TSTP Solution File: SYN354+1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SYN354+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 : n022.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 08:25:31 EDT 2022

% Result   : Theorem 0.21s 0.43s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   30
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   67 (  42 unt;   5 typ;   0 def)
%            Number of atoms       :  605 (  95 equ;   0 cnn)
%            Maximal formula atoms :   11 (   9 avg)
%            Number of connectives : 1904 ( 373   ~; 281   |;  24   &;1178   @)
%                                         (  12 <=>;  36  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :  125 (   0   ^ 113   !;  12   ?; 125   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_big_f,type,
    big_f: $i > $i > $o ).

thf(tp_big_g,type,
    big_g: $i > $i > $o ).

thf(tp_sK1_X1,type,
    sK1_X1: $i ).

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

thf(tp_sK3_SY11,type,
    sK3_SY11: $i > $i > $i ).

thf(1,conjecture,
    ! [X1: $i,X2: $i] :
    ? [Y1: $i,Y2: $i] :
    ! [Z: $i] :
      ( ( big_f @ X1 @ X2 )
     => ( ( big_g @ X1 @ X2 )
       => ( ( ( ( big_g @ X2 @ Z )
            <=> ( big_g @ Y2 @ Z ) )
           => ( ( big_f @ Y1 @ Y2 )
             => ( big_f @ X2 @ Y2 ) ) )
         => ( ( ( big_g @ X2 @ Z )
            <=> ( big_g @ Y1 @ Z ) )
           => ( ( big_f @ X1 @ Y1 )
              & ( big_f @ X2 @ Y1 )
              & ( big_f @ Y1 @ Y2 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',church_46_20_1) ).

thf(2,negated_conjecture,
    ( ( ! [X1: $i,X2: $i] :
        ? [Y1: $i,Y2: $i] :
        ! [Z: $i] :
          ( ( big_f @ X1 @ X2 )
         => ( ( big_g @ X1 @ X2 )
           => ( ( ( ( big_g @ X2 @ Z )
                <=> ( big_g @ Y2 @ Z ) )
               => ( ( big_f @ Y1 @ Y2 )
                 => ( big_f @ X2 @ Y2 ) ) )
             => ( ( ( big_g @ X2 @ Z )
                <=> ( big_g @ Y1 @ Z ) )
               => ( ( big_f @ X1 @ Y1 )
                  & ( big_f @ X2 @ Y1 )
                  & ( big_f @ Y1 @ Y2 ) ) ) ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ! [X1: $i,X2: $i] :
        ? [Y1: $i,Y2: $i] :
        ! [Z: $i] :
          ( ( big_f @ X1 @ X2 )
         => ( ( big_g @ X1 @ X2 )
           => ( ( ( ( big_g @ X2 @ Z )
                <=> ( big_g @ Y2 @ Z ) )
               => ( ( big_f @ Y1 @ Y2 )
                 => ( big_f @ X2 @ Y2 ) ) )
             => ( ( ( big_g @ X2 @ Z )
                <=> ( big_g @ Y1 @ Z ) )
               => ( ( big_f @ X1 @ Y1 )
                  & ( big_f @ X2 @ Y1 )
                  & ( big_f @ Y1 @ Y2 ) ) ) ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ! [SY5: $i] :
        ? [SY6: $i,SY7: $i] :
        ! [SY8: $i] :
          ( ( big_f @ sK1_X1 @ SY5 )
         => ( ( big_g @ sK1_X1 @ SY5 )
           => ( ( ( ( big_g @ SY5 @ SY8 )
                <=> ( big_g @ SY7 @ SY8 ) )
               => ( ( big_f @ SY6 @ SY7 )
                 => ( big_f @ SY5 @ SY7 ) ) )
             => ( ( ( big_g @ SY5 @ SY8 )
                <=> ( big_g @ SY6 @ SY8 ) )
               => ( ( big_f @ sK1_X1 @ SY6 )
                  & ( big_f @ SY5 @ SY6 )
                  & ( big_f @ SY6 @ SY7 ) ) ) ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[3]) ).

thf(5,plain,
    ( ( ? [SY9: $i,SY10: $i] :
        ! [SY11: $i] :
          ( ( big_f @ sK1_X1 @ sK2_SY5 )
         => ( ( big_g @ sK1_X1 @ sK2_SY5 )
           => ( ( ( ( big_g @ sK2_SY5 @ SY11 )
                <=> ( big_g @ SY10 @ SY11 ) )
               => ( ( big_f @ SY9 @ SY10 )
                 => ( big_f @ sK2_SY5 @ SY10 ) ) )
             => ( ( ( big_g @ sK2_SY5 @ SY11 )
                <=> ( big_g @ SY9 @ SY11 ) )
               => ( ( big_f @ sK1_X1 @ SY9 )
                  & ( big_f @ sK2_SY5 @ SY9 )
                  & ( big_f @ SY9 @ SY10 ) ) ) ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[4]) ).

