TSTP Solution File: SYN056+1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SYN056+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n021.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 : Thu Jul 21 08:23:04 EDT 2022

% Result   : Theorem 0.12s 0.40s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   11
% Syntax   : Number of formulae    :  130 (  79 unt;   8 typ;   0 def)
%            Number of atoms       :  773 ( 186 equ;   0 cnn)
%            Maximal formula atoms :    4 (   6 avg)
%            Number of connectives :  947 ( 270   ~; 236   |;  16   &; 398   @)
%                                         (   7 <=>;  20  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :  182 (   0   ^ 178   !;   4   ?; 182   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_big_p,type,
    big_p: $i > $o ).

thf(tp_big_q,type,
    big_q: $i > $o ).

thf(tp_big_r,type,
    big_r: $i > $o ).

thf(tp_big_s,type,
    big_s: $i > $o ).

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

thf(tp_sK2_X,type,
    sK2_X: $i ).

thf(tp_sK3_X,type,
    sK3_X: $i ).

thf(tp_sK4_Y,type,
    sK4_Y: $i ).

thf(1,axiom,
    ! [X: $i,Y: $i] :
      ( ( ( big_p @ X )
        & ( big_q @ Y ) )
     => ( ( big_r @ X )
      <=> ( big_s @ Y ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel26_2) ).

thf(2,axiom,
    ( ? [X: $i] : ( big_p @ X )
  <=> ? [Y: $i] : ( big_q @ Y ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel26_1) ).

thf(3,conjecture,
    ( ! [X: $i] :
        ( ( big_p @ X )
       => ( big_r @ X ) )
  <=> ! [Y: $i] :
        ( ( big_q @ Y )
       => ( big_s @ Y ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel26) ).

thf(4,negated_conjecture,
    ( ( ! [X: $i] :
          ( ( big_p @ X )
         => ( big_r @ X ) )
    <=> ! [Y: $i] :
          ( ( big_q @ Y )
         => ( big_s @ Y ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[3]) ).

thf(5,plain,
    ( ( ! [X: $i] :
          ( ( big_p @ X )
         => ( big_r @ X ) )
    <=> ! [Y: $i] :
          ( ( big_q @ Y )
         => ( big_s @ Y ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(6,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( ( big_p @ X )
            & ( big_q @ Y ) )
         => ( ( big_r @ X )
          <=> ( big_s @ Y ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(7,plain,
    ( ( ? [X: $i] : ( big_p @ X )
    <=> ? [Y: $i] : ( big_q @ Y ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(8,plain,
    ( ( ! [X: $i] :
          ( ( big_p @ X )
         => ( big_r @ X ) )
     => ! [Y: $i] :
          ( ( big_q @ Y )
         => ( big_s @ Y ) ) )
    = $false ),
    inference(split_conjecture,[split_conjecture(split,[])],[5]) ).

thf(9,plain,
    ( ( ! [Y: $i] :
          ( ( big_q @ Y )
         => ( big_s @ Y ) )
     => ! [X: $i] :
          ( ( big_p @ X )
         => ( big_r @ X ) ) )
    = $false ),
    inference(split_conjecture,[split_conjecture(split,[])],[5]) ).

thf(10,plain,
    ( ( ~ ( ! [X: $i] :
              ( ( big_p @ X )
             => ( big_r @ X ) )
         => ! [Y: $i] :
              ( ( big_q @ Y )
             => ( big_s @ Y ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[8]) ).

thf(11,plain,
    ( ( ~ ( ! [Y: $i] :
              ( ( big_q @ Y )
             => ( big_s @ Y ) )
         => ! [X: $i] :
              ( ( big_p @ X )
             => ( big_r @ X ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[9]) ).

thf(12,plain,
    ( ( ! [X: $i] :
          ( ~ ( big_p @ X )
          | ( big_r @ X ) )
      & ( big_q @ sK1_Y )
      & ~ ( big_s @ sK1_Y ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[10]) ).

thf(13,plain,
    ( ( ! [Y: $i] :
          ( ~ ( big_q @ Y )
          | ( big_s @ Y ) )
      & ( big_p @ sK2_X )
      & ~ ( big_r @ sK2_X ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[11]) ).

