TSTP Solution File: SEU083+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU083+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n003.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 13:14:45 EDT 2022
% Result : Theorem 2.10s 2.27s
% Output : Refutation 2.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 4
% Syntax : Number of clauses : 6 ( 5 unt; 0 nHn; 6 RR)
% Number of literals : 8 ( 0 equ; 3 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 2 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(36,axiom,
( ~ finite(A)
| ~ finite(B)
| finite(set_union2(A,B)) ),
file('SEU083+1.p',unknown),
[] ).
cnf(45,axiom,
~ finite(set_union2(dollar_c23,dollar_c22)),
file('SEU083+1.p',unknown),
[] ).
cnf(143,axiom,
finite(dollar_c23),
file('SEU083+1.p',unknown),
[] ).
cnf(144,axiom,
finite(dollar_c22),
file('SEU083+1.p',unknown),
[] ).
cnf(402,plain,
finite(set_union2(dollar_c23,dollar_c22)),
inference(hyper,[status(thm)],[144,36,143]),
[iquote('hyper,144,36,143')] ).
cnf(403,plain,
$false,
inference(binary,[status(thm)],[402,45]),
[iquote('binary,402.1,45.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU083+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n003.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 07:39:56 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.10/2.26 ----- Otter 3.3f, August 2004 -----
% 2.10/2.26 The process was started by sandbox on n003.cluster.edu,
% 2.10/2.26 Wed Jul 27 07:39:56 2022
% 2.10/2.26 The command was "./otter". The process ID is 9443.
% 2.10/2.26
% 2.10/2.26 set(prolog_style_variables).
% 2.10/2.26 set(auto).
% 2.10/2.26 dependent: set(auto1).
% 2.10/2.26 dependent: set(process_input).
% 2.10/2.26 dependent: clear(print_kept).
% 2.10/2.26 dependent: clear(print_new_demod).
% 2.10/2.26 dependent: clear(print_back_demod).
% 2.10/2.26 dependent: clear(print_back_sub).
% 2.10/2.26 dependent: set(control_memory).
% 2.10/2.26 dependent: assign(max_mem, 12000).
% 2.10/2.26 dependent: assign(pick_given_ratio, 4).
% 2.10/2.26 dependent: assign(stats_level, 1).
% 2.10/2.26 dependent: assign(max_seconds, 10800).
% 2.10/2.26 clear(print_given).
% 2.10/2.26
% 2.10/2.26 formula_list(usable).
% 2.10/2.26 all A (A=A).
% 2.10/2.26 all A B subset(A,A).
% 2.10/2.26 all A B (in(A,B)-> -in(B,A)).
% 2.10/2.26 empty(empty_set).
% 2.10/2.26 relation(empty_set).
% 2.10/2.26 empty(empty_set).
% 2.10/2.26 relation(empty_set).
% 2.10/2.26 relation_empty_yielding(empty_set).
% 2.10/2.26 relation(empty_set).
% 2.10/2.26 relation_empty_yielding(empty_set).
% 2.10/2.26 function(empty_set).
% 2.10/2.26 one_to_one(empty_set).
% 2.10/2.26 empty(empty_set).
% 2.10/2.26 epsilon_transitive(empty_set).
% 2.10/2.26 epsilon_connected(empty_set).
% 2.10/2.26 ordinal(empty_set).
% 2.10/2.26 empty(empty_set).
% 2.10/2.26 all A (set_union2(A,empty_set)=A).
% 2.10/2.26 all A B (in(A,B)->element(A,B)).
% 2.10/2.26 all A B C (in(A,B)&element(B,powerset(C))->element(A,C)).
% 2.10/2.26 all A B C (-(in(A,B)&element(B,powerset(C))&empty(C))).
% 2.10/2.26 all A exists B element(B,A).
% 2.10/2.26 all A (empty(A)->finite(A)).
% 2.10/2.26 all A (finite(A)-> (all B (element(B,powerset(A))->finite(B)))).
% 2.10/2.26 all A (empty(A)->function(A)).
% 2.10/2.26 all A (relation(A)&empty(A)&function(A)->relation(A)&function(A)&one_to_one(A)).
% 2.10/2.26 all A B (relation(A)&relation(B)->relation(set_union2(A,B))).
% 2.10/2.26 all A (empty(A)->relation(A)).
% 2.10/2.26 -empty(positive_rationals).
% 2.10/2.26 all A (ordinal(A)-> (all B (element(B,A)->epsilon_transitive(B)&epsilon_connected(B)&ordinal(B)))).
% 2.10/2.26 all A (empty(A)&ordinal(A)->epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)&natural(A)).
% 2.10/2.26 all A (element(A,positive_rationals)-> (ordinal(A)->epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)&natural(A))).
