TSTP Solution File: SEU171+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU171+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n016.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 13:15:02 EDT 2022
% Result : Theorem 2.11s 2.34s
% Output : Refutation 2.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 13
% Syntax : Number of clauses : 23 ( 16 unt; 3 nHn; 22 RR)
% Number of literals : 34 ( 11 equ; 15 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 13 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( empty(A)
| ~ element(B,A)
| in(B,A) ),
file('SEU171+1.p',unknown),
[] ).
cnf(8,axiom,
( A != set_difference(B,C)
| in(D,A)
| ~ in(D,B)
| in(D,C) ),
file('SEU171+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ element(A,powerset(B))
| subset_complement(B,A) = set_difference(B,A) ),
file('SEU171+1.p',unknown),
[] ).
cnf(17,axiom,
dollar_c5 != empty_set,
file('SEU171+1.p',unknown),
[] ).
cnf(18,plain,
empty_set != dollar_c5,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[17])]),
[iquote('copy,17,flip.1')] ).
cnf(19,axiom,
~ in(dollar_c3,dollar_c4),
file('SEU171+1.p',unknown),
[] ).
cnf(20,axiom,
~ in(dollar_c3,subset_complement(dollar_c5,dollar_c4)),
file('SEU171+1.p',unknown),
[] ).
cnf(21,axiom,
( ~ empty(A)
| A = empty_set ),
file('SEU171+1.p',unknown),
[] ).
cnf(23,axiom,
( ~ empty(A)
| A = B
| ~ empty(B) ),
file('SEU171+1.p',unknown),
[] ).
cnf(30,axiom,
A = A,
file('SEU171+1.p',unknown),
[] ).
cnf(33,axiom,
empty(empty_set),
file('SEU171+1.p',unknown),
[] ).
cnf(35,axiom,
empty(dollar_c1),
file('SEU171+1.p',unknown),
[] ).
cnf(42,axiom,
element(dollar_c4,powerset(dollar_c5)),
file('SEU171+1.p',unknown),
[] ).
cnf(43,axiom,
element(dollar_c3,dollar_c5),
file('SEU171+1.p',unknown),
[] ).
cnf(50,plain,
empty_set = dollar_c1,
inference(hyper,[status(thm)],[35,23,33]),
[iquote('hyper,35,23,33')] ).
cnf(57,plain,
( ~ empty(A)
| A = dollar_c1 ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[21]),50]),
[iquote('back_demod,21,demod,50')] ).
cnf(58,plain,
dollar_c5 != dollar_c1,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[18]),50])]),
[iquote('back_demod,18,demod,50,flip.1')] ).
cnf(64,plain,
( empty(dollar_c5)
| in(dollar_c3,dollar_c5) ),
inference(hyper,[status(thm)],[43,2]),
[iquote('hyper,43,2')] ).
cnf(225,plain,
subset_complement(dollar_c5,dollar_c4) = set_difference(dollar_c5,dollar_c4),
inference(hyper,[status(thm)],[42,11]),
[iquote('hyper,42,11')] ).
cnf(234,plain,
~ in(dollar_c3,set_difference(dollar_c5,dollar_c4)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[20]),225]),
[iquote('back_demod,20,demod,225')] ).
cnf(392,plain,
~ empty(dollar_c5),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[57,58]),30]),
[iquote('para_from,57.2.1,58.1.1,unit_del,30')] ).
cnf(454,plain,
in(dollar_c3,dollar_c5),
inference(hyper,[status(thm)],[64,392]),
[iquote('hyper,64,392')] ).
cnf(2079,plain,
$false,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[225,8,454]),225]),234,19]),
[iquote('hyper,224,8,454,demod,225,unit_del,234,19')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU171+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n016.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 08:22:22 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.81/2.03 ----- Otter 3.3f, August 2004 -----
% 1.81/2.03 The process was started by sandbox2 on n016.cluster.edu,
% 1.81/2.03 Wed Jul 27 08:22:22 2022
% 1.81/2.03 The command was "./otter". The process ID is 32197.
% 1.81/2.03
% 1.81/2.03 set(prolog_style_variables).
% 1.81/2.03 set(auto).
% 1.81/2.03 dependent: set(auto1).
% 1.81/2.03 dependent: set(process_input).
% 1.81/2.03 dependent: clear(print_kept).
% 1.81/2.03 dependent: clear(print_new_demod).
% 1.81/2.03 dependent: clear(print_back_demod).
% 1.81/2.03 dependent: clear(print_back_sub).
% 1.81/2.03 dependent: set(control_memory).
% 1.81/2.03 dependent: assign(max_mem, 12000).
% 1.81/2.03 dependent: assign(pick_given_ratio, 4).
