TSTP Solution File: ITP019^2 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : ITP019^2 : 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 22:21:56 EDT 2024

% Result   : Theorem 4.39s 2.03s
% Output   : Refutation 4.63s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   70
% Syntax   : Number of formulae    :  111 (  48 unt;  31 typ;   0 def)
%            Number of atoms       :  187 (  55 equ;   0 cnn)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  532 (  13   ~;   0   |;   6   &; 454   @)
%                                         (   0 <=>;  59  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Number of types       :    6 (   4 usr)
%            Number of type conns  :   25 (  25   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   30 (  27 usr;  14 con; 0-2 aty)
%            Number of variables   :   94 (   0   ^  94   !;   0   ?;  94   :)

% Comments : 
%------------------------------------------------------------------------------
thf(del_type,type,
    del: $tType ).

thf(bool_type,type,
    bool: del ).

thf(arr_type,type,
    arr: del > del > del ).

thf(mem_type,type,
    mem: $i > del > $o ).

thf(ap_type,type,
    ap: $i > $i > $i ).

thf(lam_type,type,
    lam: del > ( $i > $i ) > $i ).

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

thf(inj__o_type,type,
    inj__o: $o > $i ).

thf(c_2Ebool_2E_7E_type,type,
    c_2Ebool_2E_7E: $i ).

thf(c_2Ebool_2EF_type,type,
    c_2Ebool_2EF: $i ).

thf(c_2Ebool_2ET_type,type,
    c_2Ebool_2ET: $i ).

thf(c_2Emin_2E_3D_3D_3E_type,type,
    c_2Emin_2E_3D_3D_3E: $i ).

thf(c_2Ebool_2E_2F_5C_type,type,
    c_2Ebool_2E_2F_5C: $i ).

thf(ty_2Enum_2Enum_type,type,
    ty_2Enum_2Enum: del ).

thf(tp__ty_2Enum_2Enum_type,type,
    tp__ty_2Enum_2Enum: $tType ).

thf(inj__ty_2Enum_2Enum_type,type,
    inj__ty_2Enum_2Enum: tp__ty_2Enum_2Enum > $i ).

thf(surj__ty_2Enum_2Enum_type,type,
    surj__ty_2Enum_2Enum: $i > tp__ty_2Enum_2Enum ).

thf(c_2Enum_2E0_type,type,
    c_2Enum_2E0: $i ).

thf(fo__c_2Enum_2E0_type,type,
    fo__c_2Enum_2E0: tp__ty_2Enum_2Enum ).

thf(ty_2Erealax_2Ereal_type,type,
    ty_2Erealax_2Ereal: del ).

thf(tp__ty_2Erealax_2Ereal_type,type,
    tp__ty_2Erealax_2Ereal: $tType ).

thf(inj__ty_2Erealax_2Ereal_type,type,
    inj__ty_2Erealax_2Ereal: tp__ty_2Erealax_2Ereal > $i ).

thf(surj__ty_2Erealax_2Ereal_type,type,
    surj__ty_2Erealax_2Ereal: $i > tp__ty_2Erealax_2Ereal ).

thf(ty_2Epair_2Eprod_type,type,
    ty_2Epair_2Eprod: del > del > del ).

thf(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal_type,type,
    tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal: $tType ).

thf(inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal_type,type,
    inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal > $i ).

thf(surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal_type,type,
    surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal: $i > tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ).

thf(c_2Ecomplex_2Ecomplex__of__num_type,type,
    c_2Ecomplex_2Ecomplex__of__num: $i ).

thf(c_2Ecomplex_2Ecomplex__inv_type,type,
    c_2Ecomplex_2Ecomplex__inv: $i ).

thf(c_2Emin_2E_3D_type,type,
    c_2Emin_2E_3D: del > $i ).

thf(c_2Ebool_2E_21_type,type,
    c_2Ebool_2E_21: del > $i ).

thf(8,axiom,
    mem @ c_2Ebool_2ET @ bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2ET) ).

thf(56,plain,
    mem @ c_2Ebool_2ET @ bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(37,axiom,
    ! [A: $i] :
      ( ( mem @ A @ bool )
     => ! [B: $i] :
          ( ( mem @ B @ bool )
         => ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ A ) @ B ) )
            = ( ( p @ A )
              & ( p @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_and_p) ).

