TSTP Solution File: SEV245^6 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SEV245^6 : TPTP v8.1.0. Released v5.1.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %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 17:35:52 EDT 2022

% Result   : Theorem 25.35s 25.62s
% Output   : CNFRefutation 25.35s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   65 (  27 unt;   5 typ;   0 def)
%            Number of atoms       :  393 ( 116 equ;   0 cnn)
%            Maximal formula atoms :    5 (   6 avg)
%            Number of connectives :  704 ( 126   ~; 102   |;  18   &; 426   @)
%                                         (   0 <=>;  32  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   3 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   92 (  92   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :  203 (  42   ^ 149   !;  12   ?; 203   :)

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

thf(tp_cK,type,
    cK: ( a > $o ) > a > $o ).

thf(tp_sK1_Xx,type,
    sK1_Xx: a ).

thf(tp_sK2_SY10,type,
    sK2_SY10: a > $o ).

thf(tp_sK3_Xx,type,
    sK3_Xx: ( a > $o ) > ( a > $o ) > a ).

thf(1,conjecture,
    ( ! [X: a > $o,Y: a > $o] :
        ( ! [Xx: a] :
            ( ( X @ Xx )
           => ( Y @ Xx ) )
       => ! [Xx: a] :
            ( ( cK @ X @ Xx )
           => ( cK @ Y @ Xx ) ) )
   => ! [Xx: a] :
        ( ? [S: a > $o] :
            ( ! [Xx0: a] :
                ( ( S @ Xx0 )
               => ( cK @ S @ Xx0 ) )
            & ( S @ Xx ) )
       => ( cK
          @ ^ [Xx0: a] :
            ? [S: a > $o] :
              ( ! [Xx1: a] :
                  ( ( S @ Xx1 )
                 => ( cK @ S @ Xx1 ) )
              & ( S @ Xx0 ) )
          @ Xx ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM116_2S) ).

thf(2,negated_conjecture,
    ( ( ! [X: a > $o,Y: a > $o] :
          ( ! [Xx: a] :
              ( ( X @ Xx )
             => ( Y @ Xx ) )
         => ! [Xx: a] :
              ( ( cK @ X @ Xx )
             => ( cK @ Y @ Xx ) ) )
     => ! [Xx: a] :
          ( ? [S: a > $o] :
              ( ! [Xx0: a] :
                  ( ( S @ Xx0 )
                 => ( cK @ S @ Xx0 ) )
              & ( S @ Xx ) )
         => ( cK
            @ ^ [Xx0: a] :
              ? [S: a > $o] :
                ( ! [Xx1: a] :
                    ( ( S @ Xx1 )
                   => ( cK @ S @ Xx1 ) )
                & ( S @ Xx0 ) )
            @ Xx ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ! [X: a > $o,Y: a > $o] :
          ( ! [Xx: a] :
              ( ( X @ Xx )
             => ( Y @ Xx ) )
         => ! [Xx: a] :
              ( ( cK @ X @ Xx )
             => ( cK @ Y @ Xx ) ) )
     => ! [Xx: a] :
          ( ? [S: a > $o] :
              ( ! [Xx0: a] :
                  ( ( S @ Xx0 )
                 => ( cK @ S @ Xx0 ) )
              & ( S @ Xx ) )
         => ( cK
            @ ^ [Xx0: a] :
              ? [S: a > $o] :
                ( ! [Xx1: a] :
                    ( ( S @ Xx1 )
                   => ( cK @ S @ Xx1 ) )
                & ( S @ Xx0 ) )
            @ Xx ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ! [X: a > $o,Y: a > $o] :
          ( ! [Xx: a] :
              ( ( X @ Xx )
             => ( Y @ Xx ) )
         => ! [Xx: a] :
              ( ( cK @ X @ Xx )
             => ( cK @ Y @ Xx ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(5,plain,
    ( ( ! [Xx: a] :
          ( ? [S: a > $o] :
              ( ! [Xx0: a] :
                  ( ( S @ Xx0 )
                 => ( cK @ S @ Xx0 ) )
              & ( S @ Xx ) )
         => ( cK
            @ ^ [Xx0: a] :
              ? [S: a > $o] :
                ( ! [Xx1: a] :
                    ( ( S @ Xx1 )
                   => ( cK @ S @ Xx1 ) )
                & ( S @ Xx0 ) )
            @ Xx ) ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(6,plain,
    ( ( ~ ! [Xx: a] :
            ( ? [S: a > $o] :
                ( ! [Xx0: a] :
                    ( ( S @ Xx0 )
                   => ( cK @ S @ Xx0 ) )
                & ( S @ Xx ) )
           => ( cK
              @ ^ [Xx0: a] :
                ? [S: a > $o] :
                  ( ! [Xx1: a] :
                      ( ( S @ Xx1 )
                     => ( cK @ S @ Xx1 ) )
                  & ( S @ Xx0 ) )
              @ Xx ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[5]) ).

