TSTP Solution File: SEV398^5 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SEV398^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n010.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 17:36:32 EDT 2022

% Result   : Theorem 0.18s 0.41s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :    9
% Syntax   : Number of formulae    :  105 (  62 unt;   8 typ;   0 def)
%            Number of atoms       :  557 ( 137 equ;   0 cnn)
%            Maximal formula atoms :   10 (   5 avg)
%            Number of connectives :  948 ( 156   ~; 126   |;  17   &; 618   @)
%                                         (   4 <=>;  27  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :  140 ( 140   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :  225 (   0   ^ 225   !;   0   ?; 225   :)

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

thf(tp_cF,type,
    cF: ( a > $o ) > a > $o ).

thf(tp_cG,type,
    cG: ( a > $o ) > a > $o ).

thf(tp_sK1_S,type,
    sK1_S: a > $o ).

thf(tp_sK2_SY9,type,
    sK2_SY9: a ).

thf(tp_sK3_S,type,
    sK3_S: a > $o ).

thf(tp_sK4_SY10,type,
    sK4_SY10: a ).

thf(tp_sK5_Xx,type,
    sK5_Xx: ( a > $o ) > ( a > $o ) > a ).

thf(1,conjecture,
    ( ( ! [S: a > $o,T: a > $o] :
          ( ! [Xx: a] :
              ( ( S @ Xx )
             => ( T @ Xx ) )
         => ! [Xx: a] :
              ( ( cF @ T @ Xx )
             => ( cF @ S @ Xx ) ) )
      & ! [S: a > $o] :
          ( ! [Xx: a] :
              ( ( S @ Xx )
             => ( cF @ ( cG @ S ) @ Xx ) )
          & ! [Xx: a] :
              ( ( S @ Xx )
             => ( cG @ ( cF @ S ) @ Xx ) ) ) )
   => ! [S: a > $o,Xx: a] :
        ( ( cF @ ( cG @ ( cF @ S ) ) @ Xx )
      <=> ( cF @ S @ Xx ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM67A_pme) ).

thf(2,negated_conjecture,
    ( ( ( ! [S: a > $o,T: a > $o] :
            ( ! [Xx: a] :
                ( ( S @ Xx )
               => ( T @ Xx ) )
           => ! [Xx: a] :
                ( ( cF @ T @ Xx )
               => ( cF @ S @ Xx ) ) )
        & ! [S: a > $o] :
            ( ! [Xx: a] :
                ( ( S @ Xx )
               => ( cF @ ( cG @ S ) @ Xx ) )
            & ! [Xx: a] :
                ( ( S @ Xx )
               => ( cG @ ( cF @ S ) @ Xx ) ) ) )
     => ! [S: a > $o,Xx: a] :
          ( ( cF @ ( cG @ ( cF @ S ) ) @ Xx )
        <=> ( cF @ S @ Xx ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ( ! [S: a > $o,T: a > $o] :
            ( ! [Xx: a] :
                ( ( S @ Xx )
               => ( T @ Xx ) )
           => ! [Xx: a] :
                ( ( cF @ T @ Xx )
               => ( cF @ S @ Xx ) ) )
        & ! [S: a > $o] :
            ( ! [Xx: a] :
                ( ( S @ Xx )
               => ( cF @ ( cG @ S ) @ Xx ) )
            & ! [Xx: a] :
                ( ( S @ Xx )
               => ( cG @ ( cF @ S ) @ Xx ) ) ) )
     => ! [S: a > $o,Xx: a] :
          ( ( cF @ ( cG @ ( cF @ S ) ) @ Xx )
        <=> ( cF @ S @ Xx ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2]) ).

