TSTP Solution File: DAT056^1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : DAT056^1 : TPTP v8.1.0. Released v5.4.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n006.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 : Sat Jul 16 01:02:33 EDT 2022

% Result   : Theorem 0.18s 0.40s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   56 (  24 unt;  14 typ;   0 def)
%            Number of atoms       :  233 ( 162 equ;   0 cnn)
%            Maximal formula atoms :    4 (   5 avg)
%            Number of connectives :  864 (  31   ~;  45   |;   2   &; 780   @)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Number of types       :    2 (   2 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   15 (  12 usr;  12 con; 0-2 aty)
%            Number of variables   :  139 (   0   ^ 139   !;   0   ?; 139   :)

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

thf(tp_lst,type,
    lst: $tType ).

thf(tp_ap,type,
    ap: lst > lst > lst ).

thf(tp_cns,type,
    cns: a > lst > lst ).

thf(tp_nl,type,
    nl: lst ).

thf(tp_sK1_Ys,type,
    sK1_Ys: lst ).

thf(tp_sK2_SY17,type,
    sK2_SY17: lst ).

thf(tp_sK3_A,type,
    sK3_A: a ).

thf(tp_sK4_SY18,type,
    sK4_SY18: lst ).

thf(tp_sK5_SY25,type,
    sK5_SY25: lst ).

thf(tp_sK6_SY27,type,
    sK6_SY27: lst ).

thf(tp_sK7_Ys,type,
    sK7_Ys: lst ).

thf(tp_sK8_SY28,type,
    sK8_SY28: lst ).

thf(tp_xs,type,
    xs: lst ).

thf(1,axiom,
    ! [Ys2: lst] :
      ( ( ap @ nl @ Ys2 )
      = Ys2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2p_Osimps_I1_J) ).

thf(2,axiom,
    ! [Ys2: lst,Xs: lst,X: a] :
      ( ( ap @ ( cns @ X @ Xs ) @ Ys2 )
      = ( cns @ X @ ( ap @ Xs @ Ys2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1p_Osimps_I2_J) ).

thf(3,axiom,
    ! [Lst: lst] :
      ( ! [Ys: lst,Zs: lst] :
          ( ( ap @ nl @ ( ap @ Ys @ Zs ) )
          = ( ap @ ( ap @ nl @ Ys ) @ Zs ) )
     => ( ! [A: a,Lst2: lst] :
            ( ! [Ys3: lst,Zs2: lst] :
                ( ( ap @ Lst2 @ ( ap @ Ys3 @ Zs2 ) )
                = ( ap @ ( ap @ Lst2 @ Ys3 ) @ Zs2 ) )
           => ! [Ys: lst,Zs: lst] :
                ( ( ap @ ( cns @ A @ Lst2 ) @ ( ap @ Ys @ Zs ) )
                = ( ap @ ( ap @ ( cns @ A @ Lst2 ) @ Ys ) @ Zs ) ) )
       => ! [Ys3: lst,Zs2: lst] :
            ( ( ap @ Lst @ ( ap @ Ys3 @ Zs2 ) )
            = ( ap @ ( ap @ Lst @ Ys3 ) @ Zs2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_lst_Oinduct_091where_AP_A_061_A_C_Fxs_O_AALL_Ays_Azs_O_Aap_Axs_A_Iap_Ays_Azs_J_A_061_Aap_A_Iap_Axs_Ays_J_Azs_C_093) ).

thf(4,conjecture,
    ! [Ys: lst,Zs: lst] :
      ( ( ap @ xs @ ( ap @ Ys @ Zs ) )
      = ( ap @ ( ap @ xs @ Ys ) @ Zs ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

thf(5,negated_conjecture,
    ( ( ! [Ys: lst,Zs: lst] :
          ( ( ap @ xs @ ( ap @ Ys @ Zs ) )
          = ( ap @ ( ap @ xs @ Ys ) @ Zs ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[4]) ).

