/2.24 0 [] -empty($c9).
% 2.04/2.24 0 [] epsilon_transitive($c9).
% 2.04/2.24 0 [] epsilon_connected($c9).
% 2.04/2.24 0 [] ordinal($c9).
% 2.04/2.24 0 [] element($f3(A),powerset(A)).
% 2.04/2.24 0 [] empty($f3(A)).
% 2.04/2.24 0 [] relation($f3(A)).
% 2.04/2.24 0 [] function($f3(A)).
% 2.04/2.24 0 [] one_to_one($f3(A)).
% 2.04/2.24 0 [] epsilon_transitive($f3(A)).
% 2.04/2.24 0 [] epsilon_connected($f3(A)).
% 2.04/2.24 0 [] ordinal($f3(A)).
% 2.04/2.24 0 [] natural($f3(A)).
% 2.04/2.24 0 [] finite($f3(A)).
% 2.04/2.24 0 [] relation($c10).
% 2.04/2.24 0 [] empty($c10).
% 2.04/2.24 0 [] function($c10).
% 2.04/2.24 0 [] relation($c11).
% 2.04/2.24 0 [] function($c11).
% 2.04/2.24 0 [] one_to_one($c11).
% 2.04/2.24 0 [] empty($c11).
% 2.04/2.24 0 [] epsilon_transitive($c11).
% 2.04/2.24 0 [] epsilon_connected($c11).
% 2.04/2.24 0 [] ordinal($c11).
% 2.04/2.24 0 [] relation($c12).
% 2.04/2.24 0 [] function($c12).
% 2.04/2.24 0 [] transfinite_se_quence($c12).
% 2.04/2.24 0 [] ordinal_yielding($c12).
% 2.04/2.24 0 [] -empty($c13).
% 2.04/2.24 0 [] relation($c13).
% 2.04/2.24 0 [] element($f4(A),powerset(A)).
% 2.04/2.24 0 [] empty($f4(A)).
% 2.04/2.24 0 [] -empty($c14).
% 2.04/2.24 0 [] element($c15,positive_rationals).
% 2.04/2.24 0 [] empty($c15).
% 2.04/2.24 0 [] epsilon_transitive($c15).
% 2.04/2.24 0 [] epsilon_connected($c15).
% 2.04/2.24 0 [] ordinal($c15).
% 2.04/2.24 0 [] natural($c15).
% 2.04/2.24 0 [] empty(A)|element($f5(A),powerset(A)).
% 2.04/2.24 0 [] empty(A)| -empty($f5(A)).
% 2.04/2.24 0 [] empty(A)|finite($f5(A)).
% 2.04/2.24 0 [] relation($c16).
% 2.04/2.24 0 [] function($c16).
% 2.04/2.24 0 [] one_to_one($c16).
% 2.04/2.24 0 [] -empty($c17).
% 2.04/2.24 0 [] epsilon_transitive($c17).
% 2.04/2.24 0 [] epsilon_connected($c17).
% 2.04/2.24 0 [] ordinal($c17).
% 2.04/2.24 0 [] relation($c18).
% 2.04/2.24 0 [] relation_empty_yielding($c18).
% 2.04/2.24 0 [] relation($c19).
% 2.04/2.24 0 [] relation_empty_yielding($c19).
% 2.04/2.24 0 [] function($c19).
% 2.04/2.24 0 [] relation($c20).
% 2.04/2.24 0 [] function($c20).
% 2.04/2.24 0 [] transfinite_se_quence($c20).
% 2.04/2.24 0 [] relation($c21).
% 2.04/2.24 0 [] relation_non_empty($c21).
% 2.04/2.24 0 [] function($c21).
% 2.04/2.24 0 [] subset(A,A).
% 2.04/2.24 0 [] -relation(B)| -function(B)| -subset(A,relation_rng(B))|relation_image(B,relation_inverse_image(B,A))=A.
% 2.04/2.24 0 [] -relation(B)| -function(B)| -finite(A)|finite(relation_image(B,A)).
% 2.04/2.24 0 [] -in(A,B)|element(A,B).
