TSTP Solution File: NUM388+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : NUM388+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n013.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 13:08:13 EDT 2022
% Result : Theorem 2.15s 2.29s
% Output : Refutation 2.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of clauses : 16 ( 10 unt; 1 nHn; 16 RR)
% Number of literals : 25 ( 0 equ; 10 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 12 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
( ~ ordinal(A)
| epsilon_transitive(A) ),
file('NUM388+1.p',unknown),
[] ).
cnf(8,axiom,
( ~ epsilon_transitive(A)
| ~ in(B,A)
| subset(B,A) ),
file('NUM388+1.p',unknown),
[] ).
cnf(12,axiom,
~ in(dollar_c12,dollar_c13),
file('NUM388+1.p',unknown),
[] ).
cnf(14,axiom,
( ~ element(A,B)
| empty(B)
| in(A,B) ),
file('NUM388+1.p',unknown),
[] ).
cnf(16,axiom,
( element(A,powerset(B))
| ~ subset(A,B) ),
file('NUM388+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ in(A,B)
| ~ element(B,powerset(C))
| element(A,C) ),
file('NUM388+1.p',unknown),
[] ).
cnf(20,axiom,
( ~ in(A,B)
| ~ empty(B) ),
file('NUM388+1.p',unknown),
[] ).
cnf(55,axiom,
ordinal(dollar_c13),
file('NUM388+1.p',unknown),
[] ).
cnf(57,axiom,
in(dollar_c12,dollar_c14),
file('NUM388+1.p',unknown),
[] ).
cnf(58,axiom,
in(dollar_c14,dollar_c13),
file('NUM388+1.p',unknown),
[] ).
cnf(93,plain,
epsilon_transitive(dollar_c13),
inference(hyper,[status(thm)],[55,3]),
[iquote('hyper,55,3')] ).
cnf(109,plain,
subset(dollar_c14,dollar_c13),
inference(hyper,[status(thm)],[58,8,93]),
[iquote('hyper,58,8,93')] ).
cnf(119,plain,
element(dollar_c14,powerset(dollar_c13)),
inference(hyper,[status(thm)],[109,16]),
[iquote('hyper,109,16')] ).
cnf(128,plain,
element(dollar_c12,dollar_c13),
inference(hyper,[status(thm)],[119,17,57]),
[iquote('hyper,119,17,57')] ).
cnf(133,plain,
empty(dollar_c13),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[128,14]),12]),
[iquote('hyper,128,14,unit_del,12')] ).
cnf(140,plain,
$false,
inference(hyper,[status(thm)],[133,20,58]),
[iquote('hyper,133,20,58')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM388+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 09:50:15 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.15/2.29 ----- Otter 3.3f, August 2004 -----
% 2.15/2.29 The process was started by sandbox on n013.cluster.edu,
% 2.15/2.29 Wed Jul 27 09:50:15 2022
% 2.15/2.29 The command was "./otter". The process ID is 32477.
% 2.15/2.29
% 2.15/2.29 set(prolog_style_variables).
% 2.15/2.29 set(auto).
% 2.15/2.29 dependent: set(auto1).
% 2.15/2.29 dependent: set(process_input).
% 2.15/2.29 dependent: clear(print_kept).
% 2.15/2.29 dependent: clear(print_new_demod).
% 2.15/2.29 dependent: clear(print_back_demod).
% 2.15/2.29 dependent: clear(print_back_sub).
% 2.15/2.29 dependent: set(control_memory).
% 2.15/2.29 dependent: assign(max_mem, 12000).
% 2.15/2.29 dependent: assign(pick_given_ratio, 4).
% 2.15/2.29 dependent: assign(stats_level, 1).
% 2.15/2.29 dependent: assign(max_seconds, 10800).
% 2.15/2.29 clear(print_given).
% 2.15/2.29
% 2.15/2.29 formula_list(usable).
% 2.15/2.29 all A (A=A).
% 2.15/2.29 all A B (in(A,B)-> -in(B,A)).
% 2.15/2.29 all A (empty(A)->function(A)).
