TSTP Solution File: SYN065+1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SYN065+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n022.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 : Thu Jul 21 08:23:14 EDT 2022

% Result   : Theorem 0.22s 0.41s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   67 (  34 unt;   6 typ;   0 def)
%            Number of atoms       :  381 (  90 equ;   0 cnn)
%            Maximal formula atoms :    5 (   6 avg)
%            Number of connectives :  689 ( 145   ~; 130   |;   6   &; 404   @)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :  180 (   0   ^ 171   !;   9   ?; 180   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_big_f,type,
    big_f: $i > $i > $o ).

thf(tp_big_g,type,
    big_g: $i > $i > $o ).

thf(tp_big_h,type,
    big_h: $i > $i > $o ).

thf(tp_sK1_X,type,
    sK1_X: $i ).

thf(tp_sK2_Y,type,
    sK2_Y: $i > $i ).

thf(tp_sK3_Y,type,
    sK3_Y: $i > $i ).

thf(1,axiom,
    ! [X: $i,Y: $i] :
      ( ( ( big_f @ X @ Y )
        | ( big_g @ X @ Y ) )
     => ! [Z: $i] :
          ( ( ( big_f @ Y @ Z )
            | ( big_g @ Y @ Z ) )
         => ( big_h @ X @ Z ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel36_3) ).

thf(2,axiom,
    ! [X: $i] :
    ? [Y: $i] : ( big_g @ X @ Y ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel36_2) ).

thf(3,axiom,
    ! [X: $i] :
    ? [Y: $i] : ( big_f @ X @ Y ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel36_1) ).

thf(4,conjecture,
    ! [X: $i] :
    ? [Y: $i] : ( big_h @ X @ Y ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel36) ).

thf(5,negated_conjecture,
    ( ( ! [X: $i] :
        ? [Y: $i] : ( big_h @ X @ Y ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[4]) ).

thf(6,plain,
    ( ( ! [X: $i] :
        ? [Y: $i] : ( big_h @ X @ Y ) )
    = $false ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(7,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( ( big_f @ X @ Y )
            | ( big_g @ X @ Y ) )
         => ! [Z: $i] :
              ( ( ( big_f @ Y @ Z )
                | ( big_g @ Y @ Z ) )
             => ( big_h @ X @ Z ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(8,plain,
    ( ( ! [X: $i] :
        ? [Y: $i] : ( big_g @ X @ Y ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(9,plain,
    ( ( ! [X: $i] :
        ? [Y: $i] : ( big_f @ X @ Y ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(10,plain,
    ( ( ? [SY9: $i] : ( big_h @ sK1_X @ SY9 ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[6]) ).

thf(11,plain,
    ( ( ~ ? [SY9: $i] : ( big_h @ sK1_X @ SY9 ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[10]) ).

thf(12,plain,
    ( ( ! [SY9: $i] :
          ~ ( big_h @ sK1_X @ SY9 ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[11]) ).

thf(13,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( big_f @ X @ Y )
          | ( ! [Z: $i] :
                ( ~ ( big_f @ Y @ Z )
                | ( big_h @ X @ Z ) )
            & ! [Z: $i] :
                ( ~ ( big_g @ Y @ Z )
                | ( big_h @ X @ Z ) ) ) )
      & ! [X: $i,Y: $i] :
          ( ~ ( big_g @ X @ Y )
          | ( ! [Z: $i] :
                ( ~ ( big_f @ Y @ Z )
                | ( big_h @ X @ Z ) )
            & ! [Z: $i] :
                ( ~ ( big_g @ Y @ Z )
                | ( big_h @ X @ Z ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[7]) ).

thf(14,plain,
    ( ( ! [X: $i] : ( big_g @ X @ ( sK2_Y @ X ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[8]) ).

thf(15,plain,
    ( ( ! [X: $i] : ( big_f @ X @ ( sK3_Y @ X ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[9]) ).

thf(16,plain,
    ( ( ! [X: $i] : ( big_f @ X @ ( sK3_Y @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[15]) ).

thf(17,plain,
    ( ( ! [X: $i] : ( big_g @ X @ ( sK2_Y @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[14]) ).

