TSTP Solution File: NUM387+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : NUM387+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 13:08:13 EDT 2022
% Result : Theorem 1.82s 2.02s
% Output : Refutation 1.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of clauses : 9 ( 8 unt; 0 nHn; 6 RR)
% Number of literals : 10 ( 3 equ; 3 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 6 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ in(A,B)
| ~ in(B,A) ),
file('NUM387+1.p',unknown),
[] ).
cnf(16,plain,
~ in(A,A),
inference(factor,[status(thm)],[1]),
[iquote('factor,1.1.2')] ).
cnf(22,axiom,
succ(A) = set_union2(A,singleton(A)),
file('NUM387+1.p',unknown),
[] ).
cnf(49,axiom,
in(A,succ(A)),
file('NUM387+1.p',unknown),
[] ).
cnf(50,plain,
in(A,set_union2(A,singleton(A))),
inference(demod,[status(thm),theory(equality)],[inference(copy,[status(thm)],[49]),22]),
[iquote('copy,49,demod,22')] ).
cnf(51,axiom,
dollar_c11 = succ(dollar_c11),
file('NUM387+1.p',unknown),
[] ).
cnf(52,plain,
set_union2(dollar_c11,singleton(dollar_c11)) = dollar_c11,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(copy,[status(thm)],[51]),22])]),
[iquote('copy,51,demod,22,flip.1')] ).
cnf(127,plain,
in(dollar_c11,dollar_c11),
inference(para_from,[status(thm),theory(equality)],[52,50]),
[iquote('para_from,52.1.1,50.1.2')] ).
cnf(128,plain,
$false,
inference(binary,[status(thm)],[127,16]),
[iquote('binary,127.1,16.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : NUM387+1 : TPTP v8.1.0. Released v3.2.0.
% 0.08/0.13 % 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 09:36:35 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.82/2.02 ----- Otter 3.3f, August 2004 -----
% 1.82/2.02 The process was started by sandbox on n022.cluster.edu,
% 1.82/2.02 Wed Jul 27 09:36:35 2022
% 1.82/2.02 The command was "./otter". The process ID is 28560.
% 1.82/2.02
% 1.82/2.02 set(prolog_style_variables).
% 1.82/2.02 set(auto).
% 1.82/2.02 dependent: set(auto1).
% 1.82/2.02 dependent: set(process_input).
% 1.82/2.02 dependent: clear(print_kept).
% 1.82/2.02 dependent: clear(print_new_demod).
% 1.82/2.02 dependent: clear(print_back_demod).
% 1.82/2.02 dependent: clear(print_back_sub).
% 1.82/2.02 dependent: set(control_memory).
% 1.82/2.02 dependent: assign(max_mem, 12000).
% 1.82/2.02 dependent: assign(pick_given_ratio, 4).
% 1.82/2.02 dependent: assign(stats_level, 1).
% 1.82/2.02 dependent: assign(max_seconds, 10800).
% 1.82/2.02 clear(print_given).
% 1.82/2.02
% 1.82/2.02 formula_list(usable).
% 1.82/2.02 all A (A=A).
% 1.82/2.02 all A B (in(A,B)-> -in(B,A)).
% 1.82/2.02 all A (empty(A)->function(A)).
% 1.82/2.02 all A (empty(A)->relation(A)).
% 1.82/2.02 all A (relation(A)&empty(A)&function(A)->relation(A)&function(A)&one_to_one(A)).
% 1.82/2.02 all A B (set_union2(A,B)=set_union2(B,A)).
% 1.82/2.02 all A (succ(A)=set_union2(A,singleton(A))).
% 1.82/2.02 all A exists B element(B,A).
% 1.82/2.02 empty(empty_set).
% 1.82/2.02 relation(empty_set).
% 1.82/2.02 relation_empty_yielding(empty_set).
% 1.82/2.02 all A (-empty(succ(A))).
% 1.82/2.02 empty(empty_set).
% 1.82/2.02 all A B (relation(A)&relation(B)->relation(set_union2(A,B))).
% 1.82/2.02 all A B (-empty(A)-> -empty(set_union2(A,B))).
% 1.82/2.02 all A B (-empty(A)-> -empty(set_union2(B,A))).
% 1.82/2.02 empty(empty_set).
% 1.82/2.02 relation(empty_set).
% 1.82/2.02 all A B (set_union2(A,A)=A).
% 1.82/2.02 exists A (relation(A)&function(A)).
% 1.82/2.02 exists A (empty(A)&relation(A)).
% 1.82/2.02 exists A empty(A).
% 1.82/2.02 exists A (relation(A)&empty(A)&function(A)).
% 1.82/2.02 exists A (-empty(A)&relation(A)).
