TSTP Solution File: SYO069^4.001 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SYO069^4.001 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n004.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 17:31:56 EDT 2022

% Result   : Theorem 77.11s 77.37s
% Output   : CNFRefutation 77.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   36
%            Number of leaves      :   60
% Syntax   : Number of formulae    :  313 (  99 unt;  38 typ;  19 def)
%            Number of atoms       : 3054 ( 665 equ;   0 cnn)
%            Maximal formula atoms :   54 (  11 avg)
%            Number of connectives : 6151 (1464   ~;1180   |;  65   &;3343   @)
%                                         (   0 <=>;  99  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  110 ( 110   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   41 (  38 usr;   5 con; 0-3 aty)
%            Number of variables   :  781 (  31   ^ 748   !;   2   ?; 781   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_a0,type,
    a0: $i > $o ).

thf(tp_a1,type,
    a1: $i > $o ).

thf(tp_b0,type,
    b0: $i > $o ).

thf(tp_b1,type,
    b1: $i > $o ).

thf(tp_f,type,
    f: $i > $o ).

thf(tp_iand,type,
    iand: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(tp_iatom,type,
    iatom: ( $i > $o ) > $i > $o ).

thf(tp_icountersatisfiable,type,
    icountersatisfiable: ( $i > $o ) > $o ).

thf(tp_iequiv,type,
    iequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(tp_ifalse,type,
    ifalse: $i > $o ).

thf(tp_iimplied,type,
    iimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(tp_iimplies,type,
    iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(tp_iinvalid,type,
    iinvalid: ( $i > $o ) > $o ).

thf(tp_inot,type,
    inot: ( $i > $o ) > $i > $o ).

thf(tp_ior,type,
    ior: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(tp_irel,type,
    irel: $i > $i > $o ).

thf(tp_isatisfiable,type,
    isatisfiable: ( $i > $o ) > $o ).

thf(tp_itrue,type,
    itrue: $i > $o ).

thf(tp_ivalid,type,
    ivalid: ( $i > $o ) > $o ).

thf(tp_ixor,type,
    ixor: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(tp_mand,type,
    mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(tp_mbox_s4,type,
    mbox_s4: ( $i > $o ) > $i > $o ).

thf(tp_mimplies,type,
    mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(tp_mnot,type,
    mnot: ( $i > $o ) > $i > $o ).

thf(tp_mor,type,
    mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(tp_sK10_SY823,type,
    sK10_SY823: $i > $i ).

thf(tp_sK11_SY647,type,
    sK11_SY647: $i > $i ).

thf(tp_sK12_SY643,type,
    sK12_SY643: $i > $i ).

thf(tp_sK13_SY825,type,
    sK13_SY825: $i > $i ).

thf(tp_sK1_SY740,type,
    sK1_SY740: $i ).

thf(tp_sK2_SY805,type,
    sK2_SY805: $i ).

thf(tp_sK3_SY371,type,
    sK3_SY371: $i > $i ).

thf(tp_sK4_SY377,type,
    sK4_SY377: $i > $i ).

thf(tp_sK5_SY819,type,
    sK5_SY819: $i > $i ).

thf(tp_sK6_SY373,type,
    sK6_SY373: $i > $i ).

thf(tp_sK7_SY821,type,
    sK7_SY821: $i > $i ).

thf(tp_sK8_SY817,type,
    sK8_SY817: $i ).

thf(tp_sK9_SY639,type,
    sK9_SY639: $i > $i ).

thf(iand,definition,
    ( iand
    = ( ^ [P: $i > $o,Q: $i > $o] : ( mand @ P @ Q ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',iand) ).

thf(iatom,definition,
    ( iatom
    = ( ^ [P: $i > $o] : P ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',iatom) ).

thf(icountersatisfiable,definition,
    ( icountersatisfiable
    = ( ^ [Phi: $i > $o] :
        ? [W: $i] :
          ~ ( Phi @ W ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',icountersatisfiable) ).

thf(iequiv,definition,
    ( iequiv
    = ( ^ [P: $i > $o,Q: $i > $o] : ( iand @ ( iimplies @ P @ Q ) @ ( iimplies @ Q @ P ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',iequiv) ).

thf(ifalse,definition,
    ( ifalse
    = ( inot @ itrue ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifalse) ).

thf(iimplied,definition,
    ( iimplied
    = ( ^ [P: $i > $o,Q: $i > $o] : ( iimplies @ Q @ P ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',iimplied) ).

thf(iimplies,definition,
    ( iimplies
    = ( ^ [P: $i > $o,Q: $i > $o] : ( mimplies @ ( mbox_s4 @ P ) @ ( mbox_s4 @ Q ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',iimplies) ).

thf(iinvalid,definition,
    ( iinvalid
    = ( ^ [Phi: $i > $o] :
        ! [W: $i] :
          ~ ( Phi @ W ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',iinvalid) ).

thf(inot,definition,
    ( inot
    = ( ^ [P: $i > $o] : ( mnot @ ( mbox_s4 @ P ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',inot) ).

thf(ior,definition,
    ( ior
    = ( ^ [P: $i > $o,Q: $i > $o] : ( mor @ ( mbox_s4 @ P ) @ ( mbox_s4 @ Q ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ior) ).

thf(isatisfiable,definition,
    ( isatisfiable
    = ( ^ [Phi: $i > $o] :
        ? [W: $i] : ( Phi @ W ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',isatisfiable) ).

thf(itrue,definition,
    ( itrue
    = ( ^ [W: $i] : $true ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',itrue) ).

thf(ivalid,definition,
    ( ivalid
    = ( ^ [Phi: $i > $o] :
        ! [W: $i] : ( Phi @ W ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ivalid) ).

thf(ixor,definition,
    ( ixor
    = ( ^ [P: $i > $o,Q: $i > $o] : ( inot @ ( iequiv @ P @ Q ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ixor) ).

thf(mand,definition,
    ( mand
    = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
          ( ( X @ U )
          & ( Y @ U ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand) ).

thf(mbox_s4,definition,
    ( mbox_s4
    = ( ^ [P: $i > $o,X: $i] :
        ! [Y: $i] :
          ( ( irel @ X @ Y )
         => ( P @ Y ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_s4) ).

thf(mimplies,definition,
    ( mimplies
    = ( ^ [U: $i > $o,V: $i > $o] : ( mor @ ( mnot @ U ) @ V ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies) ).

thf(mnot,definition,
    ( mnot
    = ( ^ [X: $i > $o,U: $i] :
          ~ ( X @ U ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot) ).

thf(mor,definition,
    ( mor
    = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
          ( ( X @ U )
          | ( Y @ U ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor) ).

thf(1,axiom,
    ! [X: $i,Y: $i,Z: $i] :
      ( ( ( irel @ X @ Y )
        & ( irel @ Y @ Z ) )
     => ( irel @ X @ Z ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',trans_axiom) ).

thf(2,axiom,
    ! [X: $i] : ( irel @ X @ X ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',refl_axiom) ).

thf(3,conjecture,
    ivalid @ ( iand @ ( iimplies @ ( iand @ ( iimplies @ ( iatom @ a0 ) @ ( iatom @ f ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b1 ) @ ( iatom @ b0 ) ) @ ( iatom @ a1 ) ) @ ( iimplies @ ( iimplies @ ( iatom @ b0 ) @ ( iatom @ a1 ) ) @ ( iatom @ a0 ) ) ) ) @ ( iatom @ f ) ) @ ( iimplies @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b0 ) @ ( iatom @ a1 ) ) @ ( iatom @ a0 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b1 ) @ ( iatom @ b0 ) ) @ ( iatom @ a1 ) ) @ ( iimplies @ ( iatom @ a0 ) @ ( iatom @ f ) ) ) ) @ ( iatom @ f ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).

thf(4,negated_conjecture,
    ( ( ivalid @ ( iand @ ( iimplies @ ( iand @ ( iimplies @ ( iatom @ a0 ) @ ( iatom @ f ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b1 ) @ ( iatom @ b0 ) ) @ ( iatom @ a1 ) ) @ ( iimplies @ ( iimplies @ ( iatom @ b0 ) @ ( iatom @ a1 ) ) @ ( iatom @ a0 ) ) ) ) @ ( iatom @ f ) ) @ ( iimplies @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b0 ) @ ( iatom @ a1 ) ) @ ( iatom @ a0 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b1 ) @ ( iatom @ b0 ) ) @ ( iatom @ a1 ) ) @ ( iimplies @ ( iatom @ a0 ) @ ( iatom @ f ) ) ) ) @ ( iatom @ f ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[3]) ).

thf(5,plain,
    ( ( ! [SY740: $i] :
          ( ( ~ ! [SY741: $i] :
                  ( ( irel @ SY740 @ SY741 )
                 => ( ( ~ ! [SY371: $i] :
                            ( ( irel @ SY741 @ SY371 )
                           => ( a0 @ SY371 ) )
                      | ! [SY372: $i] :
                          ( ( irel @ SY741 @ SY372 )
                         => ( f @ SY372 ) ) )
                    & ( ~ ! [SY373: $i] :
                            ( ( irel @ SY741 @ SY373 )
                           => ( ~ ! [SY258: $i] :
                                    ( ( irel @ SY373 @ SY258 )
                                   => ( b1 @ SY258 ) )
                              | ! [SY259: $i] :
                                  ( ( irel @ SY373 @ SY259 )
                                 => ( b0 @ SY259 ) ) ) )
                      | ! [SY376: $i] :
                          ( ( irel @ SY741 @ SY376 )
                         => ( a1 @ SY376 ) ) )
                    & ( ~ ! [SY377: $i] :
                            ( ( irel @ SY741 @ SY377 )
                           => ( ~ ! [SY320: $i] :
                                    ( ( irel @ SY377 @ SY320 )
                                   => ( b0 @ SY320 ) )
                              | ! [SY321: $i] :
                                  ( ( irel @ SY377 @ SY321 )
                                 => ( a1 @ SY321 ) ) ) )
                      | ! [SY380: $i] :
                          ( ( irel @ SY741 @ SY380 )
                         => ( a0 @ SY380 ) ) ) ) )
            | ! [SY752: $i] :
                ( ( irel @ SY740 @ SY752 )
               => ( f @ SY752 ) ) )
          & ( ~ ! [SY753: $i] :
                  ( ( irel @ SY740 @ SY753 )
                 => ( ( ~ ! [SY639: $i] :
                            ( ( irel @ SY753 @ SY639 )
                           => ( ~ ! [SY497: $i] :
                                    ( ( irel @ SY639 @ SY497 )
                                   => ( b0 @ SY497 ) )
                              | ! [SY498: $i] :
                                  ( ( irel @ SY639 @ SY498 )
                                 => ( a1 @ SY498 ) ) ) )
                      | ! [SY642: $i] :
                          ( ( irel @ SY753 @ SY642 )
                         => ( a0 @ SY642 ) ) )
                    & ( ~ ! [SY643: $i] :
                            ( ( irel @ SY753 @ SY643 )
                           => ( ~ ! [SY559: $i] :
                                    ( ( irel @ SY643 @ SY559 )
                                   => ( b1 @ SY559 ) )
                              | ! [SY560: $i] :
                                  ( ( irel @ SY643 @ SY560 )
                                 => ( b0 @ SY560 ) ) ) )
                      | ! [SY646: $i] :
                          ( ( irel @ SY753 @ SY646 )
                         => ( a1 @ SY646 ) ) )
                    & ( ~ ! [SY647: $i] :
                            ( ( irel @ SY753 @ SY647 )
                           => ( a0 @ SY647 ) )
                      | ! [SY648: $i] :
                          ( ( irel @ SY753 @ SY648 )
                         => ( f @ SY648 ) ) ) ) )
            | ! [SY764: $i] :
                ( ( irel @ SY740 @ SY764 )
               => ( f @ SY764 ) ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[4,iand,iatom,icountersatisfiable,iequiv,ifalse,iimplied,iimplies,iinvalid,inot,ior,isatisfiable,itrue,ivalid,ixor,mand,mbox_s4,mimplies,mnot,mor]) ).

thf(6,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ( ( irel @ X @ Y )
            & ( irel @ Y @ Z ) )
         => ( irel @ X @ Z ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1,iand,iatom,icountersatisfiable,iequiv,ifalse,iimplied,iimplies,iinvalid,inot,ior,isatisfiable,itrue,ivalid,ixor,mand,mbox_s4,mimplies,mnot,mor]) ).

thf(7,plain,
    ( ( ! [X: $i] : ( irel @ X @ X ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2,iand,iatom,icountersatisfiable,iequiv,ifalse,iimplied,iimplies,iinvalid,inot,ior,isatisfiable,itrue,ivalid,ixor,mand,mbox_s4,mimplies,mnot,mor]) ).

thf(8,plain,
    ( ( ( ~ ! [SY794: $i] :
              ( ( irel @ sK1_SY740 @ SY794 )
             => ( ( ~ ! [SY371: $i] :
                        ( ( irel @ SY794 @ SY371 )
                       => ( a0 @ SY371 ) )
                  | ! [SY372: $i] :
                      ( ( irel @ SY794 @ SY372 )
                     => ( f @ SY372 ) ) )
                & ( ~ ! [SY373: $i] :
                        ( ( irel @ SY794 @ SY373 )
                       => ( ~ ! [SY258: $i] :
                                ( ( irel @ SY373 @ SY258 )
                               => ( b1 @ SY258 ) )
                          | ! [SY259: $i] :
                              ( ( irel @ SY373 @ SY259 )
                             => ( b0 @ SY259 ) ) ) )
                  | ! [SY376: $i] :
                      ( ( irel @ SY794 @ SY376 )
                     => ( a1 @ SY376 ) ) )
                & ( ~ ! [SY377: $i] :
                        ( ( irel @ SY794 @ SY377 )
                       => ( ~ ! [SY320: $i] :
                                ( ( irel @ SY377 @ SY320 )
                               => ( b0 @ SY320 ) )
                          | ! [SY321: $i] :
                              ( ( irel @ SY377 @ SY321 )
                             => ( a1 @ SY321 ) ) ) )
                  | ! [SY380: $i] :
                      ( ( irel @ SY794 @ SY380 )
                     => ( a0 @ SY380 ) ) ) ) )
        | ! [SY805: $i] :
            ( ( irel @ sK1_SY740 @ SY805 )
           => ( f @ SY805 ) ) )
      & ( ~ ! [SY806: $i] :
              ( ( irel @ sK1_SY740 @ SY806 )
             => ( ( ~ ! [SY639: $i] :
                        ( ( irel @ SY806 @ SY639 )
                       => ( ~ ! [SY497: $i] :
                                ( ( irel @ SY639 @ SY497 )
                               => ( b0 @ SY497 ) )
                          | ! [SY498: $i] :
                              ( ( irel @ SY639 @ SY498 )
                             => ( a1 @ SY498 ) ) ) )
                  | ! [SY642: $i] :
                      ( ( irel @ SY806 @ SY642 )
                     => ( a0 @ SY642 ) ) )
                & ( ~ ! [SY643: $i] :
                        ( ( irel @ SY806 @ SY643 )
                       => ( ~ ! [SY559: $i] :
                                ( ( irel @ SY643 @ SY559 )
                               => ( b1 @ SY559 ) )
                          | ! [SY560: $i] :
                              ( ( irel @ SY643 @ SY560 )
                             => ( b0 @ SY560 ) ) ) )
                  | ! [SY646: $i] :
                      ( ( irel @ SY806 @ SY646 )
                     => ( a1 @ SY646 ) ) )
                & ( ~ ! [SY647: $i] :
                        ( ( irel @ SY806 @ SY647 )
                       => ( a0 @ SY647 ) )
                  | ! [SY648: $i] :
                      ( ( irel @ SY806 @ SY648 )
                     => ( f @ SY648 ) ) ) ) )
        | ! [SY817: $i] :
            ( ( irel @ sK1_SY740 @ SY817 )
           => ( f @ SY817 ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[5]) ).

thf(9,plain,
    ( ( ~ ! [SY794: $i] :
            ( ( irel @ sK1_SY740 @ SY794 )
           => ( ( ~ ! [SY371: $i] :
                      ( ( irel @ SY794 @ SY371 )
                     => ( a0 @ SY371 ) )
                | ! [SY372: $i] :
                    ( ( irel @ SY794 @ SY372 )
                   => ( f @ SY372 ) ) )
              & ( ~ ! [SY373: $i] :
                      ( ( irel @ SY794 @ SY373 )
                     => ( ~ ! [SY258: $i] :
                              ( ( irel @ SY373 @ SY258 )
                             => ( b1 @ SY258 ) )
                        | ! [SY259: $i] :
                            ( ( irel @ SY373 @ SY259 )
                           => ( b0 @ SY259 ) ) ) )
                | ! [SY376: $i] :
                    ( ( irel @ SY794 @ SY376 )
                   => ( a1 @ SY376 ) ) )
              & ( ~ ! [SY377: $i] :
                      ( ( irel @ SY794 @ SY377 )
                     => ( ~ ! [SY320: $i] :
                              ( ( irel @ SY377 @ SY320 )
                             => ( b0 @ SY320 ) )
                        | ! [SY321: $i] :
                            ( ( irel @ SY377 @ SY321 )
                           => ( a1 @ SY321 ) ) ) )
                | ! [SY380: $i] :
                    ( ( irel @ SY794 @ SY380 )
                   => ( a0 @ SY380 ) ) ) ) )
      | ! [SY805: $i] :
          ( ( irel @ sK1_SY740 @ SY805 )
         => ( f @ SY805 ) ) )
    = $false ),
    inference(split_conjecture,[split_conjecture(split,[])],[8]) ).