% 2.10/2.26 all A (ordinal(A)->epsilon_transitive(A)&epsilon_connected(A)).
% 2.10/2.26 all A (epsilon_transitive(A)&epsilon_connected(A)->ordinal(A)).
% 2.10/2.26 all A (empty(A)->epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)).
% 2.10/2.26 all A (-empty(powerset(A))).
% 2.10/2.26 all A B (-empty(A)-> -empty(set_union2(A,B))).
% 2.10/2.26 all A B (-empty(A)-> -empty(set_union2(B,A))).
% 2.10/2.26 all A B (element(A,B)->empty(B)|in(A,B)).
% 2.10/2.26 all A B (element(A,powerset(B))<->subset(A,B)).
% 2.10/2.26 all A (empty(A)->A=empty_set).
% 2.10/2.26 all A B (-(in(A,B)&empty(B))).
% 2.10/2.26 all A B (-(empty(A)&A!=B&empty(B))).
% 2.10/2.26 all A B (set_union2(A,B)=set_union2(B,A)).
% 2.10/2.26 all A B (set_union2(A,A)=A).
% 2.10/2.26 all A B (finite(A)&finite(B)->finite(set_union2(A,B))).
% 2.10/2.26 exists A (-empty(A)&finite(A)).
% 2.10/2.26 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)).
% 2.10/2.26 all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)&finite(B)))).
% 2.10/2.26 exists A (relation(A)&function(A)).
% 2.10/2.26 exists A (relation(A)&empty(A)&function(A)).
% 2.10/2.26 exists A (relation(A)&function(A)&one_to_one(A)).
% 2.10/2.26 exists A (relation(A)&relation_empty_yielding(A)&function(A)).
% 2.10/2.26 exists A (relation(A)&relation_non_empty(A)&function(A)).
% 2.10/2.26 exists A (epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)&being_limit_ordinal(A)).
% 2.10/2.26 exists A (relation(A)&function(A)&transfinite_se_quence(A)&ordinal_yielding(A)).
% 2.10/2.26 exists A (empty(A)&relation(A)).
% 2.10/2.26 exists A (-empty(A)&relation(A)).
% 2.10/2.26 exists A (relation(A)&relation_empty_yielding(A)).
% 2.10/2.26 exists A (-empty(A)&epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)&natural(A)).
% 2.10/2.26 exists A (element(A,positive_rationals)& -empty(A)&epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)).
% 2.10/2.26 exists A (element(A,positive_rationals)&empty(A)&epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)&natural(A)).
% 2.10/2.26 exists A (epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)).
% 2.10/2.26 exists A (relation(A)&function(A)&one_to_one(A)&empty(A)&epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)).
% 2.10/2.26 exists A (-empty(A)&epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)).
% 2.10/2.26 exists A (relation(A)&function(A)&transfinite_se_quence(A)).
% 2.10/2.26 all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)))).
% 2.10/2.26 all A exists B (element(B,powerset(A))&empty(B)).
% 2.10/2.27 exists A empty(A).
% 2.10/2.27 exists A (-empty(A)).
% 2.10/2.27 exists A (relation(A)&function(A)&function_yielding(A)).
% 2.10/2.27 -(all A B (finite(A)&finite(B)->finite(set_union2(A,B)))).
% 2.10/2.27 all A B (finite(A)&finite(B)->finite(set_union2(A,B))).
% 2.10/2.27 end_of_list.
% 2.10/2.27
% 2.10/2.27 -------> usable clausifies to:
% 2.10/2.27
% 2.10/2.27 list(usable).
% 2.10/2.27 0 [] A=A.
% 2.10/2.27 0 [] subset(A,A).
% 2.10/2.27 0 [] -in(A,B)| -in(B,A).
% 2.10/2.27 0 [] empty(empty_set).
% 2.10/2.27 0 [] relation(empty_set).
% 2.10/2.27 0 [] empty(empty_set).
% 2.10/2.27 0 [] relation(empty_set).
% 2.10/2.27 0 [] relation_empty_yielding(empty_set).
% 2.10/2.27 0 [] relation(empty_set).
% 2.10/2.27 0 [] relation_empty_yielding(empty_set).
% 2.10/2.27 0 [] function(empty_set).
% 2.10/2.27 0 [] one_to_one(empty_set).
% 2.10/2.27 0 [] empty(empty_set).
% 2.10/2.27 0 [] epsilon_transitive(empty_set).
% 2.10/2.27 0 [] epsilon_connected(empty_set).
% 2.10/2.27 0 [] ordinal(empty_set).
% 2.10/2.27 0 [] empty(empty_set).
% 2.10/2.27 0 [] set_union2(A,empty_set)=A.
% 2.10/2.27 0 [] -in(A,B)|element(A,B).
