%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU174+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n015.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 13:15:03 EDT 2022
% Result : Theorem 6.33s 6.54s
% Output : Refutation 6.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 11
% Syntax : Number of clauses : 22 ( 16 unt; 3 nHn; 18 RR)
% Number of literals : 34 ( 12 equ; 11 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 15 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(7,axiom,
( ~ element(A,powerset(powerset(B)))
| ~ element(C,powerset(powerset(B)))
| C = complements_of_subsets(B,A)
| in(dollar_f2(B,A,C),C)
| in(subset_complement(B,dollar_f2(B,A,C)),A) ),
file('SEU174+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ element(A,powerset(powerset(B)))
| complements_of_subsets(B,complements_of_subsets(B,A)) = A ),
file('SEU174+1.p',unknown),
[] ).
cnf(20,axiom,
dollar_c3 != empty_set,
file('SEU174+1.p',unknown),
[] ).
cnf(21,plain,
empty_set != dollar_c3,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[20])]),
[iquote('copy,20,flip.1')] ).
cnf(25,axiom,
( ~ in(A,B)
| ~ empty(B) ),
file('SEU174+1.p',unknown),
[] ).
cnf(26,axiom,
( ~ empty(A)
| A = B
| ~ empty(B) ),
file('SEU174+1.p',unknown),
[] ).
cnf(31,plain,
( ~ element(A,powerset(powerset(B)))
| complements_of_subsets(B,A) = A
| in(dollar_f2(B,A,A),A)
| in(subset_complement(B,dollar_f2(B,A,A)),A) ),
inference(flip,[status(thm),theory(equality)],[inference(factor,[status(thm)],[7])]),
[iquote('factor,7.1.2,flip.2')] ).
cnf(37,axiom,
empty(empty_set),
file('SEU174+1.p',unknown),
[] ).
cnf(39,axiom,
empty(dollar_c1),
file('SEU174+1.p',unknown),
[] ).
cnf(40,axiom,
element(dollar_f5(A),powerset(A)),
file('SEU174+1.p',unknown),
[] ).
cnf(41,axiom,
empty(dollar_f5(A)),
file('SEU174+1.p',unknown),
[] ).
cnf(43,axiom,
element(dollar_c3,powerset(powerset(dollar_c4))),
file('SEU174+1.p',unknown),
[] ).
cnf(44,axiom,
complements_of_subsets(dollar_c4,dollar_c3) = empty_set,
file('SEU174+1.p',unknown),
[] ).
cnf(53,plain,
empty_set = dollar_c1,
inference(hyper,[status(thm)],[39,26,37]),
[iquote('hyper,39,26,37')] ).
cnf(61,plain,
complements_of_subsets(dollar_c4,dollar_c3) = dollar_c1,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[44]),53]),
[iquote('back_demod,44,demod,53')] ).
cnf(63,plain,
dollar_c3 != dollar_c1,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[21]),53])]),
[iquote('back_demod,21,demod,53,flip.1')] ).
cnf(66,plain,
dollar_f5(A) = dollar_c1,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[41,26,39])]),
[iquote('hyper,41,26,39,flip.1')] ).
cnf(67,plain,
element(dollar_c1,powerset(A)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[40]),66]),
[iquote('back_demod,40,demod,66')] ).
cnf(188,plain,
complements_of_subsets(dollar_c4,dollar_c1) = dollar_c3,
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[43,13]),61]),
[iquote('hyper,43,13,demod,61')] ).
cnf(405,plain,
( in(dollar_f2(dollar_c4,dollar_c1,dollar_c1),dollar_c1)
| in(subset_complement(dollar_c4,dollar_f2(dollar_c4,dollar_c1,dollar_c1)),dollar_c1) ),
inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[188,31]),63,67]),
[iquote('para_into,188.1.1,31.2.1,unit_del,63,67')] ).
cnf(1530,plain,
in(dollar_f2(dollar_c4,dollar_c1,dollar_c1),dollar_c1),
inference(hyper,[status(thm)],[405,25,39]),
[iquote('hyper,405,25,39')] ).
cnf(1538,plain,
$false,
inference(hyper,[status(thm)],[1530,25,39]),
[iquote('hyper,1530,25,39')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SEU174+1 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n015.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 07:48:56 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.91/2.11 ----- Otter 3.3f, August 2004 -----
% 1.91/2.11 The process was started by sandbox on n015.cluster.edu,
% 1.91/2.11 Wed Jul 27 07:48:57 2022
% 1.91/2.11 The command was "./otter". The process ID is 22484.
