TSTP Solution File: SEU080+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU080+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n026.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 13:14:44 EDT 2022
% Result : Theorem 2.36s 2.56s
% Output : Refutation 2.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 9
% Syntax : Number of clauses : 15 ( 11 unt; 0 nHn; 14 RR)
% Number of literals : 24 ( 4 equ; 10 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 8 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(7,axiom,
( A = B
| ~ subset(A,B)
| ~ subset(B,A) ),
file('SEU080+1.p',unknown),
[] ).
cnf(15,axiom,
( ~ relation(A)
| ~ function(A)
| ~ subset(relation_inverse_image(A,B),relation_inverse_image(A,C))
| ~ subset(B,relation_rng(A))
| subset(B,C) ),
file('SEU080+1.p',unknown),
[] ).
cnf(16,axiom,
dollar_c11 != dollar_c10,
file('SEU080+1.p',unknown),
[] ).
cnf(51,axiom,
subset(A,A),
file('SEU080+1.p',unknown),
[] ).
cnf(52,axiom,
relation(dollar_c9),
file('SEU080+1.p',unknown),
[] ).
cnf(53,axiom,
function(dollar_c9),
file('SEU080+1.p',unknown),
[] ).
cnf(54,axiom,
relation_inverse_image(dollar_c9,dollar_c11) = relation_inverse_image(dollar_c9,dollar_c10),
file('SEU080+1.p',unknown),
[] ).
cnf(56,axiom,
subset(dollar_c11,relation_rng(dollar_c9)),
file('SEU080+1.p',unknown),
[] ).
cnf(57,axiom,
subset(dollar_c10,relation_rng(dollar_c9)),
file('SEU080+1.p',unknown),
[] ).
cnf(150,plain,
( ~ subset(relation_inverse_image(dollar_c9,A),relation_inverse_image(dollar_c9,dollar_c10))
| ~ subset(A,relation_rng(dollar_c9))
| subset(A,dollar_c11) ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[54,15]),52,53]),
[iquote('para_from,54.1.1,15.3.2,unit_del,52,53')] ).
cnf(151,plain,
( ~ subset(relation_inverse_image(dollar_c9,dollar_c10),relation_inverse_image(dollar_c9,A))
| subset(dollar_c11,A) ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[54,15]),52,53,56]),
[iquote('para_from,54.1.1,15.3.1,unit_del,52,53,56')] ).
cnf(2254,plain,
subset(dollar_c10,dollar_c11),
inference(hyper,[status(thm)],[150,51,57]),
[iquote('hyper,150,51,57')] ).
cnf(2367,plain,
subset(dollar_c11,dollar_c10),
inference(hyper,[status(thm)],[151,51]),
[iquote('hyper,151,51')] ).
cnf(2414,plain,
dollar_c11 = dollar_c10,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[2367,7,2254])]),
[iquote('hyper,2367,7,2254,flip.1')] ).
cnf(2416,plain,
$false,
inference(binary,[status(thm)],[2414,16]),
[iquote('binary,2414.1,16.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU080+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n026.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 08:08:24 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.08/2.26 ----- Otter 3.3f, August 2004 -----
% 2.08/2.26 The process was started by sandbox on n026.cluster.edu,
% 2.08/2.26 Wed Jul 27 08:08:24 2022
% 2.08/2.26 The command was "./otter". The process ID is 28958.
% 2.08/2.26
% 2.08/2.26 set(prolog_style_variables).
% 2.08/2.26 set(auto).
% 2.08/2.26 dependent: set(auto1).
% 2.08/2.26 dependent: set(process_input).
% 2.08/2.26 dependent: clear(print_kept).
% 2.08/2.26 dependent: clear(print_new_demod).
% 2.08/2.26 dependent: clear(print_back_demod).
% 2.08/2.26 dependent: clear(print_back_sub).
% 2.08/2.26 dependent: set(control_memory).
% 2.08/2.26 dependent: assign(max_mem, 12000).
% 2.08/2.26 dependent: assign(pick_given_ratio, 4).
% 2.08/2.26 dependent: assign(stats_level, 1).
% 2.08/2.26 dependent: assign(max_seconds, 10800).
% 2.08/2.26 clear(print_given).
% 2.08/2.26
% 2.08/2.26 formula_list(usable).