% 1.82/2.02 exists A (-empty(A)).
% 1.82/2.02 exists A (relation(A)&function(A)&one_to_one(A)).
% 1.82/2.02 exists A (relation(A)&relation_empty_yielding(A)).
% 1.82/2.02 exists A (relation(A)&relation_empty_yielding(A)&function(A)).
% 1.82/2.02 exists A (relation(A)&relation_non_empty(A)&function(A)).
% 1.82/2.02 all A in(A,succ(A)).
% 1.82/2.02 -(all A (A!=succ(A))).
% 1.82/2.02 all A (set_union2(A,empty_set)=A).
% 1.82/2.02 all A B (in(A,B)->element(A,B)).
% 1.82/2.02 all A B (element(A,B)->empty(B)|in(A,B)).
% 1.82/2.02 all A (empty(A)->A=empty_set).
% 1.82/2.02 all A B (-(in(A,B)&empty(B))).
% 1.82/2.02 all A B (-(empty(A)&A!=B&empty(B))).
% 1.82/2.02 end_of_list.
% 1.82/2.02
% 1.82/2.02 -------> usable clausifies to:
% 1.82/2.02
% 1.82/2.02 list(usable).
% 1.82/2.02 0 [] A=A.
% 1.82/2.02 0 [] -in(A,B)| -in(B,A).
% 1.82/2.02 0 [] -empty(A)|function(A).
% 1.82/2.02 0 [] -empty(A)|relation(A).
% 1.82/2.02 0 [] -relation(A)| -empty(A)| -function(A)|one_to_one(A).
% 1.82/2.02 0 [] set_union2(A,B)=set_union2(B,A).
% 1.82/2.02 0 [] succ(A)=set_union2(A,singleton(A)).
% 1.82/2.02 0 [] element($f1(A),A).
% 1.82/2.02 0 [] empty(empty_set).
% 1.82/2.02 0 [] relation(empty_set).
% 1.82/2.02 0 [] relation_empty_yielding(empty_set).
% 1.82/2.02 0 [] -empty(succ(A)).
% 1.82/2.02 0 [] empty(empty_set).
% 1.82/2.02 0 [] -relation(A)| -relation(B)|relation(set_union2(A,B)).
% 1.82/2.02 0 [] empty(A)| -empty(set_union2(A,B)).
% 1.82/2.02 0 [] empty(A)| -empty(set_union2(B,A)).
% 1.82/2.02 0 [] empty(empty_set).
% 1.82/2.02 0 [] relation(empty_set).
% 1.82/2.02 0 [] set_union2(A,A)=A.
% 1.82/2.02 0 [] relation($c1).
% 1.82/2.02 0 [] function($c1).
% 1.82/2.02 0 [] empty($c2).
% 1.82/2.02 0 [] relation($c2).
% 1.82/2.02 0 [] empty($c3).
% 1.82/2.02 0 [] relation($c4).
% 1.82/2.02 0 [] empty($c4).
% 1.82/2.02 0 [] function($c4).
% 1.82/2.02 0 [] -empty($c5).
% 1.82/2.02 0 [] relation($c5).
% 1.82/2.02 0 [] -empty($c6).
% 1.82/2.02 0 [] relation($c7).
% 1.82/2.02 0 [] function($c7).
% 1.82/2.02 0 [] one_to_one($c7).
% 1.82/2.02 0 [] relation($c8).
% 1.82/2.02 0 [] relation_empty_yielding($c8).
% 1.82/2.02 0 [] relation($c9).
% 1.82/2.02 0 [] relation_empty_yielding($c9).
% 1.82/2.02 0 [] function($c9).
% 1.82/2.02 0 [] relation($c10).
% 1.82/2.02 0 [] relation_non_empty($c10).
% 1.82/2.02 0 [] function($c10).
% 1.82/2.02 0 [] in(A,succ(A)).
% 1.82/2.02 0 [] $c11=succ($c11).
% 1.82/2.02 0 [] set_union2(A,empty_set)=A.
% 1.82/2.02 0 [] -in(A,B)|element(A,B).
% 1.82/2.02 0 [] -element(A,B)|empty(B)|in(A,B).
% 1.82/2.02 0 [] -empty(A)|A=empty_set.
% 1.82/2.02 0 [] -in(A,B)| -empty(B).
% 1.82/2.02 0 [] -empty(A)|A=B| -empty(B).
% 1.82/2.02 end_of_list.
% 1.82/2.02
% 1.82/2.02 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.82/2.02
% 1.82/2.02 This ia a non-Horn set with equality. The strategy will be
% 1.82/2.02 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.82/2.02 deletion, with positive clauses in sos and nonpositive
% 1.82/2.02 clauses in usable.
