TSTP Solution File: SEV070^5 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SEV070^5 : TPTP v6.4.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n123.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32218.75MB
% OS       : Linux 3.10.0-327.36.3.el7.x86_64
% CPULimit : 300s
% DateTime : Wed Jan 18 14:55:00 EST 2017

% Result   : Theorem 0.02s
% Output   : CNFRefutation 0.02s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   64 (  34 unt;   7 typ;   0 def)
%            Number of atoms       :  232 (  95 equ;   0 cnn)
%            Maximal formula atoms :    3 (   3 avg)
%            Number of connectives :  610 ( 115   ~;  85   |;  36   &; 324   @)
%                                         (   0 <=>;  50  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   56 (  56   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :   96 (   0   ^  96   !;   0   ?;  96   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_cS,type,
    cS: $i > $i ).

thf(tp_sK1_Xx,type,
    sK1_Xx: $i ).

thf(tp_sK2_SY9,type,
    sK2_SY9: $i ).

thf(tp_sK3_SY17,type,
    sK3_SY17: $i ).

thf(tp_sK4_SY28,type,
    sK4_SY28: $i > $o ).

thf(tp_sK5_Xn,type,
    sK5_Xn: ( $i > $o ) > $i ).

thf(tp_sK6_Xn,type,
    sK6_Xn: ( $i > $o ) > $i ).

thf(1,conjecture,
    ! [Xx: $i,Xy: $i,Xz: $i] :
      ( ( ! [Xp: $i > $o] :
            ( ( ( Xp @ Xx )
              & ! [Xn: $i] :
                  ( ( Xp @ Xn )
                 => ( Xp @ ( cS @ Xn ) ) ) )
           => ( Xp @ Xy ) )
        & ! [Xp: $i > $o] :
            ( ( ( Xp @ Xy )
              & ! [Xn: $i] :
                  ( ( Xp @ Xn )
                 => ( Xp @ ( cS @ Xn ) ) ) )
           => ( Xp @ Xz ) ) )
     => ! [Xp: $i > $o] :
          ( ( ( Xp @ Xx )
            & ! [Xn: $i] :
                ( ( Xp @ Xn )
               => ( Xp @ ( cS @ Xn ) ) ) )
         => ( Xp @ Xz ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM577_pme) ).

thf(2,negated_conjecture,
    ( ( ! [Xx: $i,Xy: $i,Xz: $i] :
          ( ( ! [Xp: $i > $o] :
                ( ( ( Xp @ Xx )
                  & ! [Xn: $i] :
                      ( ( Xp @ Xn )
                     => ( Xp @ ( cS @ Xn ) ) ) )
               => ( Xp @ Xy ) )
            & ! [Xp: $i > $o] :
                ( ( ( Xp @ Xy )
                  & ! [Xn: $i] :
                      ( ( Xp @ Xn )
                     => ( Xp @ ( cS @ Xn ) ) ) )
               => ( Xp @ Xz ) ) )
         => ! [Xp: $i > $o] :
              ( ( ( Xp @ Xx )
                & ! [Xn: $i] :
                    ( ( Xp @ Xn )
                   => ( Xp @ ( cS @ Xn ) ) ) )
             => ( Xp @ Xz ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ! [Xx: $i,Xy: $i,Xz: $i] :
          ( ( ! [Xp: $i > $o] :
                ( ( ( Xp @ Xx )
                  & ! [Xn: $i] :
                      ( ( Xp @ Xn )
                     => ( Xp @ ( cS @ Xn ) ) ) )
               => ( Xp @ Xy ) )
            & ! [Xp: $i > $o] :
                ( ( ( Xp @ Xy )
                  & ! [Xn: $i] :
                      ( ( Xp @ Xn )
                     => ( Xp @ ( cS @ Xn ) ) ) )
               => ( Xp @ Xz ) ) )
         => ! [Xp: $i > $o] :
              ( ( ( Xp @ Xx )
                & ! [Xn: $i] :
                    ( ( Xp @ Xn )
                   => ( Xp @ ( cS @ Xn ) ) ) )
             => ( Xp @ Xz ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ! [SY9: $i,SY10: $i] :
          ( ( ! [SY11: $i > $o] :
                ( ( ( SY11 @ sK1_Xx )
                  & ! [Xn: $i] :
                      ( ( SY11 @ Xn )
                     => ( SY11 @ ( cS @ Xn ) ) ) )
               => ( SY11 @ SY9 ) )
            & ! [Xp: $i > $o] :
                ( ( ( Xp @ SY9 )
                  & ! [Xn: $i] :
                      ( ( Xp @ Xn )
                     => ( Xp @ ( cS @ Xn ) ) ) )
               => ( Xp @ SY10 ) ) )
         => ! [SY15: $i > $o] :
              ( ( ( SY15 @ sK1_Xx )
                & ! [Xn: $i] :
                    ( ( SY15 @ Xn )
                   => ( SY15 @ ( cS @ Xn ) ) ) )
             => ( SY15 @ SY10 ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[3]) ).

