TSTP Solution File: COM134+1 by Leo-III---1.7.7

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : COM134+1 : TPTP v8.1.2. Released v6.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n026.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 : Fri May 19 10:14:10 EDT 2023

% Result   : Theorem 9.48s 3.26s
% Output   : Refutation 9.48s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   83
% Syntax   : Number of formulae    :  145 (  16 unt;  23 typ;   0 def)
%            Number of atoms       :  601 ( 450 equ;   0 cnn)
%            Maximal formula atoms :   33 (   4 avg)
%            Number of connectives : 1710 (  78   ~;  34   |; 250   &;1153   @)
%                                         (   0 <=>; 195  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   24 (  10 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   30 (  30   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   26 (  23 usr;   7 con; 0-3 aty)
%            Number of variables   :  679 (   0   ^; 543   !; 136   ?; 679   :)

% Comments : 
%------------------------------------------------------------------------------
thf(vtcheck_type,type,
    vtcheck: $i > $i > $i > $o ).

thf(vbind_type,type,
    vbind: $i > $i > $i > $i ).

thf(vapp_type,type,
    vapp: $i > $i > $i ).

thf(ve1_type,type,
    ve1: $i ).

thf(ve2_type,type,
    ve2: $i ).

thf(vsubst_type,type,
    vsubst: $i > $i > $i > $i ).

thf(vnoType_type,type,
    vnoType: $i ).

thf(vsomeType_type,type,
    vsomeType: $i > $i ).

thf(varrow_type,type,
    varrow: $i > $i > $i ).

thf(vabs_type,type,
    vabs: $i > $i > $i > $i ).

thf(visValue_type,type,
    visValue: $i > $o ).

thf(vnoExp_type,type,
    vnoExp: $i ).

thf(vvar_type,type,
    vvar: $i > $i ).

thf(vreduce_type,type,
    vreduce: $i > $i ).

thf(visSomeExp_type,type,
    visSomeExp: $i > $o ).

thf(vsomeExp_type,type,
    vsomeExp: $i > $i ).

thf(visSomeType_type,type,
    visSomeType: $i > $o ).

thf(visFreeVar_type,type,
    visFreeVar: $i > $i > $o ).

thf(vempty_type,type,
    vempty: $i ).

thf(vgetSomeExp_type,type,
    vgetSomeExp: $i > $i ).

thf(vlookup_type,type,
    vlookup: $i > $i > $i ).

thf(vgetSomeType_type,type,
    vgetSomeType: $i > $i ).

thf(vgensym_type,type,
    vgensym: $i > $i ).

thf(30,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( vabs @ A @ B @ C )
     != ( vapp @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','DIFF-abs-app') ).

thf(288,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( vabs @ A @ B @ C )
     != ( vapp @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(44,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( ( C = B )
        & ( D = A )
        & ( E
          = ( vabs @ G @ H @ I ) ) )
     => ( ( B = G )
       => ( ( F
            = ( vsubst @ C @ D @ E ) )
         => ( F
            = ( vabs @ G @ H @ I ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subst3) ).

thf(357,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( ( C = B )
        & ( D = A )
        & ( E
          = ( vabs @ G @ H @ I ) ) )
     => ( ( B = G )
       => ( ( F
            = ( vsubst @ C @ D @ E ) )
         => ( F
            = ( vabs @ G @ H @ I ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(61,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( F
        = ( vapp @ ( vabs @ A @ B @ C ) @ E ) )
     => ( ( ( D
            = ( vreduce @ E ) )
          & ~ ( visSomeExp @ D )
          & ~ ( visValue @ E ) )
       => ( ( G
            = ( vreduce @ F ) )
         => ( G = vnoExp ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reduce4) ).

thf(559,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( F
        = ( vapp @ ( vabs @ A @ B @ C ) @ E ) )
     => ( ( ( D
            = ( vreduce @ E ) )
          & ~ ( visSomeExp @ D )
          & ~ ( visValue @ E ) )
       => ( ( G
            = ( vreduce @ F ) )
         => ( G = vnoExp ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(15,axiom,
    ( ( ( vnoType = vnoType )
     => $true )
    & ( $true
     => ( vnoType = vnoType ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','EQ-noType') ).

thf(133,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(7,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B
        = ( vvar @ A ) )
     => ( ( C
          = ( vreduce @ B ) )
       => ( C = vnoExp ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reduce0) ).

thf(86,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B
        = ( vvar @ A ) )
     => ( ( C
          = ( vreduce @ B ) )
       => ( C = vnoExp ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(5,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D
        = ( vabs @ A @ B @ C ) )
     => ( visValue @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isValue0) ).

thf(81,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D
        = ( vabs @ A @ B @ C ) )
     => ( visValue @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(52,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( ( vlookup @ A @ C )
          = vnoType )
        & ( vtcheck @ C @ D @ E ) )
     => ( vtcheck @ ( vbind @ A @ B @ C ) @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Weak') ).

thf(497,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( ( vlookup @ A @ C )
          = vnoType )
        & ( vtcheck @ C @ D @ E ) )
     => ( vtcheck @ ( vbind @ A @ B @ C ) @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(17,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( B = E )
        & ( C
          = ( vabs @ D @ A @ F ) ) )
     => ( ( ( ( D != E )
            & ( visFreeVar @ E @ F ) )
         => ( visFreeVar @ B @ C ) )
        & ( ( visFreeVar @ B @ C )
         => ( ( D != E )
            & ( visFreeVar @ E @ F ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isFreeVar1) ).