% 2.10/2.27 0 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 2.10/2.27 0 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 2.10/2.27 0 [] element($f1(A),A).
% 2.10/2.27 0 [] -empty(A)|finite(A).
% 2.10/2.27 0 [] -finite(A)| -element(B,powerset(A))|finite(B).
% 2.10/2.27 0 [] -empty(A)|function(A).
% 2.10/2.27 0 [] -relation(A)| -empty(A)| -function(A)|one_to_one(A).
% 2.10/2.27 0 [] -relation(A)| -relation(B)|relation(set_union2(A,B)).
% 2.10/2.27 0 [] -empty(A)|relation(A).
% 2.10/2.27 0 [] -empty(positive_rationals).
% 2.10/2.27 0 [] -ordinal(A)| -element(B,A)|epsilon_transitive(B).
% 2.10/2.27 0 [] -ordinal(A)| -element(B,A)|epsilon_connected(B).
% 2.10/2.27 0 [] -ordinal(A)| -element(B,A)|ordinal(B).
% 2.10/2.27 0 [] -empty(A)| -ordinal(A)|epsilon_transitive(A).
% 2.10/2.27 0 [] -empty(A)| -ordinal(A)|epsilon_connected(A).
% 2.10/2.27 0 [] -empty(A)| -ordinal(A)|natural(A).
% 2.10/2.27 0 [] -element(A,positive_rationals)| -ordinal(A)|epsilon_transitive(A).
% 2.10/2.27 0 [] -element(A,positive_rationals)| -ordinal(A)|epsilon_connected(A).
% 2.10/2.27 0 [] -element(A,positive_rationals)| -ordinal(A)|natural(A).
% 2.10/2.27 0 [] -ordinal(A)|epsilon_transitive(A).
% 2.10/2.27 0 [] -ordinal(A)|epsilon_connected(A).
% 2.10/2.27 0 [] -epsilon_transitive(A)| -epsilon_connected(A)|ordinal(A).
% 2.10/2.27 0 [] -empty(A)|epsilon_transitive(A).
% 2.10/2.27 0 [] -empty(A)|epsilon_connected(A).
% 2.10/2.27 0 [] -empty(A)|ordinal(A).
% 2.10/2.27 0 [] -empty(powerset(A)).
% 2.10/2.27 0 [] empty(A)| -empty(set_union2(A,B)).
% 2.10/2.27 0 [] empty(A)| -empty(set_union2(B,A)).
% 2.10/2.27 0 [] -element(A,B)|empty(B)|in(A,B).
% 2.10/2.27 0 [] -element(A,powerset(B))|subset(A,B).
% 2.10/2.27 0 [] element(A,powerset(B))| -subset(A,B).
% 2.10/2.27 0 [] -empty(A)|A=empty_set.
% 2.10/2.27 0 [] -in(A,B)| -empty(B).
% 2.10/2.27 0 [] -empty(A)|A=B| -empty(B).
% 2.10/2.27 0 [] set_union2(A,B)=set_union2(B,A).
% 2.10/2.27 0 [] set_union2(A,A)=A.
% 2.10/2.27 0 [] -finite(A)| -finite(B)|finite(set_union2(A,B)).
% 2.10/2.27 0 [] -empty($c1).
% 2.10/2.27 0 [] finite($c1).
% 2.10/2.27 0 [] element($f2(A),powerset(A)).
% 2.10/2.27 0 [] empty($f2(A)).
% 2.10/2.27 0 [] relation($f2(A)).
% 2.10/2.27 0 [] function($f2(A)).
% 2.10/2.27 0 [] one_to_one($f2(A)).
% 2.10/2.27 0 [] epsilon_transitive($f2(A)).
% 2.10/2.27 0 [] epsilon_connected($f2(A)).
% 2.10/2.27 0 [] ordinal($f2(A)).
% 2.10/2.27 0 [] natural($f2(A)).
% 2.10/2.27 0 [] finite($f2(A)).
% 2.10/2.27 0 [] empty(A)|element($f3(A),powerset(A)).
% 2.10/2.27 0 [] empty(A)| -empty($f3(A)).
% 2.10/2.27 0 [] empty(A)|finite($f3(A)).
% 2.10/2.27 0 [] relation($c2).
% 2.10/2.27 0 [] function($c2).
% 2.10/2.27 0 [] relation($c3).
% 2.10/2.27 0 [] empty($c3).
% 2.10/2.27 0 [] function($c3).
% 2.10/2.27 0 [] relation($c4).
% 2.10/2.27 0 [] function($c4).
% 2.10/2.27 0 [] one_to_one($c4).
% 2.10/2.27 0 [] relation($c5).
% 2.10/2.27 0 [] relation_empty_yielding($c5).
% 2.10/2.27 0 [] function($c5).
% 2.10/2.27 0 [] relation($c6).
