TSTP Solution File: NUM395+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : NUM395+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n026.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 2.07s 2.27s
% Output : Refutation 2.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of clauses : 18 ( 15 unt; 0 nHn; 18 RR)
% Number of literals : 23 ( 4 equ; 8 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 4 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(8,axiom,
( ~ empty(A)
| A = B
| ~ empty(B) ),
file('NUM395+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ epsilon_transitive(A)
| ~ epsilon_connected(A)
| ordinal(A) ),
file('NUM395+1.p',unknown),
[] ).
cnf(14,axiom,
( ~ empty(A)
| A = empty_set ),
file('NUM395+1.p',unknown),
[] ).
cnf(15,axiom,
~ ordinal(empty_set),
file('NUM395+1.p',unknown),
[] ).
cnf(26,axiom,
empty(dollar_c3),
file('NUM395+1.p',unknown),
[] ).
cnf(45,axiom,
empty(dollar_c10),
file('NUM395+1.p',unknown),
[] ).
cnf(46,axiom,
epsilon_transitive(empty_set),
file('NUM395+1.p',unknown),
[] ).
cnf(47,axiom,
epsilon_connected(empty_set),
file('NUM395+1.p',unknown),
[] ).
cnf(56,plain,
empty_set = dollar_c3,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[26,14])]),
[iquote('hyper,26,14,flip.1')] ).
cnf(58,plain,
epsilon_connected(dollar_c3),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[47]),56]),
[iquote('back_demod,47,demod,56')] ).
cnf(59,plain,
epsilon_transitive(dollar_c3),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[46]),56]),
[iquote('back_demod,46,demod,56')] ).
cnf(61,plain,
~ ordinal(dollar_c3),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[15]),56]),
[iquote('back_demod,15,demod,56')] ).
cnf(71,plain,
dollar_c3 = dollar_c10,
inference(hyper,[status(thm)],[45,8,26]),
[iquote('hyper,45,8,26')] ).
cnf(78,plain,
~ ordinal(dollar_c10),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[61]),71]),
[iquote('back_demod,61,demod,71')] ).
cnf(80,plain,
epsilon_transitive(dollar_c10),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[59]),71]),
[iquote('back_demod,59,demod,71')] ).
cnf(81,plain,
epsilon_connected(dollar_c10),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[58]),71]),
[iquote('back_demod,58,demod,71')] ).
cnf(103,plain,
ordinal(dollar_c10),
inference(hyper,[status(thm)],[81,11,80]),
[iquote('hyper,81,11,80')] ).
cnf(104,plain,
$false,
inference(binary,[status(thm)],[103,78]),
[iquote('binary,103.1,78.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM395+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n026.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 10:04:54 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.07/2.27 ----- Otter 3.3f, August 2004 -----
% 2.07/2.27 The process was started by sandbox2 on n026.cluster.edu,
% 2.07/2.27 Wed Jul 27 10:04:54 2022
% 2.07/2.27 The command was "./otter". The process ID is 7972.
% 2.07/2.27
% 2.07/2.27 set(prolog_style_variables).
% 2.07/2.27 set(auto).
% 2.07/2.27 dependent: set(auto1).
% 2.07/2.27 dependent: set(process_input).
% 2.07/2.27 dependent: clear(print_kept).
% 2.07/2.27 dependent: clear(print_new_demod).
% 2.07/2.27 dependent: clear(print_back_demod).
% 2.07/2.27 dependent: clear(print_back_sub).
% 2.07/2.27 dependent: set(control_memory).
% 2.07/2.27 dependent: assign(max_mem, 12000).
% 2.07/2.27 dependent: assign(pick_given_ratio, 4).
% 2.07/2.27 dependent: assign(stats_level, 1).
% 2.07/2.27 dependent: assign(max_seconds, 10800).
% 2.07/2.27 clear(print_given).
% 2.07/2.27
% 2.07/2.27 formula_list(usable).
% 2.07/2.27 all A (A=A).
% 2.07/2.27 all A exists B element(B,A).
% 2.07/2.27 all A B (element(A,B)->empty(B)|in(A,B)).
% 2.07/2.27 all A B (in(A,B)-> -in(B,A)).
% 2.07/2.27 all A B (in(A,B)->element(A,B)).
% 2.07/2.27 all A (empty(A)->function(A)).
% 2.07/2.27 all A (relation(A)&empty(A)&function(A)->relation(A)&function(A)&one_to_one(A)).
% 2.07/2.27 all A (empty(A)->relation(A)).
% 2.07/2.27 all A B (-(in(A,B)&empty(B))).
% 2.07/2.27 all A B (-(empty(A)&A!=B&empty(B))).
% 2.07/2.27 all A (ordinal(A)->epsilon_transitive(A)&epsilon_connected(A)).