% 1.82/2.02
% 1.82/2.02 dependent: set(knuth_bendix).
% 1.82/2.02 dependent: set(anl_eq).
% 1.82/2.02 dependent: set(para_from).
% 1.82/2.02 dependent: set(para_into).
% 1.82/2.02 dependent: clear(para_from_right).
% 1.82/2.02 dependent: clear(para_into_right).
% 1.82/2.02 dependent: set(para_from_vars).
% 1.82/2.02 dependent: set(eq_units_both_ways).
% 1.82/2.02 dependent: set(dynamic_demod_all).
% 1.82/2.02 dependent: set(dynamic_demod).
% 1.82/2.02 dependent: set(order_eq).
% 1.82/2.02 dependent: set(back_demod).
% 1.82/2.02 dependent: set(lrpo).
% 1.82/2.02 dependent: set(hyper_res).
% 1.82/2.02 dependent: set(unit_deletion).
% 1.82/2.02 dependent: set(factor).
% 1.82/2.02
% 1.82/2.02 ------------> process usable:
% 1.82/2.02 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.82/2.02 ** KEPT (pick-wt=4): 2 [] -empty(A)|function(A).
% 1.82/2.02 ** KEPT (pick-wt=4): 3 [] -empty(A)|relation(A).
% 1.82/2.02 ** KEPT (pick-wt=8): 4 [] -relation(A)| -empty(A)| -function(A)|one_to_one(A).
% 1.82/2.02 ** KEPT (pick-wt=3): 5 [] -empty(succ(A)).
% 1.82/2.02 ** KEPT (pick-wt=8): 6 [] -relation(A)| -relation(B)|relation(set_union2(A,B)).
% 1.82/2.02 ** KEPT (pick-wt=6): 7 [] empty(A)| -empty(set_union2(A,B)).
% 1.82/2.02 ** KEPT (pick-wt=6): 8 [] empty(A)| -empty(set_union2(B,A)).
% 1.82/2.02 ** KEPT (pick-wt=2): 9 [] -empty($c5).
% 1.82/2.02 ** KEPT (pick-wt=2): 10 [] -empty($c6).
% 1.82/2.02 ** KEPT (pick-wt=6): 11 [] -in(A,B)|element(A,B).
% 1.82/2.02 ** KEPT (pick-wt=8): 12 [] -element(A,B)|empty(B)|in(A,B).
% 1.82/2.02 ** KEPT (pick-wt=5): 13 [] -empty(A)|A=empty_set.
% 1.82/2.02 ** KEPT (pick-wt=5): 14 [] -in(A,B)| -empty(B).
% 1.82/2.02 ** KEPT (pick-wt=7): 15 [] -empty(A)|A=B| -empty(B).
% 1.82/2.02
% 1.82/2.02 ------------> process sos:
% 1.82/2.02 ** KEPT (pick-wt=3): 19 [] A=A.
% 1.82/2.02 ** KEPT (pick-wt=7): 20 [] set_union2(A,B)=set_union2(B,A).
% 1.82/2.02 ** KEPT (pick-wt=7): 21 [] succ(A)=set_union2(A,singleton(A)).
% 1.82/2.02 ---> New Demodulator: 22 [new_demod,21] succ(A)=set_union2(A,singleton(A)).
% 1.82/2.02 ** KEPT (pick-wt=4): 23 [] element($f1(A),A).
% 1.82/2.02 ** KEPT (pick-wt=2): 24 [] empty(empty_set).
% 1.82/2.02 ** KEPT (pick-wt=2): 25 [] relation(empty_set).
% 1.82/2.02 ** KEPT (pick-wt=2): 26 [] relation_empty_yielding(empty_set).
% 1.82/2.02 Following clause subsumed by 24 during input processing: 0 [] empty(empty_set).
% 1.82/2.02 Following clause subsumed by 24 during input processing: 0 [] empty(empty_set).
% 1.82/2.02 Following clause subsumed by 25 during input processing: 0 [] relation(empty_set).
% 1.82/2.02 ** KEPT (pick-wt=5): 27 [] set_union2(A,A)=A.
% 1.82/2.02 ---> New Demodulator: 28 [new_demod,27] set_union2(A,A)=A.
% 1.82/2.02 ** KEPT (pick-wt=2): 29 [] relation($c1).
% 1.82/2.02 ** KEPT (pick-wt=2): 30 [] function($c1).
% 1.82/2.02 ** KEPT (pick-wt=2): 31 [] empty($c2).
% 1.82/2.02 ** KEPT (pick-wt=2): 32 [] relation($c2).
% 1.82/2.02 ** KEPT (pick-wt=2): 33 [] empty($c3).
