TSTP Solution File: SEU188+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU188+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n024.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 13:15:06 EDT 2022
% Result : Theorem 1.95s 2.15s
% Output : Refutation 1.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 10
% Syntax : Number of clauses : 18 ( 11 unt; 2 nHn; 17 RR)
% Number of literals : 28 ( 13 equ; 12 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 7 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(14,axiom,
( empty(A)
| ~ relation(A)
| ~ empty(relation_dom(A)) ),
file('SEU188+1.p',unknown),
[] ).
cnf(15,axiom,
( empty(A)
| ~ relation(A)
| ~ empty(relation_rng(A)) ),
file('SEU188+1.p',unknown),
[] ).
cnf(25,axiom,
dollar_c5 != empty_set,
file('SEU188+1.p',unknown),
[] ).
cnf(26,plain,
empty_set != dollar_c5,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[25])]),
[iquote('copy,25,flip.1')] ).
cnf(27,axiom,
( ~ empty(A)
| A = empty_set ),
file('SEU188+1.p',unknown),
[] ).
cnf(29,axiom,
( ~ empty(A)
| A = B
| ~ empty(B) ),
file('SEU188+1.p',unknown),
[] ).
cnf(32,axiom,
A = A,
file('SEU188+1.p',unknown),
[] ).
cnf(38,axiom,
empty(empty_set),
file('SEU188+1.p',unknown),
[] ).
cnf(40,axiom,
empty(dollar_c1),
file('SEU188+1.p',unknown),
[] ).
cnf(44,axiom,
relation(dollar_c5),
file('SEU188+1.p',unknown),
[] ).
cnf(45,axiom,
( relation_dom(dollar_c5) = empty_set
| relation_rng(dollar_c5) = empty_set ),
file('SEU188+1.p',unknown),
[] ).
cnf(61,plain,
empty_set = dollar_c1,
inference(hyper,[status(thm)],[40,29,38]),
[iquote('hyper,40,29,38')] ).
cnf(76,plain,
( relation_dom(dollar_c5) = dollar_c1
| relation_rng(dollar_c5) = dollar_c1 ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[45]),61,61]),
[iquote('back_demod,45,demod,61,61')] ).
cnf(77,plain,
( ~ empty(A)
| A = dollar_c1 ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[27]),61]),
[iquote('back_demod,27,demod,61')] ).
cnf(78,plain,
dollar_c5 != dollar_c1,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[26]),61])]),
[iquote('back_demod,26,demod,61,flip.1')] ).
cnf(242,plain,
~ empty(dollar_c5),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[77,78]),32]),
[iquote('para_from,77.2.1,78.1.1,unit_del,32')] ).
cnf(778,plain,
relation_rng(dollar_c5) = dollar_c1,
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[76,14]),242,44,40]),
[iquote('para_from,76.1.1,14.3.1,unit_del,242,44,40')] ).
cnf(791,plain,
$false,
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[778,15]),242,44,40]),
[iquote('para_from,778.1.1,15.3.1,unit_del,242,44,40')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU188+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n024.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 07:37:40 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.87/2.07 ----- Otter 3.3f, August 2004 -----
% 1.87/2.07 The process was started by sandbox on n024.cluster.edu,
% 1.87/2.07 Wed Jul 27 07:37:40 2022
% 1.87/2.07 The command was "./otter". The process ID is 8596.
% 1.87/2.07
% 1.87/2.07 set(prolog_style_variables).
% 1.87/2.07 set(auto).
% 1.87/2.07 dependent: set(auto1).
% 1.87/2.07 dependent: set(process_input).
% 1.87/2.07 dependent: clear(print_kept).
% 1.87/2.07 dependent: clear(print_new_demod).
% 1.87/2.07 dependent: clear(print_back_demod).
% 1.87/2.07 dependent: clear(print_back_sub).
% 1.87/2.07 dependent: set(control_memory).
% 1.87/2.07 dependent: assign(max_mem, 12000).
% 1.87/2.07 dependent: assign(pick_given_ratio, 4).
% 1.87/2.07 dependent: assign(stats_level, 1).
