TSTP Solution File: KRS105+1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : KRS105+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n027.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  : 600s
% DateTime : Sun Jul 17 03:14:37 EDT 2022

% Result   : Unsatisfiable 0.18s 0.39s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   26
% Syntax   : Number of formulae    :  144 (  83 unt;  15 typ;   0 def)
%            Number of atoms       :  621 ( 158 equ;   0 cnn)
%            Maximal formula atoms :    3 (   4 avg)
%            Number of connectives :  767 ( 177   ~; 142   |;  14   &; 414   @)
%                                         (   8 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   16 (  16   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   18 (  15 usr;   3 con; 0-2 aty)
%            Number of variables   :  187 (   0   ^ 183   !;   4   ?; 187   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_cUnsatisfiable,type,
    cUnsatisfiable: $i > $o ).

thf(tp_ca_Ax2,type,
    ca_Ax2: $i > $o ).

thf(tp_cc,type,
    cc: $i > $o ).

thf(tp_cd,type,
    cd: $i > $o ).

thf(tp_cdxcomp,type,
    cdxcomp: $i > $o ).

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

thf(tp_cowlThing,type,
    cowlThing: $i > $o ).

thf(tp_i2003_11_14_17_20_53634,type,
    i2003_11_14_17_20_53634: $i ).

thf(tp_ra_Px1,type,
    ra_Px1: $i > $i > $o ).

thf(tp_rr,type,
    rr: $i > $i > $o ).

thf(tp_sK1_Y,type,
    sK1_Y: $i > $i ).

thf(tp_sK2_Y0,type,
    sK2_Y0: $i > $i ).

thf(tp_sK3_Y,type,
    sK3_Y: $i > $i ).

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

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

thf(1,axiom,
    cUnsatisfiable @ i2003_11_14_17_20_53634,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_9) ).

thf(2,axiom,
    ! [X: $i] :
      ( ( ca_Ax2 @ X )
     => ( cd @ X ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_8) ).

thf(3,axiom,
    ! [X: $i] :
      ( ( ca_Ax2 @ X )
    <=> ! [Y: $i] :
          ( ( rr @ X @ Y )
         => ( cc @ Y ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7) ).

thf(4,axiom,
    ! [X: $i] :
      ( ( cdxcomp @ X )
    <=> ? [Y0: $i] : ( ra_Px1 @ X @ Y0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).

thf(5,axiom,
    ! [X: $i] :
      ( ( cd @ X )
    <=> ~ ? [Y: $i] : ( ra_Px1 @ X @ Y ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).

thf(6,axiom,
    ! [X: $i] :
      ( ( cc @ X )
     => ! [Y: $i] :
          ( ( rr @ X @ Y )
         => ( cc @ Y ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).

thf(7,axiom,
    ! [X: $i] :
      ( ( cUnsatisfiable @ X )
     => ( cc @ X ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).

thf(8,axiom,
    ! [X: $i] :
      ( ( cUnsatisfiable @ X )
     => ( cdxcomp @ X ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).

thf(9,axiom,
    ! [X: $i] :
      ( ( xsd_string @ X )
    <=> ~ ( xsd_integer @ X ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).

thf(10,axiom,
    ! [X: $i] :
      ( ( cowlThing @ X )
      & ~ ( cowlNothing @ X ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_0) ).

thf(11,conjecture,
    $false,
    file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).

thf(12,negated_conjecture,
    $false = $false,
    inference(negate_conjecture,[status(cth)],[11]) ).

thf(13,plain,
    $false = $false,
    inference(unfold_def,[status(thm)],[12]) ).

thf(14,plain,
    ( ( cUnsatisfiable @ i2003_11_14_17_20_53634 )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(15,plain,
    ( ( ! [X: $i] :
          ( ( ca_Ax2 @ X )
         => ( cd @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(16,plain,
    ( ( ! [X: $i] :
          ( ( ca_Ax2 @ X )
        <=> ! [Y: $i] :
              ( ( rr @ X @ Y )
             => ( cc @ Y ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(17,plain,
    ( ( ! [X: $i] :
          ( ( cdxcomp @ X )
        <=> ? [Y0: $i] : ( ra_Px1 @ X @ Y0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(18,plain,
    ( ( ! [X: $i] :
          ( ( cd @ X )
        <=> ~ ? [Y: $i] : ( ra_Px1 @ X @ Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(19,plain,
    ( ( ! [X: $i] :
          ( ( cc @ X )
         => ! [Y: $i] :
              ( ( rr @ X @ Y )
             => ( cc @ Y ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(20,plain,
    ( ( ! [X: $i] :
          ( ( cUnsatisfiable @ X )
         => ( cc @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(21,plain,
    ( ( ! [X: $i] :
          ( ( cUnsatisfiable @ X )
         => ( cdxcomp @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8]) ).

