TSTP Solution File: ITP013+1 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : ITP013+1 : TPTP v8.2.0. Bugfixed v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n004.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  : 300s
% DateTime : Mon May 20 22:21:38 EDT 2024

% Result   : Theorem 6.20s 2.57s
% Output   : Refutation 6.68s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   88
% Syntax   : Number of formulae    :  136 (  44 unt;  42 typ;   0 def)
%            Number of atoms       :  284 (  94 equ;   0 cnn)
%            Maximal formula atoms :   25 (   3 avg)
%            Number of connectives : 3102 (  21   ~;   8   |;  57   &;2891   @)
%                                         (  26 <=>;  99  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   35 (  35   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   44 (  42 usr;  23 con; 0-3 aty)
%            Number of variables   :  241 (   0   ^ 238   !;   3   ?; 241   :)

% Comments : 
%------------------------------------------------------------------------------
thf(p_type,type,
    p: $i > $o ).

thf(s_type,type,
    s: $i > $i > $i ).

thf(tyop_2Emin_2Ebool_type,type,
    tyop_2Emin_2Ebool: $i ).

thf(c_2Earithmetic_2E_3C_3D_2E2_type,type,
    c_2Earithmetic_2E_3C_3D_2E2: $i > $i > $i ).

thf(tyop_2Enum_2Enum_type,type,
    tyop_2Enum_2Enum: $i ).

thf(tyop_2Efcp_2Ecart_type,type,
    tyop_2Efcp_2Ecart: $i > $i > $i ).

thf(c_2Ewords_2En2w_2E1_type,type,
    c_2Ewords_2En2w_2E1: $i > $i ).

thf(c_2Earithmetic_2E_2D_2E2_type,type,
    c_2Earithmetic_2E_2D_2E2: $i > $i > $i ).

thf(c_2Ewords_2Eword__sub_2E2_type,type,
    c_2Ewords_2Eword__sub_2E2: $i > $i > $i ).

thf(c_2Ebool_2ET_2E0_type,type,
    c_2Ebool_2ET_2E0: $i ).

thf(c_2Ebool_2EF_2E0_type,type,
    c_2Ebool_2EF_2E0: $i ).

thf(c_2Ebool_2E_3F_2E1_type,type,
    c_2Ebool_2E_3F_2E1: $i > $i ).

thf(tyop_2Emin_2Efun_type,type,
    tyop_2Emin_2Efun: $i > $i > $i ).

thf(app_2E2_type,type,
    app_2E2: $i > $i > $i ).

thf(c_2Ebool_2E_7E_2E0_type,type,
    c_2Ebool_2E_7E_2E0: $i ).

thf(c_2Ebool_2E_7E_2E1_type,type,
    c_2Ebool_2E_7E_2E1: $i > $i ).

thf(c_2Ewords_2Eword__add_2E2_type,type,
    c_2Ewords_2Eword__add_2E2: $i > $i > $i ).

thf(c_2Ewords_2Eword__add_2E0_type,type,
    c_2Ewords_2Eword__add_2E0: $i ).

thf(c_2Ewords_2Eword__2comp_2E1_type,type,
    c_2Ewords_2Eword__2comp_2E1: $i > $i ).

thf(c_2Earithmetic_2E_2B_2E2_type,type,
    c_2Earithmetic_2E_2B_2E2: $i > $i > $i ).

thf(c_2Ebool_2ECOND_2E3_type,type,
    c_2Ebool_2ECOND_2E3: $i > $i > $i > $i ).

thf(c_2Ewords_2Eword__2comp_2E0_type,type,
    c_2Ewords_2Eword__2comp_2E0: $i ).

thf(c_2Emin_2E_3D_3D_3E_2E0_type,type,
    c_2Emin_2E_3D_3D_3E_2E0: $i ).

thf(c_2Earithmetic_2E_2B_2E0_type,type,
    c_2Earithmetic_2E_2B_2E0: $i ).

thf(combin_k_2E0_type,type,
    combin_k_2E0: $i ).

thf(c_2Ebool_2ECOND_2E0_type,type,
    c_2Ebool_2ECOND_2E0: $i ).

thf(c_2Ewords_2En2w_2E0_type,type,
    c_2Ewords_2En2w_2E0: $i ).

thf(c_2Ebool_2E_21_2E1_type,type,
    c_2Ebool_2E_21_2E1: $i > $i ).