thf(6,plain,
    ( ( ~ ? [SY9: $i,SY10: $i] :
          ! [SY11: $i] :
            ( ( big_f @ sK1_X1 @ sK2_SY5 )
           => ( ( big_g @ sK1_X1 @ sK2_SY5 )
             => ( ( ( ( big_g @ sK2_SY5 @ SY11 )
                  <=> ( big_g @ SY10 @ SY11 ) )
                 => ( ( big_f @ SY9 @ SY10 )
                   => ( big_f @ sK2_SY5 @ SY10 ) ) )
               => ( ( ( big_g @ sK2_SY5 @ SY11 )
                  <=> ( big_g @ SY9 @ SY11 ) )
                 => ( ( big_f @ sK1_X1 @ SY9 )
                    & ( big_f @ sK2_SY5 @ SY9 )
                    & ( big_f @ SY9 @ SY10 ) ) ) ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[5]) ).

thf(7,plain,
    ( ( ! [SY9: $i] :
          ( ( big_f @ sK1_X1 @ sK2_SY5 )
          & ( big_g @ sK1_X1 @ sK2_SY5 )
          & ! [SY10: $i] :
              ( ( ~ ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SY10 @ SY9 ) )
                | ~ ( big_g @ SY10 @ ( sK3_SY11 @ SY10 @ SY9 ) )
                | ~ ( big_f @ SY9 @ SY10 )
                | ( big_f @ sK2_SY5 @ SY10 ) )
              & ( ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SY10 @ SY9 ) )
                | ( big_g @ SY10 @ ( sK3_SY11 @ SY10 @ SY9 ) )
                | ~ ( big_f @ SY9 @ SY10 )
                | ( big_f @ sK2_SY5 @ SY10 ) )
              & ( ~ ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SY10 @ SY9 ) )
                | ( big_g @ SY9 @ ( sK3_SY11 @ SY10 @ SY9 ) ) )
              & ( ~ ( big_g @ SY9 @ ( sK3_SY11 @ SY10 @ SY9 ) )
                | ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SY10 @ SY9 ) ) )
              & ( ~ ( big_f @ sK1_X1 @ SY9 )
                | ~ ( big_f @ sK2_SY5 @ SY9 )
                | ~ ( big_f @ SY9 @ SY10 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[6]) ).

thf(8,plain,
    ( ( ! [SY9: $i] :
          ( ( big_f @ sK1_X1 @ sK2_SY5 )
          & ( big_g @ sK1_X1 @ sK2_SY5 )
          & ! [SY10: $i] :
              ( ( ~ ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SY10 @ SY9 ) )
                | ~ ( big_g @ SY10 @ ( sK3_SY11 @ SY10 @ SY9 ) )
                | ~ ( big_f @ SY9 @ SY10 )
                | ( big_f @ sK2_SY5 @ SY10 ) )
              & ( ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SY10 @ SY9 ) )
                | ( big_g @ SY10 @ ( sK3_SY11 @ SY10 @ SY9 ) )
                | ~ ( big_f @ SY9 @ SY10 )
                | ( big_f @ sK2_SY5 @ SY10 ) )
              & ( ~ ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SY10 @ SY9 ) )
                | ( big_g @ SY9 @ ( sK3_SY11 @ SY10 @ SY9 ) ) )
              & ( ~ ( big_g @ SY9 @ ( sK3_SY11 @ SY10 @ SY9 ) )
                | ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SY10 @ SY9 ) ) )
              & ( ~ ( big_f @ sK1_X1 @ SY9 )
                | ~ ( big_f @ sK2_SY5 @ SY9 )
                | ~ ( big_f @ SY9 @ SY10 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[7]) ).

thf(9,plain,
    ( ( ! [SX0: $i] :
          ~ ( ~ ( big_f @ sK1_X1 @ sK2_SY5 )
            | ~ ~ ( ~ ( big_g @ sK1_X1 @ sK2_SY5 )
                  | ~ ! [SX1: $i] :
                        ~ ( ~ ~ ( ~ ( ~ ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SX1 @ SX0 ) )
                                    | ~ ( big_g @ SX1 @ ( sK3_SY11 @ SX1 @ SX0 ) )
                                    | ~ ( big_f @ SX0 @ SX1 )
                                    | ( big_f @ sK2_SY5 @ SX1 ) )
                                | ~ ( ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SX1 @ SX0 ) )
                                    | ( big_g @ SX1 @ ( sK3_SY11 @ SX1 @ SX0 ) )
                                    | ~ ( big_f @ SX0 @ SX1 )
                                    | ( big_f @ sK2_SY5 @ SX1 ) ) )
                          | ~ ~ ( ~ ~ ( ~ ( ~ ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SX1 @ SX0 ) )
                                          | ( big_g @ SX0 @ ( sK3_SY11 @ SX1 @ SX0 ) ) )
                                      | ~ ( ~ ( big_g @ SX0 @ ( sK3_SY11 @ SX1 @ SX0 ) )
                                          | ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SX1 @ SX0 ) ) ) )
                                | ~ ( ~ ( big_f @ sK1_X1 @ SX0 )
                                    | ~ ( big_f @ sK2_SY5 @ SX0 )
                                    | ~ ( big_f @ SX0 @ SX1 ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8]) ).