% 2.15/2.29 all A (ordinal(A)->epsilon_transitive(A)&epsilon_connected(A)).
% 2.15/2.29 all A (empty(A)->relation(A)).
% 2.15/2.29 all A (relation(A)&empty(A)&function(A)->relation(A)&function(A)&one_to_one(A)).
% 2.15/2.29 all A (epsilon_transitive(A)&epsilon_connected(A)->ordinal(A)).
% 2.15/2.29 all A (epsilon_transitive(A)<-> (all B (in(B,A)->subset(B,A)))).
% 2.15/2.29 all A exists B element(B,A).
% 2.15/2.29 empty(empty_set).
% 2.15/2.29 relation(empty_set).
% 2.15/2.29 relation_empty_yielding(empty_set).
% 2.15/2.29 empty(empty_set).
% 2.15/2.29 empty(empty_set).
% 2.15/2.29 relation(empty_set).
% 2.15/2.29 exists A (relation(A)&function(A)).
% 2.15/2.29 exists A (epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)).
% 2.15/2.29 exists A (empty(A)&relation(A)).
% 2.15/2.29 exists A empty(A).
% 2.15/2.29 exists A (relation(A)&empty(A)&function(A)).
% 2.15/2.29 exists A (-empty(A)&relation(A)).
% 2.15/2.29 exists A (-empty(A)).
% 2.15/2.29 exists A (relation(A)&function(A)&one_to_one(A)).
% 2.15/2.29 exists A (relation(A)&relation_empty_yielding(A)).
% 2.15/2.29 exists A (relation(A)&relation_empty_yielding(A)&function(A)).
% 2.15/2.29 exists A (relation(A)&relation_non_empty(A)&function(A)).
% 2.15/2.29 all A B subset(A,A).
% 2.15/2.29 -(all A (ordinal(A)-> (all B (ordinal(B)-> (all C (epsilon_transitive(C)-> (in(C,A)&in(A,B)->in(C,B)))))))).
% 2.15/2.29 all A B (in(A,B)->element(A,B)).
% 2.15/2.29 all A B (element(A,B)->empty(B)|in(A,B)).
% 2.15/2.29 all A B (element(A,powerset(B))<->subset(A,B)).
% 2.15/2.29 all A B C (in(A,B)&element(B,powerset(C))->element(A,C)).
% 2.15/2.29 all A B C (-(in(A,B)&element(B,powerset(C))&empty(C))).
% 2.15/2.29 all A (empty(A)->A=empty_set).
% 2.15/2.29 all A B (-(in(A,B)&empty(B))).
% 2.15/2.29 all A B (-(empty(A)&A!=B&empty(B))).
% 2.15/2.29 end_of_list.
% 2.15/2.29
% 2.15/2.29 -------> usable clausifies to:
% 2.15/2.29
% 2.15/2.29 list(usable).
% 2.15/2.29 0 [] A=A.
% 2.15/2.29 0 [] -in(A,B)| -in(B,A).
% 2.15/2.29 0 [] -empty(A)|function(A).
% 2.15/2.29 0 [] -ordinal(A)|epsilon_transitive(A).
% 2.15/2.29 0 [] -ordinal(A)|epsilon_connected(A).
% 2.15/2.29 0 [] -empty(A)|relation(A).
% 2.15/2.29 0 [] -relation(A)| -empty(A)| -function(A)|one_to_one(A).
% 2.15/2.29 0 [] -epsilon_transitive(A)| -epsilon_connected(A)|ordinal(A).
% 2.15/2.29 0 [] -epsilon_transitive(A)| -in(B,A)|subset(B,A).
% 2.15/2.29 0 [] epsilon_transitive(A)|in($f1(A),A).
% 2.15/2.29 0 [] epsilon_transitive(A)| -subset($f1(A),A).
% 2.15/2.29 0 [] element($f2(A),A).
% 2.15/2.29 0 [] empty(empty_set).
% 2.15/2.29 0 [] relation(empty_set).
% 2.15/2.29 0 [] relation_empty_yielding(empty_set).
% 2.15/2.29 0 [] empty(empty_set).
