TSTP Solution File: SET923+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET923+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n006.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 13:14:32 EDT 2022
% Result : Theorem 1.97s 2.14s
% Output : Refutation 1.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 5
% Syntax : Number of clauses : 9 ( 7 unt; 1 nHn; 9 RR)
% Number of literals : 12 ( 8 equ; 6 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 4 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ subset(A,singleton(B))
| A = empty_set
| A = singleton(B) ),
file('SET923+1.p',unknown),
[] ).
cnf(5,axiom,
( set_difference(A,B) != empty_set
| subset(A,B) ),
file('SET923+1.p',unknown),
[] ).
cnf(7,axiom,
dollar_c4 != empty_set,
file('SET923+1.p',unknown),
[] ).
cnf(8,plain,
empty_set != dollar_c4,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[7])]),
[iquote('copy,7,flip.1')] ).
cnf(9,axiom,
dollar_c4 != singleton(dollar_c3),
file('SET923+1.p',unknown),
[] ).
cnf(10,plain,
singleton(dollar_c3) != dollar_c4,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[9])]),
[iquote('copy,9,flip.1')] ).
cnf(15,axiom,
set_difference(dollar_c4,singleton(dollar_c3)) = empty_set,
file('SET923+1.p',unknown),
[] ).
cnf(23,plain,
subset(dollar_c4,singleton(dollar_c3)),
inference(hyper,[status(thm)],[15,5]),
[iquote('hyper,15,5')] ).
cnf(29,plain,
$false,
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[23,1]),8,10]),
[iquote('hyper,23,1,unit_del,8,10')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET923+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n006.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 10:52:46 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.97/2.14 ----- Otter 3.3f, August 2004 -----
% 1.97/2.14 The process was started by sandbox on n006.cluster.edu,
% 1.97/2.14 Wed Jul 27 10:52:47 2022
% 1.97/2.14 The command was "./otter". The process ID is 17943.
% 1.97/2.14
% 1.97/2.14 set(prolog_style_variables).
% 1.97/2.14 set(auto).
% 1.97/2.14 dependent: set(auto1).
% 1.97/2.14 dependent: set(process_input).
% 1.97/2.14 dependent: clear(print_kept).
% 1.97/2.14 dependent: clear(print_new_demod).
% 1.97/2.14 dependent: clear(print_back_demod).
% 1.97/2.14 dependent: clear(print_back_sub).
% 1.97/2.14 dependent: set(control_memory).
% 1.97/2.14 dependent: assign(max_mem, 12000).
% 1.97/2.14 dependent: assign(pick_given_ratio, 4).
% 1.97/2.14 dependent: assign(stats_level, 1).
% 1.97/2.14 dependent: assign(max_seconds, 10800).
% 1.97/2.14 clear(print_given).
% 1.97/2.14
% 1.97/2.14 formula_list(usable).
% 1.97/2.14 all A (A=A).
% 1.97/2.14 empty(empty_set).
% 1.97/2.14 all A B (subset(A,singleton(B))<->A=empty_set|A=singleton(B)).
% 1.97/2.14 exists A empty(A).
% 1.97/2.14 exists A (-empty(A)).
% 1.97/2.14 all A B subset(A,A).
% 1.97/2.14 all A B (set_difference(A,B)=empty_set<->subset(A,B)).
% 1.97/2.14 -(all A B (-(set_difference(A,singleton(B))=empty_set&A!=empty_set&A!=singleton(B)))).
% 1.97/2.14 end_of_list.
% 1.97/2.14
% 1.97/2.14 -------> usable clausifies to:
% 1.97/2.14
% 1.97/2.14 list(usable).
% 1.97/2.14 0 [] A=A.
% 1.97/2.14 0 [] empty(empty_set).
% 1.97/2.14 0 [] -subset(A,singleton(B))|A=empty_set|A=singleton(B).
% 1.97/2.14 0 [] subset(A,singleton(B))|A!=empty_set.
% 1.97/2.14 0 [] subset(A,singleton(B))|A!=singleton(B).
% 1.97/2.14 0 [] empty($c1).
% 1.97/2.14 0 [] -empty($c2).
% 1.97/2.14 0 [] subset(A,A).
% 1.97/2.14 0 [] set_difference(A,B)!=empty_set|subset(A,B).
% 1.97/2.14 0 [] set_difference(A,B)=empty_set| -subset(A,B).
% 1.97/2.14 0 [] set_difference($c4,singleton($c3))=empty_set.
% 1.97/2.14 0 [] $c4!=empty_set.
% 1.97/2.14 0 [] $c4!=singleton($c3).
% 1.97/2.14 end_of_list.
% 1.97/2.14
% 1.97/2.14 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.97/2.14
% 1.97/2.14 This ia a non-Horn set with equality. The strategy will be
% 1.97/2.14 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.97/2.14 deletion, with positive clauses in sos and nonpositive
% 1.97/2.14 clauses in usable.
