TSTP Solution File: KRS148+1 by Leo-III---1.7.10

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.10
% Problem  : KRS148+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 07:51:59 EDT 2024

% Result   : Theorem 5.28s 2.28s
% Output   : Refutation 5.58s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  155
% Syntax   : Number of formulae    :  239 (  27 unt;  73 typ;   0 def)
%            Number of atoms       :  637 (   0 equ;   0 cnn)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives : 1368 ( 137   ~;   0   |; 270   &; 760   @)
%                                         (  65 <=>; 136  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   71 (  71   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   74 (  73 usr;   4 con; 0-2 aty)
%            Number of variables   :  256 (   0   ^ 142   !; 114   ?; 256   :)

% 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(cC138_type,type,
    cC138: $i > $o ).

thf(iV5475_type,type,
    iV5475: $i ).

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

thf(cC140_type,type,
    cC140: $i > $o ).

thf(cC78_type,type,
    cC78: $i > $o ).

thf(cC76_type,type,
    cC76: $i > $o ).

thf(cC2_type,type,
    cC2: $i > $o ).

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

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

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

thf(cC96_type,type,
    cC96: $i > $o ).

thf(cC100_type,type,
    cC100: $i > $o ).

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

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

thf(cC120_type,type,
    cC120: $i > $o ).

thf(cC70_type,type,
    cC70: $i > $o ).

thf(cC68_type,type,
    cC68: $i > $o ).

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

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

thf(cC26_type,type,
    cC26: $i > $o ).

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

thf(cC24_type,type,
    cC24: $i > $o ).

thf(cC42_type,type,
    cC42: $i > $o ).

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

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

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

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

thf(cC16_type,type,
    cC16: $i > $o ).

thf(cC6_type,type,
    cC6: $i > $o ).

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

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

thf(cC126_type,type,
    cC126: $i > $o ).

thf(cC124_type,type,
    cC124: $i > $o ).

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

thf(cC90_type,type,
    cC90: $i > $o ).

thf(cC22_type,type,
    cC22: $i > $o ).

thf(cC20_type,type,
    cC20: $i > $o ).

thf(cC104_type,type,
    cC104: $i > $o ).

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

thf(cC88_type,type,
    cC88: $i > $o ).

thf(cC134_type,type,
    cC134: $i > $o ).

thf(cC132_type,type,
    cC132: $i > $o ).

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

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

thf(cC54_type,type,
    cC54: $i > $o ).

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

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

thf(cC32_type,type,
    cC32: $i > $o ).

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

thf(cC8_type,type,
    cC8: $i > $o ).

thf(cC52_type,type,
    cC52: $i > $o ).

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

thf(iV5478_type,type,
    iV5478: $i ).

thf(cC106_type,type,
    cC106: $i > $o ).

thf(cC12_type,type,
    cC12: $i > $o ).

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

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

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

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

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

thf(cC114_type,type,
    cC114: $i > $o ).

thf(cC112_type,type,
    cC112: $i > $o ).

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

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

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

thf(cC36_type,type,
    cC36: $i > $o ).

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

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

thf(iV5476_type,type,
    iV5476: $i ).

thf(57,axiom,
    ! [A: $i] :
      ( ( cC136 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC134 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_22) ).

thf(385,plain,
    ! [A: $i] :
      ( ( ( cC136 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC134 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC134 @ B ) )
       => ( cC136 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(22,axiom,
    ! [A: $i] :
      ( ( cC56 @ A )
    <=> ( ~ ( cC54 @ A )
        & ~ ( cC2 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_47) ).

thf(204,plain,
    ! [A: $i] :
      ( ( ( cC56 @ A )
       => ( ~ ( cC54 @ A )
          & ~ ( cC2 @ A ) ) )
      & ( ( ~ ( cC54 @ A )
          & ~ ( cC2 @ A ) )
       => ( cC56 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(27,axiom,
    ! [A: $i] :
      ( ( cC64 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ~ ( cC2 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_52) ).

