TSTP Solution File: SEU323+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU323+1 : TPTP v8.1.0. Released v3.3.0.
% 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 13:15:39 EDT 2022
% Result : Theorem 1.77s 1.98s
% Output : Refutation 1.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 9
% Syntax : Number of clauses : 16 ( 10 unt; 0 nHn; 16 RR)
% Number of literals : 30 ( 3 equ; 15 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 12 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ topological_space(A)
| ~ top_str(A)
| ~ closed_subset(B,A)
| ~ element(B,powerset(the_carrier(A)))
| open_subset(subset_complement(the_carrier(A),B),A) ),
file('SEU323+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ element(A,powerset(B))
| element(subset_complement(B,A),powerset(B)) ),
file('SEU323+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ top_str(A)
| ~ element(B,powerset(the_carrier(A)))
| element(topstr_closure(A,B),powerset(the_carrier(A))) ),
file('SEU323+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ topological_space(A)
| ~ top_str(A)
| ~ element(B,powerset(the_carrier(A)))
| closed_subset(topstr_closure(A,B),A) ),
file('SEU323+1.p',unknown),
[] ).
cnf(15,axiom,
( ~ top_str(A)
| ~ element(B,powerset(the_carrier(A)))
| interior(A,B) = subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B))) ),
file('SEU323+1.p',unknown),
[] ).
cnf(16,plain,
( ~ top_str(A)
| ~ element(B,powerset(the_carrier(A)))
| subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B))) = interior(A,B) ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[15])]),
[iquote('copy,15,flip.3')] ).
cnf(17,axiom,
~ open_subset(interior(dollar_c4,dollar_c3),dollar_c4),
file('SEU323+1.p',unknown),
[] ).
cnf(23,axiom,
topological_space(dollar_c4),
file('SEU323+1.p',unknown),
[] ).
cnf(24,axiom,
top_str(dollar_c4),
file('SEU323+1.p',unknown),
[] ).
cnf(25,axiom,
element(dollar_c3,powerset(the_carrier(dollar_c4))),
file('SEU323+1.p',unknown),
[] ).
cnf(47,plain,
subset_complement(the_carrier(dollar_c4),topstr_closure(dollar_c4,subset_complement(the_carrier(dollar_c4),dollar_c3))) = interior(dollar_c4,dollar_c3),
inference(hyper,[status(thm)],[25,16,24]),
[iquote('hyper,25,16,24')] ).
cnf(52,plain,
element(subset_complement(the_carrier(dollar_c4),dollar_c3),powerset(the_carrier(dollar_c4))),
inference(hyper,[status(thm)],[25,5]),
[iquote('hyper,25,5')] ).
cnf(178,plain,
closed_subset(topstr_closure(dollar_c4,subset_complement(the_carrier(dollar_c4),dollar_c3)),dollar_c4),
inference(hyper,[status(thm)],[52,7,23,24]),
[iquote('hyper,52,7,23,24')] ).
cnf(179,plain,
element(topstr_closure(dollar_c4,subset_complement(the_carrier(dollar_c4),dollar_c3)),powerset(the_carrier(dollar_c4))),
inference(hyper,[status(thm)],[52,6,24]),
[iquote('hyper,52,6,24')] ).
cnf(406,plain,
open_subset(interior(dollar_c4,dollar_c3),dollar_c4),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[179,1,23,24,178]),47]),
[iquote('hyper,179,1,23,24,178,demod,47')] ).
cnf(407,plain,
$false,
inference(binary,[status(thm)],[406,17]),
[iquote('binary,406.1,17.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU323+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.11/0.32 % Computer : n019.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Wed Jul 27 08:06:06 EDT 2022
% 0.11/0.33 % CPUTime :
% 1.77/1.97 ----- Otter 3.3f, August 2004 -----
% 1.77/1.97 The process was started by sandbox on n019.cluster.edu,
% 1.77/1.97 Wed Jul 27 08:06:07 2022
% 1.77/1.97 The command was "./otter". The process ID is 9652.
% 1.77/1.97
% 1.77/1.97 set(prolog_style_variables).
% 1.77/1.97 set(auto).
% 1.77/1.97 dependent: set(auto1).
% 1.77/1.97 dependent: set(process_input).
% 1.77/1.97 dependent: clear(print_kept).
% 1.77/1.97 dependent: clear(print_new_demod).