thf(125,plain,
    ! [A: $i] :
      ( ( mem @ A @ bool )
     => ! [B: $i] :
          ( ( mem @ B @ bool )
         => ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ A ) @ B ) )
            = ( ( p @ A )
              & ( p @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(1,conjecture,
    ! [A: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
      ( ( A
       != ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
     => ( ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__inv @ ( inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ A ) ) )
       != ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ecomplex_2ECOMPLEX__INV__NZ) ).

thf(2,negated_conjecture,
    ~ ! [A: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
        ( ( A
         != ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
       => ( ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__inv @ ( inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ A ) ) )
         != ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(41,plain,
    ~ ! [A: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
        ( ( A
         != ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
       => ( ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__inv @ ( inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ A ) ) )
         != ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(18,axiom,
    mem @ c_2Enum_2E0 @ ty_2Enum_2Enum,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Enum_2E0) ).

thf(76,plain,
    mem @ c_2Enum_2E0 @ ty_2Enum_2Enum,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(39,axiom,
    ! [A: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
      ( ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) ).

thf(130,plain,
    ! [A: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
      ( ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(12,axiom,
    ! [A: del,B: del,C: $i > $i] :
      ( ! [D: $i] :
          ( ( mem @ D @ A )
         => ( mem @ ( C @ D ) @ B ) )
     => ( mem @ ( lam @ A @ C ) @ ( arr @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lam_tp) ).

thf(63,plain,
    ! [A: del,B: del,C: $i > $i] :
      ( ! [D: $i] :
          ( ( mem @ D @ A )
         => ( mem @ ( C @ D ) @ B ) )
     => ( mem @ ( lam @ A @ C ) @ ( arr @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(15,axiom,
    p @ c_2Ebool_2ET,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_true_p) ).

thf(72,plain,
    p @ c_2Ebool_2ET,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(6,axiom,
    ! [A: $i] :
      ( ( mem @ A @ bool )
     => ( A
        = ( inj__o @ ( p @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_iso_mem_o) ).

thf(51,plain,
    ! [A: $i] :
      ( ( mem @ A @ bool )
     => ( A
        = ( inj__o @ ( p @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(4,axiom,
    ! [A: tp__ty_2Erealax_2Ereal] :
      ( ( surj__ty_2Erealax_2Ereal @ ( inj__ty_2Erealax_2Ereal @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_surj_ty_2Erealax_2Ereal) ).

thf(47,plain,
    ! [A: tp__ty_2Erealax_2Ereal] :
      ( ( surj__ty_2Erealax_2Ereal @ ( inj__ty_2Erealax_2Ereal @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(3,axiom,
    $true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2ETRUTH) ).

thf(46,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(9,axiom,
    mem @ c_2Ebool_2EF @ bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2EF) ).

thf(57,plain,
    mem @ c_2Ebool_2EF @ bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(11,axiom,
    ! [A: del] : ( mem @ ( c_2Emin_2E_3D @ A ) @ ( arr @ A @ ( arr @ A @ bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Emin_2E_3D) ).

thf(61,plain,
    ! [A: del] : ( mem @ ( c_2Emin_2E_3D @ A ) @ ( arr @ A @ ( arr @ A @ bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(34,axiom,
    ! [A: del,B: $i] :
      ( ( mem @ B @ A )
     => ! [C: $i] :
          ( ( mem @ C @ A )
         => ( ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A ) @ B ) @ C ) )
            = ( B = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_eq_p) ).

thf(116,plain,
    ! [A: del,B: $i] :
      ( ( mem @ B @ A )
     => ! [C: $i] :
          ( ( mem @ C @ A )
         => ( ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A ) @ B ) @ C ) )
            = ( B = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(24,axiom,
    ! [A: $i] :
      ( ( mem @ A @ ty_2Enum_2Enum )
     => ( A
        = ( inj__ty_2Enum_2Enum @ ( surj__ty_2Enum_2Enum @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_iso_mem_ty_2Enum_2Enum) ).

thf(89,plain,
    ! [A: $i] :
      ( ( mem @ A @ ty_2Enum_2Enum )
     => ( A
        = ( inj__ty_2Enum_2Enum @ ( surj__ty_2Enum_2Enum @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(40,axiom,
    mem @ c_2Ecomplex_2Ecomplex__of__num @ ( arr @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ecomplex_2Ecomplex__of__num) ).