% 2.15/2.29 0 [] empty(empty_set).
% 2.15/2.29 0 [] relation(empty_set).
% 2.15/2.29 0 [] relation($c1).
% 2.15/2.29 0 [] function($c1).
% 2.15/2.29 0 [] epsilon_transitive($c2).
% 2.15/2.29 0 [] epsilon_connected($c2).
% 2.15/2.29 0 [] ordinal($c2).
% 2.15/2.29 0 [] empty($c3).
% 2.15/2.29 0 [] relation($c3).
% 2.15/2.29 0 [] empty($c4).
% 2.15/2.29 0 [] relation($c5).
% 2.15/2.29 0 [] empty($c5).
% 2.15/2.29 0 [] function($c5).
% 2.15/2.29 0 [] -empty($c6).
% 2.15/2.29 0 [] relation($c6).
% 2.15/2.29 0 [] -empty($c7).
% 2.15/2.29 0 [] relation($c8).
% 2.15/2.29 0 [] function($c8).
% 2.15/2.29 0 [] one_to_one($c8).
% 2.15/2.29 0 [] relation($c9).
% 2.15/2.29 0 [] relation_empty_yielding($c9).
% 2.15/2.29 0 [] relation($c10).
% 2.15/2.29 0 [] relation_empty_yielding($c10).
% 2.15/2.29 0 [] function($c10).
% 2.15/2.29 0 [] relation($c11).
% 2.15/2.29 0 [] relation_non_empty($c11).
% 2.15/2.29 0 [] function($c11).
% 2.15/2.29 0 [] subset(A,A).
% 2.15/2.29 0 [] ordinal($c14).
% 2.15/2.29 0 [] ordinal($c13).
% 2.15/2.29 0 [] epsilon_transitive($c12).
% 2.15/2.29 0 [] in($c12,$c14).
% 2.15/2.29 0 [] in($c14,$c13).
% 2.15/2.29 0 [] -in($c12,$c13).
% 2.15/2.29 0 [] -in(A,B)|element(A,B).
% 2.15/2.29 0 [] -element(A,B)|empty(B)|in(A,B).
% 2.15/2.29 0 [] -element(A,powerset(B))|subset(A,B).
% 2.15/2.29 0 [] element(A,powerset(B))| -subset(A,B).
% 2.15/2.29 0 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 2.15/2.29 0 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 2.15/2.29 0 [] -empty(A)|A=empty_set.
% 2.15/2.29 0 [] -in(A,B)| -empty(B).
% 2.15/2.29 0 [] -empty(A)|A=B| -empty(B).
% 2.15/2.29 end_of_list.
% 2.15/2.29
% 2.15/2.29 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 2.15/2.29
% 2.15/2.29 This ia a non-Horn set with equality. The strategy will be
% 2.15/2.29 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.15/2.29 deletion, with positive clauses in sos and nonpositive
% 2.15/2.29 clauses in usable.
% 2.15/2.29
% 2.15/2.29 dependent: set(knuth_bendix).
% 2.15/2.29 dependent: set(anl_eq).
% 2.15/2.29 dependent: set(para_from).
% 2.15/2.29 dependent: set(para_into).
% 2.15/2.29 dependent: clear(para_from_right).
% 2.15/2.29 dependent: clear(para_into_right).
% 2.15/2.29 dependent: set(para_from_vars).
% 2.15/2.29 dependent: set(eq_units_both_ways).
% 2.15/2.29 dependent: set(dynamic_demod_all).
% 2.15/2.29 dependent: set(dynamic_demod).
% 2.15/2.29 dependent: set(order_eq).
% 2.15/2.29 dependent: set(back_demod).
% 2.15/2.29 dependent: set(lrpo).
% 2.15/2.29 dependent: set(hyper_res).
% 2.15/2.29 dependent: set(unit_deletion).
% 2.15/2.29 dependent: set(factor).
% 2.15/2.29
% 2.15/2.29 ------------> process usable:
% 2.15/2.29 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 2.15/2.29 ** KEPT (pick-wt=4): 2 [] -empty(A)|function(A).
