TSTP Solution File: SET063+3 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET063+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n016.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 13:12:58 EDT 2022
% Result : Theorem 1.71s 1.93s
% Output : Refutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 4
% Syntax : Number of clauses : 7 ( 6 unt; 0 nHn; 6 RR)
% Number of literals : 9 ( 4 equ; 4 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 3 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(6,axiom,
( A = B
| ~ subset(A,B)
| ~ subset(B,A) ),
file('SET063+3.p',unknown),
[] ).
cnf(8,axiom,
dollar_c1 != empty_set,
file('SET063+3.p',unknown),
[] ).
cnf(9,plain,
empty_set != dollar_c1,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[8])]),
[iquote('copy,8,flip.1')] ).
cnf(12,axiom,
subset(empty_set,A),
file('SET063+3.p',unknown),
[] ).
cnf(16,axiom,
subset(dollar_c1,empty_set),
file('SET063+3.p',unknown),
[] ).
cnf(18,plain,
empty_set = dollar_c1,
inference(hyper,[status(thm)],[16,6,12]),
[iquote('hyper,16,6,12')] ).
cnf(20,plain,
$false,
inference(binary,[status(thm)],[18,9]),
[iquote('binary,18.1,9.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SET063+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n016.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 11:07:22 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.71/1.93 ----- Otter 3.3f, August 2004 -----
% 1.71/1.93 The process was started by sandbox on n016.cluster.edu,
% 1.71/1.93 Wed Jul 27 11:07:22 2022
% 1.71/1.93 The command was "./otter". The process ID is 24939.
% 1.71/1.93
% 1.71/1.93 set(prolog_style_variables).
% 1.71/1.93 set(auto).
% 1.71/1.93 dependent: set(auto1).
% 1.71/1.93 dependent: set(process_input).
% 1.71/1.93 dependent: clear(print_kept).
% 1.71/1.93 dependent: clear(print_new_demod).
% 1.71/1.93 dependent: clear(print_back_demod).
% 1.71/1.93 dependent: clear(print_back_sub).
% 1.71/1.93 dependent: set(control_memory).
% 1.71/1.93 dependent: assign(max_mem, 12000).
% 1.71/1.93 dependent: assign(pick_given_ratio, 4).
% 1.71/1.93 dependent: assign(stats_level, 1).
% 1.71/1.93 dependent: assign(max_seconds, 10800).
% 1.71/1.93 clear(print_given).
% 1.71/1.93
% 1.71/1.93 formula_list(usable).
% 1.71/1.93 all A (A=A).
% 1.71/1.93 all B subset(empty_set,B).
% 1.71/1.93 all B (-member(B,empty_set)).
% 1.71/1.93 all B C (subset(B,C)<-> (all D (member(D,B)->member(D,C)))).
% 1.71/1.93 all B C (B=C<->subset(B,C)&subset(C,B)).
% 1.71/1.93 all B subset(B,B).
% 1.71/1.93 all B (empty(B)<-> (all C (-member(C,B)))).
% 1.71/1.93 -(all B (subset(B,empty_set)->B=empty_set)).
% 1.71/1.93 end_of_list.
% 1.71/1.93
% 1.71/1.93 -------> usable clausifies to:
% 1.71/1.93
% 1.71/1.93 list(usable).
% 1.71/1.93 0 [] A=A.
% 1.71/1.93 0 [] subset(empty_set,B).
% 1.71/1.93 0 [] -member(B,empty_set).
% 1.71/1.93 0 [] -subset(B,C)| -member(D,B)|member(D,C).
% 1.71/1.93 0 [] subset(B,C)|member($f1(B,C),B).
% 1.71/1.93 0 [] subset(B,C)| -member($f1(B,C),C).
% 1.71/1.93 0 [] B!=C|subset(B,C).
% 1.71/1.93 0 [] B!=C|subset(C,B).
% 1.71/1.93 0 [] B=C| -subset(B,C)| -subset(C,B).
% 1.71/1.93 0 [] subset(B,B).
% 1.71/1.93 0 [] -empty(B)| -member(C,B).
% 1.71/1.93 0 [] empty(B)|member($f2(B),B).
% 1.71/1.93 0 [] subset($c1,empty_set).
% 1.71/1.93 0 [] $c1!=empty_set.
% 1.71/1.93 end_of_list.
% 1.71/1.93
% 1.71/1.93 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.71/1.93
% 1.71/1.93 This ia a non-Horn set with equality. The strategy will be
% 1.71/1.93 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.71/1.93 deletion, with positive clauses in sos and nonpositive
% 1.71/1.93 clauses in usable.
% 1.71/1.93
% 1.71/1.93 dependent: set(knuth_bendix).
