TSTP Solution File: NUM393+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : NUM393+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n027.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 13:08:14 EDT 2022
% Result : Theorem 1.82s 2.04s
% Output : Refutation 1.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of clauses : 13 ( 7 unt; 3 nHn; 13 RR)
% Number of literals : 23 ( 0 equ; 8 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 8 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(8,axiom,
( ~ ordinal(A)
| ~ ordinal(B)
| ordinal_subset(A,B)
| ordinal_subset(B,A) ),
file('NUM393+1.p',unknown),
[] ).
cnf(10,axiom,
( inclusion_comparable(A,B)
| ~ subset(A,B) ),
file('NUM393+1.p',unknown),
[] ).
cnf(11,axiom,
( inclusion_comparable(A,B)
| ~ subset(B,A) ),
file('NUM393+1.p',unknown),
[] ).
cnf(14,axiom,
( ~ ordinal(A)
| ~ ordinal(B)
| ~ ordinal_subset(A,B)
| subset(A,B) ),
file('NUM393+1.p',unknown),
[] ).
cnf(20,axiom,
~ inclusion_comparable(dollar_c13,dollar_c12),
file('NUM393+1.p',unknown),
[] ).
cnf(63,axiom,
ordinal(dollar_c13),
file('NUM393+1.p',unknown),
[] ).
cnf(64,axiom,
ordinal(dollar_c12),
file('NUM393+1.p',unknown),
[] ).
cnf(99,plain,
( ordinal_subset(dollar_c13,dollar_c12)
| ordinal_subset(dollar_c12,dollar_c13) ),
inference(hyper,[status(thm)],[64,8,63]),
[iquote('hyper,64,8,63')] ).
cnf(217,plain,
( ordinal_subset(dollar_c12,dollar_c13)
| subset(dollar_c13,dollar_c12) ),
inference(hyper,[status(thm)],[99,14,63,64]),
[iquote('hyper,99,14,63,64')] ).
cnf(321,plain,
ordinal_subset(dollar_c12,dollar_c13),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[217,10]),20]),
[iquote('hyper,217,10,unit_del,20')] ).
cnf(325,plain,
subset(dollar_c12,dollar_c13),
inference(hyper,[status(thm)],[321,14,64,63]),
[iquote('hyper,321,14,64,63')] ).
cnf(331,plain,
inclusion_comparable(dollar_c13,dollar_c12),
inference(hyper,[status(thm)],[325,11]),
[iquote('hyper,325,11')] ).
cnf(332,plain,
$false,
inference(binary,[status(thm)],[331,20]),
[iquote('binary,331.1,20.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : NUM393+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n027.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 09:55:06 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.82/2.03 ----- Otter 3.3f, August 2004 -----
% 1.82/2.03 The process was started by sandbox2 on n027.cluster.edu,
% 1.82/2.03 Wed Jul 27 09:55:07 2022
% 1.82/2.03 The command was "./otter". The process ID is 23542.
% 1.82/2.03
% 1.82/2.03 set(prolog_style_variables).
% 1.82/2.03 set(auto).
% 1.82/2.03 dependent: set(auto1).
% 1.82/2.03 dependent: set(process_input).
% 1.82/2.03 dependent: clear(print_kept).
% 1.82/2.03 dependent: clear(print_new_demod).
% 1.82/2.03 dependent: clear(print_back_demod).
% 1.82/2.03 dependent: clear(print_back_sub).
% 1.82/2.03 dependent: set(control_memory).
% 1.82/2.03 dependent: assign(max_mem, 12000).
% 1.82/2.03 dependent: assign(pick_given_ratio, 4).
% 1.82/2.03 dependent: assign(stats_level, 1).
% 1.82/2.03 dependent: assign(max_seconds, 10800).
% 1.82/2.03 clear(print_given).
% 1.82/2.03
% 1.82/2.03 formula_list(usable).
% 1.82/2.03 all A (A=A).
% 1.82/2.03 all A B (in(A,B)-> -in(B,A)).
% 1.82/2.03 all A (empty(A)->function(A)).
% 1.82/2.03 all A (ordinal(A)->epsilon_transitive(A)&epsilon_connected(A)).
% 1.82/2.03 all A (empty(A)->relation(A)).
% 1.82/2.03 all A (relation(A)&empty(A)&function(A)->relation(A)&function(A)&one_to_one(A)).
% 1.82/2.03 all A (epsilon_transitive(A)&epsilon_connected(A)->ordinal(A)).