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

thf(5,plain,
    ( ( ! [S: a > $o] :
          ( ! [Xx: a] :
              ( ( S @ Xx )
             => ( cF @ ( cG @ S ) @ Xx ) )
          & ! [Xx: a] :
              ( ( S @ Xx )
             => ( cG @ ( cF @ S ) @ Xx ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(6,plain,
    ( ( ! [S: a > $o,Xx: a] :
          ( ( cF @ ( cG @ ( cF @ S ) ) @ Xx )
        <=> ( cF @ S @ Xx ) ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(7,plain,
    ( ( ! [S: a > $o,Xx: a] :
          ( ( cF @ ( cG @ ( cF @ S ) ) @ Xx )
         => ( cF @ S @ Xx ) ) )
    = $false ),
    inference(split_conjecture,[split_conjecture(split,[])],[6]) ).

thf(8,plain,
    ( ( ! [S: a > $o,Xx: a] :
          ( ( cF @ S @ Xx )
         => ( cF @ ( cG @ ( cF @ S ) ) @ Xx ) ) )
    = $false ),
    inference(split_conjecture,[split_conjecture(split,[])],[6]) ).

thf(9,plain,
    ( ( ~ ! [S: a > $o,Xx: a] :
            ( ( cF @ ( cG @ ( cF @ S ) ) @ Xx )
           => ( cF @ S @ Xx ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[7]) ).

thf(10,plain,
    ( ( ~ ! [S: a > $o,Xx: a] :
            ( ( cF @ S @ Xx )
           => ( cF @ ( cG @ ( cF @ S ) ) @ Xx ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[8]) ).

thf(11,plain,
    ( ( ( cF @ ( cG @ ( cF @ sK1_S ) ) @ sK2_SY9 )
      & ~ ( cF @ sK1_S @ sK2_SY9 ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[9]) ).

thf(12,plain,
    ( ( ( cF @ sK3_S @ sK4_SY10 )
      & ~ ( cF @ ( cG @ ( cF @ sK3_S ) ) @ sK4_SY10 ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[10]) ).

thf(13,plain,
    ( ( ! [S: a > $o,T: a > $o] :
          ( ( ( S @ ( sK5_Xx @ T @ S ) )
            & ~ ( T @ ( sK5_Xx @ T @ S ) ) )
          | ! [Xx: a] :
              ( ~ ( cF @ T @ Xx )
              | ( cF @ S @ Xx ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[4]) ).

thf(14,plain,
    ( ( ! [S: a > $o,Xx: a] :
          ( ~ ( S @ Xx )
          | ( cF @ ( cG @ S ) @ Xx ) )
      & ! [S: a > $o,Xx: a] :
          ( ~ ( S @ Xx )
          | ( cG @ ( cF @ S ) @ Xx ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5]) ).

thf(15,plain,
    ( ( ! [S: a > $o,Xx: a] :
          ( ~ ( S @ Xx )
          | ( cF @ ( cG @ S ) @ Xx ) )
      & ! [S: a > $o,Xx: a] :
          ( ~ ( S @ Xx )
          | ( cG @ ( cF @ S ) @ Xx ) ) )
    = $true ),
    inference(copy,[status(thm)],[14]) ).

thf(16,plain,
    ( ( ! [S: a > $o,T: a > $o] :
          ( ( ( S @ ( sK5_Xx @ T @ S ) )
            & ~ ( T @ ( sK5_Xx @ T @ S ) ) )
          | ! [Xx: a] :
              ( ~ ( cF @ T @ Xx )
              | ( cF @ S @ Xx ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[13]) ).

thf(17,plain,
    ( ( ( cF @ ( cG @ ( cF @ sK1_S ) ) @ sK2_SY9 )
      & ~ ( cF @ sK1_S @ sK2_SY9 ) )
    = $true ),
    inference(copy,[status(thm)],[11]) ).

thf(18,plain,
    ( ( ~ ( ~ ! [SX0: a > $o,SX1: a] :
                ( ~ ( SX0 @ SX1 )
                | ( cF @ ( cG @ SX0 ) @ SX1 ) )
          | ~ ! [SX0: a > $o,SX1: a] :
                ( ~ ( SX0 @ SX1 )
                | ( cG @ ( cF @ SX0 ) @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[15]) ).