% 1.91/2.11
% 1.91/2.11 set(prolog_style_variables).
% 1.91/2.11 set(auto).
% 1.91/2.11 dependent: set(auto1).
% 1.91/2.11 dependent: set(process_input).
% 1.91/2.11 dependent: clear(print_kept).
% 1.91/2.11 dependent: clear(print_new_demod).
% 1.91/2.11 dependent: clear(print_back_demod).
% 1.91/2.11 dependent: clear(print_back_sub).
% 1.91/2.11 dependent: set(control_memory).
% 1.91/2.11 dependent: assign(max_mem, 12000).
% 1.91/2.11 dependent: assign(pick_given_ratio, 4).
% 1.91/2.11 dependent: assign(stats_level, 1).
% 1.91/2.11 dependent: assign(max_seconds, 10800).
% 1.91/2.11 clear(print_given).
% 1.91/2.11
% 1.91/2.11 formula_list(usable).
% 1.91/2.11 all A (A=A).
% 1.91/2.11 all A B (in(A,B)-> -in(B,A)).
% 1.91/2.11 all A B (subset(A,B)<-> (all C (in(C,A)->in(C,B)))).
% 1.91/2.11 all A B (element(B,powerset(powerset(A)))-> (all C (element(C,powerset(powerset(A)))-> (C=complements_of_subsets(A,B)<-> (all D (element(D,powerset(A))-> (in(D,C)<->in(subset_complement(A,D),B)))))))).
% 1.91/2.11 $T.
% 1.91/2.11 $T.
% 1.91/2.11 all A B (element(B,powerset(A))->element(subset_complement(A,B),powerset(A))).
% 1.91/2.11 all A B (element(B,powerset(powerset(A)))->element(complements_of_subsets(A,B),powerset(powerset(A)))).
% 1.91/2.11 $T.
% 1.91/2.11 all A exists B element(B,A).
% 1.91/2.11 all A (-empty(powerset(A))).
% 1.91/2.11 empty(empty_set).
% 1.91/2.11 all A B (element(B,powerset(A))->subset_complement(A,subset_complement(A,B))=B).
% 1.91/2.11 all A B (element(B,powerset(powerset(A)))->complements_of_subsets(A,complements_of_subsets(A,B))=B).
% 1.91/2.11 all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)))).
% 1.91/2.11 exists A empty(A).
% 1.91/2.11 all A exists B (element(B,powerset(A))&empty(B)).
% 1.91/2.11 exists A (-empty(A)).
% 1.91/2.11 all A B subset(A,A).
% 1.91/2.11 all A B (in(A,B)->element(A,B)).
% 1.91/2.11 all A B (element(A,B)->empty(B)|in(A,B)).
% 1.91/2.11 all A B (element(A,powerset(B))<->subset(A,B)).
% 1.91/2.11 -(all A B (element(B,powerset(powerset(A)))-> -(B!=empty_set&complements_of_subsets(A,B)=empty_set))).
% 1.91/2.11 all A B C (in(A,B)&element(B,powerset(C))->element(A,C)).
% 1.91/2.11 all A B C (-(in(A,B)&element(B,powerset(C))&empty(C))).
% 1.91/2.11 all A (empty(A)->A=empty_set).
% 1.91/2.11 all A B (-(in(A,B)&empty(B))).
% 1.91/2.11 all A B (-(empty(A)&A!=B&empty(B))).
% 1.91/2.11 end_of_list.
% 1.91/2.11
% 1.91/2.11 -------> usable clausifies to:
% 1.91/2.11
% 1.91/2.11 list(usable).
% 1.91/2.11 0 [] A=A.
% 1.91/2.11 0 [] -in(A,B)| -in(B,A).
% 1.91/2.11 0 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.91/2.11 0 [] subset(A,B)|in($f1(A,B),A).
% 1.91/2.11 0 [] subset(A,B)| -in($f1(A,B),B).
