TSTP Solution File: SEU355+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU355+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n005.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 13:15:50 EDT 2022
% Result : Theorem 1.79s 2.00s
% Output : Refutation 1.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 9
% Syntax : Number of clauses : 16 ( 8 unt; 4 nHn; 12 RR)
% Number of literals : 29 ( 2 equ; 12 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 12 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(5,axiom,
( ~ rel_str(A)
| ~ element(B,the_carrier(A))
| relstr_element_smaller(A,C,B)
| in(dollar_f1(A,C,B),C) ),
file('SEU355+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ rel_str(A)
| ~ element(B,the_carrier(A))
| relstr_set_smaller(A,C,B)
| in(dollar_f2(A,C,B),C) ),
file('SEU355+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ relstr_set_smaller(dollar_c7,empty_set,dollar_c6)
| ~ relstr_element_smaller(dollar_c7,empty_set,dollar_c6) ),
file('SEU355+1.p',unknown),
[] ).
cnf(18,axiom,
( ~ in(A,B)
| ~ empty(B) ),
file('SEU355+1.p',unknown),
[] ).
cnf(19,axiom,
( ~ empty(A)
| A = B
| ~ empty(B) ),
file('SEU355+1.p',unknown),
[] ).
cnf(28,axiom,
empty(empty_set),
file('SEU355+1.p',unknown),
[] ).
cnf(30,axiom,
empty(dollar_c4),
file('SEU355+1.p',unknown),
[] ).
cnf(31,axiom,
rel_str(dollar_c7),
file('SEU355+1.p',unknown),
[] ).
cnf(32,axiom,
element(dollar_c6,the_carrier(dollar_c7)),
file('SEU355+1.p',unknown),
[] ).
cnf(47,plain,
empty_set = dollar_c4,
inference(hyper,[status(thm)],[30,19,28]),
[iquote('hyper,30,19,28')] ).
cnf(52,plain,
( ~ relstr_set_smaller(dollar_c7,dollar_c4,dollar_c6)
| ~ relstr_element_smaller(dollar_c7,dollar_c4,dollar_c6) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[17]),47,47]),
[iquote('back_demod,17,demod,47,47')] ).
cnf(62,plain,
( relstr_set_smaller(dollar_c7,A,dollar_c6)
| in(dollar_f2(dollar_c7,A,dollar_c6),A) ),
inference(hyper,[status(thm)],[32,9,31]),
[iquote('hyper,32,9,31')] ).
cnf(64,plain,
( relstr_element_smaller(dollar_c7,A,dollar_c6)
| in(dollar_f1(dollar_c7,A,dollar_c6),A) ),
inference(hyper,[status(thm)],[32,5,31]),
[iquote('hyper,32,5,31')] ).
cnf(701,plain,
relstr_set_smaller(dollar_c7,dollar_c4,dollar_c6),
inference(hyper,[status(thm)],[62,18,30]),
[iquote('hyper,62,18,30')] ).
cnf(796,plain,
relstr_element_smaller(dollar_c7,dollar_c4,dollar_c6),
inference(hyper,[status(thm)],[64,18,30]),
[iquote('hyper,64,18,30')] ).
cnf(813,plain,
$false,
inference(hyper,[status(thm)],[796,52,701]),
[iquote('hyper,796,52,701')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU355+1 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n005.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 07:42:20 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.73/1.94 ----- Otter 3.3f, August 2004 -----
% 1.73/1.94 The process was started by sandbox on n005.cluster.edu,
% 1.73/1.94 Wed Jul 27 07:42:20 2022
% 1.73/1.94 The command was "./otter". The process ID is 25623.
% 1.73/1.94
% 1.73/1.94 set(prolog_style_variables).
% 1.73/1.94 set(auto).
% 1.73/1.94 dependent: set(auto1).
% 1.73/1.94 dependent: set(process_input).
% 1.73/1.94 dependent: clear(print_kept).
% 1.73/1.94 dependent: clear(print_new_demod).
% 1.73/1.94 dependent: clear(print_back_demod).
% 1.73/1.94 dependent: clear(print_back_sub).
% 1.73/1.94 dependent: set(control_memory).
% 1.73/1.94 dependent: assign(max_mem, 12000).
% 1.73/1.94 dependent: assign(pick_given_ratio, 4).
% 1.73/1.94 dependent: assign(stats_level, 1).
