%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU186+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n029.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 13:15:05 EDT 2022
% Result : Theorem 1.92s 2.08s
% Output : Refutation 1.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of clauses : 22 ( 15 unt; 2 nHn; 19 RR)
% Number of literals : 33 ( 11 equ; 15 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 15 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
( ~ relation(A)
| ~ in(B,A)
| B = ordered_pair(dollar_f2(A,B),dollar_f1(A,B)) ),
file('SEU186+1.p',unknown),
[] ).
cnf(4,plain,
( ~ relation(A)
| ~ in(B,A)
| ordered_pair(dollar_f2(A,B),dollar_f1(A,B)) = B ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[3])]),
[iquote('copy,3,flip.3')] ).
cnf(12,axiom,
( ~ element(A,B)
| empty(B)
| in(A,B) ),
file('SEU186+1.p',unknown),
[] ).
cnf(13,axiom,
~ in(ordered_pair(A,B),dollar_c5),
file('SEU186+1.p',unknown),
[] ).
cnf(14,axiom,
dollar_c5 != empty_set,
file('SEU186+1.p',unknown),
[] ).
cnf(15,plain,
empty_set != dollar_c5,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[14])]),
[iquote('copy,14,flip.1')] ).
cnf(16,axiom,
( ~ empty(A)
| A = empty_set ),
file('SEU186+1.p',unknown),
[] ).
cnf(18,axiom,
( ~ empty(A)
| A = B
| ~ empty(B) ),
file('SEU186+1.p',unknown),
[] ).
cnf(21,axiom,
A = A,
file('SEU186+1.p',unknown),
[] ).
cnf(27,axiom,
element(dollar_f4(A),A),
file('SEU186+1.p',unknown),
[] ).
cnf(28,axiom,
empty(empty_set),
file('SEU186+1.p',unknown),
[] ).
cnf(30,axiom,
empty(dollar_c1),
file('SEU186+1.p',unknown),
[] ).
cnf(34,axiom,
relation(dollar_c5),
file('SEU186+1.p',unknown),
[] ).
cnf(36,plain,
empty_set = dollar_c1,
inference(hyper,[status(thm)],[30,18,28]),
[iquote('hyper,30,18,28')] ).
cnf(37,plain,
( ~ empty(A)
| A = dollar_c1 ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[16]),36]),
[iquote('back_demod,16,demod,36')] ).
cnf(38,plain,
dollar_c5 != dollar_c1,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[15]),36])]),
[iquote('back_demod,15,demod,36,flip.1')] ).
cnf(43,plain,
( empty(A)
| in(dollar_f4(A),A) ),
inference(hyper,[status(thm)],[27,12]),
[iquote('hyper,27,12')] ).
cnf(46,plain,
~ empty(dollar_c5),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[37,38]),21]),
[iquote('para_from,37.2.1,38.1.1,unit_del,21')] ).
cnf(57,plain,
in(dollar_f4(dollar_c5),dollar_c5),
inference(hyper,[status(thm)],[43,46]),
[iquote('hyper,43,46')] ).
cnf(69,plain,
ordered_pair(dollar_f2(dollar_c5,dollar_f4(dollar_c5)),dollar_f1(dollar_c5,dollar_f4(dollar_c5))) = dollar_f4(dollar_c5),
inference(hyper,[status(thm)],[57,4,34]),
[iquote('hyper,57,4,34')] ).
cnf(423,plain,
~ in(dollar_f4(dollar_c5),dollar_c5),
inference(para_from,[status(thm),theory(equality)],[69,13]),
[iquote('para_from,69.1.1,13.1.1')] ).
cnf(424,plain,
$false,
inference(binary,[status(thm)],[423,57]),
[iquote('binary,423.1,57.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU186+1 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 07:56:14 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.83/2.03 ----- Otter 3.3f, August 2004 -----
% 1.83/2.03 The process was started by sandbox2 on n029.cluster.edu,
% 1.83/2.03 Wed Jul 27 07:56:14 2022
% 1.83/2.03 The command was "./otter". The process ID is 22271.