thf(19,plain,
    ( ( ! [SX0: a > $o,SX1: a > $o] :
          ( ~ ( ~ ( SX0 @ ( sK5_Xx @ SX1 @ SX0 ) )
              | ~ ~ ( SX1 @ ( sK5_Xx @ SX1 @ SX0 ) ) )
          | ! [SX2: a] :
              ( ~ ( cF @ SX1 @ SX2 )
              | ( cF @ SX0 @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[16]) ).

thf(20,plain,
    ( ( ~ ( ~ ( cF @ ( cG @ ( cF @ sK1_S ) ) @ sK2_SY9 )
          | ~ ~ ( cF @ sK1_S @ sK2_SY9 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[17]) ).

thf(21,plain,
    ( ( ~ ! [SX0: a > $o,SX1: a] :
            ( ~ ( SX0 @ SX1 )
            | ( cF @ ( cG @ SX0 ) @ SX1 ) )
      | ~ ! [SX0: a > $o,SX1: a] :
            ( ~ ( SX0 @ SX1 )
            | ( cG @ ( cF @ SX0 ) @ SX1 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[18]) ).

thf(22,plain,
    ! [SV1: a > $o] :
      ( ( ! [SY11: a > $o] :
            ( ~ ( ~ ( SV1 @ ( sK5_Xx @ SY11 @ SV1 ) )
                | ~ ~ ( SY11 @ ( sK5_Xx @ SY11 @ SV1 ) ) )
            | ! [SY12: a] :
                ( ~ ( cF @ SY11 @ SY12 )
                | ( cF @ SV1 @ SY12 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[19]) ).

thf(23,plain,
    ( ( ~ ( cF @ ( cG @ ( cF @ sK1_S ) ) @ sK2_SY9 )
      | ~ ~ ( cF @ sK1_S @ sK2_SY9 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[20]) ).

thf(24,plain,
    ( ( ~ ! [SX0: a > $o,SX1: a] :
            ( ~ ( SX0 @ SX1 )
            | ( cF @ ( cG @ SX0 ) @ SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[21]) ).

thf(25,plain,
    ( ( ~ ! [SX0: a > $o,SX1: a] :
            ( ~ ( SX0 @ SX1 )
            | ( cG @ ( cF @ SX0 ) @ SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[21]) ).

thf(26,plain,
    ! [SV2: a > $o,SV1: a > $o] :
      ( ( ~ ( ~ ( SV1 @ ( sK5_Xx @ SV2 @ SV1 ) )
            | ~ ~ ( SV2 @ ( sK5_Xx @ SV2 @ SV1 ) ) )
        | ! [SY13: a] :
            ( ~ ( cF @ SV2 @ SY13 )
            | ( cF @ SV1 @ SY13 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[22]) ).

thf(27,plain,
    ( ( ~ ( cF @ ( cG @ ( cF @ sK1_S ) ) @ sK2_SY9 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[23]) ).

thf(28,plain,
    ( ( ~ ~ ( cF @ sK1_S @ sK2_SY9 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[23]) ).

thf(29,plain,
    ( ( ! [SX0: a > $o,SX1: a] :
          ( ~ ( SX0 @ SX1 )
          | ( cF @ ( cG @ SX0 ) @ SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[24]) ).

thf(30,plain,
    ( ( ! [SX0: a > $o,SX1: a] :
          ( ~ ( SX0 @ SX1 )
          | ( cG @ ( cF @ SX0 ) @ SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[25]) ).

thf(31,plain,
    ! [SV2: a > $o,SV1: a > $o] :
      ( ( ( ~ ( ~ ( SV1 @ ( sK5_Xx @ SV2 @ SV1 ) )
              | ~ ~ ( SV2 @ ( sK5_Xx @ SV2 @ SV1 ) ) ) )
        = $true )
      | ( ( ! [SY13: a] :
              ( ~ ( cF @ SV2 @ SY13 )
              | ( cF @ SV1 @ SY13 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[26]) ).

thf(32,plain,
    ( ( cF @ ( cG @ ( cF @ sK1_S ) ) @ sK2_SY9 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[27]) ).

