TSTP Solution File: KRS157+1 by Leo-III---1.7.10

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.10
% Problem  : KRS157+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n011.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 07:52:01 EDT 2024

% Result   : Theorem 5.47s 2.59s
% Output   : Refutation 5.86s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  187
% Syntax   : Number of formulae    :  275 (  25 unt; 101 typ;   0 def)
%            Number of atoms       :  639 (   0 equ;   0 cnn)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives : 1277 (  38   ~;   0   |; 250   &; 774   @)
%                                         (  69 <=>; 146  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  115 ( 115   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  102 ( 101 usr;   2 con; 0-2 aty)
%            Number of variables   :  278 (   0   ^ 152   !; 126   ?; 278   :)

% Comments : 
%------------------------------------------------------------------------------
thf(cowlThing_type,type,
    cowlThing: $i > $o ).

thf(cowlNothing_type,type,
    cowlNothing: $i > $o ).

thf(xsd_string_type,type,
    xsd_string: $i > $o ).

thf(xsd_integer_type,type,
    xsd_integer: $i > $o ).

thf(cC14_type,type,
    cC14: $i > $o ).

thf(iV3102_type,type,
    iV3102: $i ).

thf(cC44_type,type,
    cC44: $i > $o ).

thf(cC216_type,type,
    cC216: $i > $o ).

thf(cC64_type,type,
    cC64: $i > $o ).

thf(cC46_type,type,
    cC46: $i > $o ).

thf(cC28_type,type,
    cC28: $i > $o ).

thf(cC30_type,type,
    cC30: $i > $o ).

thf(cC58_type,type,
    cC58: $i > $o ).

thf(rR1_type,type,
    rR1: $i > $i > $o ).

thf(cC56_type,type,
    cC56: $i > $o ).

thf(cC94_type,type,
    cC94: $i > $o ).

thf(cC92_type,type,
    cC92: $i > $o ).

thf(cC152_type,type,
    cC152: $i > $o ).

thf(cC150_type,type,
    cC150: $i > $o ).

thf(cC40_type,type,
    cC40: $i > $o ).

thf(ra_Px86_type,type,
    ra_Px86: $i > $i > $o ).

thf(cC164_type,type,
    cC164: $i > $o ).

thf(cC162_type,type,
    cC162: $i > $o ).

thf(cC82_type,type,
    cC82: $i > $o ).

thf(cC80_type,type,
    cC80: $i > $o ).

thf(cC188_type,type,
    cC188: $i > $o ).

thf(cC186_type,type,
    cC186: $i > $o ).

thf(cC118_type,type,
    cC118: $i > $o ).

thf(cC116_type,type,
    cC116: $i > $o ).

thf(cC10_type,type,
    cC10: $i > $o ).

thf(ra_Px87_type,type,
    ra_Px87: $i > $i > $o ).

thf(cC130_type,type,
    cC130: $i > $o ).

thf(cC128_type,type,
    cC128: $i > $o ).

thf(cC200_type,type,
    cC200: $i > $o ).

thf(cC198_type,type,
    cC198: $i > $o ).

thf(cC180_type,type,
    cC180: $i > $o ).

thf(cC16xcomp_type,type,
    cC16xcomp: $i > $o ).

thf(cC126xcomp_type,type,
    cC126xcomp: $i > $o ).

thf(cC114xcomp_type,type,
    cC114xcomp: $i > $o ).

thf(cC50_type,type,
    cC50: $i > $o ).

thf(cC156_type,type,
    cC156: $i > $o ).

thf(ra_Px5_type,type,
    ra_Px5: $i > $i > $o ).

thf(cC4_type,type,
    cC4: $i > $o ).

thf(cC2xcomp_type,type,
    cC2xcomp: $i > $o ).

thf(cC142_type,type,
    cC142: $i > $o ).

thf(cC140xcomp_type,type,
    cC140xcomp: $i > $o ).

thf(cC98_type,type,
    cC98: $i > $o ).

thf(cC72xcomp_type,type,
    cC72xcomp: $i > $o ).

thf(cC96xcomp_type,type,
    cC96xcomp: $i > $o ).

thf(cC26xcomp_type,type,
    cC26xcomp: $i > $o ).

thf(ra_Px9_type,type,
    ra_Px9: $i > $i > $o ).

thf(cC214xcomp_type,type,
    cC214xcomp: $i > $o ).

thf(ra_Px75_type,type,
    ra_Px75: $i > $i > $o ).

thf(cC40xcomp_type,type,
    cC40xcomp: $i > $o ).

thf(cC48_type,type,
    cC48: $i > $o ).

thf(cC160xcomp_type,type,
    cC160xcomp: $i > $o ).

thf(cC78xcomp_type,type,
    cC78xcomp: $i > $o ).

thf(cC172_type,type,
    cC172: $i > $o ).

thf(cC34_type,type,
    cC34: $i > $o ).

thf(cC32xcomp_type,type,
    cC32xcomp: $i > $o ).

thf(cC60xcomp_type,type,
    cC60xcomp: $i > $o ).

thf(ra_Px85_type,type,
    ra_Px85: $i > $i > $o ).

thf(cC148xcomp_type,type,
    cC148xcomp: $i > $o ).

thf(ra_Px1_type,type,
    ra_Px1: $i > $i > $o ).

