TSTP Solution File: SET867+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET867+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n007.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 13:14:26 EDT 2022
% Result : Theorem 1.79s 1.97s
% Output : Refutation 1.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of clauses : 8 ( 5 unt; 1 nHn; 6 RR)
% Number of literals : 12 ( 5 equ; 5 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-3 aty)
% Number of variables : 7 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( A != empty_set
| ~ in(B,A) ),
file('SET867+1.p',unknown),
[] ).
cnf(4,axiom,
( A != union(B)
| ~ in(C,A)
| in(dollar_f2(B,A,C),B) ),
file('SET867+1.p',unknown),
[] ).
cnf(8,axiom,
union(empty_set) != empty_set,
file('SET867+1.p',unknown),
[] ).
cnf(11,axiom,
A = A,
file('SET867+1.p',unknown),
[] ).
cnf(12,axiom,
( A = empty_set
| in(dollar_f1(A),A) ),
file('SET867+1.p',unknown),
[] ).
cnf(27,plain,
in(dollar_f1(union(empty_set)),union(empty_set)),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[12,8]),11]),
[iquote('para_from,12.1.1,8.1.1,unit_del,11')] ).
cnf(92,plain,
in(dollar_f2(empty_set,union(empty_set),dollar_f1(union(empty_set))),empty_set),
inference(hyper,[status(thm)],[27,4,11]),
[iquote('hyper,27,4,11')] ).
cnf(140,plain,
$false,
inference(hyper,[status(thm)],[92,2,11]),
[iquote('hyper,92,2,11')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET867+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n007.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 10:35:01 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.79/1.97 ----- Otter 3.3f, August 2004 -----
% 1.79/1.97 The process was started by sandbox on n007.cluster.edu,
% 1.79/1.97 Wed Jul 27 10:35:01 2022
% 1.79/1.97 The command was "./otter". The process ID is 29477.
% 1.79/1.97
% 1.79/1.97 set(prolog_style_variables).
% 1.79/1.97 set(auto).
% 1.79/1.97 dependent: set(auto1).
% 1.79/1.97 dependent: set(process_input).
% 1.79/1.97 dependent: clear(print_kept).
% 1.79/1.97 dependent: clear(print_new_demod).
% 1.79/1.97 dependent: clear(print_back_demod).
% 1.79/1.97 dependent: clear(print_back_sub).
% 1.79/1.97 dependent: set(control_memory).
% 1.79/1.97 dependent: assign(max_mem, 12000).
% 1.79/1.97 dependent: assign(pick_given_ratio, 4).
% 1.79/1.97 dependent: assign(stats_level, 1).
% 1.79/1.97 dependent: assign(max_seconds, 10800).
% 1.79/1.97 clear(print_given).
% 1.79/1.97
% 1.79/1.97 formula_list(usable).
% 1.79/1.97 all A (A=A).
% 1.79/1.97 all A B (in(A,B)-> -in(B,A)).
% 1.79/1.97 all A (A=empty_set<-> (all B (-in(B,A)))).
% 1.79/1.97 all A B (B=union(A)<-> (all C (in(C,B)<-> (exists D (in(C,D)&in(D,A)))))).
% 1.79/1.97 empty(empty_set).
% 1.79/1.97 exists A empty(A).
% 1.79/1.97 exists A (-empty(A)).
% 1.79/1.97 union(empty_set)!=empty_set.
% 1.79/1.97 end_of_list.
% 1.79/1.97
% 1.79/1.97 -------> usable clausifies to:
% 1.79/1.97
% 1.79/1.97 list(usable).
% 1.79/1.97 0 [] A=A.
% 1.79/1.97 0 [] -in(A,B)| -in(B,A).
% 1.79/1.97 0 [] A!=empty_set| -in(B,A).
% 1.79/1.97 0 [] A=empty_set|in($f1(A),A).
% 1.79/1.97 0 [] B!=union(A)| -in(C,B)|in(C,$f2(A,B,C)).
% 1.79/1.97 0 [] B!=union(A)| -in(C,B)|in($f2(A,B,C),A).
% 1.79/1.97 0 [] B!=union(A)|in(C,B)| -in(C,D)| -in(D,A).
% 1.79/1.97 0 [] B=union(A)|in($f4(A,B),B)|in($f4(A,B),$f3(A,B)).
% 1.79/1.97 0 [] B=union(A)|in($f4(A,B),B)|in($f3(A,B),A).
% 1.79/1.97 0 [] B=union(A)| -in($f4(A,B),B)| -in($f4(A,B),X1)| -in(X1,A).
% 1.79/1.97 0 [] empty(empty_set).
% 1.79/1.97 0 [] empty($c1).
% 1.79/1.97 0 [] -empty($c2).
% 1.79/1.97 0 [] union(empty_set)!=empty_set.
% 1.79/1.97 end_of_list.