% 2.10/2.27 0 [] relation_non_empty($c6).
% 2.10/2.27 0 [] function($c6).
% 2.10/2.27 0 [] epsilon_transitive($c7).
% 2.10/2.27 0 [] epsilon_connected($c7).
% 2.10/2.27 0 [] ordinal($c7).
% 2.10/2.27 0 [] being_limit_ordinal($c7).
% 2.10/2.27 0 [] relation($c8).
% 2.10/2.27 0 [] function($c8).
% 2.10/2.27 0 [] transfinite_se_quence($c8).
% 2.10/2.27 0 [] ordinal_yielding($c8).
% 2.10/2.27 0 [] empty($c9).
% 2.10/2.27 0 [] relation($c9).
% 2.10/2.27 0 [] -empty($c10).
% 2.10/2.27 0 [] relation($c10).
% 2.10/2.27 0 [] relation($c11).
% 2.10/2.27 0 [] relation_empty_yielding($c11).
% 2.10/2.27 0 [] -empty($c12).
% 2.10/2.27 0 [] epsilon_transitive($c12).
% 2.10/2.27 0 [] epsilon_connected($c12).
% 2.10/2.27 0 [] ordinal($c12).
% 2.10/2.27 0 [] natural($c12).
% 2.10/2.27 0 [] element($c13,positive_rationals).
% 2.10/2.27 0 [] -empty($c13).
% 2.10/2.27 0 [] epsilon_transitive($c13).
% 2.10/2.27 0 [] epsilon_connected($c13).
% 2.10/2.27 0 [] ordinal($c13).
% 2.10/2.27 0 [] element($c14,positive_rationals).
% 2.10/2.27 0 [] empty($c14).
% 2.10/2.27 0 [] epsilon_transitive($c14).
% 2.10/2.27 0 [] epsilon_connected($c14).
% 2.10/2.27 0 [] ordinal($c14).
% 2.10/2.27 0 [] natural($c14).
% 2.10/2.27 0 [] epsilon_transitive($c15).
% 2.10/2.27 0 [] epsilon_connected($c15).
% 2.10/2.27 0 [] ordinal($c15).
% 2.10/2.27 0 [] relation($c16).
% 2.10/2.27 0 [] function($c16).
% 2.10/2.27 0 [] one_to_one($c16).
% 2.10/2.27 0 [] empty($c16).
% 2.10/2.27 0 [] epsilon_transitive($c16).
% 2.10/2.27 0 [] epsilon_connected($c16).
% 2.10/2.27 0 [] ordinal($c16).
% 2.10/2.27 0 [] -empty($c17).
% 2.10/2.27 0 [] epsilon_transitive($c17).
% 2.10/2.27 0 [] epsilon_connected($c17).
% 2.10/2.27 0 [] ordinal($c17).
% 2.10/2.27 0 [] relation($c18).
% 2.10/2.27 0 [] function($c18).
% 2.10/2.27 0 [] transfinite_se_quence($c18).
% 2.10/2.27 0 [] empty(A)|element($f4(A),powerset(A)).
% 2.10/2.27 0 [] empty(A)| -empty($f4(A)).
% 2.10/2.27 0 [] element($f5(A),powerset(A)).
% 2.10/2.27 0 [] empty($f5(A)).
% 2.10/2.27 0 [] empty($c19).
% 2.10/2.27 0 [] -empty($c20).
% 2.10/2.27 0 [] relation($c21).
% 2.10/2.27 0 [] function($c21).
% 2.10/2.27 0 [] function_yielding($c21).
% 2.10/2.27 0 [] finite($c23).
% 2.10/2.27 0 [] finite($c22).
% 2.10/2.27 0 [] -finite(set_union2($c23,$c22)).
% 2.10/2.27 0 [] -finite(A)| -finite(B)|finite(set_union2(A,B)).
% 2.10/2.27 end_of_list.
% 2.10/2.27
% 2.10/2.27 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 2.10/2.27
% 2.10/2.27 This ia a non-Horn set with equality. The strategy will be
% 2.10/2.27 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.10/2.27 deletion, with positive clauses in sos and nonpositive
% 2.10/2.27 clauses in usable.
% 2.10/2.27
% 2.10/2.27 dependent: set(knuth_bendix).
% 2.10/2.27 dependent: set(anl_eq).
% 2.10/2.27 dependent: set(para_from).
% 2.10/2.27 dependent: set(para_into).
% 2.10/2.27 dependent: clear(para_from_right).
% 2.10/2.27 dependent: clear(para_into_right).
% 2.10/2.27 dependent: set(para_from_vars).
% 2.10/2.27 dependent: set(eq_units_both_ways).
% 2.10/2.27 dependent: set(dynamic_demod_all).