thf(230,plain,
    ! [A: $i] :
      ( ( ( cC64 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC2 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC2 @ B ) )
       => ( cC64 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(70,axiom,
    ! [A: $i] :
      ( ( cTEST @ A )
    <=> ( ( cC140 @ A )
        & ( cC116 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_71) ).

thf(455,plain,
    ! [A: $i] :
      ( ( ( cTEST @ A )
       => ( ( cC140 @ A )
          & ( cC116 @ A ) ) )
      & ( ( ( cC140 @ A )
          & ( cC116 @ A ) )
       => ( cTEST @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(82,axiom,
    cTEST @ iV5475,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_72) ).

thf(497,plain,
    cTEST @ iV5475,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(39,axiom,
    ! [A: $i] :
      ( ( cC82 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ~ ( cC80 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_62) ).

thf(290,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)],[39]) ).

thf(64,axiom,
    ~ ( cC130 @ iV5478 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_83) ).

thf(427,plain,
    ~ ( cC130 @ iV5478 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(11,axiom,
    ! [A: $i] :
      ( ( cC42 @ A )
    <=> ( ~ ( cC2 @ A )
        & ( cC40 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_40) ).

thf(138,plain,
    ! [A: $i] :
      ( ( ( cC42 @ A )
       => ( ~ ( cC2 @ A )
          & ( cC40 @ A ) ) )
      & ( ( ~ ( cC2 @ A )
          & ( cC40 @ A ) )
       => ( cC42 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(74,axiom,
    ! [A: $i] :
      ( ( cC116 @ A )
    <=> ( ( cTOP @ A )
        & ~ ( cC114 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_11) ).

thf(468,plain,
    ! [A: $i] :
      ( ( ( cC116 @ A )
       => ( ( cTOP @ A )
          & ~ ( cC114 @ A ) ) )
      & ( ( ( cTOP @ A )
          & ~ ( cC114 @ A ) )
       => ( cC116 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(77,axiom,
    cowlThing @ iV5478,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_85) ).

thf(481,plain,
    cowlThing @ iV5478,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(36,axiom,
    ! [A: $i] :
      ( ( cC30 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC28 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_33) ).

thf(276,plain,
    ! [A: $i] :
      ( ( ( cC30 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC28 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC28 @ B ) )
       => ( cC30 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(69,axiom,
    ! [A: $i] :
      ( ( cC50 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ~ ( cC2 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_44) ).

thf(449,plain,
    ! [A: $i] :
      ( ( ( cC50 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC2 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC2 @ B ) )
       => ( cC50 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(8,axiom,
    ! [A: $i] :
      ( ( cC70 @ A )
    <=> ( ( cC2 @ A )
        & ( cC68 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_55) ).

thf(120,plain,
    ! [A: $i] :
      ( ( ( cC70 @ A )
       => ( ( cC2 @ A )
          & ( cC68 @ A ) ) )
      & ( ( ( cC2 @ A )
          & ( cC68 @ A ) )
       => ( cC70 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(56,axiom,
    ! [A: $i] :
      ( ( cC94 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC92 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_68) ).

thf(379,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)],[56]) ).

thf(17,axiom,
    ! [A: $i] :
      ( ( cC92 @ A )
    <=> ( ( cC2 @ A )
        & ( cC90 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_67) ).

thf(174,plain,
    ! [A: $i] :
      ( ( ( cC92 @ A )
       => ( ( cC2 @ A )
          & ( cC90 @ A ) ) )
      & ( ( ( cC2 @ A )
          & ( cC90 @ A ) )
       => ( cC92 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(38,axiom,
    ~ ( cC12 @ iV5478 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_80) ).

thf(288,plain,
    ~ ( cC12 @ iV5478 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(63,axiom,
    ! [A: $i] :
      ( ( cC36 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC34 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_36) ).