thf(5,plain,
    ( ( ! [SY17: $i] :
          ( ( ! [SY18: $i > $o] :
                ( ( ( SY18 @ sK1_Xx )
                  & ! [Xn: $i] :
                      ( ( SY18 @ Xn )
                     => ( SY18 @ ( cS @ Xn ) ) ) )
               => ( SY18 @ sK2_SY9 ) )
            & ! [SY20: $i > $o] :
                ( ( ( SY20 @ sK2_SY9 )
                  & ! [Xn: $i] :
                      ( ( SY20 @ Xn )
                     => ( SY20 @ ( cS @ Xn ) ) ) )
               => ( SY20 @ SY17 ) ) )
         => ! [SY15: $i > $o] :
              ( ( ( SY15 @ sK1_Xx )
                & ! [Xn: $i] :
                    ( ( SY15 @ Xn )
                   => ( SY15 @ ( cS @ Xn ) ) ) )
             => ( SY15 @ SY17 ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[4]) ).

thf(6,plain,
    ( ( ( ! [SY18: $i > $o] :
            ( ( ( SY18 @ sK1_Xx )
              & ! [Xn: $i] :
                  ( ( SY18 @ Xn )
                 => ( SY18 @ ( cS @ Xn ) ) ) )
           => ( SY18 @ sK2_SY9 ) )
        & ! [SY26: $i > $o] :
            ( ( ( SY26 @ sK2_SY9 )
              & ! [Xn: $i] :
                  ( ( SY26 @ Xn )
                 => ( SY26 @ ( cS @ Xn ) ) ) )
           => ( SY26 @ sK3_SY17 ) ) )
     => ! [SY28: $i > $o] :
          ( ( ( SY28 @ sK1_Xx )
            & ! [Xn: $i] :
                ( ( SY28 @ Xn )
               => ( SY28 @ ( cS @ Xn ) ) ) )
         => ( SY28 @ sK3_SY17 ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[5]) ).

thf(7,plain,
    ( ( ! [SY18: $i > $o] :
          ( ( ( SY18 @ sK1_Xx )
            & ! [Xn: $i] :
                ( ( SY18 @ Xn )
               => ( SY18 @ ( cS @ Xn ) ) ) )
         => ( SY18 @ sK2_SY9 ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[6]) ).

thf(8,plain,
    ( ( ! [SY26: $i > $o] :
          ( ( ( SY26 @ sK2_SY9 )
            & ! [Xn: $i] :
                ( ( SY26 @ Xn )
               => ( SY26 @ ( cS @ Xn ) ) ) )
         => ( SY26 @ sK3_SY17 ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[6]) ).

thf(9,plain,
    ( ( ! [SY28: $i > $o] :
          ( ( ( SY28 @ sK1_Xx )
            & ! [Xn: $i] :
                ( ( SY28 @ Xn )
               => ( SY28 @ ( cS @ Xn ) ) ) )
         => ( SY28 @ sK3_SY17 ) ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[6]) ).