% 1.91/2.11 0 [] -element(B,powerset(powerset(A)))| -element(C,powerset(powerset(A)))|C!=complements_of_subsets(A,B)| -element(D,powerset(A))| -in(D,C)|in(subset_complement(A,D),B).
% 1.91/2.11 0 [] -element(B,powerset(powerset(A)))| -element(C,powerset(powerset(A)))|C!=complements_of_subsets(A,B)| -element(D,powerset(A))|in(D,C)| -in(subset_complement(A,D),B).
% 1.91/2.11 0 [] -element(B,powerset(powerset(A)))| -element(C,powerset(powerset(A)))|C=complements_of_subsets(A,B)|element($f2(A,B,C),powerset(A)).
% 1.91/2.11 0 [] -element(B,powerset(powerset(A)))| -element(C,powerset(powerset(A)))|C=complements_of_subsets(A,B)|in($f2(A,B,C),C)|in(subset_complement(A,$f2(A,B,C)),B).
% 1.91/2.11 0 [] -element(B,powerset(powerset(A)))| -element(C,powerset(powerset(A)))|C=complements_of_subsets(A,B)| -in($f2(A,B,C),C)| -in(subset_complement(A,$f2(A,B,C)),B).
% 1.91/2.11 0 [] $T.
% 1.91/2.11 0 [] $T.
% 1.91/2.11 0 [] -element(B,powerset(A))|element(subset_complement(A,B),powerset(A)).
% 1.91/2.11 0 [] -element(B,powerset(powerset(A)))|element(complements_of_subsets(A,B),powerset(powerset(A))).
% 1.91/2.11 0 [] $T.
% 1.91/2.11 0 [] element($f3(A),A).
% 1.91/2.11 0 [] -empty(powerset(A)).
% 1.91/2.11 0 [] empty(empty_set).
% 1.91/2.11 0 [] -element(B,powerset(A))|subset_complement(A,subset_complement(A,B))=B.
% 1.91/2.11 0 [] -element(B,powerset(powerset(A)))|complements_of_subsets(A,complements_of_subsets(A,B))=B.
% 1.91/2.11 0 [] empty(A)|element($f4(A),powerset(A)).
% 1.91/2.11 0 [] empty(A)| -empty($f4(A)).
% 1.91/2.11 0 [] empty($c1).
% 1.91/2.11 0 [] element($f5(A),powerset(A)).
% 1.91/2.11 0 [] empty($f5(A)).
% 1.91/2.11 0 [] -empty($c2).
% 1.91/2.11 0 [] subset(A,A).
% 1.91/2.11 0 [] -in(A,B)|element(A,B).
% 1.91/2.11 0 [] -element(A,B)|empty(B)|in(A,B).
% 1.91/2.11 0 [] -element(A,powerset(B))|subset(A,B).
% 1.91/2.11 0 [] element(A,powerset(B))| -subset(A,B).
% 1.91/2.11 0 [] element($c3,powerset(powerset($c4))).
% 1.91/2.11 0 [] $c3!=empty_set.
% 1.91/2.11 0 [] complements_of_subsets($c4,$c3)=empty_set.
% 1.91/2.11 0 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 1.91/2.11 0 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 1.91/2.11 0 [] -empty(A)|A=empty_set.
% 1.91/2.11 0 [] -in(A,B)| -empty(B).
% 1.91/2.11 0 [] -empty(A)|A=B| -empty(B).
% 2.14/2.31 end_of_list.
% 2.14/2.31
% 2.14/2.31 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=6.
% 2.14/2.31
% 2.14/2.31 This ia a non-Horn set with equality. The strategy will be
% 2.14/2.31 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.14/2.31 deletion, with positive clauses in sos and nonpositive
% 2.14/2.31 clauses in usable.
% 2.14/2.31
% 2.14/2.31 dependent: set(knuth_bendix).
% 2.14/2.31 dependent: set(anl_eq).
% 2.14/2.31 dependent: set(para_from).
% 2.14/2.31 dependent: set(para_into).
% 2.14/2.31 dependent: clear(para_from_right).
% 2.14/2.31 dependent: clear(para_into_right).
% 2.14/2.31 dependent: set(para_from_vars).
% 2.14/2.31 dependent: set(eq_units_both_ways).
% 2.14/2.31 dependent: set(dynamic_demod_all).
% 2.14/2.31 dependent: set(dynamic_demod).
