TSTP Solution File: NUM383+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : NUM383+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n018.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 1.77s 1.99s
% Output : Refutation 1.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of clauses : 12 ( 7 unt; 1 nHn; 12 RR)
% Number of literals : 20 ( 0 equ; 10 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 13 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ in(A,B)
| ~ in(B,A) ),
file('NUM383+1.p',unknown),
[] ).
cnf(8,axiom,
( ~ element(A,B)
| empty(B)
| in(A,B) ),
file('NUM383+1.p',unknown),
[] ).
cnf(10,axiom,
( element(A,powerset(B))
| ~ subset(A,B) ),
file('NUM383+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ in(A,B)
| ~ element(B,powerset(C))
| element(A,C) ),
file('NUM383+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ in(A,B)
| ~ element(B,powerset(C))
| ~ empty(C) ),
file('NUM383+1.p',unknown),
[] ).
cnf(16,plain,
~ in(A,A),
inference(factor,[status(thm)],[1]),
[iquote('factor,1.1.2')] ).
cnf(44,axiom,
in(dollar_c12,dollar_c11),
file('NUM383+1.p',unknown),
[] ).
cnf(45,axiom,
subset(dollar_c11,dollar_c12),
file('NUM383+1.p',unknown),
[] ).
cnf(70,plain,
element(dollar_c11,powerset(dollar_c12)),
inference(hyper,[status(thm)],[45,10]),
[iquote('hyper,45,10')] ).
cnf(79,plain,
element(dollar_c12,dollar_c12),
inference(hyper,[status(thm)],[70,11,44]),
[iquote('hyper,70,11,44')] ).
cnf(84,plain,
empty(dollar_c12),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[79,8]),16]),
[iquote('hyper,79,8,unit_del,16')] ).
cnf(105,plain,
$false,
inference(hyper,[status(thm)],[84,12,44,70]),
[iquote('hyper,84,12,44,70')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : NUM383+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n018.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 09:52:01 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.77/1.99 ----- Otter 3.3f, August 2004 -----
% 1.77/1.99 The process was started by sandbox on n018.cluster.edu,
% 1.77/1.99 Wed Jul 27 09:52:01 2022
% 1.77/1.99 The command was "./otter". The process ID is 17146.
% 1.77/1.99
% 1.77/1.99 set(prolog_style_variables).
% 1.77/1.99 set(auto).
% 1.77/1.99 dependent: set(auto1).
% 1.77/1.99 dependent: set(process_input).
% 1.77/1.99 dependent: clear(print_kept).
% 1.77/1.99 dependent: clear(print_new_demod).
% 1.77/1.99 dependent: clear(print_back_demod).
% 1.77/1.99 dependent: clear(print_back_sub).
% 1.77/1.99 dependent: set(control_memory).
% 1.77/1.99 dependent: assign(max_mem, 12000).
% 1.77/1.99 dependent: assign(pick_given_ratio, 4).
% 1.77/1.99 dependent: assign(stats_level, 1).
% 1.77/1.99 dependent: assign(max_seconds, 10800).
% 1.77/1.99 clear(print_given).
% 1.77/1.99
% 1.77/1.99 formula_list(usable).
% 1.77/1.99 all A (A=A).
% 1.77/1.99 all A B (in(A,B)-> -in(B,A)).
% 1.77/1.99 all A (empty(A)->function(A)).
% 1.77/1.99 all A (empty(A)->relation(A)).
% 1.77/1.99 all A (relation(A)&empty(A)&function(A)->relation(A)&function(A)&one_to_one(A)).
% 1.77/1.99 all A exists B element(B,A).
% 1.77/1.99 empty(empty_set).
% 1.77/1.99 relation(empty_set).
% 1.77/1.99 relation_empty_yielding(empty_set).
% 1.77/1.99 empty(empty_set).
% 1.77/1.99 empty(empty_set).
% 1.77/1.99 relation(empty_set).
% 1.77/1.99 exists A (relation(A)&function(A)).
% 1.77/1.99 exists A (empty(A)&relation(A)).
% 1.77/1.99 exists A empty(A).
% 1.77/1.99 exists A (relation(A)&empty(A)&function(A)).