% 2.15/2.29 ** KEPT (pick-wt=4): 3 [] -ordinal(A)|epsilon_transitive(A).
% 2.15/2.29 ** KEPT (pick-wt=4): 4 [] -ordinal(A)|epsilon_connected(A).
% 2.15/2.29 ** KEPT (pick-wt=4): 5 [] -empty(A)|relation(A).
% 2.15/2.29 ** KEPT (pick-wt=8): 6 [] -relation(A)| -empty(A)| -function(A)|one_to_one(A).
% 2.15/2.29 ** KEPT (pick-wt=6): 7 [] -epsilon_transitive(A)| -epsilon_connected(A)|ordinal(A).
% 2.15/2.29 ** KEPT (pick-wt=8): 8 [] -epsilon_transitive(A)| -in(B,A)|subset(B,A).
% 2.15/2.29 ** KEPT (pick-wt=6): 9 [] epsilon_transitive(A)| -subset($f1(A),A).
% 2.15/2.29 ** KEPT (pick-wt=2): 10 [] -empty($c6).
% 2.15/2.29 ** KEPT (pick-wt=2): 11 [] -empty($c7).
% 2.15/2.29 ** KEPT (pick-wt=3): 12 [] -in($c12,$c13).
% 2.15/2.29 ** KEPT (pick-wt=6): 13 [] -in(A,B)|element(A,B).
% 2.15/2.29 ** KEPT (pick-wt=8): 14 [] -element(A,B)|empty(B)|in(A,B).
% 2.15/2.29 ** KEPT (pick-wt=7): 15 [] -element(A,powerset(B))|subset(A,B).
% 2.15/2.29 ** KEPT (pick-wt=7): 16 [] element(A,powerset(B))| -subset(A,B).
% 2.15/2.29 ** KEPT (pick-wt=10): 17 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 2.15/2.29 ** KEPT (pick-wt=9): 18 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 2.15/2.29 ** KEPT (pick-wt=5): 19 [] -empty(A)|A=empty_set.
% 2.15/2.29 ** KEPT (pick-wt=5): 20 [] -in(A,B)| -empty(B).
% 2.15/2.29 ** KEPT (pick-wt=7): 21 [] -empty(A)|A=B| -empty(B).
% 2.15/2.29
% 2.15/2.29 ------------> process sos:
% 2.15/2.29 ** KEPT (pick-wt=3): 24 [] A=A.
% 2.15/2.29 ** KEPT (pick-wt=6): 25 [] epsilon_transitive(A)|in($f1(A),A).
% 2.15/2.29 ** KEPT (pick-wt=4): 26 [] element($f2(A),A).
% 2.15/2.29 ** KEPT (pick-wt=2): 27 [] empty(empty_set).
% 2.15/2.29 ** KEPT (pick-wt=2): 28 [] relation(empty_set).
% 2.15/2.29 ** KEPT (pick-wt=2): 29 [] relation_empty_yielding(empty_set).
% 2.15/2.29 Following clause subsumed by 27 during input processing: 0 [] empty(empty_set).
% 2.15/2.29 Following clause subsumed by 27 during input processing: 0 [] empty(empty_set).
% 2.15/2.29 Following clause subsumed by 28 during input processing: 0 [] relation(empty_set).
% 2.15/2.29 ** KEPT (pick-wt=2): 30 [] relation($c1).
% 2.15/2.29 ** KEPT (pick-wt=2): 31 [] function($c1).
% 2.15/2.29 ** KEPT (pick-wt=2): 32 [] epsilon_transitive($c2).
% 2.15/2.29 ** KEPT (pick-wt=2): 33 [] epsilon_connected($c2).
% 2.15/2.29 ** KEPT (pick-wt=2): 34 [] ordinal($c2).
% 2.15/2.29 ** KEPT (pick-wt=2): 35 [] empty($c3).
% 2.15/2.29 ** KEPT (pick-wt=2): 36 [] relation($c3).
% 2.15/2.29 ** KEPT (pick-wt=2): 37 [] empty($c4).