% 2.04/2.24 0 [] relation($c22).
% 2.04/2.24 0 [] function($c22).
% 2.04/2.24 0 [] subset($c23,relation_rng($c22)).
% 2.04/2.24 0 [] finite(relation_inverse_image($c22,$c23)).
% 2.04/2.24 0 [] -finite($c23).
% 2.04/2.24 0 [] -element(A,B)|empty(B)|in(A,B).
% 2.04/2.24 0 [] -element(A,powerset(B))|subset(A,B).
% 2.04/2.24 0 [] element(A,powerset(B))| -subset(A,B).
% 2.04/2.24 0 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 2.04/2.24 0 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 2.04/2.24 0 [] -empty(A)|A=empty_set.
% 2.04/2.24 0 [] -in(A,B)| -empty(B).
% 2.04/2.24 0 [] -empty(A)|A=B| -empty(B).
% 2.04/2.24 end_of_list.
% 2.04/2.24
% 2.04/2.24 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 2.04/2.24
% 2.04/2.24 This ia a non-Horn set with equality. The strategy will be
% 2.04/2.24 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.04/2.24 deletion, with positive clauses in sos and nonpositive
% 2.04/2.24 clauses in usable.
% 2.04/2.24
% 2.04/2.24 dependent: set(knuth_bendix).
% 2.04/2.24 dependent: set(anl_eq).
% 2.04/2.24 dependent: set(para_from).
% 2.04/2.24 dependent: set(para_into).
% 2.04/2.24 dependent: clear(para_from_right).
% 2.04/2.24 dependent: clear(para_into_right).
% 2.04/2.24 dependent: set(para_from_vars).
% 2.04/2.24 dependent: set(eq_units_both_ways).
% 2.04/2.24 dependent: set(dynamic_demod_all).
% 2.04/2.24 dependent: set(dynamic_demod).
% 2.04/2.24 dependent: set(order_eq).
% 2.04/2.24 dependent: set(back_demod).
% 2.04/2.24 dependent: set(lrpo).
% 2.04/2.24 dependent: set(hyper_res).
% 2.04/2.24 dependent: set(unit_deletion).
% 2.04/2.24 dependent: set(factor).
% 2.04/2.24
% 2.04/2.24 ------------> process usable:
% 2.04/2.24 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 2.04/2.24 ** KEPT (pick-wt=7): 2 [] -ordinal(A)| -element(B,A)|epsilon_transitive(B).
% 2.04/2.24 ** KEPT (pick-wt=7): 3 [] -ordinal(A)| -element(B,A)|epsilon_connected(B).
% 2.04/2.24 ** KEPT (pick-wt=7): 4 [] -ordinal(A)| -element(B,A)|ordinal(B).
% 2.04/2.24 ** KEPT (pick-wt=4): 5 [] -empty(A)|finite(A).
% 2.04/2.24 ** KEPT (pick-wt=4): 6 [] -empty(A)|function(A).
% 2.04/2.24 ** KEPT (pick-wt=4): 7 [] -ordinal(A)|epsilon_transitive(A).
% 2.04/2.24 ** KEPT (pick-wt=4): 8 [] -ordinal(A)|epsilon_connected(A).
% 2.04/2.24 ** KEPT (pick-wt=4): 9 [] -empty(A)|relation(A).
% 2.04/2.24 Following clause subsumed by 7 during input processing: 0 [] -empty(A)| -ordinal(A)|epsilon_transitive(A).
% 2.04/2.24 Following clause subsumed by 8 during input processing: 0 [] -empty(A)| -ordinal(A)|epsilon_connected(A).
% 2.04/2.24 ** KEPT (pick-wt=6): 10 [] -empty(A)| -ordinal(A)|natural(A).
% 2.04/2.24 ** KEPT (pick-wt=8): 11 [] -finite(A)| -element(B,powerset(A))|finite(B).
% 2.04/2.24 ** KEPT (pick-wt=8): 12 [] -relation(A)| -empty(A)| -function(A)|one_to_one(A).
