TSTP Solution File: SEV195^5 by Satallax---3.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEV195^5 : 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 : n019.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 18:05:18 EDT 2022

% Result   : Theorem 36.67s 37.25s
% Output   : Proof 36.67s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   58 (  17 unt;   0 typ;   0 def)
%            Number of atoms       :  180 (  32 equ;   0 cnn)
%            Maximal formula atoms :    9 (   3 avg)
%            Number of connectives :  239 (  97   ~;  43   |;   2   &;  59   @)
%                                         (   0 <=>;  33  =>;   2  <=;   0 <~>)
%            Maximal formula depth :   18 (   4 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   22 (  19 usr;  21 con; 0-2 aty)
%                                         (   3  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :   46 (   0   ^  46   !;   0   ?;  46   :)

% Comments : 
%------------------------------------------------------------------------------
thf(cS_LEM1D_pme,conjecture,
    ( ~ ( ~ ( ! [X1: a,X2: a] :
                ( ( cP @ X1 @ X2 )
               != cZ )
           => ~ ! [X1: a,X2: a,X3: a,X4: a] :
                  ( ( ( cP @ X1 @ X3 )
                    = ( cP @ X2 @ X4 ) )
                 => ~ ( ( X1 = X2 )
                     => ( X3 != X4 ) ) ) )
       => ~ ! [X1: a > $o] :
              ( ~ ( ( X1 @ cZ )
                 => ~ ! [X2: a,X3: a] :
                        ( ~ ( ( X1 @ X2 )
                           => ~ ( X1 @ X3 ) )
                       => ( X1 @ ( cP @ X2 @ X3 ) ) ) )
             => ( !! @ X1 ) ) )
   => ! [X1: a] :
        ( ( X1 != cZ )
       => ~ ! [X2: a,X3: a] :
              ( X1
             != ( cP @ X2 @ X3 ) ) ) ) ).

thf(h0,negated_conjecture,
    ~ ( ~ ( ~ ( ! [X1: a,X2: a] :
                  ( ( cP @ X1 @ X2 )
                 != cZ )
             => ~ ! [X1: a,X2: a,X3: a,X4: a] :
                    ( ( ( cP @ X1 @ X3 )
                      = ( cP @ X2 @ X4 ) )
                   => ~ ( ( X1 = X2 )
                       => ( X3 != X4 ) ) ) )
         => ~ ! [X1: a > $o] :
                ( ~ ( ( X1 @ cZ )
                   => ~ ! [X2: a,X3: a] :
                          ( ~ ( ( X1 @ X2 )
                             => ~ ( X1 @ X3 ) )
                         => ( X1 @ ( cP @ X2 @ X3 ) ) ) )
               => ( !! @ X1 ) ) )
     => ! [X1: a] :
          ( ( X1 != cZ )
         => ~ ! [X2: a,X3: a] :
                ( X1
               != ( cP @ X2 @ X3 ) ) ) ),
    inference(assume_negation,[status(cth)],[cS_LEM1D_pme]) ).

thf(ax1375,axiom,
    ( p1
    | ~ p3 ),
    file('<stdin>',ax1375) ).

thf(ax1377,axiom,
    ~ p1,
    file('<stdin>',ax1377) ).

thf(ax1376,axiom,
    ( p1
    | ~ p2 ),
    file('<stdin>',ax1376) ).

thf(ax1372,axiom,
    ( p3
    | ~ p6 ),
    file('<stdin>',ax1372) ).

thf(nax223,axiom,
    ( p223
   <= ( f__0 = f__0 ) ),
    file('<stdin>',nax223) ).

thf(ax1366,axiom,
    ( p6
    | ~ p13 ),
    file('<stdin>',ax1366) ).

thf(ax1350,axiom,
    ( ~ p5
    | p28 ),
    file('<stdin>',ax1350) ).

thf(ax1373,axiom,
    ( p2
    | p5 ),
    file('<stdin>',ax1373) ).

thf(ax533,axiom,
    ( ~ p52
    | ~ p223 ),
    file('<stdin>',ax533) ).

thf(ax539,axiom,
    ( ~ p51
    | p13
    | ~ p740 ),
    file('<stdin>',ax539) ).

thf(ax1330,axiom,
    ( ~ p28
    | p51
    | p52 ),
    file('<stdin>',ax1330) ).

thf(pax14,axiom,
    ( p14
   => ! [X1: a,X2: a] :
        ( f__0
       != ( fcP @ X1 @ X2 ) ) ),
    file('<stdin>',pax14) ).

thf(ax1365,axiom,
    ( p6
    | p14 ),
    file('<stdin>',ax1365) ).

thf(nax740,axiom,
    ( p740
   <= ! [X1: a,X2: a] :
        ( ~ ( ( f__0 != X1 )
           => ( f__0 = X2 ) )
       => ( f__0
         != ( fcP @ X1 @ X2 ) ) ) ),
    file('<stdin>',nax740) ).

