TSTP Solution File: SET741^4 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SET741^4 : TPTP v8.1.0. Released v3.6.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n009.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 03:04:36 EDT 2022

% Result   : Theorem 0.21s 0.41s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :   26
% Syntax   : Number of formulae    :   76 (  39 unt;  17 typ;   8 def)
%            Number of atoms       :  256 ( 148 equ;   0 cnn)
%            Maximal formula atoms :    4 (   4 avg)
%            Number of connectives :  376 (  75   ~;  32   |;  13   &; 248   @)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   60 (  60   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   20 (  17 usr;   6 con; 0-3 aty)
%            Number of variables   :  104 (  16   ^  85   !;   3   ?; 104   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_fun_bijective,type,
    fun_bijective: ( $i > $i ) > $o ).

thf(tp_fun_composition,type,
    fun_composition: ( $i > $i ) > ( $i > $i ) > $i > $i ).

thf(tp_fun_decreasing,type,
    fun_decreasing: ( $i > $i ) > ( $i > $i > $o ) > $o ).

thf(tp_fun_image,type,
    fun_image: ( $i > $i ) > ( $i > $o ) > $i > $o ).

thf(tp_fun_increasing,type,
    fun_increasing: ( $i > $i ) > ( $i > $i > $o ) > $o ).

thf(tp_fun_injective,type,
    fun_injective: ( $i > $i ) > $o ).

thf(tp_fun_inv_image,type,
    fun_inv_image: ( $i > $i ) > ( $i > $o ) > $i > $o ).

thf(tp_fun_surjective,type,
    fun_surjective: ( $i > $i ) > $o ).

thf(tp_sK1_F,type,
    sK1_F: $i > $i ).

thf(tp_sK2_SY0,type,
    sK2_SY0: $i > $i ).

thf(tp_sK3_SY2,type,
    sK3_SY2: $i > $i ).

thf(tp_sK4_SY4,type,
    sK4_SY4: $i > $i ).

thf(tp_sK5_SY5,type,
    sK5_SY5: $i > $i ).

thf(tp_sK6_SX0,type,
    sK6_SX0: $i ).

thf(tp_sK7_SY6,type,
    sK7_SY6: $i ).

thf(tp_sK8_SX0,type,
    sK8_SX0: $i ).

thf(tp_sK9_SX0,type,
    sK9_SX0: $i ).

thf(fun_bijective,definition,
    ( fun_bijective
    = ( ^ [F: $i > $i] :
          ( ( fun_injective @ F )
          & ( fun_surjective @ F ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fun_bijective) ).

thf(fun_composition,definition,
    ( fun_composition
    = ( ^ [F: $i > $i,G: $i > $i,X: $i] : ( G @ ( F @ X ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fun_composition) ).

thf(fun_decreasing,definition,
    ( fun_decreasing
    = ( ^ [F: $i > $i,SMALLER: $i > $i > $o] :
        ! [X: $i,Y: $i] :
          ( ( SMALLER @ X @ Y )
         => ( SMALLER @ ( F @ Y ) @ ( F @ X ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fun_decreasing) ).

thf(fun_image,definition,
    ( fun_image
    = ( ^ [F: $i > $i,A: $i > $o,Y: $i] :
        ? [X: $i] :
          ( ( A @ X )
          & ( Y
            = ( F @ X ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fun_image) ).

thf(fun_increasing,definition,
    ( fun_increasing
    = ( ^ [F: $i > $i,SMALLER: $i > $i > $o] :
        ! [X: $i,Y: $i] :
          ( ( SMALLER @ X @ Y )
         => ( SMALLER @ ( F @ X ) @ ( F @ Y ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fun_increasing) ).

thf(fun_injective,definition,
    ( fun_injective
    = ( ^ [F: $i > $i] :
        ! [X: $i,Y: $i] :
          ( ( ( F @ X )
            = ( F @ Y ) )
         => ( X = Y ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fun_injective) ).

thf(fun_inv_image,definition,
    ( fun_inv_image
    = ( ^ [F: $i > $i,B: $i > $o,X: $i] :
        ? [Y: $i] :
          ( ( B @ Y )
          & ( Y
            = ( F @ X ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fun_inv_image) ).

thf(fun_surjective,definition,
    ( fun_surjective
    = ( ^ [F: $i > $i] :
        ! [Y: $i] :
        ? [X: $i] :
          ( Y
          = ( F @ X ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fun_surjective) ).

