TSTP Solution File: SET591+3 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET591+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n004.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 13:13:46 EDT 2022
% Result : Theorem 1.72s 1.90s
% Output : Refutation 1.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of clauses : 16 ( 7 unt; 5 nHn; 11 RR)
% Number of literals : 28 ( 7 equ; 11 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 18 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ subset(A,B)
| ~ member(C,A)
| member(C,B) ),
file('SET591+3.p',unknown),
[] ).
cnf(4,axiom,
( ~ member(A,difference(B,C))
| ~ member(A,C) ),
file('SET591+3.p',unknown),
[] ).
cnf(6,axiom,
~ member(A,empty_set),
file('SET591+3.p',unknown),
[] ).
cnf(9,axiom,
( A = B
| ~ subset(A,B)
| ~ subset(B,A) ),
file('SET591+3.p',unknown),
[] ).
cnf(10,axiom,
( ~ empty(A)
| ~ member(B,A) ),
file('SET591+3.p',unknown),
[] ).
cnf(11,axiom,
dollar_c2 != empty_set,
file('SET591+3.p',unknown),
[] ).
cnf(12,plain,
empty_set != dollar_c2,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[11])]),
[iquote('copy,11,flip.1')] ).
cnf(15,axiom,
( subset(A,B)
| member(dollar_f1(A,B),A) ),
file('SET591+3.p',unknown),
[] ).
cnf(17,axiom,
( empty(A)
| member(dollar_f2(A),A) ),
file('SET591+3.p',unknown),
[] ).
cnf(18,axiom,
subset(dollar_c2,difference(dollar_c1,dollar_c2)),
file('SET591+3.p',unknown),
[] ).
cnf(25,plain,
( member(dollar_f1(A,B),A)
| B = A
| member(dollar_f1(B,A),B) ),
inference(hyper,[status(thm)],[15,9,15]),
[iquote('hyper,15,9,15')] ).
cnf(91,plain,
( A = empty_set
| member(dollar_f1(A,empty_set),A) ),
inference(hyper,[status(thm)],[25,6]),
[iquote('hyper,25,6')] ).
cnf(200,plain,
( A = empty_set
| member(dollar_f2(A),A) ),
inference(hyper,[status(thm)],[91,10,17]),
[iquote('hyper,91,10,17')] ).
cnf(283,plain,
member(dollar_f2(dollar_c2),difference(dollar_c1,dollar_c2)),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[200,1,18]),12]),
[iquote('hyper,200,1,18,unit_del,12')] ).
cnf(362,plain,
empty_set = dollar_c2,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[283,4,200])]),
[iquote('hyper,283,4,200,flip.1')] ).
cnf(364,plain,
$false,
inference(binary,[status(thm)],[362,12]),
[iquote('binary,362.1,12.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET591+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n004.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 10:36:21 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.72/1.90 ----- Otter 3.3f, August 2004 -----
% 1.72/1.90 The process was started by sandbox2 on n004.cluster.edu,
% 1.72/1.90 Wed Jul 27 10:36:21 2022
% 1.72/1.90 The command was "./otter". The process ID is 17681.
% 1.72/1.90
% 1.72/1.90 set(prolog_style_variables).
% 1.72/1.90 set(auto).
% 1.72/1.90 dependent: set(auto1).
% 1.72/1.90 dependent: set(process_input).
% 1.72/1.90 dependent: clear(print_kept).
% 1.72/1.90 dependent: clear(print_new_demod).
% 1.72/1.90 dependent: clear(print_back_demod).
% 1.72/1.90 dependent: clear(print_back_sub).
% 1.72/1.90 dependent: set(control_memory).
% 1.72/1.90 dependent: assign(max_mem, 12000).
% 1.72/1.90 dependent: assign(pick_given_ratio, 4).
% 1.72/1.90 dependent: assign(stats_level, 1).
% 1.72/1.90 dependent: assign(max_seconds, 10800).
% 1.72/1.90 clear(print_given).
% 1.72/1.90
% 1.72/1.90 formula_list(usable).
% 1.72/1.90 all A (A=A).
% 1.72/1.90 all B C (subset(B,C)<-> (all D (member(D,B)->member(D,C)))).
% 1.72/1.90 all B C D (member(D,difference(B,C))<->member(D,B)& -member(D,C)).
% 1.72/1.90 all B (-member(B,empty_set)).
% 1.72/1.90 all B C (B=C<->subset(B,C)&subset(C,B)).
% 1.72/1.90 all B subset(B,B).
% 1.72/1.90 all B (empty(B)<-> (all C (-member(C,B)))).
% 1.72/1.90 -(all B C (subset(B,difference(C,B))->B=empty_set)).
% 1.72/1.90 end_of_list.
% 1.72/1.90
% 1.72/1.90 -------> usable clausifies to:
% 1.72/1.90
% 1.72/1.90 list(usable).
% 1.72/1.90 0 [] A=A.
% 1.72/1.90 0 [] -subset(B,C)| -member(D,B)|member(D,C).
% 1.72/1.90 0 [] subset(B,C)|member($f1(B,C),B).
% 1.72/1.90 0 [] subset(B,C)| -member($f1(B,C),C).
% 1.72/1.90 0 [] -member(D,difference(B,C))|member(D,B).
% 1.72/1.90 0 [] -member(D,difference(B,C))| -member(D,C).
% 1.72/1.90 0 [] member(D,difference(B,C))| -member(D,B)|member(D,C).
% 1.72/1.90 0 [] -member(B,empty_set).
% 1.72/1.90 0 [] B!=C|subset(B,C).
% 1.72/1.90 0 [] B!=C|subset(C,B).
% 1.72/1.90 0 [] B=C| -subset(B,C)| -subset(C,B).
% 1.72/1.90 0 [] subset(B,B).