thf(421,plain,
    ! [A: $i] :
      ( ( ( cC36 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC34 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC34 @ B ) )
       => ( cC36 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(47,axiom,
    ! [A: $i] :
      ( ( cC72 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC70 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_56) ).

thf(325,plain,
    ! [A: $i] :
      ( ( ( cC72 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC70 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC70 @ B ) )
       => ( cC72 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(26,axiom,
    ! [A: $i] :
      ( ( rR1 @ iV5478 @ A )
     => ( cC2 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_81) ).

thf(228,plain,
    ! [A: $i] :
      ( ( rR1 @ iV5478 @ A )
     => ( cC2 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(24,axiom,
    ! [A: $i] :
      ( ( cC10 @ A )
    <=> ( ~ ( cC8 @ A )
        & ~ ( cC2 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).

thf(216,plain,
    ! [A: $i] :
      ( ( ( cC10 @ A )
       => ( ~ ( cC8 @ A )
          & ~ ( cC2 @ A ) ) )
      & ( ( ~ ( cC8 @ A )
          & ~ ( cC2 @ A ) )
       => ( cC10 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(1,conjecture,
    ( ! [A: $i] :
        ( ( cowlThing @ A )
        & ~ ( cowlNothing @ A ) )
    & ! [A: $i] :
        ( ( xsd_string @ A )
      <=> ~ ( xsd_integer @ A ) )
    & ( cC138 @ iV5475 )
    & ( cowlThing @ iV5475 )
    & ( cC116 @ iV5475 )
    & ( cC140 @ iV5475 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',the_axiom) ).

thf(2,negated_conjecture,
    ~ ( ! [A: $i] :
          ( ( cowlThing @ A )
          & ~ ( cowlNothing @ A ) )
      & ! [A: $i] :
          ( ( xsd_string @ A )
        <=> ~ ( xsd_integer @ A ) )
      & ( cC138 @ iV5475 )
      & ( cowlThing @ iV5475 )
      & ( cC116 @ iV5475 )
      & ( cC140 @ iV5475 ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(84,plain,
    ~ ( ! [A: $i] :
          ( ( cowlThing @ A )
          & ~ ( cowlNothing @ A ) )
      & ! [A: $i] :
          ( ( ( xsd_string @ A )
           => ~ ( xsd_integer @ A ) )
          & ( ~ ( xsd_integer @ A )
           => ( xsd_string @ A ) ) )
      & ( cC138 @ iV5475 )
      & ( cowlThing @ iV5475 )
      & ( cC116 @ iV5475 )
      & ( cC140 @ iV5475 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(76,axiom,
    rR1 @ iV5475 @ iV5476,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_77) ).

thf(480,plain,
    rR1 @ iV5475 @ iV5476,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(59,axiom,
    ! [A: $i] :
      ( ( cC44 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ~ ( cC2 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_41) ).

thf(397,plain,
    ! [A: $i] :
      ( ( ( cC44 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC2 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC2 @ B ) )
       => ( cC44 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(10,axiom,
    ! [A: $i] :
      ( ( cC26 @ A )
    <=> ( ( cC14 @ A )
        & ~ ( cC24 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_31) ).

thf(132,plain,
    ! [A: $i] :
      ( ( ( cC26 @ A )
       => ( ( cC14 @ A )
          & ~ ( cC24 @ A ) ) )
      & ( ( ( cC14 @ A )
          & ~ ( cC24 @ A ) )
       => ( cC26 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(30,axiom,
    ! [A: $i] :
      ( ( cC68 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ~ ( cC2 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_54) ).

thf(248,plain,
    ! [A: $i] :
      ( ( ( cC68 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC2 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC2 @ B ) )
       => ( cC68 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(35,axiom,
    ! [A: $i] :
      ( ( cC12 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC10 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_13) ).

thf(270,plain,
    ! [A: $i] :
      ( ( ( cC12 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC10 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC10 @ B ) )
       => ( cC12 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(5,axiom,
    ! [A: $i] :
      ( ( cC98 @ A )
    <=> ( ( cC96 @ A )
        & ( cC2 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_70) ).