thf(1,conjecture,
    ! [F: $i > $i,G: $i > $i,H: $i > $i] :
      ( ( ( fun_injective @ ( fun_composition @ ( fun_composition @ F @ G ) @ H ) )
        & ( fun_surjective @ ( fun_composition @ ( fun_composition @ G @ H ) @ F ) )
        & ( fun_surjective @ ( fun_composition @ ( fun_composition @ H @ F ) @ G ) ) )
     => ( fun_bijective @ H ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).

thf(2,negated_conjecture,
    ( ( ! [F: $i > $i,G: $i > $i,H: $i > $i] :
          ( ( ( fun_injective @ ( fun_composition @ ( fun_composition @ F @ G ) @ H ) )
            & ( fun_surjective @ ( fun_composition @ ( fun_composition @ G @ H ) @ F ) )
            & ( fun_surjective @ ( fun_composition @ ( fun_composition @ H @ F ) @ G ) ) )
         => ( fun_bijective @ H ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ! [SY0: $i > $i,SY1: $i > $i] :
          ( ( ( fun_injective @ ( fun_composition @ ( fun_composition @ sK1_F @ SY0 ) @ SY1 ) )
            & ( fun_surjective @ ( fun_composition @ ( fun_composition @ SY0 @ SY1 ) @ sK1_F ) )
            & ( fun_surjective @ ( fun_composition @ ( fun_composition @ SY1 @ sK1_F ) @ SY0 ) ) )
         => ( fun_bijective @ SY1 ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[2]) ).

thf(4,plain,
    ( ( ! [SY2: $i > $i] :
          ( ( ( fun_injective @ ( fun_composition @ ( fun_composition @ sK1_F @ sK2_SY0 ) @ SY2 ) )
            & ( fun_surjective @ ( fun_composition @ ( fun_composition @ sK2_SY0 @ SY2 ) @ sK1_F ) )
            & ( fun_surjective @ ( fun_composition @ ( fun_composition @ SY2 @ sK1_F ) @ sK2_SY0 ) ) )
         => ( fun_bijective @ SY2 ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[3]) ).

thf(5,plain,
    ( ( ( ( fun_injective @ ( fun_composition @ ( fun_composition @ sK1_F @ sK2_SY0 ) @ sK3_SY2 ) )
        & ( fun_surjective @ ( fun_composition @ ( fun_composition @ sK2_SY0 @ sK3_SY2 ) @ sK1_F ) )
        & ( fun_surjective @ ( fun_composition @ ( fun_composition @ sK3_SY2 @ sK1_F ) @ sK2_SY0 ) ) )
     => ( fun_bijective @ sK3_SY2 ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[4]) ).

thf(6,plain,
    ( ( fun_injective @ ( fun_composition @ ( fun_composition @ sK1_F @ sK2_SY0 ) @ sK3_SY2 ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[5]) ).

thf(7,plain,
    ( ( fun_surjective @ ( fun_composition @ ( fun_composition @ sK2_SY0 @ sK3_SY2 ) @ sK1_F ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[5]) ).

thf(8,plain,
    ( ( fun_surjective @ ( fun_composition @ ( fun_composition @ sK3_SY2 @ sK1_F ) @ sK2_SY0 ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[5]) ).

thf(9,plain,
    ( ( fun_bijective @ sK3_SY2 )
    = $false ),
    inference(standard_cnf,[status(thm)],[5]) ).

thf(10,plain,
    ( ( ~ ( fun_bijective @ sK3_SY2 ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[9]) ).

thf(11,plain,
    ( ( fun_surjective @ ( fun_composition @ ( fun_composition @ sK3_SY2 @ sK1_F ) @ sK2_SY0 ) )
    = $true ),
    inference(copy,[status(thm)],[8]) ).

thf(12,plain,
    ( ( fun_surjective @ ( fun_composition @ ( fun_composition @ sK2_SY0 @ sK3_SY2 ) @ sK1_F ) )
    = $true ),
    inference(copy,[status(thm)],[7]) ).

thf(13,plain,
    ( ( fun_injective @ ( fun_composition @ ( fun_composition @ sK1_F @ sK2_SY0 ) @ sK3_SY2 ) )
    = $true ),
    inference(copy,[status(thm)],[6]) ).

thf(14,plain,
    ( ( ~ ( fun_bijective @ sK3_SY2 ) )
    = $true ),
    inference(copy,[status(thm)],[10]) ).

