TSTP Solution File: SWV019-1 by Otter---3.3

View Problem - 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
%------------------------------------------------------------------------------