% 1.87/2.07 dependent: assign(max_seconds, 10800).
% 1.87/2.07 clear(print_given).
% 1.87/2.07
% 1.87/2.07 formula_list(usable).
% 1.87/2.07 all A (A=A).
% 1.87/2.07 all A B (in(A,B)-> -in(B,A)).
% 1.87/2.07 all A (empty(A)->relation(A)).
% 1.87/2.07 all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 1.87/2.07 all A (relation(A)-> (all B (B=relation_dom(A)<-> (all C (in(C,B)<-> (exists D in(ordered_pair(C,D),A))))))).
% 1.87/2.07 all A (relation(A)-> (all B (B=relation_rng(A)<-> (all C (in(C,B)<-> (exists D in(ordered_pair(D,C),A))))))).
% 1.87/2.07 all A B (ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A))).
% 1.87/2.07 $T.
% 1.87/2.07 $T.
% 1.87/2.07 $T.
% 1.87/2.07 $T.
% 1.87/2.07 $T.
% 1.87/2.07 $T.
% 1.87/2.07 $T.
% 1.87/2.07 all A exists B element(B,A).
% 1.87/2.07 empty(empty_set).
% 1.87/2.07 all A B (-empty(ordered_pair(A,B))).
% 1.87/2.07 all A (-empty(singleton(A))).
% 1.87/2.07 all A B (-empty(unordered_pair(A,B))).
% 1.87/2.07 empty(empty_set).
% 1.87/2.07 relation(empty_set).
% 1.87/2.07 all A (-empty(A)&relation(A)-> -empty(relation_dom(A))).
% 1.87/2.07 all A (-empty(A)&relation(A)-> -empty(relation_rng(A))).
% 1.87/2.07 all A (empty(A)->empty(relation_dom(A))&relation(relation_dom(A))).
% 1.87/2.07 all A (empty(A)->empty(relation_rng(A))&relation(relation_rng(A))).
% 1.87/2.07 exists A (empty(A)&relation(A)).
% 1.87/2.07 exists A empty(A).
% 1.87/2.07 exists A (-empty(A)&relation(A)).
% 1.87/2.07 exists A (-empty(A)).
% 1.87/2.07 all A B (in(A,B)->element(A,B)).
% 1.87/2.07 all A B (element(A,B)->empty(B)|in(A,B)).
% 1.87/2.07 all A (relation(A)-> ((all B C (-in(ordered_pair(B,C),A)))->A=empty_set)).
% 1.87/2.07 -(all A (relation(A)-> (relation_dom(A)=empty_set|relation_rng(A)=empty_set->A=empty_set))).
% 1.87/2.07 all A (empty(A)->A=empty_set).
% 1.87/2.07 all A B (-(in(A,B)&empty(B))).
% 1.87/2.07 all A B (-(empty(A)&A!=B&empty(B))).
% 1.87/2.07 end_of_list.
% 1.87/2.07
% 1.87/2.07 -------> usable clausifies to:
% 1.87/2.07
% 1.87/2.07 list(usable).
% 1.87/2.07 0 [] A=A.
% 1.87/2.07 0 [] -in(A,B)| -in(B,A).
% 1.87/2.07 0 [] -empty(A)|relation(A).
% 1.87/2.07 0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.87/2.07 0 [] -relation(A)|B!=relation_dom(A)| -in(C,B)|in(ordered_pair(C,$f1(A,B,C)),A).
% 1.87/2.07 0 [] -relation(A)|B!=relation_dom(A)|in(C,B)| -in(ordered_pair(C,D),A).
% 1.87/2.07 0 [] -relation(A)|B=relation_dom(A)|in($f3(A,B),B)|in(ordered_pair($f3(A,B),$f2(A,B)),A).
% 1.87/2.07 0 [] -relation(A)|B=relation_dom(A)| -in($f3(A,B),B)| -in(ordered_pair($f3(A,B),X1),A).
% 1.87/2.07 0 [] -relation(A)|B!=relation_rng(A)| -in(C,B)|in(ordered_pair($f4(A,B,C),C),A).