thf(7,plain,
    ( ( ! [SY15: a] :
          ( ~ ( sK2_SY10 @ SY15 )
          | ( cK @ sK2_SY10 @ SY15 ) )
      & ( sK2_SY10 @ sK1_Xx )
      & ~ ( cK
          @ ^ [Xx0: a] :
            ? [S: a > $o] :
              ( ! [Xx1: a] :
                  ( ( S @ Xx1 )
                 => ( cK @ S @ Xx1 ) )
              & ( S @ Xx0 ) )
          @ sK1_Xx ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[6]) ).

thf(8,plain,
    ( ( ! [X: a > $o,Y: a > $o] :
          ( ( ( X @ ( sK3_Xx @ Y @ X ) )
            & ~ ( Y @ ( sK3_Xx @ Y @ X ) ) )
          | ! [Xx: a] :
              ( ~ ( cK @ X @ Xx )
              | ( cK @ Y @ Xx ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[4]) ).

thf(9,plain,
    ( ( ! [X: a > $o,Y: a > $o] :
          ( ( ( X @ ( sK3_Xx @ Y @ X ) )
            & ~ ( Y @ ( sK3_Xx @ Y @ X ) ) )
          | ! [Xx: a] :
              ( ~ ( cK @ X @ Xx )
              | ( cK @ Y @ Xx ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[8]) ).

thf(10,plain,
    ( ( ! [SY15: a] :
          ( ~ ( sK2_SY10 @ SY15 )
          | ( cK @ sK2_SY10 @ SY15 ) )
      & ( sK2_SY10 @ sK1_Xx )
      & ~ ( cK
          @ ^ [Xx0: a] :
            ? [S: a > $o] :
              ( ! [Xx1: a] :
                  ( ( S @ Xx1 )
                 => ( cK @ S @ Xx1 ) )
              & ( S @ Xx0 ) )
          @ sK1_Xx ) )
    = $true ),
    inference(copy,[status(thm)],[7]) ).

thf(11,plain,
    ( ( ! [SX0: a > $o,SX1: a > $o] :
          ( ~ ( ~ ( SX0 @ ( sK3_Xx @ SX1 @ SX0 ) )
              | ~ ~ ( SX1 @ ( sK3_Xx @ SX1 @ SX0 ) ) )
          | ! [SX2: a] :
              ( ~ ( cK @ SX0 @ SX2 )
              | ( cK @ SX1 @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9]) ).

thf(12,plain,
    ( ( ~ ( ~ ~ ( ~ ! [SX0: a] :
                      ( ~ ( sK2_SY10 @ SX0 )
                      | ( cK @ sK2_SY10 @ SX0 ) )
                | ~ ( sK2_SY10 @ sK1_Xx ) )
          | ~ ~ ( cK
                @ ^ [SX0: a] :
                    ~ ! [SX1: a > $o] :
                        ~ ~ ( ~ ! [SX2: a] :
                                  ( ~ ( SX1 @ SX2 )
                                  | ( cK @ SX1 @ SX2 ) )
                            | ~ ( SX1 @ SX0 ) )
                @ sK1_Xx ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(13,plain,
    ! [SV1: a > $o] :
      ( ( ! [SY16: a > $o] :
            ( ~ ( ~ ( SV1 @ ( sK3_Xx @ SY16 @ SV1 ) )
                | ~ ~ ( SY16 @ ( sK3_Xx @ SY16 @ SV1 ) ) )
            | ! [SY17: a] :
                ( ~ ( cK @ SV1 @ SY17 )
                | ( cK @ SY16 @ SY17 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11]) ).