thf(6,plain,
    ( ( ! [Ys: lst,Zs: lst] :
          ( ( ap @ xs @ ( ap @ Ys @ Zs ) )
          = ( ap @ ( ap @ xs @ Ys ) @ Zs ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(7,plain,
    ( ( ! [Ys2: lst] :
          ( ( ap @ nl @ Ys2 )
          = Ys2 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(8,plain,
    ( ( ! [Ys2: lst,Xs: lst,X: a] :
          ( ( ap @ ( cns @ X @ Xs ) @ Ys2 )
          = ( cns @ X @ ( ap @ Xs @ Ys2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(9,plain,
    ( ( ! [Lst: lst] :
          ( ! [Ys: lst,Zs: lst] :
              ( ( ap @ nl @ ( ap @ Ys @ Zs ) )
              = ( ap @ ( ap @ nl @ Ys ) @ Zs ) )
         => ( ! [A: a,Lst2: lst] :
                ( ! [Ys3: lst,Zs2: lst] :
                    ( ( ap @ Lst2 @ ( ap @ Ys3 @ Zs2 ) )
                    = ( ap @ ( ap @ Lst2 @ Ys3 ) @ Zs2 ) )
               => ! [Ys: lst,Zs: lst] :
                    ( ( ap @ ( cns @ A @ Lst2 ) @ ( ap @ Ys @ Zs ) )
                    = ( ap @ ( ap @ ( cns @ A @ Lst2 ) @ Ys ) @ Zs ) ) )
           => ! [Ys3: lst,Zs2: lst] :
                ( ( ap @ Lst @ ( ap @ Ys3 @ Zs2 ) )
                = ( ap @ ( ap @ Lst @ Ys3 ) @ Zs2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(10,plain,
    ( ( ! [SY17: lst] :
          ( ( ap @ xs @ ( ap @ sK1_Ys @ SY17 ) )
          = ( ap @ ( ap @ xs @ sK1_Ys ) @ SY17 ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[6]) ).

thf(11,plain,
    ( ( ( ap @ xs @ ( ap @ sK1_Ys @ sK2_SY17 ) )
      = ( ap @ ( ap @ xs @ sK1_Ys ) @ sK2_SY17 ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[10]) ).

thf(12,plain,
    ( ( ( ( ap @ xs @ ( ap @ sK1_Ys @ sK2_SY17 ) )
       != ( ap @ ( ap @ xs @ sK1_Ys ) @ sK2_SY17 ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[11]) ).

thf(13,plain,
    ( ( ( ( ap @ nl @ ( ap @ sK7_Ys @ sK8_SY28 ) )
       != ( ap @ ( ap @ nl @ sK7_Ys ) @ sK8_SY28 ) )
      | ( ! [SY23: lst,SY24: lst] :
            ( ( ap @ sK4_SY18 @ ( ap @ SY23 @ SY24 ) )
            = ( ap @ ( ap @ sK4_SY18 @ SY23 ) @ SY24 ) )
        & ( ( ap @ ( cns @ sK3_A @ sK4_SY18 ) @ ( ap @ sK5_SY25 @ sK6_SY27 ) )
         != ( ap @ ( ap @ ( cns @ sK3_A @ sK4_SY18 ) @ sK5_SY25 ) @ sK6_SY27 ) ) )
      | ! [Lst: lst,Ys3: lst,Zs2: lst] :
          ( ( ap @ Lst @ ( ap @ Ys3 @ Zs2 ) )
          = ( ap @ ( ap @ Lst @ Ys3 ) @ Zs2 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[9]) ).

thf(14,plain,
    ( ( ( ( ap @ nl @ ( ap @ sK7_Ys @ sK8_SY28 ) )
       != ( ap @ ( ap @ nl @ sK7_Ys ) @ sK8_SY28 ) )
      | ( ! [SY23: lst,SY24: lst] :
            ( ( ap @ sK4_SY18 @ ( ap @ SY23 @ SY24 ) )
            = ( ap @ ( ap @ sK4_SY18 @ SY23 ) @ SY24 ) )
        & ( ( ap @ ( cns @ sK3_A @ sK4_SY18 ) @ ( ap @ sK5_SY25 @ sK6_SY27 ) )
         != ( ap @ ( ap @ ( cns @ sK3_A @ sK4_SY18 ) @ sK5_SY25 ) @ sK6_SY27 ) ) )
      | ! [Lst: lst,Ys3: lst,Zs2: lst] :
          ( ( ap @ Lst @ ( ap @ Ys3 @ Zs2 ) )
          = ( ap @ ( ap @ Lst @ Ys3 ) @ Zs2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[13]) ).

