TSTP Solution File: SYN939+1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SYN939+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 : n016.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 08:30:41 EDT 2022

% Result   : Theorem 0.14s 0.40s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   63 (  31 unt;   6 typ;   0 def)
%            Number of atoms       :  493 ( 109 equ;   0 cnn)
%            Maximal formula atoms :    7 (   8 avg)
%            Number of connectives :  716 ( 179   ~; 172   |;  27   &; 319   @)
%                                         (   0 <=>;  19  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :  138 (   0   ^ 124   !;  14   ?; 138   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_f,type,
    f: $i > $i ).

thf(tp_p,type,
    p: $i > $o ).

thf(tp_q,type,
    q: $i > $o ).

thf(tp_r,type,
    r: $i > $o ).

thf(tp_sK1_C,type,
    sK1_C: $i ).

thf(tp_sK2_SY5,type,
    sK2_SY5: $i ).

thf(1,conjecture,
    ! [C: $i,B: $i] :
      ( ! [Z: $i] : ( q @ ( f @ Z ) )
     => ? [X: $i,Y: $i] :
          ( ( ( p @ ( f @ Y ) )
           => ( p @ X ) )
          & ( ( r @ Y )
           => ( ( r @ B )
              & ( r @ C ) ) )
          & ( q @ X ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).

thf(2,negated_conjecture,
    ( ( ! [C: $i,B: $i] :
          ( ! [Z: $i] : ( q @ ( f @ Z ) )
         => ? [X: $i,Y: $i] :
              ( ( ( p @ ( f @ Y ) )
               => ( p @ X ) )
              & ( ( r @ Y )
               => ( ( r @ B )
                  & ( r @ C ) ) )
              & ( q @ X ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ! [C: $i,B: $i] :
          ( ! [Z: $i] : ( q @ ( f @ Z ) )
         => ? [X: $i,Y: $i] :
              ( ( ( p @ ( f @ Y ) )
               => ( p @ X ) )
              & ( ( r @ Y )
               => ( ( r @ B )
                  & ( r @ C ) ) )
              & ( q @ X ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ! [SY5: $i] :
          ( ! [Z: $i] : ( q @ ( f @ Z ) )
         => ? [SY7: $i,SY8: $i] :
              ( ( ( p @ ( f @ SY8 ) )
               => ( p @ SY7 ) )
              & ( ( r @ SY8 )
               => ( ( r @ SY5 )
                  & ( r @ sK1_C ) ) )
              & ( q @ SY7 ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[3]) ).

thf(5,plain,
    ( ( ! [Z: $i] : ( q @ ( f @ Z ) )
     => ? [SY10: $i,SY11: $i] :
          ( ( ( p @ ( f @ SY11 ) )
           => ( p @ SY10 ) )
          & ( ( r @ SY11 )
           => ( ( r @ sK2_SY5 )
              & ( r @ sK1_C ) ) )
          & ( q @ SY10 ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[4]) ).

thf(6,plain,
    ( ( ! [Z: $i] : ( q @ ( f @ Z ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[5]) ).

thf(7,plain,
    ( ( ? [SY10: $i,SY11: $i] :
          ( ( ( p @ ( f @ SY11 ) )
           => ( p @ SY10 ) )
          & ( ( r @ SY11 )
           => ( ( r @ sK2_SY5 )
              & ( r @ sK1_C ) ) )
          & ( q @ SY10 ) ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[5]) ).

thf(8,plain,
    ( ( ~ ? [SY10: $i,SY11: $i] :
            ( ( ( p @ ( f @ SY11 ) )
             => ( p @ SY10 ) )
            & ( ( r @ SY11 )
             => ( ( r @ sK2_SY5 )
                & ( r @ sK1_C ) ) )
            & ( q @ SY10 ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[7]) ).

