TSTP Solution File: SET027+3 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET027+3 : TPTP v8.1.0. Released v2.2.0.
% 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 13:12:51 EDT 2022
% Result : Theorem 1.86s 2.08s
% Output : Refutation 1.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of clauses : 11 ( 8 unt; 1 nHn; 10 RR)
% Number of literals : 15 ( 0 equ; 4 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 7 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ subset(A,B)
| ~ member(C,A)
| member(C,B) ),
file('SET027+3.p',unknown),
[] ).
cnf(2,axiom,
( subset(A,B)
| ~ member(dollar_f1(A,B),B) ),
file('SET027+3.p',unknown),
[] ).
cnf(3,axiom,
~ subset(dollar_c3,dollar_c1),
file('SET027+3.p',unknown),
[] ).
cnf(4,axiom,
( subset(A,B)
| member(dollar_f1(A,B),A) ),
file('SET027+3.p',unknown),
[] ).
cnf(6,axiom,
subset(dollar_c3,dollar_c2),
file('SET027+3.p',unknown),
[] ).
cnf(7,axiom,
subset(dollar_c2,dollar_c1),
file('SET027+3.p',unknown),
[] ).
cnf(8,plain,
member(dollar_f1(dollar_c3,dollar_c1),dollar_c3),
inference(hyper,[status(thm)],[4,3]),
[iquote('hyper,4,3')] ).
cnf(9,plain,
member(dollar_f1(dollar_c3,dollar_c1),dollar_c2),
inference(hyper,[status(thm)],[8,1,6]),
[iquote('hyper,8,1,6')] ).
cnf(11,plain,
member(dollar_f1(dollar_c3,dollar_c1),dollar_c1),
inference(hyper,[status(thm)],[9,1,7]),
[iquote('hyper,9,1,7')] ).
cnf(13,plain,
subset(dollar_c3,dollar_c1),
inference(hyper,[status(thm)],[11,2]),
[iquote('hyper,11,2')] ).
cnf(14,plain,
$false,
inference(binary,[status(thm)],[13,3]),
[iquote('binary,13.1,3.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SET027+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 10:45:42 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.86/2.08 ----- Otter 3.3f, August 2004 -----
% 1.86/2.08 The process was started by sandbox on n015.cluster.edu,
% 1.86/2.08 Wed Jul 27 10:45:42 2022
% 1.86/2.08 The command was "./otter". The process ID is 13690.
% 1.86/2.08
% 1.86/2.08 set(prolog_style_variables).
% 1.86/2.08 set(auto).
% 1.86/2.08 dependent: set(auto1).
% 1.86/2.08 dependent: set(process_input).
% 1.86/2.08 dependent: clear(print_kept).
% 1.86/2.08 dependent: clear(print_new_demod).
% 1.86/2.08 dependent: clear(print_back_demod).
% 1.86/2.08 dependent: clear(print_back_sub).
% 1.86/2.08 dependent: set(control_memory).
% 1.86/2.08 dependent: assign(max_mem, 12000).
% 1.86/2.08 dependent: assign(pick_given_ratio, 4).
% 1.86/2.08 dependent: assign(stats_level, 1).
% 1.86/2.08 dependent: assign(max_seconds, 10800).
% 1.86/2.08 clear(print_given).
% 1.86/2.08
% 1.86/2.08 formula_list(usable).
% 1.86/2.08 all B C (subset(B,C)<-> (all D (member(D,B)->member(D,C)))).
% 1.86/2.08 all B subset(B,B).
% 1.86/2.08 -(all B C D (subset(B,C)&subset(C,D)->subset(B,D))).
% 1.86/2.08 end_of_list.
% 1.86/2.08
% 1.86/2.08 -------> usable clausifies to:
% 1.86/2.08
% 1.86/2.08 list(usable).
% 1.86/2.08 0 [] -subset(B,C)| -member(D,B)|member(D,C).
% 1.86/2.08 0 [] subset(B,C)|member($f1(B,C),B).
% 1.86/2.08 0 [] subset(B,C)| -member($f1(B,C),C).
% 1.86/2.08 0 [] subset(B,B).
% 1.86/2.08 0 [] subset($c3,$c2).
% 1.86/2.08 0 [] subset($c2,$c1).
% 1.86/2.08 0 [] -subset($c3,$c1).
% 1.86/2.08 end_of_list.
% 1.86/2.08
% 1.86/2.08 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=3.
% 1.86/2.08
% 1.86/2.08 This is a non-Horn set without equality. The strategy will
% 1.86/2.08 be ordered hyper_res, unit deletion, and factoring, with
% 1.86/2.08 satellites in sos and with nuclei in usable.
% 1.86/2.08
% 1.86/2.08 dependent: set(hyper_res).
% 1.86/2.08 dependent: set(factor).
% 1.86/2.08 dependent: set(unit_deletion).
% 1.86/2.08
% 1.86/2.08 ------------> process usable:
% 1.86/2.08 ** KEPT (pick-wt=9): 1 [] -subset(A,B)| -member(C,A)|member(C,B).
% 1.86/2.08 ** KEPT (pick-wt=8): 2 [] subset(A,B)| -member($f1(A,B),B).
% 1.86/2.08 ** KEPT (pick-wt=3): 3 [] -subset($c3,$c1).
% 1.86/2.08
% 1.86/2.08 ------------> process sos:
% 1.86/2.08 ** KEPT (pick-wt=8): 4 [] subset(A,B)|member($f1(A,B),A).
% 1.86/2.08 ** KEPT (pick-wt=3): 5 [] subset(A,A).
% 1.86/2.08 ** KEPT (pick-wt=3): 6 [] subset($c3,$c2).
% 1.86/2.08 ** KEPT (pick-wt=3): 7 [] subset($c2,$c1).
% 1.86/2.08
% 1.86/2.08 ======= end of input processing =======
% 1.86/2.08
% 1.86/2.08 =========== start of search ===========
% 1.86/2.08
% 1.86/2.08 -------- PROOF --------
% 1.86/2.08
% 1.86/2.08 ----> UNIT CONFLICT at 0.00 sec ----> 14 [binary,13.1,3.1] $F.
% 1.86/2.08
% 1.86/2.08 Length of proof is 4. Level of proof is 4.
% 1.86/2.08
% 1.86/2.08 ---------------- PROOF ----------------
% 1.86/2.08 % SZS status Theorem
% 1.86/2.08 % SZS output start Refutation
% See solution above
% 1.86/2.08 ------------ end of proof -------------
% 1.86/2.08
% 1.86/2.08
% 1.86/2.08 Search stopped by max_proofs option.
% 1.86/2.08
% 1.86/2.08
% 1.86/2.08 Search stopped by max_proofs option.
% 1.86/2.08
% 1.86/2.08 ============ end of search ============
% 1.86/2.08
% 1.86/2.08 -------------- statistics -------------
% 1.86/2.08 clauses given 7
% 1.86/2.08 clauses generated 8
% 1.86/2.08 clauses kept 13
% 1.86/2.08 clauses forward subsumed 2
% 1.86/2.08 clauses back subsumed 0
% 1.86/2.08 Kbytes malloced 976
% 1.86/2.08
% 1.86/2.08 ----------- times (seconds) -----------
% 1.86/2.08 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.86/2.08 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.86/2.08 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.86/2.08
% 1.86/2.08 That finishes the proof of the theorem.
% 1.86/2.08
% 1.86/2.08 Process 13690 finished Wed Jul 27 10:45:43 2022
% 1.86/2.08 Otter interrupted
% 1.86/2.08 PROOF FOUND
%------------------------------------------------------------------------------