thf(33,plain,
    ( ( ~ ( cF @ sK1_S @ sK2_SY9 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[28]) ).

thf(34,plain,
    ! [SV3: a > $o] :
      ( ( ! [SY14: a] :
            ( ~ ( SV3 @ SY14 )
            | ( cF @ ( cG @ SV3 ) @ SY14 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[29]) ).

thf(35,plain,
    ! [SV4: a > $o] :
      ( ( ! [SY15: a] :
            ( ~ ( SV4 @ SY15 )
            | ( cG @ ( cF @ SV4 ) @ SY15 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[30]) ).

thf(36,plain,
    ! [SV2: a > $o,SV1: a > $o] :
      ( ( ( ~ ( SV1 @ ( sK5_Xx @ SV2 @ SV1 ) )
          | ~ ~ ( SV2 @ ( sK5_Xx @ SV2 @ SV1 ) ) )
        = $false )
      | ( ( ! [SY13: a] :
              ( ~ ( cF @ SV2 @ SY13 )
              | ( cF @ SV1 @ SY13 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[31]) ).

thf(37,plain,
    ( ( cF @ sK1_S @ sK2_SY9 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[33]) ).

thf(38,plain,
    ! [SV5: a,SV3: a > $o] :
      ( ( ~ ( SV3 @ SV5 )
        | ( cF @ ( cG @ SV3 ) @ SV5 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[34]) ).

thf(39,plain,
    ! [SV6: a,SV4: a > $o] :
      ( ( ~ ( SV4 @ SV6 )
        | ( cG @ ( cF @ SV4 ) @ SV6 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[35]) ).

thf(40,plain,
    ! [SV2: a > $o,SV1: a > $o] :
      ( ( ( ~ ( SV1 @ ( sK5_Xx @ SV2 @ SV1 ) ) )
        = $false )
      | ( ( ! [SY13: a] :
              ( ~ ( cF @ SV2 @ SY13 )
              | ( cF @ SV1 @ SY13 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[36]) ).

thf(41,plain,
    ! [SV1: a > $o,SV2: a > $o] :
      ( ( ( ~ ~ ( SV2 @ ( sK5_Xx @ SV2 @ SV1 ) ) )
        = $false )
      | ( ( ! [SY13: a] :
              ( ~ ( cF @ SV2 @ SY13 )
              | ( cF @ SV1 @ SY13 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[36]) ).

thf(42,plain,
    ! [SV5: a,SV3: a > $o] :
      ( ( ( ~ ( SV3 @ SV5 ) )
        = $true )
      | ( ( cF @ ( cG @ SV3 ) @ SV5 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[38]) ).

thf(43,plain,
    ! [SV6: a,SV4: a > $o] :
      ( ( ( ~ ( SV4 @ SV6 ) )
        = $true )
      | ( ( cG @ ( cF @ SV4 ) @ SV6 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[39]) ).

thf(44,plain,
    ! [SV2: a > $o,SV1: a > $o] :
      ( ( ( SV1 @ ( sK5_Xx @ SV2 @ SV1 ) )
        = $true )
      | ( ( ! [SY13: a] :
              ( ~ ( cF @ SV2 @ SY13 )
              | ( cF @ SV1 @ SY13 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[40]) ).

thf(45,plain,
    ! [SV1: a > $o,SV2: a > $o] :
      ( ( ( ~ ( SV2 @ ( sK5_Xx @ SV2 @ SV1 ) ) )
        = $true )
      | ( ( ! [SY13: a] :
              ( ~ ( cF @ SV2 @ SY13 )
              | ( cF @ SV1 @ SY13 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[41]) ).

thf(46,plain,
    ! [SV5: a,SV3: a > $o] :
      ( ( ( SV3 @ SV5 )
        = $false )
      | ( ( cF @ ( cG @ SV3 ) @ SV5 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[42]) ).