% 1.82/2.03 all A B (ordinal(A)&ordinal(B)->ordinal_subset(A,B)|ordinal_subset(B,A)).
% 1.82/2.03 all A B (inclusion_comparable(A,B)<->subset(A,B)|subset(B,A)).
% 1.82/2.03 all A exists B element(B,A).
% 1.82/2.03 empty(empty_set).
% 1.82/2.03 relation(empty_set).
% 1.82/2.03 relation_empty_yielding(empty_set).
% 1.82/2.03 empty(empty_set).
% 1.82/2.03 empty(empty_set).
% 1.82/2.03 relation(empty_set).
% 1.82/2.03 exists A (relation(A)&function(A)).
% 1.82/2.03 exists A (epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)).
% 1.82/2.03 exists A (empty(A)&relation(A)).
% 1.82/2.03 exists A empty(A).
% 1.82/2.03 exists A (relation(A)&empty(A)&function(A)).
% 1.82/2.03 exists A (-empty(A)&relation(A)).
% 1.82/2.03 exists A (-empty(A)).
% 1.82/2.03 exists A (relation(A)&function(A)&one_to_one(A)).
% 1.82/2.03 exists A (relation(A)&relation_empty_yielding(A)).
% 1.82/2.03 exists A (relation(A)&relation_empty_yielding(A)&function(A)).
% 1.82/2.03 exists A (relation(A)&relation_non_empty(A)&function(A)).
% 1.82/2.03 all A B (ordinal(A)&ordinal(B)-> (ordinal_subset(A,B)<->subset(A,B))).
% 1.82/2.03 all A B (ordinal(A)&ordinal(B)->ordinal_subset(A,A)).
% 1.82/2.03 all A B subset(A,A).
% 1.82/2.03 all A B inclusion_comparable(A,A).
% 1.82/2.03 all A B (inclusion_comparable(A,B)->inclusion_comparable(B,A)).
% 1.82/2.03 all A B (in(A,B)->element(A,B)).
% 1.82/2.03 -(all A (ordinal(A)-> (all B (ordinal(B)->inclusion_comparable(A,B))))).
% 1.82/2.03 all A B (element(A,B)->empty(B)|in(A,B)).
% 1.82/2.03 all A B (element(A,powerset(B))<->subset(A,B)).
% 1.82/2.03 all A B C (in(A,B)&element(B,powerset(C))->element(A,C)).
% 1.82/2.03 all A B C (-(in(A,B)&element(B,powerset(C))&empty(C))).
% 1.82/2.03 all A (empty(A)->A=empty_set).
% 1.82/2.03 all A B (-(in(A,B)&empty(B))).
% 1.82/2.03 all A B (-(empty(A)&A!=B&empty(B))).
% 1.82/2.03 end_of_list.
% 1.82/2.03
% 1.82/2.03 -------> usable clausifies to:
% 1.82/2.03
% 1.82/2.03 list(usable).
% 1.82/2.03 0 [] A=A.
% 1.82/2.03 0 [] -in(A,B)| -in(B,A).
% 1.82/2.03 0 [] -empty(A)|function(A).
% 1.82/2.03 0 [] -ordinal(A)|epsilon_transitive(A).
% 1.82/2.03 0 [] -ordinal(A)|epsilon_connected(A).
% 1.82/2.03 0 [] -empty(A)|relation(A).
% 1.82/2.03 0 [] -relation(A)| -empty(A)| -function(A)|one_to_one(A).
% 1.82/2.03 0 [] -epsilon_transitive(A)| -epsilon_connected(A)|ordinal(A).
% 1.82/2.03 0 [] -ordinal(A)| -ordinal(B)|ordinal_subset(A,B)|ordinal_subset(B,A).
% 1.82/2.03 0 [] -inclusion_comparable(A,B)|subset(A,B)|subset(B,A).
% 1.82/2.03 0 [] inclusion_comparable(A,B)| -subset(A,B).
% 1.82/2.03 0 [] inclusion_comparable(A,B)| -subset(B,A).
% 1.82/2.03 0 [] element($f1(A),A).
% 1.82/2.03 0 [] empty(empty_set).
% 1.82/2.03 0 [] relation(empty_set).
% 1.82/2.03 0 [] relation_empty_yielding(empty_set).
% 1.82/2.03 0 [] empty(empty_set).
% 1.82/2.03 0 [] empty(empty_set).