thf(9,plain,
    ( ( ( ! [SY11: $i] :
            ( ( p @ ( f @ SY11 ) )
            | ( r @ SY11 ) )
        | ! [SY10: $i] :
            ~ ( q @ SY10 ) )
      & ( ! [SY11: $i] : ( p @ ( f @ SY11 ) )
        | ~ ( r @ sK2_SY5 )
        | ~ ( r @ sK1_C )
        | ! [SY10: $i] :
            ~ ( q @ SY10 ) )
      & ! [SY10: $i] :
          ( ~ ( p @ SY10 )
          | ! [SY11: $i] : ( r @ SY11 )
          | ~ ( q @ SY10 ) )
      & ! [SY10: $i] :
          ( ~ ( p @ SY10 )
          | ~ ( r @ sK2_SY5 )
          | ~ ( r @ sK1_C )
          | ~ ( q @ SY10 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[8]) ).

thf(10,plain,
    ( ( ! [Z: $i] : ( q @ ( f @ Z ) ) )
    = $true ),
    inference(copy,[status(thm)],[6]) ).

thf(11,plain,
    ( ( ( ! [SY11: $i] :
            ( ( p @ ( f @ SY11 ) )
            | ( r @ SY11 ) )
        | ! [SY10: $i] :
            ~ ( q @ SY10 ) )
      & ( ! [SY11: $i] : ( p @ ( f @ SY11 ) )
        | ~ ( r @ sK2_SY5 )
        | ~ ( r @ sK1_C )
        | ! [SY10: $i] :
            ~ ( q @ SY10 ) )
      & ! [SY10: $i] :
          ( ~ ( p @ SY10 )
          | ! [SY11: $i] : ( r @ SY11 )
          | ~ ( q @ SY10 ) )
      & ! [SY10: $i] :
          ( ~ ( p @ SY10 )
          | ~ ( r @ sK2_SY5 )
          | ~ ( r @ sK1_C )
          | ~ ( q @ SY10 ) ) )
    = $true ),
    inference(copy,[status(thm)],[9]) ).

thf(12,plain,
    ( ( ~ ( ~ ~ ( ~ ( ! [SX0: $i] :
                        ( ( p @ ( f @ SX0 ) )
                        | ( r @ SX0 ) )
                    | ! [SX0: $i] :
                        ~ ( q @ SX0 ) )
                | ~ ( ! [SX0: $i] : ( p @ ( f @ SX0 ) )
                    | ~ ( r @ sK2_SY5 )
                    | ~ ( r @ sK1_C )
                    | ! [SX0: $i] :
                        ~ ( q @ SX0 ) ) )
          | ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( p @ SX0 )
                      | ! [SX1: $i] : ( r @ SX1 )
                      | ~ ( q @ SX0 ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( p @ SX0 )
                      | ~ ( r @ sK2_SY5 )
                      | ~ ( r @ sK1_C )
                      | ~ ( q @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11]) ).

thf(13,plain,
    ! [SV1: $i] :
      ( ( q @ ( f @ SV1 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10]) ).

thf(14,plain,
    ( ( ~ ~ ( ~ ( ! [SX0: $i] :
                    ( ( p @ ( f @ SX0 ) )
                    | ( r @ SX0 ) )
                | ! [SX0: $i] :
                    ~ ( q @ SX0 ) )
            | ~ ( ! [SX0: $i] : ( p @ ( f @ SX0 ) )
                | ~ ( r @ sK2_SY5 )
                | ~ ( r @ sK1_C )
                | ! [SX0: $i] :
                    ~ ( q @ SX0 ) ) )
      | ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( p @ SX0 )
                  | ! [SX1: $i] : ( r @ SX1 )
                  | ~ ( q @ SX0 ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( p @ SX0 )
                  | ~ ( r @ sK2_SY5 )
                  | ~ ( r @ sK1_C )
                  | ~ ( q @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[12]) ).

thf(15,plain,
    ( ( ~ ~ ( ~ ( ! [SX0: $i] :
                    ( ( p @ ( f @ SX0 ) )
                    | ( r @ SX0 ) )
                | ! [SX0: $i] :
                    ~ ( q @ SX0 ) )
            | ~ ( ! [SX0: $i] : ( p @ ( f @ SX0 ) )
                | ~ ( r @ sK2_SY5 )
                | ~ ( r @ sK1_C )
                | ! [SX0: $i] :
                    ~ ( q @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[14]) ).

thf(16,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( p @ SX0 )
                  | ! [SX1: $i] : ( r @ SX1 )
                  | ~ ( q @ SX0 ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( p @ SX0 )
                  | ~ ( r @ sK2_SY5 )
                  | ~ ( r @ sK1_C )
                  | ~ ( q @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[14]) ).

