TSTP Solution File: ITP018^2 by Leo-III---1.7.10

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.10
% Problem  : ITP018^2 : TPTP v8.1.2. 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 : Tue May  7 07:46:56 EDT 2024

% Result   : Theorem 3.80s 1.99s
% Output   : Refutation 3.80s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   53
% Syntax   : Number of formulae    :   83 (  39 unt;  25 typ;   0 def)
%            Number of atoms       :  105 (  31 equ;   0 cnn)
%            Maximal formula atoms :    5 (   1 avg)
%            Number of connectives :  497 (   2   ~;   0   |;   0   &; 462   @)
%                                         (   0 <=>;  33  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   6 avg)
%            Number of types       :    4 (   2 usr)
%            Number of type conns  :   34 (  34   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   26 (  23 usr;   6 con; 0-2 aty)
%            Number of variables   :   98 (   0   ^  98   !;   0   ?;  98   :)

% 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(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(c_2Erealax_2Ereal__neg_type,type,
    c_2Erealax_2Ereal__neg: $i ).

thf(fo__c_2Erealax_2Ereal__neg_type,type,
    fo__c_2Erealax_2Ereal__neg: tp__ty_2Erealax_2Ereal > tp__ty_2Erealax_2Ereal ).

thf(ty_2Ebinary__ieee_2Efloat_type,type,
    ty_2Ebinary__ieee_2Efloat: del > del > del ).

thf(c_2Ebinary__ieee_2Efloat__negate_type,type,
    c_2Ebinary__ieee_2Efloat__negate: del > del > $i ).

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

thf(ty_2Ebool_2Eitself_type,type,
    ty_2Ebool_2Eitself: del > del ).

thf(c_2Ebinary__ieee_2Efloat__plus__min_type,type,
    c_2Ebinary__ieee_2Efloat__plus__min: del > del > $i ).

thf(c_2Ebinary__ieee_2Efloat__to__real_type,type,
    c_2Ebinary__ieee_2Efloat__to__real: del > del > $i ).

thf(c_2Ebool_2Ethe__value_type,type,
    c_2Ebool_2Ethe__value: del > $i ).

thf(c_2Ebinary__ieee_2Eulp_type,type,
    c_2Ebinary__ieee_2Eulp: del > del > $i ).

thf(c_2Ebool_2ET_type,type,
    c_2Ebool_2ET: $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(24,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/sandbox2/benchmark/theBenchmark.p',ap_tp) ).

thf(85,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)],[24]) ).

thf(12,axiom,
    ! [A: del] : ( mem @ ( c_2Ebool_2E_21 @ A ) @ ( arr @ ( arr @ A @ bool ) @ bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebool_2E_21) ).

thf(53,plain,
    ! [A: del] : ( mem @ ( c_2Ebool_2E_21 @ A ) @ ( arr @ ( arr @ A @ bool ) @ bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(29,axiom,
    ! [A: tp__ty_2Erealax_2Ereal] :
      ( ( surj__ty_2Erealax_2Ereal @ ( inj__ty_2Erealax_2Ereal @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stp_inj_surj_ty_2Erealax_2Ereal) ).

thf(96,plain,
    ! [A: tp__ty_2Erealax_2Ereal] :
      ( ( surj__ty_2Erealax_2Ereal @ ( inj__ty_2Erealax_2Ereal @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(15,axiom,
    ! [A: tp__ty_2Erealax_2Ereal] :
      ( ( inj__ty_2Erealax_2Ereal @ ( fo__c_2Erealax_2Ereal__neg @ A ) )
      = ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stp_eq_fo_c_2Erealax_2Ereal__neg) ).

thf(59,plain,
    ! [A: tp__ty_2Erealax_2Ereal] :
      ( ( inj__ty_2Erealax_2Ereal @ ( fo__c_2Erealax_2Ereal__neg @ A ) )
      = ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(10,axiom,
    p @ c_2Ebool_2ET,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_true_p) ).

