TSTP Solution File: SEU116+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU116+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n026.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 13:14:48 EDT 2022
% Result : Theorem 2.02s 2.21s
% Output : Refutation 2.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 3
% Syntax : Number of clauses : 5 ( 4 unt; 0 nHn; 5 RR)
% Number of literals : 6 ( 0 equ; 2 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 2 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(18,axiom,
( ~ element(A,finite_subsets(B))
| finite(A) ),
file('SEU116+1.p',unknown),
[] ).
cnf(25,axiom,
~ finite(dollar_c5),
file('SEU116+1.p',unknown),
[] ).
cnf(61,axiom,
element(dollar_c5,finite_subsets(dollar_c6)),
file('SEU116+1.p',unknown),
[] ).
cnf(107,plain,
finite(dollar_c5),
inference(hyper,[status(thm)],[61,18]),
[iquote('hyper,61,18')] ).
cnf(108,plain,
$false,
inference(binary,[status(thm)],[107,25]),
[iquote('binary,107.1,25.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU116+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n026.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 07:56:54 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.02/2.21 ----- Otter 3.3f, August 2004 -----
% 2.02/2.21 The process was started by sandbox on n026.cluster.edu,
% 2.02/2.21 Wed Jul 27 07:56:54 2022
% 2.02/2.21 The command was "./otter". The process ID is 27295.
% 2.02/2.21
% 2.02/2.21 set(prolog_style_variables).
% 2.02/2.21 set(auto).
% 2.02/2.21 dependent: set(auto1).
% 2.02/2.21 dependent: set(process_input).
% 2.02/2.21 dependent: clear(print_kept).
% 2.02/2.21 dependent: clear(print_new_demod).
% 2.02/2.21 dependent: clear(print_back_demod).
% 2.02/2.21 dependent: clear(print_back_sub).
% 2.02/2.21 dependent: set(control_memory).
% 2.02/2.21 dependent: assign(max_mem, 12000).
% 2.02/2.21 dependent: assign(pick_given_ratio, 4).
% 2.02/2.21 dependent: assign(stats_level, 1).
% 2.02/2.21 dependent: assign(max_seconds, 10800).
% 2.02/2.21 clear(print_given).
% 2.02/2.21
% 2.02/2.21 formula_list(usable).
% 2.02/2.21 all A (A=A).
% 2.02/2.21 all A B subset(A,A).
% 2.02/2.21 all A B (in(A,B)-> -in(B,A)).
% 2.02/2.21 empty(empty_set).
% 2.02/2.21 all A B (in(A,B)->element(A,B)).
% 2.02/2.21 all A B C (in(A,B)&element(B,powerset(C))->element(A,C)).
% 2.02/2.21 all A B C (-(in(A,B)&element(B,powerset(C))&empty(C))).
% 2.02/2.21 all A B (-(empty(A)&A!=B&empty(B))).
% 2.02/2.21 all A (-empty(powerset(A))&cup_closed(powerset(A))&diff_closed(powerset(A))&preboolean(powerset(A))).
% 2.02/2.21 all A (preboolean(A)->cup_closed(A)&diff_closed(A)).
% 2.02/2.21 all A (cup_closed(A)&diff_closed(A)->preboolean(A)).
% 2.02/2.21 all A (empty(A)->finite(A)).
% 2.02/2.21 all A (finite(A)-> (all B (element(B,powerset(A))->finite(B)))).
% 2.02/2.21 all A (-empty(powerset(A))).
% 2.02/2.21 all A B (element(A,B)->empty(B)|in(A,B)).
% 2.02/2.21 all A B (element(A,powerset(B))<->subset(A,B)).
% 2.02/2.21 all A (empty(A)->A=empty_set).
% 2.02/2.21 all A B (-(in(A,B)&empty(B))).
% 2.02/2.21 all A exists B element(B,A).
% 2.02/2.21 all A preboolean(finite_subsets(A)).
