TSTP Solution File: ITP118^1 by Satallax---3.5

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%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : ITP118^1 : 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 : n024.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 00:29:10 EDT 2022

% Result   : Theorem 2.59s 2.84s
% Output   : Proof 2.59s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   25
% Syntax   : Number of formulae    :   52 (  26 unt;  11 typ;   0 def)
%            Number of atoms       :  223 (  27 equ;   0 cnn)
%            Maximal formula atoms :    2 (   5 avg)
%            Number of connectives :  214 (  17   ~;  10   |;   0   &; 182   @)
%                                         (   0 <=>;   4  =>;   1  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Number of types       :    4 (   4 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   29 (  27 usr;  25 con; 0-2 aty)
%            Number of variables   :   17 (   0   ^  17   !;   0   ?;  17   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_finite1489363574real_n,type,
    finite1489363574real_n: $tType ).

thf(ty_n,type,
    n: $tType ).

thf(ty_int,type,
    int: $tType ).

thf(ty_real,type,
    real: $tType ).

thf(ty_minus_minus_real,type,
    minus_minus_real: real > real > real ).

thf(ty_eigen__0,type,
    eigen__0: int ).

thf(ty_y,type,
    y: finite1489363574real_n ).

thf(ty_i,type,
    i: n ).

thf(ty_finite772340589real_n,type,
    finite772340589real_n: finite1489363574real_n > n > real ).

thf(ty_x,type,
    x: finite1489363574real_n ).

thf(ty_ring_1_of_int_real,type,
    ring_1_of_int_real: int > real ).

thf(conj_0,conjecture,
    ( ( ring_1_of_int_real @ ( abs_abs_int @ m ) )
    = ( abs_abs_real @ ( finite772340589real_n @ ( minus_1037315151real_n @ x @ y ) @ i ) ) ) ).

thf(h0,negated_conjecture,
    ( ring_1_of_int_real @ ( abs_abs_int @ m ) )
 != ( abs_abs_real @ ( finite772340589real_n @ ( minus_1037315151real_n @ x @ y ) @ i ) ),
    inference(assume_negation,[status(cth)],[conj_0]) ).

thf(h1,assumption,
    ( ( ring_1_of_int_real @ eigen__0 )
    = ( minus_minus_real @ ( finite772340589real_n @ x @ i ) @ ( finite772340589real_n @ y @ i ) ) ),
    introduced(assumption,[]) ).

thf(pax4,axiom,
    ( p4
   => ( ( fring_1_of_int_real @ f__0 )
      = ( fminus_minus_real @ ( ffinite772340589real_n @ fx @ fi ) @ ( ffinite772340589real_n @ fy @ fi ) ) ) ),
    file('<stdin>',pax4) ).

thf(pax3,axiom,
    ( p3
   => ( ( fring_1_of_int_real @ fm )
      = ( fminus_minus_real @ ( ffinite772340589real_n @ fx @ fi ) @ ( ffinite772340589real_n @ fy @ fi ) ) ) ),
    file('<stdin>',pax3) ).

thf(ax106,axiom,
    p4,
    file('<stdin>',ax106) ).

thf(pax7,axiom,
    ( p7
   => ! [X92: int] :
        ( ( fring_1_of_int_real @ ( fabs_abs_int @ X92 ) )
        = ( fabs_abs_real @ ( fring_1_of_int_real @ X92 ) ) ) ),
    file('<stdin>',pax7) ).

thf(ax107,axiom,
    p3,
    file('<stdin>',ax107) ).

thf(pax5,axiom,
    ( p5
   => ! [X94: finite1489363574real_n,X95: finite1489363574real_n,X96: n] :
        ( ( ffinite772340589real_n @ ( fminus_1037315151real_n @ X94 @ X95 ) @ X96 )
        = ( fminus_minus_real @ ( ffinite772340589real_n @ X94 @ X96 ) @ ( ffinite772340589real_n @ X95 @ X96 ) ) ) ),
    file('<stdin>',pax5) ).