% 2.08/2.26 all A (A=A).
% 2.08/2.26 all A B (in(A,B)-> -in(B,A)).
% 2.08/2.26 all A (empty(A)->function(A)).
% 2.08/2.26 all A (empty(A)->relation(A)).
% 2.08/2.26 all A (relation(A)&empty(A)&function(A)->relation(A)&function(A)&one_to_one(A)).
% 2.08/2.26 all A B (A=B<->subset(A,B)&subset(B,A)).
% 2.08/2.26 all A exists B element(B,A).
% 2.08/2.26 empty(empty_set).
% 2.08/2.26 relation(empty_set).
% 2.08/2.26 relation_empty_yielding(empty_set).
% 2.08/2.26 all A (-empty(powerset(A))).
% 2.08/2.26 empty(empty_set).
% 2.08/2.26 empty(empty_set).
% 2.08/2.26 relation(empty_set).
% 2.08/2.26 all A (-empty(A)&relation(A)-> -empty(relation_rng(A))).
% 2.08/2.26 all A (empty(A)->empty(relation_rng(A))&relation(relation_rng(A))).
% 2.08/2.26 exists A (relation(A)&function(A)).
% 2.08/2.26 exists A (empty(A)&relation(A)).
% 2.08/2.26 all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)))).
% 2.08/2.26 exists A empty(A).
% 2.08/2.26 exists A (relation(A)&empty(A)&function(A)).
% 2.08/2.26 exists A (-empty(A)&relation(A)).
% 2.08/2.26 all A exists B (element(B,powerset(A))&empty(B)).
% 2.08/2.26 exists A (-empty(A)).
% 2.08/2.26 exists A (relation(A)&function(A)&one_to_one(A)).
% 2.08/2.26 exists A (relation(A)&relation_empty_yielding(A)).
% 2.08/2.26 all A B subset(A,A).
% 2.08/2.26 all A B C (relation(C)&function(C)-> (subset(relation_inverse_image(C,A),relation_inverse_image(C,B))&subset(A,relation_rng(C))->subset(A,B))).
% 2.08/2.26 -(all A B C (relation(C)&function(C)-> (relation_inverse_image(C,A)=relation_inverse_image(C,B)&subset(A,relation_rng(C))&subset(B,relation_rng(C))->A=B))).
% 2.08/2.26 all A B (in(A,B)->element(A,B)).
% 2.08/2.26 all A B (element(A,B)->empty(B)|in(A,B)).
% 2.08/2.26 all A B (element(A,powerset(B))<->subset(A,B)).
% 2.08/2.26 all A B C (in(A,B)&element(B,powerset(C))->element(A,C)).
% 2.08/2.26 all A B C (-(in(A,B)&element(B,powerset(C))&empty(C))).
% 2.08/2.26 all A (empty(A)->A=empty_set).
% 2.08/2.26 all A B (-(in(A,B)&empty(B))).
% 2.08/2.26 all A B (-(empty(A)&A!=B&empty(B))).
% 2.08/2.26 end_of_list.
% 2.08/2.26
% 2.08/2.26 -------> usable clausifies to:
% 2.08/2.26
% 2.08/2.26 list(usable).
% 2.08/2.26 0 [] A=A.
% 2.08/2.26 0 [] -in(A,B)| -in(B,A).
% 2.08/2.26 0 [] -empty(A)|function(A).
% 2.08/2.26 0 [] -empty(A)|relation(A).
% 2.08/2.26 0 [] -relation(A)| -empty(A)| -function(A)|one_to_one(A).
% 2.08/2.26 0 [] A!=B|subset(A,B).
% 2.08/2.26 0 [] A!=B|subset(B,A).
% 2.08/2.26 0 [] A=B| -subset(A,B)| -subset(B,A).
% 2.08/2.26 0 [] element($f1(A),A).
% 2.08/2.26 0 [] empty(empty_set).
% 2.08/2.26 0 [] relation(empty_set).
% 2.08/2.26 0 [] relation_empty_yielding(empty_set).
% 2.08/2.26 0 [] -empty(powerset(A)).
% 2.08/2.26 0 [] empty(empty_set).
% 2.08/2.26 0 [] empty(empty_set).
