TSTP Solution File: SEV136^5 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SEV136^5 : 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 : n028.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 17:35:15 EDT 2022

% Result   : Theorem 0.18s 0.41s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   24
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   64 (  32 unt;   7 typ;   0 def)
%            Number of atoms       :  323 (  88 equ;   0 cnn)
%            Maximal formula atoms :    3 (   5 avg)
%            Number of connectives :  764 ( 120   ~;  93   |;  29   &; 477   @)
%                                         (   0 <=>;  45  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   3 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   69 (  69   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   6 usr;   4 con; 0-3 aty)
%            Number of variables   :  144 (   0   ^ 144   !;   0   ?; 144   :)

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

thf(tp_sK1_Xr,type,
    sK1_Xr: a > a > $o ).

thf(tp_sK2_SY13,type,
    sK2_SY13: ( a > a > $o ) > a > a > $o ).

thf(tp_sK3_SY31,type,
    sK3_SY31: a ).

thf(tp_sK4_SY36,type,
    sK4_SY36: a ).

thf(tp_sK5_SY23,type,
    sK5_SY23: ( a > $o ) > a ).

thf(tp_sK6_SY43,type,
    sK6_SY43: ( a > $o ) > a ).

thf(1,conjecture,
    ! [Xr: a > a > $o,T: ( a > a > $o ) > a > a > $o] :
      ( ( ! [Xx: a] : ( T @ Xr @ Xx @ Xx )
        & ! [Xx: a,Xy: a,Xz: a] :
            ( ( ( T @ Xr @ Xx @ Xy )
              & ( T @ Xr @ Xy @ Xz ) )
           => ( T @ Xr @ Xx @ Xz ) )
        & ! [Xx: a,Xy: a] :
            ( ( Xr @ Xx @ Xy )
           => ( T @ Xr @ Xx @ Xy ) ) )
     => ! [Xx: a,Xy: a] :
          ( ! [Xx0: a > $o] :
              ( ! [Xy0: a,Xz: a] :
                  ( ( ( Xr @ Xy0 @ Xz )
                    & ( Xx0 @ Xy0 ) )
                 => ( Xx0 @ Xz ) )
             => ( ( Xx0 @ Xx )
               => ( Xx0 @ Xy ) ) )
         => ( T @ Xr @ Xx @ Xy ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM203_pme) ).

thf(2,negated_conjecture,
    ( ( ! [Xr: a > a > $o,T: ( a > a > $o ) > a > a > $o] :
          ( ( ! [Xx: a] : ( T @ Xr @ Xx @ Xx )
            & ! [Xx: a,Xy: a,Xz: a] :
                ( ( ( T @ Xr @ Xx @ Xy )
                  & ( T @ Xr @ Xy @ Xz ) )
               => ( T @ Xr @ Xx @ Xz ) )
            & ! [Xx: a,Xy: a] :
                ( ( Xr @ Xx @ Xy )
               => ( T @ Xr @ Xx @ Xy ) ) )
         => ! [Xx: a,Xy: a] :
              ( ! [Xx0: a > $o] :
                  ( ! [Xy0: a,Xz: a] :
                      ( ( ( Xr @ Xy0 @ Xz )
                        & ( Xx0 @ Xy0 ) )
                     => ( Xx0 @ Xz ) )
                 => ( ( Xx0 @ Xx )
                   => ( Xx0 @ Xy ) ) )
             => ( T @ Xr @ Xx @ Xy ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ! [Xr: a > a > $o,T: ( a > a > $o ) > a > a > $o] :
          ( ( ! [Xx: a] : ( T @ Xr @ Xx @ Xx )
            & ! [Xx: a,Xy: a,Xz: a] :
                ( ( ( T @ Xr @ Xx @ Xy )
                  & ( T @ Xr @ Xy @ Xz ) )
               => ( T @ Xr @ Xx @ Xz ) )
            & ! [Xx: a,Xy: a] :
                ( ( Xr @ Xx @ Xy )
               => ( T @ Xr @ Xx @ Xy ) ) )
         => ! [Xx: a,Xy: a] :
              ( ! [Xx0: a > $o] :
                  ( ! [Xy0: a,Xz: a] :
                      ( ( ( Xr @ Xy0 @ Xz )
                        & ( Xx0 @ Xy0 ) )
                     => ( Xx0 @ Xz ) )
                 => ( ( Xx0 @ Xx )
                   => ( Xx0 @ Xy ) ) )
             => ( T @ Xr @ Xx @ Xy ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ! [SY13: ( a > a > $o ) > a > a > $o] :
          ( ( ! [SY14: a] : ( SY13 @ sK1_Xr @ SY14 @ SY14 )
            & ! [SY15: a,SY16: a,SY17: a] :
                ( ( ( SY13 @ sK1_Xr @ SY15 @ SY16 )
                  & ( SY13 @ sK1_Xr @ SY16 @ SY17 ) )
               => ( SY13 @ sK1_Xr @ SY15 @ SY17 ) )
            & ! [SY18: a,SY19: a] :
                ( ( sK1_Xr @ SY18 @ SY19 )
               => ( SY13 @ sK1_Xr @ SY18 @ SY19 ) ) )
         => ! [SY20: a,SY21: a] :
              ( ! [SY22: a > $o] :
                  ( ! [SY23: a,SY24: a] :
                      ( ( ( sK1_Xr @ SY23 @ SY24 )
                        & ( SY22 @ SY23 ) )
                     => ( SY22 @ SY24 ) )
                 => ( ( SY22 @ SY20 )
                   => ( SY22 @ SY21 ) ) )
             => ( SY13 @ sK1_Xr @ SY20 @ SY21 ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[3]) ).