thf(102,plain,
    ! [A: $i] :
      ( ( ( cC98 @ A )
       => ( ( cC96 @ A )
          & ( cC2 @ A ) ) )
      & ( ( ( cC96 @ A )
          & ( cC2 @ A ) )
       => ( cC98 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(51,axiom,
    ! [A: $i] :
      ( ( cC16 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ~ ( cC2 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_26) ).

thf(349,plain,
    ! [A: $i] :
      ( ( ( cC16 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC2 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC2 @ B ) )
       => ( cC16 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(20,axiom,
    ! [A: $i] :
      ( ( cC134 @ A )
    <=> ( ( cC122 @ A )
        & ~ ( cC132 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_21) ).

thf(192,plain,
    ! [A: $i] :
      ( ( ( cC134 @ A )
       => ( ( cC122 @ A )
          & ~ ( cC132 @ A ) ) )
      & ( ( ( cC122 @ A )
          & ~ ( cC132 @ A ) )
       => ( cC134 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(65,axiom,
    ! [A: $i] :
      ( ( cC40 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ~ ( cC2 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_39) ).

thf(429,plain,
    ! [A: $i] :
      ( ( ( cC40 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC2 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC2 @ B ) )
       => ( cC40 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(73,axiom,
    cowlThing @ iV5476,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_78) ).

thf(467,plain,
    cowlThing @ iV5476,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(53,axiom,
    ! [A: $i] :
      ( ( cC90 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ~ ( cC2 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_66) ).

thf(361,plain,
    ! [A: $i] :
      ( ( ( cC90 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC2 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC2 @ B ) )
       => ( cC90 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(66,axiom,
    ! [A: $i] :
      ( ( cC128 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC126 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_18) ).

thf(435,plain,
    ! [A: $i] :
      ( ( ( cC128 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC126 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC126 @ B ) )
       => ( cC128 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(71,axiom,
    cTOP @ iV5475,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_73) ).

thf(461,plain,
    cTOP @ iV5475,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(14,axiom,
    ! [A: $i] :
      ( ( cC6 @ A )
    <=> ( ( cC2 @ A )
        & ( cC4 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_49) ).

thf(156,plain,
    ! [A: $i] :
      ( ( ( cC6 @ A )
       => ( ( cC2 @ A )
          & ( cC4 @ A ) ) )
      & ( ( ( cC2 @ A )
          & ( cC4 @ A ) )
       => ( cC6 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(60,axiom,
    ! [A: $i] :
      ( ( cC58 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC56 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_48) ).

thf(403,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)],[60]) ).

thf(32,axiom,
    ! [A: $i] :
      ( ( cC96 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ~ ( cC2 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_69) ).

thf(256,plain,
    ! [A: $i] :
      ( ( ( cC96 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC2 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC2 @ B ) )
       => ( cC96 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(80,axiom,
    ! [A: $i] :
      ( ( cC140 @ A )
    <=> ( ( cTOP @ A )
        & ( cC138 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_25) ).

thf(489,plain,
    ! [A: $i] :
      ( ( ( cC140 @ A )
       => ( ( cTOP @ A )
          & ( cC138 @ A ) ) )
      & ( ( ( cTOP @ A )
          & ( cC138 @ A ) )
       => ( cC140 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(4,axiom,
    ! [A: $i] :
      ( ( cC130 @ A )
    <=> ( ~ ( cC2 @ A )
        & ~ ( cC128 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_19) ).

thf(96,plain,
    ! [A: $i] :
      ( ( ( cC130 @ A )
       => ( ~ ( cC2 @ A )
          & ~ ( cC128 @ A ) ) )
      & ( ( ~ ( cC2 @ A )
          & ~ ( cC128 @ A ) )
       => ( cC130 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(50,axiom,
    ! [A: $i] :
      ( ( cC86 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ~ ( cC2 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_64) ).