thf(133,plain,
    mem @ c_2Ecomplex_2Ecomplex__of__num @ ( arr @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(22,axiom,
    ! [A: $i] :
      ( ( mem @ A @ bool )
     => ( ( ( $true
           => ( p @ A ) )
          = ( p @ A ) )
        & ( ( ( p @ A )
           => $true )
          = $true )
        & ( ( $false
           => ( p @ A ) )
          = $true )
        & ( ( ( p @ A )
           => ( p @ A ) )
          = $true )
        & ( ( ( p @ A )
           => $false )
          = ( ~ ( p @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2EIMP__CLAUSES) ).

thf(85,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(30,axiom,
    ! [A: $i] :
      ( ( mem @ A @ bool )
     => ! [B: $i] :
          ( ( mem @ B @ bool )
         => ( ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ A ) @ B ) )
            = ( ( p @ A )
             => ( p @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_imp_p) ).

thf(102,plain,
    ! [A: $i] :
      ( ( mem @ A @ bool )
     => ! [B: $i] :
          ( ( mem @ B @ bool )
         => ( ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ A ) @ B ) )
            = ( ( p @ A )
             => ( p @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(25,axiom,
    ! [A: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( mem @ ( inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ A ) @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_mem_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) ).

thf(92,plain,
    ! [A: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( mem @ ( inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ A ) @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(28,axiom,
    ! [A: del,B: $i] :
      ( ( mem @ B @ ( arr @ A @ bool ) )
     => ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ A ) @ B ) )
        = ( ! [C: $i] :
              ( ( mem @ C @ A )
             => ( p @ ( ap @ B @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_all_p) ).

thf(97,plain,
    ! [A: del,B: $i] :
      ( ( mem @ B @ ( arr @ A @ bool ) )
     => ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ A ) @ B ) )
        = ( ! [C: $i] :
              ( ( mem @ C @ A )
             => ( p @ ( ap @ B @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(19,axiom,
    ! [A: tp__ty_2Erealax_2Ereal] : ( mem @ ( inj__ty_2Erealax_2Ereal @ A ) @ ty_2Erealax_2Ereal ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_mem_ty_2Erealax_2Ereal) ).

thf(77,plain,
    ! [A: tp__ty_2Erealax_2Ereal] : ( mem @ ( inj__ty_2Erealax_2Ereal @ A ) @ ty_2Erealax_2Ereal ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(27,axiom,
    mem @ c_2Ecomplex_2Ecomplex__inv @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ecomplex_2Ecomplex__inv) ).

thf(96,plain,
    mem @ c_2Ecomplex_2Ecomplex__inv @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(16,axiom,
    ! [A: del] : ( mem @ ( c_2Ebool_2E_21 @ A ) @ ( arr @ ( arr @ A @ bool ) @ bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2E_21) ).

thf(73,plain,
    ! [A: del] : ( mem @ ( c_2Ebool_2E_21 @ A ) @ ( arr @ ( arr @ A @ bool ) @ bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(38,axiom,
    ! [A: del,B: del,C: $i] :
      ( ( mem @ C @ ( arr @ A @ B ) )
     => ! [D: $i] :
          ( ( mem @ D @ A )
         => ( mem @ ( ap @ C @ D ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_tp) ).

thf(128,plain,
    ! [A: del,B: del,C: $i] :
      ( ( mem @ C @ ( arr @ A @ B ) )
     => ! [D: $i] :
          ( ( mem @ D @ A )
         => ( mem @ ( ap @ C @ D ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(31,axiom,
    ! [A: $i] :
      ( ( mem @ A @ bool )
     => ( ( p @ ( ap @ c_2Ebool_2E_7E @ A ) )
        = ( ~ ( p @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_neg_p) ).

thf(105,plain,
    ! [A: $i] :
      ( ( mem @ A @ bool )
     => ( ( p @ ( ap @ c_2Ebool_2E_7E @ A ) )
        = ( ~ ( p @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(7,axiom,
    ~ ( p @ c_2Ebool_2EF ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_false_p) ).