thf(5,plain,
    ( ( ( ! [SY25: a] : ( sK2_SY13 @ sK1_Xr @ SY25 @ SY25 )
        & ! [SY26: a,SY27: a,SY28: a] :
            ( ( ( sK2_SY13 @ sK1_Xr @ SY26 @ SY27 )
              & ( sK2_SY13 @ sK1_Xr @ SY27 @ SY28 ) )
           => ( sK2_SY13 @ sK1_Xr @ SY26 @ SY28 ) )
        & ! [SY29: a,SY30: a] :
            ( ( sK1_Xr @ SY29 @ SY30 )
           => ( sK2_SY13 @ sK1_Xr @ SY29 @ SY30 ) ) )
     => ! [SY31: a,SY32: a] :
          ( ! [SY22: a > $o] :
              ( ! [SY23: a,SY24: a] :
                  ( ( ( sK1_Xr @ SY23 @ SY24 )
                    & ( SY22 @ SY23 ) )
                 => ( SY22 @ SY24 ) )
             => ( ( SY22 @ SY31 )
               => ( SY22 @ SY32 ) ) )
         => ( sK2_SY13 @ sK1_Xr @ SY31 @ SY32 ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[4]) ).

thf(6,plain,
    ( ( ! [SY25: a] : ( sK2_SY13 @ sK1_Xr @ SY25 @ SY25 ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[5]) ).

thf(7,plain,
    ( ( ! [SY26: a,SY27: a,SY28: a] :
          ( ( ( sK2_SY13 @ sK1_Xr @ SY26 @ SY27 )
            & ( sK2_SY13 @ sK1_Xr @ SY27 @ SY28 ) )
         => ( sK2_SY13 @ sK1_Xr @ SY26 @ SY28 ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[5]) ).

thf(8,plain,
    ( ( ! [SY29: a,SY30: a] :
          ( ( sK1_Xr @ SY29 @ SY30 )
         => ( sK2_SY13 @ sK1_Xr @ SY29 @ SY30 ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[5]) ).

thf(9,plain,
    ( ( ! [SY31: a,SY32: a] :
          ( ! [SY22: a > $o] :
              ( ! [SY23: a,SY24: a] :
                  ( ( ( sK1_Xr @ SY23 @ SY24 )
                    & ( SY22 @ SY23 ) )
                 => ( SY22 @ SY24 ) )
             => ( ( SY22 @ SY31 )
               => ( SY22 @ SY32 ) ) )
         => ( sK2_SY13 @ sK1_Xr @ SY31 @ SY32 ) ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[5]) ).

thf(10,plain,
    ( ( ~ ! [SY31: a,SY32: a] :
            ( ! [SY22: a > $o] :
                ( ! [SY23: a,SY24: a] :
                    ( ( ( sK1_Xr @ SY23 @ SY24 )
                      & ( SY22 @ SY23 ) )
                   => ( SY22 @ SY24 ) )
               => ( ( SY22 @ SY31 )
                 => ( SY22 @ SY32 ) ) )
           => ( sK2_SY13 @ sK1_Xr @ SY31 @ SY32 ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[9]) ).