thf(14,plain,
    ( ( ~ ~ ( ~ ! [SX0: a] :
                  ( ~ ( sK2_SY10 @ SX0 )
                  | ( cK @ sK2_SY10 @ SX0 ) )
            | ~ ( sK2_SY10 @ sK1_Xx ) )
      | ~ ~ ( cK
            @ ^ [SX0: a] :
                ~ ! [SX1: a > $o] :
                    ~ ~ ( ~ ! [SX2: a] :
                              ( ~ ( SX1 @ SX2 )
                              | ( cK @ SX1 @ SX2 ) )
                        | ~ ( SX1 @ SX0 ) )
            @ sK1_Xx ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[12]) ).

thf(15,plain,
    ! [SV2: a > $o,SV1: a > $o] :
      ( ( ~ ( ~ ( SV1 @ ( sK3_Xx @ SV2 @ SV1 ) )
            | ~ ~ ( SV2 @ ( sK3_Xx @ SV2 @ SV1 ) ) )
        | ! [SY18: a] :
            ( ~ ( cK @ SV1 @ SY18 )
            | ( cK @ SV2 @ SY18 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[13]) ).

thf(16,plain,
    ( ( ~ ~ ( ~ ! [SX0: a] :
                  ( ~ ( sK2_SY10 @ SX0 )
                  | ( cK @ sK2_SY10 @ SX0 ) )
            | ~ ( sK2_SY10 @ sK1_Xx ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[14]) ).

thf(17,plain,
    ( ( ~ ~ ( cK
            @ ^ [SX0: a] :
                ~ ! [SX1: a > $o] :
                    ~ ~ ( ~ ! [SX2: a] :
                              ( ~ ( SX1 @ SX2 )
                              | ( cK @ SX1 @ SX2 ) )
                        | ~ ( SX1 @ SX0 ) )
            @ sK1_Xx ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[14]) ).

thf(18,plain,
    ! [SV2: a > $o,SV1: a > $o] :
      ( ( ( ~ ( ~ ( SV1 @ ( sK3_Xx @ SV2 @ SV1 ) )
              | ~ ~ ( SV2 @ ( sK3_Xx @ SV2 @ SV1 ) ) ) )
        = $true )
      | ( ( ! [SY18: a] :
              ( ~ ( cK @ SV1 @ SY18 )
              | ( cK @ SV2 @ SY18 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[15]) ).

thf(19,plain,
    ( ( ~ ( ~ ! [SX0: a] :
                ( ~ ( sK2_SY10 @ SX0 )
                | ( cK @ sK2_SY10 @ SX0 ) )
          | ~ ( sK2_SY10 @ sK1_Xx ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[16]) ).

thf(20,plain,
    ( ( ~ ( cK
          @ ^ [SX0: a] :
              ~ ! [SX1: a > $o] :
                  ~ ~ ( ~ ! [SX2: a] :
                            ( ~ ( SX1 @ SX2 )
                            | ( cK @ SX1 @ SX2 ) )
                      | ~ ( SX1 @ SX0 ) )
          @ sK1_Xx ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[17]) ).

thf(21,plain,
    ! [SV2: a > $o,SV1: a > $o] :
      ( ( ( ~ ( SV1 @ ( sK3_Xx @ SV2 @ SV1 ) )
          | ~ ~ ( SV2 @ ( sK3_Xx @ SV2 @ SV1 ) ) )
        = $false )
      | ( ( ! [SY18: a] :
              ( ~ ( cK @ SV1 @ SY18 )
              | ( cK @ SV2 @ SY18 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[18]) ).

thf(22,plain,
    ( ( ~ ! [SX0: a] :
            ( ~ ( sK2_SY10 @ SX0 )
            | ( cK @ sK2_SY10 @ SX0 ) )
      | ~ ( sK2_SY10 @ sK1_Xx ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[19]) ).

