%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET997+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n028.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 13:14:39 EDT 2022
% Result : Theorem 2.62s 2.80s
% Output : Refutation 2.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 9
% Syntax : Number of clauses : 16 ( 10 unt; 1 nHn; 14 RR)
% Number of literals : 26 ( 6 equ; 10 neg)
% Maximal clause size : 6 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 12 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(5,axiom,
( subset(A,B)
| ~ in(dollar_f1(A,B),B) ),
file('SET997+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ relation(A)
| ~ function(A)
| B != relation_rng(A)
| in(C,B)
| ~ in(D,relation_dom(A))
| C != apply(A,D) ),
file('SET997+1.p',unknown),
[] ).
cnf(24,axiom,
( ~ in(A,dollar_c8)
| in(dollar_f8(A),relation_dom(dollar_c7)) ),
file('SET997+1.p',unknown),
[] ).
cnf(25,axiom,
( ~ in(A,dollar_c8)
| A = apply(dollar_c7,dollar_f8(A)) ),
file('SET997+1.p',unknown),
[] ).
cnf(26,plain,
( ~ in(A,dollar_c8)
| apply(dollar_c7,dollar_f8(A)) = A ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[25])]),
[iquote('copy,25,flip.2')] ).
cnf(27,axiom,
~ subset(dollar_c8,relation_rng(dollar_c7)),
file('SET997+1.p',unknown),
[] ).
cnf(40,axiom,
A = A,
file('SET997+1.p',unknown),
[] ).
cnf(41,axiom,
( subset(A,B)
| in(dollar_f1(A,B),A) ),
file('SET997+1.p',unknown),
[] ).
cnf(58,axiom,
relation(dollar_c7),
file('SET997+1.p',unknown),
[] ).
cnf(59,axiom,
function(dollar_c7),
file('SET997+1.p',unknown),
[] ).
cnf(79,plain,
in(dollar_f1(dollar_c8,relation_rng(dollar_c7)),dollar_c8),
inference(hyper,[status(thm)],[41,27]),
[iquote('hyper,41,27')] ).
cnf(517,plain,
apply(dollar_c7,dollar_f8(dollar_f1(dollar_c8,relation_rng(dollar_c7)))) = dollar_f1(dollar_c8,relation_rng(dollar_c7)),
inference(hyper,[status(thm)],[79,26]),
[iquote('hyper,79,26')] ).
cnf(518,plain,
in(dollar_f8(dollar_f1(dollar_c8,relation_rng(dollar_c7))),relation_dom(dollar_c7)),
inference(hyper,[status(thm)],[79,24]),
[iquote('hyper,79,24')] ).
cnf(1398,plain,
in(dollar_f1(dollar_c8,relation_rng(dollar_c7)),relation_rng(dollar_c7)),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[518,9,58,59,40,40]),517]),
[iquote('hyper,518,9,58,59,40,40,demod,517')] ).
cnf(1400,plain,
subset(dollar_c8,relation_rng(dollar_c7)),
inference(hyper,[status(thm)],[1398,5]),
[iquote('hyper,1398,5')] ).
cnf(1401,plain,
$false,
inference(binary,[status(thm)],[1400,27]),
[iquote('binary,1400.1,27.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET997+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n028.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 10:36:04 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.87/2.09 ----- Otter 3.3f, August 2004 -----
% 1.87/2.09 The process was started by sandbox on n028.cluster.edu,
% 1.87/2.09 Wed Jul 27 10:36:04 2022
% 1.87/2.09 The command was "./otter". The process ID is 15921.
% 1.87/2.09
% 1.87/2.09 set(prolog_style_variables).
% 1.87/2.09 set(auto).
% 1.87/2.09 dependent: set(auto1).
% 1.87/2.09 dependent: set(process_input).
% 1.87/2.09 dependent: clear(print_kept).
% 1.87/2.09 dependent: clear(print_new_demod).
% 1.87/2.09 dependent: clear(print_back_demod).
% 1.87/2.09 dependent: clear(print_back_sub).
% 1.87/2.09 dependent: set(control_memory).
% 1.87/2.09 dependent: assign(max_mem, 12000).
% 1.87/2.09 dependent: assign(pick_given_ratio, 4).
% 1.87/2.09 dependent: assign(stats_level, 1).
% 1.87/2.09 dependent: assign(max_seconds, 10800).
% 1.87/2.09 clear(print_given).
% 1.87/2.09
% 1.87/2.09 formula_list(usable).
% 1.87/2.09 all A (A=A).