% 1.82/2.03 0 [] relation(empty_set).
% 1.82/2.03 0 [] relation($c1).
% 1.82/2.03 0 [] function($c1).
% 1.82/2.03 0 [] epsilon_transitive($c2).
% 1.82/2.03 0 [] epsilon_connected($c2).
% 1.82/2.03 0 [] ordinal($c2).
% 1.82/2.03 0 [] empty($c3).
% 1.82/2.03 0 [] relation($c3).
% 1.82/2.03 0 [] empty($c4).
% 1.82/2.03 0 [] relation($c5).
% 1.82/2.03 0 [] empty($c5).
% 1.82/2.03 0 [] function($c5).
% 1.82/2.03 0 [] -empty($c6).
% 1.82/2.03 0 [] relation($c6).
% 1.82/2.03 0 [] -empty($c7).
% 1.82/2.03 0 [] relation($c8).
% 1.82/2.03 0 [] function($c8).
% 1.82/2.03 0 [] one_to_one($c8).
% 1.82/2.03 0 [] relation($c9).
% 1.82/2.03 0 [] relation_empty_yielding($c9).
% 1.82/2.03 0 [] relation($c10).
% 1.82/2.03 0 [] relation_empty_yielding($c10).
% 1.82/2.03 0 [] function($c10).
% 1.82/2.03 0 [] relation($c11).
% 1.82/2.03 0 [] relation_non_empty($c11).
% 1.82/2.03 0 [] function($c11).
% 1.82/2.03 0 [] -ordinal(A)| -ordinal(B)| -ordinal_subset(A,B)|subset(A,B).
% 1.82/2.03 0 [] -ordinal(A)| -ordinal(B)|ordinal_subset(A,B)| -subset(A,B).
% 1.82/2.03 0 [] -ordinal(A)| -ordinal(B)|ordinal_subset(A,A).
% 1.82/2.03 0 [] subset(A,A).
% 1.82/2.03 0 [] inclusion_comparable(A,A).
% 1.82/2.03 0 [] -inclusion_comparable(A,B)|inclusion_comparable(B,A).
% 1.82/2.03 0 [] -in(A,B)|element(A,B).
% 1.82/2.03 0 [] ordinal($c13).
% 1.82/2.03 0 [] ordinal($c12).
% 1.82/2.03 0 [] -inclusion_comparable($c13,$c12).
% 1.82/2.03 0 [] -element(A,B)|empty(B)|in(A,B).
% 1.82/2.03 0 [] -element(A,powerset(B))|subset(A,B).
% 1.82/2.03 0 [] element(A,powerset(B))| -subset(A,B).
% 1.82/2.03 0 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 1.82/2.03 0 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 1.82/2.03 0 [] -empty(A)|A=empty_set.
% 1.82/2.03 0 [] -in(A,B)| -empty(B).
% 1.82/2.03 0 [] -empty(A)|A=B| -empty(B).
% 1.82/2.03 end_of_list.
% 1.82/2.03
% 1.82/2.03 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.82/2.03
% 1.82/2.03 This ia a non-Horn set with equality. The strategy will be
% 1.82/2.03 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.82/2.03 deletion, with positive clauses in sos and nonpositive
% 1.82/2.03 clauses in usable.
% 1.82/2.03
% 1.82/2.03 dependent: set(knuth_bendix).
% 1.82/2.03 dependent: set(anl_eq).
% 1.82/2.03 dependent: set(para_from).
% 1.82/2.03 dependent: set(para_into).
% 1.82/2.03 dependent: clear(para_from_right).
% 1.82/2.03 dependent: clear(para_into_right).
% 1.82/2.03 dependent: set(para_from_vars).
% 1.82/2.03 dependent: set(eq_units_both_ways).
% 1.82/2.03 dependent: set(dynamic_demod_all).
% 1.82/2.03 dependent: set(dynamic_demod).
% 1.82/2.03 dependent: set(order_eq).
% 1.82/2.03 dependent: set(back_demod).
% 1.82/2.03 dependent: set(lrpo).
% 1.82/2.03 dependent: set(hyper_res).
% 1.82/2.03 dependent: set(unit_deletion).
% 1.82/2.03 dependent: set(factor).
% 1.82/2.03
% 1.82/2.03 ------------> process usable:
% 1.82/2.03 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.82/2.03 ** KEPT (pick-wt=4): 2 [] -empty(A)|function(A).