% 2.14/2.31 dependent: set(order_eq).
% 2.14/2.31 dependent: set(back_demod).
% 2.14/2.31 dependent: set(lrpo).
% 2.14/2.31 dependent: set(hyper_res).
% 2.14/2.31 dependent: set(unit_deletion).
% 2.14/2.31 dependent: set(factor).
% 2.14/2.31
% 2.14/2.31 ------------> process usable:
% 2.14/2.31 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 2.14/2.31 ** KEPT (pick-wt=9): 2 [] -subset(A,B)| -in(C,A)|in(C,B).
% 2.14/2.31 ** KEPT (pick-wt=8): 3 [] subset(A,B)| -in($f1(A,B),B).
% 2.14/2.31 ** KEPT (pick-wt=27): 4 [] -element(A,powerset(powerset(B)))| -element(C,powerset(powerset(B)))|C!=complements_of_subsets(B,A)| -element(D,powerset(B))| -in(D,C)|in(subset_complement(B,D),A).
% 2.14/2.31 ** KEPT (pick-wt=27): 5 [] -element(A,powerset(powerset(B)))| -element(C,powerset(powerset(B)))|C!=complements_of_subsets(B,A)| -element(D,powerset(B))|in(D,C)| -in(subset_complement(B,D),A).
% 2.14/2.31 ** KEPT (pick-wt=22): 6 [] -element(A,powerset(powerset(B)))| -element(C,powerset(powerset(B)))|C=complements_of_subsets(B,A)|element($f2(B,A,C),powerset(B)).
% 2.14/2.31 ** KEPT (pick-wt=29): 7 [] -element(A,powerset(powerset(B)))| -element(C,powerset(powerset(B)))|C=complements_of_subsets(B,A)|in($f2(B,A,C),C)|in(subset_complement(B,$f2(B,A,C)),A).
% 2.14/2.31 ** KEPT (pick-wt=29): 8 [] -element(A,powerset(powerset(B)))| -element(C,powerset(powerset(B)))|C=complements_of_subsets(B,A)| -in($f2(B,A,C),C)| -in(subset_complement(B,$f2(B,A,C)),A).
% 2.14/2.31 ** KEPT (pick-wt=10): 9 [] -element(A,powerset(B))|element(subset_complement(B,A),powerset(B)).
% 2.14/2.31 ** KEPT (pick-wt=12): 10 [] -element(A,powerset(powerset(B)))|element(complements_of_subsets(B,A),powerset(powerset(B))).
% 2.14/2.31 ** KEPT (pick-wt=3): 11 [] -empty(powerset(A)).
% 2.14/2.31 ** KEPT (pick-wt=11): 12 [] -element(A,powerset(B))|subset_complement(B,subset_complement(B,A))=A.
% 2.14/2.31 ** KEPT (pick-wt=12): 13 [] -element(A,powerset(powerset(B)))|complements_of_subsets(B,complements_of_subsets(B,A))=A.
% 2.14/2.31 ** KEPT (pick-wt=5): 14 [] empty(A)| -empty($f4(A)).
% 2.14/2.31 ** KEPT (pick-wt=2): 15 [] -empty($c2).
% 2.14/2.31 ** KEPT (pick-wt=6): 16 [] -in(A,B)|element(A,B).
% 2.14/2.31 ** KEPT (pick-wt=8): 17 [] -element(A,B)|empty(B)|in(A,B).
% 2.14/2.31 ** KEPT (pick-wt=7): 18 [] -element(A,powerset(B))|subset(A,B).
% 2.14/2.31 ** KEPT (pick-wt=7): 19 [] element(A,powerset(B))| -subset(A,B).
% 2.14/2.31 ** KEPT (pick-wt=3): 21 [copy,20,flip.1] empty_set!=$c3.
% 2.14/2.31 ** KEPT (pick-wt=10): 22 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 2.14/2.31 ** KEPT (pick-wt=9): 23 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 2.14/2.31 ** KEPT (pick-wt=5): 24 [] -empty(A)|A=empty_set.
% 2.14/2.31 ** KEPT (pick-wt=5): 25 [] -in(A,B)| -empty(B).
% 2.14/2.31 ** KEPT (pick-wt=7): 26 [] -empty(A)|A=B| -empty(B).
