%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET589+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n003.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 13:13:45 EDT 2022
% Result : Theorem 1.70s 1.89s
% Output : Refutation 1.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 6
% Syntax : Number of clauses : 10 ( 7 unt; 0 nHn; 6 RR)
% Number of literals : 14 ( 0 equ; 5 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 11 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ subset(A,B)
| ~ subset(B,C)
| subset(A,C) ),
file('SET589+3.p',unknown),
[] ).
cnf(2,axiom,
( ~ subset(A,B)
| subset(difference(A,C),difference(B,C)) ),
file('SET589+3.p',unknown),
[] ).
cnf(3,axiom,
( ~ subset(A,B)
| subset(difference(C,B),difference(C,A)) ),
file('SET589+3.p',unknown),
[] ).
cnf(9,axiom,
~ subset(difference(dollar_c4,dollar_c1),difference(dollar_c3,dollar_c2)),
file('SET589+3.p',unknown),
[] ).
cnf(12,axiom,
subset(dollar_c4,dollar_c3),
file('SET589+3.p',unknown),
[] ).
cnf(13,axiom,
subset(dollar_c2,dollar_c1),
file('SET589+3.p',unknown),
[] ).
cnf(19,plain,
subset(difference(dollar_c4,A),difference(dollar_c3,A)),
inference(hyper,[status(thm)],[12,2]),
[iquote('hyper,12,2')] ).
cnf(22,plain,
subset(difference(A,dollar_c1),difference(A,dollar_c2)),
inference(hyper,[status(thm)],[13,3]),
[iquote('hyper,13,3')] ).
cnf(42,plain,
subset(difference(dollar_c4,dollar_c1),difference(dollar_c3,dollar_c2)),
inference(hyper,[status(thm)],[22,1,19]),
[iquote('hyper,22,1,19')] ).
cnf(43,plain,
$false,
inference(binary,[status(thm)],[42,9]),
[iquote('binary,42.1,9.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET589+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n003.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 10:39:41 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.70/1.89 ----- Otter 3.3f, August 2004 -----
% 1.70/1.89 The process was started by sandbox on n003.cluster.edu,
% 1.70/1.89 Wed Jul 27 10:39:41 2022
% 1.70/1.89 The command was "./otter". The process ID is 17517.
% 1.70/1.89
% 1.70/1.89 set(prolog_style_variables).
% 1.70/1.89 set(auto).
% 1.70/1.89 dependent: set(auto1).
% 1.70/1.89 dependent: set(process_input).
% 1.70/1.89 dependent: clear(print_kept).
% 1.70/1.89 dependent: clear(print_new_demod).
% 1.70/1.89 dependent: clear(print_back_demod).
% 1.70/1.89 dependent: clear(print_back_sub).
% 1.70/1.89 dependent: set(control_memory).
% 1.70/1.89 dependent: assign(max_mem, 12000).
% 1.70/1.89 dependent: assign(pick_given_ratio, 4).
% 1.70/1.89 dependent: assign(stats_level, 1).
% 1.70/1.89 dependent: assign(max_seconds, 10800).
% 1.70/1.89 clear(print_given).
% 1.70/1.89
% 1.70/1.89 formula_list(usable).
% 1.70/1.89 all B C D (subset(B,C)&subset(C,D)->subset(B,D)).
% 1.70/1.89 all B C D (subset(B,C)->subset(difference(B,D),difference(C,D))).
% 1.70/1.89 all B C D (subset(B,C)->subset(difference(D,C),difference(D,B))).
% 1.70/1.89 all B C D (member(D,difference(B,C))<->member(D,B)& -member(D,C)).
% 1.70/1.89 all B C (subset(B,C)<-> (all D (member(D,B)->member(D,C)))).
% 1.70/1.89 all B subset(B,B).
% 1.70/1.89 -(all B C D E (subset(B,C)&subset(D,E)->subset(difference(B,E),difference(C,D)))).
% 1.70/1.89 end_of_list.
% 1.70/1.89
% 1.70/1.89 -------> usable clausifies to:
% 1.70/1.89
% 1.70/1.89 list(usable).
% 1.70/1.89 0 [] -subset(B,C)| -subset(C,D)|subset(B,D).
% 1.70/1.89 0 [] -subset(B,C)|subset(difference(B,D),difference(C,D)).
% 1.70/1.89 0 [] -subset(B,C)|subset(difference(D,C),difference(D,B)).
% 1.70/1.89 0 [] -member(D,difference(B,C))|member(D,B).
% 1.70/1.89 0 [] -member(D,difference(B,C))| -member(D,C).
% 1.70/1.89 0 [] member(D,difference(B,C))| -member(D,B)|member(D,C).
% 1.70/1.89 0 [] -subset(B,C)| -member(D,B)|member(D,C).