thf(10,plain,
    ( ( ~ ! [SY28: $i > $o] :
            ( ( ( SY28 @ sK1_Xx )
              & ! [Xn: $i] :
                  ( ( SY28 @ Xn )
                 => ( SY28 @ ( cS @ Xn ) ) ) )
           => ( SY28 @ sK3_SY17 ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[9]) ).

thf(11,plain,
    ( ( ! [SY30: $i] :
          ( ~ ( sK4_SY28 @ SY30 )
          | ( sK4_SY28 @ ( cS @ SY30 ) ) )
      & ( sK4_SY28 @ sK1_Xx )
      & ~ ( sK4_SY28 @ sK3_SY17 ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[10]) ).

thf(12,plain,
    ( ( ! [SY18: $i > $o] :
          ( ( ( SY18 @ ( sK5_Xn @ SY18 ) )
            & ~ ( SY18 @ ( cS @ ( sK5_Xn @ SY18 ) ) ) )
          | ~ ( SY18 @ sK1_Xx )
          | ( SY18 @ sK2_SY9 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[7]) ).

thf(13,plain,
    ( ( ! [SY26: $i > $o] :
          ( ( ( SY26 @ ( sK6_Xn @ SY26 ) )
            & ~ ( SY26 @ ( cS @ ( sK6_Xn @ SY26 ) ) ) )
          | ~ ( SY26 @ sK2_SY9 )
          | ( SY26 @ sK3_SY17 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[8]) ).

thf(14,plain,
    ( ( ! [SY26: $i > $o] :
          ( ( ( SY26 @ ( sK6_Xn @ SY26 ) )
            & ~ ( SY26 @ ( cS @ ( sK6_Xn @ SY26 ) ) ) )
          | ~ ( SY26 @ sK2_SY9 )
          | ( SY26 @ sK3_SY17 ) ) )
    = $true ),
    inference(copy,[status(thm)],[13]) ).

thf(15,plain,
    ( ( ! [SY18: $i > $o] :
          ( ( ( SY18 @ ( sK5_Xn @ SY18 ) )
            & ~ ( SY18 @ ( cS @ ( sK5_Xn @ SY18 ) ) ) )
          | ~ ( SY18 @ sK1_Xx )
          | ( SY18 @ sK2_SY9 ) ) )
    = $true ),
    inference(copy,[status(thm)],[12]) ).

thf(16,plain,
    ( ( ! [SY30: $i] :
          ( ~ ( sK4_SY28 @ SY30 )
          | ( sK4_SY28 @ ( cS @ SY30 ) ) )
      & ( sK4_SY28 @ sK1_Xx )
      & ~ ( sK4_SY28 @ sK3_SY17 ) )
    = $true ),
    inference(copy,[status(thm)],[11]) ).

thf(17,plain,
    ( ( ! [SX0: $i > $o] :
          ( ~ ( ~ ( SX0 @ ( sK6_Xn @ SX0 ) )
              | ~ ~ ( SX0 @ ( cS @ ( sK6_Xn @ SX0 ) ) ) )
          | ~ ( SX0 @ sK2_SY9 )
          | ( SX0 @ sK3_SY17 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[14]) ).

thf(18,plain,
    ( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( sK4_SY28 @ SX0 )
                      | ( sK4_SY28 @ ( cS @ SX0 ) ) )
                | ~ ( sK4_SY28 @ sK1_Xx ) )
          | ~ ~ ( sK4_SY28 @ sK3_SY17 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[16]) ).

thf(19,plain,
    ( ( ! [SX0: $i > $o] :
          ( ~ ( ~ ( SX0 @ ( sK5_Xn @ SX0 ) )
              | ~ ~ ( SX0 @ ( cS @ ( sK5_Xn @ SX0 ) ) ) )
          | ~ ( SX0 @ sK1_Xx )
          | ( SX0 @ sK2_SY9 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[15]) ).

thf(20,plain,
    ! [SV1: $i > $o] :
      ( ( ~ ( ~ ( SV1 @ ( sK6_Xn @ SV1 ) )
            | ~ ~ ( SV1 @ ( cS @ ( sK6_Xn @ SV1 ) ) ) )
        | ~ ( SV1 @ sK2_SY9 )
        | ( SV1 @ sK3_SY17 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[17]) ).