thf(10,plain,
    ( ( ~ ! [SY806: $i] :
            ( ( irel @ sK1_SY740 @ SY806 )
           => ( ( ~ ! [SY639: $i] :
                      ( ( irel @ SY806 @ SY639 )
                     => ( ~ ! [SY497: $i] :
                              ( ( irel @ SY639 @ SY497 )
                             => ( b0 @ SY497 ) )
                        | ! [SY498: $i] :
                            ( ( irel @ SY639 @ SY498 )
                           => ( a1 @ SY498 ) ) ) )
                | ! [SY642: $i] :
                    ( ( irel @ SY806 @ SY642 )
                   => ( a0 @ SY642 ) ) )
              & ( ~ ! [SY643: $i] :
                      ( ( irel @ SY806 @ SY643 )
                     => ( ~ ! [SY559: $i] :
                              ( ( irel @ SY643 @ SY559 )
                             => ( b1 @ SY559 ) )
                        | ! [SY560: $i] :
                            ( ( irel @ SY643 @ SY560 )
                           => ( b0 @ SY560 ) ) ) )
                | ! [SY646: $i] :
                    ( ( irel @ SY806 @ SY646 )
                   => ( a1 @ SY646 ) ) )
              & ( ~ ! [SY647: $i] :
                      ( ( irel @ SY806 @ SY647 )
                     => ( a0 @ SY647 ) )
                | ! [SY648: $i] :
                    ( ( irel @ SY806 @ SY648 )
                   => ( f @ SY648 ) ) ) ) )
      | ! [SY817: $i] :
          ( ( irel @ sK1_SY740 @ SY817 )
         => ( f @ SY817 ) ) )
    = $false ),
    inference(split_conjecture,[split_conjecture(split,[])],[8]) ).

thf(11,plain,
    ( ( ~ ( ~ ! [SY794: $i] :
                ( ( irel @ sK1_SY740 @ SY794 )
               => ( ( ~ ! [SY371: $i] :
                          ( ( irel @ SY794 @ SY371 )
                         => ( a0 @ SY371 ) )
                    | ! [SY372: $i] :
                        ( ( irel @ SY794 @ SY372 )
                       => ( f @ SY372 ) ) )
                  & ( ~ ! [SY373: $i] :
                          ( ( irel @ SY794 @ SY373 )
                         => ( ~ ! [SY258: $i] :
                                  ( ( irel @ SY373 @ SY258 )
                                 => ( b1 @ SY258 ) )
                            | ! [SY259: $i] :
                                ( ( irel @ SY373 @ SY259 )
                               => ( b0 @ SY259 ) ) ) )
                    | ! [SY376: $i] :
                        ( ( irel @ SY794 @ SY376 )
                       => ( a1 @ SY376 ) ) )
                  & ( ~ ! [SY377: $i] :
                          ( ( irel @ SY794 @ SY377 )
                         => ( ~ ! [SY320: $i] :
                                  ( ( irel @ SY377 @ SY320 )
                                 => ( b0 @ SY320 ) )
                            | ! [SY321: $i] :
                                ( ( irel @ SY377 @ SY321 )
                               => ( a1 @ SY321 ) ) ) )
                    | ! [SY380: $i] :
                        ( ( irel @ SY794 @ SY380 )
                       => ( a0 @ SY380 ) ) ) ) )
          | ! [SY805: $i] :
              ( ( irel @ sK1_SY740 @ SY805 )
             => ( f @ SY805 ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[9]) ).

thf(12,plain,
    ( ( ~ ( ~ ! [SY806: $i] :
                ( ( irel @ sK1_SY740 @ SY806 )
               => ( ( ~ ! [SY639: $i] :
                          ( ( irel @ SY806 @ SY639 )
                         => ( ~ ! [SY497: $i] :
                                  ( ( irel @ SY639 @ SY497 )
                                 => ( b0 @ SY497 ) )
                            | ! [SY498: $i] :
                                ( ( irel @ SY639 @ SY498 )
                               => ( a1 @ SY498 ) ) ) )
                    | ! [SY642: $i] :
                        ( ( irel @ SY806 @ SY642 )
                       => ( a0 @ SY642 ) ) )
                  & ( ~ ! [SY643: $i] :
                          ( ( irel @ SY806 @ SY643 )
                         => ( ~ ! [SY559: $i] :
                                  ( ( irel @ SY643 @ SY559 )
                                 => ( b1 @ SY559 ) )
                            | ! [SY560: $i] :
                                ( ( irel @ SY643 @ SY560 )
                               => ( b0 @ SY560 ) ) ) )
                    | ! [SY646: $i] :
                        ( ( irel @ SY806 @ SY646 )
                       => ( a1 @ SY646 ) ) )
                  & ( ~ ! [SY647: $i] :
                          ( ( irel @ SY806 @ SY647 )
                         => ( a0 @ SY647 ) )
                    | ! [SY648: $i] :
                        ( ( irel @ SY806 @ SY648 )
                       => ( f @ SY648 ) ) ) ) )
          | ! [SY817: $i] :
              ( ( irel @ sK1_SY740 @ SY817 )
             => ( f @ SY817 ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[10]) ).

thf(13,plain,
    ( ( ! [SY794: $i] :
          ( ~ ( irel @ sK1_SY740 @ SY794 )
          | ( ( irel @ SY794 @ ( sK6_SY373 @ SY794 ) )
            & ! [SY820: $i] :
                ( ~ ( irel @ ( sK6_SY373 @ SY794 ) @ SY820 )
                | ( b1 @ SY820 ) )
            & ( irel @ ( sK6_SY373 @ SY794 ) @ ( sK7_SY821 @ SY794 ) )
            & ~ ( b0 @ ( sK7_SY821 @ SY794 ) ) )
          | ! [SY376: $i] :
              ( ~ ( irel @ SY794 @ SY376 )
              | ( a1 @ SY376 ) ) )
      & ! [SY794: $i] :
          ( ~ ( irel @ sK1_SY740 @ SY794 )
          | ( ( irel @ SY794 @ ( sK4_SY377 @ SY794 ) )
            & ! [SY818: $i] :
                ( ~ ( irel @ ( sK4_SY377 @ SY794 ) @ SY818 )
                | ( b0 @ SY818 ) )
            & ( irel @ ( sK4_SY377 @ SY794 ) @ ( sK5_SY819 @ SY794 ) )
            & ~ ( a1 @ ( sK5_SY819 @ SY794 ) ) )
          | ! [SY380: $i] :
              ( ~ ( irel @ SY794 @ SY380 )
              | ( a0 @ SY380 ) ) )
      & ! [SY794: $i] :
          ( ~ ( irel @ sK1_SY740 @ SY794 )
          | ( ( irel @ SY794 @ ( sK3_SY371 @ SY794 ) )
            & ~ ( a0 @ ( sK3_SY371 @ SY794 ) ) )
          | ! [SY372: $i] :
              ( ~ ( irel @ SY794 @ SY372 )
              | ( f @ SY372 ) ) )
      & ( irel @ sK1_SY740 @ sK2_SY805 )
      & ~ ( f @ sK2_SY805 ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[11]) ).

thf(14,plain,
    ( ( ! [SY806: $i] :
          ( ~ ( irel @ sK1_SY740 @ SY806 )
          | ( ( irel @ SY806 @ ( sK12_SY643 @ SY806 ) )
            & ! [SY824: $i] :
                ( ~ ( irel @ ( sK12_SY643 @ SY806 ) @ SY824 )
                | ( b1 @ SY824 ) )
            & ( irel @ ( sK12_SY643 @ SY806 ) @ ( sK13_SY825 @ SY806 ) )
            & ~ ( b0 @ ( sK13_SY825 @ SY806 ) ) )
          | ! [SY646: $i] :
              ( ~ ( irel @ SY806 @ SY646 )
              | ( a1 @ SY646 ) ) )
      & ! [SY806: $i] :
          ( ~ ( irel @ sK1_SY740 @ SY806 )
          | ( ( irel @ SY806 @ ( sK11_SY647 @ SY806 ) )
            & ~ ( a0 @ ( sK11_SY647 @ SY806 ) ) )
          | ! [SY648: $i] :
              ( ~ ( irel @ SY806 @ SY648 )
              | ( f @ SY648 ) ) )
      & ! [SY806: $i] :
          ( ~ ( irel @ sK1_SY740 @ SY806 )
          | ( ( irel @ SY806 @ ( sK9_SY639 @ SY806 ) )
            & ! [SY822: $i] :
                ( ~ ( irel @ ( sK9_SY639 @ SY806 ) @ SY822 )
                | ( b0 @ SY822 ) )
            & ( irel @ ( sK9_SY639 @ SY806 ) @ ( sK10_SY823 @ SY806 ) )
            & ~ ( a1 @ ( sK10_SY823 @ SY806 ) ) )
          | ! [SY642: $i] :
              ( ~ ( irel @ SY806 @ SY642 )
              | ( a0 @ SY642 ) ) )
      & ( irel @ sK1_SY740 @ sK8_SY817 )
      & ~ ( f @ sK8_SY817 ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[12]) ).

thf(15,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ~ ( irel @ X @ Y )
          | ~ ( irel @ Y @ Z )
          | ( irel @ X @ Z ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[6]) ).

thf(16,plain,
    ( ( ! [X: $i] : ( irel @ X @ X ) )
    = $true ),
    inference(copy,[status(thm)],[7]) ).

thf(17,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ~ ( irel @ X @ Y )
          | ~ ( irel @ Y @ Z )
          | ( irel @ X @ Z ) ) )
    = $true ),
    inference(copy,[status(thm)],[15]) ).

thf(18,plain,
    ( ( ! [SY794: $i] :
          ( ~ ( irel @ sK1_SY740 @ SY794 )
          | ( ( irel @ SY794 @ ( sK6_SY373 @ SY794 ) )
            & ! [SY820: $i] :
                ( ~ ( irel @ ( sK6_SY373 @ SY794 ) @ SY820 )
                | ( b1 @ SY820 ) )
            & ( irel @ ( sK6_SY373 @ SY794 ) @ ( sK7_SY821 @ SY794 ) )
            & ~ ( b0 @ ( sK7_SY821 @ SY794 ) ) )
          | ! [SY376: $i] :
              ( ~ ( irel @ SY794 @ SY376 )
              | ( a1 @ SY376 ) ) )
      & ! [SY794: $i] :
          ( ~ ( irel @ sK1_SY740 @ SY794 )
          | ( ( irel @ SY794 @ ( sK4_SY377 @ SY794 ) )
            & ! [SY818: $i] :
                ( ~ ( irel @ ( sK4_SY377 @ SY794 ) @ SY818 )
                | ( b0 @ SY818 ) )
            & ( irel @ ( sK4_SY377 @ SY794 ) @ ( sK5_SY819 @ SY794 ) )
            & ~ ( a1 @ ( sK5_SY819 @ SY794 ) ) )
          | ! [SY380: $i] :
              ( ~ ( irel @ SY794 @ SY380 )
              | ( a0 @ SY380 ) ) )
      & ! [SY794: $i] :
          ( ~ ( irel @ sK1_SY740 @ SY794 )
          | ( ( irel @ SY794 @ ( sK3_SY371 @ SY794 ) )
            & ~ ( a0 @ ( sK3_SY371 @ SY794 ) ) )
          | ! [SY372: $i] :
              ( ~ ( irel @ SY794 @ SY372 )
              | ( f @ SY372 ) ) )
      & ( irel @ sK1_SY740 @ sK2_SY805 )
      & ~ ( f @ sK2_SY805 ) )
    = $true ),
    inference(copy,[status(thm)],[13]) ).

thf(19,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                            ( ~ ( irel @ sK1_SY740 @ SX0 )
                            | ~ ( ~ ( irel @ SX0 @ ( sK6_SY373 @ SX0 ) )
                                | ~ ~ ( ~ ! [SX1: $i] :
                                            ( ~ ( irel @ ( sK6_SY373 @ SX0 ) @ SX1 )
                                            | ( b1 @ SX1 ) )
                                      | ~ ~ ( ~ ( irel @ ( sK6_SY373 @ SX0 ) @ ( sK7_SY821 @ SX0 ) )
                                            | ~ ~ ( b0 @ ( sK7_SY821 @ SX0 ) ) ) ) )
                            | ! [SX1: $i] :
                                ( ~ ( irel @ SX0 @ SX1 )
                                | ( a1 @ SX1 ) ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( irel @ sK1_SY740 @ SX0 )
                            | ~ ( ~ ( irel @ SX0 @ ( sK4_SY377 @ SX0 ) )
                                | ~ ~ ( ~ ! [SX1: $i] :
                                            ( ~ ( irel @ ( sK4_SY377 @ SX0 ) @ SX1 )
                                            | ( b0 @ SX1 ) )
                                      | ~ ~ ( ~ ( irel @ ( sK4_SY377 @ SX0 ) @ ( sK5_SY819 @ SX0 ) )
                                            | ~ ~ ( a1 @ ( sK5_SY819 @ SX0 ) ) ) ) )
                            | ! [SX1: $i] :
                                ( ~ ( irel @ SX0 @ SX1 )
                                | ( a0 @ SX1 ) ) ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( irel @ sK1_SY740 @ SX0 )
                      | ~ ( ~ ( irel @ SX0 @ ( sK3_SY371 @ SX0 ) )
                          | ~ ~ ( a0 @ ( sK3_SY371 @ SX0 ) ) )
                      | ! [SX1: $i] :
                          ( ~ ( irel @ SX0 @ SX1 )
                          | ( f @ SX1 ) ) ) )
          | ~ ~ ( ~ ( irel @ sK1_SY740 @ sK2_SY805 )
                | ~ ~ ( f @ sK2_SY805 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[18,iand,iatom,icountersatisfiable,iequiv,ifalse,iimplied,iimplies,iinvalid,inot,ior,isatisfiable,itrue,ivalid,ixor,mand,mbox_s4,mimplies,mnot,mor]) ).

thf(20,plain,
    ! [SV1: $i] :
      ( ( irel @ SV1 @ SV1 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[16]) ).

thf(21,plain,
    ! [SV2: $i] :
      ( ( ! [SY826: $i,SY827: $i] :
            ( ~ ( irel @ SV2 @ SY826 )
            | ~ ( irel @ SY826 @ SY827 )
            | ( irel @ SV2 @ SY827 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[17]) ).

thf(22,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( irel @ sK1_SY740 @ SX0 )
                        | ~ ( ~ ( irel @ SX0 @ ( sK6_SY373 @ SX0 ) )
                            | ~ ~ ( ~ ! [SX1: $i] :
                                        ( ~ ( irel @ ( sK6_SY373 @ SX0 ) @ SX1 )
                                        | ( b1 @ SX1 ) )
                                  | ~ ~ ( ~ ( irel @ ( sK6_SY373 @ SX0 ) @ ( sK7_SY821 @ SX0 ) )
                                        | ~ ~ ( b0 @ ( sK7_SY821 @ SX0 ) ) ) ) )
                        | ! [SX1: $i] :
                            ( ~ ( irel @ SX0 @ SX1 )
                            | ( a1 @ SX1 ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( irel @ sK1_SY740 @ SX0 )
                        | ~ ( ~ ( irel @ SX0 @ ( sK4_SY377 @ SX0 ) )
                            | ~ ~ ( ~ ! [SX1: $i] :
                                        ( ~ ( irel @ ( sK4_SY377 @ SX0 ) @ SX1 )
                                        | ( b0 @ SX1 ) )
                                  | ~ ~ ( ~ ( irel @ ( sK4_SY377 @ SX0 ) @ ( sK5_SY819 @ SX0 ) )
                                        | ~ ~ ( a1 @ ( sK5_SY819 @ SX0 ) ) ) ) )
                        | ! [SX1: $i] :
                            ( ~ ( irel @ SX0 @ SX1 )
                            | ( a0 @ SX1 ) ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( irel @ sK1_SY740 @ SX0 )
                  | ~ ( ~ ( irel @ SX0 @ ( sK3_SY371 @ SX0 ) )
                      | ~ ~ ( a0 @ ( sK3_SY371 @ SX0 ) ) )
                  | ! [SX1: $i] :
                      ( ~ ( irel @ SX0 @ SX1 )
                      | ( f @ SX1 ) ) ) )
      | ~ ~ ( ~ ( irel @ sK1_SY740 @ sK2_SY805 )
            | ~ ~ ( f @ sK2_SY805 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[19]) ).