thf(49,plain,
    p @ c_2Ebool_2ET,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(6,axiom,
    ! [A: del,B: $i] :
      ( ( mem @ B @ A )
     => ( ( B = B )
        = $true ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ebool_2EREFL__CLAUSE) ).

thf(39,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(27,axiom,
    ! [A: del] : ( mem @ ( c_2Ebool_2Ethe__value @ A ) @ ( ty_2Ebool_2Eitself @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebool_2Ethe__value) ).

thf(91,plain,
    ! [A: del] : ( mem @ ( c_2Ebool_2Ethe__value @ A ) @ ( ty_2Ebool_2Eitself @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(22,axiom,
    ! [A: del,B: del] : ( mem @ ( c_2Ebinary__ieee_2Efloat__negate @ A @ B ) @ ( arr @ ( ty_2Ebinary__ieee_2Efloat @ A @ B ) @ ( ty_2Ebinary__ieee_2Efloat @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebinary__ieee_2Efloat__negate) ).

thf(80,plain,
    ! [A: del,B: del] : ( mem @ ( c_2Ebinary__ieee_2Efloat__negate @ A @ B ) @ ( arr @ ( ty_2Ebinary__ieee_2Efloat @ A @ B ) @ ( ty_2Ebinary__ieee_2Efloat @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(9,axiom,
    mem @ c_2Ebool_2ET @ bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebool_2ET) ).

thf(48,plain,
    mem @ c_2Ebool_2ET @ bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(25,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/sandbox2/benchmark/theBenchmark.p',ax_all_p) ).

thf(87,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)],[25]) ).

thf(16,axiom,
    ! [A: del,B: del] : ( mem @ ( c_2Ebinary__ieee_2Eulp @ A @ B ) @ ( arr @ ( ty_2Ebool_2Eitself @ ( ty_2Epair_2Eprod @ A @ B ) ) @ ty_2Erealax_2Ereal ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebinary__ieee_2Eulp) ).

thf(62,plain,
    ! [A: del,B: del] : ( mem @ ( c_2Ebinary__ieee_2Eulp @ A @ B ) @ ( arr @ ( ty_2Ebool_2Eitself @ ( ty_2Epair_2Eprod @ A @ B ) ) @ ty_2Erealax_2Ereal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(26,axiom,
    mem @ c_2Erealax_2Ereal__neg @ ( arr @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Erealax_2Ereal__neg) ).

thf(90,plain,
    mem @ c_2Erealax_2Ereal__neg @ ( arr @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(28,axiom,
    ! [A: del,B: del,C: $i] :
      ( ( mem @ C @ ( ty_2Ebinary__ieee_2Efloat @ A @ B ) )
     => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ A @ B ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__negate @ A @ B ) @ C ) ) )
        = ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ A @ B ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ebinary__ieee_2Efloat__to__real__negate) ).

thf(93,plain,
    ! [A: del,B: del,C: $i] :
      ( ( mem @ C @ ( ty_2Ebinary__ieee_2Efloat @ A @ B ) )
     => ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ A @ B ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__negate @ A @ B ) @ C ) ) )
        = ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ A @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(14,axiom,
    ! [A: del,B: del] : ( mem @ ( c_2Ebinary__ieee_2Efloat__to__real @ A @ B ) @ ( arr @ ( ty_2Ebinary__ieee_2Efloat @ A @ B ) @ ty_2Erealax_2Ereal ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebinary__ieee_2Efloat__to__real) ).

thf(57,plain,
    ! [A: del,B: del] : ( mem @ ( c_2Ebinary__ieee_2Efloat__to__real @ A @ B ) @ ( arr @ ( ty_2Ebinary__ieee_2Efloat @ A @ B ) @ ty_2Erealax_2Ereal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(21,axiom,
    ! [A: del,B: del] : ( mem @ ( c_2Ebinary__ieee_2Efloat__plus__min @ A @ B ) @ ( arr @ ( ty_2Ebool_2Eitself @ ( ty_2Epair_2Eprod @ A @ B ) ) @ ( ty_2Ebinary__ieee_2Efloat @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebinary__ieee_2Efloat__plus__min) ).