thf(18,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( big_f @ X @ Y )
          | ( ! [Z: $i] :
                ( ~ ( big_f @ Y @ Z )
                | ( big_h @ X @ Z ) )
            & ! [Z: $i] :
                ( ~ ( big_g @ Y @ Z )
                | ( big_h @ X @ Z ) ) ) )
      & ! [X: $i,Y: $i] :
          ( ~ ( big_g @ X @ Y )
          | ( ! [Z: $i] :
                ( ~ ( big_f @ Y @ Z )
                | ( big_h @ X @ Z ) )
            & ! [Z: $i] :
                ( ~ ( big_g @ Y @ Z )
                | ( big_h @ X @ Z ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[13]) ).

thf(19,plain,
    ( ( ! [SY9: $i] :
          ~ ( big_h @ sK1_X @ SY9 ) )
    = $true ),
    inference(copy,[status(thm)],[12]) ).

thf(20,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( big_f @ SX0 @ SX1 )
                | ~ ( ~ ! [SX2: $i] :
                          ( ~ ( big_f @ SX1 @ SX2 )
                          | ( big_h @ SX0 @ SX2 ) )
                    | ~ ! [SX2: $i] :
                          ( ~ ( big_g @ SX1 @ SX2 )
                          | ( big_h @ SX0 @ SX2 ) ) ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( big_g @ SX0 @ SX1 )
                | ~ ( ~ ! [SX2: $i] :
                          ( ~ ( big_f @ SX1 @ SX2 )
                          | ( big_h @ SX0 @ SX2 ) )
                    | ~ ! [SX2: $i] :
                          ( ~ ( big_g @ SX1 @ SX2 )
                          | ( big_h @ SX0 @ SX2 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[18]) ).

thf(21,plain,
    ! [SV1: $i] :
      ( ( big_f @ SV1 @ ( sK3_Y @ SV1 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[16]) ).

thf(22,plain,
    ! [SV2: $i] :
      ( ( big_g @ SV2 @ ( sK2_Y @ SV2 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[17]) ).

thf(23,plain,
    ! [SV3: $i] :
      ( ( ~ ( big_h @ sK1_X @ SV3 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[19]) ).

thf(24,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( big_f @ SX0 @ SX1 )
            | ~ ( ~ ! [SX2: $i] :
                      ( ~ ( big_f @ SX1 @ SX2 )
                      | ( big_h @ SX0 @ SX2 ) )
                | ~ ! [SX2: $i] :
                      ( ~ ( big_g @ SX1 @ SX2 )
                      | ( big_h @ SX0 @ SX2 ) ) ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( big_g @ SX0 @ SX1 )
            | ~ ( ~ ! [SX2: $i] :
                      ( ~ ( big_f @ SX1 @ SX2 )
                      | ( big_h @ SX0 @ SX2 ) )
                | ~ ! [SX2: $i] :
                      ( ~ ( big_g @ SX1 @ SX2 )
                      | ( big_h @ SX0 @ SX2 ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[20]) ).

thf(25,plain,
    ! [SV3: $i] :
      ( ( big_h @ sK1_X @ SV3 )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[23]) ).

thf(26,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( big_f @ SX0 @ SX1 )
            | ~ ( ~ ! [SX2: $i] :
                      ( ~ ( big_f @ SX1 @ SX2 )
                      | ( big_h @ SX0 @ SX2 ) )
                | ~ ! [SX2: $i] :
                      ( ~ ( big_g @ SX1 @ SX2 )
                      | ( big_h @ SX0 @ SX2 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[24]) ).

thf(27,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( big_g @ SX0 @ SX1 )
            | ~ ( ~ ! [SX2: $i] :
                      ( ~ ( big_f @ SX1 @ SX2 )
                      | ( big_h @ SX0 @ SX2 ) )
                | ~ ! [SX2: $i] :
                      ( ~ ( big_g @ SX1 @ SX2 )
                      | ( big_h @ SX0 @ SX2 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[24]) ).

thf(28,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( big_f @ SX0 @ SX1 )
          | ~ ( ~ ! [SX2: $i] :
                    ( ~ ( big_f @ SX1 @ SX2 )
                    | ( big_h @ SX0 @ SX2 ) )
              | ~ ! [SX2: $i] :
                    ( ~ ( big_g @ SX1 @ SX2 )
                    | ( big_h @ SX0 @ SX2 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[26]) ).

thf(29,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( big_g @ SX0 @ SX1 )
          | ~ ( ~ ! [SX2: $i] :
                    ( ~ ( big_f @ SX1 @ SX2 )
                    | ( big_h @ SX0 @ SX2 ) )
              | ~ ! [SX2: $i] :
                    ( ~ ( big_g @ SX1 @ SX2 )
                    | ( big_h @ SX0 @ SX2 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[27]) ).