thf(c_2Ebool_2E_21_2E0_type,type,
    c_2Ebool_2E_21_2E0: $i ).

thf(c_2Emin_2E_3D_2E0_type,type,
    c_2Emin_2E_3D_2E0: $i ).

thf(c_2Earithmetic_2E_3C_3D_2E0_type,type,
    c_2Earithmetic_2E_3C_3D_2E0: $i ).

thf(c_2Ebool_2E_3F_2E0_type,type,
    c_2Ebool_2E_3F_2E0: $i ).

thf(c_2Ewords_2Eword__sub_2E0_type,type,
    c_2Ewords_2Eword__sub_2E0: $i ).

thf(c_2Earithmetic_2E_2D_2E0_type,type,
    c_2Earithmetic_2E_2D_2E0: $i ).

thf(c_2Ebool_2E_5C_2F_2E0_type,type,
    c_2Ebool_2E_5C_2F_2E0: $i ).

thf(c_2Ebool_2E_2F_5C_2E2_type,type,
    c_2Ebool_2E_2F_5C_2E2: $i > $i > $i ).

thf(c_2Ebool_2E_5C_2F_2E2_type,type,
    c_2Ebool_2E_5C_2F_2E2: $i > $i > $i ).

thf(c_2Emin_2E_3D_3D_3E_2E2_type,type,
    c_2Emin_2E_3D_3D_3E_2E2: $i > $i > $i ).

thf(combin_s_2E0_type,type,
    combin_s_2E0: $i ).

thf(c_2Ebool_2E_2F_5C_2E0_type,type,
    c_2Ebool_2E_2F_5C_2E0: $i ).

thf(combin_i_2E0_type,type,
    combin_i_2E0: $i ).

thf(c_2Emin_2E_3D_2E2_type,type,
    c_2Emin_2E_3D_2E2: $i > $i > $i ).

thf(31,axiom,
    ! [A: $i,B: $i] :
      ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) ) )
      = ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) @ c_2Ewords_2Eword__2comp_2E0 ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ewords_2Eword__2comp_2E1_2Emono_2EA_27b) ).

thf(217,plain,
    ! [A: $i,B: $i] :
      ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) ) )
      = ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) @ c_2Ewords_2Eword__2comp_2E0 ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(17,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ A ) ) @ combin_k_2E0 ) @ ( s @ A @ C ) ) ) @ ( s @ B @ D ) ) )
      = ( s @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Ek__thm) ).

thf(153,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ A ) ) @ combin_k_2E0 ) @ ( s @ A @ C ) ) ) @ ( s @ B @ D ) ) )
      = ( s @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(25,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( s @ A @ B )
        = ( s @ A @ C ) )
    <=> ( ( s @ A @ C )
        = ( s @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__SYM__EQ) ).

thf(185,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( s @ A @ B )
          = ( s @ A @ C ) )
       => ( ( s @ A @ C )
          = ( s @ A @ B ) ) )
      & ( ( ( s @ A @ C )
          = ( s @ A @ B ) )
       => ( ( s @ A @ B )
          = ( s @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(29,axiom,
    ! [A: $i,B: $i] :
      ( ( s @ tyop_2Emin_2Ebool @ ( c_2Earithmetic_2E_3C_3D_2E2 @ ( s @ tyop_2Enum_2Enum @ A ) @ ( s @ tyop_2Enum_2Enum @ B ) ) )
      = ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ c_2Earithmetic_2E_3C_3D_2E0 ) @ ( s @ tyop_2Enum_2Enum @ A ) ) ) @ ( s @ tyop_2Enum_2Enum @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2) ).

thf(211,plain,
    ! [A: $i,B: $i] :
      ( ( s @ tyop_2Emin_2Ebool @ ( c_2Earithmetic_2E_3C_3D_2E2 @ ( s @ tyop_2Enum_2Enum @ A ) @ ( s @ tyop_2Enum_2Enum @ B ) ) )
      = ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ c_2Earithmetic_2E_3C_3D_2E0 ) @ ( s @ tyop_2Enum_2Enum @ A ) ) ) @ ( s @ tyop_2Enum_2Enum @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(18,axiom,
    ! [A: $i,B: $i] :
      ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
      <=> ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) )
     => ( ( s @ tyop_2Emin_2Ebool @ A )
        = ( s @ tyop_2Emin_2Ebool @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Eboolext) ).