% 2.04/2.24 ** KEPT (pick-wt=6): 13 [] -epsilon_transitive(A)| -epsilon_connected(A)|ordinal(A).
% 2.04/2.24 ** KEPT (pick-wt=4): 14 [] -empty(A)|epsilon_transitive(A).
% 2.04/2.24 ** KEPT (pick-wt=4): 15 [] -empty(A)|epsilon_connected(A).
% 2.04/2.24 ** KEPT (pick-wt=4): 16 [] -empty(A)|ordinal(A).
% 2.04/2.24 Following clause subsumed by 7 during input processing: 0 [] -element(A,positive_rationals)| -ordinal(A)|epsilon_transitive(A).
% 2.04/2.24 Following clause subsumed by 8 during input processing: 0 [] -element(A,positive_rationals)| -ordinal(A)|epsilon_connected(A).
% 2.04/2.24 ** KEPT (pick-wt=7): 17 [] -element(A,positive_rationals)| -ordinal(A)|natural(A).
% 2.04/2.24 ** KEPT (pick-wt=10): 18 [] -relation(A)| -function(A)| -finite(B)|finite(relation_image(A,B)).
% 2.04/2.24 ** KEPT (pick-wt=3): 19 [] -empty(powerset(A)).
% 2.04/2.24 ** KEPT (pick-wt=9): 20 [] -relation(A)| -relation_non_empty(A)| -function(A)|with_non_empty_elements(relation_rng(A)).
% 2.04/2.24 ** KEPT (pick-wt=7): 21 [] empty(A)| -relation(A)| -empty(relation_rng(A)).
% 2.04/2.24 ** KEPT (pick-wt=2): 22 [] -empty(positive_rationals).
% 2.04/2.24 ** KEPT (pick-wt=5): 23 [] -empty(A)|empty(relation_rng(A)).
% 2.04/2.24 ** KEPT (pick-wt=5): 24 [] -empty(A)|relation(relation_rng(A)).
% 2.04/2.24 ** KEPT (pick-wt=2): 25 [] -empty($c1).
% 2.04/2.24 ** KEPT (pick-wt=2): 26 [] -empty($c2).
% 2.04/2.24 ** KEPT (pick-wt=5): 27 [] empty(A)| -empty($f2(A)).
% 2.04/2.24 ** KEPT (pick-wt=2): 28 [] -empty($c9).
% 2.04/2.24 ** KEPT (pick-wt=2): 29 [] -empty($c13).
% 2.04/2.24 ** KEPT (pick-wt=2): 30 [] -empty($c14).
% 2.04/2.24 ** KEPT (pick-wt=5): 31 [] empty(A)| -empty($f5(A)).
% 2.04/2.24 ** KEPT (pick-wt=2): 32 [] -empty($c17).
% 2.04/2.24 ** KEPT (pick-wt=15): 33 [] -relation(A)| -function(A)| -subset(B,relation_rng(A))|relation_image(A,relation_inverse_image(A,B))=B.
% 2.04/2.24 Following clause subsumed by 18 during input processing: 0 [] -relation(A)| -function(A)| -finite(B)|finite(relation_image(A,B)).
% 2.04/2.24 ** KEPT (pick-wt=6): 34 [] -in(A,B)|element(A,B).
% 2.04/2.24 ** KEPT (pick-wt=2): 35 [] -finite($c23).
% 2.04/2.24 ** KEPT (pick-wt=8): 36 [] -element(A,B)|empty(B)|in(A,B).
% 2.04/2.24 ** KEPT (pick-wt=7): 37 [] -element(A,powerset(B))|subset(A,B).
% 2.04/2.24 ** KEPT (pick-wt=7): 38 [] element(A,powerset(B))| -subset(A,B).
% 2.04/2.24 ** KEPT (pick-wt=10): 39 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 2.04/2.24 ** KEPT (pick-wt=9): 40 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 2.04/2.24 ** KEPT (pick-wt=5): 41 [] -empty(A)|A=empty_set.
% 2.04/2.24 ** KEPT (pick-wt=5): 42 [] -in(A,B)| -empty(B).