% 1.79/1.97
% 1.79/1.97 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.79/1.97
% 1.79/1.97 This ia a non-Horn set with equality. The strategy will be
% 1.79/1.97 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.79/1.97 deletion, with positive clauses in sos and nonpositive
% 1.79/1.97 clauses in usable.
% 1.79/1.97
% 1.79/1.97 dependent: set(knuth_bendix).
% 1.79/1.97 dependent: set(anl_eq).
% 1.79/1.97 dependent: set(para_from).
% 1.79/1.97 dependent: set(para_into).
% 1.79/1.97 dependent: clear(para_from_right).
% 1.79/1.97 dependent: clear(para_into_right).
% 1.79/1.97 dependent: set(para_from_vars).
% 1.79/1.97 dependent: set(eq_units_both_ways).
% 1.79/1.97 dependent: set(dynamic_demod_all).
% 1.79/1.97 dependent: set(dynamic_demod).
% 1.79/1.97 dependent: set(order_eq).
% 1.79/1.97 dependent: set(back_demod).
% 1.79/1.97 dependent: set(lrpo).
% 1.79/1.97 dependent: set(hyper_res).
% 1.79/1.97 dependent: set(unit_deletion).
% 1.79/1.97 dependent: set(factor).
% 1.79/1.97
% 1.79/1.97 ------------> process usable:
% 1.79/1.97 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.79/1.97 ** KEPT (pick-wt=6): 2 [] A!=empty_set| -in(B,A).
% 1.79/1.97 ** KEPT (pick-wt=13): 3 [] A!=union(B)| -in(C,A)|in(C,$f2(B,A,C)).
% 1.79/1.97 ** KEPT (pick-wt=13): 4 [] A!=union(B)| -in(C,A)|in($f2(B,A,C),B).
% 1.79/1.97 ** KEPT (pick-wt=13): 5 [] A!=union(B)|in(C,A)| -in(C,D)| -in(D,B).
% 1.79/1.97 ** KEPT (pick-wt=17): 6 [] A=union(B)| -in($f4(B,A),A)| -in($f4(B,A),C)| -in(C,B).
% 1.79/1.97 ** KEPT (pick-wt=2): 7 [] -empty($c2).
% 1.79/1.97 ** KEPT (pick-wt=4): 8 [] union(empty_set)!=empty_set.
% 1.79/1.97
% 1.79/1.97 ------------> process sos:
% 1.79/1.97 ** KEPT (pick-wt=3): 11 [] A=A.
% 1.79/1.97 ** KEPT (pick-wt=7): 12 [] A=empty_set|in($f1(A),A).
% 1.79/1.97 ** KEPT (pick-wt=16): 13 [] A=union(B)|in($f4(B,A),A)|in($f4(B,A),$f3(B,A)).
% 1.79/1.97 ** KEPT (pick-wt=14): 14 [] A=union(B)|in($f4(B,A),A)|in($f3(B,A),B).
% 1.79/1.97 ** KEPT (pick-wt=2): 15 [] empty(empty_set).
% 1.79/1.97 ** KEPT (pick-wt=2): 16 [] empty($c1).
% 1.79/1.97 Following clause subsumed by 11 during input processing: 0 [copy,11,flip.1] A=A.
% 1.79/1.97
% 1.79/1.97 ======= end of input processing =======
% 1.79/1.97
% 1.79/1.97 =========== start of search ===========
% 1.79/1.97
% 1.79/1.97 -------- PROOF --------
% 1.79/1.97
% 1.79/1.97 -----> EMPTY CLAUSE at 0.01 sec ----> 140 [hyper,92,2,11] $F.
% 1.79/1.97
% 1.79/1.97 Length of proof is 2. Level of proof is 2.
% 1.79/1.97
% 1.79/1.97 ---------------- PROOF ----------------
% 1.79/1.97 % SZS status Theorem
% 1.79/1.97 % SZS output start Refutation
% See solution above
% 1.79/1.97 ------------ end of proof -------------
% 1.79/1.97
% 1.79/1.97
% 1.79/1.97 Search stopped by max_proofs option.
% 1.79/1.97
% 1.79/1.97
% 1.79/1.97 Search stopped by max_proofs option.
% 1.79/1.97
% 1.79/1.97 ============ end of search ============
% 1.79/1.97
% 1.79/1.97 -------------- statistics -------------
% 1.79/1.97 clauses given 9
% 1.79/1.97 clauses generated 218
% 1.79/1.97 clauses kept 139
% 1.79/1.97 clauses forward subsumed 93
% 1.79/1.97 clauses back subsumed 0
% 1.79/1.97 Kbytes malloced 1953
% 1.79/1.97
% 1.79/1.97 ----------- times (seconds) -----------
% 1.79/1.97 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.79/1.97 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.79/1.97 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.79/1.97
% 1.79/1.97 That finishes the proof of the theorem.
% 1.79/1.97
% 1.79/1.97 Process 29477 finished Wed Jul 27 10:35:02 2022
% 1.79/1.97 Otter interrupted
% 1.79/1.97 PROOF FOUND
%------------------------------------------------------------------------------