TSTP Solution File: SET900+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET900+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n015.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 13:14:29 EDT 2022
% Result : Theorem 1.57s 2.14s
% Output : Refutation 1.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of clauses : 9 ( 5 unt; 3 nHn; 7 RR)
% Number of literals : 15 ( 12 equ; 6 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 6 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
dollar_c4 != singleton(dollar_c3),
file('SET900+1.p',unknown),
[] ).
cnf(4,plain,
singleton(dollar_c3) != dollar_c4,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[3])]),
[iquote('copy,3,flip.1')] ).
cnf(5,axiom,
dollar_c4 != empty_set,
file('SET900+1.p',unknown),
[] ).
cnf(6,plain,
empty_set != dollar_c4,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[5])]),
[iquote('copy,5,flip.1')] ).
cnf(7,axiom,
( ~ in(A,dollar_c4)
| A = dollar_c3 ),
file('SET900+1.p',unknown),
[] ).
cnf(8,axiom,
( A = singleton(B)
| A = empty_set
| dollar_f1(A,B) != B ),
file('SET900+1.p',unknown),
[] ).
cnf(13,axiom,
( A = singleton(B)
| A = empty_set
| in(dollar_f1(A,B),A) ),
file('SET900+1.p',unknown),
[] ).
cnf(22,plain,
( singleton(A) = dollar_c4
| dollar_f1(dollar_c4,A) = dollar_c3 ),
inference(flip,[status(thm),theory(equality)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[13,7]),6])]),
[iquote('hyper,13,7,unit_del,6,flip.1')] ).
cnf(45,plain,
$false,
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[22,8]),4,4,6]),
[iquote('hyper,22,8,unit_del,4,4,6')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET900+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n015.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 10:41:42 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.57/2.14 ----- Otter 3.3f, August 2004 -----
% 1.57/2.14 The process was started by sandbox2 on n015.cluster.edu,
% 1.57/2.14 Wed Jul 27 10:41:42 2022
% 1.57/2.14 The command was "./otter". The process ID is 2920.
% 1.57/2.14
% 1.57/2.14 set(prolog_style_variables).
% 1.57/2.14 set(auto).
% 1.57/2.14 dependent: set(auto1).
% 1.57/2.14 dependent: set(process_input).
% 1.57/2.14 dependent: clear(print_kept).
% 1.57/2.14 dependent: clear(print_new_demod).
% 1.57/2.14 dependent: clear(print_back_demod).
% 1.57/2.14 dependent: clear(print_back_sub).
% 1.57/2.14 dependent: set(control_memory).
% 1.57/2.14 dependent: assign(max_mem, 12000).
% 1.57/2.14 dependent: assign(pick_given_ratio, 4).
% 1.57/2.14 dependent: assign(stats_level, 1).
% 1.57/2.14 dependent: assign(max_seconds, 10800).
% 1.57/2.14 clear(print_given).
% 1.57/2.14
% 1.57/2.14 formula_list(usable).
% 1.57/2.14 all A (A=A).
% 1.57/2.14 all A B (in(A,B)-> -in(B,A)).
% 1.57/2.14 empty(empty_set).
% 1.57/2.14 exists A empty(A).
% 1.57/2.14 exists A (-empty(A)).
% 1.57/2.14 -(all A B (-(A!=singleton(B)&A!=empty_set& (all C (-(in(C,A)&C!=B)))))).
% 1.57/2.14 all A B (-(A!=singleton(B)&A!=empty_set& (all C (-(in(C,A)&C!=B))))).
% 1.57/2.14 end_of_list.
% 1.57/2.14
% 1.57/2.14 -------> usable clausifies to:
% 1.57/2.14
% 1.57/2.14 list(usable).
% 1.57/2.14 0 [] A=A.
% 1.57/2.14 0 [] -in(A,B)| -in(B,A).
% 1.57/2.14 0 [] empty(empty_set).
% 1.57/2.14 0 [] empty($c1).
% 1.57/2.14 0 [] -empty($c2).
% 1.57/2.14 0 [] $c4!=singleton($c3).
% 1.57/2.14 0 [] $c4!=empty_set.
% 1.57/2.14 0 [] -in(C,$c4)|C=$c3.
% 1.57/2.14 0 [] A=singleton(B)|A=empty_set|in($f1(A,B),A).
% 1.57/2.14 0 [] A=singleton(B)|A=empty_set|$f1(A,B)!=B.
% 1.57/2.14 end_of_list.