% 2.04/2.24 ** KEPT (pick-wt=7): 43 [] -empty(A)|A=B| -empty(B).
% 2.04/2.24
% 2.04/2.24 ------------> process sos:
% 2.04/2.24 ** KEPT (pick-wt=3): 46 [] A=A.
% 2.04/2.24 ** KEPT (pick-wt=4): 47 [] element($f1(A),A).
% 2.04/2.24 ** KEPT (pick-wt=2): 48 [] empty(empty_set).
% 2.04/2.24 ** KEPT (pick-wt=2): 49 [] relation(empty_set).
% 2.04/2.24 ** KEPT (pick-wt=2): 50 [] relation_empty_yielding(empty_set).
% 2.04/2.24 Following clause subsumed by 48 during input processing: 0 [] empty(empty_set).
% 2.04/2.24 Following clause subsumed by 49 during input processing: 0 [] relation(empty_set).
% 2.04/2.24 Following clause subsumed by 50 during input processing: 0 [] relation_empty_yielding(empty_set).
% 2.04/2.24 ** KEPT (pick-wt=2): 51 [] function(empty_set).
% 2.04/2.24 ** KEPT (pick-wt=2): 52 [] one_to_one(empty_set).
% 2.04/2.24 Following clause subsumed by 48 during input processing: 0 [] empty(empty_set).
% 2.04/2.24 ** KEPT (pick-wt=2): 53 [] epsilon_transitive(empty_set).
% 2.04/2.24 ** KEPT (pick-wt=2): 54 [] epsilon_connected(empty_set).
% 2.04/2.24 ** KEPT (pick-wt=2): 55 [] ordinal(empty_set).
% 2.04/2.24 Following clause subsumed by 48 during input processing: 0 [] empty(empty_set).
% 2.04/2.24 Following clause subsumed by 49 during input processing: 0 [] relation(empty_set).
% 2.04/2.24 ** KEPT (pick-wt=2): 56 [] epsilon_transitive($c1).
% 2.04/2.24 ** KEPT (pick-wt=2): 57 [] epsilon_connected($c1).
% 2.04/2.24 ** KEPT (pick-wt=2): 58 [] ordinal($c1).
% 2.04/2.24 ** KEPT (pick-wt=2): 59 [] natural($c1).
% 2.04/2.24 ** KEPT (pick-wt=2): 60 [] finite($c2).
% 2.04/2.24 ** KEPT (pick-wt=2): 61 [] relation($c3).
% 2.04/2.24 ** KEPT (pick-wt=2): 62 [] function($c3).
% 2.04/2.24 ** KEPT (pick-wt=2): 63 [] function_yielding($c3).
% 2.04/2.24 ** KEPT (pick-wt=2): 64 [] relation($c4).
% 2.04/2.24 ** KEPT (pick-wt=2): 65 [] function($c4).
% 2.04/2.24 ** KEPT (pick-wt=2): 66 [] epsilon_transitive($c5).
% 2.04/2.24 ** KEPT (pick-wt=2): 67 [] epsilon_connected($c5).
% 2.04/2.24 ** KEPT (pick-wt=2): 68 [] ordinal($c5).
% 2.04/2.24 ** KEPT (pick-wt=2): 69 [] epsilon_transitive($c6).
% 2.04/2.24 ** KEPT (pick-wt=2): 70 [] epsilon_connected($c6).
% 2.04/2.24 ** KEPT (pick-wt=2): 71 [] ordinal($c6).
% 2.04/2.24 ** KEPT (pick-wt=2): 72 [] being_limit_ordinal($c6).
% 2.04/2.24 ** KEPT (pick-wt=2): 73 [] empty($c7).
% 2.04/2.24 ** KEPT (pick-wt=2): 74 [] relation($c7).
% 2.04/2.24 ** KEPT (pick-wt=7): 75 [] empty(A)|element($f2(A),powerset(A)).
% 2.04/2.24 ** KEPT (pick-wt=2): 76 [] empty($c8).
% 2.04/2.24 ** KEPT (pick-wt=3): 77 [] element($c9,positive_rationals).
