TSTP Solution File: SEU212+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU212+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n019.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 13:15:10 EDT 2022
% Result : Theorem 1.69s 1.92s
% Output : Refutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 9
% Syntax : Number of clauses : 15 ( 7 unt; 3 nHn; 14 RR)
% Number of literals : 33 ( 9 equ; 17 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 11 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
( ~ relation(A)
| ~ function(A)
| ~ in(B,relation_dom(A))
| C != apply(A,B)
| in(ordered_pair(B,C),A) ),
file('SEU212+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ relation(A)
| ~ function(A)
| ~ in(B,relation_dom(A))
| C = apply(A,B)
| ~ in(ordered_pair(B,C),A) ),
file('SEU212+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ relation(A)
| B != relation_dom(A)
| in(C,B)
| ~ in(ordered_pair(C,D),A) ),
file('SEU212+1.p',unknown),
[] ).
cnf(25,axiom,
( ~ in(ordered_pair(dollar_c9,dollar_c8),dollar_c7)
| ~ in(dollar_c9,relation_dom(dollar_c7))
| dollar_c8 != apply(dollar_c7,dollar_c9) ),
file('SEU212+1.p',unknown),
[] ).
cnf(26,plain,
( ~ in(ordered_pair(dollar_c9,dollar_c8),dollar_c7)
| ~ in(dollar_c9,relation_dom(dollar_c7))
| apply(dollar_c7,dollar_c9) != dollar_c8 ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[25])]),
[iquote('copy,25,flip.3')] ).
cnf(29,axiom,
A = A,
file('SEU212+1.p',unknown),
[] ).
cnf(46,axiom,
relation(dollar_c7),
file('SEU212+1.p',unknown),
[] ).
cnf(47,axiom,
function(dollar_c7),
file('SEU212+1.p',unknown),
[] ).
cnf(48,axiom,
( in(ordered_pair(dollar_c9,dollar_c8),dollar_c7)
| in(dollar_c9,relation_dom(dollar_c7)) ),
file('SEU212+1.p',unknown),
[] ).
cnf(49,axiom,
( in(ordered_pair(dollar_c9,dollar_c8),dollar_c7)
| dollar_c8 = apply(dollar_c7,dollar_c9) ),
file('SEU212+1.p',unknown),
[] ).
cnf(50,plain,
( in(ordered_pair(dollar_c9,dollar_c8),dollar_c7)
| apply(dollar_c7,dollar_c9) = dollar_c8 ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[49])]),
[iquote('copy,49,flip.2')] ).
cnf(152,plain,
in(dollar_c9,relation_dom(dollar_c7)),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[48,9,46,29])]),
[iquote('hyper,48,9,46,29,factor_simp')] ).
cnf(197,plain,
apply(dollar_c7,dollar_c9) = dollar_c8,
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[152,5,46,47,50])]),
[iquote('hyper,152,5,46,47,50,factor_simp')] ).
cnf(198,plain,
in(ordered_pair(dollar_c9,dollar_c8),dollar_c7),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[152,4,46,47,29]),197]),
[iquote('hyper,152,4,46,47,29,demod,197')] ).
cnf(199,plain,
$false,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[26]),197]),198,152,29]),
[iquote('back_demod,26,demod,197,unit_del,198,152,29')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU212+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n019.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 07:52:22 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.69/1.92 ----- Otter 3.3f, August 2004 -----
% 1.69/1.92 The process was started by sandbox2 on n019.cluster.edu,
% 1.69/1.92 Wed Jul 27 07:52:22 2022
% 1.69/1.92 The command was "./otter". The process ID is 19999.
% 1.69/1.92
% 1.69/1.92 set(prolog_style_variables).
% 1.69/1.92 set(auto).
% 1.69/1.92 dependent: set(auto1).
% 1.69/1.92 dependent: set(process_input).
% 1.69/1.92 dependent: clear(print_kept).
% 1.69/1.92 dependent: clear(print_new_demod).
% 1.69/1.92 dependent: clear(print_back_demod).
% 1.69/1.92 dependent: clear(print_back_sub).
% 1.69/1.92 dependent: set(control_memory).
% 1.69/1.92 dependent: assign(max_mem, 12000).
% 1.69/1.92 dependent: assign(pick_given_ratio, 4).
% 1.69/1.92 dependent: assign(stats_level, 1).