thf(138,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( B = E )
        & ( C
          = ( vabs @ D @ A @ F ) ) )
     => ( ( ( ( D != E )
            & ( visFreeVar @ E @ F ) )
         => ( visFreeVar @ B @ C ) )
        & ( ( visFreeVar @ B @ C )
         => ( ( D != E )
            & ( visFreeVar @ E @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(60,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( ( A = F )
        & ( B = G )
        & ( C
          = ( vapp @ E @ H ) ) )
     => ( ( D
          = ( vsubst @ A @ B @ C ) )
       => ( D
          = ( vapp @ ( vsubst @ F @ G @ E ) @ ( vsubst @ F @ G @ H ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subst2) ).

thf(555,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( ( A = F )
        & ( B = G )
        & ( C
          = ( vapp @ E @ H ) ) )
     => ( ( D
          = ( vsubst @ A @ B @ C ) )
       => ( D
          = ( vapp @ ( vsubst @ F @ G @ E ) @ ( vsubst @ F @ G @ H ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(36,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( ( vbind @ A @ B @ C )
          = ( vbind @ D @ E @ F ) )
       => ( ( A = D )
          & ( B = E )
          & ( C = F ) ) )
      & ( ( ( A = D )
          & ( B = E )
          & ( C = F ) )
       => ( ( vbind @ A @ B @ C )
          = ( vbind @ D @ E @ F ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','EQ-bind') ).

thf(308,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( ( vbind @ A @ B @ C )
          = ( vbind @ D @ E @ F ) )
       => ( ( A = D )
          & ( B = E )
          & ( C = F ) ) )
      & ( ( ( A = D )
          & ( B = E )
          & ( C = F ) )
       => ( ( vbind @ A @ B @ C )
          = ( vbind @ D @ E @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(29,axiom,
    ! [A: $i,B: $i] :
      ( ( ( vreduce @ A )
        = B )
     => ( ? [C: $i] :
            ( ( A
              = ( vvar @ C ) )
            & ( B = vnoExp ) )
        | ? [C: $i,D: $i,E: $i] :
            ( ( A
              = ( vabs @ C @ D @ E ) )
            & ( B = vnoExp ) )
        | ? [C: $i,D: $i,E: $i,F: $i,G: $i] :
            ( ( A
              = ( vapp @ ( vabs @ D @ E @ F ) @ C ) )
            & ( G
              = ( vreduce @ C ) )
            & ( visSomeExp @ G )
            & ( B
              = ( vsomeExp @ ( vapp @ ( vabs @ D @ E @ F ) @ ( vgetSomeExp @ G ) ) ) ) )
        | ? [C: $i,D: $i,E: $i,F: $i,G: $i] :
            ( ( A
              = ( vapp @ ( vabs @ E @ C @ G ) @ F ) )
            & ( D
              = ( vreduce @ F ) )
            & ~ ( visSomeExp @ D )
            & ( visValue @ F )
            & ( B
              = ( vsomeExp @ ( vsubst @ E @ F @ G ) ) ) )
        | ? [C: $i,D: $i,E: $i,F: $i,G: $i] :
            ( ( A
              = ( vapp @ ( vabs @ C @ D @ E ) @ G ) )
            & ( F
              = ( vreduce @ G ) )
            & ~ ( visSomeExp @ F )
            & ~ ( visValue @ G )
            & ( B = vnoExp ) )
        | ? [C: $i,D: $i,E: $i] :
            ( ( A
              = ( vapp @ C @ E ) )
            & ! [F: $i,G: $i,H: $i] :
                ( C
               != ( vabs @ F @ G @ H ) )
            & ( D
              = ( vreduce @ C ) )
            & ( visSomeExp @ D )
            & ( B
              = ( vsomeExp @ ( vapp @ ( vgetSomeExp @ D ) @ E ) ) ) )
        | ? [C: $i,D: $i,E: $i] :
            ( ( A
              = ( vapp @ D @ C ) )
            & ! [F: $i,G: $i,H: $i] :
                ( D
               != ( vabs @ F @ G @ H ) )
            & ( E
              = ( vreduce @ D ) )
            & ~ ( visSomeExp @ E )
            & ( B = vnoExp ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','reduce-INV') ).