thf(23,plain,
    ! [SV3: $i,SV2: $i] :
      ( ( ! [SY828: $i] :
            ( ~ ( irel @ SV2 @ SV3 )
            | ~ ( irel @ SV3 @ SY828 )
            | ( irel @ SV2 @ SY828 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[21]) ).

thf(24,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( irel @ sK1_SY740 @ SX0 )
                        | ~ ( ~ ( irel @ SX0 @ ( sK6_SY373 @ SX0 ) )
                            | ~ ~ ( ~ ! [SX1: $i] :
                                        ( ~ ( irel @ ( sK6_SY373 @ SX0 ) @ SX1 )
                                        | ( b1 @ SX1 ) )
                                  | ~ ~ ( ~ ( irel @ ( sK6_SY373 @ SX0 ) @ ( sK7_SY821 @ SX0 ) )
                                        | ~ ~ ( b0 @ ( sK7_SY821 @ SX0 ) ) ) ) )
                        | ! [SX1: $i] :
                            ( ~ ( irel @ SX0 @ SX1 )
                            | ( a1 @ SX1 ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( irel @ sK1_SY740 @ SX0 )
                        | ~ ( ~ ( irel @ SX0 @ ( sK4_SY377 @ SX0 ) )
                            | ~ ~ ( ~ ! [SX1: $i] :
                                        ( ~ ( irel @ ( sK4_SY377 @ SX0 ) @ SX1 )
                                        | ( b0 @ SX1 ) )
                                  | ~ ~ ( ~ ( irel @ ( sK4_SY377 @ SX0 ) @ ( sK5_SY819 @ SX0 ) )
                                        | ~ ~ ( a1 @ ( sK5_SY819 @ SX0 ) ) ) ) )
                        | ! [SX1: $i] :
                            ( ~ ( irel @ SX0 @ SX1 )
                            | ( a0 @ SX1 ) ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( irel @ sK1_SY740 @ SX0 )
                  | ~ ( ~ ( irel @ SX0 @ ( sK3_SY371 @ SX0 ) )
                      | ~ ~ ( a0 @ ( sK3_SY371 @ SX0 ) ) )
                  | ! [SX1: $i] :
                      ( ~ ( irel @ SX0 @ SX1 )
                      | ( f @ SX1 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[22]) ).

thf(25,plain,
    ( ( ~ ~ ( ~ ( irel @ sK1_SY740 @ sK2_SY805 )
            | ~ ~ ( f @ sK2_SY805 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[22]) ).

thf(26,plain,
    ! [SV4: $i,SV3: $i,SV2: $i] :
      ( ( ~ ( irel @ SV2 @ SV3 )
        | ~ ( irel @ SV3 @ SV4 )
        | ( irel @ SV2 @ SV4 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[23]) ).

thf(27,plain,
    ( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( irel @ sK1_SY740 @ SX0 )
                      | ~ ( ~ ( irel @ SX0 @ ( sK6_SY373 @ SX0 ) )
                          | ~ ~ ( ~ ! [SX1: $i] :
                                      ( ~ ( irel @ ( sK6_SY373 @ SX0 ) @ SX1 )
                                      | ( b1 @ SX1 ) )
                                | ~ ~ ( ~ ( irel @ ( sK6_SY373 @ SX0 ) @ ( sK7_SY821 @ SX0 ) )
                                      | ~ ~ ( b0 @ ( sK7_SY821 @ SX0 ) ) ) ) )
                      | ! [SX1: $i] :
                          ( ~ ( irel @ SX0 @ SX1 )
                          | ( a1 @ SX1 ) ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( irel @ sK1_SY740 @ SX0 )
                      | ~ ( ~ ( irel @ SX0 @ ( sK4_SY377 @ SX0 ) )
                          | ~ ~ ( ~ ! [SX1: $i] :
                                      ( ~ ( irel @ ( sK4_SY377 @ SX0 ) @ SX1 )
                                      | ( b0 @ SX1 ) )
                                | ~ ~ ( ~ ( irel @ ( sK4_SY377 @ SX0 ) @ ( sK5_SY819 @ SX0 ) )
                                      | ~ ~ ( a1 @ ( sK5_SY819 @ SX0 ) ) ) ) )
                      | ! [SX1: $i] :
                          ( ~ ( irel @ SX0 @ SX1 )
                          | ( a0 @ SX1 ) ) ) )
          | ~ ! [SX0: $i] :
                ( ~ ( irel @ sK1_SY740 @ SX0 )
                | ~ ( ~ ( irel @ SX0 @ ( sK3_SY371 @ SX0 ) )
                    | ~ ~ ( a0 @ ( sK3_SY371 @ SX0 ) ) )
                | ! [SX1: $i] :
                    ( ~ ( irel @ SX0 @ SX1 )
                    | ( f @ SX1 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[24]) ).

thf(28,plain,
    ( ( ~ ( ~ ( irel @ sK1_SY740 @ sK2_SY805 )
          | ~ ~ ( f @ sK2_SY805 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[25]) ).

thf(29,plain,
    ! [SV4: $i,SV3: $i,SV2: $i] :
      ( ( ( ~ ( irel @ SV2 @ SV3 )
          | ~ ( irel @ SV3 @ SV4 ) )
        = $true )
      | ( ( irel @ SV2 @ SV4 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[26]) ).

thf(30,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( irel @ sK1_SY740 @ SX0 )
                  | ~ ( ~ ( irel @ SX0 @ ( sK6_SY373 @ SX0 ) )
                      | ~ ~ ( ~ ! [SX1: $i] :
                                  ( ~ ( irel @ ( sK6_SY373 @ SX0 ) @ SX1 )
                                  | ( b1 @ SX1 ) )
                            | ~ ~ ( ~ ( irel @ ( sK6_SY373 @ SX0 ) @ ( sK7_SY821 @ SX0 ) )
                                  | ~ ~ ( b0 @ ( sK7_SY821 @ SX0 ) ) ) ) )
                  | ! [SX1: $i] :
                      ( ~ ( irel @ SX0 @ SX1 )
                      | ( a1 @ SX1 ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( irel @ sK1_SY740 @ SX0 )
                  | ~ ( ~ ( irel @ SX0 @ ( sK4_SY377 @ SX0 ) )
                      | ~ ~ ( ~ ! [SX1: $i] :
                                  ( ~ ( irel @ ( sK4_SY377 @ SX0 ) @ SX1 )
                                  | ( b0 @ SX1 ) )
                            | ~ ~ ( ~ ( irel @ ( sK4_SY377 @ SX0 ) @ ( sK5_SY819 @ SX0 ) )
                                  | ~ ~ ( a1 @ ( sK5_SY819 @ SX0 ) ) ) ) )
                  | ! [SX1: $i] :
                      ( ~ ( irel @ SX0 @ SX1 )
                      | ( a0 @ SX1 ) ) ) )
      | ~ ! [SX0: $i] :
            ( ~ ( irel @ sK1_SY740 @ SX0 )
            | ~ ( ~ ( irel @ SX0 @ ( sK3_SY371 @ SX0 ) )
                | ~ ~ ( a0 @ ( sK3_SY371 @ SX0 ) ) )
            | ! [SX1: $i] :
                ( ~ ( irel @ SX0 @ SX1 )
                | ( f @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[27]) ).

thf(31,plain,
    ( ( ~ ( irel @ sK1_SY740 @ sK2_SY805 )
      | ~ ~ ( f @ sK2_SY805 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[28]) ).

thf(32,plain,
    ! [SV4: $i,SV3: $i,SV2: $i] :
      ( ( ( ~ ( irel @ SV2 @ SV3 ) )
        = $true )
      | ( ( ~ ( irel @ SV3 @ SV4 ) )
        = $true )
      | ( ( irel @ SV2 @ SV4 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[29]) ).

thf(33,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( irel @ sK1_SY740 @ SX0 )
                  | ~ ( ~ ( irel @ SX0 @ ( sK6_SY373 @ SX0 ) )
                      | ~ ~ ( ~ ! [SX1: $i] :
                                  ( ~ ( irel @ ( sK6_SY373 @ SX0 ) @ SX1 )
                                  | ( b1 @ SX1 ) )
                            | ~ ~ ( ~ ( irel @ ( sK6_SY373 @ SX0 ) @ ( sK7_SY821 @ SX0 ) )
                                  | ~ ~ ( b0 @ ( sK7_SY821 @ SX0 ) ) ) ) )
                  | ! [SX1: $i] :
                      ( ~ ( irel @ SX0 @ SX1 )
                      | ( a1 @ SX1 ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( irel @ sK1_SY740 @ SX0 )
                  | ~ ( ~ ( irel @ SX0 @ ( sK4_SY377 @ SX0 ) )
                      | ~ ~ ( ~ ! [SX1: $i] :
                                  ( ~ ( irel @ ( sK4_SY377 @ SX0 ) @ SX1 )
                                  | ( b0 @ SX1 ) )
                            | ~ ~ ( ~ ( irel @ ( sK4_SY377 @ SX0 ) @ ( sK5_SY819 @ SX0 ) )
                                  | ~ ~ ( a1 @ ( sK5_SY819 @ SX0 ) ) ) ) )
                  | ! [SX1: $i] :
                      ( ~ ( irel @ SX0 @ SX1 )
                      | ( a0 @ SX1 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[30]) ).

thf(34,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( irel @ sK1_SY740 @ SX0 )
            | ~ ( ~ ( irel @ SX0 @ ( sK3_SY371 @ SX0 ) )
                | ~ ~ ( a0 @ ( sK3_SY371 @ SX0 ) ) )
            | ! [SX1: $i] :
                ( ~ ( irel @ SX0 @ SX1 )
                | ( f @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[30]) ).

thf(35,plain,
    ( ( ~ ( irel @ sK1_SY740 @ sK2_SY805 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[31]) ).

thf(36,plain,
    ( ( ~ ~ ( f @ sK2_SY805 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[31]) ).

thf(37,plain,
    ! [SV4: $i,SV3: $i,SV2: $i] :
      ( ( ( irel @ SV2 @ SV3 )
        = $false )
      | ( ( ~ ( irel @ SV3 @ SV4 ) )
        = $true )
      | ( ( irel @ SV2 @ SV4 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[32]) ).

thf(38,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( irel @ sK1_SY740 @ SX0 )
                | ~ ( ~ ( irel @ SX0 @ ( sK6_SY373 @ SX0 ) )
                    | ~ ~ ( ~ ! [SX1: $i] :
                                ( ~ ( irel @ ( sK6_SY373 @ SX0 ) @ SX1 )
                                | ( b1 @ SX1 ) )
                          | ~ ~ ( ~ ( irel @ ( sK6_SY373 @ SX0 ) @ ( sK7_SY821 @ SX0 ) )
                                | ~ ~ ( b0 @ ( sK7_SY821 @ SX0 ) ) ) ) )
                | ! [SX1: $i] :
                    ( ~ ( irel @ SX0 @ SX1 )
                    | ( a1 @ SX1 ) ) )
          | ~ ! [SX0: $i] :
                ( ~ ( irel @ sK1_SY740 @ SX0 )
                | ~ ( ~ ( irel @ SX0 @ ( sK4_SY377 @ SX0 ) )
                    | ~ ~ ( ~ ! [SX1: $i] :
                                ( ~ ( irel @ ( sK4_SY377 @ SX0 ) @ SX1 )
                                | ( b0 @ SX1 ) )
                          | ~ ~ ( ~ ( irel @ ( sK4_SY377 @ SX0 ) @ ( sK5_SY819 @ SX0 ) )
                                | ~ ~ ( a1 @ ( sK5_SY819 @ SX0 ) ) ) ) )
                | ! [SX1: $i] :
                    ( ~ ( irel @ SX0 @ SX1 )
                    | ( a0 @ SX1 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[33]) ).

thf(39,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( irel @ sK1_SY740 @ SX0 )
          | ~ ( ~ ( irel @ SX0 @ ( sK3_SY371 @ SX0 ) )
              | ~ ~ ( a0 @ ( sK3_SY371 @ SX0 ) ) )
          | ! [SX1: $i] :
              ( ~ ( irel @ SX0 @ SX1 )
              | ( f @ SX1 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[34]) ).

thf(40,plain,
    ( ( irel @ sK1_SY740 @ sK2_SY805 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[35]) ).

thf(41,plain,
    ( ( ~ ( f @ sK2_SY805 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[36]) ).

thf(42,plain,
    ! [SV2: $i,SV4: $i,SV3: $i] :
      ( ( ( irel @ SV3 @ SV4 )
        = $false )
      | ( ( irel @ SV2 @ SV3 )
        = $false )
      | ( ( irel @ SV2 @ SV4 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[37]) ).

thf(43,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( irel @ sK1_SY740 @ SX0 )
            | ~ ( ~ ( irel @ SX0 @ ( sK6_SY373 @ SX0 ) )
                | ~ ~ ( ~ ! [SX1: $i] :
                            ( ~ ( irel @ ( sK6_SY373 @ SX0 ) @ SX1 )
                            | ( b1 @ SX1 ) )
                      | ~ ~ ( ~ ( irel @ ( sK6_SY373 @ SX0 ) @ ( sK7_SY821 @ SX0 ) )
                            | ~ ~ ( b0 @ ( sK7_SY821 @ SX0 ) ) ) ) )
            | ! [SX1: $i] :
                ( ~ ( irel @ SX0 @ SX1 )
                | ( a1 @ SX1 ) ) )
      | ~ ! [SX0: $i] :
            ( ~ ( irel @ sK1_SY740 @ SX0 )
            | ~ ( ~ ( irel @ SX0 @ ( sK4_SY377 @ SX0 ) )
                | ~ ~ ( ~ ! [SX1: $i] :
                            ( ~ ( irel @ ( sK4_SY377 @ SX0 ) @ SX1 )
                            | ( b0 @ SX1 ) )
                      | ~ ~ ( ~ ( irel @ ( sK4_SY377 @ SX0 ) @ ( sK5_SY819 @ SX0 ) )
                            | ~ ~ ( a1 @ ( sK5_SY819 @ SX0 ) ) ) ) )
            | ! [SX1: $i] :
                ( ~ ( irel @ SX0 @ SX1 )
                | ( a0 @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[38]) ).

thf(44,plain,
    ! [SV5: $i] :
      ( ( ~ ( irel @ sK1_SY740 @ SV5 )
        | ~ ( ~ ( irel @ SV5 @ ( sK3_SY371 @ SV5 ) )
            | ~ ~ ( a0 @ ( sK3_SY371 @ SV5 ) ) )
        | ! [SY829: $i] :
            ( ~ ( irel @ SV5 @ SY829 )
            | ( f @ SY829 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[39]) ).

thf(45,plain,
    ( ( f @ sK2_SY805 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[41]) ).

thf(46,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( irel @ sK1_SY740 @ SX0 )
            | ~ ( ~ ( irel @ SX0 @ ( sK6_SY373 @ SX0 ) )
                | ~ ~ ( ~ ! [SX1: $i] :
                            ( ~ ( irel @ ( sK6_SY373 @ SX0 ) @ SX1 )
                            | ( b1 @ SX1 ) )
                      | ~ ~ ( ~ ( irel @ ( sK6_SY373 @ SX0 ) @ ( sK7_SY821 @ SX0 ) )
                            | ~ ~ ( b0 @ ( sK7_SY821 @ SX0 ) ) ) ) )
            | ! [SX1: $i] :
                ( ~ ( irel @ SX0 @ SX1 )
                | ( a1 @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[43]) ).

thf(47,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( irel @ sK1_SY740 @ SX0 )
            | ~ ( ~ ( irel @ SX0 @ ( sK4_SY377 @ SX0 ) )
                | ~ ~ ( ~ ! [SX1: $i] :
                            ( ~ ( irel @ ( sK4_SY377 @ SX0 ) @ SX1 )
                            | ( b0 @ SX1 ) )
                      | ~ ~ ( ~ ( irel @ ( sK4_SY377 @ SX0 ) @ ( sK5_SY819 @ SX0 ) )
                            | ~ ~ ( a1 @ ( sK5_SY819 @ SX0 ) ) ) ) )
            | ! [SX1: $i] :
                ( ~ ( irel @ SX0 @ SX1 )
                | ( a0 @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[43]) ).

thf(48,plain,
    ! [SV5: $i] :
      ( ( ( ~ ( irel @ sK1_SY740 @ SV5 ) )
        = $true )
      | ( ( ~ ( ~ ( irel @ SV5 @ ( sK3_SY371 @ SV5 ) )
              | ~ ~ ( a0 @ ( sK3_SY371 @ SV5 ) ) )
          | ! [SY829: $i] :
              ( ~ ( irel @ SV5 @ SY829 )
              | ( f @ SY829 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[44]) ).

thf(49,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( irel @ sK1_SY740 @ SX0 )
          | ~ ( ~ ( irel @ SX0 @ ( sK6_SY373 @ SX0 ) )
              | ~ ~ ( ~ ! [SX1: $i] :
                          ( ~ ( irel @ ( sK6_SY373 @ SX0 ) @ SX1 )
                          | ( b1 @ SX1 ) )
                    | ~ ~ ( ~ ( irel @ ( sK6_SY373 @ SX0 ) @ ( sK7_SY821 @ SX0 ) )
                          | ~ ~ ( b0 @ ( sK7_SY821 @ SX0 ) ) ) ) )
          | ! [SX1: $i] :
              ( ~ ( irel @ SX0 @ SX1 )
              | ( a1 @ SX1 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[46]) ).