% 1.81/2.03 dependent: assign(stats_level, 1).
% 1.81/2.03 dependent: assign(max_seconds, 10800).
% 1.81/2.03 clear(print_given).
% 1.81/2.03
% 1.81/2.03 formula_list(usable).
% 1.81/2.03 all A (A=A).
% 1.81/2.03 all A B (in(A,B)-> -in(B,A)).
% 1.81/2.03 all A B ((-empty(A)-> (element(B,A)<->in(B,A)))& (empty(A)-> (element(B,A)<->empty(B)))).
% 1.81/2.03 all A B C (C=set_difference(A,B)<-> (all D (in(D,C)<->in(D,A)& -in(D,B)))).
% 1.81/2.03 all A B (element(B,powerset(A))->subset_complement(A,B)=set_difference(A,B)).
% 1.81/2.03 $T.
% 1.81/2.03 $T.
% 1.81/2.03 all A B (element(B,powerset(A))->element(subset_complement(A,B),powerset(A))).
% 1.81/2.03 $T.
% 1.81/2.03 $T.
% 1.81/2.03 all A exists B element(B,A).
% 1.81/2.03 all A (-empty(powerset(A))).
% 1.81/2.03 empty(empty_set).
% 1.81/2.03 all A B (element(B,powerset(A))->subset_complement(A,subset_complement(A,B))=B).
% 1.81/2.03 all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)))).
% 1.81/2.03 exists A empty(A).
% 1.81/2.03 all A exists B (element(B,powerset(A))&empty(B)).
% 1.81/2.03 exists A (-empty(A)).
% 1.81/2.03 all A (set_difference(A,empty_set)=A).
% 1.81/2.03 all A (set_difference(empty_set,A)=empty_set).
% 1.81/2.03 -(all A (A!=empty_set-> (all B (element(B,powerset(A))-> (all C (element(C,A)-> (-in(C,B)->in(C,subset_complement(A,B))))))))).
% 1.81/2.03 all A (empty(A)->A=empty_set).
% 1.81/2.03 all A B (-(in(A,B)&empty(B))).
% 1.81/2.03 all A B (-(empty(A)&A!=B&empty(B))).
% 1.81/2.03 end_of_list.
% 1.81/2.03
% 1.81/2.03 -------> usable clausifies to:
% 1.81/2.03
% 1.81/2.03 list(usable).
% 1.81/2.03 0 [] A=A.
% 1.81/2.03 0 [] -in(A,B)| -in(B,A).
% 1.81/2.03 0 [] empty(A)| -element(B,A)|in(B,A).
% 1.81/2.03 0 [] empty(A)|element(B,A)| -in(B,A).
% 1.81/2.03 0 [] -empty(A)| -element(B,A)|empty(B).
% 1.81/2.03 0 [] -empty(A)|element(B,A)| -empty(B).
% 1.81/2.03 0 [] C!=set_difference(A,B)| -in(D,C)|in(D,A).
% 1.81/2.03 0 [] C!=set_difference(A,B)| -in(D,C)| -in(D,B).
% 1.81/2.03 0 [] C!=set_difference(A,B)|in(D,C)| -in(D,A)|in(D,B).
% 1.81/2.03 0 [] C=set_difference(A,B)|in($f1(A,B,C),C)|in($f1(A,B,C),A).
% 1.81/2.03 0 [] C=set_difference(A,B)|in($f1(A,B,C),C)| -in($f1(A,B,C),B).
% 1.81/2.03 0 [] C=set_difference(A,B)| -in($f1(A,B,C),C)| -in($f1(A,B,C),A)|in($f1(A,B,C),B).
% 1.81/2.03 0 [] -element(B,powerset(A))|subset_complement(A,B)=set_difference(A,B).
% 1.81/2.03 0 [] $T.
% 1.81/2.03 0 [] $T.
% 1.81/2.03 0 [] -element(B,powerset(A))|element(subset_complement(A,B),powerset(A)).
% 1.81/2.03 0 [] $T.
% 1.81/2.03 0 [] $T.
% 1.81/2.03 0 [] element($f2(A),A).
% 1.81/2.03 0 [] -empty(powerset(A)).
% 1.81/2.03 0 [] empty(empty_set).
% 1.81/2.03 0 [] -element(B,powerset(A))|subset_complement(A,subset_complement(A,B))=B.
% 1.81/2.03 0 [] empty(A)|element($f3(A),powerset(A)).
% 1.81/2.03 0 [] empty(A)| -empty($f3(A)).
% 1.81/2.03 0 [] empty($c1).
% 1.81/2.03 0 [] element($f4(A),powerset(A)).
% 1.81/2.03 0 [] empty($f4(A)).