% 1.87/2.09 all A B (in(A,B)-> -in(B,A)).
% 1.87/2.09 all A (empty(A)->function(A)).
% 1.87/2.09 all A (empty(A)->relation(A)).
% 1.87/2.09 all A B (subset(A,B)<-> (all C (in(C,A)->in(C,B)))).
% 1.87/2.09 all A (relation(A)&function(A)-> (all B (B=relation_rng(A)<-> (all C (in(C,B)<-> (exists D (in(D,relation_dom(A))&C=apply(A,D)))))))).
% 1.87/2.09 all A exists B element(B,A).
% 1.87/2.09 empty(empty_set).
% 1.87/2.09 relation(empty_set).
% 1.87/2.09 relation_empty_yielding(empty_set).
% 1.87/2.09 all A (-empty(powerset(A))).
% 1.87/2.09 empty(empty_set).
% 1.87/2.09 empty(empty_set).
% 1.87/2.09 relation(empty_set).
% 1.87/2.09 all A (-empty(A)&relation(A)-> -empty(relation_dom(A))).
% 1.87/2.09 all A (-empty(A)&relation(A)-> -empty(relation_rng(A))).
% 1.87/2.09 all A (empty(A)->empty(relation_dom(A))&relation(relation_dom(A))).
% 1.87/2.09 all A (empty(A)->empty(relation_rng(A))&relation(relation_rng(A))).
% 1.87/2.09 exists A (relation(A)&function(A)).
% 1.87/2.09 exists A (empty(A)&relation(A)).
% 1.87/2.09 all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)))).
% 1.87/2.09 exists A empty(A).
% 1.87/2.09 exists A (-empty(A)&relation(A)).
% 1.87/2.09 all A exists B (element(B,powerset(A))&empty(B)).
% 1.87/2.09 exists A (-empty(A)).
% 1.87/2.09 exists A (relation(A)&relation_empty_yielding(A)).
% 1.87/2.09 all A B subset(A,A).
% 1.87/2.09 -(all A B (relation(B)&function(B)-> ((all C (-(in(C,A)& (all D (-(in(D,relation_dom(B))&C=apply(B,D)))))))->subset(A,relation_rng(B))))).
% 1.87/2.09 all A B (in(A,B)->element(A,B)).
% 1.87/2.09 all A B (element(A,B)->empty(B)|in(A,B)).
% 1.87/2.09 all A B (element(A,powerset(B))<->subset(A,B)).
% 1.87/2.09 all A B C (in(A,B)&element(B,powerset(C))->element(A,C)).
% 1.87/2.09 all A B C (-(in(A,B)&element(B,powerset(C))&empty(C))).
% 1.87/2.09 all A (empty(A)->A=empty_set).
% 1.87/2.09 all A B (-(in(A,B)&empty(B))).
% 1.87/2.09 all A B (-(empty(A)&A!=B&empty(B))).
% 1.87/2.09 end_of_list.
% 1.87/2.09
% 1.87/2.09 -------> usable clausifies to:
% 1.87/2.09
% 1.87/2.09 list(usable).
% 1.87/2.09 0 [] A=A.
% 1.87/2.09 0 [] -in(A,B)| -in(B,A).
% 1.87/2.09 0 [] -empty(A)|function(A).
% 1.87/2.09 0 [] -empty(A)|relation(A).
% 1.87/2.09 0 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.87/2.09 0 [] subset(A,B)|in($f1(A,B),A).
% 1.87/2.09 0 [] subset(A,B)| -in($f1(A,B),B).
% 1.87/2.09 0 [] -relation(A)| -function(A)|B!=relation_rng(A)| -in(C,B)|in($f2(A,B,C),relation_dom(A)).
% 1.87/2.09 0 [] -relation(A)| -function(A)|B!=relation_rng(A)| -in(C,B)|C=apply(A,$f2(A,B,C)).
% 1.87/2.09 0 [] -relation(A)| -function(A)|B!=relation_rng(A)|in(C,B)| -in(D,relation_dom(A))|C!=apply(A,D).
% 1.87/2.09 0 [] -relation(A)| -function(A)|B=relation_rng(A)|in($f4(A,B),B)|in($f3(A,B),relation_dom(A)).
% 1.87/2.09 0 [] -relation(A)| -function(A)|B=relation_rng(A)|in($f4(A,B),B)|$f4(A,B)=apply(A,$f3(A,B)).
% 1.87/2.09 0 [] -relation(A)| -function(A)|B=relation_rng(A)| -in($f4(A,B),B)| -in(X1,relation_dom(A))|$f4(A,B)!=apply(A,X1).