% 1.57/2.14
% 1.57/2.14 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.57/2.14
% 1.57/2.14 This ia a non-Horn set with equality. The strategy will be
% 1.57/2.14 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.57/2.14 deletion, with positive clauses in sos and nonpositive
% 1.57/2.14 clauses in usable.
% 1.57/2.14
% 1.57/2.14 dependent: set(knuth_bendix).
% 1.57/2.14 dependent: set(anl_eq).
% 1.57/2.14 dependent: set(para_from).
% 1.57/2.14 dependent: set(para_into).
% 1.57/2.14 dependent: clear(para_from_right).
% 1.57/2.14 dependent: clear(para_into_right).
% 1.57/2.14 dependent: set(para_from_vars).
% 1.57/2.14 dependent: set(eq_units_both_ways).
% 1.57/2.14 dependent: set(dynamic_demod_all).
% 1.57/2.14 dependent: set(dynamic_demod).
% 1.57/2.14 dependent: set(order_eq).
% 1.57/2.14 dependent: set(back_demod).
% 1.57/2.14 dependent: set(lrpo).
% 1.57/2.14 dependent: set(hyper_res).
% 1.57/2.14 dependent: set(unit_deletion).
% 1.57/2.14 dependent: set(factor).
% 1.57/2.14
% 1.57/2.14 ------------> process usable:
% 1.57/2.14 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.57/2.14 ** KEPT (pick-wt=2): 2 [] -empty($c2).
% 1.57/2.14 ** KEPT (pick-wt=4): 4 [copy,3,flip.1] singleton($c3)!=$c4.
% 1.57/2.14 ** KEPT (pick-wt=3): 6 [copy,5,flip.1] empty_set!=$c4.
% 1.57/2.14 ** KEPT (pick-wt=6): 7 [] -in(A,$c4)|A=$c3.
% 1.57/2.14 ** KEPT (pick-wt=12): 8 [] A=singleton(B)|A=empty_set|$f1(A,B)!=B.
% 1.57/2.14
% 1.57/2.14 ------------> process sos:
% 1.57/2.14 ** KEPT (pick-wt=3): 10 [] A=A.
% 1.57/2.14 ** KEPT (pick-wt=2): 11 [] empty(empty_set).
% 1.57/2.14 ** KEPT (pick-wt=2): 12 [] empty($c1).
% 1.57/2.14 ** KEPT (pick-wt=12): 13 [] A=singleton(B)|A=empty_set|in($f1(A,B),A).
% 1.57/2.14 Following clause subsumed by 10 during input processing: 0 [copy,10,flip.1] A=A.
% 1.57/2.14
% 1.57/2.14 ======= end of input processing =======
% 1.57/2.14
% 1.57/2.14 =========== start of search ===========
% 1.57/2.14
% 1.57/2.14 -------- PROOF --------
% 1.57/2.14
% 1.57/2.14 -----> EMPTY CLAUSE at 0.00 sec ----> 45 [hyper,22,8,unit_del,4,4,6] $F.
% 1.57/2.14
% 1.57/2.14 Length of proof is 3. Level of proof is 2.
% 1.57/2.14
% 1.57/2.14 ---------------- PROOF ----------------
% 1.57/2.14 % SZS status Theorem
% 1.57/2.14 % SZS output start Refutation
% See solution above
% 1.57/2.14 ------------ end of proof -------------
% 1.57/2.14
% 1.57/2.14
% 1.57/2.14 Search stopped by max_proofs option.
% 1.57/2.14
% 1.57/2.14
% 1.57/2.14 Search stopped by max_proofs option.
% 1.57/2.14
% 1.57/2.14 ============ end of search ============
% 1.57/2.14
% 1.57/2.14 -------------- statistics -------------
% 1.57/2.14 clauses given 7
% 1.57/2.14 clauses generated 63
% 1.57/2.14 clauses kept 41
% 1.57/2.14 clauses forward subsumed 32
% 1.57/2.14 clauses back subsumed 0
% 1.57/2.14 Kbytes malloced 976
% 1.57/2.14
% 1.57/2.14 ----------- times (seconds) -----------
% 1.57/2.14 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.57/2.14 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.57/2.14 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.57/2.14
% 1.57/2.14 That finishes the proof of the theorem.
% 1.57/2.14
% 1.57/2.14 Process 2920 finished Wed Jul 27 10:41:43 2022
% 1.57/2.14 Otter interrupted
% 1.57/2.14 PROOF FOUND
%------------------------------------------------------------------------------