TSTP Solution File: SEU230+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU230+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n020.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 13:15:15 EDT 2022
% Result : Theorem 1.92s 2.21s
% Output : Refutation 1.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 6
% Syntax : Number of clauses : 10 ( 8 unt; 0 nHn; 5 RR)
% Number of literals : 14 ( 6 equ; 6 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 13 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(6,axiom,
( A != singleton(B)
| in(C,A)
| C != B ),
file('SEU230+1.p',unknown),
[] ).
cnf(10,axiom,
( A != set_union2(B,C)
| in(D,A)
| ~ in(D,C) ),
file('SEU230+1.p',unknown),
[] ).
cnf(19,axiom,
~ in(dollar_c10,succ(dollar_c10)),
file('SEU230+1.p',unknown),
[] ).
cnf(31,axiom,
A = A,
file('SEU230+1.p',unknown),
[] ).
cnf(34,axiom,
succ(A) = set_union2(A,singleton(A)),
file('SEU230+1.p',unknown),
[] ).
cnf(42,axiom,
set_union2(A,A) = A,
file('SEU230+1.p',unknown),
[] ).
cnf(62,plain,
~ in(dollar_c10,set_union2(dollar_c10,singleton(dollar_c10))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[19]),34]),
[iquote('back_demod,19,demod,34')] ).
cnf(68,plain,
in(A,singleton(A)),
inference(hyper,[status(thm)],[31,6,31]),
[iquote('hyper,31,6,31')] ).
cnf(667,plain,
in(A,set_union2(B,singleton(A))),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[68,10,42]),42]),
[iquote('hyper,68,10,41,demod,42')] ).
cnf(668,plain,
$false,
inference(binary,[status(thm)],[667,62]),
[iquote('binary,667.1,62.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU230+1 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n020.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 07:32:53 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.92/2.16 ----- Otter 3.3f, August 2004 -----
% 1.92/2.16 The process was started by sandbox on n020.cluster.edu,
% 1.92/2.16 Wed Jul 27 07:32:53 2022
% 1.92/2.16 The command was "./otter". The process ID is 5159.
% 1.92/2.16
% 1.92/2.16 set(prolog_style_variables).
% 1.92/2.16 set(auto).
% 1.92/2.16 dependent: set(auto1).
% 1.92/2.16 dependent: set(process_input).
% 1.92/2.16 dependent: clear(print_kept).
% 1.92/2.16 dependent: clear(print_new_demod).
% 1.92/2.16 dependent: clear(print_back_demod).
% 1.92/2.16 dependent: clear(print_back_sub).
% 1.92/2.16 dependent: set(control_memory).
% 1.92/2.16 dependent: assign(max_mem, 12000).
% 1.92/2.16 dependent: assign(pick_given_ratio, 4).
% 1.92/2.16 dependent: assign(stats_level, 1).
% 1.92/2.16 dependent: assign(max_seconds, 10800).
% 1.92/2.16 clear(print_given).
% 1.92/2.16
% 1.92/2.16 formula_list(usable).
% 1.92/2.16 all A (A=A).
% 1.92/2.16 all A B (in(A,B)-> -in(B,A)).
% 1.92/2.16 all A (empty(A)->function(A)).
% 1.92/2.16 all A (empty(A)->relation(A)).
% 1.92/2.16 all A (relation(A)&empty(A)&function(A)->relation(A)&function(A)&one_to_one(A)).
% 1.92/2.16 all A B (set_union2(A,B)=set_union2(B,A)).
% 1.92/2.16 all A (succ(A)=set_union2(A,singleton(A))).
% 1.92/2.16 all A B (B=singleton(A)<-> (all C (in(C,B)<->C=A))).
% 1.92/2.16 all A B C (C=set_union2(A,B)<-> (all D (in(D,C)<->in(D,A)|in(D,B)))).
% 1.92/2.16 $T.
% 1.92/2.16 $T.
% 1.92/2.16 $T.
% 1.92/2.16 $T.
% 1.92/2.16 $T.
% 1.92/2.16 all A exists B element(B,A).
% 1.92/2.16 empty(empty_set).
% 1.92/2.16 relation(empty_set).
% 1.92/2.16 relation_empty_yielding(empty_set).
% 1.92/2.16 all A (-empty(succ(A))).
