TSTP Solution File: NUM405+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : NUM405+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n022.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 13:08:15 EDT 2022
% Result : Theorem 1.74s 1.94s
% Output : Refutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of clauses : 10 ( 3 unt; 3 nHn; 7 RR)
% Number of literals : 18 ( 0 equ; 6 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 9 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(15,axiom,
( ~ in(A,dollar_f2(B))
| ordinal(A) ),
file('NUM405+1.p',unknown),
[] ).
cnf(16,axiom,
( in(A,dollar_f2(B))
| ~ in(A,B)
| ~ ordinal(A) ),
file('NUM405+1.p',unknown),
[] ).
cnf(19,axiom,
( ~ in(dollar_f3(A),A)
| ~ ordinal(dollar_f3(A)) ),
file('NUM405+1.p',unknown),
[] ).
cnf(20,axiom,
( ~ ordinal(A)
| in(A,dollar_c14) ),
file('NUM405+1.p',unknown),
[] ).
cnf(69,axiom,
( in(dollar_f3(A),A)
| ordinal(dollar_f3(A)) ),
file('NUM405+1.p',unknown),
[] ).
cnf(96,plain,
( in(dollar_f3(A),A)
| in(dollar_f3(A),dollar_c14) ),
inference(hyper,[status(thm)],[69,20]),
[iquote('hyper,69,20')] ).
cnf(185,plain,
( in(dollar_f3(A),A)
| in(dollar_f3(A),dollar_f2(dollar_c14)) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[96,16,69])]),
[iquote('hyper,96,16,69,factor_simp')] ).
cnf(187,plain,
in(dollar_f3(dollar_f2(dollar_c14)),dollar_f2(dollar_c14)),
inference(factor,[status(thm)],[185]),
[iquote('factor,185.1.2')] ).
cnf(352,plain,
ordinal(dollar_f3(dollar_f2(dollar_c14))),
inference(hyper,[status(thm)],[187,15]),
[iquote('hyper,187,15')] ).
cnf(353,plain,
$false,
inference(hyper,[status(thm)],[352,19,187]),
[iquote('hyper,352,19,187')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM405+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n022.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 09:46:35 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.74/1.92 ----- Otter 3.3f, August 2004 -----
% 1.74/1.92 The process was started by sandbox2 on n022.cluster.edu,
% 1.74/1.92 Wed Jul 27 09:46:35 2022
% 1.74/1.92 The command was "./otter". The process ID is 4451.
% 1.74/1.92
% 1.74/1.92 set(prolog_style_variables).
% 1.74/1.92 set(auto).
% 1.74/1.92 dependent: set(auto1).
% 1.74/1.92 dependent: set(process_input).
% 1.74/1.92 dependent: clear(print_kept).
% 1.74/1.92 dependent: clear(print_new_demod).
% 1.74/1.92 dependent: clear(print_back_demod).
% 1.74/1.92 dependent: clear(print_back_sub).
% 1.74/1.92 dependent: set(control_memory).
% 1.74/1.92 dependent: assign(max_mem, 12000).
% 1.74/1.92 dependent: assign(pick_given_ratio, 4).
% 1.74/1.92 dependent: assign(stats_level, 1).
% 1.74/1.92 dependent: assign(max_seconds, 10800).
% 1.74/1.92 clear(print_given).
% 1.74/1.92
% 1.74/1.92 formula_list(usable).
% 1.74/1.92 all A (A=A).
% 1.74/1.92 all A B (in(A,B)-> -in(B,A)).
% 1.74/1.92 all A (empty(A)->function(A)).
% 1.74/1.92 all A (ordinal(A)->epsilon_transitive(A)&epsilon_connected(A)).
% 1.74/1.92 all A (empty(A)->relation(A)).
% 1.74/1.92 all A (relation(A)&empty(A)&function(A)->relation(A)&function(A)&one_to_one(A)).
% 1.74/1.92 all A (epsilon_transitive(A)&epsilon_connected(A)->ordinal(A)).
% 1.74/1.92 all A (empty(A)->epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)).
% 1.74/1.92 all A exists B element(B,A).
% 1.74/1.92 empty(empty_set).
% 1.74/1.92 relation(empty_set).
% 1.74/1.92 relation_empty_yielding(empty_set).
% 1.74/1.92 empty(empty_set).
% 1.74/1.92 relation(empty_set).
% 1.74/1.92 relation_empty_yielding(empty_set).
% 1.74/1.92 function(empty_set).
% 1.74/1.92 one_to_one(empty_set).
% 1.74/1.92 empty(empty_set).