thf(15,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                  ( ( ( sK3_SY2 @ SX0 )
                   != ( sK3_SY2 @ SX1 ) )
                  | ( SX0 = SX1 ) )
            | ~ ! [SX0: $i] :
                  ~ ! [SX1: $i] :
                      ( SX0
                     != ( sK3_SY2 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[14,fun_bijective,fun_composition,fun_decreasing,fun_image,fun_increasing,fun_injective,fun_inv_image,fun_surjective]) ).

thf(16,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( ( sK3_SY2 @ ( sK2_SY0 @ ( sK1_F @ SX0 ) ) )
           != ( sK3_SY2 @ ( sK2_SY0 @ ( sK1_F @ SX1 ) ) ) )
          | ( SX0 = SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[13,fun_bijective,fun_composition,fun_decreasing,fun_image,fun_increasing,fun_injective,fun_inv_image,fun_surjective]) ).

thf(17,plain,
    ( ( ! [SX0: $i] :
          ~ ! [SX1: $i] :
              ( SX0
             != ( sK1_F @ ( sK3_SY2 @ ( sK2_SY0 @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[12,fun_bijective,fun_composition,fun_decreasing,fun_image,fun_increasing,fun_injective,fun_inv_image,fun_surjective]) ).

thf(18,plain,
    ( ( ! [SX0: $i] :
          ~ ! [SX1: $i] :
              ( SX0
             != ( sK2_SY0 @ ( sK1_F @ ( sK3_SY2 @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11,fun_bijective,fun_composition,fun_decreasing,fun_image,fun_increasing,fun_injective,fun_inv_image,fun_surjective]) ).

thf(19,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ( ( sK3_SY2 @ SX0 )
                 != ( sK3_SY2 @ SX1 ) )
                | ( SX0 = SX1 ) )
          | ~ ! [SX0: $i] :
                ~ ! [SX1: $i] :
                    ( SX0
                   != ( sK3_SY2 @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[15]) ).

thf(20,plain,
    ! [SV1: $i] :
      ( ( ! [SY3: $i] :
            ( ( ( sK3_SY2 @ ( sK2_SY0 @ ( sK1_F @ SV1 ) ) )
             != ( sK3_SY2 @ ( sK2_SY0 @ ( sK1_F @ SY3 ) ) ) )
            | ( SV1 = SY3 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[16]) ).

thf(21,plain,
    ! [SV2: $i] :
      ( ( ~ ! [SY4: $i] :
              ( SV2
             != ( sK1_F @ ( sK3_SY2 @ ( sK2_SY0 @ SY4 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[17]) ).

thf(22,plain,
    ! [SV3: $i] :
      ( ( ~ ! [SY5: $i] :
              ( SV3
             != ( sK2_SY0 @ ( sK1_F @ ( sK3_SY2 @ SY5 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[18]) ).

thf(23,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( ( sK3_SY2 @ SX0 )
             != ( sK3_SY2 @ SX1 ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: $i] :
            ~ ! [SX1: $i] :
                ( SX0
               != ( sK3_SY2 @ SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[19]) ).

thf(24,plain,
    ! [SV4: $i,SV1: $i] :
      ( ( ( ( sK3_SY2 @ ( sK2_SY0 @ ( sK1_F @ SV1 ) ) )
         != ( sK3_SY2 @ ( sK2_SY0 @ ( sK1_F @ SV4 ) ) ) )
        | ( SV1 = SV4 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[20]) ).

thf(25,plain,
    ! [SV2: $i] :
      ( ( ! [SY4: $i] :
            ( SV2
           != ( sK1_F @ ( sK3_SY2 @ ( sK2_SY0 @ SY4 ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[21]) ).

thf(26,plain,
    ! [SV3: $i] :
      ( ( ! [SY5: $i] :
            ( SV3
           != ( sK2_SY0 @ ( sK1_F @ ( sK3_SY2 @ SY5 ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[22]) ).

thf(27,plain,
    ( ( ( ~ ! [SX0: $i,SX1: $i] :
              ( ( ( sK3_SY2 @ SX0 )
               != ( sK3_SY2 @ SX1 ) )
              | ( SX0 = SX1 ) ) )
      = $true )
    | ( ( ~ ! [SX0: $i] :
              ~ ! [SX1: $i] :
                  ( SX0
                 != ( sK3_SY2 @ SX1 ) ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[23]) ).