thf(156,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
         => ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) )
        & ( ( p @ ( s @ tyop_2Emin_2Ebool @ B ) )
         => ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) )
     => ( ( s @ tyop_2Emin_2Ebool @ A )
        = ( s @ tyop_2Emin_2Ebool @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(12,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( s @ tyop_2Emin_2Ebool @ A )
          = ( s @ tyop_2Emin_2Ebool @ B ) )
        & ( ( p @ ( s @ tyop_2Emin_2Ebool @ B ) )
         => ( ( s @ tyop_2Emin_2Ebool @ C )
            = ( s @ tyop_2Emin_2Ebool @ D ) ) ) )
     => ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
         => ( p @ ( s @ tyop_2Emin_2Ebool @ C ) ) )
      <=> ( ( p @ ( s @ tyop_2Emin_2Ebool @ B ) )
         => ( p @ ( s @ tyop_2Emin_2Ebool @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__CONG) ).

thf(129,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( s @ tyop_2Emin_2Ebool @ A )
          = ( s @ tyop_2Emin_2Ebool @ B ) )
        & ( ( p @ ( s @ tyop_2Emin_2Ebool @ B ) )
         => ( ( s @ tyop_2Emin_2Ebool @ C )
            = ( s @ tyop_2Emin_2Ebool @ D ) ) ) )
     => ( ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
           => ( p @ ( s @ tyop_2Emin_2Ebool @ C ) ) )
         => ( ( p @ ( s @ tyop_2Emin_2Ebool @ B ) )
           => ( p @ ( s @ tyop_2Emin_2Ebool @ D ) ) ) )
        & ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ B ) )
           => ( p @ ( s @ tyop_2Emin_2Ebool @ D ) ) )
         => ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
           => ( p @ ( s @ tyop_2Emin_2Ebool @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(43,axiom,
    ! [A: $i,B: $i] :
      ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
        & ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) )
    <=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_2F_5C_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) ).

thf(266,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
          & ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) )
       => ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_2F_5C_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) ) )
      & ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_2F_5C_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) )
       => ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
          & ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(28,axiom,
    ! [A: $i,B: $i] :
      ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ B ) ) )
      = ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) @ c_2Ewords_2En2w_2E0 ) @ ( s @ tyop_2Enum_2Enum @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2EA_27a) ).

thf(208,plain,
    ! [A: $i,B: $i] :
      ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ B ) ) )
      = ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) @ c_2Ewords_2En2w_2E0 ) @ ( s @ tyop_2Enum_2Enum @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(8,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2Eword__add_2E2 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ C ) ) )
      = ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) ) @ c_2Ewords_2Eword__add_2E0 ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Ewords_2Eword__add_2E2_2Emono_2EA_27b) ).

thf(91,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2Eword__add_2E2 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ C ) ) )
      = ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) ) @ c_2Ewords_2Eword__add_2E0 ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(27,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( ( ( s @ tyop_2Emin_2Ebool @ B )
          = ( s @ tyop_2Emin_2Ebool @ C ) )
        & ( ( p @ ( s @ tyop_2Emin_2Ebool @ C ) )
         => ( ( s @ A @ D )
            = ( s @ A @ E ) ) )
        & ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ C ) )
         => ( ( s @ A @ F )
            = ( s @ A @ G ) ) ) )
     => ( ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ B ) @ ( s @ A @ D ) @ ( s @ A @ F ) ) )
        = ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ C ) @ ( s @ A @ E ) @ ( s @ A @ G ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__CONG) ).

thf(199,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( ( ( s @ tyop_2Emin_2Ebool @ B )
          = ( s @ tyop_2Emin_2Ebool @ C ) )
        & ( ( p @ ( s @ tyop_2Emin_2Ebool @ C ) )
         => ( ( s @ A @ D )
            = ( s @ A @ E ) ) )
        & ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ C ) )
         => ( ( s @ A @ F )
            = ( s @ A @ G ) ) ) )
     => ( ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ B ) @ ( s @ A @ D ) @ ( s @ A @ F ) ) )
        = ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ C ) @ ( s @ A @ E ) @ ( s @ A @ G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(21,axiom,
    ! [A: $i] :
      ( ! [B: $i,C: $i] :
          ( ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) @ ( s @ A @ B ) @ ( s @ A @ C ) ) )
          = ( s @ A @ B ) )
      & ! [B: $i,C: $i] :
          ( ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) @ ( s @ A @ B ) @ ( s @ A @ C ) ) )
          = ( s @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2Ebool__case__thm) ).

