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

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---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 : n017.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 05:50:19 EDT 2024

% Result   : Unsatisfiable 15.69s 3.75s
% Output   : Refutation 15.94s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   74 (  22 unt;  10 typ;   0 def)
%            Number of atoms       :  175 (  24 equ;   0 cnn)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  534 (  79   ~;  93   |;   0   &; 362   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  10 usr;   8 con; 0-2 aty)
%            Number of variables   :   43 (   0   ^  43   !;   0   ?;  43   :)

% 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(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/sandbox/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(12,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(cnf,[status(esa)],[11]) ).

thf(13,plain,
    ( ( ( array_value_at @ array @ index_of_maximal )
     != maximal_value )
    | ~ ( 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 ) ),
    inference(lifteq,[status(thm)],[12]) ).

thf(10,axiom,
    ~ ( less_than @ index_of_maximal @ lower_bound ),
    file('/export/starexec/sandbox/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(30,plain,
    ~ ( less_than @ index_of_maximal @ lower_bound ),
    inference(polarity_switch,[status(thm)],[29]) ).

thf(48,plain,
    ( ( ( array_value_at @ array @ index_of_maximal )
     != maximal_value )
    | ~ ( in_array_bounds @ array @ an_index )
    | ( less_than @ ( successor @ an_index ) @ lower_bound )
    | ( less_than @ ( successor @ upper_bound ) @ ( successor @ an_index ) )
    | $false
    | ~ ( less_than @ index_of_maximal @ ( successor @ an_index ) )
    | ~ ( in_array_bounds @ array @ index_of_maximal ) ),
    inference(rewrite,[status(thm)],[13,30]) ).

thf(49,plain,
    ( ( ( array_value_at @ array @ index_of_maximal )
     != maximal_value )
    | ~ ( 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 ) ),
    inference(simp,[status(thm)],[48]) ).

thf(2,axiom,
    ! [A: $i] :
      ( ( less_than @ A @ lower_bound )
      | ( less_than @ upper_bound @ A )
      | ( in_array_bounds @ array @ A ) ),
    file('/export/starexec/sandbox/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(15,plain,
    ! [A: $i] :
      ( ( less_than @ A @ lower_bound )
      | ( less_than @ upper_bound @ A )
      | ( in_array_bounds @ array @ A ) ),
    inference(cnf,[status(esa)],[14]) ).

thf(9,axiom,
    ~ ( less_than @ upper_bound @ an_index ),
    file('/export/starexec/sandbox/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(28,plain,
    ~ ( less_than @ upper_bound @ an_index ),
    inference(polarity_switch,[status(thm)],[27]) ).

thf(62,plain,
    ! [A: $i] :
      ( ( less_than @ A @ lower_bound )
      | ( in_array_bounds @ array @ A )
      | ( ( less_than @ upper_bound @ A )
       != ( less_than @ upper_bound @ an_index ) ) ),
    inference(paramod_ordered,[status(thm)],[15,28]) ).

thf(63,plain,
    ( ( less_than @ an_index @ lower_bound )
    | ( in_array_bounds @ array @ an_index ) ),
    inference(pattern_uni,[status(thm)],[62:[bind(A,$thf( an_index ))]]) ).

thf(8,axiom,
    ~ ( less_than @ an_index @ lower_bound ),
    file('/export/starexec/sandbox/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(26,plain,
    ~ ( less_than @ an_index @ lower_bound ),
    inference(polarity_switch,[status(thm)],[25]) ).

thf(127,plain,
    ( $false
    | ( in_array_bounds @ array @ an_index ) ),
    inference(rewrite,[status(thm)],[63,26]) ).

thf(128,plain,
    in_array_bounds @ array @ an_index,
    inference(simp,[status(thm)],[127]) ).

thf(131,plain,
    ( ( ( array_value_at @ array @ index_of_maximal )
     != maximal_value )
    | ~ $true
    | ( 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 ) ),
    inference(rewrite,[status(thm)],[49,128]) ).

thf(132,plain,
    ( ( ( array_value_at @ array @ index_of_maximal )
     != maximal_value )
    | ( 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 ) ),
    inference(simp,[status(thm)],[131]) ).