% 2.02/2.21 all A (-empty(finite_subsets(A))&cup_closed(finite_subsets(A))&diff_closed(finite_subsets(A))&preboolean(finite_subsets(A))).
% 2.02/2.21 all A B (element(B,finite_subsets(A))->finite(B)).
% 2.02/2.21 exists A (-empty(A)&cup_closed(A)&cap_closed(A)&diff_closed(A)&preboolean(A)).
% 2.02/2.21 exists A (-empty(A)&finite(A)).
% 2.02/2.21 all A exists B (element(B,powerset(A))&empty(B)&relation(B)&function(B)&one_to_one(B)&epsilon_transitive(B)&epsilon_connected(B)&ordinal(B)&natural(B)&finite(B)).
% 2.02/2.21 all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)&finite(B)))).
% 2.02/2.21 all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)&finite(B)))).
% 2.02/2.21 all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)))).
% 2.02/2.21 all A exists B (element(B,powerset(A))&empty(B)).
% 2.02/2.21 exists A empty(A).
% 2.02/2.21 exists A (-empty(A)).
% 2.02/2.21 -(all A B (element(B,finite_subsets(A))->finite(B))).
% 2.02/2.21 end_of_list.
% 2.02/2.21
% 2.02/2.21 -------> usable clausifies to:
% 2.02/2.21
% 2.02/2.21 list(usable).
% 2.02/2.21 0 [] A=A.
% 2.02/2.21 0 [] subset(A,A).
% 2.02/2.21 0 [] -in(A,B)| -in(B,A).
% 2.02/2.21 0 [] empty(empty_set).
% 2.02/2.21 0 [] -in(A,B)|element(A,B).
% 2.02/2.21 0 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 2.02/2.21 0 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 2.02/2.21 0 [] -empty(A)|A=B| -empty(B).
% 2.02/2.21 0 [] -empty(powerset(A)).
% 2.02/2.21 0 [] cup_closed(powerset(A)).
% 2.02/2.21 0 [] diff_closed(powerset(A)).
% 2.02/2.21 0 [] preboolean(powerset(A)).
% 2.02/2.21 0 [] -preboolean(A)|cup_closed(A).
% 2.02/2.21 0 [] -preboolean(A)|diff_closed(A).
% 2.02/2.21 0 [] -cup_closed(A)| -diff_closed(A)|preboolean(A).
% 2.02/2.21 0 [] -empty(A)|finite(A).
% 2.02/2.21 0 [] -finite(A)| -element(B,powerset(A))|finite(B).
% 2.02/2.21 0 [] -empty(powerset(A)).
% 2.02/2.21 0 [] -element(A,B)|empty(B)|in(A,B).
% 2.02/2.21 0 [] -element(A,powerset(B))|subset(A,B).
% 2.02/2.21 0 [] element(A,powerset(B))| -subset(A,B).
% 2.02/2.21 0 [] -empty(A)|A=empty_set.
% 2.02/2.21 0 [] -in(A,B)| -empty(B).
% 2.02/2.21 0 [] element($f1(A),A).
% 2.02/2.21 0 [] preboolean(finite_subsets(A)).
% 2.02/2.21 0 [] -empty(finite_subsets(A)).
% 2.02/2.21 0 [] cup_closed(finite_subsets(A)).
% 2.02/2.21 0 [] diff_closed(finite_subsets(A)).
% 2.02/2.21 0 [] preboolean(finite_subsets(A)).
% 2.02/2.21 0 [] -element(B,finite_subsets(A))|finite(B).
% 2.02/2.21 0 [] -empty($c1).
% 2.02/2.21 0 [] cup_closed($c1).
% 2.02/2.21 0 [] cap_closed($c1).
% 2.02/2.21 0 [] diff_closed($c1).
% 2.02/2.21 0 [] preboolean($c1).
% 2.02/2.21 0 [] -empty($c2).
% 2.02/2.21 0 [] finite($c2).