% 1.87/2.07 0 [] -relation(A)|B!=relation_rng(A)|in(C,B)| -in(ordered_pair(D,C),A).
% 1.87/2.07 0 [] -relation(A)|B=relation_rng(A)|in($f6(A,B),B)|in(ordered_pair($f5(A,B),$f6(A,B)),A).
% 1.87/2.07 0 [] -relation(A)|B=relation_rng(A)| -in($f6(A,B),B)| -in(ordered_pair(X2,$f6(A,B)),A).
% 1.87/2.07 0 [] ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A)).
% 1.87/2.07 0 [] $T.
% 1.87/2.07 0 [] $T.
% 1.87/2.07 0 [] $T.
% 1.87/2.07 0 [] $T.
% 1.87/2.07 0 [] $T.
% 1.87/2.07 0 [] $T.
% 1.87/2.07 0 [] $T.
% 1.87/2.07 0 [] element($f7(A),A).
% 1.87/2.07 0 [] empty(empty_set).
% 1.87/2.07 0 [] -empty(ordered_pair(A,B)).
% 1.87/2.07 0 [] -empty(singleton(A)).
% 1.87/2.07 0 [] -empty(unordered_pair(A,B)).
% 1.87/2.07 0 [] empty(empty_set).
% 1.87/2.07 0 [] relation(empty_set).
% 1.87/2.07 0 [] empty(A)| -relation(A)| -empty(relation_dom(A)).
% 1.87/2.07 0 [] empty(A)| -relation(A)| -empty(relation_rng(A)).
% 1.87/2.07 0 [] -empty(A)|empty(relation_dom(A)).
% 1.87/2.07 0 [] -empty(A)|relation(relation_dom(A)).
% 1.87/2.07 0 [] -empty(A)|empty(relation_rng(A)).
% 1.87/2.07 0 [] -empty(A)|relation(relation_rng(A)).
% 1.87/2.07 0 [] empty($c1).
% 1.87/2.07 0 [] relation($c1).
% 1.87/2.07 0 [] empty($c2).
% 1.87/2.07 0 [] -empty($c3).
% 1.87/2.07 0 [] relation($c3).
% 1.87/2.07 0 [] -empty($c4).
% 1.87/2.07 0 [] -in(A,B)|element(A,B).
% 1.87/2.07 0 [] -element(A,B)|empty(B)|in(A,B).
% 1.87/2.07 0 [] -relation(A)|in(ordered_pair($f9(A),$f8(A)),A)|A=empty_set.
% 1.87/2.07 0 [] relation($c5).
% 1.87/2.07 0 [] relation_dom($c5)=empty_set|relation_rng($c5)=empty_set.
% 1.87/2.07 0 [] $c5!=empty_set.
% 1.87/2.07 0 [] -empty(A)|A=empty_set.
% 1.87/2.07 0 [] -in(A,B)| -empty(B).
% 1.87/2.07 0 [] -empty(A)|A=B| -empty(B).
% 1.87/2.07 end_of_list.
% 1.87/2.07
% 1.87/2.07 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.87/2.07
% 1.87/2.07 This ia a non-Horn set with equality. The strategy will be
% 1.87/2.07 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.87/2.07 deletion, with positive clauses in sos and nonpositive
% 1.95/2.15 clauses in usable.
% 1.95/2.15
% 1.95/2.15 dependent: set(knuth_bendix).
% 1.95/2.15 dependent: set(anl_eq).
% 1.95/2.15 dependent: set(para_from).
% 1.95/2.15 dependent: set(para_into).
% 1.95/2.15 dependent: clear(para_from_right).
% 1.95/2.15 dependent: clear(para_into_right).
% 1.95/2.15 dependent: set(para_from_vars).
% 1.95/2.15 dependent: set(eq_units_both_ways).
% 1.95/2.15 dependent: set(dynamic_demod_all).
% 1.95/2.15 dependent: set(dynamic_demod).
% 1.95/2.15 dependent: set(order_eq).
% 1.95/2.15 dependent: set(back_demod).
% 1.95/2.15 dependent: set(lrpo).
% 1.95/2.15 dependent: set(hyper_res).