% 1.71/1.93 dependent: set(anl_eq).
% 1.71/1.93 dependent: set(para_from).
% 1.71/1.93 dependent: set(para_into).
% 1.71/1.93 dependent: clear(para_from_right).
% 1.71/1.93 dependent: clear(para_into_right).
% 1.71/1.93 dependent: set(para_from_vars).
% 1.71/1.93 dependent: set(eq_units_both_ways).
% 1.71/1.93 dependent: set(dynamic_demod_all).
% 1.71/1.93 dependent: set(dynamic_demod).
% 1.71/1.93 dependent: set(order_eq).
% 1.71/1.93 dependent: set(back_demod).
% 1.71/1.93 dependent: set(lrpo).
% 1.71/1.93 dependent: set(hyper_res).
% 1.71/1.93 dependent: set(unit_deletion).
% 1.71/1.93 dependent: set(factor).
% 1.71/1.93
% 1.71/1.93 ------------> process usable:
% 1.71/1.93 ** KEPT (pick-wt=3): 1 [] -member(A,empty_set).
% 1.71/1.93 ** KEPT (pick-wt=9): 2 [] -subset(A,B)| -member(C,A)|member(C,B).
% 1.71/1.93 ** KEPT (pick-wt=8): 3 [] subset(A,B)| -member($f1(A,B),B).
% 1.71/1.93 ** KEPT (pick-wt=6): 4 [] A!=B|subset(A,B).
% 1.71/1.93 ** KEPT (pick-wt=6): 5 [] A!=B|subset(B,A).
% 1.71/1.93 ** KEPT (pick-wt=9): 6 [] A=B| -subset(A,B)| -subset(B,A).
% 1.71/1.93 ** KEPT (pick-wt=5): 7 [] -empty(A)| -member(B,A).
% 1.71/1.93 ** KEPT (pick-wt=3): 9 [copy,8,flip.1] empty_set!=$c1.
% 1.71/1.93
% 1.71/1.93 ------------> process sos:
% 1.71/1.93 ** KEPT (pick-wt=3): 11 [] A=A.
% 1.71/1.93 ** KEPT (pick-wt=3): 12 [] subset(empty_set,A).
% 1.71/1.93 ** KEPT (pick-wt=8): 13 [] subset(A,B)|member($f1(A,B),A).
% 1.71/1.93 ** KEPT (pick-wt=3): 14 [] subset(A,A).
% 1.71/1.93 ** KEPT (pick-wt=6): 15 [] empty(A)|member($f2(A),A).
% 1.71/1.93 ** KEPT (pick-wt=3): 16 [] subset($c1,empty_set).
% 1.71/1.93 Following clause subsumed by 11 during input processing: 0 [copy,11,flip.1] A=A.
% 1.71/1.93 11 back subsumes 10.
% 1.71/1.93
% 1.71/1.93 ======= end of input processing =======
% 1.71/1.93
% 1.71/1.93 =========== start of search ===========
% 1.71/1.93
% 1.71/1.93 -------- PROOF --------
% 1.71/1.93
% 1.71/1.93 ----> UNIT CONFLICT at 0.00 sec ----> 20 [binary,18.1,9.1] $F.
% 1.71/1.93
% 1.71/1.93 Length of proof is 2. Level of proof is 1.
% 1.71/1.93
% 1.71/1.93 ---------------- PROOF ----------------
% 1.71/1.93 % SZS status Theorem
% 1.71/1.93 % SZS output start Refutation
% See solution above
% 1.71/1.93 ------------ end of proof -------------
% 1.71/1.93
% 1.71/1.93
% 1.71/1.93 Search stopped by max_proofs option.
% 1.71/1.93
% 1.71/1.93
% 1.71/1.93 Search stopped by max_proofs option.
% 1.71/1.93
% 1.71/1.93 ============ end of search ============
% 1.71/1.93
% 1.71/1.93 -------------- statistics -------------
% 1.71/1.93 clauses given 4
% 1.71/1.93 clauses generated 11
% 1.71/1.93 clauses kept 17
% 1.71/1.93 clauses forward subsumed 9
% 1.71/1.93 clauses back subsumed 1
% 1.71/1.93 Kbytes malloced 976
% 1.71/1.93
% 1.71/1.93 ----------- times (seconds) -----------
% 1.71/1.93 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.71/1.93 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.71/1.93 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.71/1.93
% 1.71/1.93 That finishes the proof of the theorem.
% 1.71/1.93
% 1.71/1.93 Process 24939 finished Wed Jul 27 11:07:24 2022
% 1.71/1.93 Otter interrupted
% 1.71/1.93 PROOF FOUND
%------------------------------------------------------------------------------