% 2.02/2.21 0 [] element($f2(A),powerset(A)).
% 2.02/2.21 0 [] empty($f2(A)).
% 2.02/2.21 0 [] relation($f2(A)).
% 2.02/2.21 0 [] function($f2(A)).
% 2.02/2.21 0 [] one_to_one($f2(A)).
% 2.02/2.21 0 [] epsilon_transitive($f2(A)).
% 2.02/2.21 0 [] epsilon_connected($f2(A)).
% 2.02/2.21 0 [] ordinal($f2(A)).
% 2.02/2.21 0 [] natural($f2(A)).
% 2.02/2.21 0 [] finite($f2(A)).
% 2.02/2.21 0 [] empty(A)|element($f3(A),powerset(A)).
% 2.02/2.21 0 [] empty(A)| -empty($f3(A)).
% 2.02/2.21 0 [] empty(A)|finite($f3(A)).
% 2.02/2.21 0 [] empty(A)|element($f4(A),powerset(A)).
% 2.02/2.21 0 [] empty(A)| -empty($f4(A)).
% 2.02/2.21 0 [] empty(A)|finite($f4(A)).
% 2.02/2.21 0 [] empty(A)|element($f5(A),powerset(A)).
% 2.02/2.21 0 [] empty(A)| -empty($f5(A)).
% 2.02/2.21 0 [] element($f6(A),powerset(A)).
% 2.02/2.21 0 [] empty($f6(A)).
% 2.02/2.21 0 [] empty($c3).
% 2.02/2.21 0 [] -empty($c4).
% 2.02/2.21 0 [] element($c5,finite_subsets($c6)).
% 2.02/2.21 0 [] -finite($c5).
% 2.02/2.21 end_of_list.
% 2.02/2.21
% 2.02/2.21 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 2.02/2.21
% 2.02/2.21 This ia a non-Horn set with equality. The strategy will be
% 2.02/2.21 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.02/2.21 deletion, with positive clauses in sos and nonpositive
% 2.02/2.21 clauses in usable.
% 2.02/2.21
% 2.02/2.21 dependent: set(knuth_bendix).
% 2.02/2.21 dependent: set(anl_eq).
% 2.02/2.21 dependent: set(para_from).
% 2.02/2.21 dependent: set(para_into).
% 2.02/2.21 dependent: clear(para_from_right).
% 2.02/2.21 dependent: clear(para_into_right).
% 2.02/2.21 dependent: set(para_from_vars).
% 2.02/2.21 dependent: set(eq_units_both_ways).
% 2.02/2.21 dependent: set(dynamic_demod_all).
% 2.02/2.21 dependent: set(dynamic_demod).
% 2.02/2.21 dependent: set(order_eq).
% 2.02/2.21 dependent: set(back_demod).
% 2.02/2.21 dependent: set(lrpo).
% 2.02/2.21 dependent: set(hyper_res).
% 2.02/2.21 dependent: set(unit_deletion).
% 2.02/2.21 dependent: set(factor).
% 2.02/2.21
% 2.02/2.21 ------------> process usable:
% 2.02/2.21 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 2.02/2.21 ** KEPT (pick-wt=6): 2 [] -in(A,B)|element(A,B).
% 2.02/2.21 ** KEPT (pick-wt=10): 3 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 2.02/2.21 ** KEPT (pick-wt=9): 4 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 2.02/2.21 ** KEPT (pick-wt=7): 5 [] -empty(A)|A=B| -empty(B).
% 2.02/2.21 ** KEPT (pick-wt=3): 6 [] -empty(powerset(A)).
% 2.02/2.21 ** KEPT (pick-wt=4): 7 [] -preboolean(A)|cup_closed(A).
% 2.02/2.21 ** KEPT (pick-wt=4): 8 [] -preboolean(A)|diff_closed(A).
% 2.02/2.21 ** KEPT (pick-wt=6): 9 [] -cup_closed(A)| -diff_closed(A)|preboolean(A).