% 1.95/2.15 dependent: set(unit_deletion).
% 1.95/2.15 dependent: set(factor).
% 1.95/2.15
% 1.95/2.15 ------------> process usable:
% 1.95/2.15 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.95/2.15 ** KEPT (pick-wt=4): 2 [] -empty(A)|relation(A).
% 1.95/2.15 ** KEPT (pick-wt=17): 3 [] -relation(A)|B!=relation_dom(A)| -in(C,B)|in(ordered_pair(C,$f1(A,B,C)),A).
% 1.95/2.15 ** KEPT (pick-wt=14): 4 [] -relation(A)|B!=relation_dom(A)|in(C,B)| -in(ordered_pair(C,D),A).
% 1.95/2.15 ** KEPT (pick-wt=20): 5 [] -relation(A)|B=relation_dom(A)|in($f3(A,B),B)|in(ordered_pair($f3(A,B),$f2(A,B)),A).
% 1.95/2.15 ** KEPT (pick-wt=18): 6 [] -relation(A)|B=relation_dom(A)| -in($f3(A,B),B)| -in(ordered_pair($f3(A,B),C),A).
% 1.95/2.15 ** KEPT (pick-wt=17): 7 [] -relation(A)|B!=relation_rng(A)| -in(C,B)|in(ordered_pair($f4(A,B,C),C),A).
% 1.95/2.15 ** KEPT (pick-wt=14): 8 [] -relation(A)|B!=relation_rng(A)|in(C,B)| -in(ordered_pair(D,C),A).
% 1.95/2.15 ** KEPT (pick-wt=20): 9 [] -relation(A)|B=relation_rng(A)|in($f6(A,B),B)|in(ordered_pair($f5(A,B),$f6(A,B)),A).
% 1.95/2.15 ** KEPT (pick-wt=18): 10 [] -relation(A)|B=relation_rng(A)| -in($f6(A,B),B)| -in(ordered_pair(C,$f6(A,B)),A).
% 1.95/2.15 ** KEPT (pick-wt=4): 11 [] -empty(ordered_pair(A,B)).
% 1.95/2.15 ** KEPT (pick-wt=3): 12 [] -empty(singleton(A)).
% 1.95/2.15 ** KEPT (pick-wt=4): 13 [] -empty(unordered_pair(A,B)).
% 1.95/2.15 ** KEPT (pick-wt=7): 14 [] empty(A)| -relation(A)| -empty(relation_dom(A)).
% 1.95/2.15 ** KEPT (pick-wt=7): 15 [] empty(A)| -relation(A)| -empty(relation_rng(A)).
% 1.95/2.15 ** KEPT (pick-wt=5): 16 [] -empty(A)|empty(relation_dom(A)).
% 1.95/2.15 ** KEPT (pick-wt=5): 17 [] -empty(A)|relation(relation_dom(A)).
% 1.95/2.15 ** KEPT (pick-wt=5): 18 [] -empty(A)|empty(relation_rng(A)).
% 1.95/2.15 ** KEPT (pick-wt=5): 19 [] -empty(A)|relation(relation_rng(A)).
% 1.95/2.15 ** KEPT (pick-wt=2): 20 [] -empty($c3).
% 1.95/2.15 ** KEPT (pick-wt=2): 21 [] -empty($c4).
% 1.95/2.15 ** KEPT (pick-wt=6): 22 [] -in(A,B)|element(A,B).
% 1.95/2.15 ** KEPT (pick-wt=8): 23 [] -element(A,B)|empty(B)|in(A,B).
% 1.95/2.15 ** KEPT (pick-wt=12): 24 [] -relation(A)|in(ordered_pair($f9(A),$f8(A)),A)|A=empty_set.
% 1.95/2.15 ** KEPT (pick-wt=3): 26 [copy,25,flip.1] empty_set!=$c5.
% 1.95/2.15 ** KEPT (pick-wt=5): 27 [] -empty(A)|A=empty_set.
% 1.95/2.15 ** KEPT (pick-wt=5): 28 [] -in(A,B)| -empty(B).
% 1.95/2.15 ** KEPT (pick-wt=7): 29 [] -empty(A)|A=B| -empty(B).