thf(30,plain,
    ! [SV4: $i] :
      ( ( ! [SY10: $i] :
            ( ~ ( big_f @ SV4 @ SY10 )
            | ~ ( ~ ! [SY11: $i] :
                      ( ~ ( big_f @ SY10 @ SY11 )
                      | ( big_h @ SV4 @ SY11 ) )
                | ~ ! [SY12: $i] :
                      ( ~ ( big_g @ SY10 @ SY12 )
                      | ( big_h @ SV4 @ SY12 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[28]) ).

thf(31,plain,
    ! [SV5: $i] :
      ( ( ! [SY13: $i] :
            ( ~ ( big_g @ SV5 @ SY13 )
            | ~ ( ~ ! [SY14: $i] :
                      ( ~ ( big_f @ SY13 @ SY14 )
                      | ( big_h @ SV5 @ SY14 ) )
                | ~ ! [SY15: $i] :
                      ( ~ ( big_g @ SY13 @ SY15 )
                      | ( big_h @ SV5 @ SY15 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[29]) ).

thf(32,plain,
    ! [SV6: $i,SV4: $i] :
      ( ( ~ ( big_f @ SV4 @ SV6 )
        | ~ ( ~ ! [SY16: $i] :
                  ( ~ ( big_f @ SV6 @ SY16 )
                  | ( big_h @ SV4 @ SY16 ) )
            | ~ ! [SY17: $i] :
                  ( ~ ( big_g @ SV6 @ SY17 )
                  | ( big_h @ SV4 @ SY17 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[30]) ).

thf(33,plain,
    ! [SV7: $i,SV5: $i] :
      ( ( ~ ( big_g @ SV5 @ SV7 )
        | ~ ( ~ ! [SY18: $i] :
                  ( ~ ( big_f @ SV7 @ SY18 )
                  | ( big_h @ SV5 @ SY18 ) )
            | ~ ! [SY19: $i] :
                  ( ~ ( big_g @ SV7 @ SY19 )
                  | ( big_h @ SV5 @ SY19 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[31]) ).

thf(34,plain,
    ! [SV6: $i,SV4: $i] :
      ( ( ( ~ ( big_f @ SV4 @ SV6 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY16: $i] :
                    ( ~ ( big_f @ SV6 @ SY16 )
                    | ( big_h @ SV4 @ SY16 ) )
              | ~ ! [SY17: $i] :
                    ( ~ ( big_g @ SV6 @ SY17 )
                    | ( big_h @ SV4 @ SY17 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[32]) ).

thf(35,plain,
    ! [SV7: $i,SV5: $i] :
      ( ( ( ~ ( big_g @ SV5 @ SV7 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY18: $i] :
                    ( ~ ( big_f @ SV7 @ SY18 )
                    | ( big_h @ SV5 @ SY18 ) )
              | ~ ! [SY19: $i] :
                    ( ~ ( big_g @ SV7 @ SY19 )
                    | ( big_h @ SV5 @ SY19 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[33]) ).

thf(36,plain,
    ! [SV6: $i,SV4: $i] :
      ( ( ( big_f @ SV4 @ SV6 )
        = $false )
      | ( ( ~ ( ~ ! [SY16: $i] :
                    ( ~ ( big_f @ SV6 @ SY16 )
                    | ( big_h @ SV4 @ SY16 ) )
              | ~ ! [SY17: $i] :
                    ( ~ ( big_g @ SV6 @ SY17 )
                    | ( big_h @ SV4 @ SY17 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[34]) ).

thf(37,plain,
    ! [SV7: $i,SV5: $i] :
      ( ( ( big_g @ SV5 @ SV7 )
        = $false )
      | ( ( ~ ( ~ ! [SY18: $i] :
                    ( ~ ( big_f @ SV7 @ SY18 )
                    | ( big_h @ SV5 @ SY18 ) )
              | ~ ! [SY19: $i] :
                    ( ~ ( big_g @ SV7 @ SY19 )
                    | ( big_h @ SV5 @ SY19 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[35]) ).

thf(38,plain,
    ! [SV4: $i,SV6: $i] :
      ( ( ( ~ ! [SY16: $i] :
                ( ~ ( big_f @ SV6 @ SY16 )
                | ( big_h @ SV4 @ SY16 ) )
          | ~ ! [SY17: $i] :
                ( ~ ( big_g @ SV6 @ SY17 )
                | ( big_h @ SV4 @ SY17 ) ) )
        = $false )
      | ( ( big_f @ SV4 @ SV6 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[36]) ).