thf(22,plain,
    ( ( ! [X: $i] :
          ( ( xsd_string @ X )
        <=> ~ ( xsd_integer @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9]) ).

thf(23,plain,
    ( ( ! [X: $i] :
          ( ( cowlThing @ X )
          & ~ ( cowlNothing @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(24,plain,
    ( ( ~ $false )
    = $true ),
    inference(polarity_switch,[status(thm)],[13]) ).

thf(25,plain,
    ( ( ! [X: $i] :
          ( ~ ( ca_Ax2 @ X )
          | ( cd @ X ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[15]) ).

thf(26,plain,
    ( ( ! [X: $i] :
          ( ( ( rr @ X @ ( sK1_Y @ X ) )
            & ~ ( cc @ ( sK1_Y @ X ) ) )
          | ( ca_Ax2 @ X ) )
      & ! [X: $i] :
          ( ~ ( ca_Ax2 @ X )
          | ! [Y: $i] :
              ( ~ ( rr @ X @ Y )
              | ( cc @ Y ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[16]) ).

thf(27,plain,
    ( ( ! [X: $i] :
          ( ! [Y0: $i] :
              ~ ( ra_Px1 @ X @ Y0 )
          | ( cdxcomp @ X ) )
      & ! [X: $i] :
          ( ~ ( cdxcomp @ X )
          | ( ra_Px1 @ X @ ( sK2_Y0 @ X ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[17]) ).

thf(28,plain,
    ( ( ! [X: $i] :
          ( ~ ( cd @ X )
          | ! [Y: $i] :
              ~ ( ra_Px1 @ X @ Y ) )
      & ! [X: $i] :
          ( ( ra_Px1 @ X @ ( sK3_Y @ X ) )
          | ( cd @ X ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[18]) ).

thf(29,plain,
    ( ( ! [X: $i] :
          ( ~ ( cc @ X )
          | ! [Y: $i] :
              ( ~ ( rr @ X @ Y )
              | ( cc @ Y ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[19]) ).

thf(30,plain,
    ( ( ! [X: $i] :
          ( ~ ( cUnsatisfiable @ X )
          | ( cc @ X ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[20]) ).

thf(31,plain,
    ( ( ! [X: $i] :
          ( ~ ( cUnsatisfiable @ X )
          | ( cdxcomp @ X ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[21]) ).

thf(32,plain,
    ( ( ! [X: $i] :
          ( ~ ( xsd_string @ X )
          | ~ ( xsd_integer @ X ) )
      & ! [X: $i] :
          ( ( xsd_integer @ X )
          | ( xsd_string @ X ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[22]) ).

thf(33,plain,
    ( ( ! [X: $i] : ( cowlThing @ X )
      & ! [X: $i] :
          ~ ( cowlNothing @ X ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[23]) ).

thf(34,plain,
    ( ( ! [X: $i] : ( cowlThing @ X )
      & ! [X: $i] :
          ~ ( cowlNothing @ X ) )
    = $true ),
    inference(copy,[status(thm)],[33]) ).

thf(35,plain,
    ( ( ! [X: $i] :
          ( ~ ( xsd_string @ X )
          | ~ ( xsd_integer @ X ) )
      & ! [X: $i] :
          ( ( xsd_integer @ X )
          | ( xsd_string @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[32]) ).

thf(36,plain,
    ( ( ! [X: $i] :
          ( ~ ( cUnsatisfiable @ X )
          | ( cdxcomp @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[31]) ).

thf(37,plain,
    ( ( ! [X: $i] :
          ( ~ ( cUnsatisfiable @ X )
          | ( cc @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[30]) ).

thf(38,plain,
    ( ( ! [X: $i] :
          ( ~ ( cc @ X )
          | ! [Y: $i] :
              ( ~ ( rr @ X @ Y )
              | ( cc @ Y ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[29]) ).