thf(50,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( irel @ sK1_SY740 @ SX0 )
          | ~ ( ~ ( irel @ SX0 @ ( sK4_SY377 @ SX0 ) )
              | ~ ~ ( ~ ! [SX1: $i] :
                          ( ~ ( irel @ ( sK4_SY377 @ SX0 ) @ SX1 )
                          | ( b0 @ SX1 ) )
                    | ~ ~ ( ~ ( irel @ ( sK4_SY377 @ SX0 ) @ ( sK5_SY819 @ SX0 ) )
                          | ~ ~ ( a1 @ ( sK5_SY819 @ SX0 ) ) ) ) )
          | ! [SX1: $i] :
              ( ~ ( irel @ SX0 @ SX1 )
              | ( a0 @ SX1 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[47]) ).

thf(51,plain,
    ! [SV5: $i] :
      ( ( ( irel @ sK1_SY740 @ SV5 )
        = $false )
      | ( ( ~ ( ~ ( irel @ SV5 @ ( sK3_SY371 @ SV5 ) )
              | ~ ~ ( a0 @ ( sK3_SY371 @ SV5 ) ) )
          | ! [SY829: $i] :
              ( ~ ( irel @ SV5 @ SY829 )
              | ( f @ SY829 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[48]) ).

thf(52,plain,
    ! [SV6: $i] :
      ( ( ~ ( irel @ sK1_SY740 @ SV6 )
        | ~ ( ~ ( irel @ SV6 @ ( sK6_SY373 @ SV6 ) )
            | ~ ~ ( ~ ! [SY830: $i] :
                        ( ~ ( irel @ ( sK6_SY373 @ SV6 ) @ SY830 )
                        | ( b1 @ SY830 ) )
                  | ~ ~ ( ~ ( irel @ ( sK6_SY373 @ SV6 ) @ ( sK7_SY821 @ SV6 ) )
                        | ~ ~ ( b0 @ ( sK7_SY821 @ SV6 ) ) ) ) )
        | ! [SY831: $i] :
            ( ~ ( irel @ SV6 @ SY831 )
            | ( a1 @ SY831 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[49]) ).

thf(53,plain,
    ! [SV7: $i] :
      ( ( ~ ( irel @ sK1_SY740 @ SV7 )
        | ~ ( ~ ( irel @ SV7 @ ( sK4_SY377 @ SV7 ) )
            | ~ ~ ( ~ ! [SY832: $i] :
                        ( ~ ( irel @ ( sK4_SY377 @ SV7 ) @ SY832 )
                        | ( b0 @ SY832 ) )
                  | ~ ~ ( ~ ( irel @ ( sK4_SY377 @ SV7 ) @ ( sK5_SY819 @ SV7 ) )
                        | ~ ~ ( a1 @ ( sK5_SY819 @ SV7 ) ) ) ) )
        | ! [SY833: $i] :
            ( ~ ( irel @ SV7 @ SY833 )
            | ( a0 @ SY833 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[50]) ).

thf(54,plain,
    ! [SV5: $i] :
      ( ( ( ~ ( ~ ( irel @ SV5 @ ( sK3_SY371 @ SV5 ) )
              | ~ ~ ( a0 @ ( sK3_SY371 @ SV5 ) ) ) )
        = $true )
      | ( ( ! [SY829: $i] :
              ( ~ ( irel @ SV5 @ SY829 )
              | ( f @ SY829 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV5 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[51]) ).

thf(55,plain,
    ! [SV6: $i] :
      ( ( ( ~ ( irel @ sK1_SY740 @ SV6 ) )
        = $true )
      | ( ( ~ ( ~ ( irel @ SV6 @ ( sK6_SY373 @ SV6 ) )
              | ~ ~ ( ~ ! [SY830: $i] :
                          ( ~ ( irel @ ( sK6_SY373 @ SV6 ) @ SY830 )
                          | ( b1 @ SY830 ) )
                    | ~ ~ ( ~ ( irel @ ( sK6_SY373 @ SV6 ) @ ( sK7_SY821 @ SV6 ) )
                          | ~ ~ ( b0 @ ( sK7_SY821 @ SV6 ) ) ) ) )
          | ! [SY831: $i] :
              ( ~ ( irel @ SV6 @ SY831 )
              | ( a1 @ SY831 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[52]) ).

thf(56,plain,
    ! [SV7: $i] :
      ( ( ( ~ ( irel @ sK1_SY740 @ SV7 ) )
        = $true )
      | ( ( ~ ( ~ ( irel @ SV7 @ ( sK4_SY377 @ SV7 ) )
              | ~ ~ ( ~ ! [SY832: $i] :
                          ( ~ ( irel @ ( sK4_SY377 @ SV7 ) @ SY832 )
                          | ( b0 @ SY832 ) )
                    | ~ ~ ( ~ ( irel @ ( sK4_SY377 @ SV7 ) @ ( sK5_SY819 @ SV7 ) )
                          | ~ ~ ( a1 @ ( sK5_SY819 @ SV7 ) ) ) ) )
          | ! [SY833: $i] :
              ( ~ ( irel @ SV7 @ SY833 )
              | ( a0 @ SY833 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[53]) ).

thf(57,plain,
    ! [SV5: $i] :
      ( ( ( ~ ( irel @ SV5 @ ( sK3_SY371 @ SV5 ) )
          | ~ ~ ( a0 @ ( sK3_SY371 @ SV5 ) ) )
        = $false )
      | ( ( ! [SY829: $i] :
              ( ~ ( irel @ SV5 @ SY829 )
              | ( f @ SY829 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV5 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[54]) ).

thf(58,plain,
    ! [SV6: $i] :
      ( ( ( irel @ sK1_SY740 @ SV6 )
        = $false )
      | ( ( ~ ( ~ ( irel @ SV6 @ ( sK6_SY373 @ SV6 ) )
              | ~ ~ ( ~ ! [SY830: $i] :
                          ( ~ ( irel @ ( sK6_SY373 @ SV6 ) @ SY830 )
                          | ( b1 @ SY830 ) )
                    | ~ ~ ( ~ ( irel @ ( sK6_SY373 @ SV6 ) @ ( sK7_SY821 @ SV6 ) )
                          | ~ ~ ( b0 @ ( sK7_SY821 @ SV6 ) ) ) ) )
          | ! [SY831: $i] :
              ( ~ ( irel @ SV6 @ SY831 )
              | ( a1 @ SY831 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[55]) ).

thf(59,plain,
    ! [SV7: $i] :
      ( ( ( irel @ sK1_SY740 @ SV7 )
        = $false )
      | ( ( ~ ( ~ ( irel @ SV7 @ ( sK4_SY377 @ SV7 ) )
              | ~ ~ ( ~ ! [SY832: $i] :
                          ( ~ ( irel @ ( sK4_SY377 @ SV7 ) @ SY832 )
                          | ( b0 @ SY832 ) )
                    | ~ ~ ( ~ ( irel @ ( sK4_SY377 @ SV7 ) @ ( sK5_SY819 @ SV7 ) )
                          | ~ ~ ( a1 @ ( sK5_SY819 @ SV7 ) ) ) ) )
          | ! [SY833: $i] :
              ( ~ ( irel @ SV7 @ SY833 )
              | ( a0 @ SY833 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[56]) ).

thf(60,plain,
    ! [SV5: $i] :
      ( ( ( ~ ( irel @ SV5 @ ( sK3_SY371 @ SV5 ) ) )
        = $false )
      | ( ( ! [SY829: $i] :
              ( ~ ( irel @ SV5 @ SY829 )
              | ( f @ SY829 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV5 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[57]) ).

thf(61,plain,
    ! [SV5: $i] :
      ( ( ( ~ ~ ( a0 @ ( sK3_SY371 @ SV5 ) ) )
        = $false )
      | ( ( ! [SY829: $i] :
              ( ~ ( irel @ SV5 @ SY829 )
              | ( f @ SY829 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV5 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[57]) ).

thf(62,plain,
    ! [SV6: $i] :
      ( ( ( ~ ( ~ ( irel @ SV6 @ ( sK6_SY373 @ SV6 ) )
              | ~ ~ ( ~ ! [SY830: $i] :
                          ( ~ ( irel @ ( sK6_SY373 @ SV6 ) @ SY830 )
                          | ( b1 @ SY830 ) )
                    | ~ ~ ( ~ ( irel @ ( sK6_SY373 @ SV6 ) @ ( sK7_SY821 @ SV6 ) )
                          | ~ ~ ( b0 @ ( sK7_SY821 @ SV6 ) ) ) ) ) )
        = $true )
      | ( ( ! [SY831: $i] :
              ( ~ ( irel @ SV6 @ SY831 )
              | ( a1 @ SY831 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV6 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[58]) ).

thf(63,plain,
    ! [SV7: $i] :
      ( ( ( ~ ( ~ ( irel @ SV7 @ ( sK4_SY377 @ SV7 ) )
              | ~ ~ ( ~ ! [SY832: $i] :
                          ( ~ ( irel @ ( sK4_SY377 @ SV7 ) @ SY832 )
                          | ( b0 @ SY832 ) )
                    | ~ ~ ( ~ ( irel @ ( sK4_SY377 @ SV7 ) @ ( sK5_SY819 @ SV7 ) )
                          | ~ ~ ( a1 @ ( sK5_SY819 @ SV7 ) ) ) ) ) )
        = $true )
      | ( ( ! [SY833: $i] :
              ( ~ ( irel @ SV7 @ SY833 )
              | ( a0 @ SY833 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV7 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[59]) ).

thf(64,plain,
    ! [SV5: $i] :
      ( ( ( irel @ SV5 @ ( sK3_SY371 @ SV5 ) )
        = $true )
      | ( ( ! [SY829: $i] :
              ( ~ ( irel @ SV5 @ SY829 )
              | ( f @ SY829 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV5 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[60]) ).

thf(65,plain,
    ! [SV5: $i] :
      ( ( ( ~ ( a0 @ ( sK3_SY371 @ SV5 ) ) )
        = $true )
      | ( ( ! [SY829: $i] :
              ( ~ ( irel @ SV5 @ SY829 )
              | ( f @ SY829 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV5 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[61]) ).

thf(66,plain,
    ! [SV6: $i] :
      ( ( ( ~ ( irel @ SV6 @ ( sK6_SY373 @ SV6 ) )
          | ~ ~ ( ~ ! [SY830: $i] :
                      ( ~ ( irel @ ( sK6_SY373 @ SV6 ) @ SY830 )
                      | ( b1 @ SY830 ) )
                | ~ ~ ( ~ ( irel @ ( sK6_SY373 @ SV6 ) @ ( sK7_SY821 @ SV6 ) )
                      | ~ ~ ( b0 @ ( sK7_SY821 @ SV6 ) ) ) ) )
        = $false )
      | ( ( ! [SY831: $i] :
              ( ~ ( irel @ SV6 @ SY831 )
              | ( a1 @ SY831 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV6 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[62]) ).

thf(67,plain,
    ! [SV7: $i] :
      ( ( ( ~ ( irel @ SV7 @ ( sK4_SY377 @ SV7 ) )
          | ~ ~ ( ~ ! [SY832: $i] :
                      ( ~ ( irel @ ( sK4_SY377 @ SV7 ) @ SY832 )
                      | ( b0 @ SY832 ) )
                | ~ ~ ( ~ ( irel @ ( sK4_SY377 @ SV7 ) @ ( sK5_SY819 @ SV7 ) )
                      | ~ ~ ( a1 @ ( sK5_SY819 @ SV7 ) ) ) ) )
        = $false )
      | ( ( ! [SY833: $i] :
              ( ~ ( irel @ SV7 @ SY833 )
              | ( a0 @ SY833 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV7 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[63]) ).

thf(68,plain,
    ! [SV8: $i,SV5: $i] :
      ( ( ( ~ ( irel @ SV5 @ SV8 )
          | ( f @ SV8 ) )
        = $true )
      | ( ( irel @ SV5 @ ( sK3_SY371 @ SV5 ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV5 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[64]) ).

thf(69,plain,
    ! [SV5: $i] :
      ( ( ( a0 @ ( sK3_SY371 @ SV5 ) )
        = $false )
      | ( ( ! [SY829: $i] :
              ( ~ ( irel @ SV5 @ SY829 )
              | ( f @ SY829 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV5 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[65]) ).

thf(70,plain,
    ! [SV6: $i] :
      ( ( ( ~ ( irel @ SV6 @ ( sK6_SY373 @ SV6 ) ) )
        = $false )
      | ( ( ! [SY831: $i] :
              ( ~ ( irel @ SV6 @ SY831 )
              | ( a1 @ SY831 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV6 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[66]) ).

thf(71,plain,
    ! [SV6: $i] :
      ( ( ( ~ ~ ( ~ ! [SY830: $i] :
                      ( ~ ( irel @ ( sK6_SY373 @ SV6 ) @ SY830 )
                      | ( b1 @ SY830 ) )
                | ~ ~ ( ~ ( irel @ ( sK6_SY373 @ SV6 ) @ ( sK7_SY821 @ SV6 ) )
                      | ~ ~ ( b0 @ ( sK7_SY821 @ SV6 ) ) ) ) )
        = $false )
      | ( ( ! [SY831: $i] :
              ( ~ ( irel @ SV6 @ SY831 )
              | ( a1 @ SY831 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV6 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[66]) ).

thf(72,plain,
    ! [SV7: $i] :
      ( ( ( ~ ( irel @ SV7 @ ( sK4_SY377 @ SV7 ) ) )
        = $false )
      | ( ( ! [SY833: $i] :
              ( ~ ( irel @ SV7 @ SY833 )
              | ( a0 @ SY833 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV7 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[67]) ).

thf(73,plain,
    ! [SV7: $i] :
      ( ( ( ~ ~ ( ~ ! [SY832: $i] :
                      ( ~ ( irel @ ( sK4_SY377 @ SV7 ) @ SY832 )
                      | ( b0 @ SY832 ) )
                | ~ ~ ( ~ ( irel @ ( sK4_SY377 @ SV7 ) @ ( sK5_SY819 @ SV7 ) )
                      | ~ ~ ( a1 @ ( sK5_SY819 @ SV7 ) ) ) ) )
        = $false )
      | ( ( ! [SY833: $i] :
              ( ~ ( irel @ SV7 @ SY833 )
              | ( a0 @ SY833 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV7 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[67]) ).

thf(74,plain,
    ! [SV8: $i,SV5: $i] :
      ( ( ( ~ ( irel @ SV5 @ SV8 ) )
        = $true )
      | ( ( f @ SV8 )
        = $true )
      | ( ( irel @ SV5 @ ( sK3_SY371 @ SV5 ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV5 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[68]) ).

thf(75,plain,
    ! [SV9: $i,SV5: $i] :
      ( ( ( ~ ( irel @ SV5 @ SV9 )
          | ( f @ SV9 ) )
        = $true )
      | ( ( a0 @ ( sK3_SY371 @ SV5 ) )
        = $false )
      | ( ( irel @ sK1_SY740 @ SV5 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[69]) ).

thf(76,plain,
    ! [SV6: $i] :
      ( ( ( irel @ SV6 @ ( sK6_SY373 @ SV6 ) )
        = $true )
      | ( ( ! [SY831: $i] :
              ( ~ ( irel @ SV6 @ SY831 )
              | ( a1 @ SY831 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV6 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[70]) ).

thf(77,plain,
    ! [SV6: $i] :
      ( ( ( ~ ( ~ ! [SY830: $i] :
                    ( ~ ( irel @ ( sK6_SY373 @ SV6 ) @ SY830 )
                    | ( b1 @ SY830 ) )
              | ~ ~ ( ~ ( irel @ ( sK6_SY373 @ SV6 ) @ ( sK7_SY821 @ SV6 ) )
                    | ~ ~ ( b0 @ ( sK7_SY821 @ SV6 ) ) ) ) )
        = $true )
      | ( ( ! [SY831: $i] :
              ( ~ ( irel @ SV6 @ SY831 )
              | ( a1 @ SY831 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV6 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[71]) ).

thf(78,plain,
    ! [SV7: $i] :
      ( ( ( irel @ SV7 @ ( sK4_SY377 @ SV7 ) )
        = $true )
      | ( ( ! [SY833: $i] :
              ( ~ ( irel @ SV7 @ SY833 )
              | ( a0 @ SY833 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV7 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[72]) ).

thf(79,plain,
    ! [SV7: $i] :
      ( ( ( ~ ( ~ ! [SY832: $i] :
                    ( ~ ( irel @ ( sK4_SY377 @ SV7 ) @ SY832 )
                    | ( b0 @ SY832 ) )
              | ~ ~ ( ~ ( irel @ ( sK4_SY377 @ SV7 ) @ ( sK5_SY819 @ SV7 ) )
                    | ~ ~ ( a1 @ ( sK5_SY819 @ SV7 ) ) ) ) )
        = $true )
      | ( ( ! [SY833: $i] :
              ( ~ ( irel @ SV7 @ SY833 )
              | ( a0 @ SY833 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV7 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[73]) ).