thf(39,plain,
    ! [SV5: $i,SV7: $i] :
      ( ( ( ~ ! [SY18: $i] :
                ( ~ ( big_f @ SV7 @ SY18 )
                | ( big_h @ SV5 @ SY18 ) )
          | ~ ! [SY19: $i] :
                ( ~ ( big_g @ SV7 @ SY19 )
                | ( big_h @ SV5 @ SY19 ) ) )
        = $false )
      | ( ( big_g @ SV5 @ SV7 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[37]) ).

thf(40,plain,
    ! [SV4: $i,SV6: $i] :
      ( ( ( ~ ! [SY16: $i] :
                ( ~ ( big_f @ SV6 @ SY16 )
                | ( big_h @ SV4 @ SY16 ) ) )
        = $false )
      | ( ( big_f @ SV4 @ SV6 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[38]) ).

thf(41,plain,
    ! [SV4: $i,SV6: $i] :
      ( ( ( ~ ! [SY17: $i] :
                ( ~ ( big_g @ SV6 @ SY17 )
                | ( big_h @ SV4 @ SY17 ) ) )
        = $false )
      | ( ( big_f @ SV4 @ SV6 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[38]) ).

thf(42,plain,
    ! [SV5: $i,SV7: $i] :
      ( ( ( ~ ! [SY18: $i] :
                ( ~ ( big_f @ SV7 @ SY18 )
                | ( big_h @ SV5 @ SY18 ) ) )
        = $false )
      | ( ( big_g @ SV5 @ SV7 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[39]) ).

thf(43,plain,
    ! [SV5: $i,SV7: $i] :
      ( ( ( ~ ! [SY19: $i] :
                ( ~ ( big_g @ SV7 @ SY19 )
                | ( big_h @ SV5 @ SY19 ) ) )
        = $false )
      | ( ( big_g @ SV5 @ SV7 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[39]) ).

thf(44,plain,
    ! [SV4: $i,SV6: $i] :
      ( ( ( ! [SY16: $i] :
              ( ~ ( big_f @ SV6 @ SY16 )
              | ( big_h @ SV4 @ SY16 ) ) )
        = $true )
      | ( ( big_f @ SV4 @ SV6 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[40]) ).

thf(45,plain,
    ! [SV4: $i,SV6: $i] :
      ( ( ( ! [SY17: $i] :
              ( ~ ( big_g @ SV6 @ SY17 )
              | ( big_h @ SV4 @ SY17 ) ) )
        = $true )
      | ( ( big_f @ SV4 @ SV6 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[41]) ).

thf(46,plain,
    ! [SV5: $i,SV7: $i] :
      ( ( ( ! [SY18: $i] :
              ( ~ ( big_f @ SV7 @ SY18 )
              | ( big_h @ SV5 @ SY18 ) ) )
        = $true )
      | ( ( big_g @ SV5 @ SV7 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[42]) ).

thf(47,plain,
    ! [SV5: $i,SV7: $i] :
      ( ( ( ! [SY19: $i] :
              ( ~ ( big_g @ SV7 @ SY19 )
              | ( big_h @ SV5 @ SY19 ) ) )
        = $true )
      | ( ( big_g @ SV5 @ SV7 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[43]) ).

thf(48,plain,
    ! [SV4: $i,SV8: $i,SV6: $i] :
      ( ( ( ~ ( big_f @ SV6 @ SV8 )
          | ( big_h @ SV4 @ SV8 ) )
        = $true )
      | ( ( big_f @ SV4 @ SV6 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[44]) ).

thf(49,plain,
    ! [SV4: $i,SV9: $i,SV6: $i] :
      ( ( ( ~ ( big_g @ SV6 @ SV9 )
          | ( big_h @ SV4 @ SV9 ) )
        = $true )
      | ( ( big_f @ SV4 @ SV6 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[45]) ).

thf(50,plain,
    ! [SV5: $i,SV10: $i,SV7: $i] :
      ( ( ( ~ ( big_f @ SV7 @ SV10 )
          | ( big_h @ SV5 @ SV10 ) )
        = $true )
      | ( ( big_g @ SV5 @ SV7 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[46]) ).