thf(10,plain,
    ! [SV1: $i] :
      ( ( ~ ( ~ ( big_f @ sK1_X1 @ sK2_SY5 )
            | ~ ~ ( ~ ( big_g @ sK1_X1 @ sK2_SY5 )
                  | ~ ! [SY12: $i] :
                        ~ ( ~ ~ ( ~ ( ~ ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SY12 @ SV1 ) )
                                    | ~ ( big_g @ SY12 @ ( sK3_SY11 @ SY12 @ SV1 ) )
                                    | ~ ( big_f @ SV1 @ SY12 )
                                    | ( big_f @ sK2_SY5 @ SY12 ) )
                                | ~ ( ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SY12 @ SV1 ) )
                                    | ( big_g @ SY12 @ ( sK3_SY11 @ SY12 @ SV1 ) )
                                    | ~ ( big_f @ SV1 @ SY12 )
                                    | ( big_f @ sK2_SY5 @ SY12 ) ) )
                          | ~ ~ ( ~ ~ ( ~ ( ~ ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SY12 @ SV1 ) )
                                          | ( big_g @ SV1 @ ( sK3_SY11 @ SY12 @ SV1 ) ) )
                                      | ~ ( ~ ( big_g @ SV1 @ ( sK3_SY11 @ SY12 @ SV1 ) )
                                          | ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SY12 @ SV1 ) ) ) )
                                | ~ ( ~ ( big_f @ sK1_X1 @ SV1 )
                                    | ~ ( big_f @ sK2_SY5 @ SV1 )
                                    | ~ ( big_f @ SV1 @ SY12 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[9]) ).

thf(11,plain,
    ! [SV1: $i] :
      ( ( ~ ( big_f @ sK1_X1 @ sK2_SY5 )
        | ~ ~ ( ~ ( big_g @ sK1_X1 @ sK2_SY5 )
              | ~ ! [SY12: $i] :
                    ~ ( ~ ~ ( ~ ( ~ ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SY12 @ SV1 ) )
                                | ~ ( big_g @ SY12 @ ( sK3_SY11 @ SY12 @ SV1 ) )
                                | ~ ( big_f @ SV1 @ SY12 )
                                | ( big_f @ sK2_SY5 @ SY12 ) )
                            | ~ ( ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SY12 @ SV1 ) )
                                | ( big_g @ SY12 @ ( sK3_SY11 @ SY12 @ SV1 ) )
                                | ~ ( big_f @ SV1 @ SY12 )
                                | ( big_f @ sK2_SY5 @ SY12 ) ) )
                      | ~ ~ ( ~ ~ ( ~ ( ~ ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SY12 @ SV1 ) )
                                      | ( big_g @ SV1 @ ( sK3_SY11 @ SY12 @ SV1 ) ) )
                                  | ~ ( ~ ( big_g @ SV1 @ ( sK3_SY11 @ SY12 @ SV1 ) )
                                      | ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SY12 @ SV1 ) ) ) )
                            | ~ ( ~ ( big_f @ sK1_X1 @ SV1 )
                                | ~ ( big_f @ sK2_SY5 @ SV1 )
                                | ~ ( big_f @ SV1 @ SY12 ) ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[10]) ).

thf(12,plain,
    ( ( ~ ( big_f @ sK1_X1 @ sK2_SY5 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[11]) ).

thf(13,plain,
    ! [SV1: $i] :
      ( ( ~ ~ ( ~ ( big_g @ sK1_X1 @ sK2_SY5 )
              | ~ ! [SY12: $i] :
                    ~ ( ~ ~ ( ~ ( ~ ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SY12 @ SV1 ) )
                                | ~ ( big_g @ SY12 @ ( sK3_SY11 @ SY12 @ SV1 ) )
                                | ~ ( big_f @ SV1 @ SY12 )
                                | ( big_f @ sK2_SY5 @ SY12 ) )
                            | ~ ( ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SY12 @ SV1 ) )
                                | ( big_g @ SY12 @ ( sK3_SY11 @ SY12 @ SV1 ) )
                                | ~ ( big_f @ SV1 @ SY12 )
                                | ( big_f @ sK2_SY5 @ SY12 ) ) )
                      | ~ ~ ( ~ ~ ( ~ ( ~ ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SY12 @ SV1 ) )
                                      | ( big_g @ SV1 @ ( sK3_SY11 @ SY12 @ SV1 ) ) )
                                  | ~ ( ~ ( big_g @ SV1 @ ( sK3_SY11 @ SY12 @ SV1 ) )
                                      | ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SY12 @ SV1 ) ) ) )
                            | ~ ( ~ ( big_f @ sK1_X1 @ SV1 )
                                | ~ ( big_f @ sK2_SY5 @ SV1 )
                                | ~ ( big_f @ SV1 @ SY12 ) ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[11]) ).