% 1.77/1.97 dependent: clear(print_back_demod).
% 1.77/1.97 dependent: clear(print_back_sub).
% 1.77/1.97 dependent: set(control_memory).
% 1.77/1.97 dependent: assign(max_mem, 12000).
% 1.77/1.97 dependent: assign(pick_given_ratio, 4).
% 1.77/1.97 dependent: assign(stats_level, 1).
% 1.77/1.97 dependent: assign(max_seconds, 10800).
% 1.77/1.97 clear(print_given).
% 1.77/1.97
% 1.77/1.97 formula_list(usable).
% 1.77/1.97 all A (A=A).
% 1.77/1.97 all A B (topological_space(A)&top_str(A)&closed_subset(B,A)&element(B,powerset(the_carrier(A)))->open_subset(subset_complement(the_carrier(A),B),A)).
% 1.77/1.97 all A (topological_space(A)&top_str(A)-> (exists B (element(B,powerset(the_carrier(A)))&closed_subset(B,A)))).
% 1.77/1.97 all A B (element(B,powerset(A))->subset_complement(A,subset_complement(A,B))=B).
% 1.77/1.97 all A B subset(A,A).
% 1.77/1.97 exists A one_sorted_str(A).
% 1.77/1.97 all A B (element(B,powerset(A))->element(subset_complement(A,B),powerset(A))).
% 1.77/1.97 all A B (top_str(A)&element(B,powerset(the_carrier(A)))->element(topstr_closure(A,B),powerset(the_carrier(A)))).
% 1.77/1.97 $T.
% 1.77/1.97 all A B (topological_space(A)&top_str(A)&element(B,powerset(the_carrier(A)))->closed_subset(topstr_closure(A,B),A)).
% 1.77/1.97 all A B (topological_space(A)&top_str(A)&open_subset(B,A)&element(B,powerset(the_carrier(A)))->closed_subset(subset_complement(the_carrier(A),B),A)).
% 1.77/1.97 exists A top_str(A).
% 1.77/1.97 all A exists B element(B,A).
% 1.77/1.97 all A B (top_str(A)&element(B,powerset(the_carrier(A)))->element(interior(A,B),powerset(the_carrier(A)))).
% 1.77/1.97 $T.
% 1.77/1.97 all A (top_str(A)->one_sorted_str(A)).
% 1.77/1.97 $T.
% 1.77/1.97 $T.
% 1.77/1.97 all A (topological_space(A)&top_str(A)-> (exists B (element(B,powerset(the_carrier(A)))&open_subset(B,A)))).
% 1.77/1.97 all A B (element(A,powerset(B))<->subset(A,B)).
% 1.77/1.97 all A (top_str(A)-> (all B (element(B,powerset(the_carrier(A)))->interior(A,B)=subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B)))))).
% 1.77/1.97 -(all A (topological_space(A)&top_str(A)-> (all B (element(B,powerset(the_carrier(A)))->open_subset(interior(A,B),A))))).
% 1.77/1.97 end_of_list.
% 1.77/1.97
% 1.77/1.97 -------> usable clausifies to:
% 1.77/1.97
% 1.77/1.97 list(usable).
% 1.77/1.97 0 [] A=A.
% 1.77/1.97 0 [] -topological_space(A)| -top_str(A)| -closed_subset(B,A)| -element(B,powerset(the_carrier(A)))|open_subset(subset_complement(the_carrier(A),B),A).
% 1.77/1.97 0 [] -topological_space(A)| -top_str(A)|element($f1(A),powerset(the_carrier(A))).
% 1.77/1.97 0 [] -topological_space(A)| -top_str(A)|closed_subset($f1(A),A).
% 1.77/1.97 0 [] -element(B,powerset(A))|subset_complement(A,subset_complement(A,B))=B.
% 1.77/1.97 0 [] subset(A,A).
% 1.77/1.97 0 [] one_sorted_str($c1).
% 1.77/1.97 0 [] -element(B,powerset(A))|element(subset_complement(A,B),powerset(A)).
% 1.77/1.97 0 [] -top_str(A)| -element(B,powerset(the_carrier(A)))|element(topstr_closure(A,B),powerset(the_carrier(A))).
% 1.77/1.97 0 [] $T.
% 1.77/1.97 0 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))|closed_subset(topstr_closure(A,B),A).