% 2.04/2.24 ** KEPT (pick-wt=2): 78 [] epsilon_transitive($c9).
% 2.04/2.24 ** KEPT (pick-wt=2): 79 [] epsilon_connected($c9).
% 2.04/2.24 ** KEPT (pick-wt=2): 80 [] ordinal($c9).
% 2.04/2.24 ** KEPT (pick-wt=5): 81 [] element($f3(A),powerset(A)).
% 2.04/2.24 ** KEPT (pick-wt=3): 82 [] empty($f3(A)).
% 2.04/2.24 ** KEPT (pick-wt=3): 83 [] relation($f3(A)).
% 2.04/2.24 ** KEPT (pick-wt=3): 84 [] function($f3(A)).
% 2.04/2.24 ** KEPT (pick-wt=3): 85 [] one_to_one($f3(A)).
% 2.04/2.24 ** KEPT (pick-wt=3): 86 [] epsilon_transitive($f3(A)).
% 2.04/2.24 ** KEPT (pick-wt=3): 87 [] epsilon_connected($f3(A)).
% 2.04/2.24 ** KEPT (pick-wt=3): 88 [] ordinal($f3(A)).
% 2.04/2.24 ** KEPT (pick-wt=3): 89 [] natural($f3(A)).
% 2.04/2.24 ** KEPT (pick-wt=3): 90 [] finite($f3(A)).
% 2.04/2.24 ** KEPT (pick-wt=2): 91 [] relation($c10).
% 2.04/2.24 ** KEPT (pick-wt=2): 92 [] empty($c10).
% 2.04/2.24 ** KEPT (pick-wt=2): 93 [] function($c10).
% 2.04/2.24 ** KEPT (pick-wt=2): 94 [] relation($c11).
% 2.04/2.24 ** KEPT (pick-wt=2): 95 [] function($c11).
% 2.04/2.24 ** KEPT (pick-wt=2): 96 [] one_to_one($c11).
% 2.04/2.24 ** KEPT (pick-wt=2): 97 [] empty($c11).
% 2.04/2.24 ** KEPT (pick-wt=2): 98 [] epsilon_transitive($c11).
% 2.04/2.24 ** KEPT (pick-wt=2): 99 [] epsilon_connected($c11).
% 2.04/2.24 ** KEPT (pick-wt=2): 100 [] ordinal($c11).
% 2.04/2.24 ** KEPT (pick-wt=2): 101 [] relation($c12).
% 2.04/2.24 ** KEPT (pick-wt=2): 102 [] function($c12).
% 2.04/2.25 ** KEPT (pick-wt=2): 103 [] transfinite_se_quence($c12).
% 2.04/2.25 ** KEPT (pick-wt=2): 104 [] ordinal_yielding($c12).
% 2.04/2.25 ** KEPT (pick-wt=2): 105 [] relation($c13).
% 2.04/2.25 ** KEPT (pick-wt=5): 106 [] element($f4(A),powerset(A)).
% 2.04/2.25 ** KEPT (pick-wt=3): 107 [] empty($f4(A)).
% 2.04/2.25 ** KEPT (pick-wt=3): 108 [] element($c15,positive_rationals).
% 2.04/2.25 ** KEPT (pick-wt=2): 109 [] empty($c15).
% 2.04/2.25 ** KEPT (pick-wt=2): 110 [] epsilon_transitive($c15).
% 2.04/2.25 ** KEPT (pick-wt=2): 111 [] epsilon_connected($c15).
% 2.04/2.25 ** KEPT (pick-wt=2): 112 [] ordinal($c15).
% 2.04/2.25 ** KEPT (pick-wt=2): 113 [] natural($c15).
% 2.04/2.25 ** KEPT (pick-wt=7): 114 [] empty(A)|element($f5(A),powerset(A)).
% 2.04/2.25 ** KEPT (pick-wt=5): 115 [] empty(A)|finite($f5(A)).
% 2.04/2.25 ** KEPT (pick-wt=2): 116 [] relation($c16).
% 2.04/2.25 ** KEPT (pick-wt=2): 117 [] function($c16).
