TSTP Solution File: SET585+3 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET585+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n023.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 13:13:44 EDT 2022
% Result : Theorem 2.05s 2.21s
% Output : Refutation 2.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 4
% Syntax : Number of clauses : 6 ( 5 unt; 0 nHn; 3 RR)
% Number of literals : 8 ( 0 equ; 3 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; 3 con; 0-2 aty)
% Number of variables : 10 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ subset(A,B)
| ~ subset(B,C)
| subset(A,C) ),
file('SET585+3.p',unknown),
[] ).
cnf(13,axiom,
~ subset(intersection(dollar_c3,dollar_c2),union(dollar_c3,dollar_c1)),
file('SET585+3.p',unknown),
[] ).
cnf(18,axiom,
subset(A,union(A,B)),
file('SET585+3.p',unknown),
[] ).
cnf(19,axiom,
subset(intersection(A,B),A),
file('SET585+3.p',unknown),
[] ).
cnf(28,plain,
subset(intersection(A,B),union(A,C)),
inference(hyper,[status(thm)],[19,1,18]),
[iquote('hyper,19,1,18')] ).
cnf(29,plain,
$false,
inference(binary,[status(thm)],[28,13]),
[iquote('binary,28.1,13.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET585+3 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 11:01:33 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.05/2.21 ----- Otter 3.3f, August 2004 -----
% 2.05/2.21 The process was started by sandbox on n023.cluster.edu,
% 2.05/2.21 Wed Jul 27 11:01:33 2022
% 2.05/2.21 The command was "./otter". The process ID is 14698.
% 2.05/2.21
% 2.05/2.21 set(prolog_style_variables).
% 2.05/2.21 set(auto).
% 2.05/2.21 dependent: set(auto1).
% 2.05/2.21 dependent: set(process_input).
% 2.05/2.21 dependent: clear(print_kept).
% 2.05/2.21 dependent: clear(print_new_demod).
% 2.05/2.21 dependent: clear(print_back_demod).
% 2.05/2.21 dependent: clear(print_back_sub).
% 2.05/2.21 dependent: set(control_memory).
% 2.05/2.21 dependent: assign(max_mem, 12000).
% 2.05/2.21 dependent: assign(pick_given_ratio, 4).
% 2.05/2.21 dependent: assign(stats_level, 1).
% 2.05/2.21 dependent: assign(max_seconds, 10800).
% 2.05/2.21 clear(print_given).
% 2.05/2.21
% 2.05/2.21 formula_list(usable).
% 2.05/2.21 all A (A=A).
% 2.05/2.21 all B C D (subset(B,C)&subset(C,D)->subset(B,D)).
% 2.05/2.21 all B C subset(B,union(B,C)).
% 2.05/2.21 all B C subset(intersection(B,C),B).
% 2.05/2.21 all B C D (member(D,union(B,C))<->member(D,B)|member(D,C)).
% 2.05/2.21 all B C D (member(D,intersection(B,C))<->member(D,B)&member(D,C)).
% 2.05/2.21 all B C (subset(B,C)<-> (all D (member(D,B)->member(D,C)))).
% 2.05/2.21 all B C (union(B,C)=union(C,B)).
% 2.05/2.21 all B C (intersection(B,C)=intersection(C,B)).
% 2.05/2.21 all B subset(B,B).
% 2.05/2.21 all B C (B=C<-> (all D (member(D,B)<->member(D,C)))).
% 2.05/2.21 -(all B C D subset(intersection(B,C),union(B,D))).
% 2.05/2.21 end_of_list.
% 2.05/2.21
% 2.05/2.21 -------> usable clausifies to:
% 2.05/2.21
% 2.05/2.21 list(usable).
% 2.05/2.21 0 [] A=A.
% 2.05/2.21 0 [] -subset(B,C)| -subset(C,D)|subset(B,D).
% 2.05/2.21 0 [] subset(B,union(B,C)).
% 2.05/2.21 0 [] subset(intersection(B,C),B).