% 1.87/2.09 0 [] element($f5(A),A).
% 1.87/2.09 0 [] empty(empty_set).
% 1.87/2.09 0 [] relation(empty_set).
% 1.87/2.09 0 [] relation_empty_yielding(empty_set).
% 1.87/2.09 0 [] -empty(powerset(A)).
% 1.87/2.09 0 [] empty(empty_set).
% 1.87/2.09 0 [] empty(empty_set).
% 1.87/2.09 0 [] relation(empty_set).
% 1.87/2.09 0 [] empty(A)| -relation(A)| -empty(relation_dom(A)).
% 1.87/2.09 0 [] empty(A)| -relation(A)| -empty(relation_rng(A)).
% 1.87/2.09 0 [] -empty(A)|empty(relation_dom(A)).
% 1.87/2.09 0 [] -empty(A)|relation(relation_dom(A)).
% 1.87/2.09 0 [] -empty(A)|empty(relation_rng(A)).
% 1.87/2.09 0 [] -empty(A)|relation(relation_rng(A)).
% 1.87/2.09 0 [] relation($c1).
% 1.87/2.09 0 [] function($c1).
% 1.87/2.09 0 [] empty($c2).
% 1.87/2.09 0 [] relation($c2).
% 1.87/2.09 0 [] empty(A)|element($f6(A),powerset(A)).
% 1.87/2.09 0 [] empty(A)| -empty($f6(A)).
% 1.87/2.09 0 [] empty($c3).
% 1.87/2.09 0 [] -empty($c4).
% 1.87/2.09 0 [] relation($c4).
% 1.87/2.09 0 [] element($f7(A),powerset(A)).
% 1.87/2.09 0 [] empty($f7(A)).
% 1.87/2.09 0 [] -empty($c5).
% 1.87/2.09 0 [] relation($c6).
% 1.87/2.09 0 [] relation_empty_yielding($c6).
% 1.87/2.09 0 [] subset(A,A).
% 1.87/2.09 0 [] relation($c7).
% 1.87/2.09 0 [] function($c7).
% 1.87/2.09 0 [] -in(C,$c8)|in($f8(C),relation_dom($c7)).
% 1.87/2.09 0 [] -in(C,$c8)|C=apply($c7,$f8(C)).
% 1.87/2.09 0 [] -subset($c8,relation_rng($c7)).
% 1.87/2.09 0 [] -in(A,B)|element(A,B).
% 1.87/2.09 0 [] -element(A,B)|empty(B)|in(A,B).
% 1.87/2.09 0 [] -element(A,powerset(B))|subset(A,B).
% 1.87/2.09 0 [] element(A,powerset(B))| -subset(A,B).
% 1.87/2.09 0 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 1.87/2.09 0 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 1.87/2.09 0 [] -empty(A)|A=empty_set.
% 1.87/2.09 0 [] -in(A,B)| -empty(B).
% 1.87/2.09 0 [] -empty(A)|A=B| -empty(B).
% 1.87/2.09 end_of_list.
% 1.87/2.09
% 1.87/2.09 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=6.
% 1.87/2.09
% 1.87/2.09 This ia a non-Horn set with equality. The strategy will be
% 1.87/2.09 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.87/2.09 deletion, with positive clauses in sos and nonpositive
% 1.87/2.09 clauses in usable.
% 1.87/2.09
% 1.87/2.09 dependent: set(knuth_bendix).
% 1.87/2.09 dependent: set(anl_eq).
% 1.87/2.09 dependent: set(para_from).
% 1.87/2.09 dependent: set(para_into).
% 1.87/2.09 dependent: clear(para_from_right).
% 1.87/2.09 dependent: clear(para_into_right).
% 1.87/2.09 dependent: set(para_from_vars).
% 1.87/2.09 dependent: set(eq_units_both_ways).
% 1.87/2.09 dependent: set(dynamic_demod_all).
% 1.87/2.09 dependent: set(dynamic_demod).
% 1.87/2.09 dependent: set(order_eq).
% 1.87/2.09 dependent: set(back_demod).
% 1.87/2.09 dependent: set(lrpo).
% 1.87/2.09 dependent: set(hyper_res).
% 1.87/2.09 dependent: set(unit_deletion).
% 1.87/2.09 dependent: set(factor).
% 1.87/2.09
% 1.87/2.09 ------------> process usable:
% 1.87/2.09 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.87/2.09 ** KEPT (pick-wt=4): 2 [] -empty(A)|function(A).