thf(39,plain,
    ( ( ! [X: $i] :
          ( ~ ( cd @ X )
          | ! [Y: $i] :
              ~ ( ra_Px1 @ X @ Y ) )
      & ! [X: $i] :
          ( ( ra_Px1 @ X @ ( sK3_Y @ X ) )
          | ( cd @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[28]) ).

thf(40,plain,
    ( ( ! [X: $i] :
          ( ! [Y0: $i] :
              ~ ( ra_Px1 @ X @ Y0 )
          | ( cdxcomp @ X ) )
      & ! [X: $i] :
          ( ~ ( cdxcomp @ X )
          | ( ra_Px1 @ X @ ( sK2_Y0 @ X ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[27]) ).

thf(41,plain,
    ( ( ! [X: $i] :
          ( ( ( rr @ X @ ( sK1_Y @ X ) )
            & ~ ( cc @ ( sK1_Y @ X ) ) )
          | ( ca_Ax2 @ X ) )
      & ! [X: $i] :
          ( ~ ( ca_Ax2 @ X )
          | ! [Y: $i] :
              ( ~ ( rr @ X @ Y )
              | ( cc @ Y ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[26]) ).

thf(42,plain,
    ( ( ! [X: $i] :
          ( ~ ( ca_Ax2 @ X )
          | ( cd @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[25]) ).

thf(43,plain,
    ( ( cUnsatisfiable @ i2003_11_14_17_20_53634 )
    = $true ),
    inference(copy,[status(thm)],[14]) ).

thf(44,plain,
    ( ( ~ $false )
    = $true ),
    inference(copy,[status(thm)],[24]) ).

thf(45,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( xsd_string @ SX0 )
                | ~ ( xsd_integer @ SX0 ) )
          | ~ ! [SX0: $i] :
                ( ( xsd_integer @ SX0 )
                | ( xsd_string @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[35]) ).

thf(46,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( cd @ SX0 )
                | ! [SX1: $i] :
                    ~ ( ra_Px1 @ SX0 @ SX1 ) )
          | ~ ! [SX0: $i] :
                ( ( ra_Px1 @ SX0 @ ( sK3_Y @ SX0 ) )
                | ( cd @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[39]) ).

thf(47,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( ~ ( rr @ SX0 @ ( sK1_Y @ SX0 ) )
                    | ~ ~ ( cc @ ( sK1_Y @ SX0 ) ) )
                | ( ca_Ax2 @ SX0 ) )
          | ~ ! [SX0: $i] :
                ( ~ ( ca_Ax2 @ SX0 )
                | ! [SX1: $i] :
                    ( ~ ( rr @ SX0 @ SX1 )
                    | ( cc @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[41]) ).

thf(48,plain,
    ( ( ~ ( ~ ! [SX0: $i] : ( cowlThing @ SX0 )
          | ~ ! [SX0: $i] :
                ~ ( cowlNothing @ SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[34]) ).

thf(49,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ! [SX1: $i] :
                    ~ ( ra_Px1 @ SX0 @ SX1 )
                | ( cdxcomp @ SX0 ) )
          | ~ ! [SX0: $i] :
                ( ~ ( cdxcomp @ SX0 )
                | ( ra_Px1 @ SX0 @ ( sK2_Y0 @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[40]) ).

thf(50,plain,
    ! [SV1: $i] :
      ( ( ~ ( cUnsatisfiable @ SV1 )
        | ( cdxcomp @ SV1 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[36]) ).

thf(51,plain,
    ! [SV2: $i] :
      ( ( ~ ( cUnsatisfiable @ SV2 )
        | ( cc @ SV2 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[37]) ).

thf(52,plain,
    ! [SV3: $i] :
      ( ( ~ ( cc @ SV3 )
        | ! [SY13: $i] :
            ( ~ ( rr @ SV3 @ SY13 )
            | ( cc @ SY13 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[38]) ).

thf(53,plain,
    ! [SV4: $i] :
      ( ( ~ ( ca_Ax2 @ SV4 )
        | ( cd @ SV4 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[42]) ).

thf(54,plain,
    $false = $false,
    inference(extcnf_not_pos,[status(thm)],[44]) ).

thf(55,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( xsd_string @ SX0 )
            | ~ ( xsd_integer @ SX0 ) )
      | ~ ! [SX0: $i] :
            ( ( xsd_integer @ SX0 )
            | ( xsd_string @ SX0 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[45]) ).

