TSTP Solution File: SWV019-1 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SWV019-1 : TPTP v8.2.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n010.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 : Tue May 21 05:43:04 EDT 2024

% Result   : Unsatisfiable 2.65s 1.57s
% Output   : Refutation 3.03s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   31 (  11 unt;  10 typ;   0 def)
%            Number of atoms       :   45 (   4 equ;   0 cnn)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  148 (  22   ~;  24   |;   0   &; 102   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (  10 usr;   7 con; 0-2 aty)
%            Number of variables   :   14 (   0   ^  14   !;   0   ?;  14   :)

% Comments : 
%------------------------------------------------------------------------------
thf(in_array_bounds_type,type,
    in_array_bounds: $i > $i > $o ).

thf(array_type,type,
    array: $i ).

thf(an_index_type,type,
    an_index: $i ).

thf(less_than_type,type,
    less_than: $i > $i > $o ).

thf(successor_type,type,
    successor: $i > $i ).

thf(lower_bound_type,type,
    lower_bound: $i ).

thf(upper_bound_type,type,
    upper_bound: $i ).

thf(index_of_maximal_type,type,
    index_of_maximal: $i ).

thf(maximal_value_type,type,
    maximal_value: $i ).

thf(array_value_at_type,type,
    array_value_at: $i > $i > $i ).

thf(2,axiom,
    ! [A: $i] :
      ( ( less_than @ A @ lower_bound )
      | ( less_than @ upper_bound @ A )
      | ( in_array_bounds @ array @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in_bounds) ).

thf(14,plain,
    ! [A: $i] :
      ( ( less_than @ A @ lower_bound )
      | ( less_than @ upper_bound @ A )
      | ( in_array_bounds @ array @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(6,axiom,
    ( ~ ( in_array_bounds @ array @ index_of_maximal )
    | ( maximal_value
      = ( array_value_at @ array @ index_of_maximal ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',this_is_maximal) ).

thf(21,plain,
    ( ~ ( in_array_bounds @ array @ index_of_maximal )
    | ( maximal_value
      = ( array_value_at @ array @ index_of_maximal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(9,axiom,
    ~ ( less_than @ upper_bound @ an_index ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',somewhere_below_upper_bound) ).

thf(27,plain,
    ~ ( less_than @ upper_bound @ an_index ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(4,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( less_than @ A @ B )
      | ~ ( less_than @ B @ C )
      | ( less_than @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_less) ).

thf(18,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( less_than @ A @ B )
      | ~ ( less_than @ B @ C )
      | ( less_than @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(3,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( less_than @ ( successor @ A ) @ ( successor @ B ) )
      | ( less_than @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',predecessor_less) ).

thf(16,plain,
    ! [B: $i,A: $i] :
      ( ~ ( less_than @ ( successor @ A ) @ ( successor @ B ) )
      | ( less_than @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(1,negated_conjecture,
    ( ~ ( 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('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).

thf(11,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 @ 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 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(7,axiom,
    less_than @ index_of_maximal @ an_index,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maximal_before_somewhere) ).

thf(24,plain,
    less_than @ index_of_maximal @ an_index,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(8,axiom,
    ~ ( less_than @ an_index @ lower_bound ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',somewhere_above_lower_bound) ).

thf(25,plain,
    ~ ( less_than @ an_index @ lower_bound ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(5,axiom,
    ! [A: $i] : ( less_than @ A @ ( successor @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_greater) ).

thf(20,plain,
    ! [A: $i] : ( less_than @ A @ ( successor @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(10,axiom,
    ~ ( less_than @ index_of_maximal @ lower_bound ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maximal_above_lower_bound) ).

thf(29,plain,
    ~ ( less_than @ index_of_maximal @ lower_bound ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(33,plain,
    $false,
    inference(cvc4,[status(thm)],[14,21,27,18,16,11,24,25,20,29]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWV019-1 : TPTP v8.2.0. Released v2.4.0.
% 0.03/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n010.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Sun May 19 06:52:39 EDT 2024
% 0.15/0.36  % CPUTime  : 
% 0.91/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.20/0.96  % [INFO] 	 Parsing done (101ms). 
% 1.20/0.96  % [INFO] 	 Running in sequential loop mode. 
% 1.57/1.17  % [INFO] 	 eprover registered as external prover. 
% 1.57/1.17  % [INFO] 	 cvc4 registered as external prover. 
% 1.67/1.18  % [INFO] 	 Scanning for conjecture ... 
% 1.82/1.23  % [INFO] 	 Found a conjecture (or negated_conjecture) and 9 axioms. Running axiom selection ... 
% 1.87/1.26  % [INFO] 	 Axiom selection finished. Selected 9 axioms (removed 0 axioms). 
% 1.87/1.26  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.87/1.27  % [INFO] 	 Type checking passed. 
% 1.87/1.27  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 2.65/1.57  % External prover 'cvc4' found a proof!
% 2.65/1.57  % [INFO] 	 Killing All external provers ... 
% 2.65/1.57  % Time passed: 1052ms (effective reasoning time: 605ms)
% 2.65/1.57  % Axioms used in derivation (9): maximal_before_somewhere, somewhere_below_upper_bound, successor_greater, this_is_maximal, somewhere_above_lower_bound, transitivity_of_less, in_bounds, maximal_above_lower_bound, predecessor_less
% 2.65/1.57  % No. of inferences in proof: 21
% 2.65/1.57  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1052 ms resp. 605 ms w/o parsing
% 3.03/1.65  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.03/1.65  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------