%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET991+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n014.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 13:14:38 EDT 2022
% Result : Theorem 1.85s 2.02s
% Output : Refutation 1.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 6
% Syntax : Number of clauses : 8 ( 7 unt; 0 nHn; 7 RR)
% Number of literals : 13 ( 3 equ; 6 neg)
% Maximal clause size : 6 ( 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; 2 con; 0-2 aty)
% Number of variables : 5 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(23,axiom,
~ in(apply(dollar_c7,dollar_c8),relation_rng(dollar_c7)),
file('SET991+1.p',unknown),
[] ).
cnf(27,axiom,
( ~ relation(A)
| ~ function(A)
| B != relation_rng(A)
| in(C,B)
| ~ in(D,relation_dom(A))
| C != apply(A,D) ),
file('SET991+1.p',unknown),
[] ).
cnf(35,axiom,
A = A,
file('SET991+1.p',unknown),
[] ).
cnf(52,axiom,
relation(dollar_c7),
file('SET991+1.p',unknown),
[] ).
cnf(53,axiom,
function(dollar_c7),
file('SET991+1.p',unknown),
[] ).
cnf(54,axiom,
in(dollar_c8,relation_dom(dollar_c7)),
file('SET991+1.p',unknown),
[] ).
cnf(157,plain,
in(apply(dollar_c7,dollar_c8),relation_rng(dollar_c7)),
inference(hyper,[status(thm)],[54,27,52,53,35,35]),
[iquote('hyper,54,27,52,53,35,35')] ).
cnf(158,plain,
$false,
inference(binary,[status(thm)],[157,23]),
[iquote('binary,157.1,23.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET991+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n014.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 10:53:09 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.85/2.01 ----- Otter 3.3f, August 2004 -----
% 1.85/2.01 The process was started by sandbox on n014.cluster.edu,
% 1.85/2.01 Wed Jul 27 10:53:09 2022
% 1.85/2.01 The command was "./otter". The process ID is 19921.
% 1.85/2.01
% 1.85/2.01 set(prolog_style_variables).
% 1.85/2.01 set(auto).
% 1.85/2.01 dependent: set(auto1).
% 1.85/2.01 dependent: set(process_input).
% 1.85/2.01 dependent: clear(print_kept).
% 1.85/2.01 dependent: clear(print_new_demod).
% 1.85/2.01 dependent: clear(print_back_demod).
% 1.85/2.01 dependent: clear(print_back_sub).
% 1.85/2.01 dependent: set(control_memory).
% 1.85/2.01 dependent: assign(max_mem, 12000).
% 1.85/2.01 dependent: assign(pick_given_ratio, 4).
% 1.85/2.01 dependent: assign(stats_level, 1).
% 1.85/2.01 dependent: assign(max_seconds, 10800).
% 1.85/2.01 clear(print_given).
% 1.85/2.01
% 1.85/2.01 formula_list(usable).
% 1.85/2.01 all A (A=A).
% 1.85/2.01 all A B subset(A,A).
% 1.85/2.01 empty(empty_set).
% 1.85/2.01 relation(empty_set).
% 1.85/2.01 empty(empty_set).
% 1.85/2.01 relation(empty_set).
% 1.85/2.01 relation_empty_yielding(empty_set).
% 1.85/2.01 empty(empty_set).
% 1.85/2.01 all A exists B element(B,A).
% 1.85/2.01 all A (empty(A)->function(A)).
% 1.85/2.01 all A (-empty(powerset(A))).
% 1.85/2.01 all A (-empty(A)&relation(A)-> -empty(relation_dom(A))).
% 1.85/2.01 all A (-empty(A)&relation(A)-> -empty(relation_rng(A))).
% 1.85/2.01 all A (empty(A)->empty(relation_dom(A))&relation(relation_dom(A))).
% 1.85/2.01 all A (empty(A)->empty(relation_rng(A))&relation(relation_rng(A))).
% 1.85/2.01 all A (empty(A)->relation(A)).