thf(171,plain,
    ! [A: $i] :
      ( ! [B: $i,C: $i] :
          ( ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) @ ( s @ A @ B ) @ ( s @ A @ C ) ) )
          = ( s @ A @ B ) )
      & ! [B: $i,C: $i] :
          ( ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) @ ( s @ A @ B ) @ ( s @ A @ C ) ) )
          = ( s @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(22,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2Eword__sub_2E2 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ C ) ) )
      = ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2Eword__add_2E2 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Eword__sub__def) ).

thf(178,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2Eword__sub_2E2 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ C ) ) )
      = ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2Eword__add_2E2 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(7,axiom,
    ! [A: $i,B: $i] :
      ( ( ( s @ A @ B )
        = ( s @ A @ B ) )
    <=> ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EREFL__CLAUSE) ).

thf(90,plain,
    p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(13,axiom,
    ! [A: $i,B: $i] :
      ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
       => ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) )
    <=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_3D_3E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) ).

thf(138,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
         => ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) )
       => ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_3D_3E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) ) )
      & ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_3D_3E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) )
       => ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
         => ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(10,axiom,
    ! [A: $i,B: $i] :
      ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) ) )
      = ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) @ c_2Ewords_2Eword__2comp_2E0 ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ewords_2Eword__2comp_2E1_2Emono_2EA_27a) ).

thf(101,plain,
    ! [A: $i,B: $i] :
      ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) ) )
      = ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) @ c_2Ewords_2Eword__2comp_2E0 ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(40,axiom,
    ! [A: $i,B: $i] :
      ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ A ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) )
    <=> ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
        | ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Elogic_2E_5C_2F) ).

thf(249,plain,
    ! [A: $i,B: $i] :
      ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ A ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) )
       => ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
          | ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) )
      & ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
          | ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) )
       => ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ A ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(36,axiom,
    p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Etruth) ).

thf(234,plain,
    p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(3,axiom,
    ! [A: $i] :
      ( ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
         => ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) )
      <=> ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) )
      & ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
         => ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) ) )
      <=> ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) ) )
      & ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) )
         => ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) )
      <=> ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) ) )
      & ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
         => ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) )
      <=> ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) ) )
      & ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
         => ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ) )
      <=> ~ ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__CLAUSES) ).

thf(52,plain,
    ! [A: $i] :
      ( ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
         => ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) )
       => ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) )
      & ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
       => ( ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
         => ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) )
      & ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
         => ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) ) )
       => ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) ) )
      & ( ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
       => ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
         => ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) ) ) )
      & ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) )
         => ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) )
       => ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) ) )
      & ( ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
       => ( ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) )
         => ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) )
      & ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
      & ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
         => ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ) )
       => ~ ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) )
      & ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
       => ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
         => ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(24,axiom,
    p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ETRUTH) ).

thf(184,plain,
    p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(45,axiom,
    ! [A: $i,B: $i] :
      ( ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ A ) @ combin_i_2E0 ) @ ( s @ A @ B ) ) )
      = ( s @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Ei__thm) ).

thf(284,plain,
    ! [A: $i,B: $i] :
      ( ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ A ) @ combin_i_2E0 ) @ ( s @ A @ B ) ) )
      = ( s @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(34,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2Eword__sub_2E2 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ C ) ) )
      = ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) ) @ c_2Ewords_2Eword__sub_2E0 ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Ewords_2Eword__sub_2E2_2Emono_2EA_27a) ).

thf(228,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2Eword__sub_2E2 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ C ) ) )
      = ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) ) @ c_2Ewords_2Eword__sub_2E0 ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(15,axiom,
    ! [A: $i] :
      ( ( ( s @ tyop_2Emin_2Ebool @ A )
        = ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
      | ( ( s @ tyop_2Emin_2Ebool @ A )
        = ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Ebool__cases__ax) ).

thf(147,plain,
    ! [A: $i] :
      ( ( ( s @ tyop_2Emin_2Ebool @ A )
        = ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
      | ( ( s @ tyop_2Emin_2Ebool @ A )
        = ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(39,axiom,
    ! [A: $i,B: $i] :
      ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ A ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) )
    <=> ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
        & ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Elogic_2E_2F_5C) ).