thf(47,plain,
    ! [SV6: a,SV4: a > $o] :
      ( ( ( SV4 @ SV6 )
        = $false )
      | ( ( cG @ ( cF @ SV4 ) @ SV6 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[43]) ).

thf(48,plain,
    ! [SV1: a > $o,SV7: a,SV2: a > $o] :
      ( ( ( ~ ( cF @ SV2 @ SV7 )
          | ( cF @ SV1 @ SV7 ) )
        = $true )
      | ( ( SV1 @ ( sK5_Xx @ SV2 @ SV1 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[44]) ).

thf(49,plain,
    ! [SV1: a > $o,SV2: a > $o] :
      ( ( ( SV2 @ ( sK5_Xx @ SV2 @ SV1 ) )
        = $false )
      | ( ( ! [SY13: a] :
              ( ~ ( cF @ SV2 @ SY13 )
              | ( cF @ SV1 @ SY13 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[45]) ).

thf(50,plain,
    ! [SV1: a > $o,SV7: a,SV2: a > $o] :
      ( ( ( ~ ( cF @ SV2 @ SV7 ) )
        = $true )
      | ( ( cF @ SV1 @ SV7 )
        = $true )
      | ( ( SV1 @ ( sK5_Xx @ SV2 @ SV1 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[48]) ).

thf(51,plain,
    ! [SV1: a > $o,SV8: a,SV2: a > $o] :
      ( ( ( ~ ( cF @ SV2 @ SV8 )
          | ( cF @ SV1 @ SV8 ) )
        = $true )
      | ( ( SV2 @ ( sK5_Xx @ SV2 @ SV1 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[49]) ).

thf(52,plain,
    ! [SV1: a > $o,SV7: a,SV2: a > $o] :
      ( ( ( cF @ SV2 @ SV7 )
        = $false )
      | ( ( cF @ SV1 @ SV7 )
        = $true )
      | ( ( SV1 @ ( sK5_Xx @ SV2 @ SV1 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[50]) ).

thf(53,plain,
    ! [SV1: a > $o,SV8: a,SV2: a > $o] :
      ( ( ( ~ ( cF @ SV2 @ SV8 ) )
        = $true )
      | ( ( cF @ SV1 @ SV8 )
        = $true )
      | ( ( SV2 @ ( sK5_Xx @ SV2 @ SV1 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[51]) ).

thf(54,plain,
    ! [SV1: a > $o,SV8: a,SV2: a > $o] :
      ( ( ( cF @ SV2 @ SV8 )
        = $false )
      | ( ( cF @ SV1 @ SV8 )
        = $true )
      | ( ( SV2 @ ( sK5_Xx @ SV2 @ SV1 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[53]) ).

thf(55,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[32,54,52,47,46,37]) ).

thf(56,plain,
    ( ( ! [S: a > $o,Xx: a] :
          ( ~ ( S @ Xx )
          | ( cF @ ( cG @ S ) @ Xx ) )
      & ! [S: a > $o,Xx: a] :
          ( ~ ( S @ Xx )
          | ( cG @ ( cF @ S ) @ Xx ) ) )
    = $true ),
    inference(copy,[status(thm)],[14]) ).

thf(57,plain,
    ( ( ! [S: a > $o,T: a > $o] :
          ( ( ( S @ ( sK5_Xx @ T @ S ) )
            & ~ ( T @ ( sK5_Xx @ T @ S ) ) )
          | ! [Xx: a] :
              ( ~ ( cF @ T @ Xx )
              | ( cF @ S @ Xx ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[13]) ).

thf(58,plain,
    ( ( ( cF @ sK3_S @ sK4_SY10 )
      & ~ ( cF @ ( cG @ ( cF @ sK3_S ) ) @ sK4_SY10 ) )
    = $true ),
    inference(copy,[status(thm)],[12]) ).

thf(59,plain,
    ( ( ! [SX0: a > $o,SX1: a > $o] :
          ( ~ ( ~ ( SX0 @ ( sK5_Xx @ SX1 @ SX0 ) )
              | ~ ~ ( SX1 @ ( sK5_Xx @ SX1 @ SX0 ) ) )
          | ! [SX2: a] :
              ( ~ ( cF @ SX1 @ SX2 )
              | ( cF @ SX0 @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[57]) ).