% 1.73/1.94 dependent: assign(max_seconds, 10800).
% 1.73/1.94 clear(print_given).
% 1.73/1.94
% 1.73/1.94 formula_list(usable).
% 1.73/1.94 all A (A=A).
% 1.73/1.94 all A B (in(A,B)-> -in(B,A)).
% 1.73/1.94 all A (empty(A)->finite(A)).
% 1.73/1.94 all A (rel_str(A)-> (all B C (element(C,the_carrier(A))-> (relstr_element_smaller(A,B,C)<-> (all D (element(D,the_carrier(A))-> (in(D,B)->related(A,C,D)))))))).
% 1.73/1.94 all A (rel_str(A)-> (all B C (element(C,the_carrier(A))-> (relstr_set_smaller(A,B,C)<-> (all D (element(D,the_carrier(A))-> (in(D,B)->related(A,D,C)))))))).
% 1.73/1.94 $T.
% 1.73/1.94 all A (rel_str(A)->one_sorted_str(A)).
% 1.73/1.94 $T.
% 1.73/1.94 $T.
% 1.73/1.94 $T.
% 1.73/1.94 exists A rel_str(A).
% 1.73/1.94 exists A one_sorted_str(A).
% 1.73/1.94 all A exists B element(B,A).
% 1.73/1.94 empty(empty_set).
% 1.73/1.94 exists A (-empty(A)&finite(A)).
% 1.73/1.94 exists A empty(A).
% 1.73/1.94 exists A (-empty(A)).
% 1.73/1.94 all A B (in(A,B)->element(A,B)).
% 1.73/1.94 all A B (element(A,B)->empty(B)|in(A,B)).
% 1.73/1.94 all A (empty(A)->A=empty_set).
% 1.73/1.94 -(all A (rel_str(A)-> (all B (element(B,the_carrier(A))->relstr_set_smaller(A,empty_set,B)&relstr_element_smaller(A,empty_set,B))))).
% 1.73/1.94 all A B (-(in(A,B)&empty(B))).
% 1.73/1.94 all A B (-(empty(A)&A!=B&empty(B))).
% 1.73/1.94 end_of_list.
% 1.73/1.94
% 1.73/1.94 -------> usable clausifies to:
% 1.73/1.94
% 1.73/1.94 list(usable).
% 1.73/1.94 0 [] A=A.
% 1.73/1.94 0 [] -in(A,B)| -in(B,A).
% 1.73/1.94 0 [] -empty(A)|finite(A).
% 1.73/1.94 0 [] -rel_str(A)| -element(C,the_carrier(A))| -relstr_element_smaller(A,B,C)| -element(D,the_carrier(A))| -in(D,B)|related(A,C,D).
% 1.73/1.94 0 [] -rel_str(A)| -element(C,the_carrier(A))|relstr_element_smaller(A,B,C)|element($f1(A,B,C),the_carrier(A)).
% 1.73/1.94 0 [] -rel_str(A)| -element(C,the_carrier(A))|relstr_element_smaller(A,B,C)|in($f1(A,B,C),B).
% 1.73/1.94 0 [] -rel_str(A)| -element(C,the_carrier(A))|relstr_element_smaller(A,B,C)| -related(A,C,$f1(A,B,C)).
% 1.73/1.94 0 [] -rel_str(A)| -element(C,the_carrier(A))| -relstr_set_smaller(A,B,C)| -element(D,the_carrier(A))| -in(D,B)|related(A,D,C).
% 1.73/1.94 0 [] -rel_str(A)| -element(C,the_carrier(A))|relstr_set_smaller(A,B,C)|element($f2(A,B,C),the_carrier(A)).
% 1.73/1.94 0 [] -rel_str(A)| -element(C,the_carrier(A))|relstr_set_smaller(A,B,C)|in($f2(A,B,C),B).
% 1.73/1.94 0 [] -rel_str(A)| -element(C,the_carrier(A))|relstr_set_smaller(A,B,C)| -related(A,$f2(A,B,C),C).
% 1.73/1.94 0 [] $T.
% 1.73/1.94 0 [] -rel_str(A)|one_sorted_str(A).
% 1.73/1.94 0 [] $T.
% 1.73/1.94 0 [] $T.
% 1.73/1.94 0 [] $T.
% 1.73/1.94 0 [] rel_str($c1).