thf(343,plain,
    ! [A: $i] :
      ( ( ( cC86 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC2 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC2 @ B ) )
       => ( cC86 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(44,axiom,
    ~ ( cC30 @ iV5478 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_82) ).

thf(311,plain,
    ~ ( cC30 @ iV5478 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(41,axiom,
    ! [A: $i] :
      ( ( cC4 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ~ ( cC2 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_38) ).

thf(298,plain,
    ! [A: $i] :
      ( ( ( cC4 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC2 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC2 @ B ) )
       => ( cC4 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(18,axiom,
    ! [A: $i] :
      ( ( cC22 @ A )
    <=> ( ~ ( cC20 @ A )
        & ~ ( cC2 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_29) ).

thf(180,plain,
    ! [A: $i] :
      ( ( ( cC22 @ A )
       => ( ~ ( cC20 @ A )
          & ~ ( cC2 @ A ) ) )
      & ( ( ~ ( cC20 @ A )
          & ~ ( cC2 @ A ) )
       => ( cC22 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(40,axiom,
    ! [A: $i] :
      ( ( rR1 @ iV5478 @ A )
     => ~ ( cC28 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_87) ).

thf(296,plain,
    ! [A: $i] :
      ( ( rR1 @ iV5478 @ A )
     => ~ ( cC28 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(58,axiom,
    ! [A: $i] :
      ( ( cC80 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC78 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_61) ).

thf(391,plain,
    ! [A: $i] :
      ( ( ( cC80 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC78 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC78 @ B ) )
       => ( cC80 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(45,axiom,
    ! [A: $i] :
      ( ( cC24 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC22 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_30) ).

thf(313,plain,
    ! [A: $i] :
      ( ( ( cC24 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC22 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC22 @ B ) )
       => ( cC24 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(12,axiom,
    ! [A: $i] :
      ( ( cC118 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ~ ( cC2 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_12) ).

thf(144,plain,
    ! [A: $i] :
      ( ( ( cC118 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC2 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC2 @ B ) )
       => ( cC118 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(83,axiom,
    cowlThing @ iV5475,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_74) ).

thf(498,plain,
    cowlThing @ iV5475,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(28,axiom,
    ! [A: $i] :
      ( ( cC106 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC104 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).

thf(236,plain,
    ! [A: $i] :
      ( ( ( cC106 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC104 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC104 @ B ) )
       => ( cC106 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(54,axiom,
    ! [A: $i] :
      ( ( cC20 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC18 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_28) ).

thf(367,plain,
    ! [A: $i] :
      ( ( ( cC20 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC18 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC18 @ B ) )
       => ( cC20 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(21,axiom,
    ! [A: $i] :
      ( ( cC88 @ A )
    <=> ( ( cC86 @ A )
        & ( cC2 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_65) ).

thf(198,plain,
    ! [A: $i] :
      ( ( ( cC88 @ A )
       => ( ( cC86 @ A )
          & ( cC2 @ A ) ) )
      & ( ( ( cC86 @ A )
          & ( cC2 @ A ) )
       => ( cC88 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(6,axiom,
    ! [A: $i] :
      ( ( cC100 @ A )
    <=> ( ~ ( cC98 @ A )
        & ( cC94 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).

thf(108,plain,
    ! [A: $i] :
      ( ( ( cC100 @ A )
       => ( ~ ( cC98 @ A )
          & ( cC94 @ A ) ) )
      & ( ( ~ ( cC98 @ A )
          & ( cC94 @ A ) )
       => ( cC100 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(72,axiom,
    ! [A: $i] :
      ( ( cowlThing @ A )
      & ~ ( cowlNothing @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_0) ).

thf(462,plain,
    ! [A: $i] :
      ( ( cowlThing @ A )
      & ~ ( cowlNothing @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(15,axiom,
    ! [A: $i] :
      ( ( cC28 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ~ ( cC2 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_32) ).