thf(15,plain,
    ( ( ! [Ys2: lst,Xs: lst,X: a] :
          ( ( ap @ ( cns @ X @ Xs ) @ Ys2 )
          = ( cns @ X @ ( ap @ Xs @ Ys2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[8]) ).

thf(16,plain,
    ( ( ! [Ys2: lst] :
          ( ( ap @ nl @ Ys2 )
          = Ys2 ) )
    = $true ),
    inference(copy,[status(thm)],[7]) ).

thf(17,plain,
    ( ( ( ( ap @ xs @ ( ap @ sK1_Ys @ sK2_SY17 ) )
       != ( ap @ ( ap @ xs @ sK1_Ys ) @ sK2_SY17 ) ) )
    = $true ),
    inference(copy,[status(thm)],[12]) ).

thf(18,plain,
    ( ( ( ( ap @ nl @ ( ap @ sK7_Ys @ sK8_SY28 ) )
       != ( ap @ ( ap @ nl @ sK7_Ys ) @ sK8_SY28 ) )
      | ~ ( ~ ! [SX0: lst,SX1: lst] :
                ( ( ap @ sK4_SY18 @ ( ap @ SX0 @ SX1 ) )
                = ( ap @ ( ap @ sK4_SY18 @ SX0 ) @ SX1 ) )
          | ~ ( ( ( ap @ ( cns @ sK3_A @ sK4_SY18 ) @ ( ap @ sK5_SY25 @ sK6_SY27 ) )
               != ( ap @ ( ap @ ( cns @ sK3_A @ sK4_SY18 ) @ sK5_SY25 ) @ sK6_SY27 ) ) ) )
      | ! [SX0: lst,SX1: lst,SX2: lst] :
          ( ( ap @ SX0 @ ( ap @ SX1 @ SX2 ) )
          = ( ap @ ( ap @ SX0 @ SX1 ) @ SX2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[14]) ).

thf(19,plain,
    ! [SV1: lst] :
      ( ( ! [SY29: lst,SY30: a] :
            ( ( ap @ ( cns @ SY30 @ SY29 ) @ SV1 )
            = ( cns @ SY30 @ ( ap @ SY29 @ SV1 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[15]) ).

thf(20,plain,
    ! [SV2: lst] :
      ( ( ( ap @ nl @ SV2 )
        = SV2 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[16]) ).

thf(21,plain,
    ( ( ( ap @ xs @ ( ap @ sK1_Ys @ sK2_SY17 ) )
      = ( ap @ ( ap @ xs @ sK1_Ys ) @ sK2_SY17 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[17]) ).

thf(22,plain,
    ( ( ( ( ( ap @ nl @ ( ap @ sK7_Ys @ sK8_SY28 ) )
         != ( ap @ ( ap @ nl @ sK7_Ys ) @ sK8_SY28 ) ) )
      = $true )
    | ( ( ~ ( ~ ! [SX0: lst,SX1: lst] :
                  ( ( ap @ sK4_SY18 @ ( ap @ SX0 @ SX1 ) )
                  = ( ap @ ( ap @ sK4_SY18 @ SX0 ) @ SX1 ) )
            | ~ ( ( ( ap @ ( cns @ sK3_A @ sK4_SY18 ) @ ( ap @ sK5_SY25 @ sK6_SY27 ) )
                 != ( ap @ ( ap @ ( cns @ sK3_A @ sK4_SY18 ) @ sK5_SY25 ) @ sK6_SY27 ) ) ) )
        | ! [SX0: lst,SX1: lst,SX2: lst] :
            ( ( ap @ SX0 @ ( ap @ SX1 @ SX2 ) )
            = ( ap @ ( ap @ SX0 @ SX1 ) @ SX2 ) ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[18]) ).