% 1.83/2.03
% 1.83/2.03 set(prolog_style_variables).
% 1.83/2.03 set(auto).
% 1.83/2.03 dependent: set(auto1).
% 1.83/2.03 dependent: set(process_input).
% 1.83/2.03 dependent: clear(print_kept).
% 1.83/2.03 dependent: clear(print_new_demod).
% 1.83/2.03 dependent: clear(print_back_demod).
% 1.83/2.03 dependent: clear(print_back_sub).
% 1.83/2.03 dependent: set(control_memory).
% 1.83/2.03 dependent: assign(max_mem, 12000).
% 1.83/2.03 dependent: assign(pick_given_ratio, 4).
% 1.83/2.03 dependent: assign(stats_level, 1).
% 1.83/2.03 dependent: assign(max_seconds, 10800).
% 1.83/2.03 clear(print_given).
% 1.83/2.03
% 1.83/2.03 formula_list(usable).
% 1.83/2.03 all A (A=A).
% 1.83/2.03 all A B (in(A,B)-> -in(B,A)).
% 1.83/2.03 all A (empty(A)->relation(A)).
% 1.83/2.03 all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 1.83/2.03 all A (relation(A)<-> (all B (-(in(B,A)& (all C D (B!=ordered_pair(C,D))))))).
% 1.83/2.03 all A B (ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A))).
% 1.83/2.03 $T.
% 1.83/2.03 $T.
% 1.83/2.03 $T.
% 1.83/2.03 $T.
% 1.83/2.03 $T.
% 1.83/2.03 all A exists B element(B,A).
% 1.83/2.03 empty(empty_set).
% 1.83/2.03 all A B (-empty(ordered_pair(A,B))).
% 1.83/2.03 all A (-empty(singleton(A))).
% 1.83/2.03 all A B (-empty(unordered_pair(A,B))).
% 1.83/2.03 empty(empty_set).
% 1.83/2.03 relation(empty_set).
% 1.83/2.03 exists A (empty(A)&relation(A)).
% 1.83/2.03 exists A empty(A).
% 1.83/2.03 exists A (-empty(A)&relation(A)).
% 1.83/2.03 exists A (-empty(A)).
% 1.83/2.03 all A B (in(A,B)->element(A,B)).
% 1.83/2.03 all A B (element(A,B)->empty(B)|in(A,B)).
% 1.83/2.03 -(all A (relation(A)-> ((all B C (-in(ordered_pair(B,C),A)))->A=empty_set))).
% 1.83/2.03 all A (empty(A)->A=empty_set).
% 1.83/2.03 all A B (-(in(A,B)&empty(B))).
% 1.83/2.03 all A B (-(empty(A)&A!=B&empty(B))).
% 1.83/2.03 end_of_list.
% 1.83/2.03
% 1.83/2.03 -------> usable clausifies to:
% 1.83/2.03
% 1.83/2.03 list(usable).
% 1.83/2.03 0 [] A=A.
% 1.83/2.03 0 [] -in(A,B)| -in(B,A).
% 1.83/2.03 0 [] -empty(A)|relation(A).
% 1.83/2.03 0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.83/2.03 0 [] -relation(A)| -in(B,A)|B=ordered_pair($f2(A,B),$f1(A,B)).
% 1.83/2.03 0 [] relation(A)|in($f3(A),A).
% 1.83/2.03 0 [] relation(A)|$f3(A)!=ordered_pair(C,D).
% 1.83/2.03 0 [] ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A)).
% 1.83/2.03 0 [] $T.
% 1.83/2.03 0 [] $T.
% 1.83/2.03 0 [] $T.
% 1.83/2.03 0 [] $T.
% 1.83/2.03 0 [] $T.
% 1.83/2.03 0 [] element($f4(A),A).
% 1.83/2.03 0 [] empty(empty_set).
% 1.83/2.03 0 [] -empty(ordered_pair(A,B)).
% 1.83/2.03 0 [] -empty(singleton(A)).