thf(80,plain,
    ! [SV8: $i,SV5: $i] :
      ( ( ( irel @ SV5 @ SV8 )
        = $false )
      | ( ( f @ SV8 )
        = $true )
      | ( ( irel @ SV5 @ ( sK3_SY371 @ SV5 ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV5 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[74]) ).

thf(81,plain,
    ! [SV9: $i,SV5: $i] :
      ( ( ( ~ ( irel @ SV5 @ SV9 ) )
        = $true )
      | ( ( f @ SV9 )
        = $true )
      | ( ( a0 @ ( sK3_SY371 @ SV5 ) )
        = $false )
      | ( ( irel @ sK1_SY740 @ SV5 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[75]) ).

thf(82,plain,
    ! [SV10: $i,SV6: $i] :
      ( ( ( ~ ( irel @ SV6 @ SV10 )
          | ( a1 @ SV10 ) )
        = $true )
      | ( ( irel @ SV6 @ ( sK6_SY373 @ SV6 ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV6 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[76]) ).

thf(83,plain,
    ! [SV6: $i] :
      ( ( ( ~ ! [SY830: $i] :
                ( ~ ( irel @ ( sK6_SY373 @ SV6 ) @ SY830 )
                | ( b1 @ SY830 ) )
          | ~ ~ ( ~ ( irel @ ( sK6_SY373 @ SV6 ) @ ( sK7_SY821 @ SV6 ) )
                | ~ ~ ( b0 @ ( sK7_SY821 @ SV6 ) ) ) )
        = $false )
      | ( ( ! [SY831: $i] :
              ( ~ ( irel @ SV6 @ SY831 )
              | ( a1 @ SY831 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV6 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[77]) ).

thf(84,plain,
    ! [SV11: $i,SV7: $i] :
      ( ( ( ~ ( irel @ SV7 @ SV11 )
          | ( a0 @ SV11 ) )
        = $true )
      | ( ( irel @ SV7 @ ( sK4_SY377 @ SV7 ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV7 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[78]) ).

thf(85,plain,
    ! [SV7: $i] :
      ( ( ( ~ ! [SY832: $i] :
                ( ~ ( irel @ ( sK4_SY377 @ SV7 ) @ SY832 )
                | ( b0 @ SY832 ) )
          | ~ ~ ( ~ ( irel @ ( sK4_SY377 @ SV7 ) @ ( sK5_SY819 @ SV7 ) )
                | ~ ~ ( a1 @ ( sK5_SY819 @ SV7 ) ) ) )
        = $false )
      | ( ( ! [SY833: $i] :
              ( ~ ( irel @ SV7 @ SY833 )
              | ( a0 @ SY833 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV7 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[79]) ).

thf(86,plain,
    ! [SV9: $i,SV5: $i] :
      ( ( ( irel @ SV5 @ SV9 )
        = $false )
      | ( ( f @ SV9 )
        = $true )
      | ( ( a0 @ ( sK3_SY371 @ SV5 ) )
        = $false )
      | ( ( irel @ sK1_SY740 @ SV5 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[81]) ).

thf(87,plain,
    ! [SV10: $i,SV6: $i] :
      ( ( ( ~ ( irel @ SV6 @ SV10 ) )
        = $true )
      | ( ( a1 @ SV10 )
        = $true )
      | ( ( irel @ SV6 @ ( sK6_SY373 @ SV6 ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV6 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[82]) ).

thf(88,plain,
    ! [SV6: $i] :
      ( ( ( ~ ! [SY830: $i] :
                ( ~ ( irel @ ( sK6_SY373 @ SV6 ) @ SY830 )
                | ( b1 @ SY830 ) ) )
        = $false )
      | ( ( ! [SY831: $i] :
              ( ~ ( irel @ SV6 @ SY831 )
              | ( a1 @ SY831 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV6 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[83]) ).

thf(89,plain,
    ! [SV6: $i] :
      ( ( ( ~ ~ ( ~ ( irel @ ( sK6_SY373 @ SV6 ) @ ( sK7_SY821 @ SV6 ) )
                | ~ ~ ( b0 @ ( sK7_SY821 @ SV6 ) ) ) )
        = $false )
      | ( ( ! [SY831: $i] :
              ( ~ ( irel @ SV6 @ SY831 )
              | ( a1 @ SY831 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV6 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[83]) ).

thf(90,plain,
    ! [SV11: $i,SV7: $i] :
      ( ( ( ~ ( irel @ SV7 @ SV11 ) )
        = $true )
      | ( ( a0 @ SV11 )
        = $true )
      | ( ( irel @ SV7 @ ( sK4_SY377 @ SV7 ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV7 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[84]) ).

thf(91,plain,
    ! [SV7: $i] :
      ( ( ( ~ ! [SY832: $i] :
                ( ~ ( irel @ ( sK4_SY377 @ SV7 ) @ SY832 )
                | ( b0 @ SY832 ) ) )
        = $false )
      | ( ( ! [SY833: $i] :
              ( ~ ( irel @ SV7 @ SY833 )
              | ( a0 @ SY833 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV7 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[85]) ).

thf(92,plain,
    ! [SV7: $i] :
      ( ( ( ~ ~ ( ~ ( irel @ ( sK4_SY377 @ SV7 ) @ ( sK5_SY819 @ SV7 ) )
                | ~ ~ ( a1 @ ( sK5_SY819 @ SV7 ) ) ) )
        = $false )
      | ( ( ! [SY833: $i] :
              ( ~ ( irel @ SV7 @ SY833 )
              | ( a0 @ SY833 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV7 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[85]) ).

thf(93,plain,
    ! [SV10: $i,SV6: $i] :
      ( ( ( irel @ SV6 @ SV10 )
        = $false )
      | ( ( a1 @ SV10 )
        = $true )
      | ( ( irel @ SV6 @ ( sK6_SY373 @ SV6 ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV6 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[87]) ).

thf(94,plain,
    ! [SV6: $i] :
      ( ( ( ! [SY830: $i] :
              ( ~ ( irel @ ( sK6_SY373 @ SV6 ) @ SY830 )
              | ( b1 @ SY830 ) ) )
        = $true )
      | ( ( ! [SY831: $i] :
              ( ~ ( irel @ SV6 @ SY831 )
              | ( a1 @ SY831 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV6 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[88]) ).

thf(95,plain,
    ! [SV6: $i] :
      ( ( ( ~ ( ~ ( irel @ ( sK6_SY373 @ SV6 ) @ ( sK7_SY821 @ SV6 ) )
              | ~ ~ ( b0 @ ( sK7_SY821 @ SV6 ) ) ) )
        = $true )
      | ( ( ! [SY831: $i] :
              ( ~ ( irel @ SV6 @ SY831 )
              | ( a1 @ SY831 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV6 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[89]) ).

thf(96,plain,
    ! [SV11: $i,SV7: $i] :
      ( ( ( irel @ SV7 @ SV11 )
        = $false )
      | ( ( a0 @ SV11 )
        = $true )
      | ( ( irel @ SV7 @ ( sK4_SY377 @ SV7 ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV7 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[90]) ).

thf(97,plain,
    ! [SV7: $i] :
      ( ( ( ! [SY832: $i] :
              ( ~ ( irel @ ( sK4_SY377 @ SV7 ) @ SY832 )
              | ( b0 @ SY832 ) ) )
        = $true )
      | ( ( ! [SY833: $i] :
              ( ~ ( irel @ SV7 @ SY833 )
              | ( a0 @ SY833 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV7 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[91]) ).

thf(98,plain,
    ! [SV7: $i] :
      ( ( ( ~ ( ~ ( irel @ ( sK4_SY377 @ SV7 ) @ ( sK5_SY819 @ SV7 ) )
              | ~ ~ ( a1 @ ( sK5_SY819 @ SV7 ) ) ) )
        = $true )
      | ( ( ! [SY833: $i] :
              ( ~ ( irel @ SV7 @ SY833 )
              | ( a0 @ SY833 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV7 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[92]) ).

thf(99,plain,
    ! [SV12: $i,SV6: $i] :
      ( ( ( ~ ( irel @ ( sK6_SY373 @ SV6 ) @ SV12 )
          | ( b1 @ SV12 ) )
        = $true )
      | ( ( ! [SY831: $i] :
              ( ~ ( irel @ SV6 @ SY831 )
              | ( a1 @ SY831 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV6 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[94]) ).

thf(100,plain,
    ! [SV6: $i] :
      ( ( ( ~ ( irel @ ( sK6_SY373 @ SV6 ) @ ( sK7_SY821 @ SV6 ) )
          | ~ ~ ( b0 @ ( sK7_SY821 @ SV6 ) ) )
        = $false )
      | ( ( ! [SY831: $i] :
              ( ~ ( irel @ SV6 @ SY831 )
              | ( a1 @ SY831 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV6 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[95]) ).

thf(101,plain,
    ! [SV13: $i,SV7: $i] :
      ( ( ( ~ ( irel @ ( sK4_SY377 @ SV7 ) @ SV13 )
          | ( b0 @ SV13 ) )
        = $true )
      | ( ( ! [SY833: $i] :
              ( ~ ( irel @ SV7 @ SY833 )
              | ( a0 @ SY833 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV7 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[97]) ).

thf(102,plain,
    ! [SV7: $i] :
      ( ( ( ~ ( irel @ ( sK4_SY377 @ SV7 ) @ ( sK5_SY819 @ SV7 ) )
          | ~ ~ ( a1 @ ( sK5_SY819 @ SV7 ) ) )
        = $false )
      | ( ( ! [SY833: $i] :
              ( ~ ( irel @ SV7 @ SY833 )
              | ( a0 @ SY833 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV7 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[98]) ).

thf(103,plain,
    ! [SV12: $i,SV6: $i] :
      ( ( ( ~ ( irel @ ( sK6_SY373 @ SV6 ) @ SV12 ) )
        = $true )
      | ( ( b1 @ SV12 )
        = $true )
      | ( ( ! [SY831: $i] :
              ( ~ ( irel @ SV6 @ SY831 )
              | ( a1 @ SY831 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV6 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[99]) ).

thf(104,plain,
    ! [SV6: $i] :
      ( ( ( ~ ( irel @ ( sK6_SY373 @ SV6 ) @ ( sK7_SY821 @ SV6 ) ) )
        = $false )
      | ( ( ! [SY831: $i] :
              ( ~ ( irel @ SV6 @ SY831 )
              | ( a1 @ SY831 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV6 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[100]) ).

thf(105,plain,
    ! [SV6: $i] :
      ( ( ( ~ ~ ( b0 @ ( sK7_SY821 @ SV6 ) ) )
        = $false )
      | ( ( ! [SY831: $i] :
              ( ~ ( irel @ SV6 @ SY831 )
              | ( a1 @ SY831 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV6 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[100]) ).

thf(106,plain,
    ! [SV13: $i,SV7: $i] :
      ( ( ( ~ ( irel @ ( sK4_SY377 @ SV7 ) @ SV13 ) )
        = $true )
      | ( ( b0 @ SV13 )
        = $true )
      | ( ( ! [SY833: $i] :
              ( ~ ( irel @ SV7 @ SY833 )
              | ( a0 @ SY833 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV7 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[101]) ).

thf(107,plain,
    ! [SV7: $i] :
      ( ( ( ~ ( irel @ ( sK4_SY377 @ SV7 ) @ ( sK5_SY819 @ SV7 ) ) )
        = $false )
      | ( ( ! [SY833: $i] :
              ( ~ ( irel @ SV7 @ SY833 )
              | ( a0 @ SY833 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV7 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[102]) ).

thf(108,plain,
    ! [SV7: $i] :
      ( ( ( ~ ~ ( a1 @ ( sK5_SY819 @ SV7 ) ) )
        = $false )
      | ( ( ! [SY833: $i] :
              ( ~ ( irel @ SV7 @ SY833 )
              | ( a0 @ SY833 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV7 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[102]) ).

thf(109,plain,
    ! [SV12: $i,SV6: $i] :
      ( ( ( irel @ ( sK6_SY373 @ SV6 ) @ SV12 )
        = $false )
      | ( ( b1 @ SV12 )
        = $true )
      | ( ( ! [SY831: $i] :
              ( ~ ( irel @ SV6 @ SY831 )
              | ( a1 @ SY831 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV6 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[103]) ).

thf(110,plain,
    ! [SV6: $i] :
      ( ( ( irel @ ( sK6_SY373 @ SV6 ) @ ( sK7_SY821 @ SV6 ) )
        = $true )
      | ( ( ! [SY831: $i] :
              ( ~ ( irel @ SV6 @ SY831 )
              | ( a1 @ SY831 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV6 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[104]) ).

thf(111,plain,
    ! [SV6: $i] :
      ( ( ( ~ ( b0 @ ( sK7_SY821 @ SV6 ) ) )
        = $true )
      | ( ( ! [SY831: $i] :
              ( ~ ( irel @ SV6 @ SY831 )
              | ( a1 @ SY831 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV6 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[105]) ).

thf(112,plain,
    ! [SV13: $i,SV7: $i] :
      ( ( ( irel @ ( sK4_SY377 @ SV7 ) @ SV13 )
        = $false )
      | ( ( b0 @ SV13 )
        = $true )
      | ( ( ! [SY833: $i] :
              ( ~ ( irel @ SV7 @ SY833 )
              | ( a0 @ SY833 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV7 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[106]) ).

thf(113,plain,
    ! [SV7: $i] :
      ( ( ( irel @ ( sK4_SY377 @ SV7 ) @ ( sK5_SY819 @ SV7 ) )
        = $true )
      | ( ( ! [SY833: $i] :
              ( ~ ( irel @ SV7 @ SY833 )
              | ( a0 @ SY833 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV7 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[107]) ).

thf(114,plain,
    ! [SV7: $i] :
      ( ( ( ~ ( a1 @ ( sK5_SY819 @ SV7 ) ) )
        = $true )
      | ( ( ! [SY833: $i] :
              ( ~ ( irel @ SV7 @ SY833 )
              | ( a0 @ SY833 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV7 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[108]) ).

thf(115,plain,
    ! [SV12: $i,SV14: $i,SV6: $i] :
      ( ( ( ~ ( irel @ SV6 @ SV14 )
          | ( a1 @ SV14 ) )
        = $true )
      | ( ( b1 @ SV12 )
        = $true )
      | ( ( irel @ ( sK6_SY373 @ SV6 ) @ SV12 )
        = $false )
      | ( ( irel @ sK1_SY740 @ SV6 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[109]) ).

thf(116,plain,
    ! [SV15: $i,SV6: $i] :
      ( ( ( ~ ( irel @ SV6 @ SV15 )
          | ( a1 @ SV15 ) )
        = $true )
      | ( ( irel @ ( sK6_SY373 @ SV6 ) @ ( sK7_SY821 @ SV6 ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV6 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[110]) ).

thf(117,plain,
    ! [SV6: $i] :
      ( ( ( b0 @ ( sK7_SY821 @ SV6 ) )
        = $false )
      | ( ( ! [SY831: $i] :
              ( ~ ( irel @ SV6 @ SY831 )
              | ( a1 @ SY831 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV6 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[111]) ).

thf(118,plain,
    ! [SV13: $i,SV16: $i,SV7: $i] :
      ( ( ( ~ ( irel @ SV7 @ SV16 )
          | ( a0 @ SV16 ) )
        = $true )
      | ( ( b0 @ SV13 )
        = $true )
      | ( ( irel @ ( sK4_SY377 @ SV7 ) @ SV13 )
        = $false )
      | ( ( irel @ sK1_SY740 @ SV7 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[112]) ).

thf(119,plain,
    ! [SV17: $i,SV7: $i] :
      ( ( ( ~ ( irel @ SV7 @ SV17 )
          | ( a0 @ SV17 ) )
        = $true )
      | ( ( irel @ ( sK4_SY377 @ SV7 ) @ ( sK5_SY819 @ SV7 ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV7 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[113]) ).

thf(120,plain,
    ! [SV7: $i] :
      ( ( ( a1 @ ( sK5_SY819 @ SV7 ) )
        = $false )
      | ( ( ! [SY833: $i] :
              ( ~ ( irel @ SV7 @ SY833 )
              | ( a0 @ SY833 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV7 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[114]) ).

thf(121,plain,
    ! [SV12: $i,SV14: $i,SV6: $i] :
      ( ( ( ~ ( irel @ SV6 @ SV14 ) )
        = $true )
      | ( ( a1 @ SV14 )
        = $true )
      | ( ( b1 @ SV12 )
        = $true )
      | ( ( irel @ ( sK6_SY373 @ SV6 ) @ SV12 )
        = $false )
      | ( ( irel @ sK1_SY740 @ SV6 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[115]) ).

thf(122,plain,
    ! [SV15: $i,SV6: $i] :
      ( ( ( ~ ( irel @ SV6 @ SV15 ) )
        = $true )
      | ( ( a1 @ SV15 )
        = $true )
      | ( ( irel @ ( sK6_SY373 @ SV6 ) @ ( sK7_SY821 @ SV6 ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV6 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[116]) ).