% 1.87/2.09 ** KEPT (pick-wt=4): 3 [] -empty(A)|relation(A).
% 1.87/2.09 ** KEPT (pick-wt=9): 4 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.87/2.09 ** KEPT (pick-wt=8): 5 [] subset(A,B)| -in($f1(A,B),B).
% 1.87/2.09 ** KEPT (pick-wt=18): 6 [] -relation(A)| -function(A)|B!=relation_rng(A)| -in(C,B)|in($f2(A,B,C),relation_dom(A)).
% 1.87/2.09 ** KEPT (pick-wt=19): 8 [copy,7,flip.5] -relation(A)| -function(A)|B!=relation_rng(A)| -in(C,B)|apply(A,$f2(A,B,C))=C.
% 1.87/2.09 ** KEPT (pick-wt=20): 9 [] -relation(A)| -function(A)|B!=relation_rng(A)|in(C,B)| -in(D,relation_dom(A))|C!=apply(A,D).
% 1.87/2.09 ** KEPT (pick-wt=19): 10 [] -relation(A)| -function(A)|B=relation_rng(A)|in($f4(A,B),B)|in($f3(A,B),relation_dom(A)).
% 1.87/2.09 ** KEPT (pick-wt=22): 12 [copy,11,flip.5] -relation(A)| -function(A)|B=relation_rng(A)|in($f4(A,B),B)|apply(A,$f3(A,B))=$f4(A,B).
% 1.87/2.09 ** KEPT (pick-wt=24): 13 [] -relation(A)| -function(A)|B=relation_rng(A)| -in($f4(A,B),B)| -in(C,relation_dom(A))|$f4(A,B)!=apply(A,C).
% 1.87/2.09 ** KEPT (pick-wt=3): 14 [] -empty(powerset(A)).
% 1.87/2.09 ** KEPT (pick-wt=7): 15 [] empty(A)| -relation(A)| -empty(relation_dom(A)).
% 1.87/2.09 ** KEPT (pick-wt=7): 16 [] empty(A)| -relation(A)| -empty(relation_rng(A)).
% 1.87/2.09 ** KEPT (pick-wt=5): 17 [] -empty(A)|empty(relation_dom(A)).
% 1.87/2.09 ** KEPT (pick-wt=5): 18 [] -empty(A)|relation(relation_dom(A)).
% 1.87/2.09 ** KEPT (pick-wt=5): 19 [] -empty(A)|empty(relation_rng(A)).
% 1.87/2.09 ** KEPT (pick-wt=5): 20 [] -empty(A)|relation(relation_rng(A)).
% 1.87/2.09 ** KEPT (pick-wt=5): 21 [] empty(A)| -empty($f6(A)).
% 1.87/2.09 ** KEPT (pick-wt=2): 22 [] -empty($c4).
% 1.87/2.09 ** KEPT (pick-wt=2): 23 [] -empty($c5).
% 1.87/2.09 ** KEPT (pick-wt=8): 24 [] -in(A,$c8)|in($f8(A),relation_dom($c7)).
% 1.87/2.09 ** KEPT (pick-wt=9): 26 [copy,25,flip.2] -in(A,$c8)|apply($c7,$f8(A))=A.
% 1.87/2.09 ** KEPT (pick-wt=4): 27 [] -subset($c8,relation_rng($c7)).
% 1.87/2.09 ** KEPT (pick-wt=6): 28 [] -in(A,B)|element(A,B).
% 1.87/2.09 ** KEPT (pick-wt=8): 29 [] -element(A,B)|empty(B)|in(A,B).
% 1.87/2.09 ** KEPT (pick-wt=7): 30 [] -element(A,powerset(B))|subset(A,B).
% 1.87/2.09 ** KEPT (pick-wt=7): 31 [] element(A,powerset(B))| -subset(A,B).
% 1.87/2.09 ** KEPT (pick-wt=10): 32 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 1.87/2.09 ** KEPT (pick-wt=9): 33 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 1.87/2.09 ** KEPT (pick-wt=5): 34 [] -empty(A)|A=empty_set.
% 1.87/2.09 ** KEPT (pick-wt=5): 35 [] -in(A,B)| -empty(B).
% 1.87/2.09 ** KEPT (pick-wt=7): 36 [] -empty(A)|A=B| -empty(B).
% 1.87/2.09
% 1.87/2.09 ------------> process sos:
% 1.87/2.09 ** KEPT (pick-wt=3): 40 [] A=A.
% 1.87/2.09 ** KEPT (pick-wt=8): 41 [] subset(A,B)|in($f1(A,B),A).