thf(243,plain,
    ! [A: $i,B: $i] :
      ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ A ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) )
       => ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
          & ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) )
      & ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
          & ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) )
       => ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ A ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(6,axiom,
    ! [A: $i] :
      ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_7E_2E1 @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) )
    <=> ~ ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Elogic_2E_7E) ).

thf(85,plain,
    ! [A: $i] :
      ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_7E_2E1 @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) )
       => ~ ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) )
      & ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
       => ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_7E_2E1 @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(32,axiom,
    ! [A: $i,B: $i] :
      ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) )
    <=> ! [C: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Equant_2E_21) ).

thf(220,plain,
    ! [A: $i,B: $i] :
      ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) )
       => ! [C: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) ) )
      & ( ! [C: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) )
       => ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(26,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( s @ A @ B )
        = ( s @ A @ C ) )
    <=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ A @ B ) ) ) @ ( s @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) ).

thf(192,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( s @ A @ B )
          = ( s @ A @ C ) )
       => ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ A @ B ) ) ) @ ( s @ A @ C ) ) ) ) )
      & ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ A @ B ) ) ) @ ( s @ A @ C ) ) ) )
       => ( ( s @ A @ B )
          = ( s @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(19,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ B ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ C ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ D ) ) )
      = ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) ) ) @ c_2Ebool_2ECOND_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ C ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27b_29) ).

thf(165,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ B ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ C ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ D ) ) )
      = ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) ) ) @ c_2Ebool_2ECOND_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ C ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(41,axiom,
    ! [A: $i,B: $i] :
      ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ A ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) )
    <=> ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
       => ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Elogic_2E_3D_3D_3E) ).

thf(256,plain,
    ! [A: $i,B: $i] :
      ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ A ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) )
       => ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
         => ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) )
      & ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
         => ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) )
       => ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ A ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(33,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2Eword__add_2E2 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ C ) ) )
      = ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) ) @ c_2Ewords_2Eword__add_2E0 ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Ewords_2Eword__add_2E2_2Emono_2EA_27a) ).

thf(225,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2Eword__add_2E2 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ C ) ) )
      = ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) ) @ c_2Ewords_2Eword__add_2E0 ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(14,axiom,
    ! [A: $i,B: $i] :
      ( ( s @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2E_2B_2E2 @ ( s @ tyop_2Enum_2Enum @ A ) @ ( s @ tyop_2Enum_2Enum @ B ) ) )
      = ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ c_2Earithmetic_2E_2B_2E0 ) @ ( s @ tyop_2Enum_2Enum @ A ) ) ) @ ( s @ tyop_2Enum_2Enum @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Earithmetic_2E_2B_2E2) ).

thf(144,plain,
    ! [A: $i,B: $i] :
      ( ( s @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2E_2B_2E2 @ ( s @ tyop_2Enum_2Enum @ A ) @ ( s @ tyop_2Enum_2Enum @ B ) ) )
      = ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ c_2Earithmetic_2E_2B_2E0 ) @ ( s @ tyop_2Enum_2Enum @ A ) ) ) @ ( s @ tyop_2Enum_2Enum @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(23,axiom,
    ! [A: $i,B: $i] :
      ( ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) )
      = ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_21_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) ).

thf(181,plain,
    ! [A: $i,B: $i] :
      ( ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) )
      = ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_21_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(38,axiom,
    ~ ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Enotfalse) ).

thf(241,plain,
    ~ ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(5,axiom,
    ! [A: $i] :
      ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
    <=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_7E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_7E_2E1) ).

thf(80,plain,
    ! [A: $i] :
      ( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
       => ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_7E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) ) )
      & ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_7E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) )
       => ~ ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(1,conjecture,
    ! [A: $i,B: $i,C: $i] :
      ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Earithmetic_2E_3C_3D_2E2 @ ( s @ tyop_2Enum_2Enum @ C ) @ ( s @ tyop_2Enum_2Enum @ B ) ) ) )
     => ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2E_2D_2E2 @ ( s @ tyop_2Enum_2Enum @ B ) @ ( s @ tyop_2Enum_2Enum @ C ) ) ) ) )
        = ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2Eword__sub_2E2 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ B ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2En2w__sub) ).