thf(11,plain,
    ( ( ! [SY40: a > $o] :
          ( ( ( SY40 @ ( sK5_SY23 @ SY40 ) )
            & ( sK1_Xr @ ( sK5_SY23 @ SY40 ) @ ( sK6_SY43 @ SY40 ) )
            & ~ ( SY40 @ ( sK6_SY43 @ SY40 ) ) )
          | ~ ( SY40 @ sK3_SY31 )
          | ( SY40 @ sK4_SY36 ) )
      & ~ ( sK2_SY13 @ sK1_Xr @ sK3_SY31 @ sK4_SY36 ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[10]) ).

thf(12,plain,
    ( ( ! [SY26: a,SY27: a,SY28: a] :
          ( ~ ( sK2_SY13 @ sK1_Xr @ SY26 @ SY27 )
          | ~ ( sK2_SY13 @ sK1_Xr @ SY27 @ SY28 )
          | ( sK2_SY13 @ sK1_Xr @ SY26 @ SY28 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[7]) ).

thf(13,plain,
    ( ( ! [SY29: a,SY30: a] :
          ( ~ ( sK1_Xr @ SY29 @ SY30 )
          | ( sK2_SY13 @ sK1_Xr @ SY29 @ SY30 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[8]) ).

thf(14,plain,
    ( ( ! [SY29: a,SY30: a] :
          ( ~ ( sK1_Xr @ SY29 @ SY30 )
          | ( sK2_SY13 @ sK1_Xr @ SY29 @ SY30 ) ) )
    = $true ),
    inference(copy,[status(thm)],[13]) ).

thf(15,plain,
    ( ( ! [SY26: a,SY27: a,SY28: a] :
          ( ~ ( sK2_SY13 @ sK1_Xr @ SY26 @ SY27 )
          | ~ ( sK2_SY13 @ sK1_Xr @ SY27 @ SY28 )
          | ( sK2_SY13 @ sK1_Xr @ SY26 @ SY28 ) ) )
    = $true ),
    inference(copy,[status(thm)],[12]) ).

thf(16,plain,
    ( ( ! [SY25: a] : ( sK2_SY13 @ sK1_Xr @ SY25 @ SY25 ) )
    = $true ),
    inference(copy,[status(thm)],[6]) ).

thf(17,plain,
    ( ( ! [SY40: a > $o] :
          ( ( ( SY40 @ ( sK5_SY23 @ SY40 ) )
            & ( sK1_Xr @ ( sK5_SY23 @ SY40 ) @ ( sK6_SY43 @ SY40 ) )
            & ~ ( SY40 @ ( sK6_SY43 @ SY40 ) ) )
          | ~ ( SY40 @ sK3_SY31 )
          | ( SY40 @ sK4_SY36 ) )
      & ~ ( sK2_SY13 @ sK1_Xr @ sK3_SY31 @ sK4_SY36 ) )
    = $true ),
    inference(copy,[status(thm)],[11]) ).

thf(18,plain,
    ( ( ~ ( ~ ! [SX0: a > $o] :
                ( ~ ( ~ ~ ( ~ ( SX0 @ ( sK5_SY23 @ SX0 ) )
                          | ~ ( sK1_Xr @ ( sK5_SY23 @ SX0 ) @ ( sK6_SY43 @ SX0 ) ) )
                    | ~ ~ ( SX0 @ ( sK6_SY43 @ SX0 ) ) )
                | ~ ( SX0 @ sK3_SY31 )
                | ( SX0 @ sK4_SY36 ) )
          | ~ ~ ( sK2_SY13 @ sK1_Xr @ sK3_SY31 @ sK4_SY36 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[17]) ).

thf(19,plain,
    ! [SV1: a] :
      ( ( ! [SY44: a] :
            ( ~ ( sK1_Xr @ SV1 @ SY44 )
            | ( sK2_SY13 @ sK1_Xr @ SV1 @ SY44 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[14]) ).

thf(20,plain,
    ! [SV2: a] :
      ( ( ! [SY45: a,SY46: a] :
            ( ~ ( sK2_SY13 @ sK1_Xr @ SV2 @ SY45 )
            | ~ ( sK2_SY13 @ sK1_Xr @ SY45 @ SY46 )
            | ( sK2_SY13 @ sK1_Xr @ SV2 @ SY46 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[15]) ).

thf(21,plain,
    ! [SV3: a] :
      ( ( sK2_SY13 @ sK1_Xr @ SV3 @ SV3 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[16]) ).