thf(14,plain,
    ( ( big_f @ sK1_X1 @ sK2_SY5 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[12]) ).

thf(15,plain,
    ! [SV1: $i] :
      ( ( ~ ( ~ ( big_g @ sK1_X1 @ sK2_SY5 )
            | ~ ! [SY12: $i] :
                  ~ ( ~ ~ ( ~ ( ~ ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SY12 @ SV1 ) )
                              | ~ ( big_g @ SY12 @ ( sK3_SY11 @ SY12 @ SV1 ) )
                              | ~ ( big_f @ SV1 @ SY12 )
                              | ( big_f @ sK2_SY5 @ SY12 ) )
                          | ~ ( ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SY12 @ SV1 ) )
                              | ( big_g @ SY12 @ ( sK3_SY11 @ SY12 @ SV1 ) )
                              | ~ ( big_f @ SV1 @ SY12 )
                              | ( big_f @ sK2_SY5 @ SY12 ) ) )
                    | ~ ~ ( ~ ~ ( ~ ( ~ ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SY12 @ SV1 ) )
                                    | ( big_g @ SV1 @ ( sK3_SY11 @ SY12 @ SV1 ) ) )
                                | ~ ( ~ ( big_g @ SV1 @ ( sK3_SY11 @ SY12 @ SV1 ) )
                                    | ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SY12 @ SV1 ) ) ) )
                          | ~ ( ~ ( big_f @ sK1_X1 @ SV1 )
                              | ~ ( big_f @ sK2_SY5 @ SV1 )
                              | ~ ( big_f @ SV1 @ SY12 ) ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[13]) ).

thf(16,plain,
    ! [SV1: $i] :
      ( ( ~ ( big_g @ sK1_X1 @ sK2_SY5 )
        | ~ ! [SY12: $i] :
              ~ ( ~ ~ ( ~ ( ~ ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SY12 @ SV1 ) )
                          | ~ ( big_g @ SY12 @ ( sK3_SY11 @ SY12 @ SV1 ) )
                          | ~ ( big_f @ SV1 @ SY12 )
                          | ( big_f @ sK2_SY5 @ SY12 ) )
                      | ~ ( ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SY12 @ SV1 ) )
                          | ( big_g @ SY12 @ ( sK3_SY11 @ SY12 @ SV1 ) )
                          | ~ ( big_f @ SV1 @ SY12 )
                          | ( big_f @ sK2_SY5 @ SY12 ) ) )
                | ~ ~ ( ~ ~ ( ~ ( ~ ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SY12 @ SV1 ) )
                                | ( big_g @ SV1 @ ( sK3_SY11 @ SY12 @ SV1 ) ) )
                            | ~ ( ~ ( big_g @ SV1 @ ( sK3_SY11 @ SY12 @ SV1 ) )
                                | ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SY12 @ SV1 ) ) ) )
                      | ~ ( ~ ( big_f @ sK1_X1 @ SV1 )
                          | ~ ( big_f @ sK2_SY5 @ SV1 )
                          | ~ ( big_f @ SV1 @ SY12 ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[15]) ).

thf(17,plain,
    ( ( ~ ( big_g @ sK1_X1 @ sK2_SY5 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[16]) ).

thf(18,plain,
    ! [SV1: $i] :
      ( ( ~ ! [SY12: $i] :
              ~ ( ~ ~ ( ~ ( ~ ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SY12 @ SV1 ) )
                          | ~ ( big_g @ SY12 @ ( sK3_SY11 @ SY12 @ SV1 ) )
                          | ~ ( big_f @ SV1 @ SY12 )
                          | ( big_f @ sK2_SY5 @ SY12 ) )
                      | ~ ( ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SY12 @ SV1 ) )
                          | ( big_g @ SY12 @ ( sK3_SY11 @ SY12 @ SV1 ) )
                          | ~ ( big_f @ SV1 @ SY12 )
                          | ( big_f @ sK2_SY5 @ SY12 ) ) )
                | ~ ~ ( ~ ~ ( ~ ( ~ ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SY12 @ SV1 ) )
                                | ( big_g @ SV1 @ ( sK3_SY11 @ SY12 @ SV1 ) ) )
                            | ~ ( ~ ( big_g @ SV1 @ ( sK3_SY11 @ SY12 @ SV1 ) )
                                | ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SY12 @ SV1 ) ) ) )
                      | ~ ( ~ ( big_f @ sK1_X1 @ SV1 )
                          | ~ ( big_f @ sK2_SY5 @ SV1 )
                          | ~ ( big_f @ SV1 @ SY12 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[16]) ).