thf(78,plain,
    ! [A: del,B: del] : ( mem @ ( c_2Ebinary__ieee_2Efloat__plus__min @ A @ B ) @ ( arr @ ( ty_2Ebool_2Eitself @ ( ty_2Epair_2Eprod @ A @ B ) ) @ ( ty_2Ebinary__ieee_2Efloat @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(19,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/sandbox2/benchmark/theBenchmark.p',funcext) ).

thf(70,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)],[19]) ).

thf(3,axiom,
    $true,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ebool_2ETRUTH) ).

thf(33,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(4,axiom,
    ! [A: del] : ( mem @ ( c_2Emin_2E_3D @ A ) @ ( arr @ A @ ( arr @ A @ bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Emin_2E_3D) ).

thf(34,plain,
    ! [A: del] : ( mem @ ( c_2Emin_2E_3D @ A ) @ ( arr @ A @ ( arr @ A @ bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(8,axiom,
    ! [A: $i] :
      ( ( mem @ A @ bool )
     => ( A
        = ( inj__o @ ( p @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stp_iso_mem_o) ).

thf(45,plain,
    ! [A: $i] :
      ( ( mem @ A @ bool )
     => ( A
        = ( inj__o @ ( p @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(17,axiom,
    ! [A: $i] :
      ( ( mem @ A @ ty_2Erealax_2Ereal )
     => ( A
        = ( inj__ty_2Erealax_2Ereal @ ( surj__ty_2Erealax_2Ereal @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stp_iso_mem_ty_2Erealax_2Ereal) ).

thf(64,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)],[17]) ).

thf(11,axiom,
    ! [A: $o] : ( mem @ ( inj__o @ A ) @ bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stp_inj_mem_o) ).

thf(50,plain,
    ! [A: $o] : ( mem @ ( inj__o @ A ) @ bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(18,axiom,
    ! [A: del,B: $i > $i,C: $i] :
      ( ( mem @ C @ A )
     => ( ( ap @ ( lam @ A @ B ) @ C )
        = ( B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',beta) ).

thf(67,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)],[18]) ).

thf(7,axiom,
    ! [A: $o] :
      ( ( p @ ( inj__o @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stp_inj_surj_o) ).

thf(40,plain,
    ! [A: $o] :
      ( ( p @ ( inj__o @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(13,axiom,
    ! [A: tp__ty_2Erealax_2Ereal] : ( mem @ ( inj__ty_2Erealax_2Ereal @ A ) @ ty_2Erealax_2Ereal ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stp_inj_mem_ty_2Erealax_2Ereal) ).

thf(55,plain,
    ! [A: tp__ty_2Erealax_2Ereal] : ( mem @ ( inj__ty_2Erealax_2Ereal @ A ) @ ty_2Erealax_2Ereal ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(20,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/sandbox2/benchmark/theBenchmark.p',ax_eq_p) ).

thf(75,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)],[20]) ).

thf(23,axiom,
    ! [A: del,B: del] :
      ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( c_2Ebinary__ieee_2Eulp @ A @ B ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ A @ B ) ) ) )
      = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ A @ B ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__plus__min @ A @ B ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ebinary__ieee_2Eulp) ).

thf(82,plain,
    ! [A: del,B: del] :
      ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( c_2Ebinary__ieee_2Eulp @ A @ B ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ A @ B ) ) ) )
      = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ A @ B ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__plus__min @ A @ B ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ A @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(5,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/sandbox2/benchmark/theBenchmark.p',lam_tp) ).

thf(36,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)],[5]) ).

thf(1,conjecture,
    ! [A: del,B: del] :
      ( ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ ( c_2Ebinary__ieee_2Eulp @ A @ B ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ A @ B ) ) ) ) )
      = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ A @ B ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__negate @ A @ B ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__plus__min @ A @ B ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ A @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ebinary__ieee_2Eneg__ulp) ).