% 1.87/2.09 ** KEPT (pick-wt=4): 42 [] element($f5(A),A).
% 1.87/2.09 ** KEPT (pick-wt=2): 43 [] empty(empty_set).
% 1.87/2.09 ** KEPT (pick-wt=2): 44 [] relation(empty_set).
% 1.87/2.09 ** KEPT (pick-wt=2): 45 [] relation_empty_yielding(empty_set).
% 1.87/2.09 Following clause subsumed by 43 during input processing: 0 [] empty(empty_set).
% 1.87/2.09 Following clause subsumed by 43 during input processing: 0 [] empty(empty_set).
% 1.87/2.09 Following clause subsumed by 44 during input processing: 0 [] relation(empty_set).
% 1.87/2.09 ** KEPT (pick-wt=2): 46 [] relation($c1).
% 1.87/2.09 ** KEPT (pick-wt=2): 47 [] function($c1).
% 1.87/2.09 ** KEPT (pick-wt=2): 48 [] empty($c2).
% 1.87/2.09 ** KEPT (pick-wt=2): 49 [] relation($c2).
% 2.62/2.80 ** KEPT (pick-wt=7): 50 [] empty(A)|element($f6(A),powerset(A)).
% 2.62/2.80 ** KEPT (pick-wt=2): 51 [] empty($c3).
% 2.62/2.80 ** KEPT (pick-wt=2): 52 [] relation($c4).
% 2.62/2.80 ** KEPT (pick-wt=5): 53 [] element($f7(A),powerset(A)).
% 2.62/2.80 ** KEPT (pick-wt=3): 54 [] empty($f7(A)).
% 2.62/2.80 ** KEPT (pick-wt=2): 55 [] relation($c6).
% 2.62/2.80 ** KEPT (pick-wt=2): 56 [] relation_empty_yielding($c6).
% 2.62/2.80 ** KEPT (pick-wt=3): 57 [] subset(A,A).
% 2.62/2.80 ** KEPT (pick-wt=2): 58 [] relation($c7).
% 2.62/2.80 ** KEPT (pick-wt=2): 59 [] function($c7).
% 2.62/2.80 Following clause subsumed by 40 during input processing: 0 [copy,40,flip.1] A=A.
% 2.62/2.80 40 back subsumes 39.
% 2.62/2.80
% 2.62/2.80 ======= end of input processing =======
% 2.62/2.80
% 2.62/2.80 =========== start of search ===========
% 2.62/2.80
% 2.62/2.80
% 2.62/2.80 Resetting weight limit to 8.
% 2.62/2.80
% 2.62/2.80
% 2.62/2.80 Resetting weight limit to 8.
% 2.62/2.80
% 2.62/2.80 sos_size=1054
% 2.62/2.80
% 2.62/2.80 -------- PROOF --------
% 2.62/2.80
% 2.62/2.80 ----> UNIT CONFLICT at 0.71 sec ----> 1401 [binary,1400.1,27.1] $F.
% 2.62/2.80
% 2.62/2.80 Length of proof is 6. Level of proof is 4.
% 2.62/2.80
% 2.62/2.80 ---------------- PROOF ----------------
% 2.62/2.80 % SZS status Theorem
% 2.62/2.80 % SZS output start Refutation
% See solution above
% 2.62/2.80 ------------ end of proof -------------
% 2.62/2.80
% 2.62/2.80
% 2.62/2.80 Search stopped by max_proofs option.
% 2.62/2.80
% 2.62/2.80
% 2.62/2.80 Search stopped by max_proofs option.
% 2.62/2.80
% 2.62/2.80 ============ end of search ============
% 2.62/2.80
% 2.62/2.80 -------------- statistics -------------
% 2.62/2.80 clauses given 220
% 2.62/2.80 clauses generated 14358
% 2.62/2.80 clauses kept 1389
% 2.62/2.80 clauses forward subsumed 1949
% 2.62/2.80 clauses back subsumed 26
% 2.62/2.80 Kbytes malloced 5859
% 2.62/2.80
% 2.62/2.80 ----------- times (seconds) -----------
% 2.62/2.80 user CPU time 0.71 (0 hr, 0 min, 0 sec)
% 2.62/2.80 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.62/2.80 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.62/2.80
% 2.62/2.80 That finishes the proof of the theorem.
% 2.62/2.80
% 2.62/2.80 Process 15921 finished Wed Jul 27 10:36:06 2022
% 2.62/2.80 Otter interrupted
% 2.62/2.80 PROOF FOUND
%------------------------------------------------------------------------------