thf(ra_Px10_type,type,
    ra_Px10: $i > $i > $o ).

thf(cC136_type,type,
    cC136: $i > $o ).

thf(cC8xcomp_type,type,
    cC8xcomp: $i > $o ).

thf(cC108_type,type,
    cC108: $i > $o ).

thf(cC106xcomp_type,type,
    cC106xcomp: $i > $o ).

thf(cC110_type,type,
    cC110: $i > $o ).

thf(cC122_type,type,
    cC122: $i > $o ).

thf(cC102_type,type,
    cC102: $i > $o ).

thf(cC62xcomp_type,type,
    cC62xcomp: $i > $o ).

thf(ra_Px20_type,type,
    ra_Px20: $i > $i > $o ).

thf(cC144_type,type,
    cC144: $i > $o ).

thf(cC42xcomp_type,type,
    cC42xcomp: $i > $o ).

thf(ra_Px14_type,type,
    ra_Px14: $i > $i > $o ).

thf(cC100xcomp_type,type,
    cC100xcomp: $i > $o ).

thf(ra_Px76_type,type,
    ra_Px76: $i > $i > $o ).

thf(cC86_type,type,
    cC86: $i > $o ).

thf(cC90xcomp_type,type,
    cC90xcomp: $i > $o ).

thf(cC66_type,type,
    cC66: $i > $o ).

thf(cC38xcomp_type,type,
    cC38xcomp: $i > $o ).

thf(cC192_type,type,
    cC192: $i > $o ).

thf(cC18_type,type,
    cC18: $i > $o ).

thf(cC196xcomp_type,type,
    cC196xcomp: $i > $o ).

thf(cC74_type,type,
    cC74: $i > $o ).

thf(cC12xcomp_type,type,
    cC12xcomp: $i > $o ).

thf(ra_Px4_type,type,
    ra_Px4: $i > $i > $o ).

thf(cC24xcomp_type,type,
    cC24xcomp: $i > $o ).

thf(ra_Px88_type,type,
    ra_Px88: $i > $i > $o ).

thf(cC178_type,type,
    cC178: $i > $o ).

thf(cC176xcomp_type,type,
    cC176xcomp: $i > $o ).

thf(cC184xcomp_type,type,
    cC184xcomp: $i > $o ).

thf(cC54xcomp_type,type,
    cC54xcomp: $i > $o ).

thf(cC10xcomp_type,type,
    cC10xcomp: $i > $o ).

thf(cC72_type,type,
    cC72: $i > $o ).

thf(cC70xcomp_type,type,
    cC70xcomp: $i > $o ).

thf(ra_Px34_type,type,
    ra_Px34: $i > $i > $o ).

thf(cTOP_type,type,
    cTOP: $i > $o ).

thf(cTEST_type,type,
    cTEST: $i > $o ).

thf(16,axiom,
    ! [A: $i] :
      ( ( cC116 @ A )
    <=> ( ( cC16xcomp @ A )
        & ( cC114xcomp @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_21) ).

thf(170,plain,
    ! [A: $i] :
      ( ( ( cC116 @ A )
       => ( ( cC16xcomp @ A )
          & ( cC114xcomp @ A ) ) )
      & ( ( ( cC16xcomp @ A )
          & ( cC114xcomp @ A ) )
       => ( cC116 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(46,axiom,
    ! [A: $i] :
      ( ( cC92 @ A )
    <=> ( ( cC16xcomp @ A )
        & ( cC90xcomp @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_191) ).

thf(340,plain,
    ! [A: $i] :
      ( ( ( cC92 @ A )
       => ( ( cC16xcomp @ A )
          & ( cC90xcomp @ A ) ) )
      & ( ( ( cC16xcomp @ A )
          & ( cC90xcomp @ A ) )
       => ( cC92 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(87,axiom,
    ! [A: $i] :
      ( ( rR1 @ iV3102 @ A )
     => ( cC24xcomp @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_204) ).

thf(504,plain,
    ! [A: $i] :
      ( ( rR1 @ iV3102 @ A )
     => ( cC24xcomp @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(17,axiom,
    ! [A: $i] :
      ( ( cC50 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC16xcomp @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_150) ).

thf(176,plain,
    ! [A: $i] :
      ( ( ( cC50 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC16xcomp @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC16xcomp @ B ) )
       => ( cC50 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(38,axiom,
    ! [A: $i] :
      ( ( cC110 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC16xcomp @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_16) ).

thf(295,plain,
    ! [A: $i] :
      ( ( ( cC110 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC16xcomp @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC16xcomp @ B ) )
       => ( cC110 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(14,axiom,
    ! [A: $i] :
      ( ( cC180 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC16xcomp @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_86) ).

thf(158,plain,
    ! [A: $i] :
      ( ( ( cC180 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC16xcomp @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC16xcomp @ B ) )
       => ( cC180 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(1,conjecture,
    ( ! [A: $i] :
        ( ( cowlThing @ A )
        & ~ ( cowlNothing @ A ) )
    & ! [A: $i] :
        ( ( xsd_string @ A )
      <=> ~ ( xsd_integer @ A ) )
    & ( cC14 @ iV3102 )
    & ( cC44 @ iV3102 )
    & ( cC216 @ iV3102 )
    & ( cC64 @ iV3102 )
    & ( cC46 @ iV3102 )
    & ( cC28 @ iV3102 )
    & ( cowlThing @ iV3102 )
    & ( cC30 @ iV3102 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',the_axiom) ).