thf(202,plain,
    ! [A: $i,B: $i] :
      ( ( ( vreduce @ A )
        = B )
     => ( ? [C: $i] :
            ( ( A
              = ( vvar @ C ) )
            & ( B = vnoExp ) )
        | ? [C: $i,D: $i,E: $i] :
            ( ( A
              = ( vabs @ C @ D @ E ) )
            & ( B = vnoExp ) )
        | ? [C: $i,D: $i,E: $i,F: $i,G: $i] :
            ( ( A
              = ( vapp @ ( vabs @ D @ E @ F ) @ C ) )
            & ( G
              = ( vreduce @ C ) )
            & ( visSomeExp @ G )
            & ( B
              = ( vsomeExp @ ( vapp @ ( vabs @ D @ E @ F ) @ ( vgetSomeExp @ G ) ) ) ) )
        | ? [C: $i,D: $i,E: $i,F: $i,G: $i] :
            ( ( A
              = ( vapp @ ( vabs @ E @ C @ G ) @ F ) )
            & ( D
              = ( vreduce @ F ) )
            & ~ ( visSomeExp @ D )
            & ( visValue @ F )
            & ( B
              = ( vsomeExp @ ( vsubst @ E @ F @ G ) ) ) )
        | ? [C: $i,D: $i,E: $i,F: $i,G: $i] :
            ( ( A
              = ( vapp @ ( vabs @ C @ D @ E ) @ G ) )
            & ( F
              = ( vreduce @ G ) )
            & ~ ( visSomeExp @ F )
            & ~ ( visValue @ G )
            & ( B = vnoExp ) )
        | ? [C: $i,D: $i,E: $i] :
            ( ( A
              = ( vapp @ C @ E ) )
            & ! [F: $i,G: $i,H: $i] :
                ( C
               != ( vabs @ F @ G @ H ) )
            & ( D
              = ( vreduce @ C ) )
            & ( visSomeExp @ D )
            & ( B
              = ( vsomeExp @ ( vapp @ ( vgetSomeExp @ D ) @ E ) ) ) )
        | ? [C: $i,D: $i,E: $i] :
            ( ( A
              = ( vapp @ D @ C ) )
            & ! [F: $i,G: $i,H: $i] :
                ( D
               != ( vabs @ F @ G @ H ) )
            & ( E
              = ( vreduce @ D ) )
            & ~ ( visSomeExp @ E )
            & ( B = vnoExp ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(53,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( ( C != A )
        & ( vtcheck @ ( vbind @ C @ D @ ( vbind @ A @ B @ E ) ) @ F @ G ) )
     => ( vtcheck @ ( vbind @ A @ B @ ( vbind @ C @ D @ E ) ) @ F @ G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Context-Swap') ).

thf(500,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( ( C != A )
        & ( vtcheck @ ( vbind @ C @ D @ ( vbind @ A @ B @ E ) ) @ F @ G ) )
     => ( vtcheck @ ( vbind @ A @ B @ ( vbind @ C @ D @ E ) ) @ F @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(19,axiom,
    ! [A: $i,B: $i] :
      ( ( ( ( vsomeExp @ A )
          = ( vsomeExp @ B ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( vsomeExp @ A )
          = ( vsomeExp @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','EQ-someExp') ).

thf(153,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( vsomeExp @ A )
          = ( vsomeExp @ B ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( vsomeExp @ A )
          = ( vsomeExp @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(13,axiom,
    ! [A: $i,B: $i] :
      ( ( ( ( vvar @ A )
          = ( vvar @ B ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( vvar @ A )
          = ( vvar @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','EQ-var') ).

thf(121,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( vvar @ A )
          = ( vvar @ B ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( vvar @ A )
          = ( vvar @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(43,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( ( C = A )
        & ( vtcheck @ ( vbind @ C @ D @ ( vbind @ A @ B @ E ) ) @ F @ G ) )
     => ( vtcheck @ ( vbind @ C @ D @ E ) @ F @ G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Context-Duplicate') ).

thf(353,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( ( C = A )
        & ( vtcheck @ ( vbind @ C @ D @ ( vbind @ A @ B @ E ) ) @ F @ G ) )
     => ( vtcheck @ ( vbind @ C @ D @ E ) @ F @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(31,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
      ( ( ( A = E )
        & ( B = F )
        & ( C
          = ( vabs @ H @ G @ J ) ) )
     => ( ( ( E != H )
          & ( visFreeVar @ H @ F )
          & ( I
            = ( vgensym @ ( vapp @ ( vapp @ F @ J ) @ ( vvar @ E ) ) ) ) )
       => ( ( D
            = ( vsubst @ A @ B @ C ) )
         => ( D
            = ( vsubst @ E @ F @ ( vabs @ I @ G @ ( vsubst @ H @ ( vvar @ I ) @ J ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subst4) ).

thf(292,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
      ( ( ( A = E )
        & ( B = F )
        & ( C
          = ( vabs @ H @ G @ J ) ) )
     => ( ( ( E != H )
          & ( visFreeVar @ H @ F )
          & ( I
            = ( vgensym @ ( vapp @ ( vapp @ F @ J ) @ ( vvar @ E ) ) ) ) )
       => ( ( D
            = ( vsubst @ A @ B @ C ) )
         => ( D
            = ( vsubst @ E @ F @ ( vabs @ I @ G @ ( vsubst @ H @ ( vvar @ I ) @ J ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(57,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( ( C = A )
        & ( D = G )
        & ( E
          = ( vvar @ B ) ) )
     => ( ( A = B )
       => ( ( F
            = ( vsubst @ C @ D @ E ) )
         => ( F = G ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subst0) ).

thf(512,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( ( C = A )
        & ( D = G )
        & ( E
          = ( vvar @ B ) ) )
     => ( ( A = B )
       => ( ( F
            = ( vsubst @ C @ D @ E ) )
         => ( F = G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(6,axiom,
    ( ( ( vnoExp = vnoExp )
     => $true )
    & ( $true
     => ( vnoExp = vnoExp ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','EQ-noExp') ).

thf(85,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(47,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( vempty
     != ( vbind @ A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','DIFF-empty-bind') ).