% 2.02/2.21 ** KEPT (pick-wt=4): 10 [] -empty(A)|finite(A).
% 2.02/2.21 ** KEPT (pick-wt=8): 11 [] -finite(A)| -element(B,powerset(A))|finite(B).
% 2.02/2.21 Following clause subsumed by 6 during input processing: 0 [] -empty(powerset(A)).
% 2.02/2.21 ** KEPT (pick-wt=8): 12 [] -element(A,B)|empty(B)|in(A,B).
% 2.02/2.21 ** KEPT (pick-wt=7): 13 [] -element(A,powerset(B))|subset(A,B).
% 2.02/2.21 ** KEPT (pick-wt=7): 14 [] element(A,powerset(B))| -subset(A,B).
% 2.02/2.21 ** KEPT (pick-wt=5): 15 [] -empty(A)|A=empty_set.
% 2.02/2.21 ** KEPT (pick-wt=5): 16 [] -in(A,B)| -empty(B).
% 2.02/2.21 ** KEPT (pick-wt=3): 17 [] -empty(finite_subsets(A)).
% 2.02/2.21 ** KEPT (pick-wt=6): 18 [] -element(A,finite_subsets(B))|finite(A).
% 2.02/2.21 ** KEPT (pick-wt=2): 19 [] -empty($c1).
% 2.02/2.21 ** KEPT (pick-wt=2): 20 [] -empty($c2).
% 2.02/2.21 ** KEPT (pick-wt=5): 21 [] empty(A)| -empty($f3(A)).
% 2.02/2.21 ** KEPT (pick-wt=5): 22 [] empty(A)| -empty($f4(A)).
% 2.02/2.21 ** KEPT (pick-wt=5): 23 [] empty(A)| -empty($f5(A)).
% 2.02/2.21 ** KEPT (pick-wt=2): 24 [] -empty($c4).
% 2.02/2.21 ** KEPT (pick-wt=2): 25 [] -finite($c5).
% 2.02/2.21
% 2.02/2.21 ------------> process sos:
% 2.02/2.21 ** KEPT (pick-wt=3): 28 [] A=A.
% 2.02/2.21 ** KEPT (pick-wt=3): 29 [] subset(A,A).
% 2.02/2.21 ** KEPT (pick-wt=2): 30 [] empty(empty_set).
% 2.02/2.21 ** KEPT (pick-wt=3): 31 [] cup_closed(powerset(A)).
% 2.02/2.21 ** KEPT (pick-wt=3): 32 [] diff_closed(powerset(A)).
% 2.02/2.21 ** KEPT (pick-wt=3): 33 [] preboolean(powerset(A)).
% 2.02/2.21 ** KEPT (pick-wt=4): 34 [] element($f1(A),A).
% 2.02/2.21 ** KEPT (pick-wt=3): 35 [] preboolean(finite_subsets(A)).
% 2.02/2.21 ** KEPT (pick-wt=3): 36 [] cup_closed(finite_subsets(A)).
% 2.02/2.21 ** KEPT (pick-wt=3): 37 [] diff_closed(finite_subsets(A)).
% 2.02/2.21 Following clause subsumed by 35 during input processing: 0 [] preboolean(finite_subsets(A)).
% 2.02/2.21 ** KEPT (pick-wt=2): 38 [] cup_closed($c1).
% 2.02/2.21 ** KEPT (pick-wt=2): 39 [] cap_closed($c1).
% 2.02/2.21 ** KEPT (pick-wt=2): 40 [] diff_closed($c1).
% 2.02/2.21 ** KEPT (pick-wt=2): 41 [] preboolean($c1).
% 2.02/2.21 ** KEPT (pick-wt=2): 42 [] finite($c2).
% 2.02/2.21 ** KEPT (pick-wt=5): 43 [] element($f2(A),powerset(A)).
% 2.02/2.21 ** KEPT (pick-wt=3): 44 [] empty($f2(A)).