% 1.74/1.92 epsilon_transitive(empty_set).
% 1.74/1.92 epsilon_connected(empty_set).
% 1.74/1.92 ordinal(empty_set).
% 1.74/1.92 empty(empty_set).
% 1.74/1.92 relation(empty_set).
% 1.74/1.92 exists A (relation(A)&function(A)).
% 1.74/1.92 exists A (epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)).
% 1.74/1.92 exists A (empty(A)&relation(A)).
% 1.74/1.92 exists A empty(A).
% 1.74/1.92 exists A (relation(A)&empty(A)&function(A)).
% 1.74/1.92 exists A (relation(A)&function(A)&one_to_one(A)&empty(A)&epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)).
% 1.74/1.92 exists A (-empty(A)&relation(A)).
% 1.74/1.92 exists A (-empty(A)).
% 1.74/1.92 exists A (relation(A)&function(A)&one_to_one(A)).
% 1.74/1.92 exists A (-empty(A)&epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)).
% 1.74/1.92 exists A (relation(A)&relation_empty_yielding(A)).
% 1.74/1.92 exists A (relation(A)&relation_empty_yielding(A)&function(A)).
% 1.74/1.92 exists A (relation(A)&relation_non_empty(A)&function(A)).
% 1.74/1.92 all A exists B all C (in(C,B)<->in(C,A)&ordinal(C)).
% 1.74/1.92 all A B (in(A,B)->element(A,B)).
% 1.74/1.92 all A B (element(A,B)->empty(B)|in(A,B)).
% 1.74/1.92 all A (-(all B (in(B,A)<->ordinal(B)))).
% 1.74/1.92 -(all A (-(all B (ordinal(B)->in(B,A))))).
% 1.74/1.92 all A (empty(A)->A=empty_set).
% 1.74/1.92 all A B (-(in(A,B)&empty(B))).
% 1.74/1.92 all A B (-(empty(A)&A!=B&empty(B))).
% 1.74/1.92 end_of_list.
% 1.74/1.92
% 1.74/1.92 -------> usable clausifies to:
% 1.74/1.92
% 1.74/1.92 list(usable).
% 1.74/1.92 0 [] A=A.
% 1.74/1.92 0 [] -in(A,B)| -in(B,A).
% 1.74/1.92 0 [] -empty(A)|function(A).
% 1.74/1.92 0 [] -ordinal(A)|epsilon_transitive(A).
% 1.74/1.92 0 [] -ordinal(A)|epsilon_connected(A).
% 1.74/1.92 0 [] -empty(A)|relation(A).
% 1.74/1.92 0 [] -relation(A)| -empty(A)| -function(A)|one_to_one(A).
% 1.74/1.92 0 [] -epsilon_transitive(A)| -epsilon_connected(A)|ordinal(A).
% 1.74/1.92 0 [] -empty(A)|epsilon_transitive(A).
% 1.74/1.92 0 [] -empty(A)|epsilon_connected(A).
% 1.74/1.92 0 [] -empty(A)|ordinal(A).
% 1.74/1.92 0 [] element($f1(A),A).
% 1.74/1.92 0 [] empty(empty_set).
% 1.74/1.92 0 [] relation(empty_set).
% 1.74/1.92 0 [] relation_empty_yielding(empty_set).
% 1.74/1.92 0 [] empty(empty_set).
% 1.74/1.92 0 [] relation(empty_set).
% 1.74/1.92 0 [] relation_empty_yielding(empty_set).
% 1.74/1.92 0 [] function(empty_set).
% 1.74/1.92 0 [] one_to_one(empty_set).
% 1.74/1.92 0 [] empty(empty_set).
% 1.74/1.92 0 [] epsilon_transitive(empty_set).
% 1.74/1.92 0 [] epsilon_connected(empty_set).
% 1.74/1.92 0 [] ordinal(empty_set).
% 1.74/1.92 0 [] empty(empty_set).
% 1.74/1.92 0 [] relation(empty_set).
% 1.74/1.92 0 [] relation($c1).
% 1.74/1.92 0 [] function($c1).
% 1.74/1.92 0 [] epsilon_transitive($c2).
% 1.74/1.92 0 [] epsilon_connected($c2).
% 1.74/1.92 0 [] ordinal($c2).
% 1.74/1.92 0 [] empty($c3).
% 1.74/1.92 0 [] relation($c3).
% 1.74/1.92 0 [] empty($c4).
% 1.74/1.92 0 [] relation($c5).
% 1.74/1.92 0 [] empty($c5).
% 1.74/1.92 0 [] function($c5).