thf(54,plain,
    ~ ( p @ c_2Ebool_2EF ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(23,axiom,
    ! [A: $i] :
      ( ( mem @ A @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
     => ( A
        = ( inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_iso_mem_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) ).

thf(86,plain,
    ! [A: $i] :
      ( ( mem @ A @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
     => ( A
        = ( inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(13,axiom,
    mem @ c_2Emin_2E_3D_3D_3E @ ( arr @ bool @ ( arr @ bool @ bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Emin_2E_3D_3D_3E) ).

thf(66,plain,
    mem @ c_2Emin_2E_3D_3D_3E @ ( arr @ bool @ ( arr @ bool @ bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(32,axiom,
    ! [A: del,B: $i > $i,C: $i] :
      ( ( mem @ C @ A )
     => ( ( ap @ ( lam @ A @ B ) @ C )
        = ( B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta) ).

thf(108,plain,
    ! [A: del,B: $i > $i,C: $i] :
      ( ( mem @ C @ A )
     => ( ( ap @ ( lam @ A @ B ) @ C )
        = ( B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(5,axiom,
    mem @ c_2Ebool_2E_2F_5C @ ( arr @ bool @ ( arr @ bool @ bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2E_2F_5C) ).

thf(50,plain,
    mem @ c_2Ebool_2E_2F_5C @ ( arr @ bool @ ( arr @ bool @ bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(14,axiom,
    ! [A: $o] :
      ( ( p @ ( inj__o @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_surj_o) ).

thf(67,plain,
    ! [A: $o] :
      ( ( p @ ( inj__o @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(17,axiom,
    mem @ c_2Ebool_2E_7E @ ( arr @ bool @ bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2E_7E) ).

thf(75,plain,
    mem @ c_2Ebool_2E_7E @ ( arr @ bool @ bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(21,axiom,
    ! [A: del,B: $i] :
      ( ( mem @ B @ bool )
     => ( ( ! [C: $i] :
              ( ( mem @ C @ A )
             => ( p @ B ) ) )
        = ( p @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2EFORALL__SIMP) ).

thf(82,plain,
    ! [A: del,B: $i] :
      ( ( mem @ B @ bool )
     => ( ( ! [C: $i] :
              ( ( mem @ C @ A )
             => ( p @ B ) ) )
        = ( p @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(35,axiom,
    ! [A: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
      ( ( ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__inv @ ( inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ A ) ) )
        = ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
      = ( A
        = ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ecomplex_2ECOMPLEX__INV__EQ__0) ).

thf(119,plain,
    ! [A: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
      ( ( ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__inv @ ( inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ A ) ) )
        = ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
      = ( A
        = ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(10,axiom,
    ! [A: $o] : ( mem @ ( inj__o @ A ) @ bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_mem_o) ).

thf(58,plain,
    ! [A: $o] : ( mem @ ( inj__o @ A ) @ bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(20,axiom,
    ! [A: $i] :
      ( ( mem @ A @ ty_2Erealax_2Ereal )
     => ( A
        = ( inj__ty_2Erealax_2Ereal @ ( surj__ty_2Erealax_2Ereal @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_iso_mem_ty_2Erealax_2Ereal) ).

thf(79,plain,
    ! [A: $i] :
      ( ( mem @ A @ ty_2Erealax_2Ereal )
     => ( A
        = ( inj__ty_2Erealax_2Ereal @ ( surj__ty_2Erealax_2Ereal @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(26,axiom,
    ( ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 )
    = c_2Enum_2E0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_eq_fo_c_2Enum_2E0) ).

thf(94,plain,
    ( ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 )
    = c_2Enum_2E0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(33,axiom,
    ! [A: del,B: del,C: $i] :
      ( ( mem @ C @ ( arr @ A @ B ) )
     => ! [D: $i] :
          ( ( mem @ D @ ( arr @ A @ B ) )
         => ( ! [E: $i] :
                ( ( mem @ E @ A )
               => ( ( ap @ C @ E )
                  = ( ap @ D @ E ) ) )
           => ( C = D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcext) ).