% 1.92/2.16 empty(empty_set).
% 1.92/2.16 all A B (relation(A)&relation(B)->relation(set_union2(A,B))).
% 1.92/2.16 all A B (-empty(A)-> -empty(set_union2(A,B))).
% 1.92/2.16 all A B (-empty(A)-> -empty(set_union2(B,A))).
% 1.92/2.16 empty(empty_set).
% 1.92/2.16 relation(empty_set).
% 1.92/2.16 all A B (set_union2(A,A)=A).
% 1.92/2.16 exists A (relation(A)&function(A)).
% 1.92/2.16 exists A (empty(A)&relation(A)).
% 1.92/2.16 exists A empty(A).
% 1.92/2.16 exists A (relation(A)&empty(A)&function(A)).
% 1.92/2.16 exists A (-empty(A)&relation(A)).
% 1.92/2.16 exists A (-empty(A)).
% 1.92/2.16 exists A (relation(A)&function(A)&one_to_one(A)).
% 1.92/2.16 exists A (relation(A)&relation_empty_yielding(A)).
% 1.92/2.16 exists A (relation(A)&relation_empty_yielding(A)&function(A)).
% 1.92/2.16 -(all A in(A,succ(A))).
% 1.92/2.16 all A (set_union2(A,empty_set)=A).
% 1.92/2.16 all A B (in(A,B)->element(A,B)).
% 1.92/2.16 all A B (element(A,B)->empty(B)|in(A,B)).
% 1.92/2.16 all A (empty(A)->A=empty_set).
% 1.92/2.16 all A B (-(in(A,B)&empty(B))).
% 1.92/2.16 all A B (-(empty(A)&A!=B&empty(B))).
% 1.92/2.16 end_of_list.
% 1.92/2.16
% 1.92/2.16 -------> usable clausifies to:
% 1.92/2.16
% 1.92/2.16 list(usable).
% 1.92/2.16 0 [] A=A.
% 1.92/2.16 0 [] -in(A,B)| -in(B,A).
% 1.92/2.16 0 [] -empty(A)|function(A).
% 1.92/2.16 0 [] -empty(A)|relation(A).
% 1.92/2.16 0 [] -relation(A)| -empty(A)| -function(A)|one_to_one(A).
% 1.92/2.16 0 [] set_union2(A,B)=set_union2(B,A).
% 1.92/2.16 0 [] succ(A)=set_union2(A,singleton(A)).
% 1.92/2.16 0 [] B!=singleton(A)| -in(C,B)|C=A.
% 1.92/2.16 0 [] B!=singleton(A)|in(C,B)|C!=A.
% 1.92/2.16 0 [] B=singleton(A)|in($f1(A,B),B)|$f1(A,B)=A.
% 1.92/2.16 0 [] B=singleton(A)| -in($f1(A,B),B)|$f1(A,B)!=A.
% 1.92/2.16 0 [] C!=set_union2(A,B)| -in(D,C)|in(D,A)|in(D,B).
% 1.92/2.16 0 [] C!=set_union2(A,B)|in(D,C)| -in(D,A).
% 1.92/2.16 0 [] C!=set_union2(A,B)|in(D,C)| -in(D,B).
% 1.92/2.16 0 [] C=set_union2(A,B)|in($f2(A,B,C),C)|in($f2(A,B,C),A)|in($f2(A,B,C),B).
% 1.92/2.16 0 [] C=set_union2(A,B)| -in($f2(A,B,C),C)| -in($f2(A,B,C),A).
% 1.92/2.16 0 [] C=set_union2(A,B)| -in($f2(A,B,C),C)| -in($f2(A,B,C),B).
% 1.92/2.16 0 [] $T.
% 1.92/2.16 0 [] $T.
% 1.92/2.16 0 [] $T.
% 1.92/2.16 0 [] $T.
% 1.92/2.16 0 [] $T.
% 1.92/2.16 0 [] element($f3(A),A).
% 1.92/2.16 0 [] empty(empty_set).
% 1.92/2.16 0 [] relation(empty_set).
% 1.92/2.16 0 [] relation_empty_yielding(empty_set).
% 1.92/2.16 0 [] -empty(succ(A)).
% 1.92/2.16 0 [] empty(empty_set).
% 1.92/2.16 0 [] -relation(A)| -relation(B)|relation(set_union2(A,B)).