thf(22,plain,
    ( ( ~ ! [SX0: a > $o] :
            ( ~ ( ~ ~ ( ~ ( SX0 @ ( sK5_SY23 @ SX0 ) )
                      | ~ ( sK1_Xr @ ( sK5_SY23 @ SX0 ) @ ( sK6_SY43 @ SX0 ) ) )
                | ~ ~ ( SX0 @ ( sK6_SY43 @ SX0 ) ) )
            | ~ ( SX0 @ sK3_SY31 )
            | ( SX0 @ sK4_SY36 ) )
      | ~ ~ ( sK2_SY13 @ sK1_Xr @ sK3_SY31 @ sK4_SY36 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[18]) ).

thf(23,plain,
    ! [SV4: a,SV1: a] :
      ( ( ~ ( sK1_Xr @ SV1 @ SV4 )
        | ( sK2_SY13 @ sK1_Xr @ SV1 @ SV4 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[19]) ).

thf(24,plain,
    ! [SV5: a,SV2: a] :
      ( ( ! [SY47: a] :
            ( ~ ( sK2_SY13 @ sK1_Xr @ SV2 @ SV5 )
            | ~ ( sK2_SY13 @ sK1_Xr @ SV5 @ SY47 )
            | ( sK2_SY13 @ sK1_Xr @ SV2 @ SY47 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[20]) ).

thf(25,plain,
    ( ( ~ ! [SX0: a > $o] :
            ( ~ ( ~ ~ ( ~ ( SX0 @ ( sK5_SY23 @ SX0 ) )
                      | ~ ( sK1_Xr @ ( sK5_SY23 @ SX0 ) @ ( sK6_SY43 @ SX0 ) ) )
                | ~ ~ ( SX0 @ ( sK6_SY43 @ SX0 ) ) )
            | ~ ( SX0 @ sK3_SY31 )
            | ( SX0 @ sK4_SY36 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[22]) ).

thf(26,plain,
    ( ( ~ ~ ( sK2_SY13 @ sK1_Xr @ sK3_SY31 @ sK4_SY36 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[22]) ).

thf(27,plain,
    ! [SV4: a,SV1: a] :
      ( ( ( ~ ( sK1_Xr @ SV1 @ SV4 ) )
        = $true )
      | ( ( sK2_SY13 @ sK1_Xr @ SV1 @ SV4 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[23]) ).

thf(28,plain,
    ! [SV6: a,SV5: a,SV2: a] :
      ( ( ~ ( sK2_SY13 @ sK1_Xr @ SV2 @ SV5 )
        | ~ ( sK2_SY13 @ sK1_Xr @ SV5 @ SV6 )
        | ( sK2_SY13 @ sK1_Xr @ SV2 @ SV6 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[24]) ).

thf(29,plain,
    ( ( ! [SX0: a > $o] :
          ( ~ ( ~ ~ ( ~ ( SX0 @ ( sK5_SY23 @ SX0 ) )
                    | ~ ( sK1_Xr @ ( sK5_SY23 @ SX0 ) @ ( sK6_SY43 @ SX0 ) ) )
              | ~ ~ ( SX0 @ ( sK6_SY43 @ SX0 ) ) )
          | ~ ( SX0 @ sK3_SY31 )
          | ( SX0 @ sK4_SY36 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[25]) ).

thf(30,plain,
    ( ( ~ ( sK2_SY13 @ sK1_Xr @ sK3_SY31 @ sK4_SY36 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[26]) ).

thf(31,plain,
    ! [SV4: a,SV1: a] :
      ( ( ( sK1_Xr @ SV1 @ SV4 )
        = $false )
      | ( ( sK2_SY13 @ sK1_Xr @ SV1 @ SV4 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[27]) ).

thf(32,plain,
    ! [SV6: a,SV5: a,SV2: a] :
      ( ( ( ~ ( sK2_SY13 @ sK1_Xr @ SV2 @ SV5 )
          | ~ ( sK2_SY13 @ sK1_Xr @ SV5 @ SV6 ) )
        = $true )
      | ( ( sK2_SY13 @ sK1_Xr @ SV2 @ SV6 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[28]) ).

thf(33,plain,
    ! [SV7: a > $o] :
      ( ( ~ ( ~ ~ ( ~ ( SV7 @ ( sK5_SY23 @ SV7 ) )
                  | ~ ( sK1_Xr @ ( sK5_SY23 @ SV7 ) @ ( sK6_SY43 @ SV7 ) ) )
            | ~ ~ ( SV7 @ ( sK6_SY43 @ SV7 ) ) )
        | ~ ( SV7 @ sK3_SY31 )
        | ( SV7 @ sK4_SY36 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[29]) ).