% 2.10/2.27 dependent: set(dynamic_demod).
% 2.10/2.27 dependent: set(order_eq).
% 2.10/2.27 dependent: set(back_demod).
% 2.10/2.27 dependent: set(lrpo).
% 2.10/2.27 dependent: set(hyper_res).
% 2.10/2.27 dependent: set(unit_deletion).
% 2.10/2.27 dependent: set(factor).
% 2.10/2.27
% 2.10/2.27 ------------> process usable:
% 2.10/2.27 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 2.10/2.27 ** KEPT (pick-wt=6): 2 [] -in(A,B)|element(A,B).
% 2.10/2.27 ** KEPT (pick-wt=10): 3 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 2.10/2.27 ** KEPT (pick-wt=9): 4 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 2.10/2.27 ** KEPT (pick-wt=4): 5 [] -empty(A)|finite(A).
% 2.10/2.27 ** KEPT (pick-wt=8): 6 [] -finite(A)| -element(B,powerset(A))|finite(B).
% 2.10/2.27 ** KEPT (pick-wt=4): 7 [] -empty(A)|function(A).
% 2.10/2.27 ** KEPT (pick-wt=8): 8 [] -relation(A)| -empty(A)| -function(A)|one_to_one(A).
% 2.10/2.27 ** KEPT (pick-wt=8): 9 [] -relation(A)| -relation(B)|relation(set_union2(A,B)).
% 2.10/2.27 ** KEPT (pick-wt=4): 10 [] -empty(A)|relation(A).
% 2.10/2.27 ** KEPT (pick-wt=2): 11 [] -empty(positive_rationals).
% 2.10/2.27 ** KEPT (pick-wt=7): 12 [] -ordinal(A)| -element(B,A)|epsilon_transitive(B).
% 2.10/2.27 ** KEPT (pick-wt=7): 13 [] -ordinal(A)| -element(B,A)|epsilon_connected(B).
% 2.10/2.27 ** KEPT (pick-wt=7): 14 [] -ordinal(A)| -element(B,A)|ordinal(B).
% 2.10/2.27 ** KEPT (pick-wt=6): 15 [] -empty(A)| -ordinal(A)|epsilon_transitive(A).
% 2.10/2.27 ** KEPT (pick-wt=6): 16 [] -empty(A)| -ordinal(A)|epsilon_connected(A).
% 2.10/2.27 ** KEPT (pick-wt=6): 17 [] -empty(A)| -ordinal(A)|natural(A).
% 2.10/2.27 ** KEPT (pick-wt=7): 18 [] -element(A,positive_rationals)| -ordinal(A)|epsilon_transitive(A).
% 2.10/2.27 ** KEPT (pick-wt=7): 19 [] -element(A,positive_rationals)| -ordinal(A)|epsilon_connected(A).
% 2.10/2.27 ** KEPT (pick-wt=7): 20 [] -element(A,positive_rationals)| -ordinal(A)|natural(A).
% 2.10/2.27 ** KEPT (pick-wt=4): 21 [] -ordinal(A)|epsilon_transitive(A).
% 2.10/2.27 ** KEPT (pick-wt=4): 22 [] -ordinal(A)|epsilon_connected(A).
% 2.10/2.27 ** KEPT (pick-wt=6): 23 [] -epsilon_transitive(A)| -epsilon_connected(A)|ordinal(A).
% 2.10/2.27 ** KEPT (pick-wt=4): 24 [] -empty(A)|epsilon_transitive(A).
% 2.10/2.27 ** KEPT (pick-wt=4): 25 [] -empty(A)|epsilon_connected(A).
% 2.10/2.27 ** KEPT (pick-wt=4): 26 [] -empty(A)|ordinal(A).
% 2.10/2.27 ** KEPT (pick-wt=3): 27 [] -empty(powerset(A)).
% 2.10/2.27 ** KEPT (pick-wt=6): 28 [] empty(A)| -empty(set_union2(A,B)).
% 2.10/2.27 ** KEPT (pick-wt=6): 29 [] empty(A)| -empty(set_union2(B,A)).
% 2.10/2.27 ** KEPT (pick-wt=8): 30 [] -element(A,B)|empty(B)|in(A,B).
% 2.10/2.27 ** KEPT (pick-wt=7): 31 [] -element(A,powerset(B))|subset(A,B).
% 2.10/2.27 ** KEPT (pick-wt=7): 32 [] element(A,powerset(B))| -subset(A,B).
% 2.10/2.27 ** KEPT (pick-wt=5): 33 [] -empty(A)|A=empty_set.
% 2.10/2.27 ** KEPT (pick-wt=5): 34 [] -in(A,B)| -empty(B).
% 2.10/2.27 ** KEPT (pick-wt=7): 35 [] -empty(A)|A=B| -empty(B).