% 1.77/1.99 exists A (-empty(A)&relation(A)).
% 1.77/1.99 exists A (-empty(A)).
% 1.77/1.99 exists A (relation(A)&function(A)&one_to_one(A)).
% 1.77/1.99 exists A (relation(A)&relation_empty_yielding(A)).
% 1.77/1.99 exists A (relation(A)&relation_empty_yielding(A)&function(A)).
% 1.77/1.99 exists A (relation(A)&relation_non_empty(A)&function(A)).
% 1.77/1.99 all A B subset(A,A).
% 1.77/1.99 all A B (in(A,B)->element(A,B)).
% 1.77/1.99 all A B (element(A,B)->empty(B)|in(A,B)).
% 1.77/1.99 all A B (element(A,powerset(B))<->subset(A,B)).
% 1.77/1.99 all A B C (in(A,B)&element(B,powerset(C))->element(A,C)).
% 1.77/1.99 all A B C (-(in(A,B)&element(B,powerset(C))&empty(C))).
% 1.77/1.99 all A (empty(A)->A=empty_set).
% 1.77/1.99 all A B (-(in(A,B)&empty(B))).
% 1.77/1.99 -(all A B (-(in(A,B)&subset(B,A)))).
% 1.77/1.99 all A B (-(empty(A)&A!=B&empty(B))).
% 1.77/1.99 end_of_list.
% 1.77/1.99
% 1.77/1.99 -------> usable clausifies to:
% 1.77/1.99
% 1.77/1.99 list(usable).
% 1.77/1.99 0 [] A=A.
% 1.77/1.99 0 [] -in(A,B)| -in(B,A).
% 1.77/1.99 0 [] -empty(A)|function(A).
% 1.77/1.99 0 [] -empty(A)|relation(A).
% 1.77/1.99 0 [] -relation(A)| -empty(A)| -function(A)|one_to_one(A).
% 1.77/1.99 0 [] element($f1(A),A).
% 1.77/1.99 0 [] empty(empty_set).
% 1.77/1.99 0 [] relation(empty_set).
% 1.77/1.99 0 [] relation_empty_yielding(empty_set).
% 1.77/1.99 0 [] empty(empty_set).
% 1.77/1.99 0 [] empty(empty_set).
% 1.77/1.99 0 [] relation(empty_set).
% 1.77/1.99 0 [] relation($c1).
% 1.77/1.99 0 [] function($c1).
% 1.77/1.99 0 [] empty($c2).
% 1.77/1.99 0 [] relation($c2).
% 1.77/1.99 0 [] empty($c3).
% 1.77/1.99 0 [] relation($c4).
% 1.77/1.99 0 [] empty($c4).
% 1.77/1.99 0 [] function($c4).
% 1.77/1.99 0 [] -empty($c5).
% 1.77/1.99 0 [] relation($c5).
% 1.77/1.99 0 [] -empty($c6).
% 1.77/1.99 0 [] relation($c7).
% 1.77/1.99 0 [] function($c7).
% 1.77/1.99 0 [] one_to_one($c7).
% 1.77/1.99 0 [] relation($c8).
% 1.77/1.99 0 [] relation_empty_yielding($c8).
% 1.77/1.99 0 [] relation($c9).
% 1.77/1.99 0 [] relation_empty_yielding($c9).
% 1.77/1.99 0 [] function($c9).
% 1.77/1.99 0 [] relation($c10).
% 1.77/1.99 0 [] relation_non_empty($c10).
% 1.77/1.99 0 [] function($c10).
% 1.77/1.99 0 [] subset(A,A).
% 1.77/1.99 0 [] -in(A,B)|element(A,B).
% 1.77/1.99 0 [] -element(A,B)|empty(B)|in(A,B).
% 1.77/1.99 0 [] -element(A,powerset(B))|subset(A,B).
% 1.77/1.99 0 [] element(A,powerset(B))| -subset(A,B).
% 1.77/1.99 0 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 1.77/1.99 0 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 1.77/1.99 0 [] -empty(A)|A=empty_set.
% 1.77/1.99 0 [] -in(A,B)| -empty(B).