thf(14,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( big_p @ X )
          | ~ ( big_q @ Y )
          | ~ ( big_r @ X )
          | ( big_s @ Y ) )
      & ! [X: $i,Y: $i] :
          ( ~ ( big_p @ X )
          | ~ ( big_q @ Y )
          | ~ ( big_s @ Y )
          | ( big_r @ X ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[6]) ).

thf(15,plain,
    ( ( ( ! [X: $i] :
            ~ ( big_p @ X )
        | ( big_q @ sK4_Y ) )
      & ( ! [Y: $i] :
            ~ ( big_q @ Y )
        | ( big_p @ sK3_X ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[7]) ).

thf(16,plain,
    ( ( ( ! [X: $i] :
            ~ ( big_p @ X )
        | ( big_q @ sK4_Y ) )
      & ( ! [Y: $i] :
            ~ ( big_q @ Y )
        | ( big_p @ sK3_X ) ) )
    = $true ),
    inference(copy,[status(thm)],[15]) ).

thf(17,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( big_p @ X )
          | ~ ( big_q @ Y )
          | ~ ( big_r @ X )
          | ( big_s @ Y ) )
      & ! [X: $i,Y: $i] :
          ( ~ ( big_p @ X )
          | ~ ( big_q @ Y )
          | ~ ( big_s @ Y )
          | ( big_r @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[14]) ).

thf(18,plain,
    ( ( ! [X: $i] :
          ( ~ ( big_p @ X )
          | ( big_r @ X ) )
      & ( big_q @ sK1_Y )
      & ~ ( big_s @ sK1_Y ) )
    = $true ),
    inference(copy,[status(thm)],[12]) ).

thf(19,plain,
    ( ( ~ ( ~ ( ! [SX0: $i] :
                  ~ ( big_p @ SX0 )
              | ( big_q @ sK4_Y ) )
          | ~ ( ! [SX0: $i] :
                  ~ ( big_q @ SX0 )
              | ( big_p @ sK3_X ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[16]) ).

thf(20,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( big_p @ SX0 )
                | ~ ( big_q @ SX1 )
                | ~ ( big_r @ SX0 )
                | ( big_s @ SX1 ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( big_p @ SX0 )
                | ~ ( big_q @ SX1 )
                | ~ ( big_s @ SX1 )
                | ( big_r @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[17]) ).

thf(21,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( big_p @ SX0 )
                | ( big_r @ SX0 ) )
          | ~ ~ ( ~ ( big_q @ sK1_Y )
                | ~ ~ ( big_s @ sK1_Y ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[18]) ).

thf(22,plain,
    ( ( ~ ( ! [SX0: $i] :
              ~ ( big_p @ SX0 )
          | ( big_q @ sK4_Y ) )
      | ~ ( ! [SX0: $i] :
              ~ ( big_q @ SX0 )
          | ( big_p @ sK3_X ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[19]) ).

thf(23,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( big_p @ SX0 )
            | ~ ( big_q @ SX1 )
            | ~ ( big_r @ SX0 )
            | ( big_s @ SX1 ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( big_p @ SX0 )
            | ~ ( big_q @ SX1 )
            | ~ ( big_s @ SX1 )
            | ( big_r @ SX0 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[20]) ).

thf(24,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( big_p @ SX0 )
            | ( big_r @ SX0 ) )
      | ~ ~ ( ~ ( big_q @ sK1_Y )
            | ~ ~ ( big_s @ sK1_Y ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[21]) ).

thf(25,plain,
    ( ( ~ ( ! [SX0: $i] :
              ~ ( big_p @ SX0 )
          | ( big_q @ sK4_Y ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[22]) ).

thf(26,plain,
    ( ( ~ ( ! [SX0: $i] :
              ~ ( big_q @ SX0 )
          | ( big_p @ sK3_X ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[22]) ).

thf(27,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( big_p @ SX0 )
            | ~ ( big_q @ SX1 )
            | ~ ( big_r @ SX0 )
            | ( big_s @ SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[23]) ).

thf(28,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( big_p @ SX0 )
            | ~ ( big_q @ SX1 )
            | ~ ( big_s @ SX1 )
            | ( big_r @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[23]) ).

thf(29,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( big_p @ SX0 )
            | ( big_r @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[24]) ).