% 1.82/2.02 ** KEPT (pick-wt=2): 34 [] relation($c4).
% 1.82/2.02 ** KEPT (pick-wt=2): 35 [] empty($c4).
% 1.82/2.02 ** KEPT (pick-wt=2): 36 [] function($c4).
% 1.82/2.02 ** KEPT (pick-wt=2): 37 [] relation($c5).
% 1.82/2.02 ** KEPT (pick-wt=2): 38 [] relation($c7).
% 1.82/2.02 ** KEPT (pick-wt=2): 39 [] function($c7).
% 1.82/2.02 ** KEPT (pick-wt=2): 40 [] one_to_one($c7).
% 1.82/2.02 ** KEPT (pick-wt=2): 41 [] relation($c8).
% 1.82/2.02 ** KEPT (pick-wt=2): 42 [] relation_empty_yielding($c8).
% 1.82/2.02 ** KEPT (pick-wt=2): 43 [] relation($c9).
% 1.82/2.02 ** KEPT (pick-wt=2): 44 [] relation_empty_yielding($c9).
% 1.82/2.02 ** KEPT (pick-wt=2): 45 [] function($c9).
% 1.82/2.02 ** KEPT (pick-wt=2): 46 [] relation($c10).
% 1.82/2.02 ** KEPT (pick-wt=2): 47 [] relation_non_empty($c10).
% 1.82/2.02 ** KEPT (pick-wt=2): 48 [] function($c10).
% 1.82/2.02 ** KEPT (pick-wt=6): 50 [copy,49,demod,22] in(A,set_union2(A,singleton(A))).
% 1.82/2.02 ** KEPT (pick-wt=6): 52 [copy,51,demod,22,flip.1] set_union2($c11,singleton($c11))=$c11.
% 1.82/2.02 ---> New Demodulator: 53 [new_demod,52] set_union2($c11,singleton($c11))=$c11.
% 1.82/2.02 ** KEPT (pick-wt=5): 54 [] set_union2(A,empty_set)=A.
% 1.82/2.02 ---> New Demodulator: 55 [new_demod,54] set_union2(A,empty_set)=A.
% 1.82/2.02 Following clause subsumed by 19 during input processing: 0 [copy,19,flip.1] A=A.
% 1.82/2.02 19 back subsumes 18.
% 1.82/2.02 Following clause subsumed by 20 during input processing: 0 [copy,20,flip.1] set_union2(A,B)=set_union2(B,A).
% 1.82/2.02 >>>> Starting back demodulation with 22.
% 1.82/2.02 >> back demodulating 5 with 22.
% 1.82/2.02 >>>> Starting back demodulation with 28.
% 1.82/2.02 >> back demodulating 17 with 28.
% 1.82/2.02 >>>> Starting back demodulation with 53.
% 1.82/2.02 >>>> Starting back demodulation with 55.
% 1.82/2.02
% 1.82/2.02 ======= end of input processing =======
% 1.82/2.02
% 1.82/2.02 =========== start of search ===========
% 1.82/2.02
% 1.82/2.02 -------- PROOF --------
% 1.82/2.02
% 1.82/2.02 ----> UNIT CONFLICT at 0.00 sec ----> 128 [binary,127.1,16.1] $F.
% 1.82/2.02
% 1.82/2.02 Length of proof is 4. Level of proof is 2.
% 1.82/2.02
% 1.82/2.02 ---------------- PROOF ----------------
% 1.82/2.02 % SZS status Theorem
% 1.82/2.02 % SZS output start Refutation
% See solution above
% 1.82/2.02 ------------ end of proof -------------
% 1.82/2.02
% 1.82/2.02
% 1.82/2.02 Search stopped by max_proofs option.
% 1.82/2.02
% 1.82/2.02
% 1.82/2.02 Search stopped by max_proofs option.
% 1.82/2.02
% 1.82/2.02 ============ end of search ============
% 1.82/2.02
% 1.82/2.02 -------------- statistics -------------
% 1.82/2.02 clauses given 36
% 1.82/2.02 clauses generated 172
% 1.82/2.02 clauses kept 116
% 1.82/2.02 clauses forward subsumed 118
% 1.82/2.02 clauses back subsumed 3
% 1.82/2.02 Kbytes malloced 976
% 1.82/2.02
% 1.82/2.02 ----------- times (seconds) -----------
% 1.82/2.02 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.82/2.02 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.82/2.02 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.82/2.02
% 1.82/2.02 That finishes the proof of the theorem.
% 1.82/2.02
% 1.82/2.02 Process 28560 finished Wed Jul 27 09:36:37 2022
% 1.82/2.02 Otter interrupted
% 1.82/2.02 PROOF FOUND
%------------------------------------------------------------------------------