TSTP Solution File: ITP200^1 by Satallax---3.5

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%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : ITP200^1 : 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 : n027.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 00:29:29 EDT 2022

% Result   : Theorem 47.68s 46.86s
% Output   : Proof 47.68s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   45 (  24 unt;   0 typ;   0 def)
%            Number of atoms       :  170 (  20 equ;   0 cnn)
%            Maximal formula atoms :    3 (   3 avg)
%            Number of connectives :  156 (  26   ~;  20   |;   0   &; 106   @)
%                                         (   0 <=>;   3  =>;   1  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Number of types       :    0 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   29 (  27 usr;  28 con; 0-2 aty)
%            Number of variables   :   21 (   0   ^  21   !;   0   ?;  21   :)

% Comments : 
%------------------------------------------------------------------------------
thf(conj_0,conjecture,
    ( uSubst516392818stappt @ sigma @ ua @ theta )
 != none_trm ).

thf(h0,negated_conjecture,
    ( ( uSubst516392818stappt @ sigma @ ua @ theta )
    = none_trm ),
    inference(assume_negation,[status(cth)],[conj_0]) ).

thf(ax1419,axiom,
    ( ~ p119
    | p120 ),
    file('<stdin>',ax1419) ).

thf(ax1418,axiom,
    ( ~ p120
    | p121 ),
    file('<stdin>',ax1418) ).

thf(ax1420,axiom,
    p119,
    file('<stdin>',ax1420) ).

thf(ax1417,axiom,
    ( ~ p121
    | ~ p1
    | p118 ),
    file('<stdin>',ax1417) ).

thf(pax13,axiom,
    ( p13
   => ! [X207: produc1418842292n_game,X203: set_variable,X208: trm,X209: trm] :
        ( ( fuSubst516392804stappf @ X207 @ X203 @ ( fgeq @ X208 @ X209 ) )
        = ( fuSubst152838031e_Geqo @ ( fuSubst516392818stappt @ X207 @ X203 @ X208 ) @ ( fuSubst516392818stappt @ X207 @ X203 @ X209 ) ) ) ),
    file('<stdin>',pax13) ).

thf(pax118,axiom,
    ( p118
   => ( fnone_trm
      = ( fuSubst516392818stappt @ fsigma @ fua @ ftheta ) ) ),
    file('<stdin>',pax118) ).

thf(ax1537,axiom,
    p1,
    file('<stdin>',ax1537) ).

thf(pax10,axiom,
    ( p10
   => ! [X215: option_trm] :
        ( ( fuSubst152838031e_Geqo @ fnone_trm @ X215 )
        = fnone_fml ) ),
    file('<stdin>',pax10) ).

thf(nax3,axiom,
    ( p3
   <= ( ( fuSubst516392804stappf @ fsigma @ fua @ ( fgeq @ ftheta @ feta ) )
      = fnone_fml ) ),
    file('<stdin>',nax3) ).

thf(ax1535,axiom,
    ~ p3,
    file('<stdin>',ax1535) ).

thf(ax1525,axiom,
    p13,
    file('<stdin>',ax1525) ).

thf(ax1528,axiom,
    p10,
    file('<stdin>',ax1528) ).

thf(c_0_12,plain,
    ( ~ p119
    | p120 ),
    inference(fof_simplification,[status(thm)],[ax1419]) ).

thf(c_0_13,plain,
    ( ~ p120
    | p121 ),
    inference(fof_simplification,[status(thm)],[ax1418]) ).

thf(c_0_14,plain,
    ( p120
    | ~ p119 ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

thf(c_0_15,plain,
    p119,
    inference(split_conjunct,[status(thm)],[ax1420]) ).

thf(c_0_16,plain,
    ( ~ p121
    | ~ p1
    | p118 ),
    inference(fof_simplification,[status(thm)],[ax1417]) ).

thf(c_0_17,plain,
    ( p121
    | ~ p120 ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

thf(c_0_18,plain,
    p120,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15])]) ).

thf(c_0_19,plain,
    ! [X1742: produc1418842292n_game,X1743: set_variable,X1744: trm,X1745: trm] :
      ( ~ p13
      | ( ( fuSubst516392804stappf @ X1742 @ X1743 @ ( fgeq @ X1744 @ X1745 ) )
        = ( fuSubst152838031e_Geqo @ ( fuSubst516392818stappt @ X1742 @ X1743 @ X1744 ) @ ( fuSubst516392818stappt @ X1742 @ X1743 @ X1745 ) ) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax13])])]) ).