thf(123,plain,
    ! [SV18: $i,SV6: $i] :
      ( ( ( ~ ( irel @ SV6 @ SV18 )
          | ( a1 @ SV18 ) )
        = $true )
      | ( ( b0 @ ( sK7_SY821 @ SV6 ) )
        = $false )
      | ( ( irel @ sK1_SY740 @ SV6 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[117]) ).

thf(124,plain,
    ! [SV13: $i,SV16: $i,SV7: $i] :
      ( ( ( ~ ( irel @ SV7 @ SV16 ) )
        = $true )
      | ( ( a0 @ SV16 )
        = $true )
      | ( ( b0 @ SV13 )
        = $true )
      | ( ( irel @ ( sK4_SY377 @ SV7 ) @ SV13 )
        = $false )
      | ( ( irel @ sK1_SY740 @ SV7 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[118]) ).

thf(125,plain,
    ! [SV17: $i,SV7: $i] :
      ( ( ( ~ ( irel @ SV7 @ SV17 ) )
        = $true )
      | ( ( a0 @ SV17 )
        = $true )
      | ( ( irel @ ( sK4_SY377 @ SV7 ) @ ( sK5_SY819 @ SV7 ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV7 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[119]) ).

thf(126,plain,
    ! [SV19: $i,SV7: $i] :
      ( ( ( ~ ( irel @ SV7 @ SV19 )
          | ( a0 @ SV19 ) )
        = $true )
      | ( ( a1 @ ( sK5_SY819 @ SV7 ) )
        = $false )
      | ( ( irel @ sK1_SY740 @ SV7 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[120]) ).

thf(127,plain,
    ! [SV12: $i,SV14: $i,SV6: $i] :
      ( ( ( irel @ SV6 @ SV14 )
        = $false )
      | ( ( a1 @ SV14 )
        = $true )
      | ( ( b1 @ SV12 )
        = $true )
      | ( ( irel @ ( sK6_SY373 @ SV6 ) @ SV12 )
        = $false )
      | ( ( irel @ sK1_SY740 @ SV6 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[121]) ).

thf(128,plain,
    ! [SV15: $i,SV6: $i] :
      ( ( ( irel @ SV6 @ SV15 )
        = $false )
      | ( ( a1 @ SV15 )
        = $true )
      | ( ( irel @ ( sK6_SY373 @ SV6 ) @ ( sK7_SY821 @ SV6 ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV6 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[122]) ).

thf(129,plain,
    ! [SV18: $i,SV6: $i] :
      ( ( ( ~ ( irel @ SV6 @ SV18 ) )
        = $true )
      | ( ( a1 @ SV18 )
        = $true )
      | ( ( b0 @ ( sK7_SY821 @ SV6 ) )
        = $false )
      | ( ( irel @ sK1_SY740 @ SV6 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[123]) ).

thf(130,plain,
    ! [SV13: $i,SV16: $i,SV7: $i] :
      ( ( ( irel @ SV7 @ SV16 )
        = $false )
      | ( ( a0 @ SV16 )
        = $true )
      | ( ( b0 @ SV13 )
        = $true )
      | ( ( irel @ ( sK4_SY377 @ SV7 ) @ SV13 )
        = $false )
      | ( ( irel @ sK1_SY740 @ SV7 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[124]) ).

thf(131,plain,
    ! [SV17: $i,SV7: $i] :
      ( ( ( irel @ SV7 @ SV17 )
        = $false )
      | ( ( a0 @ SV17 )
        = $true )
      | ( ( irel @ ( sK4_SY377 @ SV7 ) @ ( sK5_SY819 @ SV7 ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV7 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[125]) ).

thf(132,plain,
    ! [SV19: $i,SV7: $i] :
      ( ( ( ~ ( irel @ SV7 @ SV19 ) )
        = $true )
      | ( ( a0 @ SV19 )
        = $true )
      | ( ( a1 @ ( sK5_SY819 @ SV7 ) )
        = $false )
      | ( ( irel @ sK1_SY740 @ SV7 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[126]) ).

thf(133,plain,
    ! [SV18: $i,SV6: $i] :
      ( ( ( irel @ SV6 @ SV18 )
        = $false )
      | ( ( a1 @ SV18 )
        = $true )
      | ( ( b0 @ ( sK7_SY821 @ SV6 ) )
        = $false )
      | ( ( irel @ sK1_SY740 @ SV6 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[129]) ).

thf(134,plain,
    ! [SV19: $i,SV7: $i] :
      ( ( ( irel @ SV7 @ SV19 )
        = $false )
      | ( ( a0 @ SV19 )
        = $true )
      | ( ( a1 @ ( sK5_SY819 @ SV7 ) )
        = $false )
      | ( ( irel @ sK1_SY740 @ SV7 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[132]) ).

thf(135,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[20,134,133,131,130,128,127,96,93,86,80,45,42,40]) ).

thf(136,plain,
    ( ( ! [X: $i] : ( irel @ X @ X ) )
    = $true ),
    inference(copy,[status(thm)],[7]) ).

thf(137,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ~ ( irel @ X @ Y )
          | ~ ( irel @ Y @ Z )
          | ( irel @ X @ Z ) ) )
    = $true ),
    inference(copy,[status(thm)],[15]) ).

thf(138,plain,
    ( ( ! [SY806: $i] :
          ( ~ ( irel @ sK1_SY740 @ SY806 )
          | ( ( irel @ SY806 @ ( sK12_SY643 @ SY806 ) )
            & ! [SY824: $i] :
                ( ~ ( irel @ ( sK12_SY643 @ SY806 ) @ SY824 )
                | ( b1 @ SY824 ) )
            & ( irel @ ( sK12_SY643 @ SY806 ) @ ( sK13_SY825 @ SY806 ) )
            & ~ ( b0 @ ( sK13_SY825 @ SY806 ) ) )
          | ! [SY646: $i] :
              ( ~ ( irel @ SY806 @ SY646 )
              | ( a1 @ SY646 ) ) )
      & ! [SY806: $i] :
          ( ~ ( irel @ sK1_SY740 @ SY806 )
          | ( ( irel @ SY806 @ ( sK11_SY647 @ SY806 ) )
            & ~ ( a0 @ ( sK11_SY647 @ SY806 ) ) )
          | ! [SY648: $i] :
              ( ~ ( irel @ SY806 @ SY648 )
              | ( f @ SY648 ) ) )
      & ! [SY806: $i] :
          ( ~ ( irel @ sK1_SY740 @ SY806 )
          | ( ( irel @ SY806 @ ( sK9_SY639 @ SY806 ) )
            & ! [SY822: $i] :
                ( ~ ( irel @ ( sK9_SY639 @ SY806 ) @ SY822 )
                | ( b0 @ SY822 ) )
            & ( irel @ ( sK9_SY639 @ SY806 ) @ ( sK10_SY823 @ SY806 ) )
            & ~ ( a1 @ ( sK10_SY823 @ SY806 ) ) )
          | ! [SY642: $i] :
              ( ~ ( irel @ SY806 @ SY642 )
              | ( a0 @ SY642 ) ) )
      & ( irel @ sK1_SY740 @ sK8_SY817 )
      & ~ ( f @ sK8_SY817 ) )
    = $true ),
    inference(copy,[status(thm)],[14]) ).

thf(139,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                            ( ~ ( irel @ sK1_SY740 @ SX0 )
                            | ~ ( ~ ( irel @ SX0 @ ( sK12_SY643 @ SX0 ) )
                                | ~ ~ ( ~ ! [SX1: $i] :
                                            ( ~ ( irel @ ( sK12_SY643 @ SX0 ) @ SX1 )
                                            | ( b1 @ SX1 ) )
                                      | ~ ~ ( ~ ( irel @ ( sK12_SY643 @ SX0 ) @ ( sK13_SY825 @ SX0 ) )
                                            | ~ ~ ( b0 @ ( sK13_SY825 @ SX0 ) ) ) ) )
                            | ! [SX1: $i] :
                                ( ~ ( irel @ SX0 @ SX1 )
                                | ( a1 @ SX1 ) ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( irel @ sK1_SY740 @ SX0 )
                            | ~ ( ~ ( irel @ SX0 @ ( sK11_SY647 @ SX0 ) )
                                | ~ ~ ( a0 @ ( sK11_SY647 @ SX0 ) ) )
                            | ! [SX1: $i] :
                                ( ~ ( irel @ SX0 @ SX1 )
                                | ( f @ SX1 ) ) ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( irel @ sK1_SY740 @ SX0 )
                      | ~ ( ~ ( irel @ SX0 @ ( sK9_SY639 @ SX0 ) )
                          | ~ ~ ( ~ ! [SX1: $i] :
                                      ( ~ ( irel @ ( sK9_SY639 @ SX0 ) @ SX1 )
                                      | ( b0 @ SX1 ) )
                                | ~ ~ ( ~ ( irel @ ( sK9_SY639 @ SX0 ) @ ( sK10_SY823 @ SX0 ) )
                                      | ~ ~ ( a1 @ ( sK10_SY823 @ SX0 ) ) ) ) )
                      | ! [SX1: $i] :
                          ( ~ ( irel @ SX0 @ SX1 )
                          | ( a0 @ SX1 ) ) ) )
          | ~ ~ ( ~ ( irel @ sK1_SY740 @ sK8_SY817 )
                | ~ ~ ( f @ sK8_SY817 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[138,iand,iatom,icountersatisfiable,iequiv,ifalse,iimplied,iimplies,iinvalid,inot,ior,isatisfiable,itrue,ivalid,ixor,mand,mbox_s4,mimplies,mnot,mor]) ).

thf(140,plain,
    ! [SV20: $i] :
      ( ( irel @ SV20 @ SV20 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[136]) ).

thf(141,plain,
    ! [SV21: $i] :
      ( ( ! [SY834: $i,SY835: $i] :
            ( ~ ( irel @ SV21 @ SY834 )
            | ~ ( irel @ SY834 @ SY835 )
            | ( irel @ SV21 @ SY835 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[137]) ).

thf(142,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( irel @ sK1_SY740 @ SX0 )
                        | ~ ( ~ ( irel @ SX0 @ ( sK12_SY643 @ SX0 ) )
                            | ~ ~ ( ~ ! [SX1: $i] :
                                        ( ~ ( irel @ ( sK12_SY643 @ SX0 ) @ SX1 )
                                        | ( b1 @ SX1 ) )
                                  | ~ ~ ( ~ ( irel @ ( sK12_SY643 @ SX0 ) @ ( sK13_SY825 @ SX0 ) )
                                        | ~ ~ ( b0 @ ( sK13_SY825 @ SX0 ) ) ) ) )
                        | ! [SX1: $i] :
                            ( ~ ( irel @ SX0 @ SX1 )
                            | ( a1 @ SX1 ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( irel @ sK1_SY740 @ SX0 )
                        | ~ ( ~ ( irel @ SX0 @ ( sK11_SY647 @ SX0 ) )
                            | ~ ~ ( a0 @ ( sK11_SY647 @ SX0 ) ) )
                        | ! [SX1: $i] :
                            ( ~ ( irel @ SX0 @ SX1 )
                            | ( f @ SX1 ) ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( irel @ sK1_SY740 @ SX0 )
                  | ~ ( ~ ( irel @ SX0 @ ( sK9_SY639 @ SX0 ) )
                      | ~ ~ ( ~ ! [SX1: $i] :
                                  ( ~ ( irel @ ( sK9_SY639 @ SX0 ) @ SX1 )
                                  | ( b0 @ SX1 ) )
                            | ~ ~ ( ~ ( irel @ ( sK9_SY639 @ SX0 ) @ ( sK10_SY823 @ SX0 ) )
                                  | ~ ~ ( a1 @ ( sK10_SY823 @ SX0 ) ) ) ) )
                  | ! [SX1: $i] :
                      ( ~ ( irel @ SX0 @ SX1 )
                      | ( a0 @ SX1 ) ) ) )
      | ~ ~ ( ~ ( irel @ sK1_SY740 @ sK8_SY817 )
            | ~ ~ ( f @ sK8_SY817 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[139]) ).

thf(143,plain,
    ! [SV22: $i,SV21: $i] :
      ( ( ! [SY836: $i] :
            ( ~ ( irel @ SV21 @ SV22 )
            | ~ ( irel @ SV22 @ SY836 )
            | ( irel @ SV21 @ SY836 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[141]) ).

thf(144,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( irel @ sK1_SY740 @ SX0 )
                        | ~ ( ~ ( irel @ SX0 @ ( sK12_SY643 @ SX0 ) )
                            | ~ ~ ( ~ ! [SX1: $i] :
                                        ( ~ ( irel @ ( sK12_SY643 @ SX0 ) @ SX1 )
                                        | ( b1 @ SX1 ) )
                                  | ~ ~ ( ~ ( irel @ ( sK12_SY643 @ SX0 ) @ ( sK13_SY825 @ SX0 ) )
                                        | ~ ~ ( b0 @ ( sK13_SY825 @ SX0 ) ) ) ) )
                        | ! [SX1: $i] :
                            ( ~ ( irel @ SX0 @ SX1 )
                            | ( a1 @ SX1 ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( irel @ sK1_SY740 @ SX0 )
                        | ~ ( ~ ( irel @ SX0 @ ( sK11_SY647 @ SX0 ) )
                            | ~ ~ ( a0 @ ( sK11_SY647 @ SX0 ) ) )
                        | ! [SX1: $i] :
                            ( ~ ( irel @ SX0 @ SX1 )
                            | ( f @ SX1 ) ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( irel @ sK1_SY740 @ SX0 )
                  | ~ ( ~ ( irel @ SX0 @ ( sK9_SY639 @ SX0 ) )
                      | ~ ~ ( ~ ! [SX1: $i] :
                                  ( ~ ( irel @ ( sK9_SY639 @ SX0 ) @ SX1 )
                                  | ( b0 @ SX1 ) )
                            | ~ ~ ( ~ ( irel @ ( sK9_SY639 @ SX0 ) @ ( sK10_SY823 @ SX0 ) )
                                  | ~ ~ ( a1 @ ( sK10_SY823 @ SX0 ) ) ) ) )
                  | ! [SX1: $i] :
                      ( ~ ( irel @ SX0 @ SX1 )
                      | ( a0 @ SX1 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[142]) ).

thf(145,plain,
    ( ( ~ ~ ( ~ ( irel @ sK1_SY740 @ sK8_SY817 )
            | ~ ~ ( f @ sK8_SY817 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[142]) ).

thf(146,plain,
    ! [SV23: $i,SV22: $i,SV21: $i] :
      ( ( ~ ( irel @ SV21 @ SV22 )
        | ~ ( irel @ SV22 @ SV23 )
        | ( irel @ SV21 @ SV23 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[143]) ).

thf(147,plain,
    ( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( irel @ sK1_SY740 @ SX0 )
                      | ~ ( ~ ( irel @ SX0 @ ( sK12_SY643 @ SX0 ) )
                          | ~ ~ ( ~ ! [SX1: $i] :
                                      ( ~ ( irel @ ( sK12_SY643 @ SX0 ) @ SX1 )
                                      | ( b1 @ SX1 ) )
                                | ~ ~ ( ~ ( irel @ ( sK12_SY643 @ SX0 ) @ ( sK13_SY825 @ SX0 ) )
                                      | ~ ~ ( b0 @ ( sK13_SY825 @ SX0 ) ) ) ) )
                      | ! [SX1: $i] :
                          ( ~ ( irel @ SX0 @ SX1 )
                          | ( a1 @ SX1 ) ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( irel @ sK1_SY740 @ SX0 )
                      | ~ ( ~ ( irel @ SX0 @ ( sK11_SY647 @ SX0 ) )
                          | ~ ~ ( a0 @ ( sK11_SY647 @ SX0 ) ) )
                      | ! [SX1: $i] :
                          ( ~ ( irel @ SX0 @ SX1 )
                          | ( f @ SX1 ) ) ) )
          | ~ ! [SX0: $i] :
                ( ~ ( irel @ sK1_SY740 @ SX0 )
                | ~ ( ~ ( irel @ SX0 @ ( sK9_SY639 @ SX0 ) )
                    | ~ ~ ( ~ ! [SX1: $i] :
                                ( ~ ( irel @ ( sK9_SY639 @ SX0 ) @ SX1 )
                                | ( b0 @ SX1 ) )
                          | ~ ~ ( ~ ( irel @ ( sK9_SY639 @ SX0 ) @ ( sK10_SY823 @ SX0 ) )
                                | ~ ~ ( a1 @ ( sK10_SY823 @ SX0 ) ) ) ) )
                | ! [SX1: $i] :
                    ( ~ ( irel @ SX0 @ SX1 )
                    | ( a0 @ SX1 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[144]) ).

thf(148,plain,
    ( ( ~ ( ~ ( irel @ sK1_SY740 @ sK8_SY817 )
          | ~ ~ ( f @ sK8_SY817 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[145]) ).