thf(5,axiom,
    ! [A: $i] : ( less_than @ A @ ( successor @ A ) ),
    file('/export/starexec/sandbox/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(7,axiom,
    less_than @ index_of_maximal @ an_index,
    file('/export/starexec/sandbox/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(4,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( less_than @ A @ B )
      | ~ ( less_than @ B @ C )
      | ( less_than @ A @ C ) ),
    file('/export/starexec/sandbox/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(19,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( less_than @ A @ B )
      | ~ ( less_than @ B @ C )
      | ( less_than @ A @ C ) ),
    inference(cnf,[status(esa)],[18]) ).

thf(183,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( less_than @ B @ C )
      | ( less_than @ A @ C )
      | ( ( less_than @ index_of_maximal @ an_index )
       != ( less_than @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[24,19]) ).

thf(184,plain,
    ! [A: $i] :
      ( ~ ( less_than @ an_index @ A )
      | ( less_than @ index_of_maximal @ A ) ),
    inference(pattern_uni,[status(thm)],[183:[bind(A,$thf( index_of_maximal )),bind(B,$thf( an_index ))]]) ).

thf(240,plain,
    ! [A: $i] :
      ( ~ ( less_than @ an_index @ A )
      | ( less_than @ index_of_maximal @ A ) ),
    inference(simp,[status(thm)],[184]) ).

thf(1025,plain,
    ! [B: $i,A: $i] :
      ( ( less_than @ index_of_maximal @ B )
      | ( ( less_than @ A @ ( successor @ A ) )
       != ( less_than @ an_index @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[20,240]) ).

thf(1026,plain,
    less_than @ index_of_maximal @ ( successor @ an_index ),
    inference(pattern_uni,[status(thm)],[1025:[bind(A,$thf( an_index )),bind(B,$thf( successor @ an_index ))]]) ).

thf(211,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( less_than @ A @ B )
      | ~ ( less_than @ B @ C )
      | ( ( less_than @ A @ C )
       != ( less_than @ an_index @ lower_bound ) ) ),
    inference(paramod_ordered,[status(thm)],[19,26]) ).

thf(212,plain,
    ! [A: $i] :
      ( ~ ( less_than @ an_index @ A )
      | ~ ( less_than @ A @ lower_bound ) ),
    inference(pattern_uni,[status(thm)],[211:[bind(A,$thf( an_index )),bind(B,$thf( B )),bind(C,$thf( lower_bound ))]]) ).

thf(238,plain,
    ! [A: $i] :
      ( ~ ( less_than @ an_index @ A )
      | ~ ( less_than @ A @ lower_bound ) ),
    inference(simp,[status(thm)],[212]) ).

thf(553,plain,
    ! [B: $i,A: $i] :
      ( ~ ( less_than @ B @ lower_bound )
      | ( ( less_than @ A @ ( successor @ A ) )
       != ( less_than @ an_index @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[20,238]) ).

thf(554,plain,
    ~ ( less_than @ ( successor @ an_index ) @ lower_bound ),
    inference(pattern_uni,[status(thm)],[553:[bind(A,$thf( an_index )),bind(B,$thf( successor @ an_index ))]]) ).

thf(58,plain,
    ! [A: $i] :
      ( ( less_than @ upper_bound @ A )
      | ( in_array_bounds @ array @ A )
      | ( ( less_than @ A @ lower_bound )
       != ( less_than @ index_of_maximal @ lower_bound ) ) ),
    inference(paramod_ordered,[status(thm)],[15,30]) ).

thf(59,plain,
    ( ( less_than @ upper_bound @ index_of_maximal )
    | ( in_array_bounds @ array @ index_of_maximal ) ),
    inference(pattern_uni,[status(thm)],[58:[bind(A,$thf( index_of_maximal ))]]) ).

thf(185,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( less_than @ A @ B )
      | ( less_than @ A @ C )
      | ( ( less_than @ index_of_maximal @ an_index )
       != ( less_than @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[24,19]) ).

thf(186,plain,
    ! [A: $i] :
      ( ~ ( less_than @ A @ index_of_maximal )
      | ( less_than @ A @ an_index ) ),
    inference(pattern_uni,[status(thm)],[185:[bind(A,$thf( A )),bind(B,$thf( index_of_maximal )),bind(C,$thf( an_index ))]]) ).

thf(250,plain,
    ! [A: $i] :
      ( ( in_array_bounds @ array @ index_of_maximal )
      | ( less_than @ A @ an_index )
      | ( ( less_than @ upper_bound @ index_of_maximal )
       != ( less_than @ A @ index_of_maximal ) ) ),
    inference(paramod_ordered,[status(thm)],[59,186]) ).