% 1.72/1.90 0 [] -empty(B)| -member(C,B).
% 1.72/1.90 0 [] empty(B)|member($f2(B),B).
% 1.72/1.90 0 [] subset($c2,difference($c1,$c2)).
% 1.72/1.90 0 [] $c2!=empty_set.
% 1.72/1.90 end_of_list.
% 1.72/1.90
% 1.72/1.90 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.72/1.90
% 1.72/1.90 This ia a non-Horn set with equality. The strategy will be
% 1.72/1.90 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.72/1.90 deletion, with positive clauses in sos and nonpositive
% 1.72/1.90 clauses in usable.
% 1.72/1.90
% 1.72/1.90 dependent: set(knuth_bendix).
% 1.72/1.90 dependent: set(anl_eq).
% 1.72/1.90 dependent: set(para_from).
% 1.72/1.90 dependent: set(para_into).
% 1.72/1.90 dependent: clear(para_from_right).
% 1.72/1.90 dependent: clear(para_into_right).
% 1.72/1.90 dependent: set(para_from_vars).
% 1.72/1.90 dependent: set(eq_units_both_ways).
% 1.72/1.90 dependent: set(dynamic_demod_all).
% 1.72/1.90 dependent: set(dynamic_demod).
% 1.72/1.90 dependent: set(order_eq).
% 1.72/1.90 dependent: set(back_demod).
% 1.72/1.90 dependent: set(lrpo).
% 1.72/1.90 dependent: set(hyper_res).
% 1.72/1.90 dependent: set(unit_deletion).
% 1.72/1.90 dependent: set(factor).
% 1.72/1.90
% 1.72/1.90 ------------> process usable:
% 1.72/1.90 ** KEPT (pick-wt=9): 1 [] -subset(A,B)| -member(C,A)|member(C,B).
% 1.72/1.90 ** KEPT (pick-wt=8): 2 [] subset(A,B)| -member($f1(A,B),B).
% 1.72/1.90 ** KEPT (pick-wt=8): 3 [] -member(A,difference(B,C))|member(A,B).
% 1.72/1.90 ** KEPT (pick-wt=8): 4 [] -member(A,difference(B,C))| -member(A,C).
% 1.72/1.90 ** KEPT (pick-wt=11): 5 [] member(A,difference(B,C))| -member(A,B)|member(A,C).
% 1.72/1.90 ** KEPT (pick-wt=3): 6 [] -member(A,empty_set).
% 1.72/1.90 ** KEPT (pick-wt=6): 7 [] A!=B|subset(A,B).
% 1.72/1.90 ** KEPT (pick-wt=6): 8 [] A!=B|subset(B,A).
% 1.72/1.90 ** KEPT (pick-wt=9): 9 [] A=B| -subset(A,B)| -subset(B,A).
% 1.72/1.90 ** KEPT (pick-wt=5): 10 [] -empty(A)| -member(B,A).
% 1.72/1.90 ** KEPT (pick-wt=3): 12 [copy,11,flip.1] empty_set!=$c2.
% 1.72/1.90
% 1.72/1.90 ------------> process sos:
% 1.72/1.90 ** KEPT (pick-wt=3): 14 [] A=A.
% 1.72/1.90 ** KEPT (pick-wt=8): 15 [] subset(A,B)|member($f1(A,B),A).
% 1.72/1.90 ** KEPT (pick-wt=3): 16 [] subset(A,A).
% 1.72/1.90 ** KEPT (pick-wt=6): 17 [] empty(A)|member($f2(A),A).
% 1.72/1.90 ** KEPT (pick-wt=5): 18 [] subset($c2,difference($c1,$c2)).
% 1.72/1.90 Following clause subsumed by 14 during input processing: 0 [copy,14,flip.1] A=A.
% 1.72/1.90 14 back subsumes 13.
% 1.72/1.90
% 1.72/1.90 ======= end of input processing =======
% 1.72/1.90
% 1.72/1.90 =========== start of search ===========
% 1.72/1.90
% 1.72/1.90 -------- PROOF --------
% 1.72/1.90
% 1.72/1.90 ----> UNIT CONFLICT at 0.03 sec ----> 364 [binary,362.1,12.1] $F.
% 1.72/1.90
% 1.72/1.90 Length of proof is 6. Level of proof is 5.
% 1.72/1.90
% 1.72/1.90 ---------------- PROOF ----------------
% 1.72/1.90 % SZS status Theorem
% 1.72/1.90 % SZS output start Refutation
% See solution above
% 1.72/1.90 ------------ end of proof -------------
% 1.72/1.90
% 1.72/1.90
% 1.72/1.90 Search stopped by max_proofs option.
% 1.72/1.90
% 1.72/1.90
% 1.72/1.90 Search stopped by max_proofs option.
% 1.72/1.90
% 1.72/1.90 ============ end of search ============
% 1.72/1.90
% 1.72/1.90 -------------- statistics -------------
% 1.72/1.90 clauses given 19
% 1.72/1.90 clauses generated 762
% 1.72/1.90 clauses kept 361
% 1.72/1.90 clauses forward subsumed 413
% 1.72/1.90 clauses back subsumed 1
% 1.72/1.90 Kbytes malloced 976
% 1.72/1.90
% 1.72/1.90 ----------- times (seconds) -----------
% 1.72/1.90 user CPU time 0.03 (0 hr, 0 min, 0 sec)
% 1.72/1.90 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.72/1.90 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.72/1.90
% 1.72/1.90 That finishes the proof of the theorem.
% 1.72/1.90
% 1.72/1.90 Process 17681 finished Wed Jul 27 10:36:22 2022
% 1.72/1.90 Otter interrupted
% 1.72/1.90 PROOF FOUND
%------------------------------------------------------------------------------