thf(17,plain,
    ( ( ~ ( ~ ( ! [SX0: $i] :
                  ( ( p @ ( f @ SX0 ) )
                  | ( r @ SX0 ) )
              | ! [SX0: $i] :
                  ~ ( q @ SX0 ) )
          | ~ ( ! [SX0: $i] : ( p @ ( f @ SX0 ) )
              | ~ ( r @ sK2_SY5 )
              | ~ ( r @ sK1_C )
              | ! [SX0: $i] :
                  ~ ( q @ SX0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[15]) ).

thf(18,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( p @ SX0 )
                | ! [SX1: $i] : ( r @ SX1 )
                | ~ ( q @ SX0 ) )
          | ~ ! [SX0: $i] :
                ( ~ ( p @ SX0 )
                | ~ ( r @ sK2_SY5 )
                | ~ ( r @ sK1_C )
                | ~ ( q @ SX0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[16]) ).

thf(19,plain,
    ( ( ~ ( ! [SX0: $i] :
              ( ( p @ ( f @ SX0 ) )
              | ( r @ SX0 ) )
          | ! [SX0: $i] :
              ~ ( q @ SX0 ) )
      | ~ ( ! [SX0: $i] : ( p @ ( f @ SX0 ) )
          | ~ ( r @ sK2_SY5 )
          | ~ ( r @ sK1_C )
          | ! [SX0: $i] :
              ~ ( q @ SX0 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[17]) ).

thf(20,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( p @ SX0 )
            | ! [SX1: $i] : ( r @ SX1 )
            | ~ ( q @ SX0 ) )
      | ~ ! [SX0: $i] :
            ( ~ ( p @ SX0 )
            | ~ ( r @ sK2_SY5 )
            | ~ ( r @ sK1_C )
            | ~ ( q @ SX0 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[18]) ).

thf(21,plain,
    ( ( ~ ( ! [SX0: $i] :
              ( ( p @ ( f @ SX0 ) )
              | ( r @ SX0 ) )
          | ! [SX0: $i] :
              ~ ( q @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[19]) ).

thf(22,plain,
    ( ( ~ ( ! [SX0: $i] : ( p @ ( f @ SX0 ) )
          | ~ ( r @ sK2_SY5 )
          | ~ ( r @ sK1_C )
          | ! [SX0: $i] :
              ~ ( q @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[19]) ).

thf(23,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( p @ SX0 )
            | ! [SX1: $i] : ( r @ SX1 )
            | ~ ( q @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[20]) ).

thf(24,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( p @ SX0 )
            | ~ ( r @ sK2_SY5 )
            | ~ ( r @ sK1_C )
            | ~ ( q @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[20]) ).

thf(25,plain,
    ( ( ! [SX0: $i] :
          ( ( p @ ( f @ SX0 ) )
          | ( r @ SX0 ) )
      | ! [SX0: $i] :
          ~ ( q @ SX0 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[21]) ).

thf(26,plain,
    ( ( ! [SX0: $i] : ( p @ ( f @ SX0 ) )
      | ~ ( r @ sK2_SY5 )
      | ~ ( r @ sK1_C )
      | ! [SX0: $i] :
          ~ ( q @ SX0 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[22]) ).

thf(27,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( p @ SX0 )
          | ! [SX1: $i] : ( r @ SX1 )
          | ~ ( q @ SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[23]) ).

thf(28,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( p @ SX0 )
          | ~ ( r @ sK2_SY5 )
          | ~ ( r @ sK1_C )
          | ~ ( q @ SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[24]) ).

thf(29,plain,
    ( ( ( ! [SX0: $i] :
            ( ( p @ ( f @ SX0 ) )
            | ( r @ SX0 ) ) )
      = $true )
    | ( ( ! [SX0: $i] :
            ~ ( q @ SX0 ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[25]) ).

thf(30,plain,
    ( ( ( ! [SX0: $i] : ( p @ ( f @ SX0 ) )
        | ~ ( r @ sK2_SY5 )
        | ~ ( r @ sK1_C ) )
      = $true )
    | ( ( ! [SX0: $i] :
            ~ ( q @ SX0 ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[26]) ).