% 1.70/1.89 0 [] subset(B,C)|member($f1(B,C),B).
% 1.70/1.89 0 [] subset(B,C)| -member($f1(B,C),C).
% 1.70/1.89 0 [] subset(B,B).
% 1.70/1.89 0 [] subset($c4,$c3).
% 1.70/1.89 0 [] subset($c2,$c1).
% 1.70/1.89 0 [] -subset(difference($c4,$c1),difference($c3,$c2)).
% 1.70/1.89 end_of_list.
% 1.70/1.89
% 1.70/1.89 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=3.
% 1.70/1.89
% 1.70/1.89 This is a non-Horn set without equality. The strategy will
% 1.70/1.89 be ordered hyper_res, unit deletion, and factoring, with
% 1.70/1.89 satellites in sos and with nuclei in usable.
% 1.70/1.89
% 1.70/1.89 dependent: set(hyper_res).
% 1.70/1.89 dependent: set(factor).
% 1.70/1.89 dependent: set(unit_deletion).
% 1.70/1.89
% 1.70/1.89 ------------> process usable:
% 1.70/1.89 ** KEPT (pick-wt=9): 1 [] -subset(A,B)| -subset(B,C)|subset(A,C).
% 1.70/1.89 ** KEPT (pick-wt=10): 2 [] -subset(A,B)|subset(difference(A,C),difference(B,C)).
% 1.70/1.89 ** KEPT (pick-wt=10): 3 [] -subset(A,B)|subset(difference(C,B),difference(C,A)).
% 1.70/1.89 ** KEPT (pick-wt=8): 4 [] -member(A,difference(B,C))|member(A,B).
% 1.70/1.89 ** KEPT (pick-wt=8): 5 [] -member(A,difference(B,C))| -member(A,C).
% 1.70/1.89 ** KEPT (pick-wt=11): 6 [] member(A,difference(B,C))| -member(A,B)|member(A,C).
% 1.70/1.89 ** KEPT (pick-wt=9): 7 [] -subset(A,B)| -member(C,A)|member(C,B).
% 1.70/1.89 ** KEPT (pick-wt=8): 8 [] subset(A,B)| -member($f1(A,B),B).
% 1.70/1.89 ** KEPT (pick-wt=7): 9 [] -subset(difference($c4,$c1),difference($c3,$c2)).
% 1.70/1.89
% 1.70/1.89 ------------> process sos:
% 1.70/1.89 ** KEPT (pick-wt=8): 10 [] subset(A,B)|member($f1(A,B),A).
% 1.70/1.89 ** KEPT (pick-wt=3): 11 [] subset(A,A).
% 1.70/1.89 ** KEPT (pick-wt=3): 12 [] subset($c4,$c3).
% 1.70/1.89 ** KEPT (pick-wt=3): 13 [] subset($c2,$c1).
% 1.70/1.89
% 1.70/1.89 ======= end of input processing =======
% 1.70/1.89
% 1.70/1.89 =========== start of search ===========
% 1.70/1.89
% 1.70/1.89 -------- PROOF --------
% 1.70/1.89
% 1.70/1.89 ----> UNIT CONFLICT at 0.00 sec ----> 43 [binary,42.1,9.1] $F.
% 1.70/1.89
% 1.70/1.89 Length of proof is 3. Level of proof is 2.
% 1.70/1.89
% 1.70/1.89 ---------------- PROOF ----------------
% 1.70/1.89 % SZS status Theorem
% 1.70/1.89 % SZS output start Refutation
% See solution above
% 1.70/1.89 ------------ end of proof -------------
% 1.70/1.89
% 1.70/1.89
% 1.70/1.89 Search stopped by max_proofs option.
% 1.70/1.89
% 1.70/1.89
% 1.70/1.89 Search stopped by max_proofs option.
% 1.70/1.89
% 1.70/1.89 ============ end of search ============
% 1.70/1.89
% 1.70/1.89 -------------- statistics -------------
% 1.70/1.89 clauses given 8
% 1.70/1.89 clauses generated 48
% 1.70/1.89 clauses kept 42
% 1.70/1.89 clauses forward subsumed 18
% 1.70/1.89 clauses back subsumed 0
% 1.70/1.89 Kbytes malloced 976
% 1.70/1.89
% 1.70/1.89 ----------- times (seconds) -----------
% 1.70/1.89 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.70/1.89 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.70/1.89 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.70/1.89
% 1.70/1.89 That finishes the proof of the theorem.
% 1.70/1.89
% 1.70/1.89 Process 17517 finished Wed Jul 27 10:39:43 2022
% 1.70/1.89 Otter interrupted
% 1.70/1.89 PROOF FOUND
%------------------------------------------------------------------------------