thf(34,plain,
    ( ( sK2_SY13 @ sK1_Xr @ sK3_SY31 @ sK4_SY36 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[30]) ).

thf(35,plain,
    ! [SV6: a,SV5: a,SV2: a] :
      ( ( ( ~ ( sK2_SY13 @ sK1_Xr @ SV2 @ SV5 ) )
        = $true )
      | ( ( ~ ( sK2_SY13 @ sK1_Xr @ SV5 @ SV6 ) )
        = $true )
      | ( ( sK2_SY13 @ sK1_Xr @ SV2 @ SV6 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[32]) ).

thf(36,plain,
    ! [SV7: a > $o] :
      ( ( ( ~ ( ~ ~ ( ~ ( SV7 @ ( sK5_SY23 @ SV7 ) )
                    | ~ ( sK1_Xr @ ( sK5_SY23 @ SV7 ) @ ( sK6_SY43 @ SV7 ) ) )
              | ~ ~ ( SV7 @ ( sK6_SY43 @ SV7 ) ) ) )
        = $true )
      | ( ( ~ ( SV7 @ sK3_SY31 )
          | ( SV7 @ sK4_SY36 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[33]) ).

thf(37,plain,
    ! [SV6: a,SV5: a,SV2: a] :
      ( ( ( sK2_SY13 @ sK1_Xr @ SV2 @ SV5 )
        = $false )
      | ( ( ~ ( sK2_SY13 @ sK1_Xr @ SV5 @ SV6 ) )
        = $true )
      | ( ( sK2_SY13 @ sK1_Xr @ SV2 @ SV6 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[35]) ).

thf(38,plain,
    ! [SV7: a > $o] :
      ( ( ( ~ ~ ( ~ ( SV7 @ ( sK5_SY23 @ SV7 ) )
                | ~ ( sK1_Xr @ ( sK5_SY23 @ SV7 ) @ ( sK6_SY43 @ SV7 ) ) )
          | ~ ~ ( SV7 @ ( sK6_SY43 @ SV7 ) ) )
        = $false )
      | ( ( ~ ( SV7 @ sK3_SY31 )
          | ( SV7 @ sK4_SY36 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[36]) ).

thf(39,plain,
    ! [SV2: a,SV6: a,SV5: a] :
      ( ( ( sK2_SY13 @ sK1_Xr @ SV5 @ SV6 )
        = $false )
      | ( ( sK2_SY13 @ sK1_Xr @ SV2 @ SV5 )
        = $false )
      | ( ( sK2_SY13 @ sK1_Xr @ SV2 @ SV6 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[37]) ).

thf(40,plain,
    ! [SV7: a > $o] :
      ( ( ( ~ ~ ( ~ ( SV7 @ ( sK5_SY23 @ SV7 ) )
                | ~ ( sK1_Xr @ ( sK5_SY23 @ SV7 ) @ ( sK6_SY43 @ SV7 ) ) ) )
        = $false )
      | ( ( ~ ( SV7 @ sK3_SY31 )
          | ( SV7 @ sK4_SY36 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[38]) ).

thf(41,plain,
    ! [SV7: a > $o] :
      ( ( ( ~ ~ ( SV7 @ ( sK6_SY43 @ SV7 ) ) )
        = $false )
      | ( ( ~ ( SV7 @ sK3_SY31 )
          | ( SV7 @ sK4_SY36 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[38]) ).

thf(42,plain,
    ! [SV7: a > $o] :
      ( ( ( ~ ( ~ ( SV7 @ ( sK5_SY23 @ SV7 ) )
              | ~ ( sK1_Xr @ ( sK5_SY23 @ SV7 ) @ ( sK6_SY43 @ SV7 ) ) ) )
        = $true )
      | ( ( ~ ( SV7 @ sK3_SY31 )
          | ( SV7 @ sK4_SY36 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[40]) ).

thf(43,plain,
    ! [SV7: a > $o] :
      ( ( ( ~ ( SV7 @ ( sK6_SY43 @ SV7 ) ) )
        = $true )
      | ( ( ~ ( SV7 @ sK3_SY31 )
          | ( SV7 @ sK4_SY36 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[41]) ).

