TSTP Solution File: SWV019-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SWV019-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n020.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 13:19:41 EDT 2022
% Result : Unsatisfiable 1.98s 2.12s
% Output : Refutation 1.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 11
% Syntax : Number of clauses : 21 ( 13 unt; 4 nHn; 18 RR)
% Number of literals : 40 ( 6 equ; 16 neg)
% Maximal clause size : 7 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 8 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ less_than(successor(A),successor(B))
| less_than(A,B) ),
file('SWV019-1.p',unknown),
[] ).
cnf(2,axiom,
( ~ less_than(A,B)
| ~ less_than(B,C)
| less_than(A,C) ),
file('SWV019-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ in_array_bounds(array,index_of_maximal)
| maximal_value = array_value_at(array,index_of_maximal) ),
file('SWV019-1.p',unknown),
[] ).
cnf(4,plain,
( ~ in_array_bounds(array,index_of_maximal)
| array_value_at(array,index_of_maximal) = maximal_value ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[3])]),
[iquote('copy,3,flip.2')] ).
cnf(5,axiom,
~ less_than(an_index,lower_bound),
file('SWV019-1.p',unknown),
[] ).
cnf(6,axiom,
~ less_than(upper_bound,an_index),
file('SWV019-1.p',unknown),
[] ).
cnf(7,axiom,
~ less_than(index_of_maximal,lower_bound),
file('SWV019-1.p',unknown),
[] ).
cnf(8,axiom,
( ~ in_array_bounds(array,an_index)
| less_than(successor(an_index),lower_bound)
| less_than(successor(upper_bound),successor(an_index))
| less_than(index_of_maximal,lower_bound)
| ~ less_than(index_of_maximal,successor(an_index))
| ~ in_array_bounds(array,index_of_maximal)
| maximal_value != array_value_at(array,index_of_maximal) ),
file('SWV019-1.p',unknown),
[] ).
cnf(9,plain,
( ~ in_array_bounds(array,an_index)
| less_than(successor(an_index),lower_bound)
| less_than(successor(upper_bound),successor(an_index))
| ~ less_than(index_of_maximal,successor(an_index))
| ~ in_array_bounds(array,index_of_maximal)
| array_value_at(array,index_of_maximal) != maximal_value ),
inference(flip,[status(thm),theory(equality)],[inference(unit_del,[status(thm)],[inference(copy,[status(thm)],[8]),7])]),
[iquote('copy,8,unit_del,7,flip.6')] ).
cnf(10,axiom,
A = A,
file('SWV019-1.p',unknown),
[] ).
cnf(11,axiom,
( less_than(A,lower_bound)
| less_than(upper_bound,A)
| in_array_bounds(array,A) ),
file('SWV019-1.p',unknown),
[] ).
cnf(12,axiom,
less_than(A,successor(A)),
file('SWV019-1.p',unknown),
[] ).
cnf(13,axiom,
less_than(index_of_maximal,an_index),
file('SWV019-1.p',unknown),
[] ).
cnf(14,plain,
less_than(index_of_maximal,successor(an_index)),
inference(hyper,[status(thm)],[12,2,13]),
[iquote('hyper,12,2,13')] ).
cnf(21,plain,
in_array_bounds(array,an_index),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[11,5]),6]),
[iquote('hyper,11,5,unit_del,6')] ).
cnf(29,plain,
in_array_bounds(array,index_of_maximal),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[11,2,13]),7,6]),
[iquote('hyper,11,2,13,unit_del,7,6')] ).
cnf(32,plain,
array_value_at(array,index_of_maximal) = maximal_value,
inference(hyper,[status(thm)],[29,4]),
[iquote('hyper,29,4')] ).
cnf(33,plain,
( less_than(successor(an_index),lower_bound)
| less_than(successor(upper_bound),successor(an_index)) ),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[9]),32]),21,14,29,10]),
[iquote('back_demod,9,demod,32,unit_del,21,14,29,10')] ).
cnf(88,plain,
less_than(successor(an_index),lower_bound),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[33,1]),6]),
[iquote('hyper,33,1,unit_del,6')] ).