thf(2,negated_conjecture,
    ~ ( ! [A: $i] :
          ( ( cowlThing @ A )
          & ~ ( cowlNothing @ A ) )
      & ! [A: $i] :
          ( ( xsd_string @ A )
        <=> ~ ( xsd_integer @ A ) )
      & ( cC14 @ iV3102 )
      & ( cC44 @ iV3102 )
      & ( cC216 @ iV3102 )
      & ( cC64 @ iV3102 )
      & ( cC46 @ iV3102 )
      & ( cC28 @ iV3102 )
      & ( cowlThing @ iV3102 )
      & ( cC30 @ iV3102 ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(88,plain,
    ~ ( ! [A: $i] :
          ( ( cowlThing @ A )
          & ~ ( cowlNothing @ A ) )
      & ! [A: $i] :
          ( ( ( xsd_string @ A )
           => ~ ( xsd_integer @ A ) )
          & ( ~ ( xsd_integer @ A )
           => ( xsd_string @ A ) ) )
      & ( cC14 @ iV3102 )
      & ( cC44 @ iV3102 )
      & ( cC216 @ iV3102 )
      & ( cC64 @ iV3102 )
      & ( cC46 @ iV3102 )
      & ( cC28 @ iV3102 )
      & ( cowlThing @ iV3102 )
      & ( cC30 @ iV3102 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(48,axiom,
    ! [A: $i] :
      ( ( cC40 @ A )
    <=> ( ( cC32xcomp @ A )
        & ( cC38xcomp @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_142) ).

thf(352,plain,
    ! [A: $i] :
      ( ( ( cC40 @ A )
       => ( ( cC32xcomp @ A )
          & ( cC38xcomp @ A ) ) )
      & ( ( ( cC32xcomp @ A )
          & ( cC38xcomp @ A ) )
       => ( cC40 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(57,axiom,
    ! [A: $i] :
      ( ( cC56 @ A )
    <=> ( ( cC16xcomp @ A )
        & ( cC54xcomp @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_155) ).

thf(404,plain,
    ! [A: $i] :
      ( ( ( cC56 @ A )
       => ( ( cC16xcomp @ A )
          & ( cC54xcomp @ A ) ) )
      & ( ( ( cC16xcomp @ A )
          & ( cC54xcomp @ A ) )
       => ( cC56 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(39,axiom,
    ! [A: $i] :
      ( ( cC122 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC16xcomp @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_27) ).

thf(301,plain,
    ! [A: $i] :
      ( ( ( cC122 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC16xcomp @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC16xcomp @ B ) )
       => ( cC122 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(65,axiom,
    ! [A: $i] :
      ( ( rR1 @ iV3102 @ A )
     => ( cC60xcomp @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_209) ).

thf(436,plain,
    ! [A: $i] :
      ( ( rR1 @ iV3102 @ A )
     => ( cC60xcomp @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(60,axiom,
    ! [A: $i] :
      ( ( cC98 @ A )
    <=> ~ ? [B: $i] : ( ra_Px34 @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_198) ).

thf(421,plain,
    ! [A: $i] :
      ( ( ( cC98 @ A )
       => ~ ? [B: $i] : ( ra_Px34 @ A @ B ) )
      & ( ~ ? [B: $i] : ( ra_Px34 @ A @ B )
       => ( cC98 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(13,axiom,
    ! [A: $i] :
      ( ( cC200 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC198 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_103) ).

thf(152,plain,
    ! [A: $i] :
      ( ( ( cC200 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC198 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC198 @ B ) )
       => ( cC200 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(37,axiom,
    ! [A: $i] :
      ( ( cC108 @ A )
    <=> ( ( cC16xcomp @ A )
        & ( cC106xcomp @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_13) ).

thf(289,plain,
    ! [A: $i] :
      ( ( ( cC108 @ A )
       => ( ( cC16xcomp @ A )
          & ( cC106xcomp @ A ) ) )
      & ( ( ( cC16xcomp @ A )
          & ( cC106xcomp @ A ) )
       => ( cC108 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(32,axiom,
    ! [A: $i] :
      ( ( cC150 @ A )
    <=> ( ( cC16xcomp @ A )
        & ( cC148xcomp @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_56) ).

thf(261,plain,
    ! [A: $i] :
      ( ( ( cC150 @ A )
       => ( ( cC16xcomp @ A )
          & ( cC148xcomp @ A ) ) )
      & ( ( ( cC16xcomp @ A )
          & ( cC148xcomp @ A ) )
       => ( cC150 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(24,axiom,
    ! [A: $i] :
      ( ( cC214xcomp @ A )
    <=> ~ ? [B: $i] : ( ra_Px75 @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_120) ).

thf(216,plain,
    ! [A: $i] :
      ( ( ( cC214xcomp @ A )
       => ~ ? [B: $i] : ( ra_Px75 @ A @ B ) )
      & ( ~ ? [B: $i] : ( ra_Px75 @ A @ B )
       => ( cC214xcomp @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(78,axiom,
    ! [A: $i] :
      ( ( rR1 @ iV3102 @ A )
     => ( cC10xcomp @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_214) ).