thf(nax110,axiom,
    ( p110
   <= ( ( fring_1_of_int_real @ ( fabs_abs_int @ fm ) )
      = ( fabs_abs_real @ ( ffinite772340589real_n @ ( fminus_1037315151real_n @ fx @ fy ) @ fi ) ) ) ),
    file('<stdin>',nax110) ).

thf(ax103,axiom,
    p7,
    file('<stdin>',ax103) ).

thf(ax0,axiom,
    ~ p110,
    file('<stdin>',ax0) ).

thf(ax105,axiom,
    p5,
    file('<stdin>',ax105) ).

thf(c_0_10,plain,
    ( ~ p4
    | ( ( fring_1_of_int_real @ f__0 )
      = ( fminus_minus_real @ ( ffinite772340589real_n @ fx @ fi ) @ ( ffinite772340589real_n @ fy @ fi ) ) ) ),
    inference(fof_nnf,[status(thm)],[pax4]) ).

thf(c_0_11,plain,
    ( ~ p3
    | ( ( fring_1_of_int_real @ fm )
      = ( fminus_minus_real @ ( ffinite772340589real_n @ fx @ fi ) @ ( ffinite772340589real_n @ fy @ fi ) ) ) ),
    inference(fof_nnf,[status(thm)],[pax3]) ).

thf(c_0_12,plain,
    ( ( ( fring_1_of_int_real @ f__0 )
      = ( fminus_minus_real @ ( ffinite772340589real_n @ fx @ fi ) @ ( ffinite772340589real_n @ fy @ fi ) ) )
    | ~ p4 ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

thf(c_0_13,plain,
    p4,
    inference(split_conjunct,[status(thm)],[ax106]) ).

thf(c_0_14,plain,
    ! [X345: int] :
      ( ~ p7
      | ( ( fring_1_of_int_real @ ( fabs_abs_int @ X345 ) )
        = ( fabs_abs_real @ ( fring_1_of_int_real @ X345 ) ) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax7])])]) ).

thf(c_0_15,plain,
    ( ( ( fring_1_of_int_real @ fm )
      = ( fminus_minus_real @ ( ffinite772340589real_n @ fx @ fi ) @ ( ffinite772340589real_n @ fy @ fi ) ) )
    | ~ p3 ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

thf(c_0_16,plain,
    ( ( fminus_minus_real @ ( ffinite772340589real_n @ fx @ fi ) @ ( ffinite772340589real_n @ fy @ fi ) )
    = ( fring_1_of_int_real @ f__0 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13])]) ).

thf(c_0_17,plain,
    p3,
    inference(split_conjunct,[status(thm)],[ax107]) ).

thf(c_0_18,plain,
    ! [X349: finite1489363574real_n,X350: finite1489363574real_n,X351: n] :
      ( ~ p5
      | ( ( ffinite772340589real_n @ ( fminus_1037315151real_n @ X349 @ X350 ) @ X351 )
        = ( fminus_minus_real @ ( ffinite772340589real_n @ X349 @ X351 ) @ ( ffinite772340589real_n @ X350 @ X351 ) ) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax5])])]) ).

thf(c_0_19,plain,
    ( ( ( fring_1_of_int_real @ ( fabs_abs_int @ fm ) )
     != ( fabs_abs_real @ ( ffinite772340589real_n @ ( fminus_1037315151real_n @ fx @ fy ) @ fi ) ) )
    | p110 ),
    inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax110])]) ).

thf(c_0_20,plain,
    ! [X3: int] :
      ( ( ( fring_1_of_int_real @ ( fabs_abs_int @ X3 ) )
        = ( fabs_abs_real @ ( fring_1_of_int_real @ X3 ) ) )
      | ~ p7 ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

thf(c_0_21,plain,
    p7,
    inference(split_conjunct,[status(thm)],[ax103]) ).

thf(c_0_22,plain,
    ~ p110,
    inference(fof_simplification,[status(thm)],[ax0]) ).