thf(56,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( cd @ SX0 )
            | ! [SX1: $i] :
                ~ ( ra_Px1 @ SX0 @ SX1 ) )
      | ~ ! [SX0: $i] :
            ( ( ra_Px1 @ SX0 @ ( sK3_Y @ SX0 ) )
            | ( cd @ SX0 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[46]) ).

thf(57,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( ~ ( rr @ SX0 @ ( sK1_Y @ SX0 ) )
                | ~ ~ ( cc @ ( sK1_Y @ SX0 ) ) )
            | ( ca_Ax2 @ SX0 ) )
      | ~ ! [SX0: $i] :
            ( ~ ( ca_Ax2 @ SX0 )
            | ! [SX1: $i] :
                ( ~ ( rr @ SX0 @ SX1 )
                | ( cc @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[47]) ).

thf(58,plain,
    ( ( ~ ! [SX0: $i] : ( cowlThing @ SX0 )
      | ~ ! [SX0: $i] :
            ~ ( cowlNothing @ SX0 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[48]) ).

thf(59,plain,
    ( ( ~ ! [SX0: $i] :
            ( ! [SX1: $i] :
                ~ ( ra_Px1 @ SX0 @ SX1 )
            | ( cdxcomp @ SX0 ) )
      | ~ ! [SX0: $i] :
            ( ~ ( cdxcomp @ SX0 )
            | ( ra_Px1 @ SX0 @ ( sK2_Y0 @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[49]) ).

thf(60,plain,
    ! [SV1: $i] :
      ( ( ( ~ ( cUnsatisfiable @ SV1 ) )
        = $true )
      | ( ( cdxcomp @ SV1 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[50]) ).

thf(61,plain,
    ! [SV2: $i] :
      ( ( ( ~ ( cUnsatisfiable @ SV2 ) )
        = $true )
      | ( ( cc @ SV2 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[51]) ).

thf(62,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( cc @ SV3 ) )
        = $true )
      | ( ( ! [SY13: $i] :
              ( ~ ( rr @ SV3 @ SY13 )
              | ( cc @ SY13 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[52]) ).

thf(63,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( ca_Ax2 @ SV4 ) )
        = $true )
      | ( ( cd @ SV4 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[53]) ).

thf(64,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( xsd_string @ SX0 )
            | ~ ( xsd_integer @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[55]) ).

thf(65,plain,
    ( ( ~ ! [SX0: $i] :
            ( ( xsd_integer @ SX0 )
            | ( xsd_string @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[55]) ).

thf(66,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( cd @ SX0 )
            | ! [SX1: $i] :
                ~ ( ra_Px1 @ SX0 @ SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[56]) ).

thf(67,plain,
    ( ( ~ ! [SX0: $i] :
            ( ( ra_Px1 @ SX0 @ ( sK3_Y @ SX0 ) )
            | ( cd @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[56]) ).

thf(68,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( ~ ( rr @ SX0 @ ( sK1_Y @ SX0 ) )
                | ~ ~ ( cc @ ( sK1_Y @ SX0 ) ) )
            | ( ca_Ax2 @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[57]) ).

thf(69,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( ca_Ax2 @ SX0 )
            | ! [SX1: $i] :
                ( ~ ( rr @ SX0 @ SX1 )
                | ( cc @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[57]) ).

thf(70,plain,
    ( ( ~ ! [SX0: $i] : ( cowlThing @ SX0 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[58]) ).

thf(71,plain,
    ( ( ~ ! [SX0: $i] :
            ~ ( cowlNothing @ SX0 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[58]) ).

thf(72,plain,
    ( ( ~ ! [SX0: $i] :
            ( ! [SX1: $i] :
                ~ ( ra_Px1 @ SX0 @ SX1 )
            | ( cdxcomp @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[59]) ).

thf(73,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( cdxcomp @ SX0 )
            | ( ra_Px1 @ SX0 @ ( sK2_Y0 @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[59]) ).

thf(74,plain,
    ! [SV1: $i] :
      ( ( ( cUnsatisfiable @ SV1 )
        = $false )
      | ( ( cdxcomp @ SV1 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[60]) ).

