TSTP Solution File: SEU972^5 by Satallax---3.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEU972^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n020.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 : Tue Jul 19 14:11:05 EDT 2022

% Result   : Theorem 36.83s 37.36s
% Output   : Proof 36.83s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   73 (  23 unt;   0 typ;   0 def)
%            Number of atoms       :  457 (  83 equ;   0 cnn)
%            Maximal formula atoms :   26 (   6 avg)
%            Number of connectives :  504 ( 143   ~;  68   |;   5   &; 229   @)
%                                         (   0 <=>;  57  =>;   2  <=;   0 <~>)
%            Maximal formula depth :   20 (   4 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   28 (  26 usr;  27 con; 0-2 aty)
%            Number of variables   :   56 (   0   ^  56   !;   0   ?;  56   :)

% Comments : 
%------------------------------------------------------------------------------
thf(cPU_LEM2E_pme,conjecture,
    ( ~ ( ~ ( ~ ( ~ ( ~ ( ( ( cL @ cZ )
                          = cZ )
                       => ( ( cR @ cZ )
                         != cZ ) )
                   => ~ ! [X1: a,X2: a] :
                          ( ( cL @ ( cP @ X1 @ X2 ) )
                          = X1 ) )
               => ~ ! [X1: a,X2: a] :
                      ( ( cR @ ( cP @ X1 @ X2 ) )
                      = X2 ) )
           => ~ ! [X1: a] :
                  ( ( ( X1 != cZ ) )
                  = ( X1
                    = ( cP @ ( cL @ X1 ) @ ( cR @ X1 ) ) ) ) )
       => ~ ! [X1: a > $o] :
              ( ! [X2: a,X3: a] :
                  ( ( X1 @ ( cP @ X2 @ X3 ) )
                 => ~ ( ~ ( ( ( X2 = cZ )
                            = ( X3 = cZ ) )
                         => ~ ( X1 @ ( cP @ ( cL @ X2 ) @ ( cL @ X3 ) ) ) )
                     => ~ ( X1 @ ( cP @ ( cR @ X2 ) @ ( cR @ X3 ) ) ) ) )
             => ! [X2: a,X3: a] :
                  ( ( X1 @ ( cP @ X2 @ X3 ) )
                 => ( X2 = X3 ) ) ) )
   => ! [X1: a] :
        ~ ! [X2: a > $o] :
            ( ( X2 @ ( cP @ cZ @ X1 ) )
           => ~ ! [X3: a,X4: a] :
                  ( ( X2 @ ( cP @ X3 @ X4 ) )
                 => ~ ( ~ ( ( ( X4 = cZ )
                           => ( X3 = cZ ) )
                         => ~ ( X2 @ ( cP @ ( cL @ X3 ) @ ( cL @ X4 ) ) ) )
                     => ~ ( X2 @ ( cP @ ( cR @ X3 ) @ ( cR @ X4 ) ) ) ) ) ) ) ).

thf(h0,negated_conjecture,
    ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( ( cL @ cZ )
                            = cZ )
                         => ( ( cR @ cZ )
                           != cZ ) )
                     => ~ ! [X1: a,X2: a] :
                            ( ( cL @ ( cP @ X1 @ X2 ) )
                            = X1 ) )
                 => ~ ! [X1: a,X2: a] :
                        ( ( cR @ ( cP @ X1 @ X2 ) )
                        = X2 ) )
             => ~ ! [X1: a] :
                    ( ( ( X1 != cZ ) )
                    = ( X1
                      = ( cP @ ( cL @ X1 ) @ ( cR @ X1 ) ) ) ) )
         => ~ ! [X1: a > $o] :
                ( ! [X2: a,X3: a] :
                    ( ( X1 @ ( cP @ X2 @ X3 ) )
                   => ~ ( ~ ( ( ( X2 = cZ )
                              = ( X3 = cZ ) )
                           => ~ ( X1 @ ( cP @ ( cL @ X2 ) @ ( cL @ X3 ) ) ) )
                       => ~ ( X1 @ ( cP @ ( cR @ X2 ) @ ( cR @ X3 ) ) ) ) )
               => ! [X2: a,X3: a] :
                    ( ( X1 @ ( cP @ X2 @ X3 ) )
                   => ( X2 = X3 ) ) ) )
     => ! [X1: a] :
          ~ ! [X2: a > $o] :
              ( ( X2 @ ( cP @ cZ @ X1 ) )
             => ~ ! [X3: a,X4: a] :
                    ( ( X2 @ ( cP @ X3 @ X4 ) )
                   => ~ ( ~ ( ( ( X4 = cZ )
                             => ( X3 = cZ ) )
                           => ~ ( X2 @ ( cP @ ( cL @ X3 ) @ ( cL @ X4 ) ) ) )
                       => ~ ( X2 @ ( cP @ ( cR @ X3 ) @ ( cR @ X4 ) ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[cPU_LEM2E_pme]) ).