thf(2,negated_conjecture,
    ~ ! [A: $i,B: $i,C: $i] :
        ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Earithmetic_2E_3C_3D_2E2 @ ( s @ tyop_2Enum_2Enum @ C ) @ ( s @ tyop_2Enum_2Enum @ B ) ) ) )
       => ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2E_2D_2E2 @ ( s @ tyop_2Enum_2Enum @ B ) @ ( s @ tyop_2Enum_2Enum @ C ) ) ) ) )
          = ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2Eword__sub_2E2 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ B ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ C ) ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(48,plain,
    ~ ! [A: $i,B: $i,C: $i] :
        ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Earithmetic_2E_3C_3D_2E2 @ ( s @ tyop_2Enum_2Enum @ C ) @ ( s @ tyop_2Enum_2Enum @ B ) ) ) )
       => ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2E_2D_2E2 @ ( s @ tyop_2Enum_2Enum @ B ) @ ( s @ tyop_2Enum_2Enum @ C ) ) ) ) )
          = ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2Eword__sub_2E2 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ B ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ C ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(16,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ! [E: $i] :
          ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ E ) ) )
          = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ E ) ) ) )
     => ( ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C )
        = ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Eeq__ext) ).

thf(150,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ! [E: $i] :
          ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ E ) ) )
          = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ E ) ) ) )
     => ( ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C )
        = ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(42,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( s @ C @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ C ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ A @ C ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ A @ C ) ) ) @ combin_s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) ) ) @ ( s @ A @ F ) ) )
      = ( s @ C @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ C ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ D ) @ ( s @ A @ F ) ) ) @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) @ ( s @ A @ F ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Es__thm) ).

thf(263,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( s @ C @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ C ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ A @ C ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ A @ C ) ) ) @ combin_s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) ) ) @ ( s @ A @ F ) ) )
      = ( s @ C @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ C ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ D ) @ ( s @ A @ F ) ) ) @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) @ ( s @ A @ F ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(35,axiom,
    ! [A: $i,B: $i] :
      ( ( s @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2E_2D_2E2 @ ( s @ tyop_2Enum_2Enum @ A ) @ ( s @ tyop_2Enum_2Enum @ B ) ) )
      = ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ c_2Earithmetic_2E_2D_2E0 ) @ ( s @ tyop_2Enum_2Enum @ A ) ) ) @ ( s @ tyop_2Enum_2Enum @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Earithmetic_2E_2D_2E2) ).

thf(231,plain,
    ! [A: $i,B: $i] :
      ( ( s @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2E_2D_2E2 @ ( s @ tyop_2Enum_2Enum @ A ) @ ( s @ tyop_2Enum_2Enum @ B ) ) )
      = ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ c_2Earithmetic_2E_2D_2E0 ) @ ( s @ tyop_2Enum_2Enum @ A ) ) ) @ ( s @ tyop_2Enum_2Enum @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(11,axiom,
    ! [A: $i] :
      ( ( ( ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 )
          = ( s @ tyop_2Emin_2Ebool @ A ) )
      <=> ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) )
      & ( ( ( s @ tyop_2Emin_2Ebool @ A )
          = ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
      <=> ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) )
      & ( ( ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 )
          = ( s @ tyop_2Emin_2Ebool @ A ) )
      <=> ~ ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) )
      & ( ( ( s @ tyop_2Emin_2Ebool @ A )
          = ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) )
      <=> ~ ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__CLAUSES) ).

thf(104,plain,
    ! [A: $i] :
      ( ( ( ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 )
          = ( s @ tyop_2Emin_2Ebool @ A ) )
       => ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) )
      & ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
       => ( ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 )
          = ( s @ tyop_2Emin_2Ebool @ A ) ) )
      & ( ( ( s @ tyop_2Emin_2Ebool @ A )
          = ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
       => ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) )
      & ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
       => ( ( s @ tyop_2Emin_2Ebool @ A )
          = ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) ) )
      & ( ( ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 )
          = ( s @ tyop_2Emin_2Ebool @ A ) )
       => ~ ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) )
      & ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
       => ( ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 )
          = ( s @ tyop_2Emin_2Ebool @ A ) ) )
      & ( ( ( s @ tyop_2Emin_2Ebool @ A )
          = ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) )
       => ~ ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) )
      & ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
       => ( ( s @ tyop_2Emin_2Ebool @ A )
          = ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(4,axiom,
    ! [A: $i,B: $i] :
      ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) )
    <=> ? [C: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Equant_2E_3F) ).

thf(75,plain,
    ! [A: $i,B: $i] :
      ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) )
       => ? [C: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) ) )
      & ( ? [C: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) )
       => ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(37,axiom,
    ! [A: $i,B: $i] :
      ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
        | ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) )
    <=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_5C_2F_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) ).