thf(51,plain,
    ! [SV5: $i,SV11: $i,SV7: $i] :
      ( ( ( ~ ( big_g @ SV7 @ SV11 )
          | ( big_h @ SV5 @ SV11 ) )
        = $true )
      | ( ( big_g @ SV5 @ SV7 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[47]) ).

thf(52,plain,
    ! [SV4: $i,SV8: $i,SV6: $i] :
      ( ( ( ~ ( big_f @ SV6 @ SV8 ) )
        = $true )
      | ( ( big_h @ SV4 @ SV8 )
        = $true )
      | ( ( big_f @ SV4 @ SV6 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[48]) ).

thf(53,plain,
    ! [SV4: $i,SV9: $i,SV6: $i] :
      ( ( ( ~ ( big_g @ SV6 @ SV9 ) )
        = $true )
      | ( ( big_h @ SV4 @ SV9 )
        = $true )
      | ( ( big_f @ SV4 @ SV6 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[49]) ).

thf(54,plain,
    ! [SV5: $i,SV10: $i,SV7: $i] :
      ( ( ( ~ ( big_f @ SV7 @ SV10 ) )
        = $true )
      | ( ( big_h @ SV5 @ SV10 )
        = $true )
      | ( ( big_g @ SV5 @ SV7 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[50]) ).

thf(55,plain,
    ! [SV5: $i,SV11: $i,SV7: $i] :
      ( ( ( ~ ( big_g @ SV7 @ SV11 ) )
        = $true )
      | ( ( big_h @ SV5 @ SV11 )
        = $true )
      | ( ( big_g @ SV5 @ SV7 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[51]) ).

thf(56,plain,
    ! [SV4: $i,SV8: $i,SV6: $i] :
      ( ( ( big_f @ SV6 @ SV8 )
        = $false )
      | ( ( big_h @ SV4 @ SV8 )
        = $true )
      | ( ( big_f @ SV4 @ SV6 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[52]) ).

thf(57,plain,
    ! [SV4: $i,SV9: $i,SV6: $i] :
      ( ( ( big_g @ SV6 @ SV9 )
        = $false )
      | ( ( big_h @ SV4 @ SV9 )
        = $true )
      | ( ( big_f @ SV4 @ SV6 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[53]) ).

thf(58,plain,
    ! [SV5: $i,SV10: $i,SV7: $i] :
      ( ( ( big_f @ SV7 @ SV10 )
        = $false )
      | ( ( big_h @ SV5 @ SV10 )
        = $true )
      | ( ( big_g @ SV5 @ SV7 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[54]) ).

thf(59,plain,
    ! [SV5: $i,SV11: $i,SV7: $i] :
      ( ( ( big_g @ SV7 @ SV11 )
        = $false )
      | ( ( big_h @ SV5 @ SV11 )
        = $true )
      | ( ( big_g @ SV5 @ SV7 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[55]) ).

thf(60,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[21,59,58,57,56,25,22]) ).

thf(61,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[60]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13  % Problem  : SYN065+1 : TPTP v8.1.0. Released v2.0.0.
% 0.09/0.14  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.15/0.36  % Computer : n022.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 600
% 0.15/0.36  % DateTime : Tue Jul 12 09:07:25 EDT 2022
% 0.15/0.36  % CPUTime  : 
% 0.15/0.36  
% 0.15/0.36   No.of.Axioms: 3
% 0.15/0.36  
% 0.15/0.36   Length.of.Defs: 0
% 0.15/0.36  
% 0.15/0.36   Contains.Choice.Funs: false
% 0.15/0.37  (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:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:5,loop_count:0,foatp_calls:0,translation:fof_full)....
% 0.22/0.41  
% 0.22/0.41  ********************************
% 0.22/0.41  *   All subproblems solved!    *
% 0.22/0.41  ********************************
% 0.22/0.41  % SZS status Theorem for /export/starexec/sandbox2/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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:60,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.22/0.41  
% 0.22/0.41  %**** Beginning of derivation protocol ****
% 0.22/0.41  % SZS output start CNFRefutation
% See solution above
% 0.22/0.41  
% 0.22/0.41  %**** End of derivation protocol ****
% 0.22/0.41  %**** no. of clauses in derivation: 61 ****
% 0.22/0.41  %**** clause counter: 60 ****
% 0.22/0.41  
% 0.22/0.41  % SZS status Theorem for /export/starexec/sandbox2/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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:60,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------