% 1.83/2.03 0 [] -empty(unordered_pair(A,B)).
% 1.83/2.03 0 [] empty(empty_set).
% 1.83/2.03 0 [] relation(empty_set).
% 1.83/2.03 0 [] empty($c1).
% 1.83/2.03 0 [] relation($c1).
% 1.83/2.03 0 [] empty($c2).
% 1.83/2.03 0 [] -empty($c3).
% 1.83/2.03 0 [] relation($c3).
% 1.83/2.03 0 [] -empty($c4).
% 1.83/2.03 0 [] -in(A,B)|element(A,B).
% 1.83/2.03 0 [] -element(A,B)|empty(B)|in(A,B).
% 1.83/2.03 0 [] relation($c5).
% 1.83/2.03 0 [] -in(ordered_pair(B,C),$c5).
% 1.83/2.03 0 [] $c5!=empty_set.
% 1.83/2.03 0 [] -empty(A)|A=empty_set.
% 1.83/2.03 0 [] -in(A,B)| -empty(B).
% 1.83/2.03 0 [] -empty(A)|A=B| -empty(B).
% 1.83/2.03 end_of_list.
% 1.83/2.03
% 1.83/2.03 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.83/2.03
% 1.83/2.03 This ia a non-Horn set with equality. The strategy will be
% 1.83/2.03 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.83/2.03 deletion, with positive clauses in sos and nonpositive
% 1.83/2.03 clauses in usable.
% 1.83/2.03
% 1.83/2.03 dependent: set(knuth_bendix).
% 1.83/2.03 dependent: set(anl_eq).
% 1.83/2.03 dependent: set(para_from).
% 1.83/2.03 dependent: set(para_into).
% 1.83/2.03 dependent: clear(para_from_right).
% 1.83/2.03 dependent: clear(para_into_right).
% 1.83/2.03 dependent: set(para_from_vars).
% 1.83/2.03 dependent: set(eq_units_both_ways).
% 1.83/2.03 dependent: set(dynamic_demod_all).
% 1.83/2.03 dependent: set(dynamic_demod).
% 1.83/2.03 dependent: set(order_eq).
% 1.83/2.03 dependent: set(back_demod).
% 1.83/2.03 dependent: set(lrpo).
% 1.83/2.03 dependent: set(hyper_res).
% 1.83/2.03 dependent: set(unit_deletion).
% 1.83/2.03 dependent: set(factor).
% 1.83/2.03
% 1.83/2.03 ------------> process usable:
% 1.83/2.03 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.83/2.03 ** KEPT (pick-wt=4): 2 [] -empty(A)|relation(A).
% 1.83/2.03 ** KEPT (pick-wt=14): 4 [copy,3,flip.3] -relation(A)| -in(B,A)|ordered_pair($f2(A,B),$f1(A,B))=B.
% 1.83/2.03 ** KEPT (pick-wt=8): 5 [] relation(A)|$f3(A)!=ordered_pair(B,C).
% 1.83/2.03 ** KEPT (pick-wt=4): 6 [] -empty(ordered_pair(A,B)).
% 1.83/2.03 ** KEPT (pick-wt=3): 7 [] -empty(singleton(A)).
% 1.83/2.03 ** KEPT (pick-wt=4): 8 [] -empty(unordered_pair(A,B)).
% 1.83/2.03 ** KEPT (pick-wt=2): 9 [] -empty($c3).
% 1.83/2.03 ** KEPT (pick-wt=2): 10 [] -empty($c4).
% 1.83/2.03 ** KEPT (pick-wt=6): 11 [] -in(A,B)|element(A,B).
% 1.83/2.03 ** KEPT (pick-wt=8): 12 [] -element(A,B)|empty(B)|in(A,B).
% 1.83/2.03 ** KEPT (pick-wt=5): 13 [] -in(ordered_pair(A,B),$c5).
% 1.83/2.03 ** KEPT (pick-wt=3): 15 [copy,14,flip.1] empty_set!=$c5.
