TSTP Solution File: SEU160+3 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU160+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n019.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 13:14:59 EDT 2022
% Result : Theorem 1.68s 1.89s
% Output : Refutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of clauses : 16 ( 6 unt; 4 nHn; 11 RR)
% Number of literals : 29 ( 16 equ; 11 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 8 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( ~ subset(dollar_c4,singleton(dollar_c3))
| dollar_c4 != empty_set ),
file('SEU160+3.p',unknown),
[] ).
cnf(3,plain,
( ~ subset(dollar_c4,singleton(dollar_c3))
| empty_set != dollar_c4 ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[2])]),
[iquote('copy,2,flip.2')] ).
cnf(4,axiom,
( ~ subset(dollar_c4,singleton(dollar_c3))
| dollar_c4 != singleton(dollar_c3) ),
file('SEU160+3.p',unknown),
[] ).
cnf(5,plain,
( ~ subset(dollar_c4,singleton(dollar_c3))
| singleton(dollar_c3) != dollar_c4 ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[4])]),
[iquote('copy,4,flip.2')] ).
cnf(6,axiom,
( ~ subset(A,singleton(B))
| A = empty_set
| A = singleton(B) ),
file('SEU160+3.p',unknown),
[] ).
cnf(7,axiom,
( subset(A,singleton(B))
| A != empty_set ),
file('SEU160+3.p',unknown),
[] ).
cnf(9,axiom,
A = A,
file('SEU160+3.p',unknown),
[] ).
cnf(10,axiom,
subset(A,A),
file('SEU160+3.p',unknown),
[] ).
cnf(13,axiom,
( subset(dollar_c4,singleton(dollar_c3))
| dollar_c4 = empty_set
| dollar_c4 = singleton(dollar_c3) ),
file('SEU160+3.p',unknown),
[] ).
cnf(14,plain,
( subset(dollar_c4,singleton(dollar_c3))
| empty_set = dollar_c4
| singleton(dollar_c3) = dollar_c4 ),
inference(flip,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[13])])]),
[iquote('copy,13,flip.2,flip.3')] ).
cnf(15,plain,
subset(empty_set,singleton(A)),
inference(hyper,[status(thm)],[9,7]),
[iquote('hyper,9,7')] ).
cnf(17,plain,
( empty_set = dollar_c4
| singleton(dollar_c3) = dollar_c4 ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[14,6])])]),
[iquote('hyper,14,6,factor_simp,factor_simp')] ).
cnf(29,plain,
( ~ subset(dollar_c4,singleton(dollar_c3))
| empty_set = dollar_c4 ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[17,5]),9]),
[iquote('para_from,17.2.1,5.2.1,unit_del,9')] ).
cnf(69,plain,
empty_set = dollar_c4,
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[29,17]),10])]),
[iquote('para_into,29.1.2,17.2.1,unit_del,10,factor_simp')] ).
cnf(76,plain,
subset(dollar_c4,singleton(A)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[15]),69]),
[iquote('back_demod,15,demod,69')] ).
cnf(79,plain,
$false,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[3]),69]),76,9]),
[iquote('back_demod,3,demod,69,unit_del,76,9')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SEU160+3 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n019.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 07:42:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.68/1.89 ----- Otter 3.3f, August 2004 -----
% 1.68/1.89 The process was started by sandbox on n019.cluster.edu,
% 1.68/1.89 Wed Jul 27 07:42:37 2022
% 1.68/1.89 The command was "./otter". The process ID is 7487.
% 1.68/1.89
% 1.68/1.89 set(prolog_style_variables).
% 1.68/1.89 set(auto).
% 1.68/1.89 dependent: set(auto1).
% 1.68/1.89 dependent: set(process_input).
% 1.68/1.89 dependent: clear(print_kept).
% 1.68/1.89 dependent: clear(print_new_demod).
% 1.68/1.89 dependent: clear(print_back_demod).
% 1.68/1.89 dependent: clear(print_back_sub).
% 1.68/1.89 dependent: set(control_memory).
% 1.68/1.89 dependent: assign(max_mem, 12000).
% 1.68/1.89 dependent: assign(pick_given_ratio, 4).
% 1.68/1.89 dependent: assign(stats_level, 1).
% 1.68/1.89 dependent: assign(max_seconds, 10800).
% 1.68/1.89 clear(print_given).
% 1.68/1.89
% 1.68/1.89 formula_list(usable).
% 1.68/1.89 all A (A=A).
% 1.68/1.89 all A B subset(A,A).
% 1.68/1.89 empty(empty_set).
% 1.68/1.89 exists A empty(A).
% 1.68/1.89 exists A (-empty(A)).
% 1.68/1.89 -(all A B (subset(A,singleton(B))<->A=empty_set|A=singleton(B))).
% 1.68/1.89 all A B (subset(A,singleton(B))<->A=empty_set|A=singleton(B)).
% 1.68/1.89 end_of_list.
% 1.68/1.89
% 1.68/1.89 -------> usable clausifies to:
% 1.68/1.89
% 1.68/1.89 list(usable).
% 1.68/1.89 0 [] A=A.
% 1.68/1.89 0 [] subset(A,A).
% 1.68/1.89 0 [] empty(empty_set).
% 1.68/1.89 0 [] empty($c1).
% 1.68/1.89 0 [] -empty($c2).
% 1.68/1.89 0 [] subset($c4,singleton($c3))|$c4=empty_set|$c4=singleton($c3).