thf(30,plain,
    ( ( ~ ~ ( ~ ( big_q @ sK1_Y )
            | ~ ~ ( big_s @ sK1_Y ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[24]) ).

thf(31,plain,
    ( ( ! [SX0: $i] :
          ~ ( big_p @ SX0 )
      | ( big_q @ sK4_Y ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[25]) ).

thf(32,plain,
    ( ( ! [SX0: $i] :
          ~ ( big_q @ SX0 )
      | ( big_p @ sK3_X ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[26]) ).

thf(33,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( big_p @ SX0 )
          | ~ ( big_q @ SX1 )
          | ~ ( big_r @ SX0 )
          | ( big_s @ SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[27]) ).

thf(34,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( big_p @ SX0 )
          | ~ ( big_q @ SX1 )
          | ~ ( big_s @ SX1 )
          | ( big_r @ SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[28]) ).

thf(35,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( big_p @ SX0 )
          | ( big_r @ SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[29]) ).

thf(36,plain,
    ( ( ~ ( ~ ( big_q @ sK1_Y )
          | ~ ~ ( big_s @ sK1_Y ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[30]) ).

thf(37,plain,
    ( ( ( ! [SX0: $i] :
            ~ ( big_p @ SX0 ) )
      = $true )
    | ( ( big_q @ sK4_Y )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[31]) ).

thf(38,plain,
    ( ( ( ! [SX0: $i] :
            ~ ( big_q @ SX0 ) )
      = $true )
    | ( ( big_p @ sK3_X )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[32]) ).

thf(39,plain,
    ! [SV1: $i] :
      ( ( ! [SY6: $i] :
            ( ~ ( big_p @ SV1 )
            | ~ ( big_q @ SY6 )
            | ~ ( big_r @ SV1 )
            | ( big_s @ SY6 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[33]) ).

thf(40,plain,
    ! [SV2: $i] :
      ( ( ! [SY7: $i] :
            ( ~ ( big_p @ SV2 )
            | ~ ( big_q @ SY7 )
            | ~ ( big_s @ SY7 )
            | ( big_r @ SV2 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[34]) ).

thf(41,plain,
    ! [SV3: $i] :
      ( ( ~ ( big_p @ SV3 )
        | ( big_r @ SV3 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[35]) ).

thf(42,plain,
    ( ( ~ ( big_q @ sK1_Y )
      | ~ ~ ( big_s @ sK1_Y ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[36]) ).

thf(43,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( big_p @ SV4 ) )
        = $true )
      | ( ( big_q @ sK4_Y )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[37]) ).

thf(44,plain,
    ! [SV5: $i] :
      ( ( ( ~ ( big_q @ SV5 ) )
        = $true )
      | ( ( big_p @ sK3_X )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[38]) ).

thf(45,plain,
    ! [SV6: $i,SV1: $i] :
      ( ( ~ ( big_p @ SV1 )
        | ~ ( big_q @ SV6 )
        | ~ ( big_r @ SV1 )
        | ( big_s @ SV6 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[39]) ).

thf(46,plain,
    ! [SV7: $i,SV2: $i] :
      ( ( ~ ( big_p @ SV2 )
        | ~ ( big_q @ SV7 )
        | ~ ( big_s @ SV7 )
        | ( big_r @ SV2 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[40]) ).

thf(47,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( big_p @ SV3 ) )
        = $true )
      | ( ( big_r @ SV3 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[41]) ).

thf(48,plain,
    ( ( ~ ( big_q @ sK1_Y ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[42]) ).

thf(49,plain,
    ( ( ~ ~ ( big_s @ sK1_Y ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[42]) ).

thf(50,plain,
    ! [SV4: $i] :
      ( ( ( big_p @ SV4 )
        = $false )
      | ( ( big_q @ sK4_Y )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[43]) ).

thf(51,plain,
    ! [SV5: $i] :
      ( ( ( big_q @ SV5 )
        = $false )
      | ( ( big_p @ sK3_X )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[44]) ).

thf(52,plain,
    ! [SV6: $i,SV1: $i] :
      ( ( ( ~ ( big_p @ SV1 )
          | ~ ( big_q @ SV6 ) )
        = $true )
      | ( ( ~ ( big_r @ SV1 )
          | ( big_s @ SV6 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[45]) ).