thf(31,plain,
    ! [SV2: $i] :
      ( ( ~ ( p @ SV2 )
        | ! [SX1: $i] : ( r @ SX1 )
        | ~ ( q @ SV2 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[27]) ).

thf(32,plain,
    ! [SV3: $i] :
      ( ( ~ ( p @ SV3 )
        | ~ ( r @ sK2_SY5 )
        | ~ ( r @ sK1_C )
        | ~ ( q @ SV3 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[28]) ).

thf(33,plain,
    ! [SV4: $i] :
      ( ( ( ( p @ ( f @ SV4 ) )
          | ( r @ SV4 ) )
        = $true )
      | ( ( ! [SX0: $i] :
              ~ ( q @ SX0 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[29]) ).

thf(34,plain,
    ( ( ( ! [SX0: $i] : ( p @ ( f @ SX0 ) ) )
      = $true )
    | ( ( ~ ( r @ sK2_SY5 )
        | ~ ( r @ sK1_C ) )
      = $true )
    | ( ( ! [SX0: $i] :
            ~ ( q @ SX0 ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[30]) ).

thf(35,plain,
    ! [SV2: $i] :
      ( ( ( ~ ( p @ SV2 )
          | ! [SX1: $i] : ( r @ SX1 ) )
        = $true )
      | ( ( ~ ( q @ SV2 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[31]) ).

thf(36,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( p @ SV3 )
          | ~ ( r @ sK2_SY5 )
          | ~ ( r @ sK1_C ) )
        = $true )
      | ( ( ~ ( q @ SV3 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[32]) ).

thf(37,plain,
    ! [SV4: $i] :
      ( ( ( p @ ( f @ SV4 ) )
        = $true )
      | ( ( r @ SV4 )
        = $true )
      | ( ( ! [SX0: $i] :
              ~ ( q @ SX0 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[33]) ).

thf(38,plain,
    ! [SV5: $i] :
      ( ( ( p @ ( f @ SV5 ) )
        = $true )
      | ( ( ~ ( r @ sK2_SY5 )
          | ~ ( r @ sK1_C ) )
        = $true )
      | ( ( ! [SX0: $i] :
              ~ ( q @ SX0 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[34]) ).

thf(39,plain,
    ! [SV2: $i] :
      ( ( ( ~ ( p @ SV2 ) )
        = $true )
      | ( ( ! [SX1: $i] : ( r @ SX1 ) )
        = $true )
      | ( ( ~ ( q @ SV2 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[35]) ).

thf(40,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( p @ SV3 ) )
        = $true )
      | ( ( ~ ( r @ sK2_SY5 )
          | ~ ( r @ sK1_C ) )
        = $true )
      | ( ( ~ ( q @ SV3 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[36]) ).

thf(41,plain,
    ! [SV4: $i,SV6: $i] :
      ( ( ( ~ ( q @ SV6 ) )
        = $true )
      | ( ( r @ SV4 )
        = $true )
      | ( ( p @ ( f @ SV4 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[37]) ).

thf(42,plain,
    ! [SV5: $i] :
      ( ( ( ~ ( r @ sK2_SY5 ) )
        = $true )
      | ( ( ~ ( r @ sK1_C ) )
        = $true )
      | ( ( p @ ( f @ SV5 ) )
        = $true )
      | ( ( ! [SX0: $i] :
              ~ ( q @ SX0 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[38]) ).

thf(43,plain,
    ! [SV2: $i] :
      ( ( ( p @ SV2 )
        = $false )
      | ( ( ! [SX1: $i] : ( r @ SX1 ) )
        = $true )
      | ( ( ~ ( q @ SV2 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[39]) ).

thf(44,plain,
    ! [SV3: $i] :
      ( ( ( p @ SV3 )
        = $false )
      | ( ( ~ ( r @ sK2_SY5 )
          | ~ ( r @ sK1_C ) )
        = $true )
      | ( ( ~ ( q @ SV3 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[40]) ).

thf(45,plain,
    ! [SV4: $i,SV6: $i] :
      ( ( ( q @ SV6 )
        = $false )
      | ( ( r @ SV4 )
        = $true )
      | ( ( p @ ( f @ SV4 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[41]) ).