% 1.68/1.89 0 [] -subset($c4,singleton($c3))|$c4!=empty_set.
% 1.68/1.89 0 [] -subset($c4,singleton($c3))|$c4!=singleton($c3).
% 1.68/1.89 0 [] -subset(A,singleton(B))|A=empty_set|A=singleton(B).
% 1.68/1.89 0 [] subset(A,singleton(B))|A!=empty_set.
% 1.68/1.89 0 [] subset(A,singleton(B))|A!=singleton(B).
% 1.68/1.89 end_of_list.
% 1.68/1.89
% 1.68/1.89 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.68/1.89
% 1.68/1.89 This ia a non-Horn set with equality. The strategy will be
% 1.68/1.89 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.68/1.89 deletion, with positive clauses in sos and nonpositive
% 1.68/1.89 clauses in usable.
% 1.68/1.89
% 1.68/1.89 dependent: set(knuth_bendix).
% 1.68/1.89 dependent: set(anl_eq).
% 1.68/1.89 dependent: set(para_from).
% 1.68/1.89 dependent: set(para_into).
% 1.68/1.89 dependent: clear(para_from_right).
% 1.68/1.89 dependent: clear(para_into_right).
% 1.68/1.89 dependent: set(para_from_vars).
% 1.68/1.89 dependent: set(eq_units_both_ways).
% 1.68/1.89 dependent: set(dynamic_demod_all).
% 1.68/1.89 dependent: set(dynamic_demod).
% 1.68/1.89 dependent: set(order_eq).
% 1.68/1.89 dependent: set(back_demod).
% 1.68/1.89 dependent: set(lrpo).
% 1.68/1.89 dependent: set(hyper_res).
% 1.68/1.89 dependent: set(unit_deletion).
% 1.68/1.89 dependent: set(factor).
% 1.68/1.89
% 1.68/1.89 ------------> process usable:
% 1.68/1.89 ** KEPT (pick-wt=2): 1 [] -empty($c2).
% 1.68/1.89 ** KEPT (pick-wt=7): 3 [copy,2,flip.2] -subset($c4,singleton($c3))|empty_set!=$c4.
% 1.68/1.89 ** KEPT (pick-wt=8): 5 [copy,4,flip.2] -subset($c4,singleton($c3))|singleton($c3)!=$c4.
% 1.68/1.89 ** KEPT (pick-wt=11): 6 [] -subset(A,singleton(B))|A=empty_set|A=singleton(B).
% 1.68/1.89 ** KEPT (pick-wt=7): 7 [] subset(A,singleton(B))|A!=empty_set.
% 1.68/1.89 ** KEPT (pick-wt=8): 8 [] subset(A,singleton(B))|A!=singleton(B).
% 1.68/1.89
% 1.68/1.89 ------------> process sos:
% 1.68/1.89 ** KEPT (pick-wt=3): 9 [] A=A.
% 1.68/1.89 ** KEPT (pick-wt=3): 10 [] subset(A,A).
% 1.68/1.89 ** KEPT (pick-wt=2): 11 [] empty(empty_set).
% 1.68/1.89 ** KEPT (pick-wt=2): 12 [] empty($c1).
% 1.68/1.89 ** KEPT (pick-wt=11): 14 [copy,13,flip.2,flip.3] subset($c4,singleton($c3))|empty_set=$c4|singleton($c3)=$c4.
% 1.68/1.89 Following clause subsumed by 9 during input processing: 0 [copy,9,flip.1] A=A.
% 1.68/1.89
% 1.68/1.89 ======= end of input processing =======
% 1.68/1.89
% 1.68/1.89 =========== start of search ===========
% 1.68/1.89
% 1.68/1.89 -------- PROOF --------
% 1.68/1.89
% 1.68/1.89 -----> EMPTY CLAUSE at 0.00 sec ----> 79 [back_demod,3,demod,69,unit_del,76,9] $F.
% 1.68/1.89
% 1.68/1.89 Length of proof is 8. Level of proof is 5.
% 1.68/1.89
% 1.68/1.89 ---------------- PROOF ----------------
% 1.68/1.89 % SZS status Theorem
% 1.68/1.89 % SZS output start Refutation
% See solution above
% 1.68/1.89 ------------ end of proof -------------
% 1.68/1.89
% 1.68/1.89
% 1.68/1.89 Search stopped by max_proofs option.
% 1.68/1.89
% 1.68/1.89
% 1.68/1.89 Search stopped by max_proofs option.
% 1.68/1.89
% 1.68/1.89 ============ end of search ============
% 1.68/1.89
% 1.68/1.89 -------------- statistics -------------
% 1.68/1.89 clauses given 15
% 1.68/1.89 clauses generated 130
% 1.68/1.89 clauses kept 74
% 1.68/1.89 clauses forward subsumed 96
% 1.68/1.89 clauses back subsumed 21
% 1.68/1.89 Kbytes malloced 976
% 1.68/1.89
% 1.68/1.89 ----------- times (seconds) -----------
% 1.68/1.89 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.68/1.89 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.68/1.89 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.68/1.89
% 1.68/1.89 That finishes the proof of the theorem.
% 1.68/1.89
% 1.68/1.89 Process 7487 finished Wed Jul 27 07:42:38 2022
% 1.68/1.89 Otter interrupted
% 1.68/1.89 PROOF FOUND
%------------------------------------------------------------------------------