TSTP Solution File: SEU146+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU146+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n017.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 13:14:54 EDT 2022
% Result : Theorem 1.61s 1.77s
% Output : Refutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of clauses : 27 ( 10 unt; 8 nHn; 21 RR)
% Number of literals : 50 ( 17 equ; 16 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 19 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
( A = B
| ~ subset(A,B)
| ~ subset(B,A) ),
file('SEU146+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ subset(singleton(A),B)
| in(A,B) ),
file('SEU146+1.p',unknown),
[] ).
cnf(6,axiom,
( subset(singleton(A),B)
| ~ in(A,B) ),
file('SEU146+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ subset(A,B)
| in(C,A)
| subset(A,set_difference(B,singleton(C))) ),
file('SEU146+1.p',unknown),
[] ).
cnf(8,axiom,
( ~ subset(dollar_c2,singleton(dollar_c1))
| dollar_c2 != empty_set ),
file('SEU146+1.p',unknown),
[] ).
cnf(9,plain,
( ~ subset(dollar_c2,singleton(dollar_c1))
| empty_set != dollar_c2 ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[8])]),
[iquote('copy,8,flip.2')] ).
cnf(10,axiom,
( ~ subset(dollar_c2,singleton(dollar_c1))
| dollar_c2 != singleton(dollar_c1) ),
file('SEU146+1.p',unknown),
[] ).
cnf(11,plain,
( ~ subset(dollar_c2,singleton(dollar_c1))
| singleton(dollar_c1) != dollar_c2 ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[10])]),
[iquote('copy,10,flip.2')] ).
cnf(14,axiom,
( set_difference(A,B) = empty_set
| ~ subset(A,B) ),
file('SEU146+1.p',unknown),
[] ).
cnf(15,axiom,
( ~ subset(A,empty_set)
| A = empty_set ),
file('SEU146+1.p',unknown),
[] ).
cnf(18,axiom,
A = A,
file('SEU146+1.p',unknown),
[] ).
cnf(20,axiom,
( subset(dollar_c2,singleton(dollar_c1))
| dollar_c2 = empty_set
| dollar_c2 = singleton(dollar_c1) ),
file('SEU146+1.p',unknown),
[] ).
cnf(21,plain,
( subset(dollar_c2,singleton(dollar_c1))
| empty_set = dollar_c2
| singleton(dollar_c1) = dollar_c2 ),
inference(flip,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[20])])]),
[iquote('copy,20,flip.2,flip.3')] ).
cnf(23,axiom,
subset(A,A),
file('SEU146+1.p',unknown),
[] ).
cnf(24,axiom,
subset(empty_set,A),
file('SEU146+1.p',unknown),
[] ).
cnf(29,plain,
( in(A,B)
| subset(B,set_difference(B,singleton(A))) ),
inference(hyper,[status(thm)],[23,7]),
[iquote('hyper,23,7')] ).
cnf(30,plain,
in(A,singleton(A)),
inference(hyper,[status(thm)],[23,5]),
[iquote('hyper,23,5')] ).
cnf(49,plain,
( subset(dollar_c2,A)
| ~ in(dollar_c1,A)
| subset(dollar_c2,singleton(dollar_c1))
| empty_set = dollar_c2 ),
inference(para_from,[status(thm),theory(equality)],[21,6]),
[iquote('para_from,21.3.1,6.1.1')] ).
cnf(51,plain,
( subset(dollar_c2,singleton(dollar_c1))
| empty_set = dollar_c2 ),
inference(unit_del,[status(thm)],[inference(factor,[status(thm)],[49]),30]),
[iquote('factor,49.1.3,unit_del,30')] ).
cnf(69,plain,
subset(dollar_c2,singleton(dollar_c1)),
inference(factor_simp,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[51,24])]),
[iquote('para_from,51.2.1,24.1.1,factor_simp')] ).
cnf(70,plain,
set_difference(dollar_c2,singleton(dollar_c1)) = empty_set,
inference(hyper,[status(thm)],[69,14]),
[iquote('hyper,69,14')] ).
cnf(90,plain,
( in(dollar_c1,dollar_c2)
| subset(dollar_c2,empty_set) ),
inference(para_into,[status(thm),theory(equality)],[29,70]),
[iquote('para_into,29.2.2,70.1.1')] ).
cnf(95,plain,
( in(dollar_c1,dollar_c2)
| empty_set = dollar_c2 ),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[90,15])]),
[iquote('hyper,90,15,flip.2')] ).
cnf(115,plain,
in(dollar_c1,dollar_c2),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[95,9]),69,18]),
[iquote('para_from,95.2.1,9.2.1,unit_del,69,18')] ).
cnf(117,plain,
subset(singleton(dollar_c1),dollar_c2),
inference(hyper,[status(thm)],[115,6]),
[iquote('hyper,115,6')] ).
cnf(126,plain,
singleton(dollar_c1) = dollar_c2,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[117,4,69])]),
[iquote('hyper,117,4,69,flip.1')] ).
cnf(127,plain,
$false,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[11]),126,126]),23,18]),
[iquote('back_demod,11,demod,126,126,unit_del,23,18')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU146+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n017.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 06:55:48 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.61/1.77 ----- Otter 3.3f, August 2004 -----
% 1.61/1.77 The process was started by sandbox on n017.cluster.edu,
% 1.61/1.77 Wed Jul 27 06:55:48 2022
% 1.61/1.77 The command was "./otter". The process ID is 23353.