cnf(90,plain,
less_than(index_of_maximal,lower_bound),
inference(hyper,[status(thm)],[88,2,14]),
[iquote('hyper,88,2,14')] ).
cnf(91,plain,
$false,
inference(binary,[status(thm)],[90,7]),
[iquote('binary,90.1,7.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SWV019-1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n020.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 05:47:38 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.98/2.12 ----- Otter 3.3f, August 2004 -----
% 1.98/2.12 The process was started by sandbox on n020.cluster.edu,
% 1.98/2.12 Wed Jul 27 05:47:38 2022
% 1.98/2.12 The command was "./otter". The process ID is 11806.
% 1.98/2.12
% 1.98/2.12 set(prolog_style_variables).
% 1.98/2.12 set(auto).
% 1.98/2.12 dependent: set(auto1).
% 1.98/2.12 dependent: set(process_input).
% 1.98/2.12 dependent: clear(print_kept).
% 1.98/2.12 dependent: clear(print_new_demod).
% 1.98/2.12 dependent: clear(print_back_demod).
% 1.98/2.12 dependent: clear(print_back_sub).
% 1.98/2.12 dependent: set(control_memory).
% 1.98/2.12 dependent: assign(max_mem, 12000).
% 1.98/2.12 dependent: assign(pick_given_ratio, 4).
% 1.98/2.12 dependent: assign(stats_level, 1).
% 1.98/2.12 dependent: assign(max_seconds, 10800).
% 1.98/2.12 clear(print_given).
% 1.98/2.12
% 1.98/2.12 list(usable).
% 1.98/2.12 0 [] A=A.
% 1.98/2.12 0 [] less_than(X1,lower_bound)|less_than(upper_bound,X1)|in_array_bounds(array,X1).
% 1.98/2.12 0 [] -less_than(successor(X),successor(Y))|less_than(X,Y).
% 1.98/2.12 0 [] -less_than(X,Y)| -less_than(Y,Z)|less_than(X,Z).
% 1.98/2.12 0 [] less_than(X,successor(X)).
% 1.98/2.12 0 [] -in_array_bounds(array,index_of_maximal)|maximal_value=array_value_at(array,index_of_maximal).
% 1.98/2.12 0 [] less_than(index_of_maximal,an_index).
% 1.98/2.12 0 [] -less_than(an_index,lower_bound).
% 1.98/2.12 0 [] -less_than(upper_bound,an_index).
% 1.98/2.12 0 [] -less_than(index_of_maximal,lower_bound).
% 1.98/2.12 0 [] -in_array_bounds(array,an_index)|less_than(successor(an_index),lower_bound)|less_than(successor(upper_bound),successor(an_index))|less_than(index_of_maximal,lower_bound)| -less_than(index_of_maximal,successor(an_index))| -in_array_bounds(array,index_of_maximal)|maximal_value!=array_value_at(array,index_of_maximal).
% 1.98/2.12 end_of_list.
% 1.98/2.12
% 1.98/2.12 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=7.
% 1.98/2.12
% 1.98/2.12 This ia a non-Horn set with equality. The strategy will be
% 1.98/2.12 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.98/2.12 deletion, with positive clauses in sos and nonpositive
% 1.98/2.12 clauses in usable.
% 1.98/2.12
% 1.98/2.12 dependent: set(knuth_bendix).
% 1.98/2.12 dependent: set(anl_eq).
% 1.98/2.12 dependent: set(para_from).
% 1.98/2.12 dependent: set(para_into).
% 1.98/2.12 dependent: clear(para_from_right).
% 1.98/2.12 dependent: clear(para_into_right).
% 1.98/2.12 dependent: set(para_from_vars).
% 1.98/2.12 dependent: set(eq_units_both_ways).
% 1.98/2.12 dependent: set(dynamic_demod_all).
% 1.98/2.12 dependent: set(dynamic_demod).
% 1.98/2.12 dependent: set(order_eq).
% 1.98/2.12 dependent: set(back_demod).
% 1.98/2.12 dependent: set(lrpo).
