TSTP Solution File: SET947+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET947+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n013.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 13:14:35 EDT 2022
% Result : Theorem 2.01s 2.17s
% Output : Refutation 2.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of clauses : 11 ( 7 unt; 1 nHn; 9 RR)
% Number of literals : 16 ( 2 equ; 5 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 10 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
( A != powerset(B)
| in(C,A)
| ~ subset(C,B) ),
file('SET947+1.p',unknown),
[] ).
cnf(6,axiom,
( subset(A,B)
| ~ in(dollar_f2(A,B),B) ),
file('SET947+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ in(A,B)
| subset(A,union(B)) ),
file('SET947+1.p',unknown),
[] ).
cnf(9,axiom,
~ subset(dollar_c3,powerset(union(dollar_c3))),
file('SET947+1.p',unknown),
[] ).
cnf(11,axiom,
A = A,
file('SET947+1.p',unknown),
[] ).
cnf(13,axiom,
( subset(A,B)
| in(dollar_f2(A,B),A) ),
file('SET947+1.p',unknown),
[] ).
cnf(81,plain,
in(dollar_f2(dollar_c3,powerset(union(dollar_c3))),dollar_c3),
inference(hyper,[status(thm)],[13,9]),
[iquote('hyper,13,9')] ).
cnf(88,plain,
subset(dollar_f2(dollar_c3,powerset(union(dollar_c3))),union(dollar_c3)),
inference(hyper,[status(thm)],[81,7]),
[iquote('hyper,81,7')] ).
cnf(190,plain,
in(dollar_f2(dollar_c3,powerset(union(dollar_c3))),powerset(union(dollar_c3))),
inference(hyper,[status(thm)],[88,3,11]),
[iquote('hyper,88,3,11')] ).
cnf(452,plain,
subset(dollar_c3,powerset(union(dollar_c3))),
inference(hyper,[status(thm)],[190,6]),
[iquote('hyper,190,6')] ).
cnf(453,plain,
$false,
inference(binary,[status(thm)],[452,9]),
[iquote('binary,452.1,9.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET947+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : otter-tptp-script %s
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Jul 27 10:46:00 EDT 2022
% 0.12/0.34 % CPUTime :
% 2.01/2.17 ----- Otter 3.3f, August 2004 -----
% 2.01/2.17 The process was started by sandbox on n013.cluster.edu,
% 2.01/2.17 Wed Jul 27 10:46:00 2022
% 2.01/2.17 The command was "./otter". The process ID is 6811.
% 2.01/2.17
% 2.01/2.17 set(prolog_style_variables).
% 2.01/2.17 set(auto).
% 2.01/2.17 dependent: set(auto1).
% 2.01/2.17 dependent: set(process_input).
% 2.01/2.17 dependent: clear(print_kept).
% 2.01/2.17 dependent: clear(print_new_demod).
% 2.01/2.17 dependent: clear(print_back_demod).
% 2.01/2.17 dependent: clear(print_back_sub).
% 2.01/2.17 dependent: set(control_memory).
% 2.01/2.17 dependent: assign(max_mem, 12000).
% 2.01/2.17 dependent: assign(pick_given_ratio, 4).
% 2.01/2.17 dependent: assign(stats_level, 1).
% 2.01/2.17 dependent: assign(max_seconds, 10800).
% 2.01/2.17 clear(print_given).
% 2.01/2.17
% 2.01/2.17 formula_list(usable).
% 2.01/2.17 all A (A=A).
% 2.01/2.17 all A B (in(A,B)-> -in(B,A)).
% 2.01/2.17 all A B (B=powerset(A)<-> (all C (in(C,B)<->subset(C,A)))).
% 2.01/2.17 all A B (subset(A,B)<-> (all C (in(C,A)->in(C,B)))).
% 2.01/2.17 all A B (in(A,B)->subset(A,union(B))).
% 2.01/2.17 exists A empty(A).
% 2.01/2.17 exists A (-empty(A)).
% 2.01/2.17 all A B subset(A,A).
% 2.01/2.17 -(all A subset(A,powerset(union(A)))).
% 2.01/2.17 end_of_list.
% 2.01/2.17
% 2.01/2.17 -------> usable clausifies to:
% 2.01/2.17
% 2.01/2.17 list(usable).
% 2.01/2.17 0 [] A=A.
% 2.01/2.17 0 [] -in(A,B)| -in(B,A).
% 2.01/2.17 0 [] B!=powerset(A)| -in(C,B)|subset(C,A).
% 2.01/2.17 0 [] B!=powerset(A)|in(C,B)| -subset(C,A).
% 2.01/2.17 0 [] B=powerset(A)|in($f1(A,B),B)|subset($f1(A,B),A).
% 2.01/2.17 0 [] B=powerset(A)| -in($f1(A,B),B)| -subset($f1(A,B),A).
% 2.01/2.17 0 [] -subset(A,B)| -in(C,A)|in(C,B).
% 2.01/2.17 0 [] subset(A,B)|in($f2(A,B),A).
% 2.01/2.17 0 [] subset(A,B)| -in($f2(A,B),B).
% 2.01/2.17 0 [] -in(A,B)|subset(A,union(B)).
% 2.01/2.17 0 [] empty($c1).
% 2.01/2.17 0 [] -empty($c2).