% 2.15/2.29 ** KEPT (pick-wt=2): 38 [] relation($c5).
% 2.15/2.29 ** KEPT (pick-wt=2): 39 [] empty($c5).
% 2.15/2.29 ** KEPT (pick-wt=2): 40 [] function($c5).
% 2.15/2.29 ** KEPT (pick-wt=2): 41 [] relation($c6).
% 2.15/2.29 ** KEPT (pick-wt=2): 42 [] relation($c8).
% 2.15/2.29 ** KEPT (pick-wt=2): 43 [] function($c8).
% 2.15/2.29 ** KEPT (pick-wt=2): 44 [] one_to_one($c8).
% 2.15/2.29 ** KEPT (pick-wt=2): 45 [] relation($c9).
% 2.15/2.29 ** KEPT (pick-wt=2): 46 [] relation_empty_yielding($c9).
% 2.15/2.29 ** KEPT (pick-wt=2): 47 [] relation($c10).
% 2.15/2.29 ** KEPT (pick-wt=2): 48 [] relation_empty_yielding($c10).
% 2.15/2.29 ** KEPT (pick-wt=2): 49 [] function($c10).
% 2.15/2.29 ** KEPT (pick-wt=2): 50 [] relation($c11).
% 2.15/2.29 ** KEPT (pick-wt=2): 51 [] relation_non_empty($c11).
% 2.15/2.29 ** KEPT (pick-wt=2): 52 [] function($c11).
% 2.15/2.29 ** KEPT (pick-wt=3): 53 [] subset(A,A).
% 2.15/2.29 ** KEPT (pick-wt=2): 54 [] ordinal($c14).
% 2.15/2.29 ** KEPT (pick-wt=2): 55 [] ordinal($c13).
% 2.15/2.29 ** KEPT (pick-wt=2): 56 [] epsilon_transitive($c12).
% 2.15/2.29 ** KEPT (pick-wt=3): 57 [] in($c12,$c14).
% 2.15/2.29 ** KEPT (pick-wt=3): 58 [] in($c14,$c13).
% 2.15/2.29 Following clause subsumed by 24 during input processing: 0 [copy,24,flip.1] A=A.
% 2.15/2.29 24 back subsumes 23.
% 2.15/2.29
% 2.15/2.29 ======= end of input processing =======
% 2.15/2.29
% 2.15/2.29 =========== start of search ===========
% 2.15/2.29
% 2.15/2.29 -------- PROOF --------
% 2.15/2.29
% 2.15/2.29 -----> EMPTY CLAUSE at 0.00 sec ----> 140 [hyper,133,20,58] $F.
% 2.15/2.29
% 2.15/2.29 Length of proof is 5. Level of proof is 5.
% 2.15/2.29
% 2.15/2.29 ---------------- PROOF ----------------
% 2.15/2.29 % SZS status Theorem
% 2.15/2.29 % SZS output start Refutation
% See solution above
% 2.15/2.29 ------------ end of proof -------------
% 2.15/2.29
% 2.15/2.29
% 2.15/2.29 Search stopped by max_proofs option.
% 2.15/2.29
% 2.15/2.29
% 2.15/2.29 Search stopped by max_proofs option.
% 2.15/2.29
% 2.15/2.29 ============ end of search ============
% 2.15/2.29
% 2.15/2.29 -------------- statistics -------------
% 2.15/2.29 clauses given 60
% 2.15/2.29 clauses generated 188
% 2.15/2.29 clauses kept 135
% 2.15/2.29 clauses forward subsumed 124
% 2.15/2.29 clauses back subsumed 6
% 2.15/2.29 Kbytes malloced 976
% 2.15/2.29
% 2.15/2.29 ----------- times (seconds) -----------
% 2.18/2.30 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.18/2.30 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.18/2.30 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.18/2.30
% 2.18/2.30 That finishes the proof of the theorem.
% 2.18/2.30
% 2.18/2.30 Process 32477 finished Wed Jul 27 09:50:17 2022
% 2.18/2.30 Otter interrupted
% 2.18/2.30 PROOF FOUND
%------------------------------------------------------------------------------