% 1.82/2.03 ** KEPT (pick-wt=4): 3 [] -ordinal(A)|epsilon_transitive(A).
% 1.82/2.03 ** KEPT (pick-wt=4): 4 [] -ordinal(A)|epsilon_connected(A).
% 1.82/2.03 ** KEPT (pick-wt=4): 5 [] -empty(A)|relation(A).
% 1.82/2.03 ** KEPT (pick-wt=8): 6 [] -relation(A)| -empty(A)| -function(A)|one_to_one(A).
% 1.82/2.03 ** KEPT (pick-wt=6): 7 [] -epsilon_transitive(A)| -epsilon_connected(A)|ordinal(A).
% 1.82/2.03 ** KEPT (pick-wt=10): 8 [] -ordinal(A)| -ordinal(B)|ordinal_subset(A,B)|ordinal_subset(B,A).
% 1.82/2.03 ** KEPT (pick-wt=9): 9 [] -inclusion_comparable(A,B)|subset(A,B)|subset(B,A).
% 1.82/2.03 ** KEPT (pick-wt=6): 10 [] inclusion_comparable(A,B)| -subset(A,B).
% 1.82/2.03 ** KEPT (pick-wt=6): 11 [] inclusion_comparable(A,B)| -subset(B,A).
% 1.82/2.03 ** KEPT (pick-wt=2): 12 [] -empty($c6).
% 1.82/2.03 ** KEPT (pick-wt=2): 13 [] -empty($c7).
% 1.82/2.03 ** KEPT (pick-wt=10): 14 [] -ordinal(A)| -ordinal(B)| -ordinal_subset(A,B)|subset(A,B).
% 1.82/2.03 ** KEPT (pick-wt=10): 15 [] -ordinal(A)| -ordinal(B)|ordinal_subset(A,B)| -subset(A,B).
% 1.82/2.03 ** KEPT (pick-wt=5): 17 [copy,16,factor_simp] -ordinal(A)|ordinal_subset(A,A).
% 1.82/2.03 ** KEPT (pick-wt=6): 18 [] -inclusion_comparable(A,B)|inclusion_comparable(B,A).
% 1.82/2.03 ** KEPT (pick-wt=6): 19 [] -in(A,B)|element(A,B).
% 1.82/2.03 ** KEPT (pick-wt=3): 20 [] -inclusion_comparable($c13,$c12).
% 1.82/2.03 ** KEPT (pick-wt=8): 21 [] -element(A,B)|empty(B)|in(A,B).
% 1.82/2.03 ** KEPT (pick-wt=7): 22 [] -element(A,powerset(B))|subset(A,B).
% 1.82/2.03 ** KEPT (pick-wt=7): 23 [] element(A,powerset(B))| -subset(A,B).
% 1.82/2.03 ** KEPT (pick-wt=10): 24 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 1.82/2.03 ** KEPT (pick-wt=9): 25 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 1.82/2.03 ** KEPT (pick-wt=5): 26 [] -empty(A)|A=empty_set.
% 1.82/2.03 ** KEPT (pick-wt=5): 27 [] -in(A,B)| -empty(B).
% 1.82/2.03 ** KEPT (pick-wt=7): 28 [] -empty(A)|A=B| -empty(B).
% 1.82/2.03
% 1.82/2.03 ------------> process sos:
% 1.82/2.03 ** KEPT (pick-wt=3): 33 [] A=A.
% 1.82/2.03 ** KEPT (pick-wt=4): 34 [] element($f1(A),A).
% 1.82/2.03 ** KEPT (pick-wt=2): 35 [] empty(empty_set).
% 1.82/2.03 ** KEPT (pick-wt=2): 36 [] relation(empty_set).
% 1.82/2.03 ** KEPT (pick-wt=2): 37 [] relation_empty_yielding(empty_set).
% 1.82/2.03 Following clause subsumed by 35 during input processing: 0 [] empty(empty_set).
% 1.82/2.03 Following clause subsumed by 35 during input processing: 0 [] empty(empty_set).
% 1.82/2.03 Following clause subsumed by 36 during input processing: 0 [] relation(empty_set).
% 1.82/2.03 ** KEPT (pick-wt=2): 38 [] relation($c1).
% 1.82/2.03 ** KEPT (pick-wt=2): 39 [] function($c1).
% 1.82/2.03 ** KEPT (pick-wt=2): 40 [] epsilon_transitive($c2).
% 1.82/2.03 ** KEPT (pick-wt=2): 41 [] epsilon_connected($c2).