thf(475,plain,
    ! [A: $i] :
      ( ( rR1 @ iV3102 @ A )
     => ( cC10xcomp @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(15,axiom,
    ! [A: $i] :
      ( ( cC128 @ A )
    <=> ( ( cC16xcomp @ A )
        & ( cC126xcomp @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_32) ).

thf(164,plain,
    ! [A: $i] :
      ( ( ( cC128 @ A )
       => ( ( cC16xcomp @ A )
          & ( cC126xcomp @ A ) ) )
      & ( ( ( cC16xcomp @ A )
          & ( cC126xcomp @ A ) )
       => ( cC128 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(52,axiom,
    ! [A: $i] :
      ( ( cC74 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC16xcomp @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_175) ).

thf(376,plain,
    ! [A: $i] :
      ( ( ( cC74 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC16xcomp @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC16xcomp @ B ) )
       => ( cC74 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(23,axiom,
    ! [A: $i] :
      ( ( cC26xcomp @ A )
    <=> ~ ? [B: $i] : ( ra_Px9 @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_130) ).

thf(211,plain,
    ! [A: $i] :
      ( ( ( cC26xcomp @ A )
       => ~ ? [B: $i] : ( ra_Px9 @ A @ B ) )
      & ( ~ ? [B: $i] : ( ra_Px9 @ A @ B )
       => ( cC26xcomp @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(5,axiom,
    ! [A: $i] :
      ( ( cC152 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC150 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_57) ).

thf(106,plain,
    ! [A: $i] :
      ( ( ( cC152 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC150 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC150 @ B ) )
       => ( cC152 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(28,axiom,
    ! [A: $i] :
      ( ( cC80 @ A )
    <=> ( ( cC16xcomp @ A )
        & ( cC78xcomp @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_183) ).

thf(238,plain,
    ! [A: $i] :
      ( ( ( cC80 @ A )
       => ( ( cC16xcomp @ A )
          & ( cC78xcomp @ A ) ) )
      & ( ( ( cC16xcomp @ A )
          & ( cC78xcomp @ A ) )
       => ( cC80 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(25,axiom,
    ! [A: $i] :
      ( ( cC40xcomp @ A )
    <=> ~ ? [B: $i] : ( ra_Px86 @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_143) ).

thf(221,plain,
    ! [A: $i] :
      ( ( ( cC40xcomp @ A )
       => ~ ? [B: $i] : ( ra_Px86 @ A @ B ) )
      & ( ~ ? [B: $i] : ( ra_Px86 @ A @ B )
       => ( cC40xcomp @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(62,axiom,
    cC214xcomp @ iV3102,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_216) ).

thf(428,plain,
    cC214xcomp @ iV3102,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(40,axiom,
    ! [A: $i] :
      ( ( cC102 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC16xcomp @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_8) ).

thf(307,plain,
    ! [A: $i] :
      ( ( ( cC102 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC16xcomp @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC16xcomp @ B ) )
       => ( cC102 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(7,axiom,
    ! [A: $i] :
      ( ( cC164 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC162 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_67) ).

thf(117,plain,
    ! [A: $i] :
      ( ( ( cC164 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC162 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC162 @ B ) )
       => ( cC164 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(45,axiom,
    ! [A: $i] :
      ( ( cC86 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC16xcomp @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_186) ).

thf(334,plain,
    ! [A: $i] :
      ( ( ( cC86 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC16xcomp @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC16xcomp @ B ) )
       => ( cC86 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(55,axiom,
    ! [A: $i] :
      ( ( cC178 @ A )
    <=> ( ( cC16xcomp @ A )
        & ( cC176xcomp @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_83) ).

thf(392,plain,
    ! [A: $i] :
      ( ( ( cC178 @ A )
       => ( ( cC16xcomp @ A )
          & ( cC176xcomp @ A ) ) )
      & ( ( ( cC16xcomp @ A )
          & ( cC176xcomp @ A ) )
       => ( cC178 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(63,axiom,
    cTOP @ iV3102,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_205) ).

thf(429,plain,
    cTOP @ iV3102,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(76,axiom,
    ! [A: $i] :
      ( ( rR1 @ iV3102 @ A )
     => ( cC40xcomp @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_213) ).

thf(467,plain,
    ! [A: $i] :
      ( ( rR1 @ iV3102 @ A )
     => ( cC40xcomp @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(81,axiom,
    ! [A: $i] :
      ( ( cC28 @ A )
    <=> ( ( cC16xcomp @ A )
        & ( cC26xcomp @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_131) ).

thf(484,plain,
    ! [A: $i] :
      ( ( ( cC28 @ A )
       => ( ( cC16xcomp @ A )
          & ( cC26xcomp @ A ) ) )
      & ( ( ( cC16xcomp @ A )
          & ( cC26xcomp @ A ) )
       => ( cC28 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(44,axiom,
    ! [A: $i] :
      ( ( cC100xcomp @ A )
    <=> ? [B: $i] : ( ra_Px76 @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).

thf(329,plain,
    ! [A: $i] :
      ( ( ( cC100xcomp @ A )
       => ? [B: $i] : ( ra_Px76 @ A @ B ) )
      & ( ? [B: $i] : ( ra_Px76 @ A @ B )
       => ( cC100xcomp @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(43,axiom,
    ! [A: $i] :
      ( ( cC42xcomp @ A )
    <=> ~ ? [B: $i] : ( ra_Px14 @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_146) ).