thf(23,plain,
    ! [SV1: lst,SV3: lst] :
      ( ( ! [SY31: a] :
            ( ( ap @ ( cns @ SY31 @ SV3 ) @ SV1 )
            = ( cns @ SY31 @ ( ap @ SV3 @ SV1 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[19]) ).

thf(24,plain,
    ( ( ( ( ap @ nl @ ( ap @ sK7_Ys @ sK8_SY28 ) )
        = ( ap @ ( ap @ nl @ sK7_Ys ) @ sK8_SY28 ) )
      = $false )
    | ( ( ~ ( ~ ! [SX0: lst,SX1: lst] :
                  ( ( ap @ sK4_SY18 @ ( ap @ SX0 @ SX1 ) )
                  = ( ap @ ( ap @ sK4_SY18 @ SX0 ) @ SX1 ) )
            | ~ ( ( ( ap @ ( cns @ sK3_A @ sK4_SY18 ) @ ( ap @ sK5_SY25 @ sK6_SY27 ) )
                 != ( ap @ ( ap @ ( cns @ sK3_A @ sK4_SY18 ) @ sK5_SY25 ) @ sK6_SY27 ) ) ) )
        | ! [SX0: lst,SX1: lst,SX2: lst] :
            ( ( ap @ SX0 @ ( ap @ SX1 @ SX2 ) )
            = ( ap @ ( ap @ SX0 @ SX1 ) @ SX2 ) ) )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[22]) ).

thf(25,plain,
    ! [SV1: lst,SV3: lst,SV4: a] :
      ( ( ( ap @ ( cns @ SV4 @ SV3 ) @ SV1 )
        = ( cns @ SV4 @ ( ap @ SV3 @ SV1 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[23]) ).

thf(26,plain,
    ( ( ( ~ ( ~ ! [SX0: lst,SX1: lst] :
                  ( ( ap @ sK4_SY18 @ ( ap @ SX0 @ SX1 ) )
                  = ( ap @ ( ap @ sK4_SY18 @ SX0 ) @ SX1 ) )
            | ~ ( ( ( ap @ ( cns @ sK3_A @ sK4_SY18 ) @ ( ap @ sK5_SY25 @ sK6_SY27 ) )
                 != ( ap @ ( ap @ ( cns @ sK3_A @ sK4_SY18 ) @ sK5_SY25 ) @ sK6_SY27 ) ) ) ) )
      = $true )
    | ( ( ! [SX0: lst,SX1: lst,SX2: lst] :
            ( ( ap @ SX0 @ ( ap @ SX1 @ SX2 ) )
            = ( ap @ ( ap @ SX0 @ SX1 ) @ SX2 ) ) )
      = $true )
    | ( ( ( ap @ nl @ ( ap @ sK7_Ys @ sK8_SY28 ) )
        = ( ap @ ( ap @ nl @ sK7_Ys ) @ sK8_SY28 ) )
      = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[24]) ).

thf(27,plain,
    ( ( ( ~ ! [SX0: lst,SX1: lst] :
              ( ( ap @ sK4_SY18 @ ( ap @ SX0 @ SX1 ) )
              = ( ap @ ( ap @ sK4_SY18 @ SX0 ) @ SX1 ) )
        | ~ ( ( ( ap @ ( cns @ sK3_A @ sK4_SY18 ) @ ( ap @ sK5_SY25 @ sK6_SY27 ) )
             != ( ap @ ( ap @ ( cns @ sK3_A @ sK4_SY18 ) @ sK5_SY25 ) @ sK6_SY27 ) ) ) )
      = $false )
    | ( ( ! [SX0: lst,SX1: lst,SX2: lst] :
            ( ( ap @ SX0 @ ( ap @ SX1 @ SX2 ) )
            = ( ap @ ( ap @ SX0 @ SX1 ) @ SX2 ) ) )
      = $true )
    | ( ( ( ap @ nl @ ( ap @ sK7_Ys @ sK8_SY28 ) )
        = ( ap @ ( ap @ nl @ sK7_Ys ) @ sK8_SY28 ) )
      = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[26]) ).