thf(149,plain,
    ! [SV23: $i,SV22: $i,SV21: $i] :
      ( ( ( ~ ( irel @ SV21 @ SV22 )
          | ~ ( irel @ SV22 @ SV23 ) )
        = $true )
      | ( ( irel @ SV21 @ SV23 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[146]) ).

thf(150,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( irel @ sK1_SY740 @ SX0 )
                  | ~ ( ~ ( irel @ SX0 @ ( sK12_SY643 @ SX0 ) )
                      | ~ ~ ( ~ ! [SX1: $i] :
                                  ( ~ ( irel @ ( sK12_SY643 @ SX0 ) @ SX1 )
                                  | ( b1 @ SX1 ) )
                            | ~ ~ ( ~ ( irel @ ( sK12_SY643 @ SX0 ) @ ( sK13_SY825 @ SX0 ) )
                                  | ~ ~ ( b0 @ ( sK13_SY825 @ SX0 ) ) ) ) )
                  | ! [SX1: $i] :
                      ( ~ ( irel @ SX0 @ SX1 )
                      | ( a1 @ SX1 ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( irel @ sK1_SY740 @ SX0 )
                  | ~ ( ~ ( irel @ SX0 @ ( sK11_SY647 @ SX0 ) )
                      | ~ ~ ( a0 @ ( sK11_SY647 @ SX0 ) ) )
                  | ! [SX1: $i] :
                      ( ~ ( irel @ SX0 @ SX1 )
                      | ( f @ SX1 ) ) ) )
      | ~ ! [SX0: $i] :
            ( ~ ( irel @ sK1_SY740 @ SX0 )
            | ~ ( ~ ( irel @ SX0 @ ( sK9_SY639 @ SX0 ) )
                | ~ ~ ( ~ ! [SX1: $i] :
                            ( ~ ( irel @ ( sK9_SY639 @ SX0 ) @ SX1 )
                            | ( b0 @ SX1 ) )
                      | ~ ~ ( ~ ( irel @ ( sK9_SY639 @ SX0 ) @ ( sK10_SY823 @ SX0 ) )
                            | ~ ~ ( a1 @ ( sK10_SY823 @ SX0 ) ) ) ) )
            | ! [SX1: $i] :
                ( ~ ( irel @ SX0 @ SX1 )
                | ( a0 @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[147]) ).

thf(151,plain,
    ( ( ~ ( irel @ sK1_SY740 @ sK8_SY817 )
      | ~ ~ ( f @ sK8_SY817 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[148]) ).

thf(152,plain,
    ! [SV23: $i,SV22: $i,SV21: $i] :
      ( ( ( ~ ( irel @ SV21 @ SV22 ) )
        = $true )
      | ( ( ~ ( irel @ SV22 @ SV23 ) )
        = $true )
      | ( ( irel @ SV21 @ SV23 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[149]) ).

thf(153,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( irel @ sK1_SY740 @ SX0 )
                  | ~ ( ~ ( irel @ SX0 @ ( sK12_SY643 @ SX0 ) )
                      | ~ ~ ( ~ ! [SX1: $i] :
                                  ( ~ ( irel @ ( sK12_SY643 @ SX0 ) @ SX1 )
                                  | ( b1 @ SX1 ) )
                            | ~ ~ ( ~ ( irel @ ( sK12_SY643 @ SX0 ) @ ( sK13_SY825 @ SX0 ) )
                                  | ~ ~ ( b0 @ ( sK13_SY825 @ SX0 ) ) ) ) )
                  | ! [SX1: $i] :
                      ( ~ ( irel @ SX0 @ SX1 )
                      | ( a1 @ SX1 ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( irel @ sK1_SY740 @ SX0 )
                  | ~ ( ~ ( irel @ SX0 @ ( sK11_SY647 @ SX0 ) )
                      | ~ ~ ( a0 @ ( sK11_SY647 @ SX0 ) ) )
                  | ! [SX1: $i] :
                      ( ~ ( irel @ SX0 @ SX1 )
                      | ( f @ SX1 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[150]) ).

thf(154,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( irel @ sK1_SY740 @ SX0 )
            | ~ ( ~ ( irel @ SX0 @ ( sK9_SY639 @ SX0 ) )
                | ~ ~ ( ~ ! [SX1: $i] :
                            ( ~ ( irel @ ( sK9_SY639 @ SX0 ) @ SX1 )
                            | ( b0 @ SX1 ) )
                      | ~ ~ ( ~ ( irel @ ( sK9_SY639 @ SX0 ) @ ( sK10_SY823 @ SX0 ) )
                            | ~ ~ ( a1 @ ( sK10_SY823 @ SX0 ) ) ) ) )
            | ! [SX1: $i] :
                ( ~ ( irel @ SX0 @ SX1 )
                | ( a0 @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[150]) ).

thf(155,plain,
    ( ( ~ ( irel @ sK1_SY740 @ sK8_SY817 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[151]) ).

thf(156,plain,
    ( ( ~ ~ ( f @ sK8_SY817 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[151]) ).

thf(157,plain,
    ! [SV23: $i,SV22: $i,SV21: $i] :
      ( ( ( irel @ SV21 @ SV22 )
        = $false )
      | ( ( ~ ( irel @ SV22 @ SV23 ) )
        = $true )
      | ( ( irel @ SV21 @ SV23 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[152]) ).

thf(158,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( irel @ sK1_SY740 @ SX0 )
                | ~ ( ~ ( irel @ SX0 @ ( sK12_SY643 @ SX0 ) )
                    | ~ ~ ( ~ ! [SX1: $i] :
                                ( ~ ( irel @ ( sK12_SY643 @ SX0 ) @ SX1 )
                                | ( b1 @ SX1 ) )
                          | ~ ~ ( ~ ( irel @ ( sK12_SY643 @ SX0 ) @ ( sK13_SY825 @ SX0 ) )
                                | ~ ~ ( b0 @ ( sK13_SY825 @ SX0 ) ) ) ) )
                | ! [SX1: $i] :
                    ( ~ ( irel @ SX0 @ SX1 )
                    | ( a1 @ SX1 ) ) )
          | ~ ! [SX0: $i] :
                ( ~ ( irel @ sK1_SY740 @ SX0 )
                | ~ ( ~ ( irel @ SX0 @ ( sK11_SY647 @ SX0 ) )
                    | ~ ~ ( a0 @ ( sK11_SY647 @ SX0 ) ) )
                | ! [SX1: $i] :
                    ( ~ ( irel @ SX0 @ SX1 )
                    | ( f @ SX1 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[153]) ).

thf(159,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( irel @ sK1_SY740 @ SX0 )
          | ~ ( ~ ( irel @ SX0 @ ( sK9_SY639 @ SX0 ) )
              | ~ ~ ( ~ ! [SX1: $i] :
                          ( ~ ( irel @ ( sK9_SY639 @ SX0 ) @ SX1 )
                          | ( b0 @ SX1 ) )
                    | ~ ~ ( ~ ( irel @ ( sK9_SY639 @ SX0 ) @ ( sK10_SY823 @ SX0 ) )
                          | ~ ~ ( a1 @ ( sK10_SY823 @ SX0 ) ) ) ) )
          | ! [SX1: $i] :
              ( ~ ( irel @ SX0 @ SX1 )
              | ( a0 @ SX1 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[154]) ).

thf(160,plain,
    ( ( irel @ sK1_SY740 @ sK8_SY817 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[155]) ).

thf(161,plain,
    ( ( ~ ( f @ sK8_SY817 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[156]) ).

thf(162,plain,
    ! [SV21: $i,SV23: $i,SV22: $i] :
      ( ( ( irel @ SV22 @ SV23 )
        = $false )
      | ( ( irel @ SV21 @ SV22 )
        = $false )
      | ( ( irel @ SV21 @ SV23 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[157]) ).

thf(163,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( irel @ sK1_SY740 @ SX0 )
            | ~ ( ~ ( irel @ SX0 @ ( sK12_SY643 @ SX0 ) )
                | ~ ~ ( ~ ! [SX1: $i] :
                            ( ~ ( irel @ ( sK12_SY643 @ SX0 ) @ SX1 )
                            | ( b1 @ SX1 ) )
                      | ~ ~ ( ~ ( irel @ ( sK12_SY643 @ SX0 ) @ ( sK13_SY825 @ SX0 ) )
                            | ~ ~ ( b0 @ ( sK13_SY825 @ SX0 ) ) ) ) )
            | ! [SX1: $i] :
                ( ~ ( irel @ SX0 @ SX1 )
                | ( a1 @ SX1 ) ) )
      | ~ ! [SX0: $i] :
            ( ~ ( irel @ sK1_SY740 @ SX0 )
            | ~ ( ~ ( irel @ SX0 @ ( sK11_SY647 @ SX0 ) )
                | ~ ~ ( a0 @ ( sK11_SY647 @ SX0 ) ) )
            | ! [SX1: $i] :
                ( ~ ( irel @ SX0 @ SX1 )
                | ( f @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[158]) ).

thf(164,plain,
    ! [SV24: $i] :
      ( ( ~ ( irel @ sK1_SY740 @ SV24 )
        | ~ ( ~ ( irel @ SV24 @ ( sK9_SY639 @ SV24 ) )
            | ~ ~ ( ~ ! [SY837: $i] :
                        ( ~ ( irel @ ( sK9_SY639 @ SV24 ) @ SY837 )
                        | ( b0 @ SY837 ) )
                  | ~ ~ ( ~ ( irel @ ( sK9_SY639 @ SV24 ) @ ( sK10_SY823 @ SV24 ) )
                        | ~ ~ ( a1 @ ( sK10_SY823 @ SV24 ) ) ) ) )
        | ! [SY838: $i] :
            ( ~ ( irel @ SV24 @ SY838 )
            | ( a0 @ SY838 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[159]) ).

thf(165,plain,
    ( ( f @ sK8_SY817 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[161]) ).

thf(166,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( irel @ sK1_SY740 @ SX0 )
            | ~ ( ~ ( irel @ SX0 @ ( sK12_SY643 @ SX0 ) )
                | ~ ~ ( ~ ! [SX1: $i] :
                            ( ~ ( irel @ ( sK12_SY643 @ SX0 ) @ SX1 )
                            | ( b1 @ SX1 ) )
                      | ~ ~ ( ~ ( irel @ ( sK12_SY643 @ SX0 ) @ ( sK13_SY825 @ SX0 ) )
                            | ~ ~ ( b0 @ ( sK13_SY825 @ SX0 ) ) ) ) )
            | ! [SX1: $i] :
                ( ~ ( irel @ SX0 @ SX1 )
                | ( a1 @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[163]) ).

thf(167,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( irel @ sK1_SY740 @ SX0 )
            | ~ ( ~ ( irel @ SX0 @ ( sK11_SY647 @ SX0 ) )
                | ~ ~ ( a0 @ ( sK11_SY647 @ SX0 ) ) )
            | ! [SX1: $i] :
                ( ~ ( irel @ SX0 @ SX1 )
                | ( f @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[163]) ).

thf(168,plain,
    ! [SV24: $i] :
      ( ( ( ~ ( irel @ sK1_SY740 @ SV24 ) )
        = $true )
      | ( ( ~ ( ~ ( irel @ SV24 @ ( sK9_SY639 @ SV24 ) )
              | ~ ~ ( ~ ! [SY837: $i] :
                          ( ~ ( irel @ ( sK9_SY639 @ SV24 ) @ SY837 )
                          | ( b0 @ SY837 ) )
                    | ~ ~ ( ~ ( irel @ ( sK9_SY639 @ SV24 ) @ ( sK10_SY823 @ SV24 ) )
                          | ~ ~ ( a1 @ ( sK10_SY823 @ SV24 ) ) ) ) )
          | ! [SY838: $i] :
              ( ~ ( irel @ SV24 @ SY838 )
              | ( a0 @ SY838 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[164]) ).

thf(169,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( irel @ sK1_SY740 @ SX0 )
          | ~ ( ~ ( irel @ SX0 @ ( sK12_SY643 @ SX0 ) )
              | ~ ~ ( ~ ! [SX1: $i] :
                          ( ~ ( irel @ ( sK12_SY643 @ SX0 ) @ SX1 )
                          | ( b1 @ SX1 ) )
                    | ~ ~ ( ~ ( irel @ ( sK12_SY643 @ SX0 ) @ ( sK13_SY825 @ SX0 ) )
                          | ~ ~ ( b0 @ ( sK13_SY825 @ SX0 ) ) ) ) )
          | ! [SX1: $i] :
              ( ~ ( irel @ SX0 @ SX1 )
              | ( a1 @ SX1 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[166]) ).

thf(170,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( irel @ sK1_SY740 @ SX0 )
          | ~ ( ~ ( irel @ SX0 @ ( sK11_SY647 @ SX0 ) )
              | ~ ~ ( a0 @ ( sK11_SY647 @ SX0 ) ) )
          | ! [SX1: $i] :
              ( ~ ( irel @ SX0 @ SX1 )
              | ( f @ SX1 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[167]) ).

thf(171,plain,
    ! [SV24: $i] :
      ( ( ( irel @ sK1_SY740 @ SV24 )
        = $false )
      | ( ( ~ ( ~ ( irel @ SV24 @ ( sK9_SY639 @ SV24 ) )
              | ~ ~ ( ~ ! [SY837: $i] :
                          ( ~ ( irel @ ( sK9_SY639 @ SV24 ) @ SY837 )
                          | ( b0 @ SY837 ) )
                    | ~ ~ ( ~ ( irel @ ( sK9_SY639 @ SV24 ) @ ( sK10_SY823 @ SV24 ) )
                          | ~ ~ ( a1 @ ( sK10_SY823 @ SV24 ) ) ) ) )
          | ! [SY838: $i] :
              ( ~ ( irel @ SV24 @ SY838 )
              | ( a0 @ SY838 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[168]) ).

thf(172,plain,
    ! [SV25: $i] :
      ( ( ~ ( irel @ sK1_SY740 @ SV25 )
        | ~ ( ~ ( irel @ SV25 @ ( sK12_SY643 @ SV25 ) )
            | ~ ~ ( ~ ! [SY839: $i] :
                        ( ~ ( irel @ ( sK12_SY643 @ SV25 ) @ SY839 )
                        | ( b1 @ SY839 ) )
                  | ~ ~ ( ~ ( irel @ ( sK12_SY643 @ SV25 ) @ ( sK13_SY825 @ SV25 ) )
                        | ~ ~ ( b0 @ ( sK13_SY825 @ SV25 ) ) ) ) )
        | ! [SY840: $i] :
            ( ~ ( irel @ SV25 @ SY840 )
            | ( a1 @ SY840 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[169]) ).

thf(173,plain,
    ! [SV26: $i] :
      ( ( ~ ( irel @ sK1_SY740 @ SV26 )
        | ~ ( ~ ( irel @ SV26 @ ( sK11_SY647 @ SV26 ) )
            | ~ ~ ( a0 @ ( sK11_SY647 @ SV26 ) ) )
        | ! [SY841: $i] :
            ( ~ ( irel @ SV26 @ SY841 )
            | ( f @ SY841 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[170]) ).

thf(174,plain,
    ! [SV24: $i] :
      ( ( ( ~ ( ~ ( irel @ SV24 @ ( sK9_SY639 @ SV24 ) )
              | ~ ~ ( ~ ! [SY837: $i] :
                          ( ~ ( irel @ ( sK9_SY639 @ SV24 ) @ SY837 )
                          | ( b0 @ SY837 ) )
                    | ~ ~ ( ~ ( irel @ ( sK9_SY639 @ SV24 ) @ ( sK10_SY823 @ SV24 ) )
                          | ~ ~ ( a1 @ ( sK10_SY823 @ SV24 ) ) ) ) ) )
        = $true )
      | ( ( ! [SY838: $i] :
              ( ~ ( irel @ SV24 @ SY838 )
              | ( a0 @ SY838 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV24 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[171]) ).

thf(175,plain,
    ! [SV25: $i] :
      ( ( ( ~ ( irel @ sK1_SY740 @ SV25 ) )
        = $true )
      | ( ( ~ ( ~ ( irel @ SV25 @ ( sK12_SY643 @ SV25 ) )
              | ~ ~ ( ~ ! [SY839: $i] :
                          ( ~ ( irel @ ( sK12_SY643 @ SV25 ) @ SY839 )
                          | ( b1 @ SY839 ) )
                    | ~ ~ ( ~ ( irel @ ( sK12_SY643 @ SV25 ) @ ( sK13_SY825 @ SV25 ) )
                          | ~ ~ ( b0 @ ( sK13_SY825 @ SV25 ) ) ) ) )
          | ! [SY840: $i] :
              ( ~ ( irel @ SV25 @ SY840 )
              | ( a1 @ SY840 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[172]) ).

thf(176,plain,
    ! [SV26: $i] :
      ( ( ( ~ ( irel @ sK1_SY740 @ SV26 ) )
        = $true )
      | ( ( ~ ( ~ ( irel @ SV26 @ ( sK11_SY647 @ SV26 ) )
              | ~ ~ ( a0 @ ( sK11_SY647 @ SV26 ) ) )
          | ! [SY841: $i] :
              ( ~ ( irel @ SV26 @ SY841 )
              | ( f @ SY841 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[173]) ).