thf(324,plain,
    ! [A: $i] :
      ( ( ( cC42xcomp @ A )
       => ~ ? [B: $i] : ( ra_Px14 @ A @ B ) )
      & ( ~ ? [B: $i] : ( ra_Px14 @ A @ B )
       => ( cC42xcomp @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(19,axiom,
    ! [A: $i] :
      ( ( cC16xcomp @ A )
    <=> ~ ? [B: $i] : ( ra_Px5 @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_62) ).

thf(188,plain,
    ! [A: $i] :
      ( ( ( cC16xcomp @ A )
       => ~ ? [B: $i] : ( ra_Px5 @ A @ B ) )
      & ( ~ ? [B: $i] : ( ra_Px5 @ A @ B )
       => ( cC16xcomp @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(11,axiom,
    ! [A: $i] :
      ( ( cC10 @ A )
    <=> ? [B: $i] : ( ra_Px87 @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).

thf(141,plain,
    ! [A: $i] :
      ( ( ( cC10 @ A )
       => ? [B: $i] : ( ra_Px87 @ A @ B ) )
      & ( ? [B: $i] : ( ra_Px87 @ A @ B )
       => ( cC10 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(31,axiom,
    ! [A: $i] :
      ( ( cC60xcomp @ A )
    <=> ? [B: $i] : ( ra_Px85 @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_162) ).

thf(256,plain,
    ! [A: $i] :
      ( ( ( cC60xcomp @ A )
       => ? [B: $i] : ( ra_Px85 @ A @ B ) )
      & ( ? [B: $i] : ( ra_Px85 @ A @ B )
       => ( cC60xcomp @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(20,axiom,
    ! [A: $i] :
      ( ( cC4 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC2xcomp @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_140) ).

thf(193,plain,
    ! [A: $i] :
      ( ( ( cC4 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC2xcomp @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC2xcomp @ B ) )
       => ( cC4 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(71,axiom,
    cC12xcomp @ iV3102,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_215) ).

thf(457,plain,
    cC12xcomp @ iV3102,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(9,axiom,
    ! [A: $i] :
      ( ( cC188 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC186 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_92) ).

thf(129,plain,
    ! [A: $i] :
      ( ( ( cC188 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC186 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC186 @ B ) )
       => ( cC188 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(86,axiom,
    cC32xcomp @ iV3102,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_207) ).

thf(503,plain,
    cC32xcomp @ iV3102,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(29,axiom,
    ! [A: $i] :
      ( ( cC172 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC16xcomp @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_77) ).

thf(244,plain,
    ! [A: $i] :
      ( ( ( cC172 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC16xcomp @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC16xcomp @ B ) )
       => ( cC172 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(22,axiom,
    ! [A: $i] :
      ( ( cC98 @ A )
    <=> ( ( cC72xcomp @ A )
        & ( cC96xcomp @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_199) ).

thf(205,plain,
    ! [A: $i] :
      ( ( ( cC98 @ A )
       => ( ( cC72xcomp @ A )
          & ( cC96xcomp @ A ) ) )
      & ( ( ( cC72xcomp @ A )
          & ( cC96xcomp @ A ) )
       => ( cC98 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(56,axiom,
    ! [A: $i] :
      ( ( cC186 @ A )
    <=> ( ( cC16xcomp @ A )
        & ( cC184xcomp @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_91) ).

thf(398,plain,
    ! [A: $i] :
      ( ( ( cC186 @ A )
       => ( ( cC16xcomp @ A )
          & ( cC184xcomp @ A ) ) )
      & ( ( ( cC16xcomp @ A )
          & ( cC184xcomp @ A ) )
       => ( cC186 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(64,axiom,
    ! [A: $i] :
      ( ( cC216 @ A )
    <=> ( ( cC64 @ A )
        & ( cC214xcomp @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_121) ).

thf(430,plain,
    ! [A: $i] :
      ( ( ( cC216 @ A )
       => ( ( cC64 @ A )
          & ( cC214xcomp @ A ) ) )
      & ( ( ( cC64 @ A )
          & ( cC214xcomp @ A ) )
       => ( cC216 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(67,axiom,
    cC16xcomp @ iV3102,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_210) ).

thf(444,plain,
    cC16xcomp @ iV3102,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(68,axiom,
    cTEST @ iV3102,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_202) ).

thf(445,plain,
    cTEST @ iV3102,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(53,axiom,
    ! [A: $i] :
      ( ( cC12xcomp @ A )
    <=> ? [B: $i] : ( ra_Px4 @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_25) ).

thf(382,plain,
    ! [A: $i] :
      ( ( ( cC12xcomp @ A )
       => ? [B: $i] : ( ra_Px4 @ A @ B ) )
      & ( ? [B: $i] : ( ra_Px4 @ A @ B )
       => ( cC12xcomp @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(41,axiom,
    ! [A: $i] :
      ( ( cC62xcomp @ A )
    <=> ~ ? [B: $i] : ( ra_Px20 @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_165) ).

thf(313,plain,
    ! [A: $i] :
      ( ( ( cC62xcomp @ A )
       => ~ ? [B: $i] : ( ra_Px20 @ A @ B ) )
      & ( ~ ? [B: $i] : ( ra_Px20 @ A @ B )
       => ( cC62xcomp @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(75,axiom,
    cC42xcomp @ iV3102,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_211) ).