thf(19,plain,
    ( ( big_g @ sK1_X1 @ sK2_SY5 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[17]) ).

thf(20,plain,
    ! [SV1: $i] :
      ( ( ! [SY12: $i] :
            ~ ( ~ ~ ( ~ ( ~ ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SY12 @ SV1 ) )
                        | ~ ( big_g @ SY12 @ ( sK3_SY11 @ SY12 @ SV1 ) )
                        | ~ ( big_f @ SV1 @ SY12 )
                        | ( big_f @ sK2_SY5 @ SY12 ) )
                    | ~ ( ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SY12 @ SV1 ) )
                        | ( big_g @ SY12 @ ( sK3_SY11 @ SY12 @ SV1 ) )
                        | ~ ( big_f @ SV1 @ SY12 )
                        | ( big_f @ sK2_SY5 @ SY12 ) ) )
              | ~ ~ ( ~ ~ ( ~ ( ~ ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SY12 @ SV1 ) )
                              | ( big_g @ SV1 @ ( sK3_SY11 @ SY12 @ SV1 ) ) )
                          | ~ ( ~ ( big_g @ SV1 @ ( sK3_SY11 @ SY12 @ SV1 ) )
                              | ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SY12 @ SV1 ) ) ) )
                    | ~ ( ~ ( big_f @ sK1_X1 @ SV1 )
                        | ~ ( big_f @ sK2_SY5 @ SV1 )
                        | ~ ( big_f @ SV1 @ SY12 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[18]) ).

thf(21,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ~ ( ~ ~ ( ~ ( ~ ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SV2 @ SV1 ) )
                      | ~ ( big_g @ SV2 @ ( sK3_SY11 @ SV2 @ SV1 ) )
                      | ~ ( big_f @ SV1 @ SV2 )
                      | ( big_f @ sK2_SY5 @ SV2 ) )
                  | ~ ( ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SV2 @ SV1 ) )
                      | ( big_g @ SV2 @ ( sK3_SY11 @ SV2 @ SV1 ) )
                      | ~ ( big_f @ SV1 @ SV2 )
                      | ( big_f @ sK2_SY5 @ SV2 ) ) )
            | ~ ~ ( ~ ~ ( ~ ( ~ ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SV2 @ SV1 ) )
                            | ( big_g @ SV1 @ ( sK3_SY11 @ SV2 @ SV1 ) ) )
                        | ~ ( ~ ( big_g @ SV1 @ ( sK3_SY11 @ SV2 @ SV1 ) )
                            | ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SV2 @ SV1 ) ) ) )
                  | ~ ( ~ ( big_f @ sK1_X1 @ SV1 )
                      | ~ ( big_f @ sK2_SY5 @ SV1 )
                      | ~ ( big_f @ SV1 @ SV2 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[20]) ).

thf(22,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ~ ~ ( ~ ( ~ ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SV2 @ SV1 ) )
                  | ~ ( big_g @ SV2 @ ( sK3_SY11 @ SV2 @ SV1 ) )
                  | ~ ( big_f @ SV1 @ SV2 )
                  | ( big_f @ sK2_SY5 @ SV2 ) )
              | ~ ( ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SV2 @ SV1 ) )
                  | ( big_g @ SV2 @ ( sK3_SY11 @ SV2 @ SV1 ) )
                  | ~ ( big_f @ SV1 @ SV2 )
                  | ( big_f @ sK2_SY5 @ SV2 ) ) )
        | ~ ~ ( ~ ~ ( ~ ( ~ ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SV2 @ SV1 ) )
                        | ( big_g @ SV1 @ ( sK3_SY11 @ SV2 @ SV1 ) ) )
                    | ~ ( ~ ( big_g @ SV1 @ ( sK3_SY11 @ SV2 @ SV1 ) )
                        | ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SV2 @ SV1 ) ) ) )
              | ~ ( ~ ( big_f @ sK1_X1 @ SV1 )
                  | ~ ( big_f @ sK2_SY5 @ SV1 )
                  | ~ ( big_f @ SV1 @ SV2 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[21]) ).

thf(23,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ~ ~ ( ~ ( ~ ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SV2 @ SV1 ) )
                  | ~ ( big_g @ SV2 @ ( sK3_SY11 @ SV2 @ SV1 ) )
                  | ~ ( big_f @ SV1 @ SV2 )
                  | ( big_f @ sK2_SY5 @ SV2 ) )
              | ~ ( ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SV2 @ SV1 ) )
                  | ( big_g @ SV2 @ ( sK3_SY11 @ SV2 @ SV1 ) )
                  | ~ ( big_f @ SV1 @ SV2 )
                  | ( big_f @ sK2_SY5 @ SV2 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[22]) ).