% 1.82/2.03 ** KEPT (pick-wt=2): 42 [] ordinal($c2).
% 1.82/2.03 ** KEPT (pick-wt=2): 43 [] empty($c3).
% 1.82/2.03 ** KEPT (pick-wt=2): 44 [] relation($c3).
% 1.82/2.03 ** KEPT (pick-wt=2): 45 [] empty($c4).
% 1.82/2.03 ** KEPT (pick-wt=2): 46 [] relation($c5).
% 1.82/2.03 ** KEPT (pick-wt=2): 47 [] empty($c5).
% 1.82/2.03 ** KEPT (pick-wt=2): 48 [] function($c5).
% 1.82/2.03 ** KEPT (pick-wt=2): 49 [] relation($c6).
% 1.82/2.03 ** KEPT (pick-wt=2): 50 [] relation($c8).
% 1.82/2.03 ** KEPT (pick-wt=2): 51 [] function($c8).
% 1.82/2.03 ** KEPT (pick-wt=2): 52 [] one_to_one($c8).
% 1.82/2.03 ** KEPT (pick-wt=2): 53 [] relation($c9).
% 1.82/2.03 ** KEPT (pick-wt=2): 54 [] relation_empty_yielding($c9).
% 1.82/2.04 ** KEPT (pick-wt=2): 55 [] relation($c10).
% 1.82/2.04 ** KEPT (pick-wt=2): 56 [] relation_empty_yielding($c10).
% 1.82/2.04 ** KEPT (pick-wt=2): 57 [] function($c10).
% 1.82/2.04 ** KEPT (pick-wt=2): 58 [] relation($c11).
% 1.82/2.04 ** KEPT (pick-wt=2): 59 [] relation_non_empty($c11).
% 1.82/2.04 ** KEPT (pick-wt=2): 60 [] function($c11).
% 1.82/2.04 ** KEPT (pick-wt=3): 61 [] subset(A,A).
% 1.82/2.04 ** KEPT (pick-wt=3): 62 [] inclusion_comparable(A,A).
% 1.82/2.04 ** KEPT (pick-wt=2): 63 [] ordinal($c13).
% 1.82/2.04 ** KEPT (pick-wt=2): 64 [] ordinal($c12).
% 1.82/2.04 Following clause subsumed by 33 during input processing: 0 [copy,33,flip.1] A=A.
% 1.82/2.04 33 back subsumes 32.
% 1.82/2.04 61 back subsumes 31.
% 1.82/2.04 61 back subsumes 30.
% 1.82/2.04
% 1.82/2.04 ======= end of input processing =======
% 1.82/2.04
% 1.82/2.04 =========== start of search ===========
% 1.82/2.04
% 1.82/2.04 -------- PROOF --------
% 1.82/2.04
% 1.82/2.04 ----> UNIT CONFLICT at 0.01 sec ----> 332 [binary,331.1,20.1] $F.
% 1.82/2.04
% 1.82/2.04 Length of proof is 5. Level of proof is 5.
% 1.82/2.04
% 1.82/2.04 ---------------- PROOF ----------------
% 1.82/2.04 % SZS status Theorem
% 1.82/2.04 % SZS output start Refutation
% See solution above
% 1.82/2.04 ------------ end of proof -------------
% 1.82/2.04
% 1.82/2.04
% 1.82/2.04 Search stopped by max_proofs option.
% 1.82/2.04
% 1.82/2.04
% 1.82/2.04 Search stopped by max_proofs option.
% 1.82/2.04
% 1.82/2.04 ============ end of search ============
% 1.82/2.04
% 1.82/2.04 -------------- statistics -------------
% 1.82/2.04 clauses given 118
% 1.82/2.04 clauses generated 778
% 1.82/2.04 clauses kept 327
% 1.82/2.04 clauses forward subsumed 525
% 1.82/2.04 clauses back subsumed 18
% 1.82/2.04 Kbytes malloced 976
% 1.82/2.04
% 1.82/2.04 ----------- times (seconds) -----------
% 1.82/2.04 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.82/2.04 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.82/2.04 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.82/2.04
% 1.82/2.04 That finishes the proof of the theorem.
% 1.82/2.04
% 1.82/2.04 Process 23542 finished Wed Jul 27 09:55:08 2022
% 1.82/2.04 Otter interrupted
% 1.82/2.04 PROOF FOUND
%------------------------------------------------------------------------------