thf(53,plain,
    ! [SV7: $i,SV2: $i] :
      ( ( ( ~ ( big_p @ SV2 )
          | ~ ( big_q @ SV7 ) )
        = $true )
      | ( ( ~ ( big_s @ SV7 )
          | ( big_r @ SV2 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[46]) ).

thf(54,plain,
    ! [SV3: $i] :
      ( ( ( big_p @ SV3 )
        = $false )
      | ( ( big_r @ SV3 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[47]) ).

thf(55,plain,
    ( ( big_q @ sK1_Y )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[48]) ).

thf(56,plain,
    ( ( ~ ( big_s @ sK1_Y ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[49]) ).

thf(57,plain,
    ! [SV6: $i,SV1: $i] :
      ( ( ( ~ ( big_p @ SV1 ) )
        = $true )
      | ( ( ~ ( big_q @ SV6 ) )
        = $true )
      | ( ( ~ ( big_r @ SV1 )
          | ( big_s @ SV6 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[52]) ).

thf(58,plain,
    ! [SV7: $i,SV2: $i] :
      ( ( ( ~ ( big_p @ SV2 ) )
        = $true )
      | ( ( ~ ( big_q @ SV7 ) )
        = $true )
      | ( ( ~ ( big_s @ SV7 )
          | ( big_r @ SV2 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[53]) ).

thf(59,plain,
    ( ( big_s @ sK1_Y )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[56]) ).

thf(60,plain,
    ! [SV6: $i,SV1: $i] :
      ( ( ( big_p @ SV1 )
        = $false )
      | ( ( ~ ( big_q @ SV6 ) )
        = $true )
      | ( ( ~ ( big_r @ SV1 )
          | ( big_s @ SV6 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[57]) ).

thf(61,plain,
    ! [SV7: $i,SV2: $i] :
      ( ( ( big_p @ SV2 )
        = $false )
      | ( ( ~ ( big_q @ SV7 ) )
        = $true )
      | ( ( ~ ( big_s @ SV7 )
          | ( big_r @ SV2 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[58]) ).

thf(62,plain,
    ! [SV1: $i,SV6: $i] :
      ( ( ( big_q @ SV6 )
        = $false )
      | ( ( big_p @ SV1 )
        = $false )
      | ( ( ~ ( big_r @ SV1 )
          | ( big_s @ SV6 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[60]) ).

thf(63,plain,
    ! [SV2: $i,SV7: $i] :
      ( ( ( big_q @ SV7 )
        = $false )
      | ( ( big_p @ SV2 )
        = $false )
      | ( ( ~ ( big_s @ SV7 )
          | ( big_r @ SV2 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[61]) ).

thf(64,plain,
    ! [SV6: $i,SV1: $i] :
      ( ( ( ~ ( big_r @ SV1 ) )
        = $true )
      | ( ( big_s @ SV6 )
        = $true )
      | ( ( big_p @ SV1 )
        = $false )
      | ( ( big_q @ SV6 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[62]) ).

thf(65,plain,
    ! [SV2: $i,SV7: $i] :
      ( ( ( ~ ( big_s @ SV7 ) )
        = $true )
      | ( ( big_r @ SV2 )
        = $true )
      | ( ( big_p @ SV2 )
        = $false )
      | ( ( big_q @ SV7 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[63]) ).

thf(66,plain,
    ! [SV6: $i,SV1: $i] :
      ( ( ( big_r @ SV1 )
        = $false )
      | ( ( big_s @ SV6 )
        = $true )
      | ( ( big_p @ SV1 )
        = $false )
      | ( ( big_q @ SV6 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[64]) ).

thf(67,plain,
    ! [SV2: $i,SV7: $i] :
      ( ( ( big_s @ SV7 )
        = $false )
      | ( ( big_r @ SV2 )
        = $true )
      | ( ( big_p @ SV2 )
        = $false )
      | ( ( big_q @ SV7 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[65]) ).

thf(68,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[50,67,66,59,55,54,51]) ).

thf(69,plain,
    ( ( ( ! [X: $i] :
            ~ ( big_p @ X )
        | ( big_q @ sK4_Y ) )
      & ( ! [Y: $i] :
            ~ ( big_q @ Y )
        | ( big_p @ sK3_X ) ) )
    = $true ),
    inference(copy,[status(thm)],[15]) ).