% 2.10/2.27 ** KEPT (pick-wt=8): 36 [] -finite(A)| -finite(B)|finite(set_union2(A,B)).
% 2.10/2.27 ** KEPT (pick-wt=2): 37 [] -empty($c1).
% 2.10/2.27 ** KEPT (pick-wt=5): 38 [] empty(A)| -empty($f3(A)).
% 2.10/2.27 ** KEPT (pick-wt=2): 39 [] -empty($c10).
% 2.10/2.27 ** KEPT (pick-wt=2): 40 [] -empty($c12).
% 2.10/2.27 ** KEPT (pick-wt=2): 41 [] -empty($c13).
% 2.10/2.27 ** KEPT (pick-wt=2): 42 [] -empty($c17).
% 2.10/2.27 ** KEPT (pick-wt=5): 43 [] empty(A)| -empty($f4(A)).
% 2.10/2.27 ** KEPT (pick-wt=2): 44 [] -empty($c20).
% 2.10/2.27 ** KEPT (pick-wt=4): 45 [] -finite(set_union2($c23,$c22)).
% 2.10/2.27 Following clause subsumed by 36 during input processing: 0 [] -finite(A)| -finite(B)|finite(set_union2(A,B)).
% 2.10/2.27 21 back subsumes 18.
% 2.10/2.27 21 back subsumes 15.
% 2.10/2.27 22 back subsumes 19.
% 2.10/2.27 22 back subsumes 16.
% 2.10/2.27
% 2.10/2.27 ------------> process sos:
% 2.10/2.27 ** KEPT (pick-wt=3): 50 [] A=A.
% 2.10/2.27 ** KEPT (pick-wt=3): 51 [] subset(A,A).
% 2.10/2.27 ** KEPT (pick-wt=2): 52 [] empty(empty_set).
% 2.10/2.27 ** KEPT (pick-wt=2): 53 [] relation(empty_set).
% 2.10/2.27 Following clause subsumed by 52 during input processing: 0 [] empty(empty_set).
% 2.10/2.27 Following clause subsumed by 53 during input processing: 0 [] relation(empty_set).
% 2.10/2.27 ** KEPT (pick-wt=2): 54 [] relation_empty_yielding(empty_set).
% 2.10/2.27 Following clause subsumed by 53 during input processing: 0 [] relation(empty_set).
% 2.10/2.27 Following clause subsumed by 54 during input processing: 0 [] relation_empty_yielding(empty_set).
% 2.10/2.27 ** KEPT (pick-wt=2): 55 [] function(empty_set).
% 2.10/2.27 ** KEPT (pick-wt=2): 56 [] one_to_one(empty_set).
% 2.10/2.27 Following clause subsumed by 52 during input processing: 0 [] empty(empty_set).
% 2.10/2.27 ** KEPT (pick-wt=2): 57 [] epsilon_transitive(empty_set).
% 2.10/2.27 ** KEPT (pick-wt=2): 58 [] epsilon_connected(empty_set).
% 2.10/2.27 ** KEPT (pick-wt=2): 59 [] ordinal(empty_set).
% 2.10/2.27 Following clause subsumed by 52 during input processing: 0 [] empty(empty_set).
% 2.10/2.27 ** KEPT (pick-wt=5): 60 [] set_union2(A,empty_set)=A.
% 2.10/2.27 ---> New Demodulator: 61 [new_demod,60] set_union2(A,empty_set)=A.
% 2.10/2.27 ** KEPT (pick-wt=4): 62 [] element($f1(A),A).
% 2.10/2.27 ** KEPT (pick-wt=7): 63 [] set_union2(A,B)=set_union2(B,A).
% 2.10/2.27 ** KEPT (pick-wt=5): 64 [] set_union2(A,A)=A.
% 2.10/2.27 ---> New Demodulator: 65 [new_demod,64] set_union2(A,A)=A.
% 2.10/2.27 ** KEPT (pick-wt=2): 66 [] finite($c1).
% 2.10/2.27 ** KEPT (pick-wt=5): 67 [] element($f2(A),powerset(A)).
% 2.10/2.27 ** KEPT (pick-wt=3): 68 [] empty($f2(A)).
% 2.10/2.27 ** KEPT (pick-wt=3): 69 [] relation($f2(A)).
% 2.10/2.27 ** KEPT (pick-wt=3): 70 [] function($f2(A)).
% 2.10/2.27 ** KEPT (pick-wt=3): 71 [] one_to_one($f2(A)).
% 2.10/2.27 ** KEPT (pick-wt=3): 72 [] epsilon_transitive($f2(A)).
% 2.10/2.27 ** KEPT (pick-wt=3): 73 [] epsilon_connected($f2(A)).
% 2.10/2.27 ** KEPT (pick-wt=3): 74 [] ordinal($f2(A)).