thf(75,plain,
    ! [SV2: $i] :
      ( ( ( cUnsatisfiable @ SV2 )
        = $false )
      | ( ( cc @ SV2 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[61]) ).

thf(76,plain,
    ! [SV3: $i] :
      ( ( ( cc @ SV3 )
        = $false )
      | ( ( ! [SY13: $i] :
              ( ~ ( rr @ SV3 @ SY13 )
              | ( cc @ SY13 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[62]) ).

thf(77,plain,
    ! [SV4: $i] :
      ( ( ( ca_Ax2 @ SV4 )
        = $false )
      | ( ( cd @ SV4 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[63]) ).

thf(78,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( xsd_string @ SX0 )
          | ~ ( xsd_integer @ SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[64]) ).

thf(79,plain,
    ( ( ! [SX0: $i] :
          ( ( xsd_integer @ SX0 )
          | ( xsd_string @ SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[65]) ).

thf(80,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( cd @ SX0 )
          | ! [SX1: $i] :
              ~ ( ra_Px1 @ SX0 @ SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[66]) ).

thf(81,plain,
    ( ( ! [SX0: $i] :
          ( ( ra_Px1 @ SX0 @ ( sK3_Y @ SX0 ) )
          | ( cd @ SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[67]) ).

thf(82,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( ~ ( rr @ SX0 @ ( sK1_Y @ SX0 ) )
              | ~ ~ ( cc @ ( sK1_Y @ SX0 ) ) )
          | ( ca_Ax2 @ SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[68]) ).

thf(83,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( ca_Ax2 @ SX0 )
          | ! [SX1: $i] :
              ( ~ ( rr @ SX0 @ SX1 )
              | ( cc @ SX1 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[69]) ).

thf(84,plain,
    ( ( ! [SX0: $i] : ( cowlThing @ SX0 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[70]) ).

thf(85,plain,
    ( ( ! [SX0: $i] :
          ~ ( cowlNothing @ SX0 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[71]) ).

thf(86,plain,
    ( ( ! [SX0: $i] :
          ( ! [SX1: $i] :
              ~ ( ra_Px1 @ SX0 @ SX1 )
          | ( cdxcomp @ SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[72]) ).

thf(87,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( cdxcomp @ SX0 )
          | ( ra_Px1 @ SX0 @ ( sK2_Y0 @ SX0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[73]) ).

thf(88,plain,
    ! [SV5: $i,SV3: $i] :
      ( ( ( ~ ( rr @ SV3 @ SV5 )
          | ( cc @ SV5 ) )
        = $true )
      | ( ( cc @ SV3 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[76]) ).

thf(89,plain,
    ! [SV6: $i] :
      ( ( ~ ( xsd_string @ SV6 )
        | ~ ( xsd_integer @ SV6 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[78]) ).

thf(90,plain,
    ! [SV7: $i] :
      ( ( ( xsd_integer @ SV7 )
        | ( xsd_string @ SV7 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[79]) ).

thf(91,plain,
    ! [SV8: $i] :
      ( ( ~ ( cd @ SV8 )
        | ! [SY14: $i] :
            ~ ( ra_Px1 @ SV8 @ SY14 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[80]) ).

thf(92,plain,
    ! [SV9: $i] :
      ( ( ( ra_Px1 @ SV9 @ ( sK3_Y @ SV9 ) )
        | ( cd @ SV9 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[81]) ).

thf(93,plain,
    ! [SV10: $i] :
      ( ( ~ ( ~ ( rr @ SV10 @ ( sK1_Y @ SV10 ) )
            | ~ ~ ( cc @ ( sK1_Y @ SV10 ) ) )
        | ( ca_Ax2 @ SV10 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[82]) ).

thf(94,plain,
    ! [SV11: $i] :
      ( ( ~ ( ca_Ax2 @ SV11 )
        | ! [SY15: $i] :
            ( ~ ( rr @ SV11 @ SY15 )
            | ( cc @ SY15 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[83]) ).

thf(95,plain,
    ! [SV12: $i] :
      ( ( cowlThing @ SV12 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[84]) ).

thf(96,plain,
    ! [SV13: $i] :
      ( ( ~ ( cowlNothing @ SV13 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[85]) ).

thf(97,plain,
    ! [SV14: $i] :
      ( ( ! [SY16: $i] :
            ~ ( ra_Px1 @ SV14 @ SY16 )
        | ( cdxcomp @ SV14 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[86]) ).