thf(24,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ~ ~ ( ~ ~ ( ~ ( ~ ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SV2 @ SV1 ) )
                        | ( big_g @ SV1 @ ( sK3_SY11 @ SV2 @ SV1 ) ) )
                    | ~ ( ~ ( big_g @ SV1 @ ( sK3_SY11 @ SV2 @ SV1 ) )
                        | ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SV2 @ SV1 ) ) ) )
              | ~ ( ~ ( big_f @ sK1_X1 @ SV1 )
                  | ~ ( big_f @ sK2_SY5 @ SV1 )
                  | ~ ( big_f @ SV1 @ SV2 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[22]) ).

thf(25,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ~ ( ~ ( ~ ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SV2 @ SV1 ) )
                | ~ ( big_g @ SV2 @ ( sK3_SY11 @ SV2 @ SV1 ) )
                | ~ ( big_f @ SV1 @ SV2 )
                | ( big_f @ sK2_SY5 @ SV2 ) )
            | ~ ( ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SV2 @ SV1 ) )
                | ( big_g @ SV2 @ ( sK3_SY11 @ SV2 @ SV1 ) )
                | ~ ( big_f @ SV1 @ SV2 )
                | ( big_f @ sK2_SY5 @ SV2 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[23]) ).

thf(26,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ~ ( ~ ~ ( ~ ( ~ ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SV2 @ SV1 ) )
                      | ( big_g @ SV1 @ ( sK3_SY11 @ SV2 @ SV1 ) ) )
                  | ~ ( ~ ( big_g @ SV1 @ ( sK3_SY11 @ SV2 @ SV1 ) )
                      | ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SV2 @ SV1 ) ) ) )
            | ~ ( ~ ( big_f @ sK1_X1 @ SV1 )
                | ~ ( big_f @ sK2_SY5 @ SV1 )
                | ~ ( big_f @ SV1 @ SV2 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[24]) ).

thf(27,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ~ ( ~ ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SV2 @ SV1 ) )
            | ~ ( big_g @ SV2 @ ( sK3_SY11 @ SV2 @ SV1 ) )
            | ~ ( big_f @ SV1 @ SV2 )
            | ( big_f @ sK2_SY5 @ SV2 ) )
        | ~ ( ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SV2 @ SV1 ) )
            | ( big_g @ SV2 @ ( sK3_SY11 @ SV2 @ SV1 ) )
            | ~ ( big_f @ SV1 @ SV2 )
            | ( big_f @ sK2_SY5 @ SV2 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[25]) ).

thf(28,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ~ ~ ( ~ ( ~ ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SV2 @ SV1 ) )
                  | ( big_g @ SV1 @ ( sK3_SY11 @ SV2 @ SV1 ) ) )
              | ~ ( ~ ( big_g @ SV1 @ ( sK3_SY11 @ SV2 @ SV1 ) )
                  | ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SV2 @ SV1 ) ) ) )
        | ~ ( ~ ( big_f @ sK1_X1 @ SV1 )
            | ~ ( big_f @ sK2_SY5 @ SV1 )
            | ~ ( big_f @ SV1 @ SV2 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[26]) ).

thf(29,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ~ ( ~ ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SV2 @ SV1 ) )
            | ~ ( big_g @ SV2 @ ( sK3_SY11 @ SV2 @ SV1 ) )
            | ~ ( big_f @ SV1 @ SV2 )
            | ( big_f @ sK2_SY5 @ SV2 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[27]) ).

thf(30,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ~ ( ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SV2 @ SV1 ) )
            | ( big_g @ SV2 @ ( sK3_SY11 @ SV2 @ SV1 ) )
            | ~ ( big_f @ SV1 @ SV2 )
            | ( big_f @ sK2_SY5 @ SV2 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[27]) ).

thf(31,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ~ ~ ( ~ ( ~ ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SV2 @ SV1 ) )
                  | ( big_g @ SV1 @ ( sK3_SY11 @ SV2 @ SV1 ) ) )
              | ~ ( ~ ( big_g @ SV1 @ ( sK3_SY11 @ SV2 @ SV1 ) )
                  | ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SV2 @ SV1 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[28]) ).

thf(32,plain,
    ! [SV2: $i,SV1: $i] :
      ( ( ~ ( ~ ( big_f @ sK1_X1 @ SV1 )
            | ~ ( big_f @ sK2_SY5 @ SV1 )
            | ~ ( big_f @ SV1 @ SV2 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[28]) ).