thf(251,plain,
    ( ( in_array_bounds @ array @ index_of_maximal )
    | ( less_than @ upper_bound @ an_index ) ),
    inference(pattern_uni,[status(thm)],[250:[bind(A,$thf( upper_bound ))]]) ).

thf(268,plain,
    ( ( in_array_bounds @ array @ index_of_maximal )
    | $false ),
    inference(rewrite,[status(thm)],[251,28]) ).

thf(269,plain,
    in_array_bounds @ array @ index_of_maximal,
    inference(simp,[status(thm)],[268]) ).

thf(6,axiom,
    ( ~ ( in_array_bounds @ array @ index_of_maximal )
    | ( maximal_value
      = ( array_value_at @ array @ index_of_maximal ) ) ),
    file('/export/starexec/sandbox/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(22,plain,
    ( ~ ( in_array_bounds @ array @ index_of_maximal )
    | ( maximal_value
      = ( array_value_at @ array @ index_of_maximal ) ) ),
    inference(cnf,[status(esa)],[21]) ).

thf(23,plain,
    ( ( ( array_value_at @ array @ index_of_maximal )
      = maximal_value )
    | ~ ( in_array_bounds @ array @ index_of_maximal ) ),
    inference(lifteq,[status(thm)],[22]) ).

thf(270,plain,
    ( ( ( array_value_at @ array @ index_of_maximal )
      = maximal_value )
    | ~ $true ),
    inference(rewrite,[status(thm)],[23,269]) ).

thf(271,plain,
    ( ( array_value_at @ array @ index_of_maximal )
    = maximal_value ),
    inference(simp,[status(thm)],[270]) ).

thf(1890,plain,
    ( ( maximal_value != maximal_value )
    | $false
    | ( less_than @ ( successor @ upper_bound ) @ ( successor @ an_index ) )
    | ~ $true
    | ~ $true ),
    inference(rewrite,[status(thm)],[132,1026,554,269,271]) ).

thf(1891,plain,
    less_than @ ( successor @ upper_bound ) @ ( successor @ an_index ),
    inference(simp,[status(thm)],[1890]) ).

thf(3,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( less_than @ ( successor @ A ) @ ( successor @ B ) )
      | ( less_than @ A @ B ) ),
    file('/export/starexec/sandbox/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(17,plain,
    ! [B: $i,A: $i] :
      ( ~ ( less_than @ ( successor @ A ) @ ( successor @ B ) )
      | ( less_than @ A @ B ) ),
    inference(cnf,[status(esa)],[16]) ).

thf(1905,plain,
    ! [B: $i,A: $i] :
      ( ( less_than @ A @ B )
      | ( ( less_than @ ( successor @ upper_bound ) @ ( successor @ an_index ) )
       != ( less_than @ ( successor @ A ) @ ( successor @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1891,17]) ).

thf(1906,plain,
    less_than @ upper_bound @ an_index,
    inference(pattern_uni,[status(thm)],[1905:[bind(A,$thf( upper_bound )),bind(B,$thf( an_index ))]]) ).

thf(1957,plain,
    $false,
    inference(rewrite,[status(thm)],[1906,28]) ).

thf(1958,plain,
    $false,
    inference(simp,[status(thm)],[1957]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SWV019-1 : TPTP v8.2.0. Released v2.4.0.
% 0.11/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n017.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Sun May 19 06:52:39 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 1.01/0.88  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.09/1.00  % [INFO] 	 Parsing done (110ms). 
% 1.09/1.00  % [INFO] 	 Running in sequential loop mode. 
% 1.66/1.22  % [INFO] 	 nitpick registered as external prover. 
% 1.66/1.23  % [INFO] 	 Scanning for conjecture ... 
% 1.77/1.29  % [INFO] 	 Found a conjecture (or negated_conjecture) and 9 axioms. Running axiom selection ... 
% 1.77/1.31  % [INFO] 	 Axiom selection finished. Selected 9 axioms (removed 0 axioms). 
% 1.77/1.31  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.77/1.32  % [INFO] 	 Type checking passed. 
% 1.77/1.32  % [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 ... 
% 15.69/3.73  % [INFO] 	 Killing All external provers ... 
% 15.69/3.74  % Time passed: 3193ms (effective reasoning time: 2729ms)
% 15.69/3.75  % 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
% 15.69/3.75  % No. of inferences in proof: 64
% 15.69/3.75  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 3193 ms resp. 2729 ms w/o parsing
% 15.90/3.84  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 15.94/3.86  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------