%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : ITP100^1 : 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 : n025.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 00:29:06 EDT 2022

% Result   : Theorem 2.65s 2.83s
% Output   : Proof 2.65s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   43 (  21 unt;  10 typ;   0 def)
%            Number of atoms       :  127 (  20 equ;   0 cnn)
%            Maximal formula atoms :    2 (   3 avg)
%            Number of connectives :  188 (  14   ~;   8   |;   0   &; 162   @)
%                                         (   0 <=>;   3  =>;   1  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Number of types       :    3 (   3 usr)
%            Number of type conns  :   11 (  11   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   21 (  19 usr;  17 con; 0-3 aty)
%            Number of variables   :   29 (   0   ^  29   !;   0   ?;  29   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_a,type,
    a: $tType ).

thf(ty_nat,type,
    nat: $tType ).

thf(ty_list_a,type,
    list_a: $tType ).

thf(ty_eigen__0,type,
    eigen__0: nat ).

thf(ty_xs,type,
    xs: list_a ).

thf(ty_f,type,
    f: nat > a ).

thf(ty_listIn1312259492pend_a,type,
    listIn1312259492pend_a: list_a > ( nat > a ) > nat > a ).

thf(ty_x,type,
    x: a ).

thf(ty_cons_a,type,
    cons_a: a > list_a > list_a ).

thf(ty_nil_a,type,
    nil_a: list_a ).

thf(conj_0,conjecture,
    ( ( listIn1312259492pend_a @ ( cons_a @ x @ xs ) @ f )
    = ( listIn1312259492pend_a @ ( cons_a @ x @ nil_a ) @ ( listIn1312259492pend_a @ xs @ f ) ) ) ).

thf(h0,negated_conjecture,
    ( listIn1312259492pend_a @ ( cons_a @ x @ xs ) @ f )
 != ( listIn1312259492pend_a @ ( cons_a @ x @ nil_a ) @ ( listIn1312259492pend_a @ xs @ f ) ),
    inference(assume_negation,[status(cth)],[conj_0]) ).

thf(h1,assumption,
    ~ ! [X1: nat] :
        ( ( listIn1312259492pend_a @ ( cons_a @ x @ xs ) @ f @ X1 )
        = ( listIn1312259492pend_a @ ( cons_a @ x @ nil_a ) @ ( listIn1312259492pend_a @ xs @ f ) @ X1 ) ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    ( listIn1312259492pend_a @ ( cons_a @ x @ xs ) @ f @ eigen__0 )
 != ( listIn1312259492pend_a @ ( cons_a @ x @ nil_a ) @ ( listIn1312259492pend_a @ xs @ f ) @ eigen__0 ),
    introduced(assumption,[]) ).

thf(pax31,axiom,
    ( p31
   => ! [X14: list_a,X9: list_a,X15: nat > a] :
        ( ( flistIn1312259492pend_a @ X14 @ ( flistIn1312259492pend_a @ X9 @ X15 ) )
        = ( flistIn1312259492pend_a @ ( fappend_a @ X14 @ X9 ) @ X15 ) ) ),
    file('<stdin>',pax31) ).

thf(pax33,axiom,
    ( p33
   => ! [X12: a,X9: list_a,X13: list_a] :
        ( ( fappend_a @ ( fcons_a @ X12 @ X9 ) @ X13 )
        = ( fcons_a @ X12 @ ( fappend_a @ X9 @ X13 ) ) ) ),
    file('<stdin>',pax33) ).

thf(pax35,axiom,
    ( p35
   => ! [X10: list_a] :
        ( ( fappend_a @ fnil_a @ X10 )
        = X10 ) ),
    file('<stdin>',pax35) ).

thf(nax59,axiom,
    ( p59
   <= ( ( flistIn1312259492pend_a @ ( fcons_a @ fx @ fxs ) @ ff @ f__0 )
      = ( flistIn1312259492pend_a @ ( fcons_a @ fx @ fnil_a ) @ ( flistIn1312259492pend_a @ fxs @ ff ) @ f__0 ) ) ),
    file('<stdin>',nax59) ).

thf(ax28,axiom,
    p31,
    file('<stdin>',ax28) ).

thf(ax26,axiom,
    p33,
    file('<stdin>',ax26) ).

thf(ax24,axiom,
    p35,
    file('<stdin>',ax24) ).

thf(ax0,axiom,
    ~ p59,
    file('<stdin>',ax0) ).

thf(c_0_8,plain,
    ! [X122: list_a,X123: list_a,X124: nat > a] :
      ( ~ p31
      | ( ( flistIn1312259492pend_a @ X122 @ ( flistIn1312259492pend_a @ X123 @ X124 ) )
        = ( flistIn1312259492pend_a @ ( fappend_a @ X122 @ X123 ) @ X124 ) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax31])])]) ).