thf(366,plain,
    ! [A: $i,B: $i,C: $i] :
      ( vempty
     != ( vbind @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(49,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( vsubst @ A @ B @ C )
        = D )
     => ( ? [E: $i,F: $i,G: $i] :
            ( ( A = E )
            & ( B = G )
            & ( C
              = ( vvar @ F ) )
            & ( E = F )
            & ( D = G ) )
        | ? [E: $i,F: $i,G: $i] :
            ( ( A = F )
            & ( B = E )
            & ( C
              = ( vvar @ G ) )
            & ( F != G )
            & ( D
              = ( vvar @ G ) ) )
        | ? [E: $i,F: $i,G: $i,H: $i] :
            ( ( A = F )
            & ( B = G )
            & ( C
              = ( vapp @ E @ H ) )
            & ( D
              = ( vapp @ ( vsubst @ F @ G @ E ) @ ( vsubst @ F @ G @ H ) ) ) )
        | ? [E: $i,F: $i,G: $i,H: $i,I: $i] :
            ( ( A = F )
            & ( B = E )
            & ( C
              = ( vabs @ G @ H @ I ) )
            & ( F = G )
            & ( D
              = ( vabs @ G @ H @ I ) ) )
        | ? [E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
            ( ( A = E )
            & ( B = F )
            & ( C
              = ( vabs @ H @ G @ J ) )
            & ( E != H )
            & ( visFreeVar @ H @ F )
            & ( I
              = ( vgensym @ ( vapp @ ( vapp @ F @ J ) @ ( vvar @ E ) ) ) )
            & ( D
              = ( vsubst @ E @ F @ ( vabs @ I @ G @ ( vsubst @ H @ ( vvar @ I ) @ J ) ) ) ) )
        | ? [E: $i,F: $i,G: $i,H: $i,I: $i] :
            ( ( A = G )
            & ( B = H )
            & ( C
              = ( vabs @ E @ F @ I ) )
            & ( G != E )
            & ~ ( visFreeVar @ E @ H )
            & ( D
              = ( vabs @ E @ F @ ( vsubst @ G @ H @ I ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','subst-INV') ).

thf(380,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( vsubst @ A @ B @ C )
        = D )
     => ( ? [E: $i,F: $i,G: $i] :
            ( ( A = E )
            & ( B = G )
            & ( C
              = ( vvar @ F ) )
            & ( E = F )
            & ( D = G ) )
        | ? [E: $i,F: $i,G: $i] :
            ( ( A = F )
            & ( B = E )
            & ( C
              = ( vvar @ G ) )
            & ( F != G )
            & ( D
              = ( vvar @ G ) ) )
        | ? [E: $i,F: $i,G: $i,H: $i] :
            ( ( A = F )
            & ( B = G )
            & ( C
              = ( vapp @ E @ H ) )
            & ( D
              = ( vapp @ ( vsubst @ F @ G @ E ) @ ( vsubst @ F @ G @ H ) ) ) )
        | ? [E: $i,F: $i,G: $i,H: $i,I: $i] :
            ( ( A = F )
            & ( B = E )
            & ( C
              = ( vabs @ G @ H @ I ) )
            & ( F = G )
            & ( D
              = ( vabs @ G @ H @ I ) ) )
        | ? [E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
            ( ( A = E )
            & ( B = F )
            & ( C
              = ( vabs @ H @ G @ J ) )
            & ( E != H )
            & ( visFreeVar @ H @ F )
            & ( I
              = ( vgensym @ ( vapp @ ( vapp @ F @ J ) @ ( vvar @ E ) ) ) )
            & ( D
              = ( vsubst @ E @ F @ ( vabs @ I @ G @ ( vsubst @ H @ ( vvar @ I ) @ J ) ) ) ) )
        | ? [E: $i,F: $i,G: $i,H: $i,I: $i] :
            ( ( A = G )
            & ( B = H )
            & ( C
              = ( vabs @ E @ F @ I ) )
            & ( G != E )
            & ~ ( visFreeVar @ E @ H )
            & ( D
              = ( vabs @ E @ F @ ( vsubst @ G @ H @ I ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(12,axiom,
    ! [A: $i,B: $i] :
      ( ( B
        = ( vvar @ A ) )
     => ~ ( visValue @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isValue1) ).

thf(117,plain,
    ! [A: $i,B: $i] :
      ( ( B
        = ( vvar @ A ) )
     => ~ ( visValue @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(40,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( vvar @ A )
     != ( vapp @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','DIFF-var-app') ).

thf(334,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( vvar @ A )
     != ( vapp @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(34,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( vtcheck @ ( vbind @ B @ D @ A ) @ C @ E )
     => ( vtcheck @ A @ ( vabs @ B @ D @ C ) @ ( varrow @ D @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-abs') ).

thf(302,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( vtcheck @ ( vbind @ B @ D @ A ) @ C @ E )
     => ( vtcheck @ A @ ( vabs @ B @ D @ C ) @ ( varrow @ D @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(42,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( ( A = G )
        & ( B = H )
        & ( C
          = ( vabs @ E @ F @ I ) ) )
     => ( ( ( G != E )
          & ~ ( visFreeVar @ E @ H ) )
       => ( ( D
            = ( vsubst @ A @ B @ C ) )
         => ( D
            = ( vabs @ E @ F @ ( vsubst @ G @ H @ I ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subst5) ).