% 1.85/2.01 all A B (element(A,B)->empty(B)|in(A,B)).
% 1.85/2.01 all A B (element(A,powerset(B))<->subset(A,B)).
% 1.85/2.01 all A B C (in(A,B)&element(B,powerset(C))->element(A,C)).
% 1.85/2.01 all A B C (-(in(A,B)&element(B,powerset(C))&empty(C))).
% 1.85/2.01 all A (empty(A)->A=empty_set).
% 1.85/2.01 all A B (-(empty(A)&A!=B&empty(B))).
% 1.85/2.01 all A B (in(A,B)-> -in(B,A)).
% 1.85/2.01 exists A (relation(A)&function(A)).
% 1.85/2.01 all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)))).
% 1.85/2.01 all A exists B (element(B,powerset(A))&empty(B)).
% 1.85/2.01 exists A (empty(A)&relation(A)).
% 1.85/2.01 exists A (-empty(A)&relation(A)).
% 1.85/2.01 exists A (relation(A)&relation_empty_yielding(A)).
% 1.85/2.01 exists A empty(A).
% 1.85/2.01 exists A (-empty(A)).
% 1.85/2.01 all A B (in(A,B)->element(A,B)).
% 1.85/2.01 all A B (-(in(A,B)&empty(B))).
% 1.85/2.01 -(all A B (relation(B)&function(B)-> (in(A,relation_dom(B))->in(apply(B,A),relation_rng(B))))).
% 1.85/2.01 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)))))))).
% 1.85/2.01 end_of_list.
% 1.85/2.01
% 1.85/2.01 -------> usable clausifies to:
% 1.85/2.01
% 1.85/2.01 list(usable).
% 1.85/2.01 0 [] A=A.
% 1.85/2.01 0 [] subset(A,A).
% 1.85/2.01 0 [] empty(empty_set).
% 1.85/2.01 0 [] relation(empty_set).
% 1.85/2.01 0 [] empty(empty_set).
% 1.85/2.01 0 [] relation(empty_set).
% 1.85/2.01 0 [] relation_empty_yielding(empty_set).
% 1.85/2.01 0 [] empty(empty_set).
% 1.85/2.01 0 [] element($f1(A),A).
% 1.85/2.01 0 [] -empty(A)|function(A).
% 1.85/2.01 0 [] -empty(powerset(A)).
% 1.85/2.01 0 [] empty(A)| -relation(A)| -empty(relation_dom(A)).
% 1.85/2.01 0 [] empty(A)| -relation(A)| -empty(relation_rng(A)).
% 1.85/2.01 0 [] -empty(A)|empty(relation_dom(A)).
% 1.85/2.01 0 [] -empty(A)|relation(relation_dom(A)).
% 1.85/2.01 0 [] -empty(A)|empty(relation_rng(A)).
% 1.85/2.01 0 [] -empty(A)|relation(relation_rng(A)).
% 1.85/2.01 0 [] -empty(A)|relation(A).
% 1.85/2.01 0 [] -element(A,B)|empty(B)|in(A,B).
% 1.85/2.01 0 [] -element(A,powerset(B))|subset(A,B).
% 1.85/2.01 0 [] element(A,powerset(B))| -subset(A,B).
% 1.85/2.01 0 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 1.85/2.01 0 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 1.85/2.01 0 [] -empty(A)|A=empty_set.
% 1.85/2.01 0 [] -empty(A)|A=B| -empty(B).
% 1.85/2.01 0 [] -in(A,B)| -in(B,A).
% 1.85/2.01 0 [] relation($c1).
% 1.85/2.01 0 [] function($c1).
% 1.85/2.01 0 [] empty(A)|element($f2(A),powerset(A)).
% 1.85/2.01 0 [] empty(A)| -empty($f2(A)).
% 1.85/2.01 0 [] element($f3(A),powerset(A)).
% 1.85/2.01 0 [] empty($f3(A)).