thf(70,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( big_p @ X )
          | ~ ( big_q @ Y )
          | ~ ( big_r @ X )
          | ( big_s @ Y ) )
      & ! [X: $i,Y: $i] :
          ( ~ ( big_p @ X )
          | ~ ( big_q @ Y )
          | ~ ( big_s @ Y )
          | ( big_r @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[14]) ).

thf(71,plain,
    ( ( ! [Y: $i] :
          ( ~ ( big_q @ Y )
          | ( big_s @ Y ) )
      & ( big_p @ sK2_X )
      & ~ ( big_r @ sK2_X ) )
    = $true ),
    inference(copy,[status(thm)],[13]) ).

thf(72,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( big_q @ SX0 )
                | ( big_s @ SX0 ) )
          | ~ ~ ( ~ ( big_p @ sK2_X )
                | ~ ~ ( big_r @ sK2_X ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[71]) ).

thf(73,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( big_p @ SX0 )
                | ~ ( big_q @ SX1 )
                | ~ ( big_r @ SX0 )
                | ( big_s @ SX1 ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( big_p @ SX0 )
                | ~ ( big_q @ SX1 )
                | ~ ( big_s @ SX1 )
                | ( big_r @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[70]) ).

thf(74,plain,
    ( ( ~ ( ~ ( ! [SX0: $i] :
                  ~ ( big_p @ SX0 )
              | ( big_q @ sK4_Y ) )
          | ~ ( ! [SX0: $i] :
                  ~ ( big_q @ SX0 )
              | ( big_p @ sK3_X ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[69]) ).

thf(75,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( big_q @ SX0 )
            | ( big_s @ SX0 ) )
      | ~ ~ ( ~ ( big_p @ sK2_X )
            | ~ ~ ( big_r @ sK2_X ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[72]) ).

thf(76,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( big_p @ SX0 )
            | ~ ( big_q @ SX1 )
            | ~ ( big_r @ SX0 )
            | ( big_s @ SX1 ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( big_p @ SX0 )
            | ~ ( big_q @ SX1 )
            | ~ ( big_s @ SX1 )
            | ( big_r @ SX0 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[73]) ).

thf(77,plain,
    ( ( ~ ( ! [SX0: $i] :
              ~ ( big_p @ SX0 )
          | ( big_q @ sK4_Y ) )
      | ~ ( ! [SX0: $i] :
              ~ ( big_q @ SX0 )
          | ( big_p @ sK3_X ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[74]) ).

thf(78,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( big_q @ SX0 )
            | ( big_s @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[75]) ).

thf(79,plain,
    ( ( ~ ~ ( ~ ( big_p @ sK2_X )
            | ~ ~ ( big_r @ sK2_X ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[75]) ).

thf(80,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( big_p @ SX0 )
            | ~ ( big_q @ SX1 )
            | ~ ( big_r @ SX0 )
            | ( big_s @ SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[76]) ).

thf(81,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( big_p @ SX0 )
            | ~ ( big_q @ SX1 )
            | ~ ( big_s @ SX1 )
            | ( big_r @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[76]) ).

thf(82,plain,
    ( ( ~ ( ! [SX0: $i] :
              ~ ( big_p @ SX0 )
          | ( big_q @ sK4_Y ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[77]) ).

thf(83,plain,
    ( ( ~ ( ! [SX0: $i] :
              ~ ( big_q @ SX0 )
          | ( big_p @ sK3_X ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[77]) ).

thf(84,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( big_q @ SX0 )
          | ( big_s @ SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[78]) ).

thf(85,plain,
    ( ( ~ ( ~ ( big_p @ sK2_X )
          | ~ ~ ( big_r @ sK2_X ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[79]) ).

thf(86,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( big_p @ SX0 )
          | ~ ( big_q @ SX1 )
          | ~ ( big_r @ SX0 )
          | ( big_s @ SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[80]) ).

thf(87,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( big_p @ SX0 )
          | ~ ( big_q @ SX1 )
          | ~ ( big_s @ SX1 )
          | ( big_r @ SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[81]) ).

thf(88,plain,
    ( ( ! [SX0: $i] :
          ~ ( big_p @ SX0 )
      | ( big_q @ sK4_Y ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[82]) ).