% 1.77/1.99 0 [] in($c12,$c11).
% 1.77/1.99 0 [] subset($c11,$c12).
% 1.77/1.99 0 [] -empty(A)|A=B| -empty(B).
% 1.77/1.99 end_of_list.
% 1.77/1.99
% 1.77/1.99 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.77/1.99
% 1.77/1.99 This ia a non-Horn set with equality. The strategy will be
% 1.77/1.99 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.77/1.99 deletion, with positive clauses in sos and nonpositive
% 1.77/1.99 clauses in usable.
% 1.77/1.99
% 1.77/1.99 dependent: set(knuth_bendix).
% 1.77/1.99 dependent: set(anl_eq).
% 1.77/1.99 dependent: set(para_from).
% 1.77/1.99 dependent: set(para_into).
% 1.77/1.99 dependent: clear(para_from_right).
% 1.77/1.99 dependent: clear(para_into_right).
% 1.77/1.99 dependent: set(para_from_vars).
% 1.77/1.99 dependent: set(eq_units_both_ways).
% 1.77/1.99 dependent: set(dynamic_demod_all).
% 1.77/1.99 dependent: set(dynamic_demod).
% 1.77/1.99 dependent: set(order_eq).
% 1.77/1.99 dependent: set(back_demod).
% 1.77/1.99 dependent: set(lrpo).
% 1.77/1.99 dependent: set(hyper_res).
% 1.77/1.99 dependent: set(unit_deletion).
% 1.77/1.99 dependent: set(factor).
% 1.77/1.99
% 1.77/1.99 ------------> process usable:
% 1.77/1.99 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.77/1.99 ** KEPT (pick-wt=4): 2 [] -empty(A)|function(A).
% 1.77/1.99 ** KEPT (pick-wt=4): 3 [] -empty(A)|relation(A).
% 1.77/1.99 ** KEPT (pick-wt=8): 4 [] -relation(A)| -empty(A)| -function(A)|one_to_one(A).
% 1.77/1.99 ** KEPT (pick-wt=2): 5 [] -empty($c5).
% 1.77/1.99 ** KEPT (pick-wt=2): 6 [] -empty($c6).
% 1.77/1.99 ** KEPT (pick-wt=6): 7 [] -in(A,B)|element(A,B).
% 1.77/1.99 ** KEPT (pick-wt=8): 8 [] -element(A,B)|empty(B)|in(A,B).
% 1.77/1.99 ** KEPT (pick-wt=7): 9 [] -element(A,powerset(B))|subset(A,B).
% 1.77/1.99 ** KEPT (pick-wt=7): 10 [] element(A,powerset(B))| -subset(A,B).
% 1.77/1.99 ** KEPT (pick-wt=10): 11 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 1.77/1.99 ** KEPT (pick-wt=9): 12 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 1.77/1.99 ** KEPT (pick-wt=5): 13 [] -empty(A)|A=empty_set.
% 1.77/1.99 ** KEPT (pick-wt=5): 14 [] -in(A,B)| -empty(B).
% 1.77/1.99 ** KEPT (pick-wt=7): 15 [] -empty(A)|A=B| -empty(B).
% 1.77/1.99
% 1.77/1.99 ------------> process sos:
% 1.77/1.99 ** KEPT (pick-wt=3): 18 [] A=A.
% 1.77/1.99 ** KEPT (pick-wt=4): 19 [] element($f1(A),A).
% 1.77/1.99 ** KEPT (pick-wt=2): 20 [] empty(empty_set).
% 1.77/1.99 ** KEPT (pick-wt=2): 21 [] relation(empty_set).
% 1.77/1.99 ** KEPT (pick-wt=2): 22 [] relation_empty_yielding(empty_set).
% 1.77/1.99 Following clause subsumed by 20 during input processing: 0 [] empty(empty_set).
% 1.77/1.99 Following clause subsumed by 20 during input processing: 0 [] empty(empty_set).
% 1.77/1.99 Following clause subsumed by 21 during input processing: 0 [] relation(empty_set).
% 1.77/1.99 ** KEPT (pick-wt=2): 23 [] relation($c1).
