TSTP Solution File: SEU189+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU189+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n011.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 2.08s 2.25s
% Output : Refutation 2.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 10
% Syntax : Number of clauses : 21 ( 12 unt; 2 nHn; 20 RR)
% Number of literals : 34 ( 26 equ; 15 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 : 6 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(15,axiom,
( ~ empty(A)
| A = empty_set ),
file('SEU189+1.p',unknown),
[] ).
cnf(16,axiom,
( relation_dom(dollar_c5) != empty_set
| relation_rng(dollar_c5) != empty_set ),
file('SEU189+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ relation(A)
| relation_dom(A) != empty_set
| A = empty_set ),
file('SEU189+1.p',unknown),
[] ).
cnf(18,axiom,
( ~ relation(A)
| relation_rng(A) != empty_set
| A = empty_set ),
file('SEU189+1.p',unknown),
[] ).
cnf(21,axiom,
A = A,
file('SEU189+1.p',unknown),
[] ).
cnf(23,axiom,
empty(dollar_c1),
file('SEU189+1.p',unknown),
[] ).
cnf(29,axiom,
relation(dollar_c5),
file('SEU189+1.p',unknown),
[] ).
cnf(30,axiom,
( relation_dom(dollar_c5) = empty_set
| relation_rng(dollar_c5) = empty_set ),
file('SEU189+1.p',unknown),
[] ).
cnf(31,axiom,
relation_dom(empty_set) = empty_set,
file('SEU189+1.p',unknown),
[] ).
cnf(33,axiom,
relation_rng(empty_set) = empty_set,
file('SEU189+1.p',unknown),
[] ).
cnf(36,plain,
empty_set = dollar_c1,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[23,15])]),
[iquote('hyper,23,15,flip.1')] ).
cnf(42,plain,
relation_rng(dollar_c1) = dollar_c1,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[33]),36,36]),
[iquote('back_demod,33,demod,36,36')] ).
cnf(44,plain,
relation_dom(dollar_c1) = dollar_c1,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[31]),36,36]),
[iquote('back_demod,31,demod,36,36')] ).
cnf(45,plain,
( relation_dom(dollar_c5) = dollar_c1
| relation_rng(dollar_c5) = dollar_c1 ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[30]),36,36]),
[iquote('back_demod,30,demod,36,36')] ).
cnf(46,plain,
( ~ relation(A)
| relation_rng(A) != dollar_c1
| A = dollar_c1 ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[18]),36,36]),
[iquote('back_demod,18,demod,36,36')] ).
cnf(47,plain,
( ~ relation(A)
| relation_dom(A) != dollar_c1
| A = dollar_c1 ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[17]),36,36]),
[iquote('back_demod,17,demod,36,36')] ).
cnf(48,plain,
( relation_dom(dollar_c5) != dollar_c1
| relation_rng(dollar_c5) != dollar_c1 ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[16]),36,36]),
[iquote('back_demod,16,demod,36,36')] ).
cnf(153,plain,
relation_rng(dollar_c5) != dollar_c1,
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[48,46]),44]),21,29])]),
[iquote('para_into,48.1.1.1,46.3.1,demod,44,unit_del,21,29,factor_simp')] ).
cnf(155,plain,
relation_dom(dollar_c5) != dollar_c1,
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[48,47]),42]),21,29])]),
[iquote('para_into,48.2.1.1,47.3.1,demod,42,unit_del,21,29,factor_simp')] ).
cnf(156,plain,
relation_dom(dollar_c5) = dollar_c1,
inference(hyper,[status(thm)],[153,45]),
[iquote('hyper,153,45')] ).
cnf(158,plain,
$false,
inference(binary,[status(thm)],[156,155]),
[iquote('binary,156.1,155.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU189+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.14/0.34 % Computer : n011.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Jul 27 07:59:10 EDT 2022
% 0.14/0.34 % CPUTime :
% 2.08/2.24 ----- Otter 3.3f, August 2004 -----
% 2.08/2.24 The process was started by sandbox on n011.cluster.edu,
% 2.08/2.24 Wed Jul 27 07:59:10 2022
% 2.08/2.24 The command was "./otter". The process ID is 18800.
% 2.08/2.24
% 2.08/2.24 set(prolog_style_variables).
% 2.08/2.24 set(auto).
% 2.08/2.24 dependent: set(auto1).