thf(28,plain,
    ! [SV4: $i,SV1: $i] :
      ( ( ( ( ( sK3_SY2 @ ( sK2_SY0 @ ( sK1_F @ SV1 ) ) )
           != ( sK3_SY2 @ ( sK2_SY0 @ ( sK1_F @ SV4 ) ) ) ) )
        = $true )
      | ( ( SV1 = SV4 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[24]) ).

thf(29,plain,
    ! [SV2: $i] :
      ( ( ( SV2
         != ( sK1_F @ ( sK3_SY2 @ ( sK2_SY0 @ ( sK4_SY4 @ SV2 ) ) ) ) ) )
      = $false ),
    inference(extcnf_forall_neg,[status(esa)],[25]) ).

thf(30,plain,
    ! [SV3: $i] :
      ( ( ( SV3
         != ( sK2_SY0 @ ( sK1_F @ ( sK3_SY2 @ ( sK5_SY5 @ SV3 ) ) ) ) ) )
      = $false ),
    inference(extcnf_forall_neg,[status(esa)],[26]) ).

thf(31,plain,
    ( ( ( ! [SX0: $i,SX1: $i] :
            ( ( ( sK3_SY2 @ SX0 )
             != ( sK3_SY2 @ SX1 ) )
            | ( SX0 = SX1 ) ) )
      = $false )
    | ( ( ~ ! [SX0: $i] :
              ~ ! [SX1: $i] :
                  ( SX0
                 != ( sK3_SY2 @ SX1 ) ) )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[27]) ).

thf(32,plain,
    ! [SV4: $i,SV1: $i] :
      ( ( ( ( sK3_SY2 @ ( sK2_SY0 @ ( sK1_F @ SV1 ) ) )
          = ( sK3_SY2 @ ( sK2_SY0 @ ( sK1_F @ SV4 ) ) ) )
        = $false )
      | ( ( SV1 = SV4 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[28]) ).

thf(33,plain,
    ! [SV2: $i] :
      ( ( SV2
        = ( sK1_F @ ( sK3_SY2 @ ( sK2_SY0 @ ( sK4_SY4 @ SV2 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[29]) ).

thf(34,plain,
    ! [SV3: $i] :
      ( ( SV3
        = ( sK2_SY0 @ ( sK1_F @ ( sK3_SY2 @ ( sK5_SY5 @ SV3 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[30]) ).

thf(35,plain,
    ( ( ( ! [SY6: $i] :
            ( ( ( sK3_SY2 @ sK6_SX0 )
             != ( sK3_SY2 @ SY6 ) )
            | ( sK6_SX0 = SY6 ) ) )
      = $false )
    | ( ( ~ ! [SX0: $i] :
              ~ ! [SX1: $i] :
                  ( SX0
                 != ( sK3_SY2 @ SX1 ) ) )
      = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[31]) ).

thf(36,plain,
    ( ( ( ( ( sK3_SY2 @ sK6_SX0 )
         != ( sK3_SY2 @ sK7_SY6 ) )
        | ( sK6_SX0 = sK7_SY6 ) )
      = $false )
    | ( ( ~ ! [SX0: $i] :
              ~ ! [SX1: $i] :
                  ( SX0
                 != ( sK3_SY2 @ SX1 ) ) )
      = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[35]) ).

thf(37,plain,
    ( ( ( ( ( sK3_SY2 @ sK6_SX0 )
         != ( sK3_SY2 @ sK7_SY6 ) ) )
      = $false )
    | ( ( ~ ! [SX0: $i] :
              ~ ! [SX1: $i] :
                  ( SX0
                 != ( sK3_SY2 @ SX1 ) ) )
      = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[36]) ).

thf(38,plain,
    ( ( ( sK6_SX0 = sK7_SY6 )
      = $false )
    | ( ( ~ ! [SX0: $i] :
              ~ ! [SX1: $i] :
                  ( SX0
                 != ( sK3_SY2 @ SX1 ) ) )
      = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[36]) ).

thf(39,plain,
    ( ( ( ( sK3_SY2 @ sK6_SX0 )
        = ( sK3_SY2 @ sK7_SY6 ) )
      = $true )
    | ( ( ~ ! [SX0: $i] :
              ~ ! [SX1: $i] :
                  ( SX0
                 != ( sK3_SY2 @ SX1 ) ) )
      = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[37]) ).