thf(c_0_14,plain,
    ( p1
    | ~ p3 ),
    inference(fof_simplification,[status(thm)],[ax1375]) ).

thf(c_0_15,plain,
    ~ p1,
    inference(fof_simplification,[status(thm)],[ax1377]) ).

thf(c_0_16,plain,
    ( p1
    | ~ p2 ),
    inference(fof_simplification,[status(thm)],[ax1376]) ).

thf(c_0_17,plain,
    ( p3
    | ~ p6 ),
    inference(fof_simplification,[status(thm)],[ax1372]) ).

thf(c_0_18,plain,
    ( p1
    | ~ p3 ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

thf(c_0_19,plain,
    ~ p1,
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

thf(c_0_20,plain,
    ( p1
    | ~ p2 ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

thf(c_0_21,plain,
    ( ( f__0 != f__0 )
    | p223 ),
    inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax223])]) ).

thf(c_0_22,plain,
    ( p6
    | ~ p13 ),
    inference(fof_simplification,[status(thm)],[ax1366]) ).

thf(c_0_23,plain,
    ( p3
    | ~ p6 ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

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

thf(c_0_25,plain,
    ( ~ p5
    | p28 ),
    inference(fof_simplification,[status(thm)],[ax1350]) ).

thf(c_0_26,plain,
    ( p2
    | p5 ),
    inference(split_conjunct,[status(thm)],[ax1373]) ).

thf(c_0_27,plain,
    ~ p2,
    inference(sr,[status(thm)],[c_0_20,c_0_19]) ).

thf(c_0_28,plain,
    ( ~ p52
    | ~ p223 ),
    inference(fof_simplification,[status(thm)],[ax533]) ).

thf(c_0_29,plain,
    ( p223
    | ( f__0 != f__0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

thf(c_0_30,plain,
    ( ~ p51
    | p13
    | ~ p740 ),
    inference(fof_simplification,[status(thm)],[ax539]) ).

thf(c_0_31,plain,
    ( p6
    | ~ p13 ),
    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,
    ( ~ p28
    | p51
    | p52 ),
    inference(fof_simplification,[status(thm)],[ax1330]) ).

thf(c_0_34,plain,
    ( p28
    | ~ p5 ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

thf(c_0_35,plain,
    p5,
    inference(sr,[status(thm)],[c_0_26,c_0_27]) ).

thf(c_0_36,plain,
    ( ~ p52
    | ~ p223 ),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

thf(c_0_37,plain,
    p223,
    inference(cn,[status(thm)],[c_0_29]) ).

thf(c_0_38,plain,
    ! [X3516: a,X3517: a] :
      ( ~ p14
      | ( f__0
       != ( fcP @ X3516 @ X3517 ) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax14])])])]) ).

thf(c_0_39,plain,
    ( p6
    | p14 ),
    inference(split_conjunct,[status(thm)],[ax1365]) ).

thf(c_0_40,plain,
    ( p13
    | ~ p51
    | ~ p740 ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

thf(c_0_41,plain,
    ~ p13,
    inference(sr,[status(thm)],[c_0_31,c_0_32]) ).

thf(c_0_42,plain,
    ( p51
    | p52
    | ~ p28 ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

thf(c_0_43,plain,
    p28,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35])]) ).

thf(c_0_44,plain,
    ~ p52,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37])]) ).

thf(c_0_45,plain,
    ( ( ( f__0 != esk438_0 )
      | p740 )
    & ( ( f__0 != esk439_0 )
      | p740 )
    & ( ( f__0
        = ( fcP @ esk438_0 @ esk439_0 ) )
      | p740 ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax740])])])])]) ).

thf(c_0_46,plain,
    ! [X1: a,X2: a] :
      ( ~ p14
      | ( f__0
       != ( fcP @ X1 @ X2 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

thf(c_0_47,plain,
    p14,
    inference(sr,[status(thm)],[c_0_39,c_0_32]) ).

thf(c_0_48,plain,
    ( ~ p51
    | ~ p740 ),
    inference(sr,[status(thm)],[c_0_40,c_0_41]) ).

thf(c_0_49,plain,
    p51,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43])]),c_0_44]) ).

thf(c_0_50,plain,
    ( ( f__0
      = ( fcP @ esk438_0 @ esk439_0 ) )
    | p740 ),
    inference(split_conjunct,[status(thm)],[c_0_45]) ).

thf(c_0_51,plain,
    ! [X1: a,X2: a] :
      ( ( fcP @ X1 @ X2 )
     != f__0 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47])]) ).

thf(c_0_52,plain,
    ~ p740,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_49])]) ).

thf(c_0_53,plain,
    $false,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_50,c_0_51]),c_0_52]),
    [proof] ).

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

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEV195^5 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33  % Computer : n019.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Mon Jun 27 21:50:09 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 36.67/37.25  % SZS status Theorem
% 36.67/37.25  % Mode: mode485
% 36.67/37.25  % Inferences: 54
% 36.67/37.25  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------