% 2.07/2.27 all A (epsilon_transitive(A)&epsilon_connected(A)->ordinal(A)).
% 2.07/2.27 exists A (epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)).
% 2.07/2.27 exists A (relation(A)&function(A)).
% 2.07/2.27 exists A (relation(A)&empty(A)&function(A)).
% 2.07/2.27 exists A (relation(A)&function(A)&one_to_one(A)).
% 2.07/2.27 exists A (relation(A)&relation_empty_yielding(A)&function(A)).
% 2.07/2.27 exists A (relation(A)&relation_non_empty(A)&function(A)).
% 2.07/2.27 empty(empty_set).
% 2.07/2.27 relation(empty_set).
% 2.07/2.27 empty(empty_set).
% 2.07/2.27 relation(empty_set).
% 2.07/2.27 relation_empty_yielding(empty_set).
% 2.07/2.27 exists A (empty(A)&relation(A)).
% 2.07/2.27 exists A (-empty(A)&relation(A)).
% 2.07/2.27 exists A (relation(A)&relation_empty_yielding(A)).
% 2.07/2.27 empty(empty_set).
% 2.07/2.27 exists A empty(A).
% 2.07/2.27 exists A (-empty(A)).
% 2.07/2.27 all A (empty(A)->A=empty_set).
% 2.07/2.27 -ordinal(empty_set).
% 2.07/2.27 all A (ordinal(A)<->epsilon_transitive(A)&epsilon_connected(A)).
% 2.07/2.27 epsilon_transitive(empty_set).
% 2.07/2.27 epsilon_connected(empty_set).
% 2.07/2.27 end_of_list.
% 2.07/2.27
% 2.07/2.27 -------> usable clausifies to:
% 2.07/2.27
% 2.07/2.27 list(usable).
% 2.07/2.27 0 [] A=A.
% 2.07/2.27 0 [] element($f1(A),A).
% 2.07/2.27 0 [] -element(A,B)|empty(B)|in(A,B).
% 2.07/2.27 0 [] -in(A,B)| -in(B,A).
% 2.07/2.27 0 [] -in(A,B)|element(A,B).
% 2.07/2.27 0 [] -empty(A)|function(A).
% 2.07/2.27 0 [] -relation(A)| -empty(A)| -function(A)|one_to_one(A).
% 2.07/2.27 0 [] -empty(A)|relation(A).
% 2.07/2.27 0 [] -in(A,B)| -empty(B).
% 2.07/2.27 0 [] -empty(A)|A=B| -empty(B).
% 2.07/2.27 0 [] -ordinal(A)|epsilon_transitive(A).
% 2.07/2.27 0 [] -ordinal(A)|epsilon_connected(A).
% 2.07/2.27 0 [] -epsilon_transitive(A)| -epsilon_connected(A)|ordinal(A).
% 2.07/2.27 0 [] epsilon_transitive($c1).
% 2.07/2.27 0 [] epsilon_connected($c1).
% 2.07/2.27 0 [] ordinal($c1).
% 2.07/2.27 0 [] relation($c2).
% 2.07/2.27 0 [] function($c2).
% 2.07/2.27 0 [] relation($c3).
% 2.07/2.27 0 [] empty($c3).
% 2.07/2.27 0 [] function($c3).
% 2.07/2.27 0 [] relation($c4).
% 2.07/2.27 0 [] function($c4).
% 2.07/2.27 0 [] one_to_one($c4).
% 2.07/2.27 0 [] relation($c5).
% 2.07/2.27 0 [] relation_empty_yielding($c5).
% 2.07/2.27 0 [] function($c5).
% 2.07/2.27 0 [] relation($c6).
% 2.07/2.27 0 [] relation_non_empty($c6).
% 2.07/2.27 0 [] function($c6).
% 2.07/2.27 0 [] empty(empty_set).
% 2.07/2.27 0 [] relation(empty_set).
% 2.07/2.27 0 [] empty(empty_set).
% 2.07/2.27 0 [] relation(empty_set).
% 2.07/2.27 0 [] relation_empty_yielding(empty_set).
% 2.07/2.27 0 [] empty($c7).
% 2.07/2.27 0 [] relation($c7).
% 2.07/2.27 0 [] -empty($c8).
% 2.07/2.27 0 [] relation($c8).
% 2.07/2.27 0 [] relation($c9).
% 2.07/2.27 0 [] relation_empty_yielding($c9).
% 2.07/2.27 0 [] empty(empty_set).
% 2.07/2.27 0 [] empty($c10).
% 2.07/2.27 0 [] -empty($c11).
% 2.07/2.27 0 [] -empty(A)|A=empty_set.