% 1.77/1.97 0 [] -topological_space(A)| -top_str(A)| -open_subset(B,A)| -element(B,powerset(the_carrier(A)))|closed_subset(subset_complement(the_carrier(A),B),A).
% 1.77/1.97 0 [] top_str($c2).
% 1.77/1.97 0 [] element($f2(A),A).
% 1.77/1.97 0 [] -top_str(A)| -element(B,powerset(the_carrier(A)))|element(interior(A,B),powerset(the_carrier(A))).
% 1.77/1.97 0 [] $T.
% 1.77/1.97 0 [] -top_str(A)|one_sorted_str(A).
% 1.77/1.97 0 [] $T.
% 1.77/1.97 0 [] $T.
% 1.77/1.97 0 [] -topological_space(A)| -top_str(A)|element($f3(A),powerset(the_carrier(A))).
% 1.77/1.97 0 [] -topological_space(A)| -top_str(A)|open_subset($f3(A),A).
% 1.77/1.97 0 [] -element(A,powerset(B))|subset(A,B).
% 1.77/1.97 0 [] element(A,powerset(B))| -subset(A,B).
% 1.77/1.97 0 [] -top_str(A)| -element(B,powerset(the_carrier(A)))|interior(A,B)=subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B))).
% 1.77/1.97 0 [] topological_space($c4).
% 1.77/1.97 0 [] top_str($c4).
% 1.77/1.97 0 [] element($c3,powerset(the_carrier($c4))).
% 1.77/1.97 0 [] -open_subset(interior($c4,$c3),$c4).
% 1.77/1.97 end_of_list.
% 1.77/1.97
% 1.77/1.97 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=5.
% 1.77/1.97
% 1.77/1.97 This is a Horn set with equality. The strategy will be
% 1.77/1.97 Knuth-Bendix and hyper_res, with positive clauses in
% 1.77/1.97 sos and nonpositive clauses in usable.
% 1.77/1.97
% 1.77/1.97 dependent: set(knuth_bendix).
% 1.77/1.98 dependent: set(anl_eq).
% 1.77/1.98 dependent: set(para_from).
% 1.77/1.98 dependent: set(para_into).
% 1.77/1.98 dependent: clear(para_from_right).
% 1.77/1.98 dependent: clear(para_into_right).
% 1.77/1.98 dependent: set(para_from_vars).
% 1.77/1.98 dependent: set(eq_units_both_ways).
% 1.77/1.98 dependent: set(dynamic_demod_all).
% 1.77/1.98 dependent: set(dynamic_demod).
% 1.77/1.98 dependent: set(order_eq).
% 1.77/1.98 dependent: set(back_demod).
% 1.77/1.98 dependent: set(lrpo).
% 1.77/1.98 dependent: set(hyper_res).
% 1.77/1.98 dependent: clear(order_hyper).
% 1.77/1.98
% 1.77/1.98 ------------> process usable:
% 1.77/1.98 ** KEPT (pick-wt=18): 1 [] -topological_space(A)| -top_str(A)| -closed_subset(B,A)| -element(B,powerset(the_carrier(A)))|open_subset(subset_complement(the_carrier(A),B),A).
% 1.77/1.98 ** KEPT (pick-wt=10): 2 [] -topological_space(A)| -top_str(A)|element($f1(A),powerset(the_carrier(A))).
% 1.77/1.98 ** KEPT (pick-wt=8): 3 [] -topological_space(A)| -top_str(A)|closed_subset($f1(A),A).
% 1.77/1.98 ** KEPT (pick-wt=11): 4 [] -element(A,powerset(B))|subset_complement(B,subset_complement(B,A))=A.
% 1.77/1.98 ** KEPT (pick-wt=10): 5 [] -element(A,powerset(B))|element(subset_complement(B,A),powerset(B)).
% 1.77/1.98 ** KEPT (pick-wt=14): 6 [] -top_str(A)| -element(B,powerset(the_carrier(A)))|element(topstr_closure(A,B),powerset(the_carrier(A))).
% 1.77/1.98 ** KEPT (pick-wt=14): 7 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))|closed_subset(topstr_closure(A,B),A).
% 1.77/1.98 ** KEPT (pick-wt=18): 8 [] -topological_space(A)| -top_str(A)| -open_subset(B,A)| -element(B,powerset(the_carrier(A)))|closed_subset(subset_complement(the_carrier(A),B),A).