% 2.08/2.24 dependent: set(process_input).
% 2.08/2.24 dependent: clear(print_kept).
% 2.08/2.24 dependent: clear(print_new_demod).
% 2.08/2.24 dependent: clear(print_back_demod).
% 2.08/2.24 dependent: clear(print_back_sub).
% 2.08/2.24 dependent: set(control_memory).
% 2.08/2.24 dependent: assign(max_mem, 12000).
% 2.08/2.24 dependent: assign(pick_given_ratio, 4).
% 2.08/2.24 dependent: assign(stats_level, 1).
% 2.08/2.24 dependent: assign(max_seconds, 10800).
% 2.08/2.24 clear(print_given).
% 2.08/2.24
% 2.08/2.24 formula_list(usable).
% 2.08/2.24 all A (A=A).
% 2.08/2.24 all A exists B element(B,A).
% 2.08/2.24 $T.
% 2.08/2.24 all A B (element(A,B)->empty(B)|in(A,B)).
% 2.08/2.24 all A B (in(A,B)-> -in(B,A)).
% 2.08/2.24 all A B (in(A,B)->element(A,B)).
% 2.08/2.24 exists A (empty(A)&relation(A)).
% 2.08/2.24 all A (empty(A)->relation(A)).
% 2.08/2.24 exists A (-empty(A)&relation(A)).
% 2.08/2.24 all A (-empty(A)&relation(A)-> -empty(relation_dom(A))).
% 2.08/2.24 all A (-empty(A)&relation(A)-> -empty(relation_rng(A))).
% 2.08/2.24 all A (empty(A)->empty(relation_dom(A))&relation(relation_dom(A))).
% 2.08/2.24 all A (empty(A)->empty(relation_rng(A))&relation(relation_rng(A))).
% 2.08/2.24 exists A empty(A).
% 2.08/2.24 exists A (-empty(A)).
% 2.08/2.24 all A B (-(in(A,B)&empty(B))).
% 2.08/2.24 all A B (-(empty(A)&A!=B&empty(B))).
% 2.08/2.24 $T.
% 2.08/2.24 $T.
% 2.08/2.24 $T.
% 2.08/2.24 empty(empty_set).
% 2.08/2.24 relation(empty_set).
% 2.08/2.24 empty(empty_set).
% 2.08/2.24 all A (empty(A)->A=empty_set).
% 2.08/2.24 -(all A (relation(A)-> (relation_dom(A)=empty_set<->relation_rng(A)=empty_set))).
% 2.08/2.24 relation_dom(empty_set)=empty_set.
% 2.08/2.24 relation_rng(empty_set)=empty_set.
% 2.08/2.24 all A (relation(A)-> (relation_dom(A)=empty_set|relation_rng(A)=empty_set->A=empty_set)).
% 2.08/2.24 end_of_list.
% 2.08/2.24
% 2.08/2.24 -------> usable clausifies to:
% 2.08/2.24
% 2.08/2.24 list(usable).
% 2.08/2.24 0 [] A=A.
% 2.08/2.24 0 [] element($f1(A),A).
% 2.08/2.24 0 [] $T.
% 2.08/2.24 0 [] -element(A,B)|empty(B)|in(A,B).
% 2.08/2.24 0 [] -in(A,B)| -in(B,A).
% 2.08/2.24 0 [] -in(A,B)|element(A,B).
% 2.08/2.24 0 [] empty($c1).
% 2.08/2.24 0 [] relation($c1).
% 2.08/2.24 0 [] -empty(A)|relation(A).
% 2.08/2.24 0 [] -empty($c2).
% 2.08/2.24 0 [] relation($c2).
% 2.08/2.24 0 [] empty(A)| -relation(A)| -empty(relation_dom(A)).
% 2.08/2.24 0 [] empty(A)| -relation(A)| -empty(relation_rng(A)).
% 2.08/2.24 0 [] -empty(A)|empty(relation_dom(A)).
% 2.08/2.24 0 [] -empty(A)|relation(relation_dom(A)).
% 2.08/2.24 0 [] -empty(A)|empty(relation_rng(A)).
% 2.08/2.24 0 [] -empty(A)|relation(relation_rng(A)).
% 2.08/2.24 0 [] empty($c3).
% 2.08/2.24 0 [] -empty($c4).
% 2.08/2.24 0 [] -in(A,B)| -empty(B).