% 2.10/2.27 ** KEPT (pick-wt=3): 75 [] natural($f2(A)).
% 2.10/2.27 ** KEPT (pick-wt=3): 76 [] finite($f2(A)).
% 2.10/2.27 ** KEPT (pick-wt=7): 77 [] empty(A)|element($f3(A),powerset(A)).
% 2.10/2.27 ** KEPT (pick-wt=5): 78 [] empty(A)|finite($f3(A)).
% 2.10/2.27 ** KEPT (pick-wt=2): 79 [] relation($c2).
% 2.10/2.27 ** KEPT (pick-wt=2): 80 [] function($c2).
% 2.10/2.27 ** KEPT (pick-wt=2): 81 [] relation($c3).
% 2.10/2.27 ** KEPT (pick-wt=2): 82 [] empty($c3).
% 2.10/2.27 ** KEPT (pick-wt=2): 83 [] function($c3).
% 2.10/2.27 ** KEPT (pick-wt=2): 84 [] relation($c4).
% 2.10/2.27 ** KEPT (pick-wt=2): 85 [] function($c4).
% 2.10/2.27 ** KEPT (pick-wt=2): 86 [] one_to_one($c4).
% 2.10/2.27 ** KEPT (pick-wt=2): 87 [] relation($c5).
% 2.10/2.27 ** KEPT (pick-wt=2): 88 [] relation_empty_yielding($c5).
% 2.10/2.27 ** KEPT (pick-wt=2): 89 [] function($c5).
% 2.10/2.27 ** KEPT (pick-wt=2): 90 [] relation($c6).
% 2.10/2.27 ** KEPT (pick-wt=2): 91 [] relation_non_empty($c6).
% 2.10/2.27 ** KEPT (pick-wt=2): 92 [] function($c6).
% 2.10/2.27 ** KEPT (pick-wt=2): 93 [] epsilon_transitive($c7).
% 2.10/2.27 ** KEPT (pick-wt=2): 94 [] epsilon_connected($c7).
% 2.10/2.27 ** KEPT (pick-wt=2): 95 [] ordinal($c7).
% 2.10/2.27 ** KEPT (pick-wt=2): 96 [] being_limit_ordinal($c7).
% 2.10/2.27 ** KEPT (pick-wt=2): 97 [] relation($c8).
% 2.10/2.27 ** KEPT (pick-wt=2): 98 [] function($c8).
% 2.10/2.27 ** KEPT (pick-wt=2): 99 [] transfinite_se_quence($c8).
% 2.10/2.27 ** KEPT (pick-wt=2): 100 [] ordinal_yielding($c8).
% 2.10/2.27 ** KEPT (pick-wt=2): 101 [] empty($c9).
% 2.10/2.27 ** KEPT (pick-wt=2): 102 [] relation($c9).
% 2.10/2.27 ** KEPT (pick-wt=2): 103 [] relation($c10).
% 2.10/2.27 ** KEPT (pick-wt=2): 104 [] relation($c11).
% 2.10/2.27 ** KEPT (pick-wt=2): 105 [] relation_empty_yielding($c11).
% 2.10/2.27 ** KEPT (pick-wt=2): 106 [] epsilon_transitive($c12).
% 2.10/2.27 ** KEPT (pick-wt=2): 107 [] epsilon_connected($c12).
% 2.10/2.27 ** KEPT (pick-wt=2): 108 [] ordinal($c12).
% 2.10/2.27 ** KEPT (pick-wt=2): 109 [] natural($c12).
% 2.10/2.27 ** KEPT (pick-wt=3): 110 [] element($c13,positive_rationals).
% 2.10/2.27 ** KEPT (pick-wt=2): 111 [] epsilon_transitive($c13).
% 2.10/2.27 ** KEPT (pick-wt=2): 112 [] epsilon_connected($c13).
% 2.10/2.27 ** KEPT (pick-wt=2): 113 [] ordinal($c13).
% 2.10/2.27 ** KEPT (pick-wt=3): 114 [] element($c14,positive_rationals).
% 2.10/2.27 ** KEPT (pick-wt=2): 115 [] empty($c14).
% 2.10/2.27 ** KEPT (pick-wt=2): 116 [] epsilon_transitive($c14).
% 2.10/2.27 ** KEPT (pick-wt=2): 117 [] epsilon_connected($c14).
% 2.10/2.27 ** KEPT (pick-wt=2): 118 [] ordinal($c14).
% 2.10/2.27 ** KEPT (pick-wt=2): 119 [] natural($c14).
% 2.10/2.27 ** KEPT (pick-wt=2): 120 [] epsilon_transitive($c15).
% 2.10/2.27 ** KEPT (pick-wt=2): 121 [] epsilon_connected($c15).