% 1.69/1.92 dependent: assign(max_seconds, 10800).
% 1.69/1.92 clear(print_given).
% 1.69/1.92
% 1.69/1.92 formula_list(usable).
% 1.69/1.92 all A (A=A).
% 1.69/1.92 all A B (in(A,B)-> -in(B,A)).
% 1.69/1.92 all A (empty(A)->function(A)).
% 1.69/1.92 all A (empty(A)->relation(A)).
% 1.69/1.92 all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 1.69/1.92 all A (relation(A)&function(A)-> (all B C ((in(B,relation_dom(A))-> (C=apply(A,B)<->in(ordered_pair(B,C),A)))& (-in(B,relation_dom(A))-> (C=apply(A,B)<->C=empty_set))))).
% 1.69/1.92 all A (relation(A)-> (all B (B=relation_dom(A)<-> (all C (in(C,B)<-> (exists D in(ordered_pair(C,D),A))))))).
% 1.69/1.92 all A B (ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A))).
% 1.69/1.92 $T.
% 1.69/1.92 $T.
% 1.69/1.92 $T.
% 1.69/1.92 $T.
% 1.69/1.92 $T.
% 1.69/1.92 $T.
% 1.69/1.92 $T.
% 1.69/1.92 all A exists B element(B,A).
% 1.69/1.92 empty(empty_set).
% 1.69/1.92 relation(empty_set).
% 1.69/1.92 relation_empty_yielding(empty_set).
% 1.69/1.92 empty(empty_set).
% 1.69/1.92 all A B (-empty(ordered_pair(A,B))).
% 1.69/1.92 all A (-empty(singleton(A))).
% 1.69/1.92 all A B (-empty(unordered_pair(A,B))).
% 1.69/1.92 empty(empty_set).
% 1.69/1.92 relation(empty_set).
% 1.69/1.92 all A (-empty(A)&relation(A)-> -empty(relation_dom(A))).
% 1.69/1.92 all A (empty(A)->empty(relation_dom(A))&relation(relation_dom(A))).
% 1.69/1.92 exists A (relation(A)&function(A)).
% 1.69/1.92 exists A (empty(A)&relation(A)).
% 1.69/1.92 exists A empty(A).
% 1.69/1.92 exists A (-empty(A)&relation(A)).
% 1.69/1.92 exists A (-empty(A)).
% 1.69/1.92 exists A (relation(A)&relation_empty_yielding(A)).
% 1.69/1.92 all A B (in(A,B)->element(A,B)).
% 1.69/1.92 all A B (element(A,B)->empty(B)|in(A,B)).
% 1.69/1.92 all A (empty(A)->A=empty_set).
% 1.69/1.92 all A B (-(in(A,B)&empty(B))).
% 1.69/1.92 all A B (-(empty(A)&A!=B&empty(B))).
% 1.69/1.92 -(all A B C (relation(C)&function(C)-> (in(ordered_pair(A,B),C)<->in(A,relation_dom(C))&B=apply(C,A)))).
% 1.69/1.92 end_of_list.
% 1.69/1.92
% 1.69/1.92 -------> usable clausifies to:
% 1.69/1.92
% 1.69/1.92 list(usable).
% 1.69/1.92 0 [] A=A.
% 1.69/1.92 0 [] -in(A,B)| -in(B,A).
% 1.69/1.92 0 [] -empty(A)|function(A).
% 1.69/1.92 0 [] -empty(A)|relation(A).
% 1.69/1.92 0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.69/1.92 0 [] -relation(A)| -function(A)| -in(B,relation_dom(A))|C!=apply(A,B)|in(ordered_pair(B,C),A).
% 1.69/1.92 0 [] -relation(A)| -function(A)| -in(B,relation_dom(A))|C=apply(A,B)| -in(ordered_pair(B,C),A).
% 1.69/1.92 0 [] -relation(A)| -function(A)|in(B,relation_dom(A))|C!=apply(A,B)|C=empty_set.
% 1.69/1.92 0 [] -relation(A)| -function(A)|in(B,relation_dom(A))|C=apply(A,B)|C!=empty_set.
% 1.69/1.92 0 [] -relation(A)|B!=relation_dom(A)| -in(C,B)|in(ordered_pair(C,$f1(A,B,C)),A).