thf(21,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( sK4_SY28 @ SX0 )
                  | ( sK4_SY28 @ ( cS @ SX0 ) ) )
            | ~ ( sK4_SY28 @ sK1_Xx ) )
      | ~ ~ ( sK4_SY28 @ sK3_SY17 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[18]) ).

thf(22,plain,
    ! [SV2: $i > $o] :
      ( ( ~ ( ~ ( SV2 @ ( sK5_Xn @ SV2 ) )
            | ~ ~ ( SV2 @ ( cS @ ( sK5_Xn @ SV2 ) ) ) )
        | ~ ( SV2 @ sK1_Xx )
        | ( SV2 @ sK2_SY9 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[19]) ).

thf(23,plain,
    ! [SV1: $i > $o] :
      ( ( ( ~ ( ~ ( SV1 @ ( sK6_Xn @ SV1 ) )
              | ~ ~ ( SV1 @ ( cS @ ( sK6_Xn @ SV1 ) ) ) )
          | ~ ( SV1 @ sK2_SY9 ) )
        = $true )
      | ( ( SV1 @ sK3_SY17 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[20]) ).

thf(24,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( sK4_SY28 @ SX0 )
                  | ( sK4_SY28 @ ( cS @ SX0 ) ) )
            | ~ ( sK4_SY28 @ sK1_Xx ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[21]) ).

thf(25,plain,
    ( ( ~ ~ ( sK4_SY28 @ sK3_SY17 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[21]) ).

thf(26,plain,
    ! [SV2: $i > $o] :
      ( ( ( ~ ( ~ ( SV2 @ ( sK5_Xn @ SV2 ) )
              | ~ ~ ( SV2 @ ( cS @ ( sK5_Xn @ SV2 ) ) ) )
          | ~ ( SV2 @ sK1_Xx ) )
        = $true )
      | ( ( SV2 @ sK2_SY9 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[22]) ).

thf(27,plain,
    ! [SV1: $i > $o] :
      ( ( ( ~ ( ~ ( SV1 @ ( sK6_Xn @ SV1 ) )
              | ~ ~ ( SV1 @ ( cS @ ( sK6_Xn @ SV1 ) ) ) ) )
        = $true )
      | ( ( ~ ( SV1 @ sK2_SY9 ) )
        = $true )
      | ( ( SV1 @ sK3_SY17 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[23]) ).

thf(28,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( sK4_SY28 @ SX0 )
                | ( sK4_SY28 @ ( cS @ SX0 ) ) )
          | ~ ( sK4_SY28 @ sK1_Xx ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[24]) ).

thf(29,plain,
    ( ( ~ ( sK4_SY28 @ sK3_SY17 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[25]) ).

thf(30,plain,
    ! [SV2: $i > $o] :
      ( ( ( ~ ( ~ ( SV2 @ ( sK5_Xn @ SV2 ) )
              | ~ ~ ( SV2 @ ( cS @ ( sK5_Xn @ SV2 ) ) ) ) )
        = $true )
      | ( ( ~ ( SV2 @ sK1_Xx ) )
        = $true )
      | ( ( SV2 @ sK2_SY9 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[26]) ).

thf(31,plain,
    ! [SV1: $i > $o] :
      ( ( ( ~ ( SV1 @ ( sK6_Xn @ SV1 ) )
          | ~ ~ ( SV1 @ ( cS @ ( sK6_Xn @ SV1 ) ) ) )
        = $false )
      | ( ( ~ ( SV1 @ sK2_SY9 ) )
        = $true )
      | ( ( SV1 @ sK3_SY17 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[27]) ).

thf(32,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( sK4_SY28 @ SX0 )
            | ( sK4_SY28 @ ( cS @ SX0 ) ) )
      | ~ ( sK4_SY28 @ sK1_Xx ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[28]) ).