thf(c_0_9,plain,
    ! [X116: a,X117: list_a,X118: list_a] :
      ( ~ p33
      | ( ( fappend_a @ ( fcons_a @ X116 @ X117 ) @ X118 )
        = ( fcons_a @ X116 @ ( fappend_a @ X117 @ X118 ) ) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax33])])]) ).

thf(c_0_10,plain,
    ! [X104: list_a] :
      ( ~ p35
      | ( ( fappend_a @ fnil_a @ X104 )
        = X104 ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax35])])]) ).

thf(c_0_11,plain,
    ( ( ( flistIn1312259492pend_a @ ( fcons_a @ fx @ fxs ) @ ff @ f__0 )
     != ( flistIn1312259492pend_a @ ( fcons_a @ fx @ fnil_a ) @ ( flistIn1312259492pend_a @ fxs @ ff ) @ f__0 ) )
    | p59 ),
    inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax59])]) ).

thf(c_0_12,plain,
    ! [X2: list_a,X3: list_a,X15: nat > a] :
      ( ( ( flistIn1312259492pend_a @ X2 @ ( flistIn1312259492pend_a @ X3 @ X15 ) )
        = ( flistIn1312259492pend_a @ ( fappend_a @ X2 @ X3 ) @ X15 ) )
      | ~ p31 ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

thf(c_0_13,plain,
    p31,
    inference(split_conjunct,[status(thm)],[ax28]) ).

thf(c_0_14,plain,
    ! [X1: a,X2: list_a,X3: list_a] :
      ( ( ( fappend_a @ ( fcons_a @ X1 @ X2 ) @ X3 )
        = ( fcons_a @ X1 @ ( fappend_a @ X2 @ X3 ) ) )
      | ~ p33 ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

thf(c_0_15,plain,
    p33,
    inference(split_conjunct,[status(thm)],[ax26]) ).

thf(c_0_16,plain,
    ! [X2: list_a] :
      ( ( ( fappend_a @ fnil_a @ X2 )
        = X2 )
      | ~ p35 ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

thf(c_0_17,plain,
    p35,
    inference(split_conjunct,[status(thm)],[ax24]) ).

thf(c_0_18,plain,
    ~ p59,
    inference(fof_simplification,[status(thm)],[ax0]) ).

thf(c_0_19,plain,
    ( p59
    | ( ( flistIn1312259492pend_a @ ( fcons_a @ fx @ fxs ) @ ff @ f__0 )
     != ( flistIn1312259492pend_a @ ( fcons_a @ fx @ fnil_a ) @ ( flistIn1312259492pend_a @ fxs @ ff ) @ f__0 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

thf(c_0_20,plain,
    ! [X2: list_a,X3: list_a,X15: nat > a] :
      ( ( flistIn1312259492pend_a @ X2 @ ( flistIn1312259492pend_a @ X3 @ X15 ) )
      = ( flistIn1312259492pend_a @ ( fappend_a @ X2 @ X3 ) @ X15 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13])]) ).

thf(c_0_21,plain,
    ! [X1: a,X2: list_a,X3: list_a] :
      ( ( fappend_a @ ( fcons_a @ X1 @ X2 ) @ X3 )
      = ( fcons_a @ X1 @ ( fappend_a @ X2 @ X3 ) ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15])]) ).

thf(c_0_22,plain,
    ! [X2: list_a] :
      ( ( fappend_a @ fnil_a @ X2 )
      = X2 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17])]) ).

thf(c_0_23,plain,
    ~ p59,
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

thf(c_0_24,plain,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_22])]),c_0_23]),
    [proof] ).

thf(1,plain,
    $false,
    inference(eprover,[status(thm),assumptions([h2,h1,h0])],]) ).

thf(2,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,1,h2]) ).

thf(3,plain,
    $false,
    inference(tab_fe,[status(thm),assumptions([h0]),tab_fe(discharge,[h1])],[h0,2,h1]) ).

thf(0,theorem,
    ( ( listIn1312259492pend_a @ ( cons_a @ x @ xs ) @ f )
    = ( listIn1312259492pend_a @ ( cons_a @ x @ nil_a ) @ ( listIn1312259492pend_a @ xs @ f ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[3,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : ITP100^1 : TPTP v8.1.0. Released v7.5.0.
% 0.10/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n025.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Fri Jun  3 18:59:30 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 2.65/2.83  % SZS status Theorem
% 2.65/2.83  % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
% 2.65/2.83  % Inferences: 1
% 2.65/2.83  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------