thf(98,plain,
    ! [SV15: $i] :
      ( ( ~ ( cdxcomp @ SV15 )
        | ( ra_Px1 @ SV15 @ ( sK2_Y0 @ SV15 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[87]) ).

thf(99,plain,
    ! [SV5: $i,SV3: $i] :
      ( ( ( ~ ( rr @ SV3 @ SV5 ) )
        = $true )
      | ( ( cc @ SV5 )
        = $true )
      | ( ( cc @ SV3 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[88]) ).

thf(100,plain,
    ! [SV6: $i] :
      ( ( ( ~ ( xsd_string @ SV6 ) )
        = $true )
      | ( ( ~ ( xsd_integer @ SV6 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[89]) ).

thf(101,plain,
    ! [SV7: $i] :
      ( ( ( xsd_integer @ SV7 )
        = $true )
      | ( ( xsd_string @ SV7 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[90]) ).

thf(102,plain,
    ! [SV8: $i] :
      ( ( ( ~ ( cd @ SV8 ) )
        = $true )
      | ( ( ! [SY14: $i] :
              ~ ( ra_Px1 @ SV8 @ SY14 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[91]) ).

thf(103,plain,
    ! [SV9: $i] :
      ( ( ( ra_Px1 @ SV9 @ ( sK3_Y @ SV9 ) )
        = $true )
      | ( ( cd @ SV9 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[92]) ).

thf(104,plain,
    ! [SV10: $i] :
      ( ( ( ~ ( ~ ( rr @ SV10 @ ( sK1_Y @ SV10 ) )
              | ~ ~ ( cc @ ( sK1_Y @ SV10 ) ) ) )
        = $true )
      | ( ( ca_Ax2 @ SV10 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[93]) ).

thf(105,plain,
    ! [SV11: $i] :
      ( ( ( ~ ( ca_Ax2 @ SV11 ) )
        = $true )
      | ( ( ! [SY15: $i] :
              ( ~ ( rr @ SV11 @ SY15 )
              | ( cc @ SY15 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[94]) ).

thf(106,plain,
    ! [SV13: $i] :
      ( ( cowlNothing @ SV13 )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[96]) ).

thf(107,plain,
    ! [SV14: $i] :
      ( ( ( ! [SY16: $i] :
              ~ ( ra_Px1 @ SV14 @ SY16 ) )
        = $true )
      | ( ( cdxcomp @ SV14 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[97]) ).

thf(108,plain,
    ! [SV15: $i] :
      ( ( ( ~ ( cdxcomp @ SV15 ) )
        = $true )
      | ( ( ra_Px1 @ SV15 @ ( sK2_Y0 @ SV15 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[98]) ).

thf(109,plain,
    ! [SV5: $i,SV3: $i] :
      ( ( ( rr @ SV3 @ SV5 )
        = $false )
      | ( ( cc @ SV5 )
        = $true )
      | ( ( cc @ SV3 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[99]) ).

thf(110,plain,
    ! [SV6: $i] :
      ( ( ( xsd_string @ SV6 )
        = $false )
      | ( ( ~ ( xsd_integer @ SV6 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[100]) ).

thf(111,plain,
    ! [SV8: $i] :
      ( ( ( cd @ SV8 )
        = $false )
      | ( ( ! [SY14: $i] :
              ~ ( ra_Px1 @ SV8 @ SY14 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[102]) ).

thf(112,plain,
    ! [SV10: $i] :
      ( ( ( ~ ( rr @ SV10 @ ( sK1_Y @ SV10 ) )
          | ~ ~ ( cc @ ( sK1_Y @ SV10 ) ) )
        = $false )
      | ( ( ca_Ax2 @ SV10 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[104]) ).

thf(113,plain,
    ! [SV11: $i] :
      ( ( ( ca_Ax2 @ SV11 )
        = $false )
      | ( ( ! [SY15: $i] :
              ( ~ ( rr @ SV11 @ SY15 )
              | ( cc @ SY15 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[105]) ).

thf(114,plain,
    ! [SV16: $i,SV14: $i] :
      ( ( ( ~ ( ra_Px1 @ SV14 @ SV16 ) )
        = $true )
      | ( ( cdxcomp @ SV14 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[107]) ).