thf(23,plain,
    ( ( cK
      @ ^ [SX0: a] :
          ~ ! [SX1: a > $o] :
              ~ ~ ( ~ ! [SX2: a] :
                        ( ~ ( SX1 @ SX2 )
                        | ( cK @ SX1 @ SX2 ) )
                  | ~ ( SX1 @ SX0 ) )
      @ sK1_Xx )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[20]) ).

thf(24,plain,
    ! [SV2: a > $o,SV1: a > $o] :
      ( ( ( ~ ( SV1 @ ( sK3_Xx @ SV2 @ SV1 ) ) )
        = $false )
      | ( ( ! [SY18: a] :
              ( ~ ( cK @ SV1 @ SY18 )
              | ( cK @ SV2 @ SY18 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[21]) ).

thf(25,plain,
    ! [SV1: a > $o,SV2: a > $o] :
      ( ( ( ~ ~ ( SV2 @ ( sK3_Xx @ SV2 @ SV1 ) ) )
        = $false )
      | ( ( ! [SY18: a] :
              ( ~ ( cK @ SV1 @ SY18 )
              | ( cK @ SV2 @ SY18 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[21]) ).

thf(26,plain,
    ( ( ~ ! [SX0: a] :
            ( ~ ( sK2_SY10 @ SX0 )
            | ( cK @ sK2_SY10 @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[22]) ).

thf(27,plain,
    ( ( ~ ( sK2_SY10 @ sK1_Xx ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[22]) ).

thf(28,plain,
    ! [SV2: a > $o,SV1: a > $o] :
      ( ( ( SV1 @ ( sK3_Xx @ SV2 @ SV1 ) )
        = $true )
      | ( ( ! [SY18: a] :
              ( ~ ( cK @ SV1 @ SY18 )
              | ( cK @ SV2 @ SY18 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[24]) ).

thf(29,plain,
    ! [SV1: a > $o,SV2: a > $o] :
      ( ( ( ~ ( SV2 @ ( sK3_Xx @ SV2 @ SV1 ) ) )
        = $true )
      | ( ( ! [SY18: a] :
              ( ~ ( cK @ SV1 @ SY18 )
              | ( cK @ SV2 @ SY18 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[25]) ).

thf(30,plain,
    ( ( ! [SX0: a] :
          ( ~ ( sK2_SY10 @ SX0 )
          | ( cK @ sK2_SY10 @ SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[26]) ).

thf(31,plain,
    ( ( sK2_SY10 @ sK1_Xx )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[27]) ).

thf(32,plain,
    ! [SV2: a > $o,SV3: a,SV1: a > $o] :
      ( ( ( ~ ( cK @ SV1 @ SV3 )
          | ( cK @ SV2 @ SV3 ) )
        = $true )
      | ( ( SV1 @ ( sK3_Xx @ SV2 @ SV1 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[28]) ).

thf(33,plain,
    ! [SV1: a > $o,SV2: a > $o] :
      ( ( ( SV2 @ ( sK3_Xx @ SV2 @ SV1 ) )
        = $false )
      | ( ( ! [SY18: a] :
              ( ~ ( cK @ SV1 @ SY18 )
              | ( cK @ SV2 @ SY18 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[29]) ).

thf(34,plain,
    ! [SV4: a] :
      ( ( ~ ( sK2_SY10 @ SV4 )
        | ( cK @ sK2_SY10 @ SV4 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[30]) ).

thf(35,plain,
    ! [SV2: a > $o,SV3: a,SV1: a > $o] :
      ( ( ( ~ ( cK @ SV1 @ SV3 ) )
        = $true )
      | ( ( cK @ SV2 @ SV3 )
        = $true )
      | ( ( SV1 @ ( sK3_Xx @ SV2 @ SV1 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[32]) ).

thf(36,plain,
    ! [SV2: a > $o,SV5: a,SV1: a > $o] :
      ( ( ( ~ ( cK @ SV1 @ SV5 )
          | ( cK @ SV2 @ SV5 ) )
        = $true )
      | ( ( SV2 @ ( sK3_Xx @ SV2 @ SV1 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[33]) ).