% 1.69/1.92 0 [] -relation(A)|B!=relation_dom(A)|in(C,B)| -in(ordered_pair(C,D),A).
% 1.69/1.92 0 [] -relation(A)|B=relation_dom(A)|in($f3(A,B),B)|in(ordered_pair($f3(A,B),$f2(A,B)),A).
% 1.69/1.92 0 [] -relation(A)|B=relation_dom(A)| -in($f3(A,B),B)| -in(ordered_pair($f3(A,B),X1),A).
% 1.69/1.92 0 [] ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A)).
% 1.69/1.92 0 [] $T.
% 1.69/1.92 0 [] $T.
% 1.69/1.92 0 [] $T.
% 1.69/1.92 0 [] $T.
% 1.69/1.92 0 [] $T.
% 1.69/1.92 0 [] $T.
% 1.69/1.92 0 [] $T.
% 1.69/1.92 0 [] element($f4(A),A).
% 1.69/1.92 0 [] empty(empty_set).
% 1.69/1.92 0 [] relation(empty_set).
% 1.69/1.92 0 [] relation_empty_yielding(empty_set).
% 1.69/1.92 0 [] empty(empty_set).
% 1.69/1.92 0 [] -empty(ordered_pair(A,B)).
% 1.69/1.92 0 [] -empty(singleton(A)).
% 1.69/1.92 0 [] -empty(unordered_pair(A,B)).
% 1.69/1.92 0 [] empty(empty_set).
% 1.69/1.92 0 [] relation(empty_set).
% 1.69/1.92 0 [] empty(A)| -relation(A)| -empty(relation_dom(A)).
% 1.69/1.92 0 [] -empty(A)|empty(relation_dom(A)).
% 1.69/1.92 0 [] -empty(A)|relation(relation_dom(A)).
% 1.69/1.92 0 [] relation($c1).
% 1.69/1.92 0 [] function($c1).
% 1.69/1.92 0 [] empty($c2).
% 1.69/1.92 0 [] relation($c2).
% 1.69/1.92 0 [] empty($c3).
% 1.69/1.92 0 [] -empty($c4).
% 1.69/1.92 0 [] relation($c4).
% 1.69/1.92 0 [] -empty($c5).
% 1.69/1.92 0 [] relation($c6).
% 1.69/1.92 0 [] relation_empty_yielding($c6).
% 1.69/1.92 0 [] -in(A,B)|element(A,B).
% 1.69/1.92 0 [] -element(A,B)|empty(B)|in(A,B).
% 1.69/1.92 0 [] -empty(A)|A=empty_set.
% 1.69/1.92 0 [] -in(A,B)| -empty(B).
% 1.69/1.92 0 [] -empty(A)|A=B| -empty(B).
% 1.69/1.92 0 [] relation($c7).
% 1.69/1.92 0 [] function($c7).
% 1.69/1.92 0 [] in(ordered_pair($c9,$c8),$c7)|in($c9,relation_dom($c7)).
% 1.69/1.92 0 [] in(ordered_pair($c9,$c8),$c7)|$c8=apply($c7,$c9).
% 1.69/1.92 0 [] -in(ordered_pair($c9,$c8),$c7)| -in($c9,relation_dom($c7))|$c8!=apply($c7,$c9).
% 1.69/1.92 end_of_list.
% 1.69/1.92
% 1.69/1.92 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=5.
% 1.69/1.92
% 1.69/1.92 This ia a non-Horn set with equality. The strategy will be
% 1.69/1.92 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.69/1.92 deletion, with positive clauses in sos and nonpositive
% 1.69/1.92 clauses in usable.
% 1.69/1.92
% 1.69/1.92 dependent: set(knuth_bendix).
% 1.69/1.92 dependent: set(anl_eq).
% 1.69/1.92 dependent: set(para_from).
% 1.69/1.92 dependent: set(para_into).
% 1.69/1.92 dependent: clear(para_from_right).
% 1.69/1.92 dependent: clear(para_into_right).
% 1.69/1.92 dependent: set(para_from_vars).
% 1.69/1.92 dependent: set(eq_units_both_ways).
% 1.69/1.92 dependent: set(dynamic_demod_all).
% 1.69/1.92 dependent: set(dynamic_demod).
% 1.69/1.92 dependent: set(order_eq).
% 1.69/1.92 dependent: set(back_demod).