% 1.92/2.16 0 [] empty(A)| -empty(set_union2(A,B)).
% 1.92/2.16 0 [] empty(A)| -empty(set_union2(B,A)).
% 1.92/2.16 0 [] empty(empty_set).
% 1.92/2.16 0 [] relation(empty_set).
% 1.92/2.16 0 [] set_union2(A,A)=A.
% 1.92/2.16 0 [] relation($c1).
% 1.92/2.16 0 [] function($c1).
% 1.92/2.16 0 [] empty($c2).
% 1.92/2.16 0 [] relation($c2).
% 1.92/2.16 0 [] empty($c3).
% 1.92/2.16 0 [] relation($c4).
% 1.92/2.16 0 [] empty($c4).
% 1.92/2.16 0 [] function($c4).
% 1.92/2.16 0 [] -empty($c5).
% 1.92/2.16 0 [] relation($c5).
% 1.92/2.16 0 [] -empty($c6).
% 1.92/2.16 0 [] relation($c7).
% 1.92/2.16 0 [] function($c7).
% 1.92/2.16 0 [] one_to_one($c7).
% 1.92/2.16 0 [] relation($c8).
% 1.92/2.16 0 [] relation_empty_yielding($c8).
% 1.92/2.16 0 [] relation($c9).
% 1.92/2.16 0 [] relation_empty_yielding($c9).
% 1.92/2.16 0 [] function($c9).
% 1.92/2.16 0 [] -in($c10,succ($c10)).
% 1.92/2.16 0 [] set_union2(A,empty_set)=A.
% 1.92/2.16 0 [] -in(A,B)|element(A,B).
% 1.92/2.16 0 [] -element(A,B)|empty(B)|in(A,B).
% 1.92/2.16 0 [] -empty(A)|A=empty_set.
% 1.92/2.16 0 [] -in(A,B)| -empty(B).
% 1.92/2.16 0 [] -empty(A)|A=B| -empty(B).
% 1.92/2.16 end_of_list.
% 1.92/2.16
% 1.92/2.16 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.92/2.16
% 1.92/2.16 This ia a non-Horn set with equality. The strategy will be
% 1.92/2.16 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.92/2.16 deletion, with positive clauses in sos and nonpositive
% 1.92/2.16 clauses in usable.
% 1.92/2.16
% 1.92/2.16 dependent: set(knuth_bendix).
% 1.92/2.16 dependent: set(anl_eq).
% 1.92/2.16 dependent: set(para_from).
% 1.92/2.16 dependent: set(para_into).
% 1.92/2.16 dependent: clear(para_from_right).
% 1.92/2.16 dependent: clear(para_into_right).
% 1.92/2.16 dependent: set(para_from_vars).
% 1.92/2.16 dependent: set(eq_units_both_ways).
% 1.92/2.16 dependent: set(dynamic_demod_all).
% 1.92/2.16 dependent: set(dynamic_demod).
% 1.92/2.16 dependent: set(order_eq).
% 1.92/2.16 dependent: set(back_demod).
% 1.92/2.16 dependent: set(lrpo).
% 1.92/2.16 dependent: set(hyper_res).
% 1.92/2.16 dependent: set(unit_deletion).
% 1.92/2.16 dependent: set(factor).
% 1.92/2.16
% 1.92/2.16 ------------> process usable:
% 1.92/2.16 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.92/2.16 ** KEPT (pick-wt=4): 2 [] -empty(A)|function(A).
% 1.92/2.16 ** KEPT (pick-wt=4): 3 [] -empty(A)|relation(A).
% 1.92/2.16 ** KEPT (pick-wt=8): 4 [] -relation(A)| -empty(A)| -function(A)|one_to_one(A).
% 1.92/2.16 ** KEPT (pick-wt=10): 5 [] A!=singleton(B)| -in(C,A)|C=B.
% 1.92/2.16 ** KEPT (pick-wt=10): 6 [] A!=singleton(B)|in(C,A)|C!=B.
% 1.92/2.16 ** KEPT (pick-wt=14): 7 [] A=singleton(B)| -in($f1(B,A),A)|$f1(B,A)!=B.
% 1.92/2.16 ** KEPT (pick-wt=14): 8 [] A!=set_union2(B,C)| -in(D,A)|in(D,B)|in(D,C).