% 1.95/2.15
% 1.95/2.15 ------------> process sos:
% 1.95/2.15 ** KEPT (pick-wt=3): 32 [] A=A.
% 1.95/2.15 ** KEPT (pick-wt=7): 33 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.95/2.15 ** KEPT (pick-wt=10): 35 [copy,34,flip.1] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 1.95/2.15 ---> New Demodulator: 36 [new_demod,35] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 1.95/2.15 ** KEPT (pick-wt=4): 37 [] element($f7(A),A).
% 1.95/2.15 ** KEPT (pick-wt=2): 38 [] empty(empty_set).
% 1.95/2.15 Following clause subsumed by 38 during input processing: 0 [] empty(empty_set).
% 1.95/2.15 ** KEPT (pick-wt=2): 39 [] relation(empty_set).
% 1.95/2.15 ** KEPT (pick-wt=2): 40 [] empty($c1).
% 1.95/2.15 ** KEPT (pick-wt=2): 41 [] relation($c1).
% 1.95/2.15 ** KEPT (pick-wt=2): 42 [] empty($c2).
% 1.95/2.15 ** KEPT (pick-wt=2): 43 [] relation($c3).
% 1.95/2.15 ** KEPT (pick-wt=2): 44 [] relation($c5).
% 1.95/2.15 ** KEPT (pick-wt=8): 45 [] relation_dom($c5)=empty_set|relation_rng($c5)=empty_set.
% 1.95/2.15 Following clause subsumed by 32 during input processing: 0 [copy,32,flip.1] A=A.
% 1.95/2.15 32 back subsumes 31.
% 1.95/2.15 Following clause subsumed by 33 during input processing: 0 [copy,33,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 1.95/2.15 >>>> Starting back demodulation with 36.
% 1.95/2.15
% 1.95/2.15 ======= end of input processing =======
% 1.95/2.15
% 1.95/2.15 =========== start of search ===========
% 1.95/2.15
% 1.95/2.15
% 1.95/2.15 Resetting weight limit to 9.
% 1.95/2.15
% 1.95/2.15
% 1.95/2.15 Resetting weight limit to 9.
% 1.95/2.15
% 1.95/2.15 sos_size=641
% 1.95/2.15
% 1.95/2.15 -------- PROOF --------
% 1.95/2.15
% 1.95/2.15 -----> EMPTY CLAUSE at 0.08 sec ----> 791 [para_from,778.1.1,15.3.1,unit_del,242,44,40] $F.
% 1.95/2.15
% 1.95/2.15 Length of proof is 7. Level of proof is 4.
% 1.95/2.15
% 1.95/2.15 ---------------- PROOF ----------------
% 1.95/2.15 % SZS status Theorem
% 1.95/2.15 % SZS output start Refutation
% See solution above
% 1.95/2.15 ------------ end of proof -------------
% 1.95/2.15
% 1.95/2.15
% 1.95/2.15 Search stopped by max_proofs option.
% 1.95/2.15
% 1.95/2.15
% 1.95/2.15 Search stopped by max_proofs option.
% 1.95/2.15
% 1.95/2.15 ============ end of search ============
% 1.95/2.15
% 1.95/2.15 -------------- statistics -------------
% 1.95/2.15 clauses given 54
% 1.95/2.15 clauses generated 1721
% 1.95/2.15 clauses kept 778
% 1.95/2.15 clauses forward subsumed 569
% 1.95/2.15 clauses back subsumed 8
% 1.95/2.15 Kbytes malloced 4882
% 1.95/2.15
% 1.95/2.15 ----------- times (seconds) -----------
% 1.95/2.15 user CPU time 0.08 (0 hr, 0 min, 0 sec)
% 1.95/2.15 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.95/2.15 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.95/2.15
% 1.95/2.15 That finishes the proof of the theorem.
% 1.95/2.15
% 1.95/2.15 Process 8596 finished Wed Jul 27 07:37:42 2022
% 1.95/2.15 Otter interrupted
% 1.95/2.15 PROOF FOUND
%------------------------------------------------------------------------------