% 2.08/2.24 0 [] -empty(A)|A=B| -empty(B).
% 2.08/2.24 0 [] $T.
% 2.08/2.24 0 [] $T.
% 2.08/2.24 0 [] $T.
% 2.08/2.24 0 [] empty(empty_set).
% 2.08/2.24 0 [] relation(empty_set).
% 2.08/2.24 0 [] empty(empty_set).
% 2.08/2.24 0 [] -empty(A)|A=empty_set.
% 2.08/2.24 0 [] relation($c5).
% 2.08/2.24 0 [] relation_dom($c5)=empty_set|relation_rng($c5)=empty_set.
% 2.08/2.24 0 [] relation_dom($c5)!=empty_set|relation_rng($c5)!=empty_set.
% 2.08/2.24 0 [] relation_dom(empty_set)=empty_set.
% 2.08/2.24 0 [] relation_rng(empty_set)=empty_set.
% 2.08/2.24 0 [] -relation(A)|relation_dom(A)!=empty_set|A=empty_set.
% 2.08/2.24 0 [] -relation(A)|relation_rng(A)!=empty_set|A=empty_set.
% 2.08/2.24 end_of_list.
% 2.08/2.24
% 2.08/2.24 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 2.08/2.24
% 2.08/2.24 This ia a non-Horn set with equality. The strategy will be
% 2.08/2.24 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.08/2.24 deletion, with positive clauses in sos and nonpositive
% 2.08/2.24 clauses in usable.
% 2.08/2.24
% 2.08/2.24 dependent: set(knuth_bendix).
% 2.08/2.24 dependent: set(anl_eq).
% 2.08/2.24 dependent: set(para_from).
% 2.08/2.24 dependent: set(para_into).
% 2.08/2.24 dependent: clear(para_from_right).
% 2.08/2.24 dependent: clear(para_into_right).
% 2.08/2.24 dependent: set(para_from_vars).
% 2.08/2.24 dependent: set(eq_units_both_ways).
% 2.08/2.24 dependent: set(dynamic_demod_all).
% 2.08/2.24 dependent: set(dynamic_demod).
% 2.08/2.24 dependent: set(order_eq).
% 2.08/2.24 dependent: set(back_demod).
% 2.08/2.24 dependent: set(lrpo).
% 2.08/2.24 dependent: set(hyper_res).
% 2.08/2.24 dependent: set(unit_deletion).
% 2.08/2.24 dependent: set(factor).
% 2.08/2.24
% 2.08/2.24 ------------> process usable:
% 2.08/2.24 ** KEPT (pick-wt=8): 1 [] -element(A,B)|empty(B)|in(A,B).
% 2.08/2.24 ** KEPT (pick-wt=6): 2 [] -in(A,B)| -in(B,A).
% 2.08/2.24 ** KEPT (pick-wt=6): 3 [] -in(A,B)|element(A,B).
% 2.08/2.24 ** KEPT (pick-wt=4): 4 [] -empty(A)|relation(A).
% 2.08/2.24 ** KEPT (pick-wt=2): 5 [] -empty($c2).
% 2.08/2.24 ** KEPT (pick-wt=7): 6 [] empty(A)| -relation(A)| -empty(relation_dom(A)).
% 2.08/2.24 ** KEPT (pick-wt=7): 7 [] empty(A)| -relation(A)| -empty(relation_rng(A)).
% 2.08/2.24 ** KEPT (pick-wt=5): 8 [] -empty(A)|empty(relation_dom(A)).
% 2.08/2.24 ** KEPT (pick-wt=5): 9 [] -empty(A)|relation(relation_dom(A)).
% 2.08/2.24 ** KEPT (pick-wt=5): 10 [] -empty(A)|empty(relation_rng(A)).
% 2.08/2.25 ** KEPT (pick-wt=5): 11 [] -empty(A)|relation(relation_rng(A)).
% 2.08/2.25 ** KEPT (pick-wt=2): 12 [] -empty($c4).
% 2.08/2.25 ** KEPT (pick-wt=5): 13 [] -in(A,B)| -empty(B).
% 2.08/2.25 ** KEPT (pick-wt=7): 14 [] -empty(A)|A=B| -empty(B).
% 2.08/2.25 ** KEPT (pick-wt=5): 15 [] -empty(A)|A=empty_set.
