TSTP Solution File: SET899+1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET899+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n018.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 1.80s
% Output : Refutation 1.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of clauses : 7 ( 5 unt; 2 nHn; 5 RR)
% Number of literals : 10 ( 0 equ; 3 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 4 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
~ in(dollar_c3,dollar_c5),
file('SET899+1.p',unknown),
[] ).
cnf(4,axiom,
~ subset(dollar_c5,set_difference(dollar_c4,singleton(dollar_c3))),
file('SET899+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ subset(A,B)
| in(C,A)
| subset(A,set_difference(B,singleton(C))) ),
file('SET899+1.p',unknown),
[] ).
cnf(9,axiom,
subset(dollar_c5,dollar_c4),
file('SET899+1.p',unknown),
[] ).
cnf(11,plain,
( in(A,dollar_c5)
| subset(dollar_c5,set_difference(dollar_c4,singleton(A))) ),
inference(hyper,[status(thm)],[9,5]),
[iquote('hyper,9,5')] ).
cnf(15,plain,
in(dollar_c3,dollar_c5),
inference(hyper,[status(thm)],[11,4]),
[iquote('hyper,11,4')] ).
cnf(16,plain,
$false,
inference(binary,[status(thm)],[15,3]),
[iquote('binary,15.1,3.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET899+1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n018.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 10:34:46 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.57/1.80 ----- Otter 3.3f, August 2004 -----
% 1.57/1.80 The process was started by sandbox on n018.cluster.edu,
% 1.57/1.80 Wed Jul 27 10:34:46 2022
% 1.57/1.80 The command was "./otter". The process ID is 23919.
% 1.57/1.80
% 1.57/1.80 set(prolog_style_variables).
% 1.57/1.80 set(auto).
% 1.57/1.80 dependent: set(auto1).
% 1.57/1.80 dependent: set(process_input).
% 1.57/1.80 dependent: clear(print_kept).
% 1.57/1.80 dependent: clear(print_new_demod).
% 1.57/1.80 dependent: clear(print_back_demod).
% 1.57/1.80 dependent: clear(print_back_sub).
% 1.57/1.80 dependent: set(control_memory).
% 1.57/1.80 dependent: assign(max_mem, 12000).
% 1.57/1.80 dependent: assign(pick_given_ratio, 4).
% 1.57/1.80 dependent: assign(stats_level, 1).
% 1.57/1.80 dependent: assign(max_seconds, 10800).
% 1.57/1.80 clear(print_given).
% 1.57/1.80
% 1.57/1.80 formula_list(usable).
% 1.57/1.80 all A B subset(A,A).
% 1.57/1.80 all A B (in(A,B)-> -in(B,A)).
% 1.57/1.80 exists A empty(A).
% 1.57/1.80 exists A (-empty(A)).
% 1.57/1.80 -(all A B C (subset(A,B)->in(C,A)|subset(A,set_difference(B,singleton(C))))).
% 1.57/1.80 all A B C (subset(A,B)->in(C,A)|subset(A,set_difference(B,singleton(C)))).
% 1.57/1.80 end_of_list.
% 1.57/1.80
% 1.57/1.80 -------> usable clausifies to:
% 1.57/1.80
% 1.57/1.80 list(usable).
% 1.57/1.80 0 [] subset(A,A).
% 1.57/1.80 0 [] -in(A,B)| -in(B,A).
% 1.57/1.80 0 [] empty($c1).
% 1.57/1.80 0 [] -empty($c2).
% 1.57/1.80 0 [] subset($c5,$c4).
% 1.57/1.80 0 [] -in($c3,$c5).
% 1.57/1.80 0 [] -subset($c5,set_difference($c4,singleton($c3))).
% 1.57/1.80 0 [] -subset(A,B)|in(C,A)|subset(A,set_difference(B,singleton(C))).
% 1.57/1.80 end_of_list.
% 1.57/1.80
% 1.57/1.80 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=3.
% 1.57/1.80
% 1.57/1.80 This is a non-Horn set without equality. The strategy will
% 1.57/1.80 be ordered hyper_res, unit deletion, and factoring, with
% 1.57/1.80 satellites in sos and with nuclei in usable.
% 1.57/1.80
% 1.57/1.80 dependent: set(hyper_res).
% 1.57/1.80 dependent: set(factor).
% 1.57/1.80 dependent: set(unit_deletion).
% 1.57/1.80
% 1.57/1.80 ------------> process usable:
% 1.57/1.80 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.57/1.80 ** KEPT (pick-wt=2): 2 [] -empty($c2).
% 1.57/1.80 ** KEPT (pick-wt=3): 3 [] -in($c3,$c5).
% 1.57/1.80 ** KEPT (pick-wt=6): 4 [] -subset($c5,set_difference($c4,singleton($c3))).
% 1.57/1.80 ** KEPT (pick-wt=12): 5 [] -subset(A,B)|in(C,A)|subset(A,set_difference(B,singleton(C))).
% 1.57/1.80
% 1.57/1.80 ------------> process sos:
% 1.57/1.80 ** KEPT (pick-wt=3): 7 [] subset(A,A).
% 1.57/1.80 ** KEPT (pick-wt=2): 8 [] empty($c1).
% 1.57/1.80 ** KEPT (pick-wt=3): 9 [] subset($c5,$c4).
% 1.57/1.80
% 1.57/1.80 ======= end of input processing =======
% 1.57/1.80
% 1.57/1.80 =========== start of search ===========
% 1.57/1.80
% 1.57/1.80 -------- PROOF --------
% 1.57/1.80
% 1.57/1.80 ----> UNIT CONFLICT at 0.00 sec ----> 16 [binary,15.1,3.1] $F.
% 1.57/1.80
% 1.57/1.80 Length of proof is 2. Level of proof is 2.
% 1.57/1.80
% 1.57/1.80 ---------------- PROOF ----------------
% 1.57/1.80 % SZS status Theorem
% 1.57/1.80 % SZS output start Refutation
% See solution above
% 1.57/1.80 ------------ end of proof -------------
% 1.57/1.80
% 1.57/1.80
% 1.57/1.80 Search stopped by max_proofs option.
% 1.57/1.80
% 1.57/1.80
% 1.57/1.80 Search stopped by max_proofs option.
% 1.57/1.80
% 1.57/1.80 ============ end of search ============
% 1.57/1.80
% 1.57/1.80 -------------- statistics -------------
% 1.57/1.80 clauses given 5
% 1.57/1.80 clauses generated 7
% 1.57/1.80 clauses kept 15
% 1.57/1.80 clauses forward subsumed 0
% 1.57/1.80 clauses back subsumed 0
% 1.57/1.80 Kbytes malloced 976
% 1.57/1.80
% 1.57/1.80 ----------- times (seconds) -----------
% 1.57/1.80 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.57/1.80 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.57/1.80 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.57/1.80
% 1.57/1.80 That finishes the proof of the theorem.
% 1.57/1.80
% 1.57/1.80 Process 23919 finished Wed Jul 27 10:34:48 2022
% 1.57/1.80 Otter interrupted
% 1.57/1.80 PROOF FOUND
%------------------------------------------------------------------------------