% 1.61/1.77
% 1.61/1.77 set(prolog_style_variables).
% 1.61/1.77 set(auto).
% 1.61/1.77 dependent: set(auto1).
% 1.61/1.77 dependent: set(process_input).
% 1.61/1.77 dependent: clear(print_kept).
% 1.61/1.77 dependent: clear(print_new_demod).
% 1.61/1.77 dependent: clear(print_back_demod).
% 1.61/1.77 dependent: clear(print_back_sub).
% 1.61/1.77 dependent: set(control_memory).
% 1.61/1.77 dependent: assign(max_mem, 12000).
% 1.61/1.77 dependent: assign(pick_given_ratio, 4).
% 1.61/1.77 dependent: assign(stats_level, 1).
% 1.61/1.77 dependent: assign(max_seconds, 10800).
% 1.61/1.77 clear(print_given).
% 1.61/1.77
% 1.61/1.77 formula_list(usable).
% 1.61/1.77 all A (A=A).
% 1.61/1.77 all A B (in(A,B)-> -in(B,A)).
% 1.61/1.77 all A B (A=B<->subset(A,B)&subset(B,A)).
% 1.61/1.77 $T.
% 1.61/1.77 $T.
% 1.61/1.77 $T.
% 1.61/1.77 empty(empty_set).
% 1.61/1.77 all A B (subset(singleton(A),B)<->in(A,B)).
% 1.61/1.77 all A B C (subset(A,B)->in(C,A)|subset(A,set_difference(B,singleton(C)))).
% 1.61/1.77 -(all A B (subset(A,singleton(B))<->A=empty_set|A=singleton(B))).
% 1.61/1.77 exists A empty(A).
% 1.61/1.77 exists A (-empty(A)).
% 1.61/1.77 all A B subset(A,A).
% 1.61/1.77 all A subset(empty_set,A).
% 1.61/1.77 all A B (set_difference(A,B)=empty_set<->subset(A,B)).
% 1.61/1.77 all A (subset(A,empty_set)->A=empty_set).
% 1.61/1.77 end_of_list.
% 1.61/1.77
% 1.61/1.77 -------> usable clausifies to:
% 1.61/1.77
% 1.61/1.77 list(usable).
% 1.61/1.77 0 [] A=A.
% 1.61/1.77 0 [] -in(A,B)| -in(B,A).
% 1.61/1.77 0 [] A!=B|subset(A,B).
% 1.61/1.77 0 [] A!=B|subset(B,A).
% 1.61/1.77 0 [] A=B| -subset(A,B)| -subset(B,A).
% 1.61/1.77 0 [] $T.
% 1.61/1.77 0 [] $T.
% 1.61/1.77 0 [] $T.
% 1.61/1.77 0 [] empty(empty_set).
% 1.61/1.77 0 [] -subset(singleton(A),B)|in(A,B).
% 1.61/1.77 0 [] subset(singleton(A),B)| -in(A,B).
% 1.61/1.77 0 [] -subset(A,B)|in(C,A)|subset(A,set_difference(B,singleton(C))).
% 1.61/1.77 0 [] subset($c2,singleton($c1))|$c2=empty_set|$c2=singleton($c1).
% 1.61/1.77 0 [] -subset($c2,singleton($c1))|$c2!=empty_set.
% 1.61/1.77 0 [] -subset($c2,singleton($c1))|$c2!=singleton($c1).
% 1.61/1.77 0 [] empty($c3).
% 1.61/1.77 0 [] -empty($c4).
% 1.61/1.77 0 [] subset(A,A).
% 1.61/1.77 0 [] subset(empty_set,A).
% 1.61/1.77 0 [] set_difference(A,B)!=empty_set|subset(A,B).
% 1.61/1.77 0 [] set_difference(A,B)=empty_set| -subset(A,B).
% 1.61/1.77 0 [] -subset(A,empty_set)|A=empty_set.
% 1.61/1.77 end_of_list.
% 1.61/1.77
% 1.61/1.77 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.61/1.77
% 1.61/1.77 This ia a non-Horn set with equality. The strategy will be
% 1.61/1.77 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.61/1.77 deletion, with positive clauses in sos and nonpositive
% 1.61/1.77 clauses in usable.
% 1.61/1.77
% 1.61/1.77 dependent: set(knuth_bendix).
% 1.61/1.77 dependent: set(anl_eq).
% 1.61/1.77 dependent: set(para_from).
% 1.61/1.77 dependent: set(para_into).
% 1.61/1.77 dependent: clear(para_from_right).
% 1.61/1.77 dependent: clear(para_into_right).
% 1.61/1.77 dependent: set(para_from_vars).