thf(115,plain,
    ! [SV15: $i] :
      ( ( ( cdxcomp @ SV15 )
        = $false )
      | ( ( ra_Px1 @ SV15 @ ( sK2_Y0 @ SV15 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[108]) ).

thf(116,plain,
    ! [SV6: $i] :
      ( ( ( xsd_integer @ SV6 )
        = $false )
      | ( ( xsd_string @ SV6 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[110]) ).

thf(117,plain,
    ! [SV17: $i,SV8: $i] :
      ( ( ( ~ ( ra_Px1 @ SV8 @ SV17 ) )
        = $true )
      | ( ( cd @ SV8 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[111]) ).

thf(118,plain,
    ! [SV10: $i] :
      ( ( ( ~ ( rr @ SV10 @ ( sK1_Y @ SV10 ) ) )
        = $false )
      | ( ( ca_Ax2 @ SV10 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[112]) ).

thf(119,plain,
    ! [SV10: $i] :
      ( ( ( ~ ~ ( cc @ ( sK1_Y @ SV10 ) ) )
        = $false )
      | ( ( ca_Ax2 @ SV10 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[112]) ).

thf(120,plain,
    ! [SV18: $i,SV11: $i] :
      ( ( ( ~ ( rr @ SV11 @ SV18 )
          | ( cc @ SV18 ) )
        = $true )
      | ( ( ca_Ax2 @ SV11 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[113]) ).

thf(121,plain,
    ! [SV16: $i,SV14: $i] :
      ( ( ( ra_Px1 @ SV14 @ SV16 )
        = $false )
      | ( ( cdxcomp @ SV14 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[114]) ).

thf(122,plain,
    ! [SV17: $i,SV8: $i] :
      ( ( ( ra_Px1 @ SV8 @ SV17 )
        = $false )
      | ( ( cd @ SV8 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[117]) ).

thf(123,plain,
    ! [SV10: $i] :
      ( ( ( rr @ SV10 @ ( sK1_Y @ SV10 ) )
        = $true )
      | ( ( ca_Ax2 @ SV10 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[118]) ).

thf(124,plain,
    ! [SV10: $i] :
      ( ( ( ~ ( cc @ ( sK1_Y @ SV10 ) ) )
        = $true )
      | ( ( ca_Ax2 @ SV10 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[119]) ).

thf(125,plain,
    ! [SV18: $i,SV11: $i] :
      ( ( ( ~ ( rr @ SV11 @ SV18 ) )
        = $true )
      | ( ( cc @ SV18 )
        = $true )
      | ( ( ca_Ax2 @ SV11 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[120]) ).

thf(126,plain,
    ! [SV10: $i] :
      ( ( ( cc @ ( sK1_Y @ SV10 ) )
        = $false )
      | ( ( ca_Ax2 @ SV10 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[124]) ).

thf(127,plain,
    ! [SV18: $i,SV11: $i] :
      ( ( ( rr @ SV11 @ SV18 )
        = $false )
      | ( ( cc @ SV18 )
        = $true )
      | ( ( ca_Ax2 @ SV11 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[125]) ).

thf(128,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[43,127,126,123,122,121,116,115,109,106,103,101,95,77,75,74,54]) ).

thf(129,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[128]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : KRS105+1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.12  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33  % Computer : n027.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Tue Jun  7 17:42:40 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  
% 0.12/0.34   No.of.Axioms: 10
% 0.12/0.34  
% 0.12/0.34   Length.of.Defs: 0
% 0.12/0.34  
% 0.12/0.34   Contains.Choice.Funs: false
% 0.12/0.34  (rf:0,axioms:10,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:12,loop_count:0,foatp_calls:0,translation:fof_full).......
% 0.18/0.39  
% 0.18/0.39  ********************************
% 0.18/0.39  *   All subproblems solved!    *
% 0.18/0.39  ********************************
% 0.18/0.39  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:10,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:128,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.18/0.40  
% 0.18/0.40  %**** Beginning of derivation protocol ****
% 0.18/0.40  % SZS output start CNFRefutation
% See solution above
% 0.18/0.40  
% 0.18/0.40  %**** End of derivation protocol ****
% 0.18/0.40  %**** no. of clauses in derivation: 129 ****
% 0.18/0.40  %**** clause counter: 128 ****
% 0.18/0.40  
% 0.18/0.40  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:10,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:128,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------