thf(349,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( ( A = G )
        & ( B = H )
        & ( C
          = ( vabs @ E @ F @ I ) ) )
     => ( ( ( G != E )
          & ~ ( visFreeVar @ E @ H ) )
       => ( ( D
            = ( vsubst @ A @ B @ C ) )
         => ( D
            = ( vabs @ E @ F @ ( vsubst @ G @ H @ I ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(4,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( varrow @ A @ B )
          = ( varrow @ C @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( varrow @ A @ B )
          = ( varrow @ C @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','EQ-arrow') ).

thf(70,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( varrow @ A @ B )
          = ( varrow @ C @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( varrow @ A @ B )
          = ( varrow @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(45,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( vlookup @ B @ A )
        = ( vsomeType @ C ) )
     => ( vtcheck @ A @ ( vvar @ B ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-var') ).

thf(361,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( vlookup @ B @ A )
        = ( vsomeType @ C ) )
     => ( vtcheck @ A @ ( vvar @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(59,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( ( D = B )
        & ( E
          = ( vbind @ C @ G @ A ) ) )
     => ( ( B = C )
       => ( ( F
            = ( vlookup @ D @ E ) )
         => ( F
            = ( vsomeType @ G ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lookup1) ).

thf(551,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( ( D = B )
        & ( E
          = ( vbind @ C @ G @ A ) ) )
     => ( ( B = C )
       => ( ( F
            = ( vlookup @ D @ E ) )
         => ( F
            = ( vsomeType @ G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(14,axiom,
    ! [A: $i,B: $i] :
      ( ( B
        = ( vsomeType @ A ) )
     => ( visSomeType @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isSomeType1) ).

thf(129,plain,
    ! [A: $i,B: $i] :
      ( ( B
        = ( vsomeType @ A ) )
     => ( visSomeType @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(54,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( D
          = ( vapp @ B @ A ) )
        & ! [F: $i,G: $i,H: $i] :
            ( B
           != ( vabs @ F @ G @ H ) ) )
     => ( ( ( C
            = ( vreduce @ B ) )
          & ~ ( visSomeExp @ C ) )
       => ( ( E
            = ( vreduce @ D ) )
         => ( E = vnoExp ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reduce6) ).

thf(503,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( D
          = ( vapp @ B @ A ) )
        & ! [F: $i,G: $i,H: $i] :
            ( B
           != ( vabs @ F @ G @ H ) ) )
     => ( ( ( C
            = ( vreduce @ B ) )
          & ~ ( visSomeExp @ C ) )
       => ( ( E
            = ( vreduce @ D ) )
         => ( E = vnoExp ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(16,axiom,
    ! [A: $i] :
      ( ( A = vnoType )
     => ~ ( visSomeType @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isSomeType0) ).

thf(134,plain,
    ! [A: $i] :
      ( ( A = vnoType )
     => ~ ( visSomeType @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(55,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( vtcheck @ B @ C @ ( varrow @ A @ E ) )
        & ( vtcheck @ B @ D @ A ) )
     => ( vtcheck @ B @ ( vapp @ C @ D ) @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-app') ).

thf(508,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( vtcheck @ B @ C @ ( varrow @ A @ E ) )
        & ( vtcheck @ B @ D @ A ) )
     => ( vtcheck @ B @ ( vapp @ C @ D ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(33,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( ( C = B )
        & ( D = A )
        & ( E
          = ( vvar @ G ) ) )
     => ( ( B != G )
       => ( ( F
            = ( vsubst @ C @ D @ E ) )
         => ( F
            = ( vvar @ G ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subst1) ).

thf(298,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( ( C = B )
        & ( D = A )
        & ( E
          = ( vvar @ G ) ) )
     => ( ( B != G )
       => ( ( F
            = ( vsubst @ C @ D @ E ) )
         => ( F
            = ( vvar @ G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(22,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B = A )
        & ( C = vempty ) )
     => ( ( D
          = ( vlookup @ B @ C ) )
       => ( D = vnoType ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lookup0) ).

thf(166,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B = A )
        & ( C = vempty ) )
     => ( ( D
          = ( vlookup @ B @ C ) )
       => ( D = vnoType ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(18,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( D
        = ( vabs @ A @ B @ C ) )
     => ( ( E
          = ( vreduce @ D ) )
       => ( E = vnoExp ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reduce1) ).

thf(148,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( D
        = ( vabs @ A @ B @ C ) )
     => ( ( E
          = ( vreduce @ D ) )
       => ( E = vnoExp ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(20,axiom,
    ( ( ( vempty = vempty )
     => $true )
    & ( $true
     => ( vempty = vempty ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','EQ-empty') ).

thf(161,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(32,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( vtcheck @ B @ D @ A )
        & ( vtcheck @ ( vbind @ C @ A @ B ) @ ve1 @ E ) )
     => ( vtcheck @ B @ ( vsubst @ C @ D @ ve1 ) @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-subst-IH-app1') ).

thf(296,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( vtcheck @ B @ D @ A )
        & ( vtcheck @ ( vbind @ C @ A @ B ) @ ve1 @ E ) )
     => ( vtcheck @ B @ ( vsubst @ C @ D @ ve1 ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(11,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( ( vabs @ A @ B @ C )
          = ( vabs @ D @ E @ F ) )
       => ( ( A = D )
          & ( B = E )
          & ( C = F ) ) )
      & ( ( ( A = D )
          & ( B = E )
          & ( C = F ) )
       => ( ( vabs @ A @ B @ C )
          = ( vabs @ D @ E @ F ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','EQ-abs') ).