thf(ax1912,axiom,
    ( p1
    | ~ p3 ),
    file('<stdin>',ax1912) ).

thf(ax1914,axiom,
    ~ p1,
    file('<stdin>',ax1914) ).

thf(ax987,axiom,
    ( ~ p455
    | p906 ),
    file('<stdin>',ax987) ).

thf(ax1913,axiom,
    ( p1
    | ~ p2 ),
    file('<stdin>',ax1913) ).

thf(ax1847,axiom,
    ( ~ p6
    | p67 ),
    file('<stdin>',ax1847) ).

thf(ax1909,axiom,
    ( p3
    | p6 ),
    file('<stdin>',ax1909) ).

thf(ax986,axiom,
    ( ~ p906
    | p905 ),
    file('<stdin>',ax986) ).

thf(ax1464,axiom,
    p455,
    file('<stdin>',ax1464) ).

thf(ax1911,axiom,
    ( p2
    | ~ p4 ),
    file('<stdin>',ax1911) ).

thf(ax985,axiom,
    ( ~ p905
    | ~ p67
    | p904 ),
    file('<stdin>',ax985) ).

thf(ax1908,axiom,
    ( p4
    | ~ p7 ),
    file('<stdin>',ax1908) ).

thf(ax984,axiom,
    ( ~ p904
    | p903 ),
    file('<stdin>',ax984) ).

thf(nax7,axiom,
    ( p7
   <= ( ~ ( ~ ( ( ( fcL @ fcZ )
                = fcZ )
             => ( ( fcR @ fcZ )
               != fcZ ) )
         => ~ ! [X1: a,X2: a] :
                ( ( fcL @ ( fcP @ X1 @ X2 ) )
                = X1 ) )
     => ~ ! [X1: a,X2: a] :
            ( ( fcR @ ( fcP @ X1 @ X2 ) )
            = X2 ) ) ),
    file('<stdin>',nax7) ).

thf(ax983,axiom,
    ( ~ p903
    | ~ p902
    | p901 ),
    file('<stdin>',ax983) ).

thf(nax902,axiom,
    ( p902
   <= ( ( fcL @ ( fcP @ fcZ @ f__0 ) )
      = fcZ ) ),
    file('<stdin>',nax902) ).

thf(pax901,axiom,
    ( p901
   => ( ( fcZ = fcZ )
     => ~ ! [X1: a,X2: a] :
            ( ( ( fcL @ ( fcP @ X1 @ X2 ) )
              = fcZ )
           => ~ ( ~ ( ( ( X2 = fcZ )
                     => ( X1 = fcZ ) )
                   => ( ( fcL @ ( fcP @ ( fcL @ X1 ) @ ( fcL @ X2 ) ) )
                     != fcZ ) )
               => ( ( fcL @ ( fcP @ ( fcR @ X1 ) @ ( fcR @ X2 ) ) )
                 != fcZ ) ) ) ) ),
    file('<stdin>',pax901) ).

thf(c_0_16,plain,
    ( p1
    | ~ p3 ),
    inference(fof_simplification,[status(thm)],[ax1912]) ).

thf(c_0_17,plain,
    ~ p1,
    inference(fof_simplification,[status(thm)],[ax1914]) ).

thf(c_0_18,plain,
    ( p1
    | ~ p3 ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

thf(c_0_19,plain,
    ~ p1,
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

thf(c_0_20,plain,
    ( ~ p455
    | p906 ),
    inference(fof_simplification,[status(thm)],[ax987]) ).

thf(c_0_21,plain,
    ( p1
    | ~ p2 ),
    inference(fof_simplification,[status(thm)],[ax1913]) ).

thf(c_0_22,plain,
    ( ~ p6
    | p67 ),
    inference(fof_simplification,[status(thm)],[ax1847]) ).

thf(c_0_23,plain,
    ( p3
    | p6 ),
    inference(split_conjunct,[status(thm)],[ax1909]) ).

thf(c_0_24,plain,
    ~ p3,
    inference(sr,[status(thm)],[c_0_18,c_0_19]) ).

thf(c_0_25,plain,
    ( ~ p906
    | p905 ),
    inference(fof_simplification,[status(thm)],[ax986]) ).

thf(c_0_26,plain,
    ( p906
    | ~ p455 ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

thf(c_0_27,plain,
    p455,
    inference(split_conjunct,[status(thm)],[ax1464]) ).

thf(c_0_28,plain,
    ( p2
    | ~ p4 ),
    inference(fof_simplification,[status(thm)],[ax1911]) ).

thf(c_0_29,plain,
    ( p1
    | ~ p2 ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

thf(c_0_30,plain,
    ( ~ p905
    | ~ p67
    | p904 ),
    inference(fof_simplification,[status(thm)],[ax985]) ).