% 1.73/1.94 0 [] one_sorted_str($c2).
% 1.73/1.94 0 [] element($f3(A),A).
% 1.73/1.94 0 [] empty(empty_set).
% 1.73/1.94 0 [] -empty($c3).
% 1.73/1.94 0 [] finite($c3).
% 1.73/1.94 0 [] empty($c4).
% 1.73/1.94 0 [] -empty($c5).
% 1.73/1.94 0 [] -in(A,B)|element(A,B).
% 1.73/1.94 0 [] -element(A,B)|empty(B)|in(A,B).
% 1.73/1.94 0 [] -empty(A)|A=empty_set.
% 1.73/1.94 0 [] rel_str($c7).
% 1.73/1.94 0 [] element($c6,the_carrier($c7)).
% 1.73/1.94 0 [] -relstr_set_smaller($c7,empty_set,$c6)| -relstr_element_smaller($c7,empty_set,$c6).
% 1.73/1.94 0 [] -in(A,B)| -empty(B).
% 1.73/1.94 0 [] -empty(A)|A=B| -empty(B).
% 1.73/1.94 end_of_list.
% 1.73/1.94
% 1.73/1.94 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=6.
% 1.73/1.94
% 1.73/1.94 This ia a non-Horn set with equality. The strategy will be
% 1.73/1.94 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.73/1.94 deletion, with positive clauses in sos and nonpositive
% 1.73/1.94 clauses in usable.
% 1.73/1.94
% 1.73/1.94 dependent: set(knuth_bendix).
% 1.73/1.94 dependent: set(anl_eq).
% 1.73/1.94 dependent: set(para_from).
% 1.73/1.94 dependent: set(para_into).
% 1.73/1.94 dependent: clear(para_from_right).
% 1.73/1.94 dependent: clear(para_into_right).
% 1.73/1.94 dependent: set(para_from_vars).
% 1.73/1.94 dependent: set(eq_units_both_ways).
% 1.73/1.94 dependent: set(dynamic_demod_all).
% 1.73/1.94 dependent: set(dynamic_demod).
% 1.73/1.94 dependent: set(order_eq).
% 1.73/1.94 dependent: set(back_demod).
% 1.73/1.94 dependent: set(lrpo).
% 1.73/1.94 dependent: set(hyper_res).
% 1.73/1.94 dependent: set(unit_deletion).
% 1.73/1.94 dependent: set(factor).
% 1.73/1.94
% 1.73/1.94 ------------> process usable:
% 1.73/1.94 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.73/1.94 ** KEPT (pick-wt=4): 2 [] -empty(A)|finite(A).
% 1.73/1.94 ** KEPT (pick-wt=21): 3 [] -rel_str(A)| -element(B,the_carrier(A))| -relstr_element_smaller(A,C,B)| -element(D,the_carrier(A))| -in(D,C)|related(A,B,D).
% 1.79/2.00 ** KEPT (pick-wt=17): 4 [] -rel_str(A)| -element(B,the_carrier(A))|relstr_element_smaller(A,C,B)|element($f1(A,C,B),the_carrier(A)).
% 1.79/2.00 ** KEPT (pick-wt=16): 5 [] -rel_str(A)| -element(B,the_carrier(A))|relstr_element_smaller(A,C,B)|in($f1(A,C,B),C).
% 1.79/2.00 ** KEPT (pick-wt=17): 6 [] -rel_str(A)| -element(B,the_carrier(A))|relstr_element_smaller(A,C,B)| -related(A,B,$f1(A,C,B)).
% 1.79/2.00 ** KEPT (pick-wt=21): 7 [] -rel_str(A)| -element(B,the_carrier(A))| -relstr_set_smaller(A,C,B)| -element(D,the_carrier(A))| -in(D,C)|related(A,D,B).
% 1.79/2.00 ** KEPT (pick-wt=17): 8 [] -rel_str(A)| -element(B,the_carrier(A))|relstr_set_smaller(A,C,B)|element($f2(A,C,B),the_carrier(A)).
% 1.79/2.00 ** KEPT (pick-wt=16): 9 [] -rel_str(A)| -element(B,the_carrier(A))|relstr_set_smaller(A,C,B)|in($f2(A,C,B),C).