thf(103,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( ( vabs @ A @ B @ C )
          = ( vabs @ D @ E @ F ) )
       => ( ( A = D )
          & ( B = E )
          & ( C = F ) ) )
      & ( ( ( A = D )
          & ( B = E )
          & ( C = F ) )
       => ( ( vabs @ A @ B @ C )
          = ( vabs @ D @ E @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(8,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( vvar @ A )
     != ( vabs @ B @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','DIFF-var-abs') ).

thf(91,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( vvar @ A )
     != ( vabs @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(3,axiom,
    ! [A: $i] :
      ( vnoType
     != ( vsomeType @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','DIFF-noType-someType') ).

thf(66,plain,
    ! [A: $i] :
      ( vnoType
     != ( vsomeType @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(28,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( C
        = ( vapp @ ( vabs @ E @ A @ G ) @ F ) )
     => ( ( ( B
            = ( vreduce @ F ) )
          & ~ ( visSomeExp @ B )
          & ( visValue @ F ) )
       => ( ( D
            = ( vreduce @ C ) )
         => ( D
            = ( vsomeExp @ ( vsubst @ E @ F @ G ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reduce3) ).

thf(198,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( C
        = ( vapp @ ( vabs @ E @ A @ G ) @ F ) )
     => ( ( ( B
            = ( vreduce @ F ) )
          & ~ ( visSomeExp @ B )
          & ( visValue @ F ) )
       => ( ( D
            = ( vreduce @ C ) )
         => ( D
            = ( vsomeExp @ ( vsubst @ E @ F @ G ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(21,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A
        = ( vsomeExp @ C ) )
     => ( ( B
          = ( vgetSomeExp @ A ) )
       => ( B = C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',getSomeExp0) ).

thf(162,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( A
        = ( vsomeExp @ C ) )
     => ( ( B
          = ( vgetSomeExp @ A ) )
       => ( B = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(58,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( vlookup @ A @ B )
        = C )
     => ( ? [D: $i] :
            ( ( A = D )
            & ( B = vempty )
            & ( C = vnoType ) )
        | ? [D: $i,E: $i,F: $i,G: $i] :
            ( ( A = E )
            & ( B
              = ( vbind @ F @ G @ D ) )
            & ( E = F )
            & ( C
              = ( vsomeType @ G ) ) )
        | ? [D: $i,E: $i,F: $i,G: $i] :
            ( ( A = F )
            & ( B
              = ( vbind @ E @ D @ G ) )
            & ( F != E )
            & ( C
              = ( vlookup @ F @ G ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lookup-INV') ).

thf(516,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( vlookup @ A @ B )
        = C )
     => ( ? [D: $i] :
            ( ( A = D )
            & ( B = vempty )
            & ( C = vnoType ) )
        | ? [D: $i,E: $i,F: $i,G: $i] :
            ( ( A = E )
            & ( B
              = ( vbind @ F @ G @ D ) )
            & ( E = F )
            & ( C
              = ( vsomeType @ G ) ) )
        | ? [D: $i,E: $i,F: $i,G: $i] :
            ( ( A = F )
            & ( B
              = ( vbind @ E @ D @ G ) )
            & ( F != E )
            & ( C
              = ( vlookup @ F @ G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(27,axiom,
    ! [A: $i,B: $i] :
      ( ( ( vgensym @ B )
        = A )
     => ~ ( visFreeVar @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','gensym-is-fresh') ).

thf(194,plain,
    ! [A: $i,B: $i] :
      ( ( ( vgensym @ B )
        = A )
     => ~ ( visFreeVar @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(9,axiom,
    ! [A: $i] :
      ( ( A = vnoExp )
     => ~ ( visSomeExp @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isSomeExp0) ).

thf(95,plain,
    ! [A: $i] :
      ( ( A = vnoExp )
     => ~ ( visSomeExp @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(38,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( B
        = ( vapp @ ( vabs @ D @ E @ F ) @ A ) )
     => ( ( ( G
            = ( vreduce @ A ) )
          & ( visSomeExp @ G ) )
       => ( ( C
            = ( vreduce @ B ) )
         => ( C
            = ( vsomeExp @ ( vapp @ ( vabs @ D @ E @ F ) @ ( vgetSomeExp @ G ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reduce2) ).

thf(327,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( B
        = ( vapp @ ( vabs @ D @ E @ F ) @ A ) )
     => ( ( ( G
            = ( vreduce @ A ) )
          & ( visSomeExp @ G ) )
       => ( ( C
            = ( vreduce @ B ) )
         => ( C
            = ( vsomeExp @ ( vapp @ ( vabs @ D @ E @ F ) @ ( vgetSomeExp @ G ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(25,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A
        = ( vsomeType @ C ) )
     => ( ( B
          = ( vgetSomeType @ A ) )
       => ( B = C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',getSomeType0) ).

thf(182,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( A
        = ( vsomeType @ C ) )
     => ( ( B
          = ( vgetSomeType @ A ) )
       => ( B = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(48,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( A = D )
        & ( B
          = ( vapp @ C @ E ) ) )
     => ( ( ( ( visFreeVar @ D @ C )
            | ( visFreeVar @ D @ E ) )
         => ( visFreeVar @ A @ B ) )
        & ( ( visFreeVar @ A @ B )
         => ( ( visFreeVar @ D @ C )
            | ( visFreeVar @ D @ E ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isFreeVar2) ).