thf(c_0_31,plain,
    ( p67
    | ~ p6 ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

thf(c_0_32,plain,
    p6,
    inference(sr,[status(thm)],[c_0_23,c_0_24]) ).

thf(c_0_33,plain,
    ( p905
    | ~ p906 ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

thf(c_0_34,plain,
    p906,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27])]) ).

thf(c_0_35,plain,
    ( p4
    | ~ p7 ),
    inference(fof_simplification,[status(thm)],[ax1908]) ).

thf(c_0_36,plain,
    ( p2
    | ~ p4 ),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

thf(c_0_37,plain,
    ~ p2,
    inference(sr,[status(thm)],[c_0_29,c_0_19]) ).

thf(c_0_38,plain,
    ( ~ p904
    | p903 ),
    inference(fof_simplification,[status(thm)],[ax984]) ).

thf(c_0_39,plain,
    ( p904
    | ~ p905
    | ~ p67 ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

thf(c_0_40,plain,
    p67,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32])]) ).

thf(c_0_41,plain,
    p905,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34])]) ).

thf(c_0_42,plain,
    ! [X2378: a,X2379: a,X2380: a,X2381: a] :
      ( ( ( ( fcL @ fcZ )
          = fcZ )
        | p7 )
      & ( ( ( fcR @ fcZ )
          = fcZ )
        | p7 )
      & ( ( ( fcL @ ( fcP @ X2378 @ X2379 ) )
          = X2378 )
        | p7 )
      & ( ( ( fcR @ ( fcP @ X2380 @ X2381 ) )
          = X2381 )
        | p7 ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax7])])])])]) ).

thf(c_0_43,plain,
    ( p4
    | ~ p7 ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

thf(c_0_44,plain,
    ~ p4,
    inference(sr,[status(thm)],[c_0_36,c_0_37]) ).

thf(c_0_45,plain,
    ( ~ p903
    | ~ p902
    | p901 ),
    inference(fof_simplification,[status(thm)],[ax983]) ).

thf(c_0_46,plain,
    ( p903
    | ~ p904 ),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

thf(c_0_47,plain,
    p904,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_40]),c_0_41])]) ).

thf(c_0_48,plain,
    ( ( ( fcL @ ( fcP @ fcZ @ f__0 ) )
     != fcZ )
    | p902 ),
    inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax902])]) ).

thf(c_0_49,plain,
    ! [X2: a,X1: a] :
      ( ( ( fcL @ ( fcP @ X1 @ X2 ) )
        = X1 )
      | p7 ),
    inference(split_conjunct,[status(thm)],[c_0_42]) ).

thf(c_0_50,plain,
    ~ p7,
    inference(sr,[status(thm)],[c_0_43,c_0_44]) ).

thf(c_0_51,plain,
    ( ( ( ( fcL @ ( fcP @ esk454_0 @ esk455_0 ) )
        = fcZ )
      | ( fcZ != fcZ )
      | ~ p901 )
    & ( ( esk455_0 = fcZ )
      | ( ( fcL @ ( fcP @ ( fcL @ esk454_0 ) @ ( fcL @ esk455_0 ) ) )
       != fcZ )
      | ( ( fcL @ ( fcP @ ( fcR @ esk454_0 ) @ ( fcR @ esk455_0 ) ) )
       != fcZ )
      | ( fcZ != fcZ )
      | ~ p901 )
    & ( ( esk454_0 != fcZ )
      | ( ( fcL @ ( fcP @ ( fcL @ esk454_0 ) @ ( fcL @ esk455_0 ) ) )
       != fcZ )
      | ( ( fcL @ ( fcP @ ( fcR @ esk454_0 ) @ ( fcR @ esk455_0 ) ) )
       != fcZ )
      | ( fcZ != fcZ )
      | ~ p901 ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax901])])])])]) ).

thf(c_0_52,plain,
    ( p901
    | ~ p903
    | ~ p902 ),
    inference(split_conjunct,[status(thm)],[c_0_45]) ).

thf(c_0_53,plain,
    p903,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47])]) ).

thf(c_0_54,plain,
    ( p902
    | ( ( fcL @ ( fcP @ fcZ @ f__0 ) )
     != fcZ ) ),
    inference(split_conjunct,[status(thm)],[c_0_48]) ).

thf(c_0_55,plain,
    ! [X2: a,X1: a] :
      ( ( fcL @ ( fcP @ X1 @ X2 ) )
      = X1 ),
    inference(sr,[status(thm)],[c_0_49,c_0_50]) ).

thf(c_0_56,plain,
    ( ( ( fcL @ ( fcP @ esk454_0 @ esk455_0 ) )
      = fcZ )
    | ( fcZ != fcZ )
    | ~ p901 ),
    inference(split_conjunct,[status(thm)],[c_0_51]) ).