% 1.77/1.98 ** KEPT (pick-wt=14): 9 [] -top_str(A)| -element(B,powerset(the_carrier(A)))|element(interior(A,B),powerset(the_carrier(A))).
% 1.77/1.98 ** KEPT (pick-wt=4): 10 [] -top_str(A)|one_sorted_str(A).
% 1.77/1.98 ** KEPT (pick-wt=10): 11 [] -topological_space(A)| -top_str(A)|element($f3(A),powerset(the_carrier(A))).
% 1.77/1.98 ** KEPT (pick-wt=8): 12 [] -topological_space(A)| -top_str(A)|open_subset($f3(A),A).
% 1.77/1.98 ** KEPT (pick-wt=7): 13 [] -element(A,powerset(B))|subset(A,B).
% 1.77/1.98 ** KEPT (pick-wt=7): 14 [] element(A,powerset(B))| -subset(A,B).
% 1.77/1.98 ** KEPT (pick-wt=20): 16 [copy,15,flip.3] -top_str(A)| -element(B,powerset(the_carrier(A)))|subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B)))=interior(A,B).
% 1.77/1.98 ** KEPT (pick-wt=5): 17 [] -open_subset(interior($c4,$c3),$c4).
% 1.77/1.98
% 1.77/1.98 ------------> process sos:
% 1.77/1.98 ** KEPT (pick-wt=3): 18 [] A=A.
% 1.77/1.98 ** KEPT (pick-wt=3): 19 [] subset(A,A).
% 1.77/1.98 ** KEPT (pick-wt=2): 20 [] one_sorted_str($c1).
% 1.77/1.98 ** KEPT (pick-wt=2): 21 [] top_str($c2).
% 1.77/1.98 ** KEPT (pick-wt=4): 22 [] element($f2(A),A).
% 1.77/1.98 ** KEPT (pick-wt=2): 23 [] topological_space($c4).
% 1.77/1.98 ** KEPT (pick-wt=2): 24 [] top_str($c4).
% 1.77/1.98 ** KEPT (pick-wt=5): 25 [] element($c3,powerset(the_carrier($c4))).
% 1.77/1.98 Following clause subsumed by 18 during input processing: 0 [copy,18,flip.1] A=A.
% 1.77/1.98
% 1.77/1.98 ======= end of input processing =======
% 1.77/1.98
% 1.77/1.98 =========== start of search ===========
% 1.77/1.98
% 1.77/1.98
% 1.77/1.98 Resetting weight limit to 10.
% 1.77/1.98
% 1.77/1.98
% 1.77/1.98 Resetting weight limit to 10.
% 1.77/1.98
% 1.77/1.98 sos_size=159
% 1.77/1.98
% 1.77/1.98 -------- PROOF --------
% 1.77/1.98
% 1.77/1.98 ----> UNIT CONFLICT at 0.01 sec ----> 407 [binary,406.1,17.1] $F.
% 1.77/1.98
% 1.77/1.98 Length of proof is 6. Level of proof is 3.
% 1.77/1.98
% 1.77/1.98 ---------------- PROOF ----------------
% 1.77/1.98 % SZS status Theorem
% 1.77/1.98 % SZS output start Refutation
% See solution above
% 1.77/1.98 ------------ end of proof -------------
% 1.77/1.98
% 1.77/1.98
% 1.77/1.98 Search stopped by max_proofs option.
% 1.77/1.98
% 1.77/1.98
% 1.77/1.98 Search stopped by max_proofs option.
% 1.77/1.98
% 1.77/1.98 ============ end of search ============
% 1.77/1.98
% 1.77/1.98 -------------- statistics -------------
% 1.77/1.98 clauses given 108
% 1.77/1.98 clauses generated 393
% 1.77/1.98 clauses kept 330
% 1.77/1.98 clauses forward subsumed 135
% 1.77/1.98 clauses back subsumed 0
% 1.77/1.98 Kbytes malloced 4882
% 1.77/1.98
% 1.77/1.98 ----------- times (seconds) -----------
% 1.77/1.98 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.77/1.98 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.77/1.98 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.77/1.98
% 1.77/1.98 That finishes the proof of the theorem.
% 1.77/1.98
% 1.77/1.98 Process 9652 finished Wed Jul 27 08:06:08 2022
% 1.77/1.98 Otter interrupted
% 1.77/1.98 PROOF FOUND
%------------------------------------------------------------------------------