thf(33,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ~ ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SV2 @ SV1 ) )
        | ~ ( big_g @ SV2 @ ( sK3_SY11 @ SV2 @ SV1 ) )
        | ~ ( big_f @ SV1 @ SV2 )
        | ( big_f @ sK2_SY5 @ SV2 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[29]) ).

thf(34,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SV2 @ SV1 ) )
        | ( big_g @ SV2 @ ( sK3_SY11 @ SV2 @ SV1 ) )
        | ~ ( big_f @ SV1 @ SV2 )
        | ( big_f @ sK2_SY5 @ SV2 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[30]) ).

thf(35,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ~ ( ~ ( ~ ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SV2 @ SV1 ) )
                | ( big_g @ SV1 @ ( sK3_SY11 @ SV2 @ SV1 ) ) )
            | ~ ( ~ ( big_g @ SV1 @ ( sK3_SY11 @ SV2 @ SV1 ) )
                | ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SV2 @ SV1 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[31]) ).

thf(36,plain,
    ! [SV2: $i,SV1: $i] :
      ( ( ~ ( big_f @ sK1_X1 @ SV1 )
        | ~ ( big_f @ sK2_SY5 @ SV1 )
        | ~ ( big_f @ SV1 @ SV2 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[32]) ).

thf(37,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ( ~ ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SV2 @ SV1 ) )
          | ~ ( big_g @ SV2 @ ( sK3_SY11 @ SV2 @ SV1 ) ) )
        = $true )
      | ( ( ~ ( big_f @ SV1 @ SV2 )
          | ( big_f @ sK2_SY5 @ SV2 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[33]) ).

thf(38,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ( ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SV2 @ SV1 ) )
          | ( big_g @ SV2 @ ( sK3_SY11 @ SV2 @ SV1 ) ) )
        = $true )
      | ( ( ~ ( big_f @ SV1 @ SV2 )
          | ( big_f @ sK2_SY5 @ SV2 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[34]) ).

thf(39,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ~ ( ~ ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SV2 @ SV1 ) )
            | ( big_g @ SV1 @ ( sK3_SY11 @ SV2 @ SV1 ) ) )
        | ~ ( ~ ( big_g @ SV1 @ ( sK3_SY11 @ SV2 @ SV1 ) )
            | ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SV2 @ SV1 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[35]) ).

thf(40,plain,
    ! [SV2: $i,SV1: $i] :
      ( ( ( ~ ( big_f @ sK1_X1 @ SV1 )
          | ~ ( big_f @ sK2_SY5 @ SV1 ) )
        = $true )
      | ( ( ~ ( big_f @ SV1 @ SV2 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[36]) ).

thf(41,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ( ~ ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SV2 @ SV1 ) ) )
        = $true )
      | ( ( ~ ( big_g @ SV2 @ ( sK3_SY11 @ SV2 @ SV1 ) ) )
        = $true )
      | ( ( ~ ( big_f @ SV1 @ SV2 )
          | ( big_f @ sK2_SY5 @ SV2 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[37]) ).

thf(42,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SV2 @ SV1 ) )
        = $true )
      | ( ( big_g @ SV2 @ ( sK3_SY11 @ SV2 @ SV1 ) )
        = $true )
      | ( ( ~ ( big_f @ SV1 @ SV2 )
          | ( big_f @ sK2_SY5 @ SV2 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[38]) ).

thf(43,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ~ ( ~ ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SV2 @ SV1 ) )
            | ( big_g @ SV1 @ ( sK3_SY11 @ SV2 @ SV1 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[39]) ).

thf(44,plain,
    ! [SV2: $i,SV1: $i] :
      ( ( ~ ( ~ ( big_g @ SV1 @ ( sK3_SY11 @ SV2 @ SV1 ) )
            | ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SV2 @ SV1 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[39]) ).

thf(45,plain,
    ! [SV2: $i,SV1: $i] :
      ( ( ( ~ ( big_f @ sK1_X1 @ SV1 ) )
        = $true )
      | ( ( ~ ( big_f @ sK2_SY5 @ SV1 ) )
        = $true )
      | ( ( ~ ( big_f @ SV1 @ SV2 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[40]) ).

thf(46,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SV2 @ SV1 ) )
        = $false )
      | ( ( ~ ( big_g @ SV2 @ ( sK3_SY11 @ SV2 @ SV1 ) ) )
        = $true )
      | ( ( ~ ( big_f @ SV1 @ SV2 )
          | ( big_f @ sK2_SY5 @ SV2 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[41]) ).

thf(47,plain,
    ! [SV2: $i,SV1: $i] :
      ( ( ( ~ ( big_f @ SV1 @ SV2 ) )
        = $true )
      | ( ( big_f @ sK2_SY5 @ SV2 )
        = $true )
      | ( ( big_g @ SV2 @ ( sK3_SY11 @ SV2 @ SV1 ) )
        = $true )
      | ( ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SV2 @ SV1 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[42]) ).