% 2.08/2.26 0 [] relation(empty_set).
% 2.08/2.26 0 [] empty(A)| -relation(A)| -empty(relation_rng(A)).
% 2.08/2.26 0 [] -empty(A)|empty(relation_rng(A)).
% 2.08/2.26 0 [] -empty(A)|relation(relation_rng(A)).
% 2.08/2.26 0 [] relation($c1).
% 2.08/2.26 0 [] function($c1).
% 2.08/2.26 0 [] empty($c2).
% 2.08/2.26 0 [] relation($c2).
% 2.08/2.26 0 [] empty(A)|element($f2(A),powerset(A)).
% 2.08/2.26 0 [] empty(A)| -empty($f2(A)).
% 2.08/2.26 0 [] empty($c3).
% 2.08/2.26 0 [] relation($c4).
% 2.08/2.26 0 [] empty($c4).
% 2.08/2.26 0 [] function($c4).
% 2.08/2.26 0 [] -empty($c5).
% 2.08/2.26 0 [] relation($c5).
% 2.08/2.26 0 [] element($f3(A),powerset(A)).
% 2.08/2.26 0 [] empty($f3(A)).
% 2.08/2.26 0 [] -empty($c6).
% 2.08/2.26 0 [] relation($c7).
% 2.08/2.26 0 [] function($c7).
% 2.08/2.26 0 [] one_to_one($c7).
% 2.08/2.26 0 [] relation($c8).
% 2.08/2.26 0 [] relation_empty_yielding($c8).
% 2.08/2.26 0 [] subset(A,A).
% 2.08/2.26 0 [] -relation(C)| -function(C)| -subset(relation_inverse_image(C,A),relation_inverse_image(C,B))| -subset(A,relation_rng(C))|subset(A,B).
% 2.08/2.26 0 [] relation($c9).
% 2.08/2.26 0 [] function($c9).
% 2.08/2.26 0 [] relation_inverse_image($c9,$c11)=relation_inverse_image($c9,$c10).
% 2.08/2.26 0 [] subset($c11,relation_rng($c9)).
% 2.08/2.26 0 [] subset($c10,relation_rng($c9)).
% 2.08/2.26 0 [] $c11!=$c10.
% 2.08/2.26 0 [] -in(A,B)|element(A,B).
% 2.08/2.26 0 [] -element(A,B)|empty(B)|in(A,B).
% 2.08/2.26 0 [] -element(A,powerset(B))|subset(A,B).
% 2.08/2.26 0 [] element(A,powerset(B))| -subset(A,B).
% 2.08/2.26 0 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 2.08/2.26 0 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 2.08/2.26 0 [] -empty(A)|A=empty_set.
% 2.08/2.26 0 [] -in(A,B)| -empty(B).
% 2.08/2.26 0 [] -empty(A)|A=B| -empty(B).
% 2.08/2.26 end_of_list.
% 2.08/2.26
% 2.08/2.26 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=5.
% 2.08/2.26
% 2.08/2.26 This ia a non-Horn set with equality. The strategy will be
% 2.08/2.26 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.08/2.26 deletion, with positive clauses in sos and nonpositive
% 2.08/2.26 clauses in usable.
% 2.08/2.26
% 2.08/2.26 dependent: set(knuth_bendix).
% 2.08/2.26 dependent: set(anl_eq).
% 2.08/2.26 dependent: set(para_from).
% 2.08/2.26 dependent: set(para_into).
% 2.08/2.26 dependent: clear(para_from_right).
% 2.08/2.26 dependent: clear(para_into_right).
% 2.08/2.26 dependent: set(para_from_vars).
% 2.08/2.26 dependent: set(eq_units_both_ways).
% 2.08/2.26 dependent: set(dynamic_demod_all).
% 2.08/2.26 dependent: set(dynamic_demod).
% 2.08/2.26 dependent: set(order_eq).
% 2.08/2.26 dependent: set(back_demod).
% 2.08/2.26 dependent: set(lrpo).
% 2.08/2.26 dependent: set(hyper_res).
% 2.08/2.26 dependent: set(unit_deletion).
% 2.08/2.26 dependent: set(factor).
% 2.08/2.26
% 2.08/2.26 ------------> process usable:
% 2.08/2.26 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 2.08/2.26 ** KEPT (pick-wt=4): 2 [] -empty(A)|function(A).