thf(37,plain,
    ! [SV4: a] :
      ( ( ( ~ ( sK2_SY10 @ SV4 ) )
        = $true )
      | ( ( cK @ sK2_SY10 @ SV4 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[34]) ).

thf(38,plain,
    ! [SV2: a > $o,SV3: a,SV1: a > $o] :
      ( ( ( cK @ SV1 @ SV3 )
        = $false )
      | ( ( cK @ SV2 @ SV3 )
        = $true )
      | ( ( SV1 @ ( sK3_Xx @ SV2 @ SV1 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[35]) ).

thf(39,plain,
    ! [SV2: a > $o,SV5: a,SV1: a > $o] :
      ( ( ( ~ ( cK @ SV1 @ SV5 ) )
        = $true )
      | ( ( cK @ SV2 @ SV5 )
        = $true )
      | ( ( SV2 @ ( sK3_Xx @ SV2 @ SV1 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[36]) ).

thf(40,plain,
    ! [SV4: a] :
      ( ( ( sK2_SY10 @ SV4 )
        = $false )
      | ( ( cK @ sK2_SY10 @ SV4 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[37]) ).

thf(41,plain,
    ! [SV2: a > $o,SV5: a,SV1: a > $o] :
      ( ( ( cK @ SV1 @ SV5 )
        = $false )
      | ( ( cK @ SV2 @ SV5 )
        = $true )
      | ( ( SV2 @ ( sK3_Xx @ SV2 @ SV1 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[39]) ).

thf(42,plain,
    ! [SV3: a,SV1: a > $o] :
      ( ( ( cK @ SV1 @ SV3 )
        = $false )
      | ( ( cK
          @ ^ [SX0: a] : $true
          @ SV3 )
        = $true )
      | ( ( SV1
          @ ( sK3_Xx
            @ ^ [SX0: a] : $true
            @ SV1 ) )
        = $true ) ),
    inference(prim_subst,[status(thm)],[38:[bind(SV2,$thf( ^ [SV9: a] : $true ))]]) ).

thf(43,plain,
    ! [SV3: a,SV1: a > $o] :
      ( ( ( cK @ SV1 @ SV3 )
        = $false )
      | ( ( cK
          @ ^ [SX0: a] : $false
          @ SV3 )
        = $true )
      | ( ( SV1
          @ ( sK3_Xx
            @ ^ [SX0: a] : $false
            @ SV1 ) )
        = $true ) ),
    inference(prim_subst,[status(thm)],[38:[bind(SV2,$thf( ^ [SV8: a] : $false ))]]) ).

thf(44,plain,
    ! [SV7: a > $o,SV3: a,SV1: a > $o] :
      ( ( ( cK @ SV1 @ SV3 )
        = $false )
      | ( ( cK
          @ ^ [SX0: a] :
              ~ ( SV7 @ SX0 )
          @ SV3 )
        = $true )
      | ( ( SV1
          @ ( sK3_Xx
            @ ^ [SX0: a] :
                ~ ( SV7 @ SX0 )
            @ SV1 ) )
        = $true ) ),
    inference(prim_subst,[status(thm)],[38:[bind(SV2,$thf( ^ [SV6: a] : ~ ( SV7 @ SV6 ) ))]]) ).

thf(45,plain,
    ! [SV3: a,SV1: a > $o] :
      ( ( ( cK @ SV1 @ SV3 )
        = $false )
      | ( ( cK
          @ ^ [SX0: a] : ( SX0 = sK1_Xx )
          @ SV3 )
        = $true )
      | ( ( SV1
          @ ( sK3_Xx
            @ ^ [SX0: a] : ( SX0 = sK1_Xx )
            @ SV1 ) )
        = $true ) ),
    inference(prim_subst,[status(thm)],[38:[bind(SV2,$thf( ^ [SV10: a] : ( SV10 = sK1_Xx ) ))]]) ).