thf(235,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
          | ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) )
       => ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_5C_2F_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) ) )
      & ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_5C_2F_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) )
       => ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
          | ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(30,axiom,
    ! [A: $i,B: $i] :
      ( ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) )
      = ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_3F_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) ).

thf(214,plain,
    ! [A: $i,B: $i] :
      ( ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) )
      = ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_3F_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(46,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ A @ B ) @ ( s @ A @ C ) ) ) )
    <=> ( ( s @ A @ B )
        = ( s @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Elogic_2E_3D) ).

thf(287,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ A @ B ) @ ( s @ A @ C ) ) ) )
       => ( ( s @ A @ B )
          = ( s @ A @ C ) ) )
      & ( ( ( s @ A @ B )
          = ( s @ A @ C ) )
       => ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ A @ B ) @ ( s @ A @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(20,axiom,
    ! [A: $i,B: $i] :
      ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ B ) ) )
      = ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) @ c_2Ewords_2En2w_2E0 ) @ ( s @ tyop_2Enum_2Enum @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2EA_27b) ).

thf(168,plain,
    ! [A: $i,B: $i] :
      ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ B ) ) )
      = ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) @ c_2Ewords_2En2w_2E0 ) @ ( s @ tyop_2Enum_2Enum @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(44,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
       => ( ( p @ ( s @ tyop_2Emin_2Ebool @ B ) )
         => ( p @ ( s @ tyop_2Emin_2Ebool @ C ) ) ) )
    <=> ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
          & ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) )
       => ( p @ ( s @ tyop_2Emin_2Ebool @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EAND__IMP__INTRO) ).

thf(273,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
         => ( ( p @ ( s @ tyop_2Emin_2Ebool @ B ) )
           => ( p @ ( s @ tyop_2Emin_2Ebool @ C ) ) ) )
       => ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
            & ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) )
         => ( p @ ( s @ tyop_2Emin_2Ebool @ C ) ) ) )
      & ( ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
            & ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) )
         => ( p @ ( s @ tyop_2Emin_2Ebool @ C ) ) )
       => ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
         => ( ( p @ ( s @ tyop_2Emin_2Ebool @ B ) )
           => ( p @ ( s @ tyop_2Emin_2Ebool @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(47,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ B ) @ ( s @ A @ C ) @ ( s @ A @ D ) ) )
      = ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) ) @ c_2Ebool_2ECOND_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) @ ( s @ A @ C ) ) ) @ ( s @ A @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a) ).

thf(294,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ B ) @ ( s @ A @ C ) @ ( s @ A @ D ) ) )
      = ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) ) @ c_2Ebool_2ECOND_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) @ ( s @ A @ C ) ) ) @ ( s @ A @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(9,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2Eword__add_2E2 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ C ) ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ D ) ) ) ) ) ) )
          = ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2E_2B_2E2 @ ( s @ tyop_2Enum_2Enum @ C ) @ ( s @ tyop_2Enum_2Enum @ D ) ) ) ) ) ) ) )
      & ! [C: $i,D: $i] :
          ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( c_2Ewords_2Eword__add_2E2 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ C ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ D ) ) ) ) ) ) )
          = ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( c_2Earithmetic_2E_3C_3D_2E2 @ ( s @ tyop_2Enum_2Enum @ D ) @ ( s @ tyop_2Enum_2Enum @ C ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2E_2D_2E2 @ ( s @ tyop_2Enum_2Enum @ C ) @ ( s @ tyop_2Enum_2Enum @ D ) ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2E_2D_2E2 @ ( s @ tyop_2Enum_2Enum @ D ) @ ( s @ tyop_2Enum_2Enum @ C ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LITERAL__ADD) ).