thf(33,plain,
    ( ( sK4_SY28 @ sK3_SY17 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[29]) ).

thf(34,plain,
    ! [SV2: $i > $o] :
      ( ( ( ~ ( SV2 @ ( sK5_Xn @ SV2 ) )
          | ~ ~ ( SV2 @ ( cS @ ( sK5_Xn @ SV2 ) ) ) )
        = $false )
      | ( ( ~ ( SV2 @ sK1_Xx ) )
        = $true )
      | ( ( SV2 @ sK2_SY9 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[30]) ).

thf(35,plain,
    ! [SV1: $i > $o] :
      ( ( ( ~ ( SV1 @ ( sK6_Xn @ SV1 ) ) )
        = $false )
      | ( ( ~ ( SV1 @ sK2_SY9 ) )
        = $true )
      | ( ( SV1 @ sK3_SY17 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[31]) ).

thf(36,plain,
    ! [SV1: $i > $o] :
      ( ( ( ~ ~ ( SV1 @ ( cS @ ( sK6_Xn @ SV1 ) ) ) )
        = $false )
      | ( ( ~ ( SV1 @ sK2_SY9 ) )
        = $true )
      | ( ( SV1 @ sK3_SY17 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[31]) ).

thf(37,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( sK4_SY28 @ SX0 )
            | ( sK4_SY28 @ ( cS @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[32]) ).

thf(38,plain,
    ( ( ~ ( sK4_SY28 @ sK1_Xx ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[32]) ).

thf(39,plain,
    ! [SV2: $i > $o] :
      ( ( ( ~ ( SV2 @ ( sK5_Xn @ SV2 ) ) )
        = $false )
      | ( ( ~ ( SV2 @ sK1_Xx ) )
        = $true )
      | ( ( SV2 @ sK2_SY9 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[34]) ).

thf(40,plain,
    ! [SV2: $i > $o] :
      ( ( ( ~ ~ ( SV2 @ ( cS @ ( sK5_Xn @ SV2 ) ) ) )
        = $false )
      | ( ( ~ ( SV2 @ sK1_Xx ) )
        = $true )
      | ( ( SV2 @ sK2_SY9 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[34]) ).

thf(41,plain,
    ! [SV1: $i > $o] :
      ( ( ( SV1 @ ( sK6_Xn @ SV1 ) )
        = $true )
      | ( ( ~ ( SV1 @ sK2_SY9 ) )
        = $true )
      | ( ( SV1 @ sK3_SY17 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[35]) ).

thf(42,plain,
    ! [SV1: $i > $o] :
      ( ( ( ~ ( SV1 @ ( cS @ ( sK6_Xn @ SV1 ) ) ) )
        = $true )
      | ( ( ~ ( SV1 @ sK2_SY9 ) )
        = $true )
      | ( ( SV1 @ sK3_SY17 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[36]) ).

thf(43,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( sK4_SY28 @ SX0 )
          | ( sK4_SY28 @ ( cS @ SX0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[37]) ).

thf(44,plain,
    ( ( sK4_SY28 @ sK1_Xx )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[38]) ).

thf(45,plain,
    ! [SV2: $i > $o] :
      ( ( ( SV2 @ ( sK5_Xn @ SV2 ) )
        = $true )
      | ( ( ~ ( SV2 @ sK1_Xx ) )
        = $true )
      | ( ( SV2 @ sK2_SY9 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[39]) ).

thf(46,plain,
    ! [SV2: $i > $o] :
      ( ( ( ~ ( SV2 @ ( cS @ ( sK5_Xn @ SV2 ) ) ) )
        = $true )
      | ( ( ~ ( SV2 @ sK1_Xx ) )
        = $true )
      | ( ( SV2 @ sK2_SY9 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[40]) ).

thf(47,plain,
    ! [SV1: $i > $o] :
      ( ( ( SV1 @ sK2_SY9 )
        = $false )
      | ( ( SV1 @ ( sK6_Xn @ SV1 ) )
        = $true )
      | ( ( SV1 @ sK3_SY17 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[41]) ).