thf(177,plain,
    ! [SV24: $i] :
      ( ( ( ~ ( irel @ SV24 @ ( sK9_SY639 @ SV24 ) )
          | ~ ~ ( ~ ! [SY837: $i] :
                      ( ~ ( irel @ ( sK9_SY639 @ SV24 ) @ SY837 )
                      | ( b0 @ SY837 ) )
                | ~ ~ ( ~ ( irel @ ( sK9_SY639 @ SV24 ) @ ( sK10_SY823 @ SV24 ) )
                      | ~ ~ ( a1 @ ( sK10_SY823 @ SV24 ) ) ) ) )
        = $false )
      | ( ( ! [SY838: $i] :
              ( ~ ( irel @ SV24 @ SY838 )
              | ( a0 @ SY838 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV24 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[174]) ).

thf(178,plain,
    ! [SV25: $i] :
      ( ( ( irel @ sK1_SY740 @ SV25 )
        = $false )
      | ( ( ~ ( ~ ( irel @ SV25 @ ( sK12_SY643 @ SV25 ) )
              | ~ ~ ( ~ ! [SY839: $i] :
                          ( ~ ( irel @ ( sK12_SY643 @ SV25 ) @ SY839 )
                          | ( b1 @ SY839 ) )
                    | ~ ~ ( ~ ( irel @ ( sK12_SY643 @ SV25 ) @ ( sK13_SY825 @ SV25 ) )
                          | ~ ~ ( b0 @ ( sK13_SY825 @ SV25 ) ) ) ) )
          | ! [SY840: $i] :
              ( ~ ( irel @ SV25 @ SY840 )
              | ( a1 @ SY840 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[175]) ).

thf(179,plain,
    ! [SV26: $i] :
      ( ( ( irel @ sK1_SY740 @ SV26 )
        = $false )
      | ( ( ~ ( ~ ( irel @ SV26 @ ( sK11_SY647 @ SV26 ) )
              | ~ ~ ( a0 @ ( sK11_SY647 @ SV26 ) ) )
          | ! [SY841: $i] :
              ( ~ ( irel @ SV26 @ SY841 )
              | ( f @ SY841 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[176]) ).

thf(180,plain,
    ! [SV24: $i] :
      ( ( ( ~ ( irel @ SV24 @ ( sK9_SY639 @ SV24 ) ) )
        = $false )
      | ( ( ! [SY838: $i] :
              ( ~ ( irel @ SV24 @ SY838 )
              | ( a0 @ SY838 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV24 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[177]) ).

thf(181,plain,
    ! [SV24: $i] :
      ( ( ( ~ ~ ( ~ ! [SY837: $i] :
                      ( ~ ( irel @ ( sK9_SY639 @ SV24 ) @ SY837 )
                      | ( b0 @ SY837 ) )
                | ~ ~ ( ~ ( irel @ ( sK9_SY639 @ SV24 ) @ ( sK10_SY823 @ SV24 ) )
                      | ~ ~ ( a1 @ ( sK10_SY823 @ SV24 ) ) ) ) )
        = $false )
      | ( ( ! [SY838: $i] :
              ( ~ ( irel @ SV24 @ SY838 )
              | ( a0 @ SY838 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV24 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[177]) ).

thf(182,plain,
    ! [SV25: $i] :
      ( ( ( ~ ( ~ ( irel @ SV25 @ ( sK12_SY643 @ SV25 ) )
              | ~ ~ ( ~ ! [SY839: $i] :
                          ( ~ ( irel @ ( sK12_SY643 @ SV25 ) @ SY839 )
                          | ( b1 @ SY839 ) )
                    | ~ ~ ( ~ ( irel @ ( sK12_SY643 @ SV25 ) @ ( sK13_SY825 @ SV25 ) )
                          | ~ ~ ( b0 @ ( sK13_SY825 @ SV25 ) ) ) ) ) )
        = $true )
      | ( ( ! [SY840: $i] :
              ( ~ ( irel @ SV25 @ SY840 )
              | ( a1 @ SY840 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV25 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[178]) ).

thf(183,plain,
    ! [SV26: $i] :
      ( ( ( ~ ( ~ ( irel @ SV26 @ ( sK11_SY647 @ SV26 ) )
              | ~ ~ ( a0 @ ( sK11_SY647 @ SV26 ) ) ) )
        = $true )
      | ( ( ! [SY841: $i] :
              ( ~ ( irel @ SV26 @ SY841 )
              | ( f @ SY841 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV26 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[179]) ).

thf(184,plain,
    ! [SV24: $i] :
      ( ( ( irel @ SV24 @ ( sK9_SY639 @ SV24 ) )
        = $true )
      | ( ( ! [SY838: $i] :
              ( ~ ( irel @ SV24 @ SY838 )
              | ( a0 @ SY838 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV24 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[180]) ).

thf(185,plain,
    ! [SV24: $i] :
      ( ( ( ~ ( ~ ! [SY837: $i] :
                    ( ~ ( irel @ ( sK9_SY639 @ SV24 ) @ SY837 )
                    | ( b0 @ SY837 ) )
              | ~ ~ ( ~ ( irel @ ( sK9_SY639 @ SV24 ) @ ( sK10_SY823 @ SV24 ) )
                    | ~ ~ ( a1 @ ( sK10_SY823 @ SV24 ) ) ) ) )
        = $true )
      | ( ( ! [SY838: $i] :
              ( ~ ( irel @ SV24 @ SY838 )
              | ( a0 @ SY838 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV24 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[181]) ).

thf(186,plain,
    ! [SV25: $i] :
      ( ( ( ~ ( irel @ SV25 @ ( sK12_SY643 @ SV25 ) )
          | ~ ~ ( ~ ! [SY839: $i] :
                      ( ~ ( irel @ ( sK12_SY643 @ SV25 ) @ SY839 )
                      | ( b1 @ SY839 ) )
                | ~ ~ ( ~ ( irel @ ( sK12_SY643 @ SV25 ) @ ( sK13_SY825 @ SV25 ) )
                      | ~ ~ ( b0 @ ( sK13_SY825 @ SV25 ) ) ) ) )
        = $false )
      | ( ( ! [SY840: $i] :
              ( ~ ( irel @ SV25 @ SY840 )
              | ( a1 @ SY840 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV25 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[182]) ).

thf(187,plain,
    ! [SV26: $i] :
      ( ( ( ~ ( irel @ SV26 @ ( sK11_SY647 @ SV26 ) )
          | ~ ~ ( a0 @ ( sK11_SY647 @ SV26 ) ) )
        = $false )
      | ( ( ! [SY841: $i] :
              ( ~ ( irel @ SV26 @ SY841 )
              | ( f @ SY841 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV26 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[183]) ).

thf(188,plain,
    ! [SV27: $i,SV24: $i] :
      ( ( ( ~ ( irel @ SV24 @ SV27 )
          | ( a0 @ SV27 ) )
        = $true )
      | ( ( irel @ SV24 @ ( sK9_SY639 @ SV24 ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV24 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[184]) ).

thf(189,plain,
    ! [SV24: $i] :
      ( ( ( ~ ! [SY837: $i] :
                ( ~ ( irel @ ( sK9_SY639 @ SV24 ) @ SY837 )
                | ( b0 @ SY837 ) )
          | ~ ~ ( ~ ( irel @ ( sK9_SY639 @ SV24 ) @ ( sK10_SY823 @ SV24 ) )
                | ~ ~ ( a1 @ ( sK10_SY823 @ SV24 ) ) ) )
        = $false )
      | ( ( ! [SY838: $i] :
              ( ~ ( irel @ SV24 @ SY838 )
              | ( a0 @ SY838 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV24 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[185]) ).

thf(190,plain,
    ! [SV25: $i] :
      ( ( ( ~ ( irel @ SV25 @ ( sK12_SY643 @ SV25 ) ) )
        = $false )
      | ( ( ! [SY840: $i] :
              ( ~ ( irel @ SV25 @ SY840 )
              | ( a1 @ SY840 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV25 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[186]) ).

thf(191,plain,
    ! [SV25: $i] :
      ( ( ( ~ ~ ( ~ ! [SY839: $i] :
                      ( ~ ( irel @ ( sK12_SY643 @ SV25 ) @ SY839 )
                      | ( b1 @ SY839 ) )
                | ~ ~ ( ~ ( irel @ ( sK12_SY643 @ SV25 ) @ ( sK13_SY825 @ SV25 ) )
                      | ~ ~ ( b0 @ ( sK13_SY825 @ SV25 ) ) ) ) )
        = $false )
      | ( ( ! [SY840: $i] :
              ( ~ ( irel @ SV25 @ SY840 )
              | ( a1 @ SY840 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV25 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[186]) ).

thf(192,plain,
    ! [SV26: $i] :
      ( ( ( ~ ( irel @ SV26 @ ( sK11_SY647 @ SV26 ) ) )
        = $false )
      | ( ( ! [SY841: $i] :
              ( ~ ( irel @ SV26 @ SY841 )
              | ( f @ SY841 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV26 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[187]) ).

thf(193,plain,
    ! [SV26: $i] :
      ( ( ( ~ ~ ( a0 @ ( sK11_SY647 @ SV26 ) ) )
        = $false )
      | ( ( ! [SY841: $i] :
              ( ~ ( irel @ SV26 @ SY841 )
              | ( f @ SY841 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV26 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[187]) ).

thf(194,plain,
    ! [SV27: $i,SV24: $i] :
      ( ( ( ~ ( irel @ SV24 @ SV27 ) )
        = $true )
      | ( ( a0 @ SV27 )
        = $true )
      | ( ( irel @ SV24 @ ( sK9_SY639 @ SV24 ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV24 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[188]) ).

thf(195,plain,
    ! [SV24: $i] :
      ( ( ( ~ ! [SY837: $i] :
                ( ~ ( irel @ ( sK9_SY639 @ SV24 ) @ SY837 )
                | ( b0 @ SY837 ) ) )
        = $false )
      | ( ( ! [SY838: $i] :
              ( ~ ( irel @ SV24 @ SY838 )
              | ( a0 @ SY838 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV24 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[189]) ).

thf(196,plain,
    ! [SV24: $i] :
      ( ( ( ~ ~ ( ~ ( irel @ ( sK9_SY639 @ SV24 ) @ ( sK10_SY823 @ SV24 ) )
                | ~ ~ ( a1 @ ( sK10_SY823 @ SV24 ) ) ) )
        = $false )
      | ( ( ! [SY838: $i] :
              ( ~ ( irel @ SV24 @ SY838 )
              | ( a0 @ SY838 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV24 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[189]) ).

thf(197,plain,
    ! [SV25: $i] :
      ( ( ( irel @ SV25 @ ( sK12_SY643 @ SV25 ) )
        = $true )
      | ( ( ! [SY840: $i] :
              ( ~ ( irel @ SV25 @ SY840 )
              | ( a1 @ SY840 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV25 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[190]) ).

thf(198,plain,
    ! [SV25: $i] :
      ( ( ( ~ ( ~ ! [SY839: $i] :
                    ( ~ ( irel @ ( sK12_SY643 @ SV25 ) @ SY839 )
                    | ( b1 @ SY839 ) )
              | ~ ~ ( ~ ( irel @ ( sK12_SY643 @ SV25 ) @ ( sK13_SY825 @ SV25 ) )
                    | ~ ~ ( b0 @ ( sK13_SY825 @ SV25 ) ) ) ) )
        = $true )
      | ( ( ! [SY840: $i] :
              ( ~ ( irel @ SV25 @ SY840 )
              | ( a1 @ SY840 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV25 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[191]) ).

thf(199,plain,
    ! [SV26: $i] :
      ( ( ( irel @ SV26 @ ( sK11_SY647 @ SV26 ) )
        = $true )
      | ( ( ! [SY841: $i] :
              ( ~ ( irel @ SV26 @ SY841 )
              | ( f @ SY841 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV26 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[192]) ).

thf(200,plain,
    ! [SV26: $i] :
      ( ( ( ~ ( a0 @ ( sK11_SY647 @ SV26 ) ) )
        = $true )
      | ( ( ! [SY841: $i] :
              ( ~ ( irel @ SV26 @ SY841 )
              | ( f @ SY841 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV26 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[193]) ).

thf(201,plain,
    ! [SV27: $i,SV24: $i] :
      ( ( ( irel @ SV24 @ SV27 )
        = $false )
      | ( ( a0 @ SV27 )
        = $true )
      | ( ( irel @ SV24 @ ( sK9_SY639 @ SV24 ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV24 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[194]) ).

thf(202,plain,
    ! [SV24: $i] :
      ( ( ( ! [SY837: $i] :
              ( ~ ( irel @ ( sK9_SY639 @ SV24 ) @ SY837 )
              | ( b0 @ SY837 ) ) )
        = $true )
      | ( ( ! [SY838: $i] :
              ( ~ ( irel @ SV24 @ SY838 )
              | ( a0 @ SY838 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV24 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[195]) ).

thf(203,plain,
    ! [SV24: $i] :
      ( ( ( ~ ( ~ ( irel @ ( sK9_SY639 @ SV24 ) @ ( sK10_SY823 @ SV24 ) )
              | ~ ~ ( a1 @ ( sK10_SY823 @ SV24 ) ) ) )
        = $true )
      | ( ( ! [SY838: $i] :
              ( ~ ( irel @ SV24 @ SY838 )
              | ( a0 @ SY838 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV24 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[196]) ).

thf(204,plain,
    ! [SV28: $i,SV25: $i] :
      ( ( ( ~ ( irel @ SV25 @ SV28 )
          | ( a1 @ SV28 ) )
        = $true )
      | ( ( irel @ SV25 @ ( sK12_SY643 @ SV25 ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV25 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[197]) ).

thf(205,plain,
    ! [SV25: $i] :
      ( ( ( ~ ! [SY839: $i] :
                ( ~ ( irel @ ( sK12_SY643 @ SV25 ) @ SY839 )
                | ( b1 @ SY839 ) )
          | ~ ~ ( ~ ( irel @ ( sK12_SY643 @ SV25 ) @ ( sK13_SY825 @ SV25 ) )
                | ~ ~ ( b0 @ ( sK13_SY825 @ SV25 ) ) ) )
        = $false )
      | ( ( ! [SY840: $i] :
              ( ~ ( irel @ SV25 @ SY840 )
              | ( a1 @ SY840 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV25 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[198]) ).

thf(206,plain,
    ! [SV29: $i,SV26: $i] :
      ( ( ( ~ ( irel @ SV26 @ SV29 )
          | ( f @ SV29 ) )
        = $true )
      | ( ( irel @ SV26 @ ( sK11_SY647 @ SV26 ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV26 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[199]) ).

thf(207,plain,
    ! [SV26: $i] :
      ( ( ( a0 @ ( sK11_SY647 @ SV26 ) )
        = $false )
      | ( ( ! [SY841: $i] :
              ( ~ ( irel @ SV26 @ SY841 )
              | ( f @ SY841 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV26 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[200]) ).

thf(208,plain,
    ! [SV30: $i,SV24: $i] :
      ( ( ( ~ ( irel @ ( sK9_SY639 @ SV24 ) @ SV30 )
          | ( b0 @ SV30 ) )
        = $true )
      | ( ( ! [SY838: $i] :
              ( ~ ( irel @ SV24 @ SY838 )
              | ( a0 @ SY838 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV24 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[202]) ).

thf(209,plain,
    ! [SV24: $i] :
      ( ( ( ~ ( irel @ ( sK9_SY639 @ SV24 ) @ ( sK10_SY823 @ SV24 ) )
          | ~ ~ ( a1 @ ( sK10_SY823 @ SV24 ) ) )
        = $false )
      | ( ( ! [SY838: $i] :
              ( ~ ( irel @ SV24 @ SY838 )
              | ( a0 @ SY838 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV24 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[203]) ).

thf(210,plain,
    ! [SV28: $i,SV25: $i] :
      ( ( ( ~ ( irel @ SV25 @ SV28 ) )
        = $true )
      | ( ( a1 @ SV28 )
        = $true )
      | ( ( irel @ SV25 @ ( sK12_SY643 @ SV25 ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV25 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[204]) ).

thf(211,plain,
    ! [SV25: $i] :
      ( ( ( ~ ! [SY839: $i] :
                ( ~ ( irel @ ( sK12_SY643 @ SV25 ) @ SY839 )
                | ( b1 @ SY839 ) ) )
        = $false )
      | ( ( ! [SY840: $i] :
              ( ~ ( irel @ SV25 @ SY840 )
              | ( a1 @ SY840 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV25 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[205]) ).

thf(212,plain,
    ! [SV25: $i] :
      ( ( ( ~ ~ ( ~ ( irel @ ( sK12_SY643 @ SV25 ) @ ( sK13_SY825 @ SV25 ) )
                | ~ ~ ( b0 @ ( sK13_SY825 @ SV25 ) ) ) )
        = $false )
      | ( ( ! [SY840: $i] :
              ( ~ ( irel @ SV25 @ SY840 )
              | ( a1