% 1.83/2.03 ** KEPT (pick-wt=5): 16 [] -empty(A)|A=empty_set.
% 1.83/2.03 ** KEPT (pick-wt=5): 17 [] -in(A,B)| -empty(B).
% 1.83/2.03 ** KEPT (pick-wt=7): 18 [] -empty(A)|A=B| -empty(B).
% 1.92/2.08
% 1.92/2.08 ------------> process sos:
% 1.92/2.08 ** KEPT (pick-wt=3): 21 [] A=A.
% 1.92/2.08 ** KEPT (pick-wt=7): 22 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.92/2.08 ** KEPT (pick-wt=6): 23 [] relation(A)|in($f3(A),A).
% 1.92/2.08 ** KEPT (pick-wt=10): 25 [copy,24,flip.1] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 1.92/2.08 ---> New Demodulator: 26 [new_demod,25] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 1.92/2.08 ** KEPT (pick-wt=4): 27 [] element($f4(A),A).
% 1.92/2.08 ** KEPT (pick-wt=2): 28 [] empty(empty_set).
% 1.92/2.08 Following clause subsumed by 28 during input processing: 0 [] empty(empty_set).
% 1.92/2.08 ** KEPT (pick-wt=2): 29 [] relation(empty_set).
% 1.92/2.08 ** KEPT (pick-wt=2): 30 [] empty($c1).
% 1.92/2.08 ** KEPT (pick-wt=2): 31 [] relation($c1).
% 1.92/2.08 ** KEPT (pick-wt=2): 32 [] empty($c2).
% 1.92/2.08 ** KEPT (pick-wt=2): 33 [] relation($c3).
% 1.92/2.08 ** KEPT (pick-wt=2): 34 [] relation($c5).
% 1.92/2.08 Following clause subsumed by 21 during input processing: 0 [copy,21,flip.1] A=A.
% 1.92/2.08 21 back subsumes 20.
% 1.92/2.08 Following clause subsumed by 22 during input processing: 0 [copy,22,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 1.92/2.08 >>>> Starting back demodulation with 26.
% 1.92/2.08
% 1.92/2.08 ======= end of input processing =======
% 1.92/2.08
% 1.92/2.08 =========== start of search ===========
% 1.92/2.08
% 1.92/2.08 -------- PROOF --------
% 1.92/2.08
% 1.92/2.08 ----> UNIT CONFLICT at 0.06 sec ----> 424 [binary,423.1,57.1] $F.
% 1.92/2.08
% 1.92/2.08 Length of proof is 10. Level of proof is 6.
% 1.92/2.08
% 1.92/2.08 ---------------- PROOF ----------------
% 1.92/2.08 % SZS status Theorem
% 1.92/2.08 % SZS output start Refutation
% See solution above
% 1.92/2.08 ------------ end of proof -------------
% 1.92/2.08
% 1.92/2.08
% 1.92/2.08 Search stopped by max_proofs option.
% 1.92/2.08
% 1.92/2.08
% 1.92/2.08 Search stopped by max_proofs option.
% 1.92/2.08
% 1.92/2.08 ============ end of search ============
% 1.92/2.08
% 1.92/2.08 -------------- statistics -------------
% 1.92/2.08 clauses given 66
% 1.92/2.08 clauses generated 1636
% 1.92/2.08 clauses kept 402
% 1.92/2.08 clauses forward subsumed 1275
% 1.92/2.08 clauses back subsumed 5
% 1.92/2.08 Kbytes malloced 2929
% 1.92/2.08
% 1.92/2.08 ----------- times (seconds) -----------
% 1.92/2.08 user CPU time 0.06 (0 hr, 0 min, 0 sec)
% 1.92/2.08 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.92/2.08 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.92/2.08
% 1.92/2.08 That finishes the proof of the theorem.
% 1.92/2.08
% 1.92/2.08 Process 22271 finished Wed Jul 27 07:56:16 2022
% 1.92/2.08 Otter interrupted
% 1.92/2.08 PROOF FOUND
%------------------------------------------------------------------------------