thf(28,plain,
    ( ( ( ~ ! [SX0: lst,SX1: lst] :
              ( ( ap @ sK4_SY18 @ ( ap @ SX0 @ SX1 ) )
              = ( ap @ ( ap @ sK4_SY18 @ SX0 ) @ SX1 ) ) )
      = $false )
    | ( ( ! [SX0: lst,SX1: lst,SX2: lst] :
            ( ( ap @ SX0 @ ( ap @ SX1 @ SX2 ) )
            = ( ap @ ( ap @ SX0 @ SX1 ) @ SX2 ) ) )
      = $true )
    | ( ( ( ap @ nl @ ( ap @ sK7_Ys @ sK8_SY28 ) )
        = ( ap @ ( ap @ nl @ sK7_Ys ) @ sK8_SY28 ) )
      = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[27]) ).

thf(29,plain,
    ( ( ( ~ ( ( ( ap @ ( cns @ sK3_A @ sK4_SY18 ) @ ( ap @ sK5_SY25 @ sK6_SY27 ) )
             != ( ap @ ( ap @ ( cns @ sK3_A @ sK4_SY18 ) @ sK5_SY25 ) @ sK6_SY27 ) ) ) )
      = $false )
    | ( ( ! [SX0: lst,SX1: lst,SX2: lst] :
            ( ( ap @ SX0 @ ( ap @ SX1 @ SX2 ) )
            = ( ap @ ( ap @ SX0 @ SX1 ) @ SX2 ) ) )
      = $true )
    | ( ( ( ap @ nl @ ( ap @ sK7_Ys @ sK8_SY28 ) )
        = ( ap @ ( ap @ nl @ sK7_Ys ) @ sK8_SY28 ) )
      = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[27]) ).

thf(30,plain,
    ( ( ( ! [SX0: lst,SX1: lst] :
            ( ( ap @ sK4_SY18 @ ( ap @ SX0 @ SX1 ) )
            = ( ap @ ( ap @ sK4_SY18 @ SX0 ) @ SX1 ) ) )
      = $true )
    | ( ( ! [SX0: lst,SX1: lst,SX2: lst] :
            ( ( ap @ SX0 @ ( ap @ SX1 @ SX2 ) )
            = ( ap @ ( ap @ SX0 @ SX1 ) @ SX2 ) ) )
      = $true )
    | ( ( ( ap @ nl @ ( ap @ sK7_Ys @ sK8_SY28 ) )
        = ( ap @ ( ap @ nl @ sK7_Ys ) @ sK8_SY28 ) )
      = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[28]) ).

thf(31,plain,
    ( ( ( ( ( ap @ ( cns @ sK3_A @ sK4_SY18 ) @ ( ap @ sK5_SY25 @ sK6_SY27 ) )
         != ( ap @ ( ap @ ( cns @ sK3_A @ sK4_SY18 ) @ sK5_SY25 ) @ sK6_SY27 ) ) )
      = $true )
    | ( ( ! [SX0: lst,SX1: lst,SX2: lst] :
            ( ( ap @ SX0 @ ( ap @ SX1 @ SX2 ) )
            = ( ap @ ( ap @ SX0 @ SX1 ) @ SX2 ) ) )
      = $true )
    | ( ( ( ap @ nl @ ( ap @ sK7_Ys @ sK8_SY28 ) )
        = ( ap @ ( ap @ nl @ sK7_Ys ) @ sK8_SY28 ) )
      = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[29]) ).

thf(32,plain,
    ! [SV5: lst] :
      ( ( ( ! [SY32: lst] :
              ( ( ap @ sK4_SY18 @ ( ap @ SV5 @ SY32 ) )
              = ( ap @ ( ap @ sK4_SY18 @ SV5 ) @ SY32 ) ) )
        = $true )
      | ( ( ! [SX0: lst,SX1: lst,SX2: lst] :
              ( ( ap @ SX0 @ ( ap @ SX1 @ SX2 ) )
              = ( ap @ ( ap @ SX0 @ SX1 ) @ SX2 ) ) )
        = $true )
      | ( ( ( ap @ nl @ ( ap @ sK7_Ys @ sK8_SY28 ) )
          = ( ap @ ( ap @ nl @ sK7_Ys ) @ sK8_SY28 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[30]) ).