thf(94,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2Eword__add_2E2 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ C ) ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ D ) ) ) ) ) ) )
          = ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2E_2B_2E2 @ ( s @ tyop_2Enum_2Enum @ C ) @ ( s @ tyop_2Enum_2Enum @ D ) ) ) ) ) ) ) )
      & ! [C: $i,D: $i] :
          ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( c_2Ewords_2Eword__add_2E2 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ C ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ D ) ) ) ) ) ) )
          = ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( c_2Earithmetic_2E_3C_3D_2E2 @ ( s @ tyop_2Enum_2Enum @ D ) @ ( s @ tyop_2Enum_2Enum @ C ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2E_2D_2E2 @ ( s @ tyop_2Enum_2Enum @ C ) @ ( s @ tyop_2Enum_2Enum @ D ) ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2E_2D_2E2 @ ( s @ tyop_2Enum_2Enum @ D ) @ ( s @ tyop_2Enum_2Enum @ C ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(413,plain,
    $false,
    inference(cvc4,[status(thm)],[217,153,185,211,156,129,266,208,91,199,171,178,90,138,101,249,234,52,184,284,228,147,243,85,220,192,165,256,225,144,181,241,80,48,150,263,231,104,75,235,214,287,168,273,294,94]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : ITP013+1 : TPTP v8.2.0. Bugfixed v7.5.0.
% 0.12/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n004.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Sat May 18 17:43:24 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 0.96/0.93  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.63/1.10  % [INFO] 	 Parsing done (168ms). 
% 1.63/1.11  % [INFO] 	 Running in sequential loop mode. 
% 1.98/1.30  % [INFO] 	 eprover registered as external prover. 
% 1.98/1.31  % [INFO] 	 cvc4 registered as external prover. 
% 1.98/1.31  % [INFO] 	 Scanning for conjecture ... 
% 2.16/1.39  % [INFO] 	 Found a conjecture (or negated_conjecture) and 45 axioms. Running axiom selection ... 
% 2.38/1.45  % [INFO] 	 Axiom selection finished. Selected 45 axioms (removed 0 axioms). 
% 2.66/1.53  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.66/1.54  % [INFO] 	 Type checking passed. 
% 2.66/1.54  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 6.20/2.57  % External prover 'cvc4' found a proof!
% 6.20/2.57  % [INFO] 	 Killing All external provers ... 
% 6.20/2.57  % Time passed: 2029ms (effective reasoning time: 1456ms)
% 6.20/2.57  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 6.20/2.57  % Axioms used in derivation (45): arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2, reserved_2Equant_2E_3F, arityeq1_2Ec_2Ewords_2Eword__2comp_2E1_2Emono_2EA_27a, arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27b_29, reserved_2Eho_2Ebool__cases__ax, arityeq2_2Ec_2Ewords_2Eword__add_2E2_2Emono_2EA_27b, arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a, arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2EA_27b, reserved_2Eho_2Enotfalse, thm_2Ewords_2Eword__sub__def, arityeq2_2Ec_2Earithmetic_2E_2D_2E2, thm_2Ebool_2EREFL__CLAUSE, reserved_2Equant_2E_21, thm_2Ebool_2EEQ__CLAUSES, arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2, thm_2Ebool_2EIMP__CONG, arityeq2_2Ec_2Ebool_2E_2F_5C_2E2, arityeq2_2Ec_2Ewords_2Eword__sub_2E2_2Emono_2EA_27a, thm_2Ewords_2EWORD__LITERAL__ADD, reserved_2Eho_2Etruth, reserved_2Elogic_2E_2F_5C, reserved_2Eho_2Ei__thm, reserved_2Eho_2Es__thm, reserved_2Elogic_2E_3D, thm_2Ebool_2ECOND__CONG, thm_2Ebool_2EAND__IMP__INTRO, arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2EA_27a, arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a, thm_2Ebool_2EIMP__CLAUSES, thm_2Ebool_2ETRUTH, reserved_2Eho_2Ek__thm, arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a, reserved_2Elogic_2E_7E, arityeq1_2Ec_2Ewords_2Eword__2comp_2E1_2Emono_2EA_27b, reserved_2Eho_2Eboolext, arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a, reserved_2Eho_2Eeq__ext, arityeq2_2Ec_2Earithmetic_2E_2B_2E2, reserved_2Elogic_2E_3D_3D_3E, arityeq1_2Ec_2Ebool_2E_7E_2E1, arityeq2_2Ec_2Ebool_2E_5C_2F_2E2, thm_2Ebool_2EEQ__SYM__EQ, reserved_2Elogic_2E_5C_2F, arityeq2_2Ec_2Ewords_2Eword__add_2E2_2Emono_2EA_27a, thm_2Ebool_2Ebool__case__thm
% 6.20/2.57  % No. of inferences in proof: 94
% 6.20/2.57  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2029 ms resp. 1456 ms w/o parsing
% 6.68/2.65  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.68/2.65  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------