TSTP Solution File: SET009+3 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET009+3 : TPTP v8.1.0. Released v2.2.0.
% 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 13:12:46 EDT 2022
% Result : Theorem 1.66s 1.89s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of clauses : 16 ( 8 unt; 4 nHn; 11 RR)
% Number of literals : 26 ( 0 equ; 8 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 : 19 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ member(A,difference(B,C))
| member(A,B) ),
file('SET009+3.p',unknown),
[] ).
cnf(2,axiom,
( ~ member(A,difference(B,C))
| ~ member(A,C) ),
file('SET009+3.p',unknown),
[] ).
cnf(3,axiom,
( member(A,difference(B,C))
| ~ member(A,B)
| member(A,C) ),
file('SET009+3.p',unknown),
[] ).
cnf(4,axiom,
( ~ subset(A,B)
| ~ member(C,A)
| member(C,B) ),
file('SET009+3.p',unknown),
[] ).
cnf(5,axiom,
( subset(A,B)
| ~ member(dollar_f1(A,B),B) ),
file('SET009+3.p',unknown),
[] ).
cnf(6,axiom,
~ subset(difference(dollar_c1,dollar_c2),difference(dollar_c1,dollar_c3)),
file('SET009+3.p',unknown),
[] ).
cnf(7,axiom,
( subset(A,B)
| member(dollar_f1(A,B),A) ),
file('SET009+3.p',unknown),
[] ).
cnf(9,axiom,
subset(dollar_c3,dollar_c2),
file('SET009+3.p',unknown),
[] ).
cnf(10,plain,
member(dollar_f1(difference(dollar_c1,dollar_c2),difference(dollar_c1,dollar_c3)),difference(dollar_c1,dollar_c2)),
inference(hyper,[status(thm)],[7,6]),
[iquote('hyper,7,6')] ).
cnf(11,plain,
( member(dollar_f1(difference(dollar_c1,dollar_c2),difference(dollar_c1,dollar_c3)),A)
| member(dollar_f1(difference(dollar_c1,dollar_c2),A),difference(dollar_c1,dollar_c2)) ),
inference(hyper,[status(thm)],[10,4,7]),
[iquote('hyper,10,4,7')] ).
cnf(13,plain,
member(dollar_f1(difference(dollar_c1,dollar_c2),difference(dollar_c1,dollar_c3)),dollar_c1),
inference(hyper,[status(thm)],[10,1]),
[iquote('hyper,10,1')] ).
cnf(15,plain,
( member(dollar_f1(difference(dollar_c1,dollar_c2),difference(dollar_c1,dollar_c3)),difference(dollar_c1,A))
| member(dollar_f1(difference(dollar_c1,dollar_c2),difference(dollar_c1,dollar_c3)),A) ),
inference(hyper,[status(thm)],[13,3]),
[iquote('hyper,13,3')] ).
cnf(110,plain,
member(dollar_f1(difference(dollar_c1,dollar_c2),difference(dollar_c1,dollar_c3)),dollar_c3),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[15,5]),6]),
[iquote('hyper,15,5,unit_del,6')] ).
cnf(137,plain,
member(dollar_f1(difference(dollar_c1,dollar_c2),difference(dollar_c1,dollar_c3)),dollar_c2),
inference(hyper,[status(thm)],[110,4,9]),
[iquote('hyper,110,4,9')] ).
cnf(143,plain,
member(dollar_f1(difference(dollar_c1,dollar_c2),difference(A,dollar_c3)),difference(dollar_c1,dollar_c2)),
inference(hyper,[status(thm)],[110,2,11]),
[iquote('hyper,110,2,11')] ).
cnf(190,plain,
$false,
inference(hyper,[status(thm)],[143,2,137]),
[iquote('hyper,143,2,137')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET009+3 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n029.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 11:04:44 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.66/1.89 ----- Otter 3.3f, August 2004 -----
% 1.66/1.89 The process was started by sandbox2 on n029.cluster.edu,
% 1.66/1.89 Wed Jul 27 11:04:44 2022
% 1.66/1.89 The command was "./otter". The process ID is 1151.
% 1.66/1.89
% 1.66/1.89 set(prolog_style_variables).
% 1.66/1.89 set(auto).
% 1.66/1.89 dependent: set(auto1).
% 1.66/1.89 dependent: set(process_input).
% 1.66/1.89 dependent: clear(print_kept).
% 1.66/1.89 dependent: clear(print_new_demod).
% 1.66/1.89 dependent: clear(print_back_demod).
% 1.66/1.89 dependent: clear(print_back_sub).
% 1.66/1.89 dependent: set(control_memory).
% 1.66/1.89 dependent: assign(max_mem, 12000).
% 1.66/1.89 dependent: assign(pick_given_ratio, 4).
% 1.66/1.89 dependent: assign(stats_level, 1).
% 1.66/1.89 dependent: assign(max_seconds, 10800).
% 1.66/1.89 clear(print_given).
% 1.66/1.89
% 1.66/1.89 formula_list(usable).