thf(33,plain,
    ( ( ( ( ap @ ( cns @ sK3_A @ sK4_SY18 ) @ ( ap @ sK5_SY25 @ sK6_SY27 ) )
        = ( ap @ ( ap @ ( cns @ sK3_A @ sK4_SY18 ) @ sK5_SY25 ) @ sK6_SY27 ) )
      = $false )
    | ( ( ! [SX0: lst,SX1: lst,SX2: lst] :
            ( ( ap @ SX0 @ ( ap @ SX1 @ SX2 ) )
            = ( ap @ ( ap @ SX0 @ SX1 ) @ SX2 ) ) )
      = $true )
    | ( ( ( ap @ nl @ ( ap @ sK7_Ys @ sK8_SY28 ) )
        = ( ap @ ( ap @ nl @ sK7_Ys ) @ sK8_SY28 ) )
      = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[31]) ).

thf(34,plain,
    ! [SV6: lst,SV5: lst] :
      ( ( ( ( ap @ sK4_SY18 @ ( ap @ SV5 @ SV6 ) )
          = ( ap @ ( ap @ sK4_SY18 @ SV5 ) @ SV6 ) )
        = $true )
      | ( ( ! [SX0: lst,SX1: lst,SX2: lst] :
              ( ( ap @ SX0 @ ( ap @ SX1 @ SX2 ) )
              = ( ap @ ( ap @ SX0 @ SX1 ) @ SX2 ) ) )
        = $true )
      | ( ( ( ap @ nl @ ( ap @ sK7_Ys @ sK8_SY28 ) )
          = ( ap @ ( ap @ nl @ sK7_Ys ) @ sK8_SY28 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[32]) ).

thf(35,plain,
    ! [SV7: lst] :
      ( ( ( ! [SY33: lst,SY34: lst] :
              ( ( ap @ SV7 @ ( ap @ SY33 @ SY34 ) )
              = ( ap @ ( ap @ SV7 @ SY33 ) @ SY34 ) ) )
        = $true )
      | ( ( ( ap @ ( cns @ sK3_A @ sK4_SY18 ) @ ( ap @ sK5_SY25 @ sK6_SY27 ) )
          = ( ap @ ( ap @ ( cns @ sK3_A @ sK4_SY18 ) @ sK5_SY25 ) @ sK6_SY27 ) )
        = $false )
      | ( ( ( ap @ nl @ ( ap @ sK7_Ys @ sK8_SY28 ) )
          = ( ap @ ( ap @ nl @ sK7_Ys ) @ sK8_SY28 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[33]) ).

thf(36,plain,
    ! [SV6: lst,SV5: lst,SV8: lst] :
      ( ( ( ! [SY35: lst,SY36: lst] :
              ( ( ap @ SV8 @ ( ap @ SY35 @ SY36 ) )
              = ( ap @ ( ap @ SV8 @ SY35 ) @ SY36 ) ) )
        = $true )
      | ( ( ( ap @ sK4_SY18 @ ( ap @ SV5 @ SV6 ) )
          = ( ap @ ( ap @ sK4_SY18 @ SV5 ) @ SV6 ) )
        = $true )
      | ( ( ( ap @ nl @ ( ap @ sK7_Ys @ sK8_SY28 ) )
          = ( ap @ ( ap @ nl @ sK7_Ys ) @ sK8_SY28 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[34]) ).

thf(37,plain,
    ! [SV9: lst,SV7: lst] :
      ( ( ( ! [SY37: lst] :
              ( ( ap @ SV7 @ ( ap @ SV9 @ SY37 ) )
              = ( ap @ ( ap @ SV7 @ SV9 ) @ SY37 ) ) )
        = $true )
      | ( ( ( ap @ ( cns @ sK3_A @ sK4_SY18 ) @ ( ap @ sK5_SY25 @ sK6_SY27 ) )
          = ( ap @ ( ap @ ( cns @ sK3_A @ sK4_SY18 ) @ sK5_SY25 ) @ sK6_SY27 ) )
        = $false )
      | ( ( ( ap @ nl @ ( ap @ sK7_Ys @ sK8_SY28 ) )
          = ( ap @ ( ap @ nl @ sK7_Ys ) @ sK8_SY28 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[35]) ).