% 1.85/2.01 0 [] empty($c2).
% 1.85/2.01 0 [] relation($c2).
% 1.85/2.01 0 [] -empty($c3).
% 1.85/2.01 0 [] relation($c3).
% 1.85/2.01 0 [] relation($c4).
% 1.85/2.01 0 [] relation_empty_yielding($c4).
% 1.85/2.01 0 [] empty($c5).
% 1.85/2.01 0 [] -empty($c6).
% 1.85/2.01 0 [] -in(A,B)|element(A,B).
% 1.85/2.01 0 [] -in(A,B)| -empty(B).
% 1.85/2.01 0 [] relation($c7).
% 1.85/2.01 0 [] function($c7).
% 1.85/2.01 0 [] in($c8,relation_dom($c7)).
% 1.85/2.01 0 [] -in(apply($c7,$c8),relation_rng($c7)).
% 1.85/2.01 0 [] -relation(A)| -function(A)|B!=relation_rng(A)| -in(C,B)|in($f4(A,B,C),relation_dom(A)).
% 1.85/2.01 0 [] -relation(A)| -function(A)|B!=relation_rng(A)| -in(C,B)|C=apply(A,$f4(A,B,C)).
% 1.85/2.01 0 [] -relation(A)| -function(A)|B!=relation_rng(A)|in(C,B)| -in(D,relation_dom(A))|C!=apply(A,D).
% 1.85/2.01 0 [] -relation(A)| -function(A)|B=relation_rng(A)|in($f6(A,B),B)|in($f5(A,B),relation_dom(A)).
% 1.85/2.01 0 [] -relation(A)| -function(A)|B=relation_rng(A)|in($f6(A,B),B)|$f6(A,B)=apply(A,$f5(A,B)).
% 1.85/2.01 0 [] -relation(A)| -function(A)|B=relation_rng(A)| -in($f6(A,B),B)| -in(X1,relation_dom(A))|$f6(A,B)!=apply(A,X1).
% 1.85/2.01 end_of_list.
% 1.85/2.01
% 1.85/2.01 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=6.
% 1.85/2.01
% 1.85/2.01 This ia a non-Horn set with equality. The strategy will be
% 1.85/2.01 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.85/2.01 deletion, with positive clauses in sos and nonpositive
% 1.85/2.01 clauses in usable.
% 1.85/2.01
% 1.85/2.01 dependent: set(knuth_bendix).
% 1.85/2.01 dependent: set(anl_eq).
% 1.85/2.01 dependent: set(para_from).
% 1.85/2.01 dependent: set(para_into).
% 1.85/2.01 dependent: clear(para_from_right).
% 1.85/2.01 dependent: clear(para_into_right).
% 1.85/2.01 dependent: set(para_from_vars).
% 1.85/2.01 dependent: set(eq_units_both_ways).
% 1.85/2.01 dependent: set(dynamic_demod_all).
% 1.85/2.01 dependent: set(dynamic_demod).
% 1.85/2.01 dependent: set(order_eq).
% 1.85/2.01 dependent: set(back_demod).
% 1.85/2.01 dependent: set(lrpo).
% 1.85/2.01 dependent: set(hyper_res).
% 1.85/2.01 dependent: set(unit_deletion).
% 1.85/2.01 dependent: set(factor).
% 1.85/2.01
% 1.85/2.01 ------------> process usable:
% 1.85/2.01 ** KEPT (pick-wt=4): 1 [] -empty(A)|function(A).
% 1.85/2.01 ** KEPT (pick-wt=3): 2 [] -empty(powerset(A)).
% 1.85/2.01 ** KEPT (pick-wt=7): 3 [] empty(A)| -relation(A)| -empty(relation_dom(A)).
% 1.85/2.01 ** KEPT (pick-wt=7): 4 [] empty(A)| -relation(A)| -empty(relation_rng(A)).
% 1.85/2.01 ** KEPT (pick-wt=5): 5 [] -empty(A)|empty(relation_dom(A)).