% 1.81/2.03 0 [] -empty($c2).
% 1.81/2.03 0 [] set_difference(A,empty_set)=A.
% 1.81/2.03 0 [] set_difference(empty_set,A)=empty_set.
% 1.81/2.03 0 [] $c5!=empty_set.
% 1.81/2.03 0 [] element($c4,powerset($c5)).
% 1.81/2.03 0 [] element($c3,$c5).
% 1.81/2.03 0 [] -in($c3,$c4).
% 1.81/2.03 0 [] -in($c3,subset_complement($c5,$c4)).
% 1.81/2.03 0 [] -empty(A)|A=empty_set.
% 1.81/2.03 0 [] -in(A,B)| -empty(B).
% 1.81/2.03 0 [] -empty(A)|A=B| -empty(B).
% 1.81/2.03 end_of_list.
% 1.81/2.03
% 1.81/2.03 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.81/2.03
% 1.81/2.03 This ia a non-Horn set with equality. The strategy will be
% 1.81/2.03 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.81/2.03 deletion, with positive clauses in sos and nonpositive
% 1.81/2.03 clauses in usable.
% 1.81/2.03
% 1.81/2.03 dependent: set(knuth_bendix).
% 1.81/2.03 dependent: set(anl_eq).
% 1.81/2.03 dependent: set(para_from).
% 1.81/2.03 dependent: set(para_into).
% 1.81/2.03 dependent: clear(para_from_right).
% 1.81/2.03 dependent: clear(para_into_right).
% 1.81/2.03 dependent: set(para_from_vars).
% 1.81/2.03 dependent: set(eq_units_both_ways).
% 1.81/2.03 dependent: set(dynamic_demod_all).
% 1.81/2.03 dependent: set(dynamic_demod).
% 1.81/2.03 dependent: set(order_eq).
% 1.81/2.03 dependent: set(back_demod).
% 1.81/2.03 dependent: set(lrpo).
% 1.81/2.03 dependent: set(hyper_res).
% 1.81/2.03 dependent: set(unit_deletion).
% 1.81/2.03 dependent: set(factor).
% 1.81/2.03
% 1.81/2.03 ------------> process usable:
% 1.81/2.03 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.81/2.03 ** KEPT (pick-wt=8): 2 [] empty(A)| -element(B,A)|in(B,A).
% 1.81/2.03 ** KEPT (pick-wt=8): 3 [] empty(A)|element(B,A)| -in(B,A).
% 1.81/2.03 ** KEPT (pick-wt=7): 4 [] -empty(A)| -element(B,A)|empty(B).
% 2.11/2.34 ** KEPT (pick-wt=7): 5 [] -empty(A)|element(B,A)| -empty(B).
% 2.11/2.34 ** KEPT (pick-wt=11): 6 [] A!=set_difference(B,C)| -in(D,A)|in(D,B).
% 2.11/2.34 ** KEPT (pick-wt=11): 7 [] A!=set_difference(B,C)| -in(D,A)| -in(D,C).
% 2.11/2.34 ** KEPT (pick-wt=14): 8 [] A!=set_difference(B,C)|in(D,A)| -in(D,B)|in(D,C).
% 2.11/2.34 ** KEPT (pick-wt=17): 9 [] A=set_difference(B,C)|in($f1(B,C,A),A)| -in($f1(B,C,A),C).
% 2.11/2.34 ** KEPT (pick-wt=23): 10 [] A=set_difference(B,C)| -in($f1(B,C,A),A)| -in($f1(B,C,A),B)|in($f1(B,C,A),C).
% 2.11/2.34 ** KEPT (pick-wt=11): 11 [] -element(A,powerset(B))|subset_complement(B,A)=set_difference(B,A).
% 2.11/2.34 ** KEPT (pick-wt=10): 12 [] -element(A,powerset(B))|element(subset_complement(B,A),powerset(B)).
% 2.11/2.34 ** KEPT (pick-wt=3): 13 [] -empty(powerset(A)).
% 2.11/2.34 ** KEPT (pick-wt=11): 14 [] -element(A,powerset(B))|subset_complement(B,subset_complement(B,A))=A.
% 2.11/2.34 ** KEPT (pick-wt=5): 15 [] empty(A)| -empty($f3(A)).
% 2.11/2.34 ** KEPT (pick-wt=2): 16 [] -empty($c2).
% 2.11/2.34 ** KEPT (pick-wt=3): 18 [copy,17,flip.1] empty_set!=$c5.
% 2.11/2.34 ** KEPT (pick-wt=3): 19 [] -in($c3,$c4).
% 2.11/2.34 ** KEPT (pick-wt=5): 20 [] -in($c3,subset_complement($c5,$c4)).