% 1.61/1.77 dependent: set(eq_units_both_ways).
% 1.61/1.77 dependent: set(dynamic_demod_all).
% 1.61/1.77 dependent: set(dynamic_demod).
% 1.61/1.77 dependent: set(order_eq).
% 1.61/1.77 dependent: set(back_demod).
% 1.61/1.77 dependent: set(lrpo).
% 1.61/1.77 dependent: set(hyper_res).
% 1.61/1.77 dependent: set(unit_deletion).
% 1.61/1.77 dependent: set(factor).
% 1.61/1.77
% 1.61/1.77 ------------> process usable:
% 1.61/1.77 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.61/1.77 ** KEPT (pick-wt=6): 2 [] A!=B|subset(A,B).
% 1.61/1.77 ** KEPT (pick-wt=6): 3 [] A!=B|subset(B,A).
% 1.61/1.77 ** KEPT (pick-wt=9): 4 [] A=B| -subset(A,B)| -subset(B,A).
% 1.61/1.77 ** KEPT (pick-wt=7): 5 [] -subset(singleton(A),B)|in(A,B).
% 1.61/1.77 ** KEPT (pick-wt=7): 6 [] subset(singleton(A),B)| -in(A,B).
% 1.61/1.77 ** KEPT (pick-wt=12): 7 [] -subset(A,B)|in(C,A)|subset(A,set_difference(B,singleton(C))).
% 1.61/1.77 ** KEPT (pick-wt=7): 9 [copy,8,flip.2] -subset($c2,singleton($c1))|empty_set!=$c2.
% 1.61/1.77 ** KEPT (pick-wt=8): 11 [copy,10,flip.2] -subset($c2,singleton($c1))|singleton($c1)!=$c2.
% 1.61/1.77 ** KEPT (pick-wt=2): 12 [] -empty($c4).
% 1.61/1.77 ** KEPT (pick-wt=8): 13 [] set_difference(A,B)!=empty_set|subset(A,B).
% 1.61/1.77 ** KEPT (pick-wt=8): 14 [] set_difference(A,B)=empty_set| -subset(A,B).
% 1.61/1.77 ** KEPT (pick-wt=6): 15 [] -subset(A,empty_set)|A=empty_set.
% 1.61/1.77
% 1.61/1.77 ------------> process sos:
% 1.61/1.77 ** KEPT (pick-wt=3): 18 [] A=A.
% 1.61/1.77 ** KEPT (pick-wt=2): 19 [] empty(empty_set).
% 1.61/1.77 ** KEPT (pick-wt=11): 21 [copy,20,flip.2,flip.3] subset($c2,singleton($c1))|empty_set=$c2|singleton($c1)=$c2.
% 1.61/1.77 ** KEPT (pick-wt=2): 22 [] empty($c3).
% 1.61/1.77 ** KEPT (pick-wt=3): 23 [] subset(A,A).
% 1.61/1.77 ** KEPT (pick-wt=3): 24 [] subset(empty_set,A).
% 1.61/1.77 Following clause subsumed by 18 during input processing: 0 [copy,18,flip.1] A=A.
% 1.61/1.77 18 back subsumes 17.
% 1.61/1.77
% 1.61/1.77 ======= end of input processing =======
% 1.61/1.77
% 1.61/1.77 =========== start of search ===========
% 1.61/1.77
% 1.61/1.77 -------- PROOF --------
% 1.61/1.77
% 1.61/1.77 -----> EMPTY CLAUSE at 0.01 sec ----> 127 [back_demod,11,demod,126,126,unit_del,23,18] $F.
% 1.61/1.77
% 1.61/1.77 Length of proof is 14. Level of proof is 10.
% 1.61/1.77
% 1.61/1.77 ---------------- PROOF ----------------
% 1.61/1.77 % SZS status Theorem
% 1.61/1.77 % SZS output start Refutation
% See solution above
% 1.61/1.77 ------------ end of proof -------------
% 1.61/1.77
% 1.61/1.77
% 1.61/1.77 Search stopped by max_proofs option.
% 1.61/1.77
% 1.61/1.77
% 1.61/1.77 Search stopped by max_proofs option.
% 1.61/1.77
% 1.61/1.77 ============ end of search ============
% 1.61/1.77
% 1.61/1.77 -------------- statistics -------------
% 1.61/1.77 clauses given 23
% 1.61/1.77 clauses generated 261
% 1.61/1.77 clauses kept 118
% 1.61/1.77 clauses forward subsumed 169
% 1.61/1.77 clauses back subsumed 53
% 1.61/1.77 Kbytes malloced 976
% 1.61/1.77
% 1.61/1.77 ----------- times (seconds) -----------
% 1.61/1.77 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.61/1.77 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.61/1.77 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.61/1.77
% 1.61/1.77 That finishes the proof of the theorem.
% 1.61/1.77
% 1.61/1.77 Process 23353 finished Wed Jul 27 06:55:49 2022
% 1.61/1.77 Otter interrupted
% 1.61/1.77 PROOF FOUND
%------------------------------------------------------------------------------