thf(c_0_57,plain,
    ( p901
    | ~ p902 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_53])]) ).

thf(c_0_58,plain,
    p902,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55])]) ).

thf(c_0_59,plain,
    ( ( esk454_0 != fcZ )
    | ( ( fcL @ ( fcP @ ( fcL @ esk454_0 ) @ ( fcL @ esk455_0 ) ) )
     != fcZ )
    | ( ( fcL @ ( fcP @ ( fcR @ esk454_0 ) @ ( fcR @ esk455_0 ) ) )
     != fcZ )
    | ( fcZ != fcZ )
    | ~ p901 ),
    inference(split_conjunct,[status(thm)],[c_0_51]) ).

thf(c_0_60,plain,
    ( ( ( fcL @ ( fcP @ esk454_0 @ esk455_0 ) )
      = fcZ )
    | ~ p901 ),
    inference(cn,[status(thm)],[c_0_56]) ).

thf(c_0_61,plain,
    p901,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_58])]) ).

thf(c_0_62,plain,
    ( ( ( fcL @ fcZ )
      = fcZ )
    | p7 ),
    inference(split_conjunct,[status(thm)],[c_0_42]) ).

thf(c_0_63,plain,
    ( ( ( fcR @ fcZ )
      = fcZ )
    | p7 ),
    inference(split_conjunct,[status(thm)],[c_0_42]) ).

thf(c_0_64,plain,
    ( ( esk454_0 != fcZ )
    | ( ( fcL @ ( fcP @ ( fcL @ esk454_0 ) @ ( fcL @ esk455_0 ) ) )
     != fcZ )
    | ( ( fcL @ ( fcP @ ( fcR @ esk454_0 ) @ ( fcR @ esk455_0 ) ) )
     != fcZ )
    | ~ p901 ),
    inference(cn,[status(thm)],[c_0_59]) ).

thf(c_0_65,plain,
    esk454_0 = fcZ,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_55]),c_0_61])]) ).

thf(c_0_66,plain,
    ( ( fcL @ fcZ )
    = fcZ ),
    inference(sr,[status(thm)],[c_0_62,c_0_50]) ).

thf(c_0_67,plain,
    ( ( fcR @ fcZ )
    = fcZ ),
    inference(sr,[status(thm)],[c_0_63,c_0_50]) ).

thf(c_0_68,plain,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_65]),c_0_65]),c_0_66]),c_0_55]),c_0_65]),c_0_67]),c_0_55]),c_0_61])]),
    [proof] ).

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

thf(0,theorem,
    ( ~ ( ~ ( ~ ( ~ ( ~ ( ( ( cL @ cZ )
                          = cZ )
                       => ( ( cR @ cZ )
                         != cZ ) )
                   => ~ ! [X1: a,X2: a] :
                          ( ( cL @ ( cP @ X1 @ X2 ) )
                          = X1 ) )
               => ~ ! [X1: a,X2: a] :
                      ( ( cR @ ( cP @ X1 @ X2 ) )
                      = X2 ) )
           => ~ ! [X1: a] :
                  ( ( ( X1 != cZ ) )
                  = ( X1
                    = ( cP @ ( cL @ X1 ) @ ( cR @ X1 ) ) ) ) )
       => ~ ! [X1: a > $o] :
              ( ! [X2: a,X3: a] :
                  ( ( X1 @ ( cP @ X2 @ X3 ) )
                 => ~ ( ~ ( ( ( X2 = cZ )
                            = ( X3 = cZ ) )
                         => ~ ( X1 @ ( cP @ ( cL @ X2 ) @ ( cL @ X3 ) ) ) )
                     => ~ ( X1 @ ( cP @ ( cR @ X2 ) @ ( cR @ X3 ) ) ) ) )
             => ! [X2: a,X3: a] :
                  ( ( X1 @ ( cP @ X2 @ X3 ) )
                 => ( X2 = X3 ) ) ) )
   => ! [X1: a] :
        ~ ! [X2: a > $o] :
            ( ( X2 @ ( cP @ cZ @ X1 ) )
           => ~ ! [X3: a,X4: a] :
                  ( ( X2 @ ( cP @ X3 @ X4 ) )
                 => ~ ( ~ ( ( ( X4 = cZ )
                           => ( X3 = cZ ) )
                         => ~ ( X2 @ ( cP @ ( cL @ X3 ) @ ( cL @ X4 ) ) ) )
                     => ~ ( X2 @ ( cP @ ( cR @ X3 ) @ ( cR @ X4 ) ) ) ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem  : SEU972^5 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.13  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34  % Computer : n020.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 : Sun Jun 19 09:33:33 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 36.83/37.36  % SZS status Theorem
% 36.83/37.36  % Mode: mode485
% 36.83/37.36  % Inferences: 39
% 36.83/37.36  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------