thf(47,plain,
    ! [SV2: a > $o,SV3: a] :
      ( ( ( cK
          @ ^ [SX0: a] : $false
          @ SV3 )
        = $false )
      | ( ( cK @ SV2 @ SV3 )
        = $true )
      | ( $false = $true ) ),
    inference(prim_subst,[status(thm)],[38:[bind(SV1,$thf( ^ [SV13: a] : $false ))]]) ).

thf(48,plain,
    ! [SV2: a > $o,SV3: a,SV12: a > $o] :
      ( ( ( cK
          @ ^ [SX0: a] :
              ~ ( SV12 @ SX0 )
          @ SV3 )
        = $false )
      | ( ( cK @ SV2 @ SV3 )
        = $true )
      | ( ( ~ ( SV12
              @ ( sK3_Xx @ SV2
                @ ^ [SX0: a] :
                    ~ ( SV12 @ SX0 ) ) ) )
        = $true ) ),
    inference(prim_subst,[status(thm)],[38:[bind(SV1,$thf( ^ [SV11: a] : ~ ( SV12 @ SV11 ) ))]]) ).

thf(49,plain,
    ! [SV2: a > $o,SV3: a] :
      ( ( ( cK
          @ ^ [SX0: a] : ( SX0 = sK1_Xx )
          @ SV3 )
        = $false )
      | ( ( cK @ SV2 @ SV3 )
        = $true )
      | ( ( ( sK3_Xx @ SV2
            @ ^ [SX0: a] : ( SX0 = sK1_Xx ) )
          = sK1_Xx )
        = $true ) ),
    inference(prim_subst,[status(thm)],[38:[bind(SV1,$thf( ^ [SV15: a] : ( SV15 = sK1_Xx ) ))]]) ).

thf(50,plain,
    ! [SV5: a,SV1: a > $o] :
      ( ( ( cK @ SV1 @ SV5 )
        = $false )
      | ( ( cK
          @ ^ [SX0: a] : $true
          @ SV5 )
        = $true )
      | ( $true = $false ) ),
    inference(prim_subst,[status(thm)],[41:[bind(SV2,$thf( ^ [SV9: a] : $true ))]]) ).

thf(52,plain,
    ! [SV7: a > $o,SV5: a,SV1: a > $o] :
      ( ( ( cK @ SV1 @ SV5 )
        = $false )
      | ( ( cK
          @ ^ [SX0: a] :
              ~ ( SV7 @ SX0 )
          @ SV5 )
        = $true )
      | ( ( ~ ( SV7
              @ ( sK3_Xx
                @ ^ [SX0: a] :
                    ~ ( SV7 @ SX0 )
                @ SV1 ) ) )
        = $false ) ),
    inference(prim_subst,[status(thm)],[41:[bind(SV2,$thf( ^ [SV6: a] : ~ ( SV7 @ SV6 ) ))]]) ).

thf(54,plain,
    ! [SV2: a > $o,SV5: a] :
      ( ( ( cK
          @ ^ [SX0: a] : $true
          @ SV5 )
        = $false )
      | ( ( cK @ SV2 @ SV5 )
        = $true )
      | ( ( SV2
          @ ( sK3_Xx @ SV2
            @ ^ [SX0: a] : $true ) )
        = $false ) ),
    inference(prim_subst,[status(thm)],[41:[bind(SV1,$thf( ^ [SV14: a] : $true ))]]) ).

thf(55,plain,
    ! [SV2: a > $o,SV5: a] :
      ( ( ( cK
          @ ^ [SX0: a] : $false
          @ SV5 )
        = $false )
      | ( ( cK @ SV2 @ SV5 )
        = $true )
      | ( ( SV2
          @ ( sK3_Xx @ SV2
            @ ^ [SX0: a] : $false ) )
        = $false ) ),
    inference(prim_subst,[status(thm)],[41:[bind(SV1,$thf( ^ [SV13: a] : $false ))]]) ).