thf(162,plain,
    ! [A: $i] :
      ( ( ( cC28 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC2 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC2 @ B ) )
       => ( cC28 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(79,axiom,
    ~ ( cC114 @ iV5475 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_76) ).

thf(487,plain,
    ~ ( cC114 @ iV5475 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(52,axiom,
    ! [A: $i] :
      ( ( cC46 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ~ ( cC44 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_42) ).

thf(355,plain,
    ! [A: $i] :
      ( ( ( cC46 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC44 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC44 @ B ) )
       => ( cC46 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(37,axiom,
    ! [A: $i] :
      ( ( cC120 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ~ ( cC118 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_14) ).

thf(282,plain,
    ! [A: $i] :
      ( ( ( cC120 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC118 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC118 @ B ) )
       => ( cC120 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(13,axiom,
    ! [A: $i] :
      ( ( cC18 @ A )
    <=> ( ( cC16 @ A )
        & ( cC2 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_27) ).

thf(150,plain,
    ! [A: $i] :
      ( ( ( cC18 @ A )
       => ( ( cC16 @ A )
          & ( cC2 @ A ) ) )
      & ( ( ( cC16 @ A )
          & ( cC2 @ A ) )
       => ( cC18 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(61,axiom,
    ! [A: $i] :
      ( ( cC124 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ~ ( cC2 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_16) ).

thf(409,plain,
    ! [A: $i] :
      ( ( ( cC124 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC2 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC2 @ B ) )
       => ( cC124 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(43,axiom,
    cC2 @ iV5478,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_86) ).

thf(310,plain,
    cC2 @ iV5478,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(48,axiom,
    ! [A: $i] :
      ( ( cC14 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC12 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_24) ).

thf(331,plain,
    ! [A: $i] :
      ( ( ( cC14 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC12 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC12 @ B ) )
       => ( cC14 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(67,axiom,
    ! [A: $i] :
      ( ( cC132 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC130 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_20) ).

thf(441,plain,
    ! [A: $i] :
      ( ( ( cC132 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC130 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC130 @ B ) )
       => ( cC132 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(78,axiom,
    ! [A: $i] :
      ( ( xsd_string @ A )
    <=> ~ ( xsd_integer @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).

thf(482,plain,
    ! [A: $i] :
      ( ( ( xsd_string @ A )
       => ~ ( xsd_integer @ A ) )
      & ( ~ ( xsd_integer @ A )
       => ( xsd_string @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(81,axiom,
    ! [A: $i] :
      ( ( rR1 @ iV5475 @ A )
     => ~ ( cC112 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_75) ).

thf(495,plain,
    ! [A: $i] :
      ( ( rR1 @ iV5475 @ A )
     => ~ ( cC112 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(46,axiom,
    ! [A: $i] :
      ( ( cC76 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ~ ( cC2 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_58) ).

thf(319,plain,
    ! [A: $i] :
      ( ( ( cC76 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC2 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC2 @ B ) )
       => ( cC76 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(42,axiom,
    ! [A: $i] :
      ( ( cC8 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC6 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_60) ).

thf(304,plain,
    ! [A: $i] :
      ( ( ( cC8 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC6 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC6 @ B ) )
       => ( cC8 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(19,axiom,
    ! [A: $i] :
      ( ( cC104 @ A )
    <=> ( ~ ( cC102 @ A )
        & ( cC88 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).

thf(186,plain,
    ! [A: $i] :
      ( ( ( cC104 @ A )
       => ( ~ ( cC102 @ A )
          & ( cC88 @ A ) ) )
      & ( ( ~ ( cC102 @ A )
          & ( cC88 @ A ) )
       => ( cC104 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(7,axiom,
    ! [A: $i] :
      ( ( cC122 @ A )
    <=> ( ~ ( cC2 @ A )
        & ( cC120 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_15) ).

