TSTP Solution File: ITP056^1 by Satallax---3.5

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%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : ITP056^1 : TPTP v8.1.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n032.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  : 600s
% DateTime : Sun Jul 17 00:28:55 EDT 2022

% Result   : Theorem 1.34s 1.60s
% Output   : Proof 1.34s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   25 (  15 unt;   0 typ;   0 def)
%            Number of atoms       :  151 (  19 equ;   0 cnn)
%            Maximal formula atoms :    3 (   6 avg)
%            Number of connectives :  120 (  16   ~;   9   |;   0   &;  91   @)
%                                         (   0 <=>;   2  =>;   2  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Number of types       :    0 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   21 (  19 usr;  20 con; 0-2 aty)
%            Number of variables   :    4 (   0   ^   4   !;   0   ?;   4   :)

% Comments : 
%------------------------------------------------------------------------------
thf(conj_0,conjecture,
    ( ( last_c571238084t_unit @ ( fe @ n ) )
    = ( nth_co1649820636t_unit @ ( fe @ n ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ n ) ) @ one_one_nat ) ) ) ).

thf(h0,negated_conjecture,
    ( last_c571238084t_unit @ ( fe @ n ) )
 != ( nth_co1649820636t_unit @ ( fe @ n ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ n ) ) @ one_one_nat ) ),
    inference(assume_negation,[status(cth)],[conj_0]) ).

thf(nax52,axiom,
    ( p52
   <= ( ( flast_c571238084t_unit @ ( ffe @ fn ) )
      = ( fnth_co1649820636t_unit @ ( ffe @ fn ) @ ( fminus_minus_nat @ ( fsize_s1406904903t_unit @ ( ffe @ fn ) ) @ fone_one_nat ) ) ) ),
    file('<stdin>',nax52) ).

thf(ax0,axiom,
    ~ p52,
    file('<stdin>',ax0) ).

thf(pax2,axiom,
    ( p2
   => ! [X14: list_c1059388851t_unit] :
        ( ( X14 != fnil_co1338500125t_unit )
       => ( ( flast_c571238084t_unit @ X14 )
          = ( fnth_co1649820636t_unit @ X14 @ ( fminus_minus_nat @ ( fsize_s1406904903t_unit @ X14 ) @ fone_one_nat ) ) ) ) ),
    file('<stdin>',pax2) ).

thf(nax1,axiom,
    ( p1
   <= ( ( ffe @ fn )
      = fnil_co1338500125t_unit ) ),
    file('<stdin>',nax1) ).

thf(ax51,axiom,
    ~ p1,
    file('<stdin>',ax51) ).

thf(ax50,axiom,
    p2,
    file('<stdin>',ax50) ).

thf(c_0_6,plain,
    ( ( ( flast_c571238084t_unit @ ( ffe @ fn ) )
     != ( fnth_co1649820636t_unit @ ( ffe @ fn ) @ ( fminus_minus_nat @ ( fsize_s1406904903t_unit @ ( ffe @ fn ) ) @ fone_one_nat ) ) )
    | p52 ),
    inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax52])]) ).

thf(c_0_7,plain,
    ~ p52,
    inference(fof_simplification,[status(thm)],[ax0]) ).

thf(c_0_8,plain,
    ! [X169: list_c1059388851t_unit] :
      ( ~ p2
      | ( X169 = fnil_co1338500125t_unit )
      | ( ( flast_c571238084t_unit @ X169 )
        = ( fnth_co1649820636t_unit @ X169 @ ( fminus_minus_nat @ ( fsize_s1406904903t_unit @ X169 ) @ fone_one_nat ) ) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax2])])])]) ).

thf(c_0_9,plain,
    ( ( ( ffe @ fn )
     != fnil_co1338500125t_unit )
    | p1 ),
    inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax1])]) ).

thf(c_0_10,plain,
    ~ p1,
    inference(fof_simplification,[status(thm)],[ax51]) ).

thf(c_0_11,plain,
    ( p52
    | ( ( flast_c571238084t_unit @ ( ffe @ fn ) )
     != ( fnth_co1649820636t_unit @ ( ffe @ fn ) @ ( fminus_minus_nat @ ( fsize_s1406904903t_unit @ ( ffe @ fn ) ) @ fone_one_nat ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

thf(c_0_12,plain,
    ~ p52,
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

thf(c_0_13,plain,
    ! [X6: list_c1059388851t_unit] :
      ( ( X6 = fnil_co1338500125t_unit )
      | ( ( flast_c571238084t_unit @ X6 )
        = ( fnth_co1649820636t_unit @ X6 @ ( fminus_minus_nat @ ( fsize_s1406904903t_unit @ X6 ) @ fone_one_nat ) ) )
      | ~ p2 ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

thf(c_0_14,plain,
    p2,
    inference(split_conjunct,[status(thm)],[ax50]) ).

thf(c_0_15,plain,
    ( p1
    | ( ( ffe @ fn )
     != fnil_co1338500125t_unit ) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

thf(c_0_16,plain,
    ~ p1,
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

thf(c_0_17,plain,
    ( fnth_co1649820636t_unit @ ( ffe @ fn ) @ ( fminus_minus_nat @ ( fsize_s1406904903t_unit @ ( ffe @ fn ) ) @ fone_one_nat ) )
 != ( flast_c571238084t_unit @ ( ffe @ fn ) ),
    inference(sr,[status(thm)],[c_0_11,c_0_12]) ).

thf(c_0_18,plain,
    ! [X6: list_c1059388851t_unit] :
      ( ( ( fnth_co1649820636t_unit @ X6 @ ( fminus_minus_nat @ ( fsize_s1406904903t_unit @ X6 ) @ fone_one_nat ) )
        = ( flast_c571238084t_unit @ X6 ) )
      | ( X6 = fnil_co1338500125t_unit ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14])]) ).

thf(c_0_19,plain,
    ( ffe @ fn )
 != fnil_co1338500125t_unit,
    inference(sr,[status(thm)],[c_0_15,c_0_16]) ).

thf(c_0_20,plain,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),
    [proof] ).

thf(1,plain,
    $false,
    inference(eprover,[status(thm),assumptions([h0])],]) ).

thf(0,theorem,
    ( ( last_c571238084t_unit @ ( fe @ n ) )
    = ( nth_co1649820636t_unit @ ( fe @ n ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ n ) ) @ one_one_nat ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.09  % Problem  : ITP056^1 : TPTP v8.1.0. Released v7.5.0.
% 0.03/0.10  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.09/0.29  % Computer : n032.cluster.edu
% 0.09/0.29  % Model    : x86_64 x86_64
% 0.09/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29  % Memory   : 8042.1875MB
% 0.09/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29  % CPULimit : 300
% 0.09/0.29  % WCLimit  : 600
% 0.09/0.29  % DateTime : Thu Jun  2 14:07:45 EDT 2022
% 0.09/0.29  % CPUTime  : 
% 1.34/1.60  % SZS status Theorem
% 1.34/1.60  % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
% 1.34/1.60  % Inferences: 1
% 1.34/1.60  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------