thf(370,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( A = D )
        & ( B
          = ( vapp @ C @ E ) ) )
     => ( ( ( ( visFreeVar @ D @ C )
            | ( visFreeVar @ D @ E ) )
         => ( visFreeVar @ A @ B ) )
        & ( ( visFreeVar @ A @ B )
         => ( ( visFreeVar @ D @ C )
            | ( visFreeVar @ D @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(41,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( vapp @ A @ B )
          = ( vapp @ C @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( vapp @ A @ B )
          = ( vapp @ C @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','EQ-app') ).

thf(338,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( vapp @ A @ B )
          = ( vapp @ C @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( vapp @ A @ B )
          = ( vapp @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(10,axiom,
    ! [A: $i,B: $i] :
      ( ( B
        = ( vsomeExp @ A ) )
     => ( visSomeExp @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isSomeExp1) ).

thf(99,plain,
    ! [A: $i,B: $i] :
      ( ( B
        = ( vsomeExp @ A ) )
     => ( visSomeExp @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(51,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( vtcheck @ C @ A @ B )
     => ( ? [D: $i] :
            ( ( A
              = ( vvar @ D ) )
            & ( ( vlookup @ D @ C )
              = ( vsomeType @ B ) ) )
        | ? [D: $i,E: $i,F: $i,G: $i] :
            ( ( A
              = ( vabs @ D @ F @ E ) )
            & ( B
              = ( varrow @ F @ G ) )
            & ( vtcheck @ ( vbind @ D @ F @ C ) @ E @ G ) )
        | ? [D: $i,E: $i,F: $i] :
            ( ( A
              = ( vapp @ D @ E ) )
            & ( vtcheck @ C @ D @ ( varrow @ F @ B ) )
            & ( vtcheck @ C @ E @ F ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-inv') ).

thf(482,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( vtcheck @ C @ A @ B )
     => ( ? [D: $i] :
            ( ( A
              = ( vvar @ D ) )
            & ( ( vlookup @ D @ C )
              = ( vsomeType @ B ) ) )
        | ? [D: $i,E: $i,F: $i,G: $i] :
            ( ( A
              = ( vabs @ D @ F @ E ) )
            & ( B
              = ( varrow @ F @ G ) )
            & ( vtcheck @ ( vbind @ D @ F @ C ) @ E @ G ) )
        | ? [D: $i,E: $i,F: $i] :
            ( ( A
              = ( vapp @ D @ E ) )
            & ( vtcheck @ C @ D @ ( varrow @ F @ B ) )
            & ( vtcheck @ C @ E @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(35,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C
        = ( vapp @ A @ B ) )
     => ~ ( visValue @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isValue2) ).

thf(304,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C
        = ( vapp @ A @ B ) )
     => ~ ( visValue @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(26,axiom,
    ! [A: $i,B: $i] :
      ( ( ( ( vsomeType @ A )
          = ( vsomeType @ B ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( vsomeType @ A )
          = ( vsomeType @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','EQ-someType') ).

thf(186,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( vsomeType @ A )
          = ( vsomeType @ B ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( vsomeType @ A )
          = ( vsomeType @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(23,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( A = D )
        & ( B
          = ( vvar @ C ) ) )
     => ( ( ( C = D )
         => ( visFreeVar @ A @ B ) )
        & ( ( visFreeVar @ A @ B )
         => ( C = D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isFreeVar0) ).

thf(171,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( A = D )
        & ( B
          = ( vvar @ C ) ) )
     => ( ( ( C = D )
         => ( visFreeVar @ A @ B ) )
        & ( ( visFreeVar @ A @ B )
         => ( C = D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(56,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ~ ( visFreeVar @ A @ D )
        & ( vtcheck @ C @ D @ E ) )
     => ( vtcheck @ ( vbind @ A @ B @ C ) @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Weak-FreeVar') ).

thf(510,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ~ ( visFreeVar @ A @ D )
        & ( vtcheck @ C @ D @ E ) )
     => ( vtcheck @ ( vbind @ A @ B @ C ) @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(50,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( ( C = F )
        & ( D
          = ( vbind @ B @ A @ G ) ) )
     => ( ( F != B )
       => ( ( E
            = ( vlookup @ C @ D ) )
         => ( E
            = ( vlookup @ F @ G ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lookup2) ).

thf(478,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( ( C = F )
        & ( D
          = ( vbind @ B @ A @ G ) ) )
     => ( ( F != B )
       => ( ( E
            = ( vlookup @ C @ D ) )
         => ( E
            = ( vlookup @ F @ G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(39,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ~ ( visFreeVar @ A @ D )
        & ( vtcheck @ ( vbind @ A @ B @ C ) @ D @ E ) )
     => ( vtcheck @ C @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Strong') ).

thf(332,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ~ ( visFreeVar @ A @ D )
        & ( vtcheck @ ( vbind @ A @ B @ C ) @ D @ E ) )
     => ( vtcheck @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(1,conjecture,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( vtcheck @ B @ D @ A )
        & ( vtcheck @ ( vbind @ C @ A @ B ) @ ( vapp @ ve1 @ ve2 ) @ E ) )
     => ( vtcheck @ B @ ( vsubst @ C @ D @ ( vapp @ ve1 @ ve2 ) ) @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-subst-app') ).