thf(48,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ~ ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SV2 @ SV1 ) )
        | ( big_g @ SV1 @ ( sK3_SY11 @ SV2 @ SV1 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[43]) ).

thf(49,plain,
    ! [SV2: $i,SV1: $i] :
      ( ( ~ ( big_g @ SV1 @ ( sK3_SY11 @ SV2 @ SV1 ) )
        | ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SV2 @ SV1 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[44]) ).

thf(50,plain,
    ! [SV2: $i,SV1: $i] :
      ( ( ( big_f @ sK1_X1 @ SV1 )
        = $false )
      | ( ( ~ ( big_f @ sK2_SY5 @ SV1 ) )
        = $true )
      | ( ( ~ ( big_f @ SV1 @ SV2 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[45]) ).

thf(51,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ( big_g @ SV2 @ ( sK3_SY11 @ SV2 @ SV1 ) )
        = $false )
      | ( ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SV2 @ SV1 ) )
        = $false )
      | ( ( ~ ( big_f @ SV1 @ SV2 )
          | ( big_f @ sK2_SY5 @ SV2 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[46]) ).

thf(52,plain,
    ! [SV2: $i,SV1: $i] :
      ( ( ( big_f @ SV1 @ SV2 )
        = $false )
      | ( ( big_f @ sK2_SY5 @ SV2 )
        = $true )
      | ( ( big_g @ SV2 @ ( sK3_SY11 @ SV2 @ SV1 ) )
        = $true )
      | ( ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SV2 @ SV1 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[47]) ).

thf(53,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ( ~ ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SV2 @ SV1 ) ) )
        = $true )
      | ( ( big_g @ SV1 @ ( sK3_SY11 @ SV2 @ SV1 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[48]) ).

thf(54,plain,
    ! [SV2: $i,SV1: $i] :
      ( ( ( ~ ( big_g @ SV1 @ ( sK3_SY11 @ SV2 @ SV1 ) ) )
        = $true )
      | ( ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SV2 @ SV1 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[49]) ).

thf(55,plain,
    ! [SV2: $i,SV1: $i] :
      ( ( ( big_f @ sK2_SY5 @ SV1 )
        = $false )
      | ( ( big_f @ sK1_X1 @ SV1 )
        = $false )
      | ( ( ~ ( big_f @ SV1 @ SV2 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[50]) ).

thf(56,plain,
    ! [SV2: $i,SV1: $i] :
      ( ( ( ~ ( big_f @ SV1 @ SV2 ) )
        = $true )
      | ( ( big_f @ sK2_SY5 @ SV2 )
        = $true )
      | ( ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SV2 @ SV1 ) )
        = $false )
      | ( ( big_g @ SV2 @ ( sK3_SY11 @ SV2 @ SV1 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[51]) ).

thf(57,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SV2 @ SV1 ) )
        = $false )
      | ( ( big_g @ SV1 @ ( sK3_SY11 @ SV2 @ SV1 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[53]) ).

thf(58,plain,
    ! [SV2: $i,SV1: $i] :
      ( ( ( big_g @ SV1 @ ( sK3_SY11 @ SV2 @ SV1 ) )
        = $false )
      | ( ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SV2 @ SV1 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[54]) ).

thf(59,plain,
    ! [SV2: $i,SV1: $i] :
      ( ( ( big_f @ SV1 @ SV2 )
        = $false )
      | ( ( big_f @ sK1_X1 @ SV1 )
        = $false )
      | ( ( big_f @ sK2_SY5 @ SV1 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[55]) ).

thf(60,plain,
    ! [SV2: $i,SV1: $i] :
      ( ( ( big_f @ SV1 @ SV2 )
        = $false )
      | ( ( big_f @ sK2_SY5 @ SV2 )
        = $true )
      | ( ( big_g @ sK2_SY5 @ ( sK3_SY11 @ SV2 @ SV1 ) )
        = $false )
      | ( ( big_g @ SV2 @ ( sK3_SY11 @ SV2 @ SV1 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[56]) ).

thf(61,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[14,60,59,58,57,52,19]) ).

thf(62,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[61]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SYN354+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.34  % Computer : n022.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Tue Jul 12 07:15:55 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)...
% 0.21/0.43  
% 0.21/0.43  ********************************
% 0.21/0.43  *   All subproblems solved!    *
% 0.21/0.43  ********************************
% 0.21/0.43  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:61,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.21/0.44  
% 0.21/0.44  %**** Beginning of derivation protocol ****
% 0.21/0.44  % SZS output start CNFRefutation
% See solution above
% 0.21/0.44  
% 0.21/0.44  %**** End of derivation protocol ****
% 0.21/0.44  %**** no. of clauses in derivation: 62 ****
% 0.21/0.44  %**** clause counter: 61 ****
% 0.21/0.44  
% 0.21/0.44  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:61,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------