thf(48,plain,
    ! [SV1: $i > $o] :
      ( ( ( SV1 @ ( cS @ ( sK6_Xn @ SV1 ) ) )
        = $false )
      | ( ( ~ ( SV1 @ sK2_SY9 ) )
        = $true )
      | ( ( SV1 @ sK3_SY17 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[42]) ).

thf(49,plain,
    ! [SV3: $i] :
      ( ( ~ ( sK4_SY28 @ SV3 )
        | ( sK4_SY28 @ ( cS @ SV3 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[43]) ).

thf(50,plain,
    ! [SV2: $i > $o] :
      ( ( ( SV2 @ sK1_Xx )
        = $false )
      | ( ( SV2 @ ( sK5_Xn @ SV2 ) )
        = $true )
      | ( ( SV2 @ sK2_SY9 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[45]) ).

thf(51,plain,
    ! [SV2: $i > $o] :
      ( ( ( SV2 @ ( cS @ ( sK5_Xn @ SV2 ) ) )
        = $false )
      | ( ( ~ ( SV2 @ sK1_Xx ) )
        = $true )
      | ( ( SV2 @ sK2_SY9 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[46]) ).

thf(52,plain,
    ! [SV1: $i > $o] :
      ( ( ( SV1 @ sK2_SY9 )
        = $false )
      | ( ( SV1 @ ( cS @ ( sK6_Xn @ SV1 ) ) )
        = $false )
      | ( ( SV1 @ sK3_SY17 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[48]) ).

thf(53,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( sK4_SY28 @ SV3 ) )
        = $true )
      | ( ( sK4_SY28 @ ( cS @ SV3 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[49]) ).

thf(54,plain,
    ! [SV2: $i > $o] :
      ( ( ( SV2 @ sK1_Xx )
        = $false )
      | ( ( SV2 @ ( cS @ ( sK5_Xn @ SV2 ) ) )
        = $false )
      | ( ( SV2 @ sK2_SY9 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[51]) ).

thf(55,plain,
    ! [SV3: $i] :
      ( ( ( sK4_SY28 @ SV3 )
        = $false )
      | ( ( sK4_SY28 @ ( cS @ SV3 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[53]) ).

thf(56,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[33,55,54,52,50,47,44]) ).

thf(57,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[56]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SEV070^5 : TPTP v6.4.0. Released v4.0.0.
% 0.00/0.04  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.02/0.22  % Computer : n123.star.cs.uiowa.edu
% 0.02/0.22  % Model    : x86_64 x86_64
% 0.02/0.22  % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.02/0.22  % Memory   : 32218.75MB
% 0.02/0.22  % OS       : Linux 3.10.0-327.36.3.el7.x86_64
% 0.02/0.22  % CPULimit : 300
% 0.02/0.22  % DateTime : Sun Jan 15 23:53:02 CST 2017
% 0.02/0.23  % CPUTime  : 
% 0.02/0.23  
% 0.02/0.23   No.of.Axioms: 0
% 0.02/0.23  
% 0.02/0.23   Length.of.Defs: 0
% 0.02/0.23  
% 0.02/0.23   Contains.Choice.Funs: false
% 0.02/0.23  (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)..
% 0.02/0.26  
% 0.02/0.26  ********************************
% 0.02/0.26  *   All subproblems solved!    *
% 0.02/0.26  ********************************
% 0.02/0.26  % SZS status Theorem for /export/starexec/sandbox2/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:56,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.02/0.26  
% 0.02/0.26  %**** Beginning of derivation protocol ****
% 0.02/0.26  % SZS output start CNFRefutation
% See solution above
% 0.02/0.26  % SZS output end CNFRefutation
% 0.02/0.26  
% 0.02/0.26  %**** End of derivation protocol ****
% 0.02/0.26  %**** no. of clauses in derivation: 57 ****
% 0.02/0.26  %**** clause counter: 56 ****
% 0.02/0.26  
% 0.02/0.26  % SZS status Theorem for /export/starexec/sandbox2/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:56,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------