% 2.07/2.27 0 [] -ordinal(empty_set).
% 2.07/2.27 0 [] -ordinal(A)|epsilon_transitive(A).
% 2.07/2.27 0 [] -ordinal(A)|epsilon_connected(A).
% 2.07/2.27 0 [] ordinal(A)| -epsilon_transitive(A)| -epsilon_connected(A).
% 2.07/2.27 0 [] epsilon_transitive(empty_set).
% 2.07/2.27 0 [] epsilon_connected(empty_set).
% 2.07/2.27 end_of_list.
% 2.07/2.27
% 2.07/2.27 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 2.07/2.27
% 2.07/2.27 This ia a non-Horn set with equality. The strategy will be
% 2.07/2.27 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.07/2.27 deletion, with positive clauses in sos and nonpositive
% 2.07/2.27 clauses in usable.
% 2.07/2.27
% 2.07/2.27 dependent: set(knuth_bendix).
% 2.07/2.27 dependent: set(anl_eq).
% 2.07/2.27 dependent: set(para_from).
% 2.07/2.27 dependent: set(para_into).
% 2.07/2.27 dependent: clear(para_from_right).
% 2.07/2.27 dependent: clear(para_into_right).
% 2.07/2.27 dependent: set(para_from_vars).
% 2.07/2.27 dependent: set(eq_units_both_ways).
% 2.07/2.27 dependent: set(dynamic_demod_all).
% 2.07/2.27 dependent: set(dynamic_demod).
% 2.07/2.27 dependent: set(order_eq).
% 2.07/2.27 dependent: set(back_demod).
% 2.07/2.27 dependent: set(lrpo).
% 2.07/2.27 dependent: set(hyper_res).
% 2.07/2.27 dependent: set(unit_deletion).
% 2.07/2.27 dependent: set(factor).
% 2.07/2.27
% 2.07/2.27 ------------> process usable:
% 2.07/2.27 ** KEPT (pick-wt=8): 1 [] -element(A,B)|empty(B)|in(A,B).
% 2.07/2.27 ** KEPT (pick-wt=6): 2 [] -in(A,B)| -in(B,A).
% 2.07/2.27 ** KEPT (pick-wt=6): 3 [] -in(A,B)|element(A,B).
% 2.07/2.27 ** KEPT (pick-wt=4): 4 [] -empty(A)|function(A).
% 2.07/2.27 ** KEPT (pick-wt=8): 5 [] -relation(A)| -empty(A)| -function(A)|one_to_one(A).
% 2.07/2.27 ** KEPT (pick-wt=4): 6 [] -empty(A)|relation(A).
% 2.07/2.27 ** KEPT (pick-wt=5): 7 [] -in(A,B)| -empty(B).
% 2.07/2.27 ** KEPT (pick-wt=7): 8 [] -empty(A)|A=B| -empty(B).
% 2.07/2.27 ** KEPT (pick-wt=4): 9 [] -ordinal(A)|epsilon_transitive(A).
% 2.07/2.27 ** KEPT (pick-wt=4): 10 [] -ordinal(A)|epsilon_connected(A).
% 2.07/2.27 ** KEPT (pick-wt=6): 11 [] -epsilon_transitive(A)| -epsilon_connected(A)|ordinal(A).
% 2.07/2.27 ** KEPT (pick-wt=2): 12 [] -empty($c8).
% 2.07/2.27 ** KEPT (pick-wt=2): 13 [] -empty($c11).
% 2.07/2.27 ** KEPT (pick-wt=5): 14 [] -empty(A)|A=empty_set.
% 2.07/2.27 ** KEPT (pick-wt=2): 15 [] -ordinal(empty_set).
% 2.07/2.27 Following clause subsumed by 9 during input processing: 0 [] -ordinal(A)|epsilon_transitive(A).
% 2.07/2.27 Following clause subsumed by 10 during input processing: 0 [] -ordinal(A)|epsilon_connected(A).
% 2.07/2.27 Following clause subsumed by 11 during input processing: 0 [] ordinal(A)| -epsilon_transitive(A)| -epsilon_connected(A).
% 2.07/2.27
% 2.07/2.27 ------------> process sos:
% 2.07/2.27 ** KEPT (pick-wt=3): 18 [] A=A.
% 2.07/2.27 ** KEPT (pick-wt=4): 19 [] element($f1(A),A).
% 2.07/2.27 ** KEPT (pick-wt=2): 20 [] epsilon_transitive($c1).
% 2.07/2.27 ** KEPT (pick-wt=2): 21 [] epsilon_connected($c1).
% 2.07/2.27 ** KEPT (pick-wt=2): 22 [] ordinal($c1).
% 2.07/2.27 ** KEPT (pick-wt=2): 23 [] relation($c2).