thf(89,plain,
    ( ( ! [SX0: $i] :
          ~ ( big_q @ SX0 )
      | ( big_p @ sK3_X ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[83]) ).

thf(90,plain,
    ! [SV8: $i] :
      ( ( ~ ( big_q @ SV8 )
        | ( big_s @ SV8 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[84]) ).

thf(91,plain,
    ( ( ~ ( big_p @ sK2_X )
      | ~ ~ ( big_r @ sK2_X ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[85]) ).

thf(92,plain,
    ! [SV9: $i] :
      ( ( ! [SY8: $i] :
            ( ~ ( big_p @ SV9 )
            | ~ ( big_q @ SY8 )
            | ~ ( big_r @ SV9 )
            | ( big_s @ SY8 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[86]) ).

thf(93,plain,
    ! [SV10: $i] :
      ( ( ! [SY9: $i] :
            ( ~ ( big_p @ SV10 )
            | ~ ( big_q @ SY9 )
            | ~ ( big_s @ SY9 )
            | ( big_r @ SV10 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[87]) ).

thf(94,plain,
    ( ( ( ! [SX0: $i] :
            ~ ( big_p @ SX0 ) )
      = $true )
    | ( ( big_q @ sK4_Y )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[88]) ).

thf(95,plain,
    ( ( ( ! [SX0: $i] :
            ~ ( big_q @ SX0 ) )
      = $true )
    | ( ( big_p @ sK3_X )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[89]) ).

thf(96,plain,
    ! [SV8: $i] :
      ( ( ( ~ ( big_q @ SV8 ) )
        = $true )
      | ( ( big_s @ SV8 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[90]) ).

thf(97,plain,
    ( ( ~ ( big_p @ sK2_X ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[91]) ).

thf(98,plain,
    ( ( ~ ~ ( big_r @ sK2_X ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[91]) ).

thf(99,plain,
    ! [SV11: $i,SV9: $i] :
      ( ( ~ ( big_p @ SV9 )
        | ~ ( big_q @ SV11 )
        | ~ ( big_r @ SV9 )
        | ( big_s @ SV11 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[92]) ).

thf(100,plain,
    ! [SV12: $i,SV10: $i] :
      ( ( ~ ( big_p @ SV10 )
        | ~ ( big_q @ SV12 )
        | ~ ( big_s @ SV12 )
        | ( big_r @ SV10 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[93]) ).

thf(101,plain,
    ! [SV13: $i] :
      ( ( ( ~ ( big_p @ SV13 ) )
        = $true )
      | ( ( big_q @ sK4_Y )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[94]) ).

thf(102,plain,
    ! [SV14: $i] :
      ( ( ( ~ ( big_q @ SV14 ) )
        = $true )
      | ( ( big_p @ sK3_X )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[95]) ).

thf(103,plain,
    ! [SV8: $i] :
      ( ( ( big_q @ SV8 )
        = $false )
      | ( ( big_s @ SV8 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[96]) ).

thf(104,plain,
    ( ( big_p @ sK2_X )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[97]) ).

thf(105,plain,
    ( ( ~ ( big_r @ sK2_X ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[98]) ).

thf(106,plain,
    ! [SV11: $i,SV9: $i] :
      ( ( ( ~ ( big_p @ SV9 )
          | ~ ( big_q @ SV11 ) )
        = $true )
      | ( ( ~ ( big_r @ SV9 )
          | ( big_s @ SV11 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[99]) ).

thf(107,plain,
    ! [SV12: $i,SV10: $i] :
      ( ( ( ~ ( big_p @ SV10 )
          | ~ ( big_q @ SV12 ) )
        = $true )
      | ( ( ~ ( big_s @ SV12 )
          | ( big_r @ SV10 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[100]) ).

thf(108,plain,
    ! [SV13: $i] :
      ( ( ( big_p @ SV13 )
        = $false )
      | ( ( big_q @ sK4_Y )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[101]) ).

thf(109,plain,
    ! [SV14: $i] :
      ( ( ( big_q @ SV14 )
        = $false )
      | ( ( big_p @ sK3_X )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[102]) ).

thf(110,plain,
    ( ( big_r @ sK2_X )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[105]) ).