thf(466,plain,
    cC42xcomp @ iV3102,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(70,axiom,
    ! [A: $i] :
      ( ( cC30 @ A )
    <=> ( ( cC28 @ A )
        & ( cC14 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_132) ).

thf(451,plain,
    ! [A: $i] :
      ( ( ( cC30 @ A )
       => ( ( cC28 @ A )
          & ( cC14 @ A ) ) )
      & ( ( ( cC28 @ A )
          & ( cC14 @ A ) )
       => ( cC30 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(42,axiom,
    ! [A: $i] :
      ( ( cC144 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC16xcomp @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_51) ).

thf(318,plain,
    ! [A: $i] :
      ( ( ( cC144 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC16xcomp @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC16xcomp @ B ) )
       => ( cC144 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(79,axiom,
    ! [A: $i] :
      ( ( cC46 @ A )
    <=> ( ( cC30 @ A )
        & ( cC44 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_148) ).

thf(477,plain,
    ! [A: $i] :
      ( ( ( cC46 @ A )
       => ( ( cC30 @ A )
          & ( cC44 @ A ) ) )
      & ( ( ( cC30 @ A )
          & ( cC44 @ A ) )
       => ( cC46 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(54,axiom,
    ! [A: $i] :
      ( ( cC24xcomp @ A )
    <=> ? [B: $i] : ( ra_Px88 @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_127) ).

thf(387,plain,
    ! [A: $i] :
      ( ( ( cC24xcomp @ A )
       => ? [B: $i] : ( ra_Px88 @ A @ B ) )
      & ( ? [B: $i] : ( ra_Px88 @ A @ B )
       => ( cC24xcomp @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(80,axiom,
    cC2xcomp @ iV3102,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_203) ).

thf(483,plain,
    cC2xcomp @ iV3102,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(10,axiom,
    ! [A: $i] :
      ( ( cC118 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC116 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_22) ).

thf(135,plain,
    ! [A: $i] :
      ( ( ( cC118 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC116 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC116 @ B ) )
       => ( cC118 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(26,axiom,
    ! [A: $i] :
      ( ( cC48 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC16xcomp @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_149) ).

thf(226,plain,
    ! [A: $i] :
      ( ( ( cC48 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC16xcomp @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC16xcomp @ B ) )
       => ( cC48 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(33,axiom,
    ! [A: $i] :
      ( ( cC2xcomp @ A )
    <=> ? [B: $i] : ( ra_Px1 @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_101) ).

thf(267,plain,
    ! [A: $i] :
      ( ( ( cC2xcomp @ A )
       => ? [B: $i] : ( ra_Px1 @ A @ B ) )
      & ( ? [B: $i] : ( ra_Px1 @ A @ B )
       => ( cC2xcomp @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(66,axiom,
    ! [A: $i] :
      ( ( cC44 @ A )
    <=> ( ( cC42xcomp @ A )
        & ( cC32xcomp @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_147) ).

thf(438,plain,
    ! [A: $i] :
      ( ( ( cC44 @ A )
       => ( ( cC42xcomp @ A )
          & ( cC32xcomp @ A ) ) )
      & ( ( ( cC42xcomp @ A )
          & ( cC32xcomp @ A ) )
       => ( cC44 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(82,axiom,
    ! [A: $i] :
      ( ( cC64 @ A )
    <=> ( ( cC62xcomp @ A )
        & ( cTOP @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_166) ).

thf(490,plain,
    ! [A: $i] :
      ( ( ( cC64 @ A )
       => ( ( cC62xcomp @ A )
          & ( cTOP @ A ) ) )
      & ( ( ( cC62xcomp @ A )
          & ( cTOP @ A ) )
       => ( cC64 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(61,axiom,
    ! [A: $i] :
      ( ( rR1 @ iV3102 @ A )
     => ( cC98 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_208) ).

thf(426,plain,
    ! [A: $i] :
      ( ( rR1 @ iV3102 @ A )
     => ( cC98 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(6,axiom,
    ! [A: $i] :
      ( ( cC40 @ A )
    <=> ? [B: $i] : ( ra_Px86 @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_141) ).

thf(112,plain,
    ! [A: $i] :
      ( ( ( cC40 @ A )
       => ? [B: $i] : ( ra_Px86 @ A @ B ) )
      & ( ? [B: $i] : ( ra_Px86 @ A @ B )
       => ( cC40 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(8,axiom,
    ! [A: $i] :
      ( ( cC82 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC80 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_184) ).

thf(123,plain,
    ! [A: $i] :
      ( ( ( cC82 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC80 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC80 @ B ) )
       => ( cC82 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(72,axiom,
    cC100xcomp @ iV3102,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_218) ).

thf(458,plain,
    cC100xcomp @ iV3102,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(21,axiom,
    ! [A: $i] :
      ( ( cC142 @ A )
    <=> ( ( cC16xcomp @ A )
        & ( cC140xcomp @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_48) ).

thf(199,plain,
    ! [A: $i] :
      ( ( ( cC142 @ A )
       => ( ( cC16xcomp @ A )
          & ( cC140xcomp @ A ) ) )
      & ( ( ( cC16xcomp @ A )
          & ( cC140xcomp @ A ) )
       => ( cC142 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(18,axiom,
    ! [A: $i] :
      ( ( cC156 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC16xcomp @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_59) ).