thf(114,plain,
    ! [A: $i] :
      ( ( ( cC122 @ A )
       => ( ~ ( cC2 @ A )
          & ( cC120 @ A ) ) )
      & ( ( ~ ( cC2 @ A )
          & ( cC120 @ A ) )
       => ( cC122 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(68,axiom,
    ~ ( cC34 @ iV5478 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_79) ).

thf(447,plain,
    ~ ( cC34 @ iV5478 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(55,axiom,
    ! [A: $i] :
      ( ( cC114 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC112 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_10) ).

thf(373,plain,
    ! [A: $i] :
      ( ( ( cC114 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC112 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC112 @ B ) )
       => ( cC114 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(16,axiom,
    ! [A: $i] :
      ( ( cC126 @ A )
    <=> ( ( cC124 @ A )
        & ( cC2 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_17) ).

thf(168,plain,
    ! [A: $i] :
      ( ( ( cC126 @ A )
       => ( ( cC124 @ A )
          & ( cC2 @ A ) ) )
      & ( ( ( cC124 @ A )
          & ( cC2 @ A ) )
       => ( cC126 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(33,axiom,
    ! [A: $i] :
      ( ( cC32 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ~ ( cC2 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_34) ).

thf(262,plain,
    ! [A: $i] :
      ( ( ( cC32 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC2 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC2 @ B ) )
       => ( cC32 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(23,axiom,
    ! [A: $i] :
      ( ( cC34 @ A )
    <=> ( ( cC30 @ A )
        & ~ ( cC32 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_35) ).

thf(210,plain,
    ! [A: $i] :
      ( ( ( cC34 @ A )
       => ( ( cC30 @ A )
          & ~ ( cC32 @ A ) ) )
      & ( ( ( cC30 @ A )
          & ~ ( cC32 @ A ) )
       => ( cC34 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(29,axiom,
    ! [A: $i] :
      ( ( cC102 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC100 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).

thf(242,plain,
    ! [A: $i] :
      ( ( ( cC102 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC100 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC100 @ B ) )
       => ( cC102 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(9,axiom,
    ! [A: $i] :
      ( ( cC66 @ A )
    <=> ( ( cC64 @ A )
        & ( cC2 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_53) ).

thf(126,plain,
    ! [A: $i] :
      ( ( ( cC66 @ A )
       => ( ( cC64 @ A )
          & ( cC2 @ A ) ) )
      & ( ( ( cC64 @ A )
          & ( cC2 @ A ) )
       => ( cC66 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(34,axiom,
    ! [A: $i] :
      ( ( rR1 @ iV5478 @ A )
     => ~ ( cC10 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_88) ).

thf(268,plain,
    ! [A: $i] :
      ( ( rR1 @ iV5478 @ A )
     => ~ ( cC10 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(75,axiom,
    ! [A: $i] :
      ( ( cC138 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC136 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_23) ).

thf(474,plain,
    ! [A: $i] :
      ( ( ( cC138 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC136 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC136 @ B ) )
       => ( cC138 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(62,axiom,
    ! [A: $i] :
      ( ( cC112 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ~ ( cC110 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_9) ).

thf(415,plain,
    ! [A: $i] :
      ( ( ( cC112 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC110 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ~ ( cC110 @ B ) )
       => ( cC112 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(3,axiom,
    ! [A: $i] :
      ( ( cC78 @ A )
    <=> ( ( cC76 @ A )
        & ( cC2 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_59) ).

thf(90,plain,
    ! [A: $i] :
      ( ( ( cC78 @ A )
       => ( ( cC76 @ A )
          & ( cC2 @ A ) ) )
      & ( ( ( cC76 @ A )
          & ( cC2 @ A ) )
       => ( cC78 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(31,axiom,
    ~ ( cC118 @ iV5478 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_84) ).

thf(254,plain,
    ~ ( cC118 @ iV5478 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(49,axiom,
    ! [A: $i] :
      ( ( cC54 @ A )
    <=> ? [B: $i] :
          ( ( rR1 @ A @ B )
          & ( cC52 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_46) ).