thf(c_0_20,plain,
    ( ~ p118
    | ( fnone_trm
      = ( fuSubst516392818stappt @ fsigma @ fua @ ftheta ) ) ),
    inference(fof_nnf,[status(thm)],[pax118]) ).

thf(c_0_21,plain,
    ( p118
    | ~ p121
    | ~ p1 ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

thf(c_0_22,plain,
    p1,
    inference(split_conjunct,[status(thm)],[ax1537]) ).

thf(c_0_23,plain,
    p121,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18])]) ).

thf(c_0_24,plain,
    ! [X1766: option_trm] :
      ( ~ p10
      | ( ( fuSubst152838031e_Geqo @ fnone_trm @ X1766 )
        = fnone_fml ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax10])])]) ).

thf(c_0_25,plain,
    ( ( ( fuSubst516392804stappf @ fsigma @ fua @ ( fgeq @ ftheta @ feta ) )
     != fnone_fml )
    | p3 ),
    inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax3])]) ).

thf(c_0_26,plain,
    ~ p3,
    inference(fof_simplification,[status(thm)],[ax1535]) ).

thf(c_0_27,plain,
    ! [X1: trm,X5: produc1418842292n_game,X3: set_variable,X2: trm] :
      ( ( ( fuSubst516392804stappf @ X5 @ X3 @ ( fgeq @ X1 @ X2 ) )
        = ( fuSubst152838031e_Geqo @ ( fuSubst516392818stappt @ X5 @ X3 @ X1 ) @ ( fuSubst516392818stappt @ X5 @ X3 @ X2 ) ) )
      | ~ p13 ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

thf(c_0_28,plain,
    p13,
    inference(split_conjunct,[status(thm)],[ax1525]) ).

thf(c_0_29,plain,
    ( ( fnone_trm
      = ( fuSubst516392818stappt @ fsigma @ fua @ ftheta ) )
    | ~ p118 ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

thf(c_0_30,plain,
    p118,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22]),c_0_23])]) ).

thf(c_0_31,plain,
    ! [X15: option_trm] :
      ( ( ( fuSubst152838031e_Geqo @ fnone_trm @ X15 )
        = fnone_fml )
      | ~ p10 ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

thf(c_0_32,plain,
    p10,
    inference(split_conjunct,[status(thm)],[ax1528]) ).

thf(c_0_33,plain,
    ( p3
    | ( ( fuSubst516392804stappf @ fsigma @ fua @ ( fgeq @ ftheta @ feta ) )
     != fnone_fml ) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

thf(c_0_34,plain,
    ~ p3,
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

thf(c_0_35,plain,
    ! [X1: trm,X5: produc1418842292n_game,X3: set_variable,X2: trm] :
      ( ( fuSubst152838031e_Geqo @ ( fuSubst516392818stappt @ X5 @ X3 @ X1 ) @ ( fuSubst516392818stappt @ X5 @ X3 @ X2 ) )
      = ( fuSubst516392804stappf @ X5 @ X3 @ ( fgeq @ X1 @ X2 ) ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28])]) ).

thf(c_0_36,plain,
    ( ( fuSubst516392818stappt @ fsigma @ fua @ ftheta )
    = fnone_trm ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30])]) ).

thf(c_0_37,plain,
    ! [X15: option_trm] :
      ( ( fuSubst152838031e_Geqo @ fnone_trm @ X15 )
      = fnone_fml ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32])]) ).

thf(c_0_38,plain,
    ( fuSubst516392804stappf @ fsigma @ fua @ ( fgeq @ ftheta @ feta ) )
 != fnone_fml,
    inference(sr,[status(thm)],[c_0_33,c_0_34]) ).

thf(c_0_39,plain,
    ! [X1: trm] :
      ( ( fuSubst516392804stappf @ fsigma @ fua @ ( fgeq @ ftheta @ X1 ) )
      = fnone_fml ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]) ).

thf(c_0_40,plain,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39])]),
    [proof] ).

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

thf(0,theorem,
    ( uSubst516392818stappt @ sigma @ ua @ theta )
 != none_trm,
    inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : ITP200^1 : TPTP v8.1.0. Released v7.5.0.
% 0.11/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n027.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Fri Jun  3 19:31:36 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 47.68/46.86  % SZS status Theorem
% 47.68/46.86  % Mode: mode485:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=4.:SINE_DEPTH=0
% 47.68/46.86  % Inferences: 3980
% 47.68/46.86  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------