thf(2,negated_conjecture,
    ~ ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
        ( ( ( vtcheck @ B @ D @ A )
          & ( vtcheck @ ( vbind @ C @ A @ B ) @ ( vapp @ ve1 @ ve2 ) @ E ) )
       => ( vtcheck @ B @ ( vsubst @ C @ D @ ( vapp @ ve1 @ ve2 ) ) @ E ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(62,plain,
    ~ ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
        ( ( ( vtcheck @ B @ D @ A )
          & ( vtcheck @ ( vbind @ C @ A @ B ) @ ( vapp @ ve1 @ ve2 ) @ E ) )
       => ( vtcheck @ B @ ( vsubst @ C @ D @ ( vapp @ ve1 @ ve2 ) ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(24,axiom,
    ! [A: $i] :
      ( vnoExp
     != ( vsomeExp @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','DIFF-noExp-someExp') ).

thf(178,plain,
    ! [A: $i] :
      ( vnoExp
     != ( vsomeExp @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(37,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( B
          = ( vapp @ A @ E ) )
        & ! [F: $i,G: $i,H: $i] :
            ( A
           != ( vabs @ F @ G @ H ) ) )
     => ( ( ( D
            = ( vreduce @ A ) )
          & ( visSomeExp @ D ) )
       => ( ( C
            = ( vreduce @ B ) )
         => ( C
            = ( vsomeExp @ ( vapp @ ( vgetSomeExp @ D ) @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reduce5) ).

thf(322,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( B
          = ( vapp @ A @ E ) )
        & ! [F: $i,G: $i,H: $i] :
            ( A
           != ( vabs @ F @ G @ H ) ) )
     => ( ( ( D
            = ( vreduce @ A ) )
          & ( visSomeExp @ D ) )
       => ( ( C
            = ( vreduce @ B ) )
         => ( C
            = ( vsomeExp @ ( vapp @ ( vgetSomeExp @ D ) @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(46,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( vtcheck @ B @ D @ A )
        & ( vtcheck @ ( vbind @ C @ A @ B ) @ ve2 @ E ) )
     => ( vtcheck @ B @ ( vsubst @ C @ D @ ve2 ) @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-subst-IH-app2') ).

thf(364,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( vtcheck @ B @ D @ A )
        & ( vtcheck @ ( vbind @ C @ A @ B ) @ ve2 @ E ) )
     => ( vtcheck @ B @ ( vsubst @ C @ D @ ve2 ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(608,plain,
    $false,
    inference(cvc4,[status(thm)],[288,357,559,133,86,81,497,138,555,308,202,500,153,121,353,292,512,85,366,380,117,334,302,349,70,361,551,129,503,134,508,298,166,148,161,296,103,91,66,198,162,516,194,95,327,182,370,338,99,482,304,186,171,510,478,332,62,178,322,364]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : COM134+1 : TPTP v8.1.2. Released v6.4.0.
% 0.14/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n026.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Fri May 19 03:33:06 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 0.96/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.47/1.05  % [INFO] 	 Parsing done (172ms). 
% 1.47/1.05  % [INFO] 	 Running in sequential loop mode. 
% 1.99/1.36  % [INFO] 	 eprover registered as external prover. 
% 1.99/1.36  % [INFO] 	 cvc4 registered as external prover. 
% 1.99/1.36  % [INFO] 	 Scanning for conjecture ... 
% 2.32/1.46  % [INFO] 	 Found a conjecture and 59 axioms. Running axiom selection ... 
% 2.56/1.53  % [INFO] 	 Axiom selection finished. Selected 59 axioms (removed 0 axioms). 
% 2.94/1.65  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.94/1.66  % [INFO] 	 Type checking passed. 
% 2.94/1.66  % [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 ... 
% 9.48/3.25  % External prover 'cvc4' found a proof!
% 9.48/3.25  % [INFO] 	 Killing All external provers ... 
% 9.48/3.25  % Time passed: 2726ms (effective reasoning time: 2196ms)
% 9.48/3.25  % 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)>
% 9.48/3.25  % Axioms used in derivation (59): EQ-bind, T-var, getSomeType0, reduce4, DIFF-noType-someType, reduce3, isSomeType0, reduce6, subst0, isSomeType1, isFreeVar0, DIFF-empty-bind, getSomeExp0, subst4, isValue2, isSomeExp0, reduce-INV, T-app, EQ-app, EQ-abs, reduce1, subst5, DIFF-var-abs, reduce5, lookup1, EQ-someExp, T-abs, reduce0, T-Weak, EQ-empty, T-inv, EQ-var, EQ-noExp, isFreeVar2, subst-INV, isValue0, subst1, subst2, T-subst-IH-app1, lookup0, T-Context-Duplicate, T-Weak-FreeVar, subst3, EQ-noType, isValue1, DIFF-abs-app, EQ-someType, EQ-arrow, gensym-is-fresh, isFreeVar1, T-subst-IH-app2, reduce2, isSomeExp1, DIFF-var-app, lookup2, DIFF-noExp-someExp, lookup-INV, T-Strong, T-Context-Swap
% 9.48/3.25  % No. of inferences in proof: 122
% 9.48/3.26  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2726 ms resp. 2196 ms w/o parsing
% 9.48/3.31  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.48/3.31  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------