% 1.97/2.14
% 1.97/2.14 dependent: set(knuth_bendix).
% 1.97/2.14 dependent: set(anl_eq).
% 1.97/2.14 dependent: set(para_from).
% 1.97/2.14 dependent: set(para_into).
% 1.97/2.14 dependent: clear(para_from_right).
% 1.97/2.14 dependent: clear(para_into_right).
% 1.97/2.14 dependent: set(para_from_vars).
% 1.97/2.14 dependent: set(eq_units_both_ways).
% 1.97/2.14 dependent: set(dynamic_demod_all).
% 1.97/2.14 dependent: set(dynamic_demod).
% 1.97/2.14 dependent: set(order_eq).
% 1.97/2.14 dependent: set(back_demod).
% 1.97/2.14 dependent: set(lrpo).
% 1.97/2.14 dependent: set(hyper_res).
% 1.97/2.14 dependent: set(unit_deletion).
% 1.97/2.14 dependent: set(factor).
% 1.97/2.14
% 1.97/2.14 ------------> process usable:
% 1.97/2.14 ** KEPT (pick-wt=11): 1 [] -subset(A,singleton(B))|A=empty_set|A=singleton(B).
% 1.97/2.14 ** KEPT (pick-wt=7): 2 [] subset(A,singleton(B))|A!=empty_set.
% 1.97/2.14 ** KEPT (pick-wt=8): 3 [] subset(A,singleton(B))|A!=singleton(B).
% 1.97/2.14 ** KEPT (pick-wt=2): 4 [] -empty($c2).
% 1.97/2.14 ** KEPT (pick-wt=8): 5 [] set_difference(A,B)!=empty_set|subset(A,B).
% 1.97/2.14 ** KEPT (pick-wt=8): 6 [] set_difference(A,B)=empty_set| -subset(A,B).
% 1.97/2.14 ** KEPT (pick-wt=3): 8 [copy,7,flip.1] empty_set!=$c4.
% 1.97/2.14 ** KEPT (pick-wt=4): 10 [copy,9,flip.1] singleton($c3)!=$c4.
% 1.97/2.14
% 1.97/2.14 ------------> process sos:
% 1.97/2.14 ** KEPT (pick-wt=3): 11 [] A=A.
% 1.97/2.14 ** KEPT (pick-wt=2): 12 [] empty(empty_set).
% 1.97/2.14 ** KEPT (pick-wt=2): 13 [] empty($c1).
% 1.97/2.14 ** KEPT (pick-wt=3): 14 [] subset(A,A).
% 1.97/2.14 ** KEPT (pick-wt=6): 15 [] set_difference($c4,singleton($c3))=empty_set.
% 1.97/2.14 ---> New Demodulator: 16 [new_demod,15] set_difference($c4,singleton($c3))=empty_set.
% 1.97/2.14 Following clause subsumed by 11 during input processing: 0 [copy,11,flip.1] A=A.
% 1.97/2.14 >>>> Starting back demodulation with 16.
% 1.97/2.14
% 1.97/2.14 ======= end of input processing =======
% 1.97/2.14
% 1.97/2.14 =========== start of search ===========
% 1.97/2.14
% 1.97/2.14 -------- PROOF --------
% 1.97/2.14
% 1.97/2.14 -----> EMPTY CLAUSE at 0.00 sec ----> 29 [hyper,23,1,unit_del,8,10] $F.
% 1.97/2.14
% 1.97/2.14 Length of proof is 3. Level of proof is 1.
% 1.97/2.14
% 1.97/2.14 ---------------- PROOF ----------------
% 1.97/2.14 % SZS status Theorem
% 1.97/2.14 % SZS output start Refutation
% See solution above
% 1.97/2.14 ------------ end of proof -------------
% 1.97/2.14
% 1.97/2.14
% 1.97/2.14 Search stopped by max_proofs option.
% 1.97/2.14
% 1.97/2.14
% 1.97/2.14 Search stopped by max_proofs option.
% 1.97/2.14
% 1.97/2.14 ============ end of search ============
% 1.97/2.14
% 1.97/2.14 -------------- statistics -------------
% 1.97/2.14 clauses given 7
% 1.97/2.14 clauses generated 31
% 1.97/2.14 clauses kept 23
% 1.97/2.14 clauses forward subsumed 21
% 1.97/2.14 clauses back subsumed 0
% 1.97/2.14 Kbytes malloced 976
% 1.97/2.14
% 1.97/2.14 ----------- times (seconds) -----------
% 1.97/2.14 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.97/2.14 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.97/2.14 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.97/2.14
% 1.97/2.14 That finishes the proof of the theorem.
% 1.97/2.14
% 1.97/2.14 Process 17943 finished Wed Jul 27 10:52:48 2022
% 1.97/2.14 Otter interrupted
% 1.97/2.14 PROOF FOUND
%------------------------------------------------------------------------------