thf(111,plain,
    ! [SV11: $i,SV9: $i] :
      ( ( ( ~ ( big_p @ SV9 ) )
        = $true )
      | ( ( ~ ( big_q @ SV11 ) )
        = $true )
      | ( ( ~ ( big_r @ SV9 )
          | ( big_s @ SV11 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[106]) ).

thf(112,plain,
    ! [SV12: $i,SV10: $i] :
      ( ( ( ~ ( big_p @ SV10 ) )
        = $true )
      | ( ( ~ ( big_q @ SV12 ) )
        = $true )
      | ( ( ~ ( big_s @ SV12 )
          | ( big_r @ SV10 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[107]) ).

thf(113,plain,
    ! [SV11: $i,SV9: $i] :
      ( ( ( big_p @ SV9 )
        = $false )
      | ( ( ~ ( big_q @ SV11 ) )
        = $true )
      | ( ( ~ ( big_r @ SV9 )
          | ( big_s @ SV11 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[111]) ).

thf(114,plain,
    ! [SV12: $i,SV10: $i] :
      ( ( ( big_p @ SV10 )
        = $false )
      | ( ( ~ ( big_q @ SV12 ) )
        = $true )
      | ( ( ~ ( big_s @ SV12 )
          | ( big_r @ SV10 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[112]) ).

thf(115,plain,
    ! [SV9: $i,SV11: $i] :
      ( ( ( big_q @ SV11 )
        = $false )
      | ( ( big_p @ SV9 )
        = $false )
      | ( ( ~ ( big_r @ SV9 )
          | ( big_s @ SV11 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[113]) ).

thf(116,plain,
    ! [SV10: $i,SV12: $i] :
      ( ( ( big_q @ SV12 )
        = $false )
      | ( ( big_p @ SV10 )
        = $false )
      | ( ( ~ ( big_s @ SV12 )
          | ( big_r @ SV10 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[114]) ).

thf(117,plain,
    ! [SV11: $i,SV9: $i] :
      ( ( ( ~ ( big_r @ SV9 ) )
        = $true )
      | ( ( big_s @ SV11 )
        = $true )
      | ( ( big_p @ SV9 )
        = $false )
      | ( ( big_q @ SV11 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[115]) ).

thf(118,plain,
    ! [SV10: $i,SV12: $i] :
      ( ( ( ~ ( big_s @ SV12 ) )
        = $true )
      | ( ( big_r @ SV10 )
        = $true )
      | ( ( big_p @ SV10 )
        = $false )
      | ( ( big_q @ SV12 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[116]) ).

thf(119,plain,
    ! [SV11: $i,SV9: $i] :
      ( ( ( big_r @ SV9 )
        = $false )
      | ( ( big_s @ SV11 )
        = $true )
      | ( ( big_p @ SV9 )
        = $false )
      | ( ( big_q @ SV11 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[117]) ).

thf(120,plain,
    ! [SV10: $i,SV12: $i] :
      ( ( ( big_s @ SV12 )
        = $false )
      | ( ( big_r @ SV10 )
        = $true )
      | ( ( big_p @ SV10 )
        = $false )
      | ( ( big_q @ SV12 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[118]) ).

thf(121,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[103,120,119,110,109,108,104]) ).

thf(122,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[121,68]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : SYN056+1 : TPTP v8.1.0. Released v2.0.0.
% 0.10/0.12  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33  % Computer : n021.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 : Mon Jul 11 21:59:23 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  
% 0.12/0.34   No.of.Axioms: 2
% 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:2,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:4,loop_count:0,foatp_calls:0,translation:fof_full)....
% 0.12/0.40  
% 0.12/0.40  ********************************
% 0.12/0.40  *   All subproblems solved!    *
% 0.12/0.40  ********************************
% 0.12/0.40  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:2,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:121,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.18/0.41  
% 0.18/0.41  %**** Beginning of derivation protocol ****
% 0.18/0.41  % SZS output start CNFRefutation
% See solution above
% 0.18/0.41  
% 0.18/0.41  %**** End of derivation protocol ****
% 0.18/0.41  %**** no. of clauses in derivation: 122 ****
% 0.18/0.41  %**** clause counter: 121 ****
% 0.18/0.41  
% 0.18/0.41  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:2,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:121,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------