% 2.10/2.27 ** KEPT (pick-wt=2): 122 [] ordinal($c15).
% 2.10/2.27 ** KEPT (pick-wt=2): 123 [] relation($c16).
% 2.10/2.27 ** KEPT (pick-wt=2): 124 [] function($c16).
% 2.10/2.27 ** KEPT (pick-wt=2): 125 [] one_to_one($c16).
% 2.10/2.27 ** KEPT (pick-wt=2): 126 [] empty($c16).
% 2.10/2.27 ** KEPT (pick-wt=2): 127 [] epsilon_transitive($c16).
% 2.10/2.27 ** KEPT (pick-wt=2): 128 [] epsilon_connected($c16).
% 2.10/2.27 ** KEPT (pick-wt=2): 129 [] ordinal($c16).
% 2.10/2.27 ** KEPT (pick-wt=2): 130 [] epsilon_transitive($c17).
% 2.10/2.27 ** KEPT (pick-wt=2): 131 [] epsilon_connected($c17).
% 2.10/2.27 ** KEPT (pick-wt=2): 132 [] ordinal($c17).
% 2.10/2.27 ** KEPT (pick-wt=2): 133 [] relation($c18).
% 2.10/2.27 ** KEPT (pick-wt=2): 134 [] function($c18).
% 2.10/2.27 ** KEPT (pick-wt=2): 135 [] transfinite_se_quence($c18).
% 2.10/2.27 ** KEPT (pick-wt=7): 136 [] empty(A)|element($f4(A),powerset(A)).
% 2.10/2.27 ** KEPT (pick-wt=5): 137 [] element($f5(A),powerset(A)).
% 2.10/2.27 ** KEPT (pick-wt=3): 138 [] empty($f5(A)).
% 2.10/2.27 ** KEPT (pick-wt=2): 139 [] empty($c19).
% 2.10/2.27 ** KEPT (pick-wt=2): 140 [] relation($c21).
% 2.10/2.27 ** KEPT (pick-wt=2): 141 [] function($c21).
% 2.10/2.27 ** KEPT (pick-wt=2): 142 [] function_yielding($c21).
% 2.10/2.27 ** KEPT (pick-wt=2): 143 [] finite($c23).
% 2.10/2.27 ** KEPT (pick-wt=2): 144 [] finite($c22).
% 2.10/2.27 Following clause subsumed by 50 during input processing: 0 [copy,50,flip.1] A=A.
% 2.10/2.27 50 back subsumes 48.
% 2.10/2.27 >>>> Starting back demodulation with 61.
% 2.10/2.27 Following clause subsumed by 63 during input processing: 0 [copy,63,flip.1] set_union2(A,B)=set_union2(B,A).
% 2.10/2.27 >>>> Starting back demodulation with 65.
% 2.10/2.27 >> back demodulating 49 with 65.
% 2.10/2.27 >> back demodulating 47 with 65.
% 2.10/2.27
% 2.10/2.27 ======= end of input processing =======
% 2.10/2.27
% 2.10/2.27 =========== start of search ===========
% 2.10/2.27
% 2.10/2.27 -------- PROOF --------
% 2.10/2.27
% 2.10/2.27 ----> UNIT CONFLICT at 0.01 sec ----> 403 [binary,402.1,45.1] $F.
% 2.10/2.27
% 2.10/2.27 Length of proof is 1. Level of proof is 1.
% 2.10/2.27
% 2.10/2.27 ---------------- PROOF ----------------
% 2.10/2.27 % SZS status Theorem
% 2.10/2.27 % SZS output start Refutation
% See solution above
% 2.10/2.27 ------------ end of proof -------------
% 2.10/2.27
% 2.10/2.27
% 2.10/2.27 Search stopped by max_proofs option.
% 2.10/2.27
% 2.10/2.27
% 2.10/2.27 Search stopped by max_proofs option.
% 2.10/2.27
% 2.10/2.27 ============ end of search ============
% 2.10/2.27
% 2.10/2.27 -------------- statistics -------------
% 2.10/2.27 clauses given 79
% 2.10/2.27 clauses generated 455
% 2.10/2.27 clauses kept 389
% 2.10/2.27 clauses forward subsumed 291
% 2.10/2.27 clauses back subsumed 7
% 2.10/2.27 Kbytes malloced 1953
% 2.10/2.27
% 2.10/2.27 ----------- times (seconds) -----------
% 2.10/2.27 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 2.10/2.27 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.10/2.27 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.10/2.27
% 2.10/2.27 That finishes the proof of the theorem.
% 2.10/2.27
% 2.10/2.27 Process 9443 finished Wed Jul 27 07:39:58 2022
% 2.10/2.27 Otter interrupted
% 2.10/2.27 PROOF FOUND
%------------------------------------------------------------------------------