% 2.05/2.21 0 [] -member(D,union(B,C))|member(D,B)|member(D,C).
% 2.05/2.21 0 [] member(D,union(B,C))| -member(D,B).
% 2.05/2.21 0 [] member(D,union(B,C))| -member(D,C).
% 2.05/2.21 0 [] -member(D,intersection(B,C))|member(D,B).
% 2.05/2.21 0 [] -member(D,intersection(B,C))|member(D,C).
% 2.05/2.21 0 [] member(D,intersection(B,C))| -member(D,B)| -member(D,C).
% 2.05/2.21 0 [] -subset(B,C)| -member(D,B)|member(D,C).
% 2.05/2.21 0 [] subset(B,C)|member($f1(B,C),B).
% 2.05/2.21 0 [] subset(B,C)| -member($f1(B,C),C).
% 2.05/2.21 0 [] union(B,C)=union(C,B).
% 2.05/2.21 0 [] intersection(B,C)=intersection(C,B).
% 2.05/2.21 0 [] subset(B,B).
% 2.05/2.21 0 [] B!=C| -member(D,B)|member(D,C).
% 2.05/2.21 0 [] B!=C|member(D,B)| -member(D,C).
% 2.05/2.21 0 [] B=C|member($f2(B,C),B)|member($f2(B,C),C).
% 2.05/2.21 0 [] B=C| -member($f2(B,C),B)| -member($f2(B,C),C).
% 2.05/2.21 0 [] -subset(intersection($c3,$c2),union($c3,$c1)).
% 2.05/2.21 end_of_list.
% 2.05/2.21
% 2.05/2.21 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 2.05/2.21
% 2.05/2.21 This ia a non-Horn set with equality. The strategy will be
% 2.05/2.21 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.05/2.21 deletion, with positive clauses in sos and nonpositive
% 2.05/2.21 clauses in usable.
% 2.05/2.21
% 2.05/2.21 dependent: set(knuth_bendix).
% 2.05/2.21 dependent: set(anl_eq).
% 2.05/2.21 dependent: set(para_from).
% 2.05/2.21 dependent: set(para_into).
% 2.05/2.21 dependent: clear(para_from_right).
% 2.05/2.21 dependent: clear(para_into_right).
% 2.05/2.21 dependent: set(para_from_vars).
% 2.05/2.21 dependent: set(eq_units_both_ways).
% 2.05/2.21 dependent: set(dynamic_demod_all).
% 2.05/2.21 dependent: set(dynamic_demod).
% 2.05/2.21 dependent: set(order_eq).
% 2.05/2.21 dependent: set(back_demod).
% 2.05/2.21 dependent: set(lrpo).
% 2.05/2.21 dependent: set(hyper_res).
% 2.05/2.21 dependent: set(unit_deletion).
% 2.05/2.21 dependent: set(factor).
% 2.05/2.21
% 2.05/2.21 ------------> process usable:
% 2.05/2.21 ** KEPT (pick-wt=9): 1 [] -subset(A,B)| -subset(B,C)|subset(A,C).
% 2.05/2.21 ** KEPT (pick-wt=11): 2 [] -member(A,union(B,C))|member(A,B)|member(A,C).
% 2.05/2.21 ** KEPT (pick-wt=8): 3 [] member(A,union(B,C))| -member(A,B).
% 2.05/2.21 ** KEPT (pick-wt=8): 4 [] member(A,union(B,C))| -member(A,C).
% 2.05/2.21 ** KEPT (pick-wt=8): 5 [] -member(A,intersection(B,C))|member(A,B).
% 2.05/2.21 ** KEPT (pick-wt=8): 6 [] -member(A,intersection(B,C))|member(A,C).
% 2.05/2.21 ** KEPT (pick-wt=11): 7 [] member(A,intersection(B,C))| -member(A,B)| -member(A,C).
% 2.05/2.21 ** KEPT (pick-wt=9): 8 [] -subset(A,B)| -member(C,A)|member(C,B).