% 2.14/2.31
% 2.14/2.31 ------------> process sos:
% 2.14/2.31 ** KEPT (pick-wt=3): 34 [] A=A.
% 2.14/2.31 ** KEPT (pick-wt=8): 35 [] subset(A,B)|in($f1(A,B),A).
% 2.14/2.31 ** KEPT (pick-wt=4): 36 [] element($f3(A),A).
% 2.14/2.31 ** KEPT (pick-wt=2): 37 [] empty(empty_set).
% 2.14/2.31 ** KEPT (pick-wt=7): 38 [] empty(A)|element($f4(A),powerset(A)).
% 2.14/2.31 ** KEPT (pick-wt=2): 39 [] empty($c1).
% 2.14/2.31 ** KEPT (pick-wt=5): 40 [] element($f5(A),powerset(A)).
% 2.14/2.31 ** KEPT (pick-wt=3): 41 [] empty($f5(A)).
% 2.14/2.31 ** KEPT (pick-wt=3): 42 [] subset(A,A).
% 2.14/2.31 ** KEPT (pick-wt=5): 43 [] element($c3,powerset(powerset($c4))).
% 2.14/2.31 ** KEPT (pick-wt=5): 44 [] complements_of_subsets($c4,$c3)=empty_set.
% 2.14/2.31 ---> New Demodulator: 45 [new_demod,44] complements_of_subsets($c4,$c3)=empty_set.
% 2.14/2.31 Following clause subsumed by 34 during input processing: 0 [copy,34,flip.1] A=A.
% 2.14/2.31 34 back subsumes 33.
% 2.14/2.31 >>>> Starting back demodulation with 45.
% 2.14/2.31
% 2.14/2.31 ======= end of input processing =======
% 2.14/2.31
% 2.14/2.31 =========== start of search ===========
% 2.14/2.31
% 2.14/2.31
% 2.14/2.31 Resetting weight limit to 9.
% 2.14/2.31
% 2.14/2.31
% 2.14/2.31 Resetting weight limit to 9.
% 2.14/2.31
% 2.14/2.31 sos_size=1032
% 2.14/2.31
% 2.14/2.31
% 2.14/2.31 Resetting weight limit to 8.
% 2.14/2.31
% 2.14/2.31
% 2.14/2.31 Resetting weight limit to 8.
% 6.33/6.54
% 6.33/6.54 sos_size=1058
% 6.33/6.54
% 6.33/6.54 -------- PROOF --------
% 6.33/6.54
% 6.33/6.54 -----> EMPTY CLAUSE at 4.43 sec ----> 1538 [hyper,1530,25,39] $F.
% 6.33/6.54
% 6.33/6.54 Length of proof is 10. Level of proof is 5.
% 6.33/6.54
% 6.33/6.54 ---------------- PROOF ----------------
% 6.33/6.54 % SZS status Theorem
% 6.33/6.54 % SZS output start Refutation
% See solution above
% 6.33/6.54 ------------ end of proof -------------
% 6.33/6.54
% 6.33/6.54
% 6.33/6.54 Search stopped by max_proofs option.
% 6.33/6.54
% 6.33/6.54
% 6.33/6.54 Search stopped by max_proofs option.
% 6.33/6.54
% 6.33/6.54 ============ end of search ============
% 6.33/6.54
% 6.33/6.54 -------------- statistics -------------
% 6.33/6.54 clauses given 625
% 6.33/6.54 clauses generated 210478
% 6.33/6.54 clauses kept 1513
% 6.33/6.54 clauses forward subsumed 4599
% 6.33/6.54 clauses back subsumed 32
% 6.33/6.54 Kbytes malloced 6835
% 6.33/6.54
% 6.33/6.54 ----------- times (seconds) -----------
% 6.33/6.54 user CPU time 4.43 (0 hr, 0 min, 4 sec)
% 6.33/6.54 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 6.33/6.54 wall-clock time 6 (0 hr, 0 min, 6 sec)
% 6.33/6.54
% 6.33/6.54 That finishes the proof of the theorem.
% 6.33/6.54
% 6.33/6.54 Process 22484 finished Wed Jul 27 07:49:03 2022
% 6.33/6.54 Otter interrupted
% 6.33/6.54 PROOF FOUND
%------------------------------------------------------------------------------