thf(2,negated_conjecture,
    ~ ! [A: del,B: del] :
        ( ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ ( c_2Ebinary__ieee_2Eulp @ A @ B ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ A @ B ) ) ) ) )
        = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ A @ B ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__negate @ A @ B ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__plus__min @ A @ B ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ A @ B ) ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(30,plain,
    ~ ! [A: del,B: del] :
        ( ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ ( c_2Ebinary__ieee_2Eulp @ A @ B ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ A @ B ) ) ) ) )
        = ( surj__ty_2Erealax_2Ereal @ ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ A @ B ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__negate @ A @ B ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__plus__min @ A @ B ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ A @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(99,plain,
    $false,
    inference(cvc4,[status(thm)],[85,53,96,59,49,39,91,80,48,87,62,90,93,57,78,70,33,34,45,64,50,67,40,55,75,82,36,30]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13  % Problem  : ITP018^2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.06/0.16  % Command  : run_Leo-III %s %d
% 0.14/0.37  % Computer : n004.cluster.edu
% 0.14/0.37  % Model    : x86_64 x86_64
% 0.14/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37  % Memory   : 8042.1875MB
% 0.14/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37  % CPULimit : 300
% 0.14/0.37  % WCLimit  : 300
% 0.14/0.37  % DateTime : Mon May  6 14:27:24 EDT 2024
% 0.14/0.37  % CPUTime  : 
% 0.90/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.03/1.02  % [INFO] 	 Parsing done (156ms). 
% 1.35/1.03  % [INFO] 	 Running in sequential loop mode. 
% 1.72/1.26  % [INFO] 	 eprover registered as external prover. 
% 1.72/1.26  % [INFO] 	 cvc4 registered as external prover. 
% 1.72/1.27  % [INFO] 	 Scanning for conjecture ... 
% 1.92/1.34  % [INFO] 	 Found a conjecture and 27 axioms. Running axiom selection ... 
% 2.07/1.39  % [INFO] 	 Axiom selection finished. Selected 27 axioms (removed 0 axioms). 
% 2.07/1.43  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.07/1.43  % [INFO] 	 Type checking passed. 
% 2.07/1.43  % [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 ... 
% 3.80/1.99  % External prover 'cvc4' found a proof!
% 3.80/1.99  % [INFO] 	 Killing All external provers ... 
% 3.80/1.99  % Time passed: 1467ms (effective reasoning time: 956ms)
% 3.80/1.99  % 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)>
% 3.80/1.99  % Axioms used in derivation (27): stp_inj_surj_o, ax_eq_p, mem_c_2Ebool_2Ethe__value, mem_c_2Ebool_2E_21, conj_thm_2Ebinary__ieee_2Efloat__to__real__negate, ax_true_p, mem_c_2Emin_2E_3D, stp_inj_mem_ty_2Erealax_2Ereal, conj_thm_2Ebool_2ETRUTH, mem_c_2Ebinary__ieee_2Efloat__to__real, stp_iso_mem_ty_2Erealax_2Ereal, ap_tp, lam_tp, conj_thm_2Ebool_2EREFL__CLAUSE, mem_c_2Ebool_2ET, stp_inj_mem_o, conj_thm_2Ebinary__ieee_2Eulp, funcext, mem_c_2Ebinary__ieee_2Eulp, mem_c_2Ebinary__ieee_2Efloat__plus__min, ax_all_p, mem_c_2Erealax_2Ereal__neg, stp_inj_surj_ty_2Erealax_2Ereal, beta, mem_c_2Ebinary__ieee_2Efloat__negate, stp_iso_mem_o, stp_eq_fo_c_2Erealax_2Ereal__neg
% 3.80/1.99  % No. of inferences in proof: 58
% 3.80/1.99  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1467 ms resp. 956 ms w/o parsing
% 3.80/2.04  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.80/2.04  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------