% 2.05/2.21 ** KEPT (pick-wt=8): 9 [] subset(A,B)| -member($f1(A,B),B).
% 2.05/2.21 ** KEPT (pick-wt=9): 10 [] A!=B| -member(C,A)|member(C,B).
% 2.05/2.21 ** KEPT (pick-wt=9): 11 [] A!=B|member(C,A)| -member(C,B).
% 2.05/2.21 ** KEPT (pick-wt=13): 12 [] A=B| -member($f2(A,B),A)| -member($f2(A,B),B).
% 2.05/2.21 ** KEPT (pick-wt=7): 13 [] -subset(intersection($c3,$c2),union($c3,$c1)).
% 2.05/2.21
% 2.05/2.21 ------------> process sos:
% 2.05/2.21 ** KEPT (pick-wt=3): 17 [] A=A.
% 2.05/2.21 ** KEPT (pick-wt=5): 18 [] subset(A,union(A,B)).
% 2.05/2.21 ** KEPT (pick-wt=5): 19 [] subset(intersection(A,B),A).
% 2.05/2.21 ** KEPT (pick-wt=8): 20 [] subset(A,B)|member($f1(A,B),A).
% 2.05/2.21 ** KEPT (pick-wt=7): 21 [] union(A,B)=union(B,A).
% 2.05/2.21 ** KEPT (pick-wt=7): 22 [] intersection(A,B)=intersection(B,A).
% 2.05/2.21 ** KEPT (pick-wt=3): 23 [] subset(A,A).
% 2.05/2.21 ** KEPT (pick-wt=13): 24 [] A=B|member($f2(A,B),A)|member($f2(A,B),B).
% 2.05/2.21 Following clause subsumed by 17 during input processing: 0 [copy,17,flip.1] A=A.
% 2.05/2.21 17 back subsumes 16.
% 2.05/2.21 Following clause subsumed by 21 during input processing: 0 [copy,21,flip.1] union(A,B)=union(B,A).
% 2.05/2.21 Following clause subsumed by 22 during input processing: 0 [copy,22,flip.1] intersection(A,B)=intersection(B,A).
% 2.05/2.21
% 2.05/2.21 ======= end of input processing =======
% 2.05/2.21
% 2.05/2.21 =========== start of search ===========
% 2.05/2.21
% 2.05/2.21 -------- PROOF --------
% 2.05/2.21
% 2.05/2.21 ----> UNIT CONFLICT at 0.00 sec ----> 29 [binary,28.1,13.1] $F.
% 2.05/2.21
% 2.05/2.21 Length of proof is 1. Level of proof is 1.
% 2.05/2.21
% 2.05/2.21 ---------------- PROOF ----------------
% 2.05/2.21 % SZS status Theorem
% 2.05/2.21 % SZS output start Refutation
% See solution above
% 2.05/2.21 ------------ end of proof -------------
% 2.05/2.21
% 2.05/2.21
% 2.05/2.21 Search stopped by max_proofs option.
% 2.05/2.21
% 2.05/2.21
% 2.05/2.21 Search stopped by max_proofs option.
% 2.05/2.21
% 2.05/2.21 ============ end of search ============
% 2.05/2.21
% 2.05/2.21 -------------- statistics -------------
% 2.05/2.21 clauses given 4
% 2.05/2.21 clauses generated 18
% 2.05/2.21 clauses kept 28
% 2.05/2.21 clauses forward subsumed 13
% 2.05/2.21 clauses back subsumed 1
% 2.05/2.21 Kbytes malloced 976
% 2.05/2.21
% 2.05/2.21 ----------- times (seconds) -----------
% 2.05/2.21 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.05/2.21 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.05/2.21 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.05/2.21
% 2.05/2.21 That finishes the proof of the theorem.
% 2.05/2.21
% 2.05/2.21 Process 14698 finished Wed Jul 27 11:01:35 2022
% 2.05/2.21 Otter interrupted
% 2.05/2.21 PROOF FOUND
%------------------------------------------------------------------------------