thf(182,plain,
    ! [A: $i] :
      ( ( ( cC156 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC16xcomp @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC16xcomp @ B ) )
       => ( cC156 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(51,axiom,
    ! [A: $i] :
      ( ( cC198 @ A )
    <=> ( ( cC16xcomp @ A )
        & ( cC196xcomp @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_99) ).

thf(370,plain,
    ! [A: $i] :
      ( ( ( cC198 @ A )
       => ( ( cC16xcomp @ A )
          & ( cC196xcomp @ A ) ) )
      & ( ( ( cC16xcomp @ A )
          & ( cC196xcomp @ A ) )
       => ( cC198 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(85,axiom,
    cC62xcomp @ iV3102,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_212) ).

thf(502,plain,
    cC62xcomp @ iV3102,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(69,axiom,
    ! [A: $i] :
      ( ( xsd_string @ A )
    <=> ~ ( xsd_integer @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).

thf(446,plain,
    ! [A: $i] :
      ( ( ( xsd_string @ A )
       => ~ ( xsd_integer @ A ) )
      & ( ~ ( xsd_integer @ A )
       => ( xsd_string @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(84,axiom,
    ! [A: $i] :
      ( ( cowlThing @ A )
      & ~ ( cowlNothing @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_0) ).

thf(497,plain,
    ! [A: $i] :
      ( ( cowlThing @ A )
      & ~ ( cowlNothing @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(30,axiom,
    ! [A: $i] :
      ( ( cC34 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC32xcomp @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_135) ).

thf(250,plain,
    ! [A: $i] :
      ( ( ( cC34 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC32xcomp @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC32xcomp @ B ) )
       => ( cC34 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(74,axiom,
    cC26xcomp @ iV3102,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_206) ).

thf(465,plain,
    cC26xcomp @ iV3102,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(34,axiom,
    ! [A: $i] :
      ( ( cC32xcomp @ A )
    <=> ? [B: $i] : ( ra_Px10 @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_134) ).

thf(272,plain,
    ! [A: $i] :
      ( ( ( cC32xcomp @ A )
       => ? [B: $i] : ( ra_Px10 @ A @ B ) )
      & ( ? [B: $i] : ( ra_Px10 @ A @ B )
       => ( cC32xcomp @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(47,axiom,
    ! [A: $i] :
      ( ( cC66 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC16xcomp @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_167) ).

thf(346,plain,
    ! [A: $i] :
      ( ( ( cC66 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC16xcomp @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC16xcomp @ B ) )
       => ( cC66 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(58,axiom,
    ! [A: $i] :
      ( ( cC10xcomp @ A )
    <=> ~ ? [B: $i] : ( ra_Px87 @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).

thf(410,plain,
    ! [A: $i] :
      ( ( ( cC10xcomp @ A )
       => ~ ? [B: $i] : ( ra_Px87 @ A @ B ) )
      & ( ~ ? [B: $i] : ( ra_Px87 @ A @ B )
       => ( cC10xcomp @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(12,axiom,
    ! [A: $i] :
      ( ( cC130 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC128 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_33) ).

thf(146,plain,
    ! [A: $i] :
      ( ( ( cC130 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC128 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC128 @ B ) )
       => ( cC130 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(49,axiom,
    ! [A: $i] :
      ( ( cC192 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC16xcomp @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_94) ).

thf(358,plain,
    ! [A: $i] :
      ( ( ( cC192 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC16xcomp @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC16xcomp @ B ) )
       => ( cC192 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(3,axiom,
    ! [A: $i] :
      ( ( cC58 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC56 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_157) ).

thf(94,plain,
    ! [A: $i] :
      ( ( ( cC58 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC56 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC56 @ B ) )
       => ( cC58 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(36,axiom,
    ! [A: $i] :
      ( ( cC10 @ A )
    <=> ( ( cC2xcomp @ A )
        & ( cC8xcomp @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).

thf(283,plain,
    ! [A: $i] :
      ( ( ( cC10 @ A )
       => ( ( cC2xcomp @ A )
          & ( cC8xcomp @ A ) ) )
      & ( ( ( cC2xcomp @ A )
          & ( cC8xcomp @ A ) )
       => ( cC10 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(59,axiom,
    ! [A: $i] :
      ( ( cC72 @ A )
    <=> ( ( cC16xcomp @ A )
        & ( cC70xcomp @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_173) ).

thf(415,plain,
    ! [A: $i] :
      ( ( ( cC72 @ A )
       => ( ( cC16xcomp @ A )
          & ( cC70xcomp @ A ) ) )
      & ( ( ( cC16xcomp @ A )
          & ( cC70xcomp @ A ) )
       => ( cC72 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(73,axiom,
    ! [A: $i] :
      ( ( cTEST @ A )
    <=> ( ( cC216 @ A )
        & ( cC46 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_201) ).

thf(459,plain,
    ! [A: $i] :
      ( ( ( cTEST @ A )
       => ( ( cC216 @ A )
          & ( cC46 @ A ) ) )
      & ( ( ( cC216 @ A )
          & ( cC46 @ A ) )
       => ( cTEST @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(35,axiom,
    ! [A: $i] :
      ( ( cC136 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC16xcomp @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_42) ).