% 1.69/1.92 dependent: set(lrpo).
% 1.69/1.92 dependent: set(hyper_res).
% 1.69/1.92 dependent: set(unit_deletion).
% 1.69/1.92 dependent: set(factor).
% 1.69/1.92
% 1.69/1.92 ------------> process usable:
% 1.69/1.92 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.69/1.92 ** KEPT (pick-wt=4): 2 [] -empty(A)|function(A).
% 1.69/1.92 ** KEPT (pick-wt=4): 3 [] -empty(A)|relation(A).
% 1.69/1.92 ** KEPT (pick-wt=18): 4 [] -relation(A)| -function(A)| -in(B,relation_dom(A))|C!=apply(A,B)|in(ordered_pair(B,C),A).
% 1.69/1.92 ** KEPT (pick-wt=18): 5 [] -relation(A)| -function(A)| -in(B,relation_dom(A))|C=apply(A,B)| -in(ordered_pair(B,C),A).
% 1.69/1.92 ** KEPT (pick-wt=16): 6 [] -relation(A)| -function(A)|in(B,relation_dom(A))|C!=apply(A,B)|C=empty_set.
% 1.69/1.92 ** KEPT (pick-wt=16): 7 [] -relation(A)| -function(A)|in(B,relation_dom(A))|C=apply(A,B)|C!=empty_set.
% 1.69/1.92 ** KEPT (pick-wt=17): 8 [] -relation(A)|B!=relation_dom(A)| -in(C,B)|in(ordered_pair(C,$f1(A,B,C)),A).
% 1.69/1.92 ** KEPT (pick-wt=14): 9 [] -relation(A)|B!=relation_dom(A)|in(C,B)| -in(ordered_pair(C,D),A).
% 1.69/1.92 ** KEPT (pick-wt=20): 10 [] -relation(A)|B=relation_dom(A)|in($f3(A,B),B)|in(ordered_pair($f3(A,B),$f2(A,B)),A).
% 1.69/1.92 ** KEPT (pick-wt=18): 11 [] -relation(A)|B=relation_dom(A)| -in($f3(A,B),B)| -in(ordered_pair($f3(A,B),C),A).
% 1.69/1.92 ** KEPT (pick-wt=4): 12 [] -empty(ordered_pair(A,B)).
% 1.69/1.92 ** KEPT (pick-wt=3): 13 [] -empty(singleton(A)).
% 1.69/1.92 ** KEPT (pick-wt=4): 14 [] -empty(unordered_pair(A,B)).
% 1.69/1.92 ** KEPT (pick-wt=7): 15 [] empty(A)| -relation(A)| -empty(relation_dom(A)).
% 1.69/1.92 ** KEPT (pick-wt=5): 16 [] -empty(A)|empty(relation_dom(A)).
% 1.69/1.92 ** KEPT (pick-wt=5): 17 [] -empty(A)|relation(relation_dom(A)).
% 1.69/1.92 ** KEPT (pick-wt=2): 18 [] -empty($c4).
% 1.69/1.92 ** KEPT (pick-wt=2): 19 [] -empty($c5).
% 1.69/1.92 ** KEPT (pick-wt=6): 20 [] -in(A,B)|element(A,B).
% 1.69/1.92 ** KEPT (pick-wt=8): 21 [] -element(A,B)|empty(B)|in(A,B).
% 1.69/1.92 ** KEPT (pick-wt=5): 22 [] -empty(A)|A=empty_set.
% 1.69/1.92 ** KEPT (pick-wt=5): 23 [] -in(A,B)| -empty(B).
% 1.69/1.92 ** KEPT (pick-wt=7): 24 [] -empty(A)|A=B| -empty(B).
% 1.69/1.92 ** KEPT (pick-wt=14): 26 [copy,25,flip.3] -in(ordered_pair($c9,$c8),$c7)| -in($c9,relation_dom($c7))|apply($c7,$c9)!=$c8.
% 1.69/1.92
% 1.69/1.92 ------------> process sos:
% 1.69/1.92 ** KEPT (pick-wt=3): 29 [] A=A.
% 1.69/1.92 ** KEPT (pick-wt=7): 30 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.69/1.92 ** KEPT (pick-wt=10): 32 [copy,31,flip.1] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 1.69/1.92 ---> New Demodulator: 33 [new_demod,32] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 1.69/1.92 ** KEPT (pick-wt=4): 34 [] element($f4(A),A).