thf(44,plain,
    ! [SV7: a > $o] :
      ( ( ( ~ ( SV7 @ ( sK5_SY23 @ SV7 ) )
          | ~ ( sK1_Xr @ ( sK5_SY23 @ SV7 ) @ ( sK6_SY43 @ SV7 ) ) )
        = $false )
      | ( ( ~ ( SV7 @ sK3_SY31 )
          | ( SV7 @ sK4_SY36 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[42]) ).

thf(45,plain,
    ! [SV7: a > $o] :
      ( ( ( SV7 @ ( sK6_SY43 @ SV7 ) )
        = $false )
      | ( ( ~ ( SV7 @ sK3_SY31 )
          | ( SV7 @ sK4_SY36 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[43]) ).

thf(46,plain,
    ! [SV7: a > $o] :
      ( ( ( ~ ( SV7 @ ( sK5_SY23 @ SV7 ) ) )
        = $false )
      | ( ( ~ ( SV7 @ sK3_SY31 )
          | ( SV7 @ sK4_SY36 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[44]) ).

thf(47,plain,
    ! [SV7: a > $o] :
      ( ( ( ~ ( sK1_Xr @ ( sK5_SY23 @ SV7 ) @ ( sK6_SY43 @ SV7 ) ) )
        = $false )
      | ( ( ~ ( SV7 @ sK3_SY31 )
          | ( SV7 @ sK4_SY36 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[44]) ).

thf(48,plain,
    ! [SV7: a > $o] :
      ( ( ( ~ ( SV7 @ sK3_SY31 ) )
        = $true )
      | ( ( SV7 @ sK4_SY36 )
        = $true )
      | ( ( SV7 @ ( sK6_SY43 @ SV7 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[45]) ).

thf(49,plain,
    ! [SV7: a > $o] :
      ( ( ( SV7 @ ( sK5_SY23 @ SV7 ) )
        = $true )
      | ( ( ~ ( SV7 @ sK3_SY31 )
          | ( SV7 @ sK4_SY36 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[46]) ).

thf(50,plain,
    ! [SV7: a > $o] :
      ( ( ( sK1_Xr @ ( sK5_SY23 @ SV7 ) @ ( sK6_SY43 @ SV7 ) )
        = $true )
      | ( ( ~ ( SV7 @ sK3_SY31 )
          | ( SV7 @ sK4_SY36 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[47]) ).

thf(51,plain,
    ! [SV7: a > $o] :
      ( ( ( SV7 @ sK3_SY31 )
        = $false )
      | ( ( SV7 @ sK4_SY36 )
        = $true )
      | ( ( SV7 @ ( sK6_SY43 @ SV7 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[48]) ).

thf(52,plain,
    ! [SV7: a > $o] :
      ( ( ( ~ ( SV7 @ sK3_SY31 ) )
        = $true )
      | ( ( SV7 @ sK4_SY36 )
        = $true )
      | ( ( SV7 @ ( sK5_SY23 @ SV7 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[49]) ).

thf(53,plain,
    ! [SV7: a > $o] :
      ( ( ( ~ ( SV7 @ sK3_SY31 ) )
        = $true )
      | ( ( SV7 @ sK4_SY36 )
        = $true )
      | ( ( sK1_Xr @ ( sK5_SY23 @ SV7 ) @ ( sK6_SY43 @ SV7 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[50]) ).

thf(54,plain,
    ! [SV7: a > $o] :
      ( ( ( SV7 @ sK3_SY31 )
        = $false )
      | ( ( SV7 @ sK4_SY36 )
        = $true )
      | ( ( SV7 @ ( sK5_SY23 @ SV7 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[52]) ).

thf(55,plain,
    ! [SV7: a > $o] :
      ( ( ( SV7 @ sK3_SY31 )
        = $false )
      | ( ( SV7 @ sK4_SY36 )
        = $true )
      | ( ( sK1_Xr @ ( sK5_SY23 @ SV7 ) @ ( sK6_SY43 @ SV7 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[53]) ).

thf(56,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[21,55,54,51,39,34,31]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem  : SEV136^5 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34  % Computer : n028.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 13:32:27 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)...
% 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:3,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)
% 0.18/0.41  
% 0.18/0.41  %**** Beginning of derivation protocol ****
% 0.18/0.41  % SZS output start CNFRefutation
% See solution above
% 0.18/0.41  
% 0.18/0.41  %**** End of derivation protocol ****
% 0.18/0.41  %**** no. of clauses in derivation: 57 ****
% 0.18/0.41  %**** clause counter: 56 ****
% 0.18/0.41  
% 0.18/0.41  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:3,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)
%------------------------------------------------------------------------------