% 2.08/2.26 ** KEPT (pick-wt=4): 3 [] -empty(A)|relation(A).
% 2.08/2.26 ** KEPT (pick-wt=8): 4 [] -relation(A)| -empty(A)| -function(A)|one_to_one(A).
% 2.08/2.26 ** KEPT (pick-wt=6): 5 [] A!=B|subset(A,B).
% 2.08/2.26 ** KEPT (pick-wt=6): 6 [] A!=B|subset(B,A).
% 2.08/2.26 ** KEPT (pick-wt=9): 7 [] A=B| -subset(A,B)| -subset(B,A).
% 2.08/2.26 ** KEPT (pick-wt=3): 8 [] -empty(powerset(A)).
% 2.08/2.26 ** KEPT (pick-wt=7): 9 [] empty(A)| -relation(A)| -empty(relation_rng(A)).
% 2.08/2.26 ** KEPT (pick-wt=5): 10 [] -empty(A)|empty(relation_rng(A)).
% 2.08/2.26 ** KEPT (pick-wt=5): 11 [] -empty(A)|relation(relation_rng(A)).
% 2.08/2.26 ** KEPT (pick-wt=5): 12 [] empty(A)| -empty($f2(A)).
% 2.08/2.26 ** KEPT (pick-wt=2): 13 [] -empty($c5).
% 2.08/2.26 ** KEPT (pick-wt=2): 14 [] -empty($c6).
% 2.08/2.26 ** KEPT (pick-wt=18): 15 [] -relation(A)| -function(A)| -subset(relation_inverse_image(A,B),relation_inverse_image(A,C))| -subset(B,relation_rng(A))|subset(B,C).
% 2.08/2.26 ** KEPT (pick-wt=3): 16 [] $c11!=$c10.
% 2.08/2.26 ** KEPT (pick-wt=6): 17 [] -in(A,B)|element(A,B).
% 2.08/2.26 ** KEPT (pick-wt=8): 18 [] -element(A,B)|empty(B)|in(A,B).
% 2.08/2.26 ** KEPT (pick-wt=7): 19 [] -element(A,powerset(B))|subset(A,B).
% 2.08/2.26 ** KEPT (pick-wt=7): 20 [] element(A,powerset(B))| -subset(A,B).
% 2.08/2.26 ** KEPT (pick-wt=10): 21 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 2.08/2.26 ** KEPT (pick-wt=9): 22 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 2.08/2.26 ** KEPT (pick-wt=5): 23 [] -empty(A)|A=empty_set.
% 2.08/2.26 ** KEPT (pick-wt=5): 24 [] -in(A,B)| -empty(B).
% 2.08/2.26 ** KEPT (pick-wt=7): 25 [] -empty(A)|A=B| -empty(B).
% 2.08/2.26
% 2.08/2.26 ------------> process sos:
% 2.08/2.26 ** KEPT (pick-wt=3): 29 [] A=A.
% 2.08/2.26 ** KEPT (pick-wt=4): 30 [] element($f1(A),A).
% 2.08/2.26 ** KEPT (pick-wt=2): 31 [] empty(empty_set).
% 2.08/2.26 ** KEPT (pick-wt=2): 32 [] relation(empty_set).
% 2.08/2.26 ** KEPT (pick-wt=2): 33 [] relation_empty_yielding(empty_set).
% 2.08/2.26 Following clause subsumed by 31 during input processing: 0 [] empty(empty_set).
% 2.08/2.26 Following clause subsumed by 31 during input processing: 0 [] empty(empty_set).
% 2.08/2.26 Following clause subsumed by 32 during input processing: 0 [] relation(empty_set).
% 2.08/2.26 ** KEPT (pick-wt=2): 34 [] relation($c1).
% 2.08/2.26 ** KEPT (pick-wt=2): 35 [] function($c1).
% 2.08/2.26 ** KEPT (pick-wt=2): 36 [] empty($c2).
% 2.08/2.26 ** KEPT (pick-wt=2): 37 [] relation($c2).
% 2.08/2.26 ** KEPT (pick-wt=7): 38 [] empty(A)|element($f2(A),powerset(A)).