thf(38,plain,
    ! [SV6: lst,SV5: lst,SV10: lst,SV8: lst] :
      ( ( ( ! [SY38: lst] :
              ( ( ap @ SV8 @ ( ap @ SV10 @ SY38 ) )
              = ( ap @ ( ap @ SV8 @ SV10 ) @ SY38 ) ) )
        = $true )
      | ( ( ( ap @ sK4_SY18 @ ( ap @ SV5 @ SV6 ) )
          = ( ap @ ( ap @ sK4_SY18 @ SV5 ) @ SV6 ) )
        = $true )
      | ( ( ( ap @ nl @ ( ap @ sK7_Ys @ sK8_SY28 ) )
          = ( ap @ ( ap @ nl @ sK7_Ys ) @ sK8_SY28 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[36]) ).

thf(39,plain,
    ! [SV11: lst,SV9: lst,SV7: lst] :
      ( ( ( ( ap @ SV7 @ ( ap @ SV9 @ SV11 ) )
          = ( ap @ ( ap @ SV7 @ SV9 ) @ SV11 ) )
        = $true )
      | ( ( ( ap @ ( cns @ sK3_A @ sK4_SY18 ) @ ( ap @ sK5_SY25 @ sK6_SY27 ) )
          = ( ap @ ( ap @ ( cns @ sK3_A @ sK4_SY18 ) @ sK5_SY25 ) @ sK6_SY27 ) )
        = $false )
      | ( ( ( ap @ nl @ ( ap @ sK7_Ys @ sK8_SY28 ) )
          = ( ap @ ( ap @ nl @ sK7_Ys ) @ sK8_SY28 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[37]) ).

thf(40,plain,
    ! [SV6: lst,SV5: lst,SV12: lst,SV10: lst,SV8: lst] :
      ( ( ( ( ap @ SV8 @ ( ap @ SV10 @ SV12 ) )
          = ( ap @ ( ap @ SV8 @ SV10 ) @ SV12 ) )
        = $true )
      | ( ( ( ap @ sK4_SY18 @ ( ap @ SV5 @ SV6 ) )
          = ( ap @ ( ap @ sK4_SY18 @ SV5 ) @ SV6 ) )
        = $true )
      | ( ( ( ap @ nl @ ( ap @ sK7_Ys @ sK8_SY28 ) )
          = ( ap @ ( ap @ nl @ sK7_Ys ) @ sK8_SY28 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[38]) ).

thf(41,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[20,40,39,25,21]) ).

thf(42,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[41]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : DAT056^1 : TPTP v8.1.0. Released v5.4.0.
% 0.03/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33  % Computer : n006.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.34  % DateTime : Fri Jul  1 20:35:52 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  
% 0.12/0.34   No.of.Axioms: 3
% 0.12/0.34  
% 0.12/0.34   Length.of.Defs: 0
% 0.12/0.34  
% 0.12/0.34   Contains.Choice.Funs: false
% 0.12/0.35  (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:5,loop_count:0,foatp_calls:0,translation:fof_full)....
% 0.18/0.40  
% 0.18/0.40  ********************************
% 0.18/0.40  *   All subproblems solved!    *
% 0.18/0.40  ********************************
% 0.18/0.40  % 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:41,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.18/0.40  
% 0.18/0.40  %**** Beginning of derivation protocol ****
% 0.18/0.40  % SZS output start CNFRefutation
% See solution above
% 0.18/0.40  
% 0.18/0.40  %**** End of derivation protocol ****
% 0.18/0.40  %**** no. of clauses in derivation: 42 ****
% 0.18/0.40  %**** clause counter: 41 ****
% 0.18/0.40  
% 0.18/0.40  % 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:41,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------