% 2.02/2.21 ** KEPT (pick-wt=3): 45 [] relation($f2(A)).
% 2.02/2.21 ** KEPT (pick-wt=3): 46 [] function($f2(A)).
% 2.02/2.21 ** KEPT (pick-wt=3): 47 [] one_to_one($f2(A)).
% 2.02/2.21 ** KEPT (pick-wt=3): 48 [] epsilon_transitive($f2(A)).
% 2.02/2.21 ** KEPT (pick-wt=3): 49 [] epsilon_connected($f2(A)).
% 2.02/2.21 ** KEPT (pick-wt=3): 50 [] ordinal($f2(A)).
% 2.02/2.21 ** KEPT (pick-wt=3): 51 [] natural($f2(A)).
% 2.02/2.21 ** KEPT (pick-wt=3): 52 [] finite($f2(A)).
% 2.02/2.21 ** KEPT (pick-wt=7): 53 [] empty(A)|element($f3(A),powerset(A)).
% 2.02/2.21 ** KEPT (pick-wt=5): 54 [] empty(A)|finite($f3(A)).
% 2.02/2.21 ** KEPT (pick-wt=7): 55 [] empty(A)|element($f4(A),powerset(A)).
% 2.02/2.21 ** KEPT (pick-wt=5): 56 [] empty(A)|finite($f4(A)).
% 2.02/2.21 ** KEPT (pick-wt=7): 57 [] empty(A)|element($f5(A),powerset(A)).
% 2.02/2.21 ** KEPT (pick-wt=5): 58 [] element($f6(A),powerset(A)).
% 2.02/2.21 ** KEPT (pick-wt=3): 59 [] empty($f6(A)).
% 2.02/2.21 ** KEPT (pick-wt=2): 60 [] empty($c3).
% 2.02/2.21 ** KEPT (pick-wt=4): 61 [] element($c5,finite_subsets($c6)).
% 2.02/2.21 Following clause subsumed by 28 during input processing: 0 [copy,28,flip.1] A=A.
% 2.02/2.21 28 back subsumes 27.
% 2.02/2.21
% 2.02/2.21 ======= end of input processing =======
% 2.02/2.21
% 2.02/2.21 =========== start of search ===========
% 2.02/2.21
% 2.02/2.21 -------- PROOF --------
% 2.02/2.21
% 2.02/2.21 ----> UNIT CONFLICT at 0.00 sec ----> 108 [binary,107.1,25.1] $F.
% 2.02/2.21
% 2.02/2.21 Length of proof is 1. Level of proof is 1.
% 2.02/2.21
% 2.02/2.21 ---------------- PROOF ----------------
% 2.02/2.21 % SZS status Theorem
% 2.02/2.21 % SZS output start Refutation
% See solution above
% 2.02/2.21 ------------ end of proof -------------
% 2.02/2.21
% 2.02/2.21
% 2.02/2.21 Search stopped by max_proofs option.
% 2.02/2.21
% 2.02/2.21
% 2.02/2.21 Search stopped by max_proofs option.
% 2.02/2.21
% 2.02/2.21 ============ end of search ============
% 2.02/2.21
% 2.02/2.21 -------------- statistics -------------
% 2.02/2.21 clauses given 30
% 2.02/2.21 clauses generated 90
% 2.02/2.21 clauses kept 104
% 2.02/2.21 clauses forward subsumed 62
% 2.02/2.21 clauses back subsumed 1
% 2.02/2.21 Kbytes malloced 976
% 2.02/2.21
% 2.02/2.21 ----------- times (seconds) -----------
% 2.02/2.21 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.02/2.21 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.02/2.21 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.02/2.21
% 2.02/2.21 That finishes the proof of the theorem.
% 2.02/2.21
% 2.02/2.21 Process 27295 finished Wed Jul 27 07:56:56 2022
% 2.02/2.21 Otter interrupted
% 2.02/2.21 PROOF FOUND
%------------------------------------------------------------------------------