thf(60,plain,
    ( ( ~ ( ~ ( cF @ sK3_S @ sK4_SY10 )
          | ~ ~ ( cF @ ( cG @ ( cF @ sK3_S ) ) @ sK4_SY10 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[58]) ).

thf(61,plain,
    ( ( ~ ( ~ ! [SX0: a > $o,SX1: a] :
                ( ~ ( SX0 @ SX1 )
                | ( cF @ ( cG @ SX0 ) @ SX1 ) )
          | ~ ! [SX0: a > $o,SX1: a] :
                ( ~ ( SX0 @ SX1 )
                | ( cG @ ( cF @ SX0 ) @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[56]) ).

thf(62,plain,
    ! [SV9: a > $o] :
      ( ( ! [SY16: a > $o] :
            ( ~ ( ~ ( SV9 @ ( sK5_Xx @ SY16 @ SV9 ) )
                | ~ ~ ( SY16 @ ( sK5_Xx @ SY16 @ SV9 ) ) )
            | ! [SY17: a] :
                ( ~ ( cF @ SY16 @ SY17 )
                | ( cF @ SV9 @ SY17 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[59]) ).

thf(63,plain,
    ( ( ~ ( cF @ sK3_S @ sK4_SY10 )
      | ~ ~ ( cF @ ( cG @ ( cF @ sK3_S ) ) @ sK4_SY10 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[60]) ).

thf(64,plain,
    ( ( ~ ! [SX0: a > $o,SX1: a] :
            ( ~ ( SX0 @ SX1 )
            | ( cF @ ( cG @ SX0 ) @ SX1 ) )
      | ~ ! [SX0: a > $o,SX1: a] :
            ( ~ ( SX0 @ SX1 )
            | ( cG @ ( cF @ SX0 ) @ SX1 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[61]) ).

thf(65,plain,
    ! [SV10: a > $o,SV9: a > $o] :
      ( ( ~ ( ~ ( SV9 @ ( sK5_Xx @ SV10 @ SV9 ) )
            | ~ ~ ( SV10 @ ( sK5_Xx @ SV10 @ SV9 ) ) )
        | ! [SY18: a] :
            ( ~ ( cF @ SV10 @ SY18 )
            | ( cF @ SV9 @ SY18 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[62]) ).

thf(66,plain,
    ( ( ~ ( cF @ sK3_S @ sK4_SY10 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[63]) ).

thf(67,plain,
    ( ( ~ ~ ( cF @ ( cG @ ( cF @ sK3_S ) ) @ sK4_SY10 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[63]) ).

thf(68,plain,
    ( ( ~ ! [SX0: a > $o,SX1: a] :
            ( ~ ( SX0 @ SX1 )
            | ( cF @ ( cG @ SX0 ) @ SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[64]) ).

thf(69,plain,
    ( ( ~ ! [SX0: a > $o,SX1: a] :
            ( ~ ( SX0 @ SX1 )
            | ( cG @ ( cF @ SX0 ) @ SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[64]) ).

thf(70,plain,
    ! [SV10: a > $o,SV9: a > $o] :
      ( ( ( ~ ( ~ ( SV9 @ ( sK5_Xx @ SV10 @ SV9 ) )
              | ~ ~ ( SV10 @ ( sK5_Xx @ SV10 @ SV9 ) ) ) )
        = $true )
      | ( ( ! [SY18: a] :
              ( ~ ( cF @ SV10 @ SY18 )
              | ( cF @ SV9 @ SY18 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[65]) ).

thf(71,plain,
    ( ( cF @ sK3_S @ sK4_SY10 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[66]) ).

thf(72,plain,
    ( ( ~ ( cF @ ( cG @ ( cF @ sK3_S ) ) @ sK4_SY10 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[67]) ).