% 2.08/2.25 ** KEPT (pick-wt=8): 16 [] relation_dom($c5)!=empty_set|relation_rng($c5)!=empty_set.
% 2.08/2.25 ** KEPT (pick-wt=9): 17 [] -relation(A)|relation_dom(A)!=empty_set|A=empty_set.
% 2.08/2.25 ** KEPT (pick-wt=9): 18 [] -relation(A)|relation_rng(A)!=empty_set|A=empty_set.
% 2.08/2.25
% 2.08/2.25 ------------> process sos:
% 2.08/2.25 ** KEPT (pick-wt=3): 21 [] A=A.
% 2.08/2.25 ** KEPT (pick-wt=4): 22 [] element($f1(A),A).
% 2.08/2.25 ** KEPT (pick-wt=2): 23 [] empty($c1).
% 2.08/2.25 ** KEPT (pick-wt=2): 24 [] relation($c1).
% 2.08/2.25 ** KEPT (pick-wt=2): 25 [] relation($c2).
% 2.08/2.25 ** KEPT (pick-wt=2): 26 [] empty($c3).
% 2.08/2.25 ** KEPT (pick-wt=2): 27 [] empty(empty_set).
% 2.08/2.25 ** KEPT (pick-wt=2): 28 [] relation(empty_set).
% 2.08/2.25 Following clause subsumed by 27 during input processing: 0 [] empty(empty_set).
% 2.08/2.25 ** KEPT (pick-wt=2): 29 [] relation($c5).
% 2.08/2.25 ** KEPT (pick-wt=8): 30 [] relation_dom($c5)=empty_set|relation_rng($c5)=empty_set.
% 2.08/2.25 ** KEPT (pick-wt=4): 31 [] relation_dom(empty_set)=empty_set.
% 2.08/2.25 ---> New Demodulator: 32 [new_demod,31] relation_dom(empty_set)=empty_set.
% 2.08/2.25 ** KEPT (pick-wt=4): 33 [] relation_rng(empty_set)=empty_set.
% 2.08/2.25 ---> New Demodulator: 34 [new_demod,33] relation_rng(empty_set)=empty_set.
% 2.08/2.25 Following clause subsumed by 21 during input processing: 0 [copy,21,flip.1] A=A.
% 2.08/2.25 21 back subsumes 20.
% 2.08/2.25 >>>> Starting back demodulation with 32.
% 2.08/2.25 >>>> Starting back demodulation with 34.
% 2.08/2.25
% 2.08/2.25 ======= end of input processing =======
% 2.08/2.25
% 2.08/2.25 =========== start of search ===========
% 2.08/2.25
% 2.08/2.25 -------- PROOF --------
% 2.08/2.25
% 2.08/2.25 ----> UNIT CONFLICT at 0.01 sec ----> 158 [binary,156.1,155.1] $F.
% 2.08/2.25
% 2.08/2.25 Length of proof is 10. Level of proof is 4.
% 2.08/2.25
% 2.08/2.25 ---------------- PROOF ----------------
% 2.08/2.25 % SZS status Theorem
% 2.08/2.25 % SZS output start Refutation
% See solution above
% 2.08/2.25 ------------ end of proof -------------
% 2.08/2.25
% 2.08/2.25
% 2.08/2.25 Search stopped by max_proofs option.
% 2.08/2.25
% 2.08/2.25
% 2.08/2.25 Search stopped by max_proofs option.
% 2.08/2.25
% 2.08/2.25 ============ end of search ============
% 2.08/2.25
% 2.08/2.25 -------------- statistics -------------
% 2.08/2.25 clauses given 32
% 2.08/2.25 clauses generated 402
% 2.08/2.25 clauses kept 150
% 2.08/2.25 clauses forward subsumed 293
% 2.08/2.25 clauses back subsumed 30
% 2.08/2.25 Kbytes malloced 976
% 2.08/2.25
% 2.08/2.25 ----------- times (seconds) -----------
% 2.08/2.25 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 2.08/2.25 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.08/2.25 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.08/2.25
% 2.08/2.25 That finishes the proof of the theorem.
% 2.08/2.25
% 2.08/2.25 Process 18800 finished Wed Jul 27 07:59:12 2022
% 2.08/2.25 Otter interrupted
% 2.08/2.25 PROOF FOUND
%------------------------------------------------------------------------------