thf(277,plain,
    ! [A: $i] :
      ( ( ( cC136 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC16xcomp @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC16xcomp @ B ) )
       => ( cC136 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(77,axiom,
    ! [A: $i] :
      ( ( cC14 @ A )
    <=> ( ( cC2xcomp @ A )
        & ( cC12xcomp @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_44) ).

thf(469,plain,
    ! [A: $i] :
      ( ( ( cC14 @ A )
       => ( ( cC2xcomp @ A )
          & ( cC12xcomp @ A ) ) )
      & ( ( ( cC2xcomp @ A )
          & ( cC12xcomp @ A ) )
       => ( cC14 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(83,axiom,
    cowlThing @ iV3102,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_217) ).

thf(496,plain,
    cowlThing @ iV3102,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(50,axiom,
    ! [A: $i] :
      ( ( cC18 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC16xcomp @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_85) ).

thf(364,plain,
    ! [A: $i] :
      ( ( ( cC18 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC16xcomp @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC16xcomp @ B ) )
       => ( cC18 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(27,axiom,
    ! [A: $i] :
      ( ( cC162 @ A )
    <=> ( ( cC16xcomp @ A )
        & ( cC160xcomp @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_66) ).

thf(232,plain,
    ! [A: $i] :
      ( ( ( cC162 @ A )
       => ( ( cC16xcomp @ A )
          & ( cC160xcomp @ A ) ) )
      & ( ( ( cC16xcomp @ A )
          & ( cC160xcomp @ A ) )
       => ( cC162 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(4,axiom,
    ! [A: $i] :
      ( ( cC94 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC92 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_193) ).

thf(100,plain,
    ! [A: $i] :
      ( ( ( cC94 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC92 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC92 @ B ) )
       => ( cC94 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(506,plain,
    $false,
    inference(e,[status(thm)],[170,340,504,176,295,158,88,352,404,301,436,421,152,289,261,216,475,164,376,211,106,238,221,428,307,117,334,392,429,467,484,329,324,188,141,256,193,457,129,503,244,205,398,430,444,445,382,313,466,451,318,477,387,483,135,226,267,438,490,426,112,123,458,199,182,370,502,446,497,250,465,272,346,410,146,358,94,283,415,459,277,469,496,364,232,100]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : KRS157+1 : TPTP v8.1.2. Released v3.1.0.
% 0.13/0.15  % Command  : run_Leo-III %s %d
% 0.17/0.37  % Computer : n011.cluster.edu
% 0.17/0.37  % Model    : x86_64 x86_64
% 0.17/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37  % Memory   : 8042.1875MB
% 0.17/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37  % CPULimit : 300
% 0.17/0.37  % WCLimit  : 300
% 0.17/0.37  % DateTime : Mon May  6 15:19:54 EDT 2024
% 0.17/0.37  % CPUTime  : 
% 0.95/0.93  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.54/1.20  % [INFO] 	 Parsing done (260ms). 
% 1.54/1.21  % [INFO] 	 Running in sequential loop mode. 
% 2.10/1.43  % [INFO] 	 eprover registered as external prover. 
% 2.10/1.43  % [INFO] 	 cvc4 registered as external prover. 
% 2.10/1.43  % [INFO] 	 Scanning for conjecture ... 
% 2.38/1.51  % [INFO] 	 Found a conjecture and 219 axioms. Running axiom selection ... 
% 2.44/1.58  % [INFO] 	 Axiom selection finished. Selected 85 axioms (removed 134 axioms). 
% 2.81/1.64  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.81/1.65  % [INFO] 	 Type checking passed. 
% 2.81/1.65  % [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 ... 
% 5.47/2.58  % External prover 'e' found a proof!
% 5.47/2.58  % [INFO] 	 Killing All external provers ... 
% 5.47/2.59  % Time passed: 2001ms (effective reasoning time: 1375ms)
% 5.47/2.59  % 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)>
% 5.47/2.59  % Axioms used in derivation (85): axiom_7, axiom_33, axiom_209, axiom_186, axiom_131, axiom_22, axiom_59, axiom_77, axiom_217, axiom_44, axiom_198, axiom_214, axiom_206, axiom_191, axiom_121, axiom_67, axiom_141, axiom_130, axiom_51, axiom_21, axiom_157, axiom_99, axiom_203, axiom_103, axiom_147, axiom_146, axiom_184, axiom_2, axiom_173, axiom_27, axiom_162, axiom_143, axiom_218, axiom_32, axiom_91, axiom_132, axiom_208, axiom_155, axiom_92, axiom_148, axiom_16, axiom_213, axiom_207, axiom_3, axiom_140, axiom_202, axiom_85, axiom_165, axiom_205, axiom_42, axiom_1, axiom_212, axiom_57, axiom_127, axiom_150, axiom_216, axiom_167, axiom_101, axiom_8, axiom_193, axiom_86, axiom_201, axiom_149, axiom_183, axiom_166, axiom_13, axiom_134, axiom_25, axiom_211, axiom_204, axiom_0, axiom_62, axiom_175, axiom_199, axiom_215, axiom_56, axiom_48, axiom_142, axiom_83, axiom_120, axiom_4, axiom_210, axiom_66, axiom_135, axiom_94
% 5.47/2.59  % No. of inferences in proof: 174
% 5.47/2.59  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2001 ms resp. 1375 ms w/o parsing
% 5.86/2.66  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.86/2.66  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------