thf(73,plain,
    ( ( ! [SX0: a > $o,SX1: a] :
          ( ~ ( SX0 @ SX1 )
          | ( cF @ ( cG @ SX0 ) @ SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[68]) ).

thf(74,plain,
    ( ( ! [SX0: a > $o,SX1: a] :
          ( ~ ( SX0 @ SX1 )
          | ( cG @ ( cF @ SX0 ) @ SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[69]) ).

thf(75,plain,
    ! [SV10: a > $o,SV9: a > $o] :
      ( ( ( ~ ( SV9 @ ( sK5_Xx @ SV10 @ SV9 ) )
          | ~ ~ ( SV10 @ ( sK5_Xx @ SV10 @ SV9 ) ) )
        = $false )
      | ( ( ! [SY18: a] :
              ( ~ ( cF @ SV10 @ SY18 )
              | ( cF @ SV9 @ SY18 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[70]) ).

thf(76,plain,
    ( ( cF @ ( cG @ ( cF @ sK3_S ) ) @ sK4_SY10 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[72]) ).

thf(77,plain,
    ! [SV11: a > $o] :
      ( ( ! [SY19: a] :
            ( ~ ( SV11 @ SY19 )
            | ( cF @ ( cG @ SV11 ) @ SY19 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[73]) ).

thf(78,plain,
    ! [SV12: a > $o] :
      ( ( ! [SY20: a] :
            ( ~ ( SV12 @ SY20 )
            | ( cG @ ( cF @ SV12 ) @ SY20 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[74]) ).

thf(79,plain,
    ! [SV10: a > $o,SV9: a > $o] :
      ( ( ( ~ ( SV9 @ ( sK5_Xx @ SV10 @ SV9 ) ) )
        = $false )
      | ( ( ! [SY18: a] :
              ( ~ ( cF @ SV10 @ SY18 )
              | ( cF @ SV9 @ SY18 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[75]) ).

thf(80,plain,
    ! [SV9: a > $o,SV10: a > $o] :
      ( ( ( ~ ~ ( SV10 @ ( sK5_Xx @ SV10 @ SV9 ) ) )
        = $false )
      | ( ( ! [SY18: a] :
              ( ~ ( cF @ SV10 @ SY18 )
              | ( cF @ SV9 @ SY18 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[75]) ).

thf(81,plain,
    ! [SV13: a,SV11: a > $o] :
      ( ( ~ ( SV11 @ SV13 )
        | ( cF @ ( cG @ SV11 ) @ SV13 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[77]) ).

thf(82,plain,
    ! [SV14: a,SV12: a > $o] :
      ( ( ~ ( SV12 @ SV14 )
        | ( cG @ ( cF @ SV12 ) @ SV14 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[78]) ).

thf(83,plain,
    ! [SV10: a > $o,SV9: a > $o] :
      ( ( ( SV9 @ ( sK5_Xx @ SV10 @ SV9 ) )
        = $true )
      | ( ( ! [SY18: a] :
              ( ~ ( cF @ SV10 @ SY18 )
              | ( cF @ SV9 @ SY18 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[79]) ).

thf(84,plain,
    ! [SV9: a > $o,SV10: a > $o] :
      ( ( ( ~ ( SV10 @ ( sK5_Xx @ SV10 @ SV9 ) ) )
        = $true )
      | ( ( ! [SY18: a] :
              ( ~ ( cF @ SV10 @ SY18 )
              | ( cF @ SV9 @ SY18 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[80]) ).

thf(85,plain,
    ! [SV13: a,SV11: a > $o] :
      ( ( ( ~ ( SV11 @ SV13 ) )
        = $true )
      | ( ( cF @ ( cG @ SV11 ) @ SV13 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[81]) ).

thf(86,plain,
    ! [SV14: a,SV12: a > $o] :
      ( ( ( ~ ( SV12 @ SV14 ) )
        = $true )
      | ( ( cG @ ( cF @ SV12 ) @ SV14 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[82]) ).