% 1.79/2.00 ** KEPT (pick-wt=17): 10 [] -rel_str(A)| -element(B,the_carrier(A))|relstr_set_smaller(A,C,B)| -related(A,$f2(A,C,B),B).
% 1.79/2.00 ** KEPT (pick-wt=4): 11 [] -rel_str(A)|one_sorted_str(A).
% 1.79/2.00 ** KEPT (pick-wt=2): 12 [] -empty($c3).
% 1.79/2.00 ** KEPT (pick-wt=2): 13 [] -empty($c5).
% 1.79/2.00 ** KEPT (pick-wt=6): 14 [] -in(A,B)|element(A,B).
% 1.79/2.00 ** KEPT (pick-wt=8): 15 [] -element(A,B)|empty(B)|in(A,B).
% 1.79/2.00 ** KEPT (pick-wt=5): 16 [] -empty(A)|A=empty_set.
% 1.79/2.00 ** KEPT (pick-wt=8): 17 [] -relstr_set_smaller($c7,empty_set,$c6)| -relstr_element_smaller($c7,empty_set,$c6).
% 1.79/2.00 ** KEPT (pick-wt=5): 18 [] -in(A,B)| -empty(B).
% 1.79/2.00 ** KEPT (pick-wt=7): 19 [] -empty(A)|A=B| -empty(B).
% 1.79/2.00
% 1.79/2.00 ------------> process sos:
% 1.79/2.00 ** KEPT (pick-wt=3): 24 [] A=A.
% 1.79/2.00 ** KEPT (pick-wt=2): 25 [] rel_str($c1).
% 1.79/2.00 ** KEPT (pick-wt=2): 26 [] one_sorted_str($c2).
% 1.79/2.00 ** KEPT (pick-wt=4): 27 [] element($f3(A),A).
% 1.79/2.00 ** KEPT (pick-wt=2): 28 [] empty(empty_set).
% 1.79/2.00 ** KEPT (pick-wt=2): 29 [] finite($c3).
% 1.79/2.00 ** KEPT (pick-wt=2): 30 [] empty($c4).
% 1.79/2.00 ** KEPT (pick-wt=2): 31 [] rel_str($c7).
% 1.79/2.00 ** KEPT (pick-wt=4): 32 [] element($c6,the_carrier($c7)).
% 1.79/2.00 Following clause subsumed by 24 during input processing: 0 [copy,24,flip.1] A=A.
% 1.79/2.00 24 back subsumes 23.
% 1.79/2.00
% 1.79/2.00 ======= end of input processing =======
% 1.79/2.00
% 1.79/2.00 =========== start of search ===========
% 1.79/2.00
% 1.79/2.00 -------- PROOF --------
% 1.79/2.00
% 1.79/2.00 -----> EMPTY CLAUSE at 0.06 sec ----> 813 [hyper,796,52,701] $F.
% 1.79/2.00
% 1.79/2.00 Length of proof is 6. Level of proof is 2.
% 1.79/2.00
% 1.79/2.00 ---------------- PROOF ----------------
% 1.79/2.00 % SZS status Theorem
% 1.79/2.00 % SZS output start Refutation
% See solution above
% 1.79/2.00 ------------ end of proof -------------
% 1.79/2.00
% 1.79/2.00
% 1.79/2.00 Search stopped by max_proofs option.
% 1.79/2.00
% 1.79/2.00
% 1.79/2.00 Search stopped by max_proofs option.
% 1.79/2.00
% 1.79/2.00 ============ end of search ============
% 1.79/2.00
% 1.79/2.00 -------------- statistics -------------
% 1.79/2.00 clauses given 87
% 1.79/2.00 clauses generated 1539
% 1.79/2.00 clauses kept 811
% 1.79/2.00 clauses forward subsumed 758
% 1.79/2.00 clauses back subsumed 1
% 1.79/2.00 Kbytes malloced 1953
% 1.79/2.00
% 1.79/2.00 ----------- times (seconds) -----------
% 1.79/2.00 user CPU time 0.06 (0 hr, 0 min, 0 sec)
% 1.79/2.00 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.79/2.00 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.79/2.00
% 1.79/2.00 That finishes the proof of the theorem.
% 1.79/2.00
% 1.79/2.00 Process 25623 finished Wed Jul 27 07:42:22 2022
% 1.79/2.00 Otter interrupted
% 1.79/2.00 PROOF FOUND
%------------------------------------------------------------------------------