% 2.04/2.25 ** KEPT (pick-wt=2): 118 [] one_to_one($c16).
% 2.04/2.25 ** KEPT (pick-wt=2): 119 [] epsilon_transitive($c17).
% 2.04/2.25 ** KEPT (pick-wt=2): 120 [] epsilon_connected($c17).
% 2.04/2.25 ** KEPT (pick-wt=2): 121 [] ordinal($c17).
% 2.04/2.25 ** KEPT (pick-wt=2): 122 [] relation($c18).
% 2.04/2.25 ** KEPT (pick-wt=2): 123 [] relation_empty_yielding($c18).
% 2.04/2.25 ** KEPT (pick-wt=2): 124 [] relation($c19).
% 2.04/2.25 ** KEPT (pick-wt=2): 125 [] relation_empty_yielding($c19).
% 2.04/2.25 ** KEPT (pick-wt=2): 126 [] function($c19).
% 2.04/2.25 ** KEPT (pick-wt=2): 127 [] relation($c20).
% 2.04/2.25 ** KEPT (pick-wt=2): 128 [] function($c20).
% 2.04/2.25 ** KEPT (pick-wt=2): 129 [] transfinite_se_quence($c20).
% 2.04/2.25 ** KEPT (pick-wt=2): 130 [] relation($c21).
% 2.04/2.25 ** KEPT (pick-wt=2): 131 [] relation_non_empty($c21).
% 2.04/2.25 ** KEPT (pick-wt=2): 132 [] function($c21).
% 2.04/2.25 ** KEPT (pick-wt=3): 133 [] subset(A,A).
% 2.04/2.25 ** KEPT (pick-wt=2): 134 [] relation($c22).
% 2.04/2.25 ** KEPT (pick-wt=2): 135 [] function($c22).
% 2.04/2.25 ** KEPT (pick-wt=4): 136 [] subset($c23,relation_rng($c22)).
% 2.04/2.25 ** KEPT (pick-wt=4): 137 [] finite(relation_inverse_image($c22,$c23)).
% 2.04/2.25 Following clause subsumed by 46 during input processing: 0 [copy,46,flip.1] A=A.
% 2.04/2.25 46 back subsumes 45.
% 2.04/2.25
% 2.04/2.25 ======= end of input processing =======
% 2.04/2.25
% 2.04/2.25 =========== start of search ===========
% 2.04/2.25
% 2.04/2.25 -------- PROOF --------
% 2.04/2.25
% 2.04/2.25 ----> UNIT CONFLICT at 0.01 sec ----> 372 [binary,371.1,35.1] $F.
% 2.04/2.25
% 2.04/2.25 Length of proof is 2. Level of proof is 2.
% 2.04/2.25
% 2.04/2.25 ---------------- PROOF ----------------
% 2.04/2.25 % SZS status Theorem
% 2.04/2.25 % SZS output start Refutation
% See solution above
% 2.04/2.25 ------------ end of proof -------------
% 2.04/2.25
% 2.04/2.25
% 2.04/2.25 Search stopped by max_proofs option.
% 2.04/2.25
% 2.04/2.25
% 2.04/2.25 Search stopped by max_proofs option.
% 2.04/2.25
% 2.04/2.25 ============ end of search ============
% 2.04/2.25
% 2.04/2.25 -------------- statistics -------------
% 2.04/2.25 clauses given 86
% 2.04/2.25 clauses generated 421
% 2.04/2.25 clauses kept 352
% 2.04/2.25 clauses forward subsumed 291
% 2.04/2.25 clauses back subsumed 3
% 2.04/2.25 Kbytes malloced 1953
% 2.04/2.25
% 2.04/2.25 ----------- times (seconds) -----------
% 2.04/2.25 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 2.04/2.25 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.04/2.25 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.04/2.25
% 2.04/2.25 That finishes the proof of the theorem.
% 2.04/2.25
% 2.04/2.25 Process 27120 finished Wed Jul 27 07:53:03 2022
% 2.04/2.25 Otter interrupted
% 2.04/2.25 PROOF FOUND
%------------------------------------------------------------------------------