% 2.11/2.34 ** KEPT (pick-wt=5): 21 [] -empty(A)|A=empty_set.
% 2.11/2.34 ** KEPT (pick-wt=5): 22 [] -in(A,B)| -empty(B).
% 2.11/2.34 ** KEPT (pick-wt=7): 23 [] -empty(A)|A=B| -empty(B).
% 2.11/2.34
% 2.11/2.34 ------------> process sos:
% 2.11/2.34 ** KEPT (pick-wt=3): 30 [] A=A.
% 2.11/2.34 ** KEPT (pick-wt=17): 31 [] A=set_difference(B,C)|in($f1(B,C,A),A)|in($f1(B,C,A),B).
% 2.11/2.34 ** KEPT (pick-wt=4): 32 [] element($f2(A),A).
% 2.11/2.34 ** KEPT (pick-wt=2): 33 [] empty(empty_set).
% 2.11/2.34 ** KEPT (pick-wt=7): 34 [] empty(A)|element($f3(A),powerset(A)).
% 2.11/2.34 ** KEPT (pick-wt=2): 35 [] empty($c1).
% 2.11/2.34 ** KEPT (pick-wt=5): 36 [] element($f4(A),powerset(A)).
% 2.11/2.34 ** KEPT (pick-wt=3): 37 [] empty($f4(A)).
% 2.11/2.34 ** KEPT (pick-wt=5): 38 [] set_difference(A,empty_set)=A.
% 2.11/2.34 ---> New Demodulator: 39 [new_demod,38] set_difference(A,empty_set)=A.
% 2.11/2.34 ** KEPT (pick-wt=5): 40 [] set_difference(empty_set,A)=empty_set.
% 2.11/2.34 ---> New Demodulator: 41 [new_demod,40] set_difference(empty_set,A)=empty_set.
% 2.11/2.34 ** KEPT (pick-wt=4): 42 [] element($c4,powerset($c5)).
% 2.11/2.34 ** KEPT (pick-wt=3): 43 [] element($c3,$c5).
% 2.11/2.34 Following clause subsumed by 30 during input processing: 0 [copy,30,flip.1] A=A.
% 2.11/2.34 30 back subsumes 29.
% 2.11/2.34 >>>> Starting back demodulation with 39.
% 2.11/2.34 >>>> Starting back demodulation with 41.
% 2.11/2.34
% 2.11/2.34 ======= end of input processing =======
% 2.11/2.34
% 2.11/2.34 =========== start of search ===========
% 2.11/2.34
% 2.11/2.34
% 2.11/2.34 Resetting weight limit to 11.
% 2.11/2.34
% 2.11/2.34
% 2.11/2.34 Resetting weight limit to 11.
% 2.11/2.34
% 2.11/2.34 sos_size=1878
% 2.11/2.34
% 2.11/2.34 -------- PROOF --------
% 2.11/2.34
% 2.11/2.34 -----> EMPTY CLAUSE at 0.31 sec ----> 2079 [hyper,224,8,454,demod,225,unit_del,234,19] $F.
% 2.11/2.34
% 2.11/2.34 Length of proof is 9. Level of proof is 4.
% 2.11/2.34
% 2.11/2.34 ---------------- PROOF ----------------
% 2.11/2.34 % SZS status Theorem
% 2.11/2.34 % SZS output start Refutation
% See solution above
% 2.11/2.34 ------------ end of proof -------------
% 2.11/2.34
% 2.11/2.34
% 2.11/2.34 Search stopped by max_proofs option.
% 2.11/2.34
% 2.11/2.34
% 2.11/2.34 Search stopped by max_proofs option.
% 2.11/2.34
% 2.11/2.34 ============ end of search ============
% 2.11/2.34
% 2.11/2.34 -------------- statistics -------------
% 2.11/2.34 clauses given 75
% 2.11/2.34 clauses generated 3860
% 2.11/2.34 clauses kept 2050
% 2.11/2.34 clauses forward subsumed 1647
% 2.11/2.34 clauses back subsumed 45
% 2.11/2.34 Kbytes malloced 4882
% 2.11/2.34
% 2.11/2.34 ----------- times (seconds) -----------
% 2.11/2.34 user CPU time 0.31 (0 hr, 0 min, 0 sec)
% 2.11/2.34 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.11/2.34 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.11/2.34
% 2.11/2.34 That finishes the proof of the theorem.
% 2.11/2.34
% 2.11/2.34 Process 32197 finished Wed Jul 27 08:22:24 2022
% 2.11/2.34 Otter interrupted
% 2.11/2.34 PROOF FOUND
%------------------------------------------------------------------------------