% 1.66/1.89 all B C D (member(D,difference(B,C))<->member(D,B)& -member(D,C)).
% 1.66/1.89 all B C (subset(B,C)<-> (all D (member(D,B)->member(D,C)))).
% 1.66/1.89 all B subset(B,B).
% 1.66/1.89 -(all B C D (subset(B,C)->subset(difference(D,C),difference(D,B)))).
% 1.66/1.89 end_of_list.
% 1.66/1.89
% 1.66/1.89 -------> usable clausifies to:
% 1.66/1.89
% 1.66/1.89 list(usable).
% 1.66/1.89 0 [] -member(D,difference(B,C))|member(D,B).
% 1.66/1.89 0 [] -member(D,difference(B,C))| -member(D,C).
% 1.66/1.89 0 [] member(D,difference(B,C))| -member(D,B)|member(D,C).
% 1.66/1.89 0 [] -subset(B,C)| -member(D,B)|member(D,C).
% 1.66/1.89 0 [] subset(B,C)|member($f1(B,C),B).
% 1.66/1.89 0 [] subset(B,C)| -member($f1(B,C),C).
% 1.66/1.89 0 [] subset(B,B).
% 1.66/1.89 0 [] subset($c3,$c2).
% 1.66/1.89 0 [] -subset(difference($c1,$c2),difference($c1,$c3)).
% 1.66/1.89 end_of_list.
% 1.66/1.89
% 1.66/1.89 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=3.
% 1.66/1.89
% 1.66/1.89 This is a non-Horn set without equality. The strategy will
% 1.66/1.89 be ordered hyper_res, unit deletion, and factoring, with
% 1.66/1.89 satellites in sos and with nuclei in usable.
% 1.66/1.89
% 1.66/1.89 dependent: set(hyper_res).
% 1.66/1.89 dependent: set(factor).
% 1.66/1.89 dependent: set(unit_deletion).
% 1.66/1.89
% 1.66/1.89 ------------> process usable:
% 1.66/1.89 ** KEPT (pick-wt=8): 1 [] -member(A,difference(B,C))|member(A,B).
% 1.66/1.89 ** KEPT (pick-wt=8): 2 [] -member(A,difference(B,C))| -member(A,C).
% 1.66/1.89 ** KEPT (pick-wt=11): 3 [] member(A,difference(B,C))| -member(A,B)|member(A,C).
% 1.66/1.89 ** KEPT (pick-wt=9): 4 [] -subset(A,B)| -member(C,A)|member(C,B).
% 1.66/1.89 ** KEPT (pick-wt=8): 5 [] subset(A,B)| -member($f1(A,B),B).
% 1.66/1.89 ** KEPT (pick-wt=7): 6 [] -subset(difference($c1,$c2),difference($c1,$c3)).
% 1.66/1.89
% 1.66/1.89 ------------> process sos:
% 1.66/1.89 ** KEPT (pick-wt=8): 7 [] subset(A,B)|member($f1(A,B),A).
% 1.66/1.89 ** KEPT (pick-wt=3): 8 [] subset(A,A).
% 1.66/1.89 ** KEPT (pick-wt=3): 9 [] subset($c3,$c2).
% 1.66/1.89
% 1.66/1.89 ======= end of input processing =======
% 1.66/1.89
% 1.66/1.89 =========== start of search ===========
% 1.66/1.89
% 1.66/1.89 -------- PROOF --------
% 1.66/1.89
% 1.66/1.89 -----> EMPTY CLAUSE at 0.01 sec ----> 190 [hyper,143,2,137] $F.
% 1.66/1.89
% 1.66/1.89 Length of proof is 7. Level of proof is 5.
% 1.66/1.89
% 1.66/1.89 ---------------- PROOF ----------------
% 1.66/1.89 % SZS status Theorem
% 1.66/1.89 % SZS output start Refutation
% See solution above
% 1.66/1.89 ------------ end of proof -------------
% 1.66/1.89
% 1.66/1.89
% 1.66/1.89 Search stopped by max_proofs option.
% 1.66/1.89
% 1.66/1.89
% 1.66/1.89 Search stopped by max_proofs option.
% 1.66/1.89
% 1.66/1.89 ============ end of search ============
% 1.66/1.89
% 1.66/1.89 -------------- statistics -------------
% 1.66/1.89 clauses given 27
% 1.66/1.89 clauses generated 403
% 1.66/1.89 clauses kept 189
% 1.66/1.89 clauses forward subsumed 222
% 1.66/1.89 clauses back subsumed 20
% 1.66/1.89 Kbytes malloced 976
% 1.66/1.89
% 1.66/1.89 ----------- times (seconds) -----------
% 1.66/1.89 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.66/1.89 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.66/1.89 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.66/1.89
% 1.66/1.89 That finishes the proof of the theorem.
% 1.66/1.89
% 1.66/1.89 Process 1151 finished Wed Jul 27 11:04:46 2022
% 1.66/1.89 Otter interrupted
% 1.66/1.89 PROOF FOUND
%------------------------------------------------------------------------------