thf(c_0_23,plain,
    ( ( fring_1_of_int_real @ f__0 )
    = ( fring_1_of_int_real @ fm ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_17])]) ).

thf(c_0_24,plain,
    ! [X9: finite1489363574real_n,X10: finite1489363574real_n,X11: n] :
      ( ( ( ffinite772340589real_n @ ( fminus_1037315151real_n @ X9 @ X10 ) @ X11 )
        = ( fminus_minus_real @ ( ffinite772340589real_n @ X9 @ X11 ) @ ( ffinite772340589real_n @ X10 @ X11 ) ) )
      | ~ p5 ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

thf(c_0_25,plain,
    p5,
    inference(split_conjunct,[status(thm)],[ax105]) ).

thf(c_0_26,plain,
    ( p110
    | ( ( fring_1_of_int_real @ ( fabs_abs_int @ fm ) )
     != ( fabs_abs_real @ ( ffinite772340589real_n @ ( fminus_1037315151real_n @ fx @ fy ) @ fi ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

thf(c_0_27,plain,
    ! [X3: int] :
      ( ( fring_1_of_int_real @ ( fabs_abs_int @ X3 ) )
      = ( fabs_abs_real @ ( fring_1_of_int_real @ X3 ) ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21])]) ).

thf(c_0_28,plain,
    ~ p110,
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

thf(c_0_29,plain,
    ( ( fminus_minus_real @ ( ffinite772340589real_n @ fx @ fi ) @ ( ffinite772340589real_n @ fy @ fi ) )
    = ( fring_1_of_int_real @ fm ) ),
    inference(rw,[status(thm)],[c_0_16,c_0_23]) ).

thf(c_0_30,plain,
    ! [X9: finite1489363574real_n,X10: finite1489363574real_n,X11: n] :
      ( ( fminus_minus_real @ ( ffinite772340589real_n @ X9 @ X11 ) @ ( ffinite772340589real_n @ X10 @ X11 ) )
      = ( ffinite772340589real_n @ ( fminus_1037315151real_n @ X9 @ X10 ) @ X11 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])]) ).

thf(c_0_31,plain,
    ( fabs_abs_real @ ( ffinite772340589real_n @ ( fminus_1037315151real_n @ fx @ fy ) @ fi ) )
 != ( fabs_abs_real @ ( fring_1_of_int_real @ fm ) ),
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).

thf(c_0_32,plain,
    ( ( ffinite772340589real_n @ ( fminus_1037315151real_n @ fx @ fy ) @ fi )
    = ( fring_1_of_int_real @ fm ) ),
    inference(rw,[status(thm)],[c_0_29,c_0_30]) ).

thf(c_0_33,plain,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32])]),
    [proof] ).

thf(1,plain,
    $false,
    inference(eprover,[status(thm),assumptions([h1,h0])],]) ).

thf(fact_3__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062m_O_Areal__of__int_Am_A_061_Ax_A_E_Ai_A_N_Ay_A_E_Ai_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
    ~ ! [X1: int] :
        ( ( ring_1_of_int_real @ X1 )
       != ( minus_minus_real @ ( finite772340589real_n @ x @ i ) @ ( finite772340589real_n @ y @ i ) ) ) ).

thf(2,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[fact_3__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062m_O_Areal__of__int_Am_A_061_Ax_A_E_Ai_A_N_Ay_A_E_Ai_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,1,h1]) ).

thf(0,theorem,
    ( ( ring_1_of_int_real @ ( abs_abs_int @ m ) )
    = ( abs_abs_real @ ( finite772340589real_n @ ( minus_1037315151real_n @ x @ y ) @ i ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[2,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : ITP118^1 : TPTP v8.1.0. Released v7.5.0.
% 0.07/0.13  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34  % Computer : n024.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Thu Jun  2 21:42:50 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 2.59/2.84  % SZS status Theorem
% 2.59/2.84  % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
% 2.59/2.84  % Inferences: 1
% 2.59/2.84  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------