thf(111,plain,
    ! [A: del,B: del,C: $i] :
      ( ( mem @ C @ ( arr @ A @ B ) )
     => ! [D: $i] :
          ( ( mem @ D @ ( arr @ A @ B ) )
         => ( ! [E: $i] :
                ( ( mem @ E @ A )
               => ( ( ap @ C @ E )
                  = ( ap @ D @ E ) ) )
           => ( C = D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(36,axiom,
    ! [A: tp__ty_2Enum_2Enum] :
      ( ( surj__ty_2Enum_2Enum @ ( inj__ty_2Enum_2Enum @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_surj_ty_2Enum_2Enum) ).

thf(122,plain,
    ! [A: tp__ty_2Enum_2Enum] :
      ( ( surj__ty_2Enum_2Enum @ ( inj__ty_2Enum_2Enum @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(29,axiom,
    ! [A: tp__ty_2Enum_2Enum] : ( mem @ ( inj__ty_2Enum_2Enum @ A ) @ ty_2Enum_2Enum ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_mem_ty_2Enum_2Enum) ).

thf(100,plain,
    ! [A: tp__ty_2Enum_2Enum] : ( mem @ ( inj__ty_2Enum_2Enum @ A ) @ ty_2Enum_2Enum ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(136,plain,
    $false,
    inference(cvc4,[status(thm)],[56,125,41,76,130,63,72,51,47,46,57,61,116,89,133,85,102,92,97,77,96,73,128,105,54,86,66,108,50,67,75,82,119,58,79,94,111,122,100]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : ITP019^2 : TPTP v8.2.0. Bugfixed v7.5.0.
% 0.03/0.14  % Command  : run_Leo-III %s %d
% 0.14/0.35  % Computer : n004.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Sat May 18 16:48:09 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.95/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.31/0.99  % [INFO] 	 Parsing done (142ms). 
% 1.31/1.00  % [INFO] 	 Running in sequential loop mode. 
% 1.83/1.23  % [INFO] 	 eprover registered as external prover. 
% 1.83/1.23  % [INFO] 	 cvc4 registered as external prover. 
% 1.83/1.24  % [INFO] 	 Scanning for conjecture ... 
% 1.95/1.30  % [INFO] 	 Found a conjecture (or negated_conjecture) and 38 axioms. Running axiom selection ... 
% 2.23/1.36  % [INFO] 	 Axiom selection finished. Selected 38 axioms (removed 0 axioms). 
% 2.44/1.40  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.44/1.41  % [INFO] 	 Type checking passed. 
% 2.44/1.41  % [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 ... 
% 4.39/2.02  % External prover 'cvc4' found a proof!
% 4.39/2.02  % [INFO] 	 Killing All external provers ... 
% 4.39/2.02  % Time passed: 1517ms (effective reasoning time: 1018ms)
% 4.39/2.02  % 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)>
% 4.39/2.03  % Axioms used in derivation (38): conj_thm_2Ebool_2EIMP__CLAUSES, stp_inj_mem_ty_2Enum_2Enum, conj_thm_2Ebool_2EFORALL__SIMP, mem_c_2Enum_2E0, funcext, ax_true_p, stp_inj_surj_ty_2Enum_2Enum, ax_and_p, mem_c_2Emin_2E_3D, mem_c_2Ebool_2EF, conj_thm_2Ebool_2ETRUTH, ax_all_p, conj_thm_2Ecomplex_2ECOMPLEX__INV__EQ__0, ap_tp, mem_c_2Ecomplex_2Ecomplex__inv, lam_tp, mem_c_2Ebool_2ET, stp_inj_mem_o, stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal, ax_neg_p, mem_c_2Ebool_2E_2F_5C, stp_inj_surj_o, ax_imp_p, ax_eq_p, stp_iso_mem_ty_2Enum_2Enum, mem_c_2Ebool_2E_21, mem_c_2Ecomplex_2Ecomplex__of__num, stp_inj_mem_ty_2Erealax_2Ereal, mem_c_2Ebool_2E_7E, stp_iso_mem_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal, stp_iso_mem_ty_2Erealax_2Ereal, beta, stp_inj_surj_ty_2Erealax_2Ereal, stp_eq_fo_c_2Enum_2E0, ax_false_p, stp_inj_mem_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal, stp_iso_mem_o, mem_c_2Emin_2E_3D_3D_3E
% 4.39/2.03  % No. of inferences in proof: 80
% 4.39/2.03  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1517 ms resp. 1018 ms w/o parsing
% 4.39/2.10  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.63/2.10  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------