% 1.85/2.01 ** KEPT (pick-wt=5): 6 [] -empty(A)|relation(relation_dom(A)).
% 1.85/2.01 ** KEPT (pick-wt=5): 7 [] -empty(A)|empty(relation_rng(A)).
% 1.85/2.01 ** KEPT (pick-wt=5): 8 [] -empty(A)|relation(relation_rng(A)).
% 1.85/2.01 ** KEPT (pick-wt=4): 9 [] -empty(A)|relation(A).
% 1.85/2.01 ** KEPT (pick-wt=8): 10 [] -element(A,B)|empty(B)|in(A,B).
% 1.85/2.01 ** KEPT (pick-wt=7): 11 [] -element(A,powerset(B))|subset(A,B).
% 1.85/2.01 ** KEPT (pick-wt=7): 12 [] element(A,powerset(B))| -subset(A,B).
% 1.85/2.01 ** KEPT (pick-wt=10): 13 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 1.85/2.01 ** KEPT (pick-wt=9): 14 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 1.85/2.01 ** KEPT (pick-wt=5): 15 [] -empty(A)|A=empty_set.
% 1.85/2.01 ** KEPT (pick-wt=7): 16 [] -empty(A)|A=B| -empty(B).
% 1.85/2.01 ** KEPT (pick-wt=6): 17 [] -in(A,B)| -in(B,A).
% 1.85/2.01 ** KEPT (pick-wt=5): 18 [] empty(A)| -empty($f2(A)).
% 1.85/2.01 ** KEPT (pick-wt=2): 19 [] -empty($c3).
% 1.85/2.01 ** KEPT (pick-wt=2): 20 [] -empty($c6).
% 1.85/2.01 ** KEPT (pick-wt=6): 21 [] -in(A,B)|element(A,B).
% 1.85/2.01 ** KEPT (pick-wt=5): 22 [] -in(A,B)| -empty(B).
% 1.85/2.01 ** KEPT (pick-wt=6): 23 [] -in(apply($c7,$c8),relation_rng($c7)).
% 1.85/2.01 ** KEPT (pick-wt=18): 24 [] -relation(A)| -function(A)|B!=relation_rng(A)| -in(C,B)|in($f4(A,B,C),relation_dom(A)).
% 1.85/2.01 ** KEPT (pick-wt=19): 26 [copy,25,flip.5] -relation(A)| -function(A)|B!=relation_rng(A)| -in(C,B)|apply(A,$f4(A,B,C))=C.
% 1.85/2.01 ** KEPT (pick-wt=20): 27 [] -relation(A)| -function(A)|B!=relation_rng(A)|in(C,B)| -in(D,relation_dom(A))|C!=apply(A,D).
% 1.85/2.01 ** KEPT (pick-wt=19): 28 [] -relation(A)| -function(A)|B=relation_rng(A)|in($f6(A,B),B)|in($f5(A,B),relation_dom(A)).
% 1.85/2.01 ** KEPT (pick-wt=22): 30 [copy,29,flip.5] -relation(A)| -function(A)|B=relation_rng(A)|in($f6(A,B),B)|apply(A,$f5(A,B))=$f6(A,B).
% 1.85/2.01 ** KEPT (pick-wt=24): 31 [] -relation(A)| -function(A)|B=relation_rng(A)| -in($f6(A,B),B)| -in(C,relation_dom(A))|$f6(A,B)!=apply(A,C).
% 1.85/2.01
% 1.85/2.01 ------------> process sos:
% 1.85/2.01 ** KEPT (pick-wt=3): 35 [] A=A.
% 1.85/2.01 ** KEPT (pick-wt=3): 36 [] subset(A,A).
% 1.85/2.01 ** KEPT (pick-wt=2): 37 [] empty(empty_set).
% 1.85/2.01 ** KEPT (pick-wt=2): 38 [] relation(empty_set).
% 1.85/2.01 Following clause subsumed by 37 during input processing: 0 [] empty(empty_set).