% 1.74/1.92 0 [] relation($c6).
% 1.74/1.92 0 [] function($c6).
% 1.74/1.92 0 [] one_to_one($c6).
% 1.74/1.92 0 [] empty($c6).
% 1.74/1.92 0 [] epsilon_transitive($c6).
% 1.74/1.92 0 [] epsilon_connected($c6).
% 1.74/1.92 0 [] ordinal($c6).
% 1.74/1.92 0 [] -empty($c7).
% 1.74/1.92 0 [] relation($c7).
% 1.74/1.92 0 [] -empty($c8).
% 1.74/1.92 0 [] relation($c9).
% 1.74/1.92 0 [] function($c9).
% 1.74/1.92 0 [] one_to_one($c9).
% 1.74/1.92 0 [] -empty($c10).
% 1.74/1.92 0 [] epsilon_transitive($c10).
% 1.74/1.92 0 [] epsilon_connected($c10).
% 1.74/1.92 0 [] ordinal($c10).
% 1.74/1.92 0 [] relation($c11).
% 1.74/1.92 0 [] relation_empty_yielding($c11).
% 1.74/1.92 0 [] relation($c12).
% 1.74/1.92 0 [] relation_empty_yielding($c12).
% 1.74/1.92 0 [] function($c12).
% 1.74/1.92 0 [] relation($c13).
% 1.74/1.92 0 [] relation_non_empty($c13).
% 1.74/1.92 0 [] function($c13).
% 1.74/1.92 0 [] -in(C,$f2(A))|in(C,A).
% 1.74/1.92 0 [] -in(C,$f2(A))|ordinal(C).
% 1.74/1.92 0 [] in(C,$f2(A))| -in(C,A)| -ordinal(C).
% 1.74/1.92 0 [] -in(A,B)|element(A,B).
% 1.74/1.92 0 [] -element(A,B)|empty(B)|in(A,B).
% 1.74/1.92 0 [] in($f3(A),A)|ordinal($f3(A)).
% 1.74/1.92 0 [] -in($f3(A),A)| -ordinal($f3(A)).
% 1.74/1.92 0 [] -ordinal(B)|in(B,$c14).
% 1.74/1.92 0 [] -empty(A)|A=empty_set.
% 1.74/1.92 0 [] -in(A,B)| -empty(B).
% 1.74/1.92 0 [] -empty(A)|A=B| -empty(B).
% 1.74/1.92 end_of_list.
% 1.74/1.92
% 1.74/1.92 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.74/1.92
% 1.74/1.92 This ia a non-Horn set with equality. The strategy will be
% 1.74/1.92 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.74/1.92 deletion, with positive clauses in sos and nonpositive
% 1.74/1.92 clauses in usable.
% 1.74/1.92
% 1.74/1.92 dependent: set(knuth_bendix).
% 1.74/1.92 dependent: set(anl_eq).
% 1.74/1.92 dependent: set(para_from).
% 1.74/1.92 dependent: set(para_into).
% 1.74/1.92 dependent: clear(para_from_right).
% 1.74/1.92 dependent: clear(para_into_right).
% 1.74/1.92 dependent: set(para_from_vars).
% 1.74/1.92 dependent: set(eq_units_both_ways).
% 1.74/1.92 dependent: set(dynamic_demod_all).
% 1.74/1.92 dependent: set(dynamic_demod).
% 1.74/1.92 dependent: set(order_eq).
% 1.74/1.92 dependent: set(back_demod).
% 1.74/1.92 dependent: set(lrpo).
% 1.74/1.92 dependent: set(hyper_res).
% 1.74/1.92 dependent: set(unit_deletion).
% 1.74/1.92 dependent: set(factor).
% 1.74/1.92
% 1.74/1.92 ------------> process usable:
% 1.74/1.92 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.74/1.92 ** KEPT (pick-wt=4): 2 [] -empty(A)|function(A).
% 1.74/1.92 ** KEPT (pick-wt=4): 3 [] -ordinal(A)|epsilon_transitive(A).
% 1.74/1.92 ** KEPT (pick-wt=4): 4 [] -ordinal(A)|epsilon_connected(A).
% 1.74/1.92 ** KEPT (pick-wt=4): 5 [] -empty(A)|relation(A).
% 1.74/1.92 ** KEPT (pick-wt=8): 6 [] -relation(A)| -empty(A)| -function(A)|one_to_one(A).
% 1.74/1.92 ** KEPT (pick-wt=6): 7 [] -epsilon_transitive(A)| -epsilon_connected(A)|ordinal(A).
