TSTP Solution File: SWV019-1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SWV019-1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n021.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 : Thu Aug 31 21:36:10 EDT 2023

% Result   : Unsatisfiable 0.20s 0.58s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   40 (  12 unt;  10 typ;   0 def)
%            Number of atoms       :   70 (   4 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   77 (  37   ~;  40   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   4   >;   3   *;   0   +;   0  <<)
%            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   :   19 (   0 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    lower_bound: $i ).

tff(decl_23,type,
    less_than: ( $i * $i ) > $o ).

tff(decl_24,type,
    upper_bound: $i ).

tff(decl_25,type,
    array: $i ).

tff(decl_26,type,
    in_array_bounds: ( $i * $i ) > $o ).

tff(decl_27,type,
    successor: $i > $i ).

tff(decl_28,type,
    index_of_maximal: $i ).

tff(decl_29,type,
    maximal_value: $i ).

tff(decl_30,type,
    array_value_at: ( $i * $i ) > $i ).

tff(decl_31,type,
    an_index: $i ).

cnf(prove_this,negated_conjecture,
    ( less_than(successor(an_index),lower_bound)
    | less_than(successor(upper_bound),successor(an_index))
    | less_than(index_of_maximal,lower_bound)
    | ~ in_array_bounds(array,an_index)
    | ~ 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) ).

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

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

cnf(predecessor_less,axiom,
    ( less_than(X1,X2)
    | ~ less_than(successor(X1),successor(X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',predecessor_less) ).

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

cnf(in_bounds,axiom,
    ( less_than(X1,lower_bound)
    | less_than(upper_bound,X1)
    | in_array_bounds(array,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in_bounds) ).

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

cnf(transitivity_of_less,axiom,
    ( less_than(X1,X3)
    | ~ less_than(X1,X2)
    | ~ less_than(X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_less) ).

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

cnf(successor_greater,axiom,
    less_than(X1,successor(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_greater) ).

cnf(c_0_10,negated_conjecture,
    ( less_than(successor(an_index),lower_bound)
    | less_than(successor(upper_bound),successor(an_index))
    | less_than(index_of_maximal,lower_bound)
    | ~ in_array_bounds(array,an_index)
    | ~ less_than(index_of_maximal,successor(an_index))
    | ~ in_array_bounds(array,index_of_maximal)
    | maximal_value != array_value_at(array,index_of_maximal) ),
    prove_this ).

cnf(c_0_11,axiom,
    ~ less_than(index_of_maximal,lower_bound),
    maximal_above_lower_bound ).

cnf(c_0_12,axiom,
    ( maximal_value = array_value_at(array,index_of_maximal)
    | ~ in_array_bounds(array,index_of_maximal) ),
    this_is_maximal ).

cnf(c_0_13,axiom,
    ( less_than(X1,X2)
    | ~ less_than(successor(X1),successor(X2)) ),
    predecessor_less ).

cnf(c_0_14,negated_conjecture,
    ( less_than(successor(upper_bound),successor(an_index))
    | less_than(successor(an_index),lower_bound)
    | ~ in_array_bounds(array,index_of_maximal)
    | ~ in_array_bounds(array,an_index)
    | ~ less_than(index_of_maximal,successor(an_index)) ),
    inference(csr,[status(thm)],[inference(sr,[status(thm)],[c_0_10,c_0_11]),c_0_12]) ).

cnf(c_0_15,axiom,
    ~ less_than(upper_bound,an_index),
    somewhere_below_upper_bound ).

cnf(c_0_16,negated_conjecture,
    ( less_than(successor(an_index),lower_bound)
    | ~ in_array_bounds(array,index_of_maximal)
    | ~ in_array_bounds(array,an_index)
    | ~ less_than(index_of_maximal,successor(an_index)) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).

cnf(c_0_17,axiom,
    ( less_than(X1,lower_bound)
    | less_than(upper_bound,X1)
    | in_array_bounds(array,X1) ),
    in_bounds ).

cnf(c_0_18,axiom,
    ~ less_than(an_index,lower_bound),
    somewhere_above_lower_bound ).

cnf(c_0_19,axiom,
    ( less_than(X1,X3)
    | ~ less_than(X1,X2)
    | ~ less_than(X2,X3) ),
    transitivity_of_less ).

cnf(c_0_20,axiom,
    less_than(index_of_maximal,an_index),
    maximal_before_somewhere ).

cnf(c_0_21,negated_conjecture,
    ( less_than(successor(an_index),lower_bound)
    | ~ in_array_bounds(array,index_of_maximal)
    | ~ less_than(index_of_maximal,successor(an_index)) ),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]),c_0_15]) ).

cnf(c_0_22,plain,
    ( less_than(X1,an_index)
    | ~ less_than(X1,index_of_maximal) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_23,negated_conjecture,
    ( less_than(successor(an_index),lower_bound)
    | less_than(upper_bound,index_of_maximal)
    | ~ less_than(index_of_maximal,successor(an_index)) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_17]),c_0_11]) ).

cnf(c_0_24,plain,
    ~ less_than(upper_bound,index_of_maximal),
    inference(spm,[status(thm)],[c_0_15,c_0_22]) ).

cnf(c_0_25,axiom,
    less_than(X1,successor(X1)),
    successor_greater ).

cnf(c_0_26,negated_conjecture,
    ( less_than(X1,lower_bound)
    | ~ less_than(index_of_maximal,successor(an_index))
    | ~ less_than(X1,successor(an_index)) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_23]),c_0_24]) ).

cnf(c_0_27,plain,
    ( less_than(X1,successor(X2))
    | ~ less_than(X1,X2) ),
    inference(spm,[status(thm)],[c_0_19,c_0_25]) ).

cnf(c_0_28,negated_conjecture,
    ( less_than(X1,lower_bound)
    | ~ less_than(X1,successor(an_index)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_20])]) ).

cnf(c_0_29,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_25]),c_0_18]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SWV019-1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.14  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35  % Computer : n021.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Tue Aug 29 04:21:44 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.57  start to proof: theBenchmark
% 0.20/0.58  % Version  : CSE_E---1.5
% 0.20/0.58  % Problem  : theBenchmark.p
% 0.20/0.58  % Proof found
% 0.20/0.58  % SZS status Theorem for theBenchmark.p
% 0.20/0.58  % SZS output start Proof
% See solution above
% 0.20/0.58  % Total time : 0.004000 s
% 0.20/0.58  % SZS output end Proof
% 0.20/0.58  % Total time : 0.006000 s
%------------------------------------------------------------------------------