% 2.08/2.26 ** KEPT (pick-wt=2): 39 [] empty($c3).
% 2.08/2.26 ** KEPT (pick-wt=2): 40 [] relation($c4).
% 2.08/2.26 ** KEPT (pick-wt=2): 41 [] empty($c4).
% 2.08/2.26 ** KEPT (pick-wt=2): 42 [] function($c4).
% 2.08/2.26 ** KEPT (pick-wt=2): 43 [] relation($c5).
% 2.08/2.26 ** KEPT (pick-wt=5): 44 [] element($f3(A),powerset(A)).
% 2.08/2.26 ** KEPT (pick-wt=3): 45 [] empty($f3(A)).
% 2.08/2.26 ** KEPT (pick-wt=2): 46 [] relation($c7).
% 2.08/2.26 ** KEPT (pick-wt=2): 47 [] function($c7).
% 2.08/2.26 ** KEPT (pick-wt=2): 48 [] one_to_one($c7).
% 2.08/2.26 ** KEPT (pick-wt=2): 49 [] relation($c8).
% 2.08/2.26 ** KEPT (pick-wt=2): 50 [] relation_empty_yielding($c8).
% 2.08/2.26 ** KEPT (pick-wt=3): 51 [] subset(A,A).
% 2.08/2.26 ** KEPT (pick-wt=2): 52 [] relation($c9).
% 2.08/2.26 ** KEPT (pick-wt=2): 53 [] function($c9).
% 2.08/2.26 ** KEPT (pick-wt=7): 54 [] relation_inverse_image($c9,$c11)=relation_inverse_image($c9,$c10).
% 2.08/2.26 ---> New Demodulator: 55 [new_demod,54] relation_inverse_image($c9,$c11)=relation_inverse_image($c9,$c10).
% 2.08/2.26 ** KEPT (pick-wt=4): 56 [] subset($c11,relation_rng($c9)).
% 2.08/2.26 ** KEPT (pick-wt=4): 57 [] subset($c10,relation_rng($c9)).
% 2.08/2.26 Following clause subsumed by 29 during input processing: 0 [copy,29,flip.1] A=A.
% 2.08/2.26 29 back subsumes 28.
% 2.08/2.26 29 back subsumes 27.
% 2.36/2.56 >>>> Starting back demodulation with 55.
% 2.36/2.56
% 2.36/2.56 ======= end of input processing =======
% 2.36/2.56
% 2.36/2.56 =========== start of search ===========
% 2.36/2.56
% 2.36/2.56 -------- PROOF --------
% 2.36/2.56
% 2.36/2.56 ----> UNIT CONFLICT at 0.30 sec ----> 2416 [binary,2414.1,16.1] $F.
% 2.36/2.56
% 2.36/2.56 Length of proof is 5. Level of proof is 3.
% 2.36/2.56
% 2.36/2.56 ---------------- PROOF ----------------
% 2.36/2.56 % SZS status Theorem
% 2.36/2.56 % SZS output start Refutation
% See solution above
% 2.36/2.56 ------------ end of proof -------------
% 2.36/2.56
% 2.36/2.56
% 2.36/2.56 Search stopped by max_proofs option.
% 2.36/2.56
% 2.36/2.56
% 2.36/2.56 Search stopped by max_proofs option.
% 2.36/2.56
% 2.36/2.56 ============ end of search ============
% 2.36/2.56
% 2.36/2.56 -------------- statistics -------------
% 2.36/2.56 clauses given 227
% 2.36/2.56 clauses generated 9566
% 2.36/2.56 clauses kept 2407
% 2.36/2.56 clauses forward subsumed 7216
% 2.36/2.56 clauses back subsumed 704
% 2.36/2.56 Kbytes malloced 3906
% 2.36/2.56
% 2.36/2.56 ----------- times (seconds) -----------
% 2.36/2.56 user CPU time 0.30 (0 hr, 0 min, 0 sec)
% 2.36/2.56 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.36/2.56 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.36/2.56
% 2.36/2.56 That finishes the proof of the theorem.
% 2.36/2.56
% 2.36/2.56 Process 28958 finished Wed Jul 27 08:08:26 2022
% 2.36/2.56 Otter interrupted
% 2.36/2.56 PROOF FOUND
%------------------------------------------------------------------------------