thf(56,plain,
    ! [SV2: a > $o,SV5: a,SV12: a > $o] :
      ( ( ( cK
          @ ^ [SX0: a] :
              ~ ( SV12 @ SX0 )
          @ SV5 )
        = $false )
      | ( ( cK @ SV2 @ SV5 )
        = $true )
      | ( ( SV2
          @ ( sK3_Xx @ SV2
            @ ^ [SX0: a] :
                ~ ( SV12 @ SX0 ) ) )
        = $false ) ),
    inference(prim_subst,[status(thm)],[41:[bind(SV1,$thf( ^ [SV11: a] : ~ ( SV12 @ SV11 ) ))]]) ).

thf(57,plain,
    ! [SV2: a > $o,SV5: a] :
      ( ( ( cK
          @ ^ [SX0: a] : ( SX0 = sK1_Xx )
          @ SV5 )
        = $false )
      | ( ( cK @ SV2 @ SV5 )
        = $true )
      | ( ( SV2
          @ ( sK3_Xx @ SV2
            @ ^ [SX0: a] : ( SX0 = sK1_Xx ) ) )
        = $false ) ),
    inference(prim_subst,[status(thm)],[41:[bind(SV1,$thf( ^ [SV15: a] : ( SV15 = sK1_Xx ) ))]]) ).

thf(58,plain,
    ! [SV3: a,SV2: a > $o,SV12: a > $o] :
      ( ( ( SV12
          @ ( sK3_Xx @ SV2
            @ ^ [SX0: a] :
                ~ ( SV12 @ SX0 ) ) )
        = $false )
      | ( ( cK @ SV2 @ SV3 )
        = $true )
      | ( ( cK
          @ ^ [SX0: a] :
              ~ ( SV12 @ SX0 )
          @ SV3 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[48]) ).

thf(59,plain,
    ! [SV5: a,SV1: a > $o,SV7: a > $o] :
      ( ( ( SV7
          @ ( sK3_Xx
            @ ^ [SX0: a] :
                ~ ( SV7 @ SX0 )
            @ SV1 ) )
        = $true )
      | ( ( cK
          @ ^ [SX0: a] :
              ~ ( SV7 @ SX0 )
          @ SV5 )
        = $true )
      | ( ( cK @ SV1 @ SV5 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[52]) ).

thf(60,plain,
    ! [SV2: a > $o,SV3: a] :
      ( ( ( cK
          @ ^ [SX0: a] : $false
          @ SV3 )
        = $false )
      | ( ( cK @ SV2 @ SV3 )
        = $true ) ),
    inference(sim,[status(thm)],[47]) ).

thf(61,plain,
    ! [SV5: a,SV1: a > $o] :
      ( ( ( cK @ SV1 @ SV5 )
        = $false )
      | ( ( cK
          @ ^ [SX0: a] : $true
          @ SV5 )
        = $true ) ),
    inference(sim,[status(thm)],[50]) ).

thf(62,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[23,61,60,59,58,57,56,55,54,49,45,44,43,42,41,40,38,31]) ).

thf(63,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[62]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : SEV245^6 : TPTP v8.1.0. Released v5.1.0.
% 0.10/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34  % Computer : n019.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 : Tue Jun 28 10:31:54 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  
% 0.13/0.35   No.of.Axioms: 0
% 0.13/0.35  
% 0.13/0.35   Length.of.Defs: 0
% 0.13/0.35  
% 0.13/0.35   Contains.Choice.Funs: false
% 0.13/0.35  (rf:0,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full)...eprover: CPU time limit exceeded, terminating
% 25.22/25.40  .
% 25.35/25.62  
% 25.35/25.62  ********************************
% 25.35/25.62  *   All subproblems solved!    *
% 25.35/25.62  ********************************
% 25.35/25.62  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:62,loop_count:0,foatp_calls:2,translation:fof_full)
% 25.35/25.63  
% 25.35/25.63  %**** Beginning of derivation protocol ****
% 25.35/25.63  % SZS output start CNFRefutation
% See solution above
% 25.35/25.63  
% 25.35/25.63  %**** End of derivation protocol ****
% 25.35/25.63  %**** no. of clauses in derivation: 60 ****
% 25.35/25.63  %**** clause counter: 62 ****
% 25.35/25.63  
% 25.35/25.63  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:62,loop_count:0,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------