% 1.85/2.01 Following clause subsumed by 38 during input processing: 0 [] relation(empty_set).
% 1.85/2.01 ** KEPT (pick-wt=2): 39 [] relation_empty_yielding(empty_set).
% 1.85/2.01 Following clause subsumed by 37 during input processing: 0 [] empty(empty_set).
% 1.85/2.01 ** KEPT (pick-wt=4): 40 [] element($f1(A),A).
% 1.85/2.01 ** KEPT (pick-wt=2): 41 [] relation($c1).
% 1.85/2.01 ** KEPT (pick-wt=2): 42 [] function($c1).
% 1.85/2.01 ** KEPT (pick-wt=7): 43 [] empty(A)|element($f2(A),powerset(A)).
% 1.85/2.01 ** KEPT (pick-wt=5): 44 [] element($f3(A),powerset(A)).
% 1.85/2.01 ** KEPT (pick-wt=3): 45 [] empty($f3(A)).
% 1.85/2.01 ** KEPT (pick-wt=2): 46 [] empty($c2).
% 1.85/2.01 ** KEPT (pick-wt=2): 47 [] relation($c2).
% 1.85/2.01 ** KEPT (pick-wt=2): 48 [] relation($c3).
% 1.85/2.01 ** KEPT (pick-wt=2): 49 [] relation($c4).
% 1.85/2.01 ** KEPT (pick-wt=2): 50 [] relation_empty_yielding($c4).
% 1.85/2.01 ** KEPT (pick-wt=2): 51 [] empty($c5).
% 1.85/2.01 ** KEPT (pick-wt=2): 52 [] relation($c7).
% 1.85/2.01 ** KEPT (pick-wt=2): 53 [] function($c7).
% 1.85/2.01 ** KEPT (pick-wt=4): 54 [] in($c8,relation_dom($c7)).
% 1.85/2.02 Following clause subsumed by 35 during input processing: 0 [copy,35,flip.1] A=A.
% 1.85/2.02 35 back subsumes 32.
% 1.85/2.02
% 1.85/2.02 ======= end of input processing =======
% 1.85/2.02
% 1.85/2.02 =========== start of search ===========
% 1.85/2.02
% 1.85/2.02 -------- PROOF --------
% 1.85/2.02
% 1.85/2.02 ----> UNIT CONFLICT at 0.01 sec ----> 158 [binary,157.1,23.1] $F.
% 1.85/2.02
% 1.85/2.02 Length of proof is 1. Level of proof is 1.
% 1.85/2.02
% 1.85/2.02 ---------------- PROOF ----------------
% 1.85/2.02 % SZS status Theorem
% 1.85/2.02 % SZS output start Refutation
% See solution above
% 1.85/2.02 ------------ end of proof -------------
% 1.85/2.02
% 1.85/2.02
% 1.85/2.02 Search stopped by max_proofs option.
% 1.85/2.02
% 1.85/2.02
% 1.85/2.02 Search stopped by max_proofs option.
% 1.85/2.02
% 1.85/2.02 ============ end of search ============
% 1.85/2.02
% 1.85/2.02 -------------- statistics -------------
% 1.85/2.02 clauses given 21
% 1.85/2.02 clauses generated 154
% 1.85/2.02 clauses kept 152
% 1.85/2.02 clauses forward subsumed 74
% 1.85/2.02 clauses back subsumed 1
% 1.85/2.02 Kbytes malloced 1953
% 1.85/2.02
% 1.85/2.02 ----------- times (seconds) -----------
% 1.85/2.02 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.85/2.02 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.85/2.02 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.85/2.02
% 1.85/2.02 That finishes the proof of the theorem.
% 1.85/2.02
% 1.85/2.02 Process 19921 finished Wed Jul 27 10:53:10 2022
% 1.85/2.02 Otter interrupted
% 1.85/2.02 PROOF FOUND
%------------------------------------------------------------------------------