% 1.92/2.16 ** KEPT (pick-wt=11): 9 [] A!=set_union2(B,C)|in(D,A)| -in(D,B).
% 1.92/2.16 ** KEPT (pick-wt=11): 10 [] A!=set_union2(B,C)|in(D,A)| -in(D,C).
% 1.92/2.16 ** KEPT (pick-wt=17): 11 [] A=set_union2(B,C)| -in($f2(B,C,A),A)| -in($f2(B,C,A),B).
% 1.92/2.16 ** KEPT (pick-wt=17): 12 [] A=set_union2(B,C)| -in($f2(B,C,A),A)| -in($f2(B,C,A),C).
% 1.92/2.16 ** KEPT (pick-wt=3): 13 [] -empty(succ(A)).
% 1.92/2.16 ** KEPT (pick-wt=8): 14 [] -relation(A)| -relation(B)|relation(set_union2(A,B)).
% 1.92/2.16 ** KEPT (pick-wt=6): 15 [] empty(A)| -empty(set_union2(A,B)).
% 1.92/2.16 ** KEPT (pick-wt=6): 16 [] empty(A)| -empty(set_union2(B,A)).
% 1.92/2.16 ** KEPT (pick-wt=2): 17 [] -empty($c5).
% 1.92/2.16 ** KEPT (pick-wt=2): 18 [] -empty($c6).
% 1.92/2.16 ** KEPT (pick-wt=4): 19 [] -in($c10,succ($c10)).
% 1.92/2.16 ** KEPT (pick-wt=6): 20 [] -in(A,B)|element(A,B).
% 1.92/2.16 ** KEPT (pick-wt=8): 21 [] -element(A,B)|empty(B)|in(A,B).
% 1.92/2.16 ** KEPT (pick-wt=5): 22 [] -empty(A)|A=empty_set.
% 1.92/2.16 ** KEPT (pick-wt=5): 23 [] -in(A,B)| -empty(B).
% 1.92/2.16 ** KEPT (pick-wt=7): 24 [] -empty(A)|A=B| -empty(B).
% 1.92/2.16
% 1.92/2.16 ------------> process sos:
% 1.92/2.16 ** KEPT (pick-wt=3): 31 [] A=A.
% 1.92/2.16 ** KEPT (pick-wt=7): 32 [] set_union2(A,B)=set_union2(B,A).
% 1.92/2.16 ** KEPT (pick-wt=7): 33 [] succ(A)=set_union2(A,singleton(A)).
% 1.92/2.16 ---> New Demodulator: 34 [new_demod,33] succ(A)=set_union2(A,singleton(A)).
% 1.92/2.16 ** KEPT (pick-wt=14): 35 [] A=singleton(B)|in($f1(B,A),A)|$f1(B,A)=B.
% 1.92/2.16 ** KEPT (pick-wt=23): 36 [] A=set_union2(B,C)|in($f2(B,C,A),A)|in($f2(B,C,A),B)|in($f2(B,C,A),C).
% 1.92/2.16 ** KEPT (pick-wt=4): 37 [] element($f3(A),A).
% 1.92/2.16 ** KEPT (pick-wt=2): 38 [] empty(empty_set).
% 1.92/2.16 ** KEPT (pick-wt=2): 39 [] relation(empty_set).
% 1.92/2.16 ** KEPT (pick-wt=2): 40 [] relation_empty_yielding(empty_set).
% 1.92/2.16 Following clause subsumed by 38 during input processing: 0 [] empty(empty_set).
% 1.92/2.16 Following clause subsumed by 38 during input processing: 0 [] empty(empty_set).
% 1.92/2.16 Following clause subsumed by 39 during input processing: 0 [] relation(empty_set).
% 1.92/2.16 ** KEPT (pick-wt=5): 41 [] set_union2(A,A)=A.
% 1.92/2.16 ---> New Demodulator: 42 [new_demod,41] set_union2(A,A)=A.
% 1.92/2.16 ** KEPT (pick-wt=2): 43 [] relation($c1).
% 1.92/2.16 ** KEPT (pick-wt=2): 44 [] function($c1).
% 1.92/2.16 ** KEPT (pick-wt=2): 45 [] empty($c2).