% 2.07/2.27 ** KEPT (pick-wt=2): 24 [] function($c2).
% 2.07/2.27 ** KEPT (pick-wt=2): 25 [] relation($c3).
% 2.07/2.27 ** KEPT (pick-wt=2): 26 [] empty($c3).
% 2.07/2.27 ** KEPT (pick-wt=2): 27 [] function($c3).
% 2.07/2.27 ** KEPT (pick-wt=2): 28 [] relation($c4).
% 2.07/2.27 ** KEPT (pick-wt=2): 29 [] function($c4).
% 2.07/2.27 ** KEPT (pick-wt=2): 30 [] one_to_one($c4).
% 2.07/2.27 ** KEPT (pick-wt=2): 31 [] relation($c5).
% 2.07/2.27 ** KEPT (pick-wt=2): 32 [] relation_empty_yielding($c5).
% 2.07/2.27 ** KEPT (pick-wt=2): 33 [] function($c5).
% 2.07/2.27 ** KEPT (pick-wt=2): 34 [] relation($c6).
% 2.07/2.27 ** KEPT (pick-wt=2): 35 [] relation_non_empty($c6).
% 2.07/2.27 ** KEPT (pick-wt=2): 36 [] function($c6).
% 2.07/2.27 ** KEPT (pick-wt=2): 37 [] empty(empty_set).
% 2.07/2.27 ** KEPT (pick-wt=2): 38 [] relation(empty_set).
% 2.07/2.27 Following clause subsumed by 37 during input processing: 0 [] empty(empty_set).
% 2.07/2.27 Following clause subsumed by 38 during input processing: 0 [] relation(empty_set).
% 2.07/2.27 ** KEPT (pick-wt=2): 39 [] relation_empty_yielding(empty_set).
% 2.07/2.27 ** KEPT (pick-wt=2): 40 [] empty($c7).
% 2.07/2.27 ** KEPT (pick-wt=2): 41 [] relation($c7).
% 2.07/2.27 ** KEPT (pick-wt=2): 42 [] relation($c8).
% 2.07/2.27 ** KEPT (pick-wt=2): 43 [] relation($c9).
% 2.07/2.27 ** KEPT (pick-wt=2): 44 [] relation_empty_yielding($c9).
% 2.07/2.27 Following clause subsumed by 37 during input processing: 0 [] empty(empty_set).
% 2.07/2.27 ** KEPT (pick-wt=2): 45 [] empty($c10).
% 2.07/2.27 ** KEPT (pick-wt=2): 46 [] epsilon_transitive(empty_set).
% 2.07/2.27 ** KEPT (pick-wt=2): 47 [] epsilon_connected(empty_set).
% 2.07/2.27 Following clause subsumed by 18 during input processing: 0 [copy,18,flip.1] A=A.
% 2.07/2.27 18 back subsumes 17.
% 2.07/2.27
% 2.07/2.27 ======= end of input processing =======
% 2.07/2.27
% 2.07/2.27 =========== start of search ===========
% 2.07/2.27
% 2.07/2.27 -------- PROOF --------
% 2.07/2.27
% 2.07/2.27 ----> UNIT CONFLICT at 0.00 sec ----> 104 [binary,103.1,78.1] $F.
% 2.07/2.27
% 2.07/2.27 Length of proof is 9. Level of proof is 4.
% 2.07/2.27
% 2.07/2.27 ---------------- PROOF ----------------
% 2.07/2.27 % SZS status Theorem
% 2.07/2.27 % SZS output start Refutation
% See solution above
% 2.07/2.27 ------------ end of proof -------------
% 2.07/2.27
% 2.07/2.27
% 2.07/2.27 Search stopped by max_proofs option.
% 2.07/2.27
% 2.07/2.27
% 2.07/2.27 Search stopped by max_proofs option.
% 2.07/2.27
% 2.07/2.27 ============ end of search ============
% 2.07/2.27
% 2.07/2.27 -------------- statistics -------------
% 2.07/2.27 clauses given 34
% 2.07/2.27 clauses generated 90
% 2.07/2.27 clauses kept 98
% 2.07/2.27 clauses forward subsumed 65
% 2.07/2.27 clauses back subsumed 7
% 2.07/2.27 Kbytes malloced 976
% 2.07/2.27
% 2.07/2.27 ----------- times (seconds) -----------
% 2.07/2.27 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.07/2.27 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.07/2.27 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.07/2.27
% 2.07/2.27 That finishes the proof of the theorem.
% 2.07/2.27
% 2.07/2.27 Process 7972 finished Wed Jul 27 10:04:56 2022
% 2.07/2.27 Otter interrupted
% 2.07/2.27 PROOF FOUND
%------------------------------------------------------------------------------