% 1.74/1.92 ** KEPT (pick-wt=4): 8 [] -empty(A)|epsilon_transitive(A).
% 1.74/1.92 ** KEPT (pick-wt=4): 9 [] -empty(A)|epsilon_connected(A).
% 1.74/1.92 ** KEPT (pick-wt=4): 10 [] -empty(A)|ordinal(A).
% 1.74/1.92 ** KEPT (pick-wt=2): 11 [] -empty($c7).
% 1.74/1.92 ** KEPT (pick-wt=2): 12 [] -empty($c8).
% 1.74/1.92 ** KEPT (pick-wt=2): 13 [] -empty($c10).
% 1.74/1.92 ** KEPT (pick-wt=7): 14 [] -in(A,$f2(B))|in(A,B).
% 1.74/1.92 ** KEPT (pick-wt=6): 15 [] -in(A,$f2(B))|ordinal(A).
% 1.74/1.92 ** KEPT (pick-wt=9): 16 [] in(A,$f2(B))| -in(A,B)| -ordinal(A).
% 1.74/1.92 ** KEPT (pick-wt=6): 17 [] -in(A,B)|element(A,B).
% 1.74/1.92 ** KEPT (pick-wt=8): 18 [] -element(A,B)|empty(B)|in(A,B).
% 1.74/1.92 ** KEPT (pick-wt=7): 19 [] -in($f3(A),A)| -ordinal($f3(A)).
% 1.74/1.92 ** KEPT (pick-wt=5): 20 [] -ordinal(A)|in(A,$c14).
% 1.74/1.92 ** KEPT (pick-wt=5): 21 [] -empty(A)|A=empty_set.
% 1.74/1.92 ** KEPT (pick-wt=5): 22 [] -in(A,B)| -empty(B).
% 1.74/1.92 ** KEPT (pick-wt=7): 23 [] -empty(A)|A=B| -empty(B).
% 1.74/1.92
% 1.74/1.92 ------------> process sos:
% 1.74/1.92 ** KEPT (pick-wt=3): 26 [] A=A.
% 1.74/1.92 ** KEPT (pick-wt=4): 27 [] element($f1(A),A).
% 1.74/1.92 ** KEPT (pick-wt=2): 28 [] empty(empty_set).
% 1.74/1.92 ** KEPT (pick-wt=2): 29 [] relation(empty_set).
% 1.74/1.92 ** KEPT (pick-wt=2): 30 [] relation_empty_yielding(empty_set).
% 1.74/1.92 Following clause subsumed by 28 during input processing: 0 [] empty(empty_set).
% 1.74/1.92 Following clause subsumed by 29 during input processing: 0 [] relation(empty_set).
% 1.74/1.92 Following clause subsumed by 30 during input processing: 0 [] relation_empty_yielding(empty_set).
% 1.74/1.92 ** KEPT (pick-wt=2): 31 [] function(empty_set).
% 1.74/1.92 ** KEPT (pick-wt=2): 32 [] one_to_one(empty_set).
% 1.74/1.92 Following clause subsumed by 28 during input processing: 0 [] empty(empty_set).
% 1.74/1.92 ** KEPT (pick-wt=2): 33 [] epsilon_transitive(empty_set).
% 1.74/1.92 ** KEPT (pick-wt=2): 34 [] epsilon_connected(empty_set).
% 1.74/1.92 ** KEPT (pick-wt=2): 35 [] ordinal(empty_set).
% 1.74/1.92 Following clause subsumed by 28 during input processing: 0 [] empty(empty_set).
% 1.74/1.92 Following clause subsumed by 29 during input processing: 0 [] relation(empty_set).
% 1.74/1.92 ** KEPT (pick-wt=2): 36 [] relation($c1).
% 1.74/1.92 ** KEPT (pick-wt=2): 37 [] function($c1).
% 1.74/1.92 ** KEPT (pick-wt=2): 38 [] epsilon_transitive($c2).
% 1.74/1.92 ** KEPT (pick-wt=2): 39 [] epsilon_connected($c2).
% 1.74/1.92 ** KEPT (pick-wt=2): 40 [] ordinal($c2).
% 1.74/1.92 ** KEPT (pick-wt=2): 41 [] empty($c3).
% 1.74/1.92 ** KEPT (pick-wt=2): 42 [] relation($c3).
% 1.74/1.92 ** KEPT (pick-wt=2): 43 [] empty($c4).
% 1.74/1.92 ** KEPT (pick-wt=2): 44 [] relation($c5).
% 1.74/1.92 ** KEPT (pick-wt=2): 45 [] empty($c5).