% 1.92/2.16 ** KEPT (pick-wt=2): 46 [] relation($c2).
% 1.92/2.16 ** KEPT (pick-wt=2): 47 [] empty($c3).
% 1.92/2.16 ** KEPT (pick-wt=2): 48 [] relation($c4).
% 1.92/2.16 ** KEPT (pick-wt=2): 49 [] empty($c4).
% 1.92/2.16 ** KEPT (pick-wt=2): 50 [] function($c4).
% 1.92/2.16 ** KEPT (pick-wt=2): 51 [] relation($c5).
% 1.92/2.16 ** KEPT (pick-wt=2): 52 [] relation($c7).
% 1.92/2.16 ** KEPT (pick-wt=2): 53 [] function($c7).
% 1.92/2.16 ** KEPT (pick-wt=2): 54 [] one_to_one($c7).
% 1.92/2.16 ** KEPT (pick-wt=2): 55 [] relation($c8).
% 1.92/2.16 ** KEPT (pick-wt=2): 56 [] relation_empty_yielding($c8).
% 1.92/2.16 ** KEPT (pick-wt=2): 57 [] relation($c9).
% 1.92/2.16 ** KEPT (pick-wt=2): 58 [] relation_empty_yielding($c9).
% 1.92/2.16 ** KEPT (pick-wt=2): 59 [] function($c9).
% 1.92/2.16 ** KEPT (pick-wt=5): 60 [] set_union2(A,empty_set)=A.
% 1.92/2.16 ---> New Demodulator: 61 [new_demod,60] set_union2(A,empty_set)=A.
% 1.92/2.16 Following clause subsumed by 31 during input processing: 0 [copy,31,flip.1] A=A.
% 1.92/2.16 31 back subsumes 30.
% 1.92/2.16 Following clause subsumed by 32 during input processing: 0 [copy,32,flip.1] set_union2(A,B)=set_union2(B,A).
% 1.92/2.16 >>>> Starting back demodulation with 34.
% 1.92/2.16 >> back demodulating 19 with 34.
% 1.92/2.21 >> back demodulating 13 with 34.
% 1.92/2.21 >>>> Starting back demodulation with 42.
% 1.92/2.21 >> back demodulating 29 with 42.
% 1.92/2.21 >> back demodulating 26 with 42.
% 1.92/2.21 >>>> Starting back demodulation with 61.
% 1.92/2.21
% 1.92/2.21 ======= end of input processing =======
% 1.92/2.21
% 1.92/2.21 =========== start of search ===========
% 1.92/2.21
% 1.92/2.21 -------- PROOF --------
% 1.92/2.21
% 1.92/2.21 ----> UNIT CONFLICT at 0.06 sec ----> 668 [binary,667.1,62.1] $F.
% 1.92/2.21
% 1.92/2.21 Length of proof is 3. Level of proof is 2.
% 1.92/2.21
% 1.92/2.21 ---------------- PROOF ----------------
% 1.92/2.21 % SZS status Theorem
% 1.92/2.21 % SZS output start Refutation
% See solution above
% 1.92/2.21 ------------ end of proof -------------
% 1.92/2.21
% 1.92/2.21
% 1.92/2.21 Search stopped by max_proofs option.
% 1.92/2.21
% 1.92/2.21
% 1.92/2.21 Search stopped by max_proofs option.
% 1.92/2.21
% 1.92/2.21 ============ end of search ============
% 1.92/2.21
% 1.92/2.21 -------------- statistics -------------
% 1.92/2.21 clauses given 33
% 1.92/2.21 clauses generated 1097
% 1.92/2.21 clauses kept 660
% 1.92/2.21 clauses forward subsumed 527
% 1.92/2.21 clauses back subsumed 57
% 1.92/2.21 Kbytes malloced 1953
% 1.92/2.21
% 1.92/2.21 ----------- times (seconds) -----------
% 1.92/2.21 user CPU time 0.06 (0 hr, 0 min, 0 sec)
% 1.92/2.21 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.92/2.21 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.92/2.21
% 1.92/2.21 That finishes the proof of the theorem.
% 1.92/2.21
% 1.92/2.21 Process 5159 finished Wed Jul 27 07:32:55 2022
% 1.92/2.21 Otter interrupted
% 1.92/2.21 PROOF FOUND
%------------------------------------------------------------------------------