thf(337,plain,
    ! [A: $i] :
      ( ( ( cC54 @ A )
       => ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC52 @ B ) ) )
      & ( ? [B: $i] :
            ( ( rR1 @ A @ B )
            & ( cC52 @ B ) )
       => ( cC54 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(25,axiom,
    ! [A: $i] :
      ( ( cC52 @ A )
    <=> ( ( cC2 @ A )
        & ( cC50 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_45) ).

thf(222,plain,
    ! [A: $i] :
      ( ( ( cC52 @ A )
       => ( ( cC2 @ A )
          & ( cC50 @ A ) ) )
      & ( ( ( cC2 @ A )
          & ( cC50 @ A ) )
       => ( cC52 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(499,plain,
    $false,
    inference(e,[status(thm)],[385,204,230,455,497,290,427,138,468,481,276,449,120,379,174,288,421,325,228,216,84,480,397,132,248,270,102,349,192,429,467,361,435,461,156,403,256,489,96,343,311,298,180,296,391,313,144,498,236,367,198,108,462,162,487,355,282,150,409,310,331,441,482,495,319,304,186,114,447,373,168,262,210,242,126,268,474,415,90,254,337,222]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : KRS148+1 : TPTP v8.1.2. Released v3.1.0.
% 0.08/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n011.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Mon May  6 15:16:24 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 0.99/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.45/1.02  % [INFO] 	 Parsing done (151ms). 
% 1.45/1.02  % [INFO] 	 Running in sequential loop mode. 
% 1.90/1.23  % [INFO] 	 eprover registered as external prover. 
% 1.90/1.24  % [INFO] 	 cvc4 registered as external prover. 
% 1.90/1.24  % [INFO] 	 Scanning for conjecture ... 
% 2.00/1.31  % [INFO] 	 Found a conjecture and 89 axioms. Running axiom selection ... 
% 2.23/1.38  % [INFO] 	 Axiom selection finished. Selected 81 axioms (removed 8 axioms). 
% 2.43/1.43  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.43/1.45  % [INFO] 	 Type checking passed. 
% 2.43/1.45  % [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 ... 
% 5.28/2.27  % External prover 'e' found a proof!
% 5.28/2.27  % [INFO] 	 Killing All external provers ... 
% 5.28/2.27  % Time passed: 1734ms (effective reasoning time: 1245ms)
% 5.28/2.27  % 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)>
% 5.28/2.28  % Axioms used in derivation (81): axiom_38, axiom_27, axiom_64, axiom_1, axiom_53, axiom_75, axiom_26, axiom_55, axiom_88, axiom_33, axiom_10, axiom_40, axiom_22, axiom_59, axiom_77, axiom_44, axiom_49, axiom_15, axiom_73, axiom_67, axiom_69, axiom_21, axiom_19, axiom_84, axiom_2, axiom_79, axiom_32, axiom_6, axiom_60, axiom_78, axiom_54, axiom_16, axiom_81, axiom_74, axiom_3, axiom_68, axiom_46, axiom_20, axiom_85, axiom_70, axiom_42, axiom_31, axiom_24, axiom_61, axiom_35, axiom_28, axiom_71, axiom_65, axiom_36, axiom_39, axiom_80, axiom_17, axiom_86, axiom_5, axiom_47, axiom_13, axiom_82, axiom_41, axiom_25, axiom_76, axiom_52, axiom_34, axiom_0, axiom_58, axiom_62, axiom_45, axiom_29, axiom_11, axiom_56, axiom_30, axiom_23, axiom_18, axiom_87, axiom_12, axiom_9, axiom_48, axiom_83, axiom_14, axiom_72, axiom_4, axiom_66
% 5.28/2.28  % No. of inferences in proof: 166
% 5.28/2.28  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1734 ms resp. 1245 ms w/o parsing
% 5.58/2.34  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.58/2.34  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------