thf(46,plain,
    ! [SV5: $i] :
      ( ( ( r @ sK2_SY5 )
        = $false )
      | ( ( ~ ( r @ sK1_C ) )
        = $true )
      | ( ( p @ ( f @ SV5 ) )
        = $true )
      | ( ( ! [SX0: $i] :
              ~ ( q @ SX0 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[42]) ).

thf(47,plain,
    ! [SV2: $i,SV7: $i] :
      ( ( ( r @ SV7 )
        = $true )
      | ( ( p @ SV2 )
        = $false )
      | ( ( ~ ( q @ SV2 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[43]) ).

thf(48,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( r @ sK2_SY5 ) )
        = $true )
      | ( ( ~ ( r @ sK1_C ) )
        = $true )
      | ( ( p @ SV3 )
        = $false )
      | ( ( ~ ( q @ SV3 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[44]) ).

thf(49,plain,
    ! [SV5: $i] :
      ( ( ( r @ sK1_C )
        = $false )
      | ( ( r @ sK2_SY5 )
        = $false )
      | ( ( p @ ( f @ SV5 ) )
        = $true )
      | ( ( ! [SX0: $i] :
              ~ ( q @ SX0 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[46]) ).

thf(50,plain,
    ! [SV7: $i,SV2: $i] :
      ( ( ( q @ SV2 )
        = $false )
      | ( ( p @ SV2 )
        = $false )
      | ( ( r @ SV7 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[47]) ).

thf(51,plain,
    ! [SV3: $i] :
      ( ( ( r @ sK2_SY5 )
        = $false )
      | ( ( ~ ( r @ sK1_C ) )
        = $true )
      | ( ( p @ SV3 )
        = $false )
      | ( ( ~ ( q @ SV3 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[48]) ).

thf(52,plain,
    ! [SV5: $i,SV8: $i] :
      ( ( ( ~ ( q @ SV8 ) )
        = $true )
      | ( ( p @ ( f @ SV5 ) )
        = $true )
      | ( ( r @ sK2_SY5 )
        = $false )
      | ( ( r @ sK1_C )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[49]) ).

thf(53,plain,
    ! [SV3: $i] :
      ( ( ( r @ sK1_C )
        = $false )
      | ( ( r @ sK2_SY5 )
        = $false )
      | ( ( p @ SV3 )
        = $false )
      | ( ( ~ ( q @ SV3 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[51]) ).

thf(54,plain,
    ! [SV5: $i,SV8: $i] :
      ( ( ( q @ SV8 )
        = $false )
      | ( ( p @ ( f @ SV5 ) )
        = $true )
      | ( ( r @ sK2_SY5 )
        = $false )
      | ( ( r @ sK1_C )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[52]) ).

thf(55,plain,
    ! [SV3: $i] :
      ( ( ( q @ SV3 )
        = $false )
      | ( ( p @ SV3 )
        = $false )
      | ( ( r @ sK2_SY5 )
        = $false )
      | ( ( r @ sK1_C )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[53]) ).

thf(56,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[13,55,54,50,45]) ).

thf(57,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[56]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SYN939+1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.14  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.35  % Computer : n016.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Tue Jul 12 06:21:44 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.14/0.35  
% 0.14/0.35   No.of.Axioms: 0
% 0.14/0.35  
% 0.14/0.35   Length.of.Defs: 0
% 0.14/0.35  
% 0.14/0.35   Contains.Choice.Funs: false
% 0.14/0.36  (rf:0,axioms:0,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:2,loop_count:0,foatp_calls:0,translation:fof_full)....
% 0.14/0.40  
% 0.14/0.40  ********************************
% 0.14/0.40  *   All subproblems solved!    *
% 0.14/0.40  ********************************
% 0.14/0.40  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,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:56,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.14/0.40  
% 0.14/0.40  %**** Beginning of derivation protocol ****
% 0.14/0.40  % SZS output start CNFRefutation
% See solution above
% 0.14/0.40  
% 0.14/0.40  %**** End of derivation protocol ****
% 0.14/0.40  %**** no. of clauses in derivation: 57 ****
% 0.14/0.40  %**** clause counter: 56 ****
% 0.14/0.40  
% 0.14/0.40  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,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:56,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------