% 1.77/1.99 ** KEPT (pick-wt=2): 24 [] function($c1).
% 1.77/1.99 ** KEPT (pick-wt=2): 25 [] empty($c2).
% 1.77/1.99 ** KEPT (pick-wt=2): 26 [] relation($c2).
% 1.77/1.99 ** KEPT (pick-wt=2): 27 [] empty($c3).
% 1.77/1.99 ** KEPT (pick-wt=2): 28 [] relation($c4).
% 1.77/1.99 ** KEPT (pick-wt=2): 29 [] empty($c4).
% 1.77/1.99 ** KEPT (pick-wt=2): 30 [] function($c4).
% 1.77/1.99 ** KEPT (pick-wt=2): 31 [] relation($c5).
% 1.77/1.99 ** KEPT (pick-wt=2): 32 [] relation($c7).
% 1.77/1.99 ** KEPT (pick-wt=2): 33 [] function($c7).
% 1.77/1.99 ** KEPT (pick-wt=2): 34 [] one_to_one($c7).
% 1.77/1.99 ** KEPT (pick-wt=2): 35 [] relation($c8).
% 1.77/1.99 ** KEPT (pick-wt=2): 36 [] relation_empty_yielding($c8).
% 1.77/1.99 ** KEPT (pick-wt=2): 37 [] relation($c9).
% 1.77/1.99 ** KEPT (pick-wt=2): 38 [] relation_empty_yielding($c9).
% 1.77/1.99 ** KEPT (pick-wt=2): 39 [] function($c9).
% 1.77/1.99 ** KEPT (pick-wt=2): 40 [] relation($c10).
% 1.77/1.99 ** KEPT (pick-wt=2): 41 [] relation_non_empty($c10).
% 1.77/1.99 ** KEPT (pick-wt=2): 42 [] function($c10).
% 1.77/1.99 ** KEPT (pick-wt=3): 43 [] subset(A,A).
% 1.77/1.99 ** KEPT (pick-wt=3): 44 [] in($c12,$c11).
% 1.77/1.99 ** KEPT (pick-wt=3): 45 [] subset($c11,$c12).
% 1.77/1.99 Following clause subsumed by 18 during input processing: 0 [copy,18,flip.1] A=A.
% 1.77/1.99 18 back subsumes 17.
% 1.77/1.99
% 1.77/1.99 ======= end of input processing =======
% 1.77/1.99
% 1.77/1.99 =========== start of search ===========
% 1.77/1.99
% 1.77/1.99 -------- PROOF --------
% 1.77/1.99
% 1.77/1.99 -----> EMPTY CLAUSE at 0.00 sec ----> 105 [hyper,84,12,44,70] $F.
% 1.77/1.99
% 1.77/1.99 Length of proof is 4. Level of proof is 3.
% 1.77/1.99
% 1.77/1.99 ---------------- PROOF ----------------
% 1.77/1.99 % SZS status Theorem
% 1.77/1.99 % SZS output start Refutation
% See solution above
% 1.77/1.99 ------------ end of proof -------------
% 1.77/1.99
% 1.77/1.99
% 1.77/1.99 Search stopped by max_proofs option.
% 1.77/1.99
% 1.77/1.99
% 1.77/1.99 Search stopped by max_proofs option.
% 1.77/1.99
% 1.77/1.99 ============ end of search ============
% 1.77/1.99
% 1.77/1.99 -------------- statistics -------------
% 1.77/1.99 clauses given 42
% 1.77/1.99 clauses generated 136
% 1.77/1.99 clauses kept 100
% 1.77/1.99 clauses forward subsumed 90
% 1.77/1.99 clauses back subsumed 4
% 1.77/1.99 Kbytes malloced 976
% 1.77/1.99
% 1.77/1.99 ----------- times (seconds) -----------
% 1.77/1.99 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.77/1.99 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.77/1.99 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.77/1.99
% 1.77/1.99 That finishes the proof of the theorem.
% 1.77/1.99
% 1.77/1.99 Process 17146 finished Wed Jul 27 09:52:03 2022
% 1.77/1.99 Otter interrupted
% 1.77/1.99 PROOF FOUND
%------------------------------------------------------------------------------