% 1.98/2.12 dependent: set(hyper_res).
% 1.98/2.12 dependent: set(unit_deletion).
% 1.98/2.12 dependent: set(factor).
% 1.98/2.12
% 1.98/2.12 ------------> process usable:
% 1.98/2.12 ** KEPT (pick-wt=8): 1 [] -less_than(successor(A),successor(B))|less_than(A,B).
% 1.98/2.12 ** KEPT (pick-wt=9): 2 [] -less_than(A,B)| -less_than(B,C)|less_than(A,C).
% 1.98/2.12 ** KEPT (pick-wt=8): 4 [copy,3,flip.2] -in_array_bounds(array,index_of_maximal)|array_value_at(array,index_of_maximal)=maximal_value.
% 1.98/2.12 ** KEPT (pick-wt=3): 5 [] -less_than(an_index,lower_bound).
% 1.98/2.12 ** KEPT (pick-wt=3): 6 [] -less_than(upper_bound,an_index).
% 1.98/2.12 ** KEPT (pick-wt=3): 7 [] -less_than(index_of_maximal,lower_bound).
% 1.98/2.12 ** KEPT (pick-wt=24): 9 [copy,8,unit_del,7,flip.6] -in_array_bounds(array,an_index)|less_than(successor(an_index),lower_bound)|less_than(successor(upper_bound),successor(an_index))| -less_than(index_of_maximal,successor(an_index))| -in_array_bounds(array,index_of_maximal)|array_value_at(array,index_of_maximal)!=maximal_value.
% 1.98/2.12
% 1.98/2.12 ------------> process sos:
% 1.98/2.12 ** KEPT (pick-wt=3): 10 [] A=A.
% 1.98/2.12 ** KEPT (pick-wt=9): 11 [] less_than(A,lower_bound)|less_than(upper_bound,A)|in_array_bounds(array,A).
% 1.98/2.12 ** KEPT (pick-wt=4): 12 [] less_than(A,successor(A)).
% 1.98/2.12 ** KEPT (pick-wt=3): 13 [] less_than(index_of_maximal,an_index).
% 1.98/2.12 Following clause subsumed by 10 during input processing: 0 [copy,10,flip.1] A=A.
% 1.98/2.12
% 1.98/2.12 ======= end of input processing =======
% 1.98/2.12
% 1.98/2.12 =========== start of search ===========
% 1.98/2.12
% 1.98/2.12 -------- PROOF --------
% 1.98/2.12
% 1.98/2.12 ----> UNIT CONFLICT at 0.01 sec ----> 91 [binary,90.1,7.1] $F.
% 1.98/2.12
% 1.98/2.12 Length of proof is 9. Level of proof is 5.
% 1.98/2.12
% 1.98/2.12 ---------------- PROOF ----------------
% 1.98/2.12 % SZS status Unsatisfiable
% 1.98/2.12 % SZS output start Refutation
% See solution above
% 1.98/2.12 ------------ end of proof -------------
% 1.98/2.12
% 1.98/2.12
% 1.98/2.12 Search stopped by max_proofs option.
% 1.98/2.12
% 1.98/2.12
% 1.98/2.12 Search stopped by max_proofs option.
% 1.98/2.12
% 1.98/2.12 ============ end of search ============
% 1.98/2.12
% 1.98/2.12 -------------- statistics -------------
% 1.98/2.12 clauses given 20
% 1.98/2.12 clauses generated 170
% 1.98/2.12 clauses kept 87
% 1.98/2.12 clauses forward subsumed 96
% 1.98/2.12 clauses back subsumed 10
% 1.98/2.12 Kbytes malloced 976
% 1.98/2.12
% 1.98/2.12 ----------- times (seconds) -----------
% 1.98/2.12 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.98/2.12 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.98/2.12 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.98/2.12
% 1.98/2.12 That finishes the proof of the theorem.
% 1.98/2.12
% 1.98/2.12 Process 11806 finished Wed Jul 27 05:47:40 2022
% 1.98/2.12 Otter interrupted
% 1.98/2.12 PROOF FOUND
%------------------------------------------------------------------------------