% 1.69/1.92 ** KEPT (pick-wt=2): 35 [] empty(empty_set).
% 1.69/1.92 ** KEPT (pick-wt=2): 36 [] relation(empty_set).
% 1.69/1.92 ** KEPT (pick-wt=2): 37 [] relation_empty_yielding(empty_set).
% 1.69/1.92 Following clause subsumed by 35 during input processing: 0 [] empty(empty_set).
% 1.69/1.92 Following clause subsumed by 35 during input processing: 0 [] empty(empty_set).
% 1.69/1.92 Following clause subsumed by 36 during input processing: 0 [] relation(empty_set).
% 1.69/1.92 ** KEPT (pick-wt=2): 38 [] relation($c1).
% 1.69/1.92 ** KEPT (pick-wt=2): 39 [] function($c1).
% 1.69/1.92 ** KEPT (pick-wt=2): 40 [] empty($c2).
% 1.69/1.92 ** KEPT (pick-wt=2): 41 [] relation($c2).
% 1.69/1.92 ** KEPT (pick-wt=2): 42 [] empty($c3).
% 1.69/1.92 ** KEPT (pick-wt=2): 43 [] relation($c4).
% 1.69/1.92 ** KEPT (pick-wt=2): 44 [] relation($c6).
% 1.69/1.92 ** KEPT (pick-wt=2): 45 [] relation_empty_yielding($c6).
% 1.69/1.92 ** KEPT (pick-wt=2): 46 [] relation($c7).
% 1.69/1.92 ** KEPT (pick-wt=2): 47 [] function($c7).
% 1.69/1.92 ** KEPT (pick-wt=9): 48 [] in(ordered_pair($c9,$c8),$c7)|in($c9,relation_dom($c7)).
% 1.69/1.92 ** KEPT (pick-wt=10): 50 [copy,49,flip.2] in(ordered_pair($c9,$c8),$c7)|apply($c7,$c9)=$c8.
% 1.69/1.92 Following clause subsumed by 29 during input processing: 0 [copy,29,flip.1] A=A.
% 1.69/1.92 29 back subsumes 28.
% 1.69/1.92 Following clause subsumed by 30 during input processing: 0 [copy,30,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 1.69/1.92 >>>> Starting back demodulation with 33.
% 1.69/1.92
% 1.69/1.92 ======= end of input processing =======
% 1.69/1.92
% 1.69/1.92 =========== start of search ===========
% 1.69/1.92
% 1.69/1.92 -------- PROOF --------
% 1.69/1.92
% 1.69/1.92 -----> EMPTY CLAUSE at 0.01 sec ----> 199 [back_demod,26,demod,197,unit_del,198,152,29] $F.
% 1.69/1.92
% 1.69/1.92 Length of proof is 5. Level of proof is 3.
% 1.69/1.92
% 1.69/1.92 ---------------- PROOF ----------------
% 1.69/1.92 % SZS status Theorem
% 1.69/1.92 % SZS output start Refutation
% See solution above
% 1.69/1.92 ------------ end of proof -------------
% 1.69/1.92
% 1.69/1.92
% 1.69/1.92 Search stopped by max_proofs option.
% 1.69/1.92
% 1.69/1.92
% 1.69/1.92 Search stopped by max_proofs option.
% 1.69/1.92
% 1.69/1.92 ============ end of search ============
% 1.69/1.92
% 1.69/1.92 -------------- statistics -------------
% 1.69/1.92 clauses given 27
% 1.69/1.92 clauses generated 222
% 1.69/1.92 clauses kept 187
% 1.69/1.92 clauses forward subsumed 134
% 1.69/1.92 clauses back subsumed 5
% 1.69/1.92 Kbytes malloced 1953
% 1.69/1.92
% 1.69/1.92 ----------- times (seconds) -----------
% 1.69/1.92 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.69/1.92 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.69/1.92 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.69/1.92
% 1.69/1.92 That finishes the proof of the theorem.
% 1.69/1.92
% 1.69/1.92 Process 19999 finished Wed Jul 27 07:52:23 2022
% 1.69/1.92 Otter interrupted
% 1.69/1.92 PROOF FOUND
%------------------------------------------------------------------------------