% 2.01/2.17 0 [] subset(A,A).
% 2.01/2.17 0 [] -subset($c3,powerset(union($c3))).
% 2.01/2.17 end_of_list.
% 2.01/2.17
% 2.01/2.17 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 2.01/2.17
% 2.01/2.17 This ia a non-Horn set with equality. The strategy will be
% 2.01/2.17 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.01/2.17 deletion, with positive clauses in sos and nonpositive
% 2.01/2.17 clauses in usable.
% 2.01/2.17
% 2.01/2.17 dependent: set(knuth_bendix).
% 2.01/2.17 dependent: set(anl_eq).
% 2.01/2.17 dependent: set(para_from).
% 2.01/2.17 dependent: set(para_into).
% 2.01/2.17 dependent: clear(para_from_right).
% 2.01/2.17 dependent: clear(para_into_right).
% 2.01/2.17 dependent: set(para_from_vars).
% 2.01/2.17 dependent: set(eq_units_both_ways).
% 2.01/2.17 dependent: set(dynamic_demod_all).
% 2.01/2.17 dependent: set(dynamic_demod).
% 2.01/2.17 dependent: set(order_eq).
% 2.01/2.17 dependent: set(back_demod).
% 2.01/2.17 dependent: set(lrpo).
% 2.01/2.17 dependent: set(hyper_res).
% 2.01/2.17 dependent: set(unit_deletion).
% 2.01/2.17 dependent: set(factor).
% 2.01/2.17
% 2.01/2.17 ------------> process usable:
% 2.01/2.17 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 2.01/2.17 ** KEPT (pick-wt=10): 2 [] A!=powerset(B)| -in(C,A)|subset(C,B).
% 2.01/2.17 ** KEPT (pick-wt=10): 3 [] A!=powerset(B)|in(C,A)| -subset(C,B).
% 2.01/2.17 ** KEPT (pick-wt=14): 4 [] A=powerset(B)| -in($f1(B,A),A)| -subset($f1(B,A),B).
% 2.01/2.17 ** KEPT (pick-wt=9): 5 [] -subset(A,B)| -in(C,A)|in(C,B).
% 2.01/2.17 ** KEPT (pick-wt=8): 6 [] subset(A,B)| -in($f2(A,B),B).
% 2.01/2.17 ** KEPT (pick-wt=7): 7 [] -in(A,B)|subset(A,union(B)).
% 2.01/2.17 ** KEPT (pick-wt=2): 8 [] -empty($c2).
% 2.01/2.17 ** KEPT (pick-wt=5): 9 [] -subset($c3,powerset(union($c3))).
% 2.01/2.17
% 2.01/2.17 ------------> process sos:
% 2.01/2.17 ** KEPT (pick-wt=3): 11 [] A=A.
% 2.01/2.17 ** KEPT (pick-wt=14): 12 [] A=powerset(B)|in($f1(B,A),A)|subset($f1(B,A),B).
% 2.01/2.17 ** KEPT (pick-wt=8): 13 [] subset(A,B)|in($f2(A,B),A).
% 2.01/2.17 ** KEPT (pick-wt=2): 14 [] empty($c1).
% 2.01/2.17 ** KEPT (pick-wt=3): 15 [] subset(A,A).
% 2.01/2.17 Following clause subsumed by 11 during input processing: 0 [copy,11,flip.1] A=A.
% 2.01/2.17
% 2.01/2.17 ======= end of input processing =======
% 2.01/2.17
% 2.01/2.17 =========== start of search ===========
% 2.01/2.17
% 2.01/2.17 -------- PROOF --------
% 2.01/2.17
% 2.01/2.17 ----> UNIT CONFLICT at 0.02 sec ----> 453 [binary,452.1,9.1] $F.
% 2.01/2.17
% 2.01/2.17 Length of proof is 4. Level of proof is 4.
% 2.01/2.17
% 2.01/2.17 ---------------- PROOF ----------------
% 2.01/2.17 % SZS status Theorem
% 2.01/2.17 % SZS output start Refutation
% See solution above
% 2.01/2.17 ------------ end of proof -------------
% 2.01/2.17
% 2.01/2.17
% 2.01/2.17 Search stopped by max_proofs option.
% 2.01/2.17
% 2.01/2.17
% 2.01/2.17 Search stopped by max_proofs option.
% 2.01/2.17
% 2.01/2.17 ============ end of search ============
% 2.01/2.17
% 2.01/2.17 -------------- statistics -------------
% 2.01/2.17 clauses given 33
% 2.01/2.17 clauses generated 517
% 2.01/2.17 clauses kept 452
% 2.01/2.17 clauses forward subsumed 80
% 2.01/2.17 clauses back subsumed 0
% 2.01/2.17 Kbytes malloced 2929
% 2.01/2.17
% 2.01/2.17 ----------- times (seconds) -----------
% 2.01/2.17 user CPU time 0.02 (0 hr, 0 min, 0 sec)
% 2.01/2.17 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.01/2.17 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 2.01/2.17
% 2.01/2.17 That finishes the proof of the theorem.
% 2.01/2.17
% 2.01/2.17 Process 6811 finished Wed Jul 27 10:46:01 2022
% 2.01/2.17 Otter interrupted
% 2.01/2.18 PROOF FOUND
%------------------------------------------------------------------------------