% 1.74/1.92 ** KEPT (pick-wt=2): 46 [] function($c5).
% 1.74/1.92 ** KEPT (pick-wt=2): 47 [] relation($c6).
% 1.74/1.92 ** KEPT (pick-wt=2): 48 [] function($c6).
% 1.74/1.92 ** KEPT (pick-wt=2): 49 [] one_to_one($c6).
% 1.74/1.92 ** KEPT (pick-wt=2): 50 [] empty($c6).
% 1.74/1.92 ** KEPT (pick-wt=2): 51 [] epsilon_transitive($c6).
% 1.74/1.94 ** KEPT (pick-wt=2): 52 [] epsilon_connected($c6).
% 1.74/1.94 ** KEPT (pick-wt=2): 53 [] ordinal($c6).
% 1.74/1.94 ** KEPT (pick-wt=2): 54 [] relation($c7).
% 1.74/1.94 ** KEPT (pick-wt=2): 55 [] relation($c9).
% 1.74/1.94 ** KEPT (pick-wt=2): 56 [] function($c9).
% 1.74/1.94 ** KEPT (pick-wt=2): 57 [] one_to_one($c9).
% 1.74/1.94 ** KEPT (pick-wt=2): 58 [] epsilon_transitive($c10).
% 1.74/1.94 ** KEPT (pick-wt=2): 59 [] epsilon_connected($c10).
% 1.74/1.94 ** KEPT (pick-wt=2): 60 [] ordinal($c10).
% 1.74/1.94 ** KEPT (pick-wt=2): 61 [] relation($c11).
% 1.74/1.94 ** KEPT (pick-wt=2): 62 [] relation_empty_yielding($c11).
% 1.74/1.94 ** KEPT (pick-wt=2): 63 [] relation($c12).
% 1.74/1.94 ** KEPT (pick-wt=2): 64 [] relation_empty_yielding($c12).
% 1.74/1.94 ** KEPT (pick-wt=2): 65 [] function($c12).
% 1.74/1.94 ** KEPT (pick-wt=2): 66 [] relation($c13).
% 1.74/1.94 ** KEPT (pick-wt=2): 67 [] relation_non_empty($c13).
% 1.74/1.94 ** KEPT (pick-wt=2): 68 [] function($c13).
% 1.74/1.94 ** KEPT (pick-wt=7): 69 [] in($f3(A),A)|ordinal($f3(A)).
% 1.74/1.94 Following clause subsumed by 26 during input processing: 0 [copy,26,flip.1] A=A.
% 1.74/1.94 26 back subsumes 25.
% 1.74/1.94
% 1.74/1.94 ======= end of input processing =======
% 1.74/1.94
% 1.74/1.94 =========== start of search ===========
% 1.74/1.94
% 1.74/1.94 -------- PROOF --------
% 1.74/1.94
% 1.74/1.94 -----> EMPTY CLAUSE at 0.02 sec ----> 353 [hyper,352,19,187] $F.
% 1.74/1.94
% 1.74/1.94 Length of proof is 4. Level of proof is 4.
% 1.74/1.94
% 1.74/1.94 ---------------- PROOF ----------------
% 1.74/1.94 % SZS status Theorem
% 1.74/1.94 % SZS output start Refutation
% See solution above
% 1.74/1.94 ------------ end of proof -------------
% 1.74/1.94
% 1.74/1.94
% 1.74/1.94 Search stopped by max_proofs option.
% 1.74/1.94
% 1.74/1.94
% 1.74/1.94 Search stopped by max_proofs option.
% 1.74/1.94
% 1.74/1.94 ============ end of search ============
% 1.74/1.94
% 1.74/1.94 -------------- statistics -------------
% 1.74/1.94 clauses given 119
% 1.74/1.94 clauses generated 1313
% 1.74/1.94 clauses kept 348
% 1.74/1.94 clauses forward subsumed 1057
% 1.74/1.94 clauses back subsumed 50
% 1.74/1.94 Kbytes malloced 1953
% 1.74/1.94
% 1.74/1.94 ----------- times (seconds) -----------
% 1.74/1.94 user CPU time 0.02 (0 hr, 0 min, 0 sec)
% 1.74/1.94 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.74/1.94 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.74/1.94
% 1.74/1.94 That finishes the proof of the theorem.
% 1.74/1.94
% 1.74/1.94 Process 4451 finished Wed Jul 27 09:46:37 2022
% 1.74/1.94 Otter interrupted
% 1.74/1.94 PROOF FOUND
%------------------------------------------------------------------------------