thf(40,plain,
    ( ( ( ! [SX0: $i] :
            ~ ! [SX1: $i] :
                ( SX0
               != ( sK3_SY2 @ SX1 ) ) )
      = $false )
    | ( ( sK6_SX0 = sK7_SY6 )
      = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[38]) ).

thf(41,plain,
    ( ( ( ! [SX0: $i] :
            ~ ! [SX1: $i] :
                ( SX0
               != ( sK3_SY2 @ SX1 ) ) )
      = $false )
    | ( ( ( sK3_SY2 @ sK6_SX0 )
        = ( sK3_SY2 @ sK7_SY6 ) )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[39]) ).

thf(42,plain,
    ( ( ( ~ ! [SY7: $i] :
              ( sK8_SX0
             != ( sK3_SY2 @ SY7 ) ) )
      = $false )
    | ( ( sK6_SX0 = sK7_SY6 )
      = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[40]) ).

thf(43,plain,
    ( ( ( ~ ! [SY8: $i] :
              ( sK9_SX0
             != ( sK3_SY2 @ SY8 ) ) )
      = $false )
    | ( ( ( sK3_SY2 @ sK6_SX0 )
        = ( sK3_SY2 @ sK7_SY6 ) )
      = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[41]) ).

thf(44,plain,
    ( ( ( ! [SY7: $i] :
            ( sK8_SX0
           != ( sK3_SY2 @ SY7 ) ) )
      = $true )
    | ( ( sK6_SX0 = sK7_SY6 )
      = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[42]) ).

thf(45,plain,
    ( ( ( ! [SY8: $i] :
            ( sK9_SX0
           != ( sK3_SY2 @ SY8 ) ) )
      = $true )
    | ( ( ( sK3_SY2 @ sK6_SX0 )
        = ( sK3_SY2 @ sK7_SY6 ) )
      = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[43]) ).

thf(46,plain,
    ! [SV5: $i] :
      ( ( ( ( sK8_SX0
           != ( sK3_SY2 @ SV5 ) ) )
        = $true )
      | ( ( sK6_SX0 = sK7_SY6 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[44]) ).

thf(47,plain,
    ! [SV6: $i] :
      ( ( ( ( sK9_SX0
           != ( sK3_SY2 @ SV6 ) ) )
        = $true )
      | ( ( ( sK3_SY2 @ sK6_SX0 )
          = ( sK3_SY2 @ sK7_SY6 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[45]) ).

thf(48,plain,
    ! [SV5: $i] :
      ( ( ( sK8_SX0
          = ( sK3_SY2 @ SV5 ) )
        = $false )
      | ( ( sK6_SX0 = sK7_SY6 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[46]) ).

thf(49,plain,
    ! [SV6: $i] :
      ( ( ( sK9_SX0
          = ( sK3_SY2 @ SV6 ) )
        = $false )
      | ( ( ( sK3_SY2 @ sK6_SX0 )
          = ( sK3_SY2 @ sK7_SY6 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[47]) ).

thf(50,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[32,49,48,34,33]) ).

thf(51,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[50]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : SET741^4 : TPTP v8.1.0. Released v3.6.0.
% 0.13/0.14  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.35  % Computer : n009.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Sun Jul 10 09:31:07 EDT 2022
% 0.13/0.36  % CPUTime  : 
% 0.21/0.36  
% 0.21/0.36   No.of.Axioms: 0
% 0.21/0.36  
% 0.21/0.36   Length.of.Defs: 1520
% 0.21/0.36  
% 0.21/0.36   Contains.Choice.Funs: false
% 0.21/0.36  (rf:0,axioms:0,ps:3,u:6,ude:false,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)..
% 0.21/0.41  
% 0.21/0.41  ********************************
% 0.21/0.41  *   All subproblems solved!    *
% 0.21/0.41  ********************************
% 0.21/0.41  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:3,ps:3,u:6,ude:false,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:50,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.21/0.41  
% 0.21/0.41  %**** Beginning of derivation protocol ****
% 0.21/0.41  % SZS output start CNFRefutation
% See solution above
% 0.21/0.41  
% 0.21/0.41  %**** End of derivation protocol ****
% 0.21/0.41  %**** no. of clauses in derivation: 51 ****
% 0.21/0.41  %**** clause counter: 50 ****
% 0.21/0.41  
% 0.21/0.41  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:3,ps:3,u:6,ude:false,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:50,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------