thf(87,plain,
    ! [SV9: a > $o,SV15: a,SV10: a > $o] :
      ( ( ( ~ ( cF @ SV10 @ SV15 )
          | ( cF @ SV9 @ SV15 ) )
        = $true )
      | ( ( SV9 @ ( sK5_Xx @ SV10 @ SV9 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[83]) ).

thf(88,plain,
    ! [SV9: a > $o,SV10: a > $o] :
      ( ( ( SV10 @ ( sK5_Xx @ SV10 @ SV9 ) )
        = $false )
      | ( ( ! [SY18: a] :
              ( ~ ( cF @ SV10 @ SY18 )
              | ( cF @ SV9 @ SY18 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[84]) ).

thf(89,plain,
    ! [SV13: a,SV11: a > $o] :
      ( ( ( SV11 @ SV13 )
        = $false )
      | ( ( cF @ ( cG @ SV11 ) @ SV13 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[85]) ).

thf(90,plain,
    ! [SV14: a,SV12: a > $o] :
      ( ( ( SV12 @ SV14 )
        = $false )
      | ( ( cG @ ( cF @ SV12 ) @ SV14 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[86]) ).

thf(91,plain,
    ! [SV9: a > $o,SV15: a,SV10: a > $o] :
      ( ( ( ~ ( cF @ SV10 @ SV15 ) )
        = $true )
      | ( ( cF @ SV9 @ SV15 )
        = $true )
      | ( ( SV9 @ ( sK5_Xx @ SV10 @ SV9 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[87]) ).

thf(92,plain,
    ! [SV9: a > $o,SV16: a,SV10: a > $o] :
      ( ( ( ~ ( cF @ SV10 @ SV16 )
          | ( cF @ SV9 @ SV16 ) )
        = $true )
      | ( ( SV10 @ ( sK5_Xx @ SV10 @ SV9 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[88]) ).

thf(93,plain,
    ! [SV9: a > $o,SV15: a,SV10: a > $o] :
      ( ( ( cF @ SV10 @ SV15 )
        = $false )
      | ( ( cF @ SV9 @ SV15 )
        = $true )
      | ( ( SV9 @ ( sK5_Xx @ SV10 @ SV9 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[91]) ).

thf(94,plain,
    ! [SV9: a > $o,SV16: a,SV10: a > $o] :
      ( ( ( ~ ( cF @ SV10 @ SV16 ) )
        = $true )
      | ( ( cF @ SV9 @ SV16 )
        = $true )
      | ( ( SV10 @ ( sK5_Xx @ SV10 @ SV9 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[92]) ).

thf(95,plain,
    ! [SV9: a > $o,SV16: a,SV10: a > $o] :
      ( ( ( cF @ SV10 @ SV16 )
        = $false )
      | ( ( cF @ SV9 @ SV16 )
        = $true )
      | ( ( SV10 @ ( sK5_Xx @ SV10 @ SV9 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[94]) ).

thf(96,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[71,95,93,90,89,76]) ).

thf(97,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[96,55]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SEV398^5 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33  % Computer : n010.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 : Tue Jun 28 17:17:19 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.13/0.34  
% 0.13/0.34   No.of.Axioms: 0
% 0.13/0.34  
% 0.13/0.34   Length.of.Defs: 0
% 0.13/0.34  
% 0.13/0.34   Contains.Choice.Funs: false
% 0.13/0.34  (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)....
% 0.18/0.41  
% 0.18/0.41  ********************************
% 0.18/0.41  *   All subproblems solved!    *
% 0.18/0.41  ********************************
% 0.18/0.41  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,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:96,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.18/0.42  
% 0.18/0.42  %**** Beginning of derivation protocol ****
% 0.18/0.42  % SZS output start CNFRefutation
% See solution above
% 0.18/0.42  
% 0.18/0.42  %**** End of derivation protocol ****
% 0.18/0.42  %**** no. of clauses in derivation: 97 ****
% 0.18/0.42  %**** clause counter: 96 ****
% 0.18/0.42  
% 0.18/0.42  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,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:96,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------