TSTP Solution File: SEU320+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU320+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n014.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 13:15:38 EDT 2022
% Result : Theorem 1.77s 1.96s
% Output : Refutation 1.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of clauses : 14 ( 7 unt; 1 nHn; 14 RR)
% Number of literals : 25 ( 2 equ; 11 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 8 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ element(A,powerset(B))
| element(subset_complement(B,A),powerset(B)) ),
file('SEU320+1.p',unknown),
[] ).
cnf(3,axiom,
( ~ element(A,powerset(B))
| subset_complement(B,subset_complement(B,A)) = A ),
file('SEU320+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ top_str(A)
| ~ element(B,powerset(the_carrier(A)))
| ~ closed_subset(B,A)
| open_subset(subset_complement(the_carrier(A),B),A) ),
file('SEU320+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ top_str(A)
| ~ element(B,powerset(the_carrier(A)))
| closed_subset(B,A)
| ~ open_subset(subset_complement(the_carrier(A),B),A) ),
file('SEU320+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ open_subset(dollar_c3,dollar_c4)
| ~ closed_subset(subset_complement(the_carrier(dollar_c4),dollar_c3),dollar_c4) ),
file('SEU320+1.p',unknown),
[] ).
cnf(14,axiom,
top_str(dollar_c4),
file('SEU320+1.p',unknown),
[] ).
cnf(15,axiom,
element(dollar_c3,powerset(the_carrier(dollar_c4))),
file('SEU320+1.p',unknown),
[] ).
cnf(16,axiom,
( open_subset(dollar_c3,dollar_c4)
| closed_subset(subset_complement(the_carrier(dollar_c4),dollar_c3),dollar_c4) ),
file('SEU320+1.p',unknown),
[] ).
cnf(29,plain,
subset_complement(the_carrier(dollar_c4),subset_complement(the_carrier(dollar_c4),dollar_c3)) = dollar_c3,
inference(hyper,[status(thm)],[15,3]),
[iquote('hyper,15,3')] ).
cnf(30,plain,
element(subset_complement(the_carrier(dollar_c4),dollar_c3),powerset(the_carrier(dollar_c4))),
inference(hyper,[status(thm)],[15,1]),
[iquote('hyper,15,1')] ).
cnf(38,plain,
( closed_subset(subset_complement(the_carrier(dollar_c4),dollar_c3),dollar_c4)
| ~ open_subset(dollar_c3,dollar_c4) ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[29,5]),14,30]),
[iquote('para_from,28.1.1,5.4.1,unit_del,14,30')] ).
cnf(40,plain,
closed_subset(subset_complement(the_carrier(dollar_c4),dollar_c3),dollar_c4),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[38,16])]),
[iquote('hyper,38,16,factor_simp')] ).
cnf(41,plain,
open_subset(dollar_c3,dollar_c4),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[40,4,14,30]),29]),
[iquote('hyper,40,4,14,30,demod,29')] ).
cnf(42,plain,
$false,
inference(hyper,[status(thm)],[41,6,40]),
[iquote('hyper,41,6,40')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU320+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n014.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 08:03:09 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.77/1.96 ----- Otter 3.3f, August 2004 -----
% 1.77/1.96 The process was started by sandbox2 on n014.cluster.edu,
% 1.77/1.96 Wed Jul 27 08:03:09 2022
% 1.77/1.96 The command was "./otter". The process ID is 6477.
% 1.77/1.96
% 1.77/1.96 set(prolog_style_variables).
% 1.77/1.96 set(auto).
% 1.77/1.96 dependent: set(auto1).
% 1.77/1.96 dependent: set(process_input).
% 1.77/1.96 dependent: clear(print_kept).
% 1.77/1.96 dependent: clear(print_new_demod).
% 1.77/1.96 dependent: clear(print_back_demod).
% 1.77/1.96 dependent: clear(print_back_sub).
% 1.77/1.96 dependent: set(control_memory).
% 1.77/1.96 dependent: assign(max_mem, 12000).
% 1.77/1.96 dependent: assign(pick_given_ratio, 4).
% 1.77/1.96 dependent: assign(stats_level, 1).
% 1.77/1.96 dependent: assign(max_seconds, 10800).
% 1.77/1.96 clear(print_given).
% 1.77/1.96
% 1.77/1.96 formula_list(usable).
% 1.77/1.96 all A (A=A).
% 1.77/1.96 $T.
% 1.77/1.96 all A B (element(B,powerset(A))->element(subset_complement(A,B),powerset(A))).
% 1.77/1.96 all A (top_str(A)->one_sorted_str(A)).
% 1.77/1.96 $T.
% 1.77/1.96 $T.
% 1.77/1.96 $T.
% 1.77/1.96 exists A top_str(A).
% 1.77/1.96 exists A one_sorted_str(A).
% 1.77/1.96 all A exists B element(B,A).
% 1.77/1.96 all A B (element(B,powerset(A))->subset_complement(A,subset_complement(A,B))=B).
% 1.77/1.96 all A B subset(A,A).
% 1.77/1.96 all A (top_str(A)-> (all B (element(B,powerset(the_carrier(A)))-> (closed_subset(B,A)<->open_subset(subset_complement(the_carrier(A),B),A))))).
% 1.77/1.96 -(all A (top_str(A)-> (all B (element(B,powerset(the_carrier(A)))-> (open_subset(B,A)<->closed_subset(subset_complement(the_carrier(A),B),A)))))).
% 1.77/1.96 all A B (element(A,powerset(B))<->subset(A,B)).
% 1.77/1.96 end_of_list.
% 1.77/1.96
% 1.77/1.96 -------> usable clausifies to:
% 1.77/1.96
% 1.77/1.96 list(usable).
% 1.77/1.96 0 [] A=A.
% 1.77/1.96 0 [] $T.
% 1.77/1.96 0 [] -element(B,powerset(A))|element(subset_complement(A,B),powerset(A)).
% 1.77/1.96 0 [] -top_str(A)|one_sorted_str(A).
% 1.77/1.96 0 [] $T.
% 1.77/1.96 0 [] $T.
% 1.77/1.96 0 [] $T.
% 1.77/1.96 0 [] top_str($c1).
% 1.77/1.96 0 [] one_sorted_str($c2).
% 1.77/1.96 0 [] element($f1(A),A).
% 1.77/1.96 0 [] -element(B,powerset(A))|subset_complement(A,subset_complement(A,B))=B.
% 1.77/1.96 0 [] subset(A,A).
% 1.77/1.96 0 [] -top_str(A)| -element(B,powerset(the_carrier(A)))| -closed_subset(B,A)|open_subset(subset_complement(the_carrier(A),B),A).
% 1.77/1.96 0 [] -top_str(A)| -element(B,powerset(the_carrier(A)))|closed_subset(B,A)| -open_subset(subset_complement(the_carrier(A),B),A).
% 1.77/1.96 0 [] top_str($c4).
% 1.77/1.96 0 [] element($c3,powerset(the_carrier($c4))).
% 1.77/1.96 0 [] open_subset($c3,$c4)|closed_subset(subset_complement(the_carrier($c4),$c3),$c4).
% 1.77/1.96 0 [] -open_subset($c3,$c4)| -closed_subset(subset_complement(the_carrier($c4),$c3),$c4).
% 1.77/1.96 0 [] -element(A,powerset(B))|subset(A,B).
% 1.77/1.96 0 [] element(A,powerset(B))| -subset(A,B).
% 1.77/1.96 end_of_list.
% 1.77/1.96
% 1.77/1.96 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.77/1.96
% 1.77/1.96 This ia a non-Horn set with equality. The strategy will be
% 1.77/1.96 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.77/1.96 deletion, with positive clauses in sos and nonpositive
% 1.77/1.96 clauses in usable.
% 1.77/1.96
% 1.77/1.96 dependent: set(knuth_bendix).
% 1.77/1.96 dependent: set(anl_eq).
% 1.77/1.96 dependent: set(para_from).
% 1.77/1.96 dependent: set(para_into).
% 1.77/1.96 dependent: clear(para_from_right).
% 1.77/1.96 dependent: clear(para_into_right).
% 1.77/1.96 dependent: set(para_from_vars).
% 1.77/1.96 dependent: set(eq_units_both_ways).
% 1.77/1.96 dependent: set(dynamic_demod_all).
% 1.77/1.96 dependent: set(dynamic_demod).
% 1.77/1.96 dependent: set(order_eq).
% 1.77/1.96 dependent: set(back_demod).
% 1.77/1.96 dependent: set(lrpo).
% 1.77/1.96 dependent: set(hyper_res).
% 1.77/1.96 dependent: set(unit_deletion).
% 1.77/1.96 dependent: set(factor).
% 1.77/1.96
% 1.77/1.96 ------------> process usable:
% 1.77/1.96 ** KEPT (pick-wt=10): 1 [] -element(A,powerset(B))|element(subset_complement(B,A),powerset(B)).
% 1.77/1.96 ** KEPT (pick-wt=4): 2 [] -top_str(A)|one_sorted_str(A).
% 1.77/1.96 ** KEPT (pick-wt=11): 3 [] -element(A,powerset(B))|subset_complement(B,subset_complement(B,A))=A.
% 1.77/1.96 ** KEPT (pick-wt=16): 4 [] -top_str(A)| -element(B,powerset(the_carrier(A)))| -closed_subset(B,A)|open_subset(subset_complement(the_carrier(A),B),A).
% 1.77/1.96 ** KEPT (pick-wt=16): 5 [] -top_str(A)| -element(B,powerset(the_carrier(A)))|closed_subset(B,A)| -open_subset(subset_complement(the_carrier(A),B),A).
% 1.77/1.96 ** KEPT (pick-wt=9): 6 [] -open_subset($c3,$c4)| -closed_subset(subset_complement(the_carrier($c4),$c3),$c4).
% 1.77/1.96 ** KEPT (pick-wt=7): 7 [] -element(A,powerset(B))|subset(A,B).
% 1.77/1.96 ** KEPT (pick-wt=7): 8 [] element(A,powerset(B))| -subset(A,B).
% 1.77/1.96
% 1.77/1.96 ------------> process sos:
% 1.77/1.96 ** KEPT (pick-wt=3): 9 [] A=A.
% 1.77/1.96 ** KEPT (pick-wt=2): 10 [] top_str($c1).
% 1.77/1.96 ** KEPT (pick-wt=2): 11 [] one_sorted_str($c2).
% 1.77/1.96 ** KEPT (pick-wt=4): 12 [] element($f1(A),A).
% 1.77/1.96 ** KEPT (pick-wt=3): 13 [] subset(A,A).
% 1.77/1.96 ** KEPT (pick-wt=2): 14 [] top_str($c4).
% 1.77/1.96 ** KEPT (pick-wt=5): 15 [] element($c3,powerset(the_carrier($c4))).
% 1.77/1.96 ** KEPT (pick-wt=9): 16 [] open_subset($c3,$c4)|closed_subset(subset_complement(the_carrier($c4),$c3),$c4).
% 1.77/1.96 Following clause subsumed by 9 during input processing: 0 [copy,9,flip.1] A=A.
% 1.77/1.96
% 1.77/1.96 ======= end of input processing =======
% 1.77/1.96
% 1.77/1.96 =========== start of search ===========
% 1.77/1.96
% 1.77/1.96 -------- PROOF --------
% 1.77/1.96
% 1.77/1.96 -----> EMPTY CLAUSE at 0.00 sec ----> 42 [hyper,41,6,40] $F.
% 1.77/1.96
% 1.77/1.96 Length of proof is 5. Level of proof is 4.
% 1.77/1.96
% 1.77/1.96 ---------------- PROOF ----------------
% 1.77/1.96 % SZS status Theorem
% 1.77/1.96 % SZS output start Refutation
% See solution above
% 1.77/1.96 ------------ end of proof -------------
% 1.77/1.96
% 1.77/1.96
% 1.77/1.96 Search stopped by max_proofs option.
% 1.77/1.96
% 1.77/1.96
% 1.77/1.96 Search stopped by max_proofs option.
% 1.77/1.96
% 1.77/1.96 ============ end of search ============
% 1.77/1.96
% 1.77/1.96 -------------- statistics -------------
% 1.77/1.96 clauses given 25
% 1.77/1.96 clauses generated 53
% 1.77/1.97 clauses kept 38
% 1.77/1.97 clauses forward subsumed 31
% 1.77/1.97 clauses back subsumed 3
% 1.77/1.97 Kbytes malloced 976
% 1.77/1.97
% 1.77/1.97 ----------- times (seconds) -----------
% 1.77/1.97 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.77/1.97 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.77/1.97 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.77/1.97
% 1.77/1.97 That finishes the proof of the theorem.
% 1.77/1.97
% 1.77/1.97 Process 6477 finished Wed Jul 27 08:03:11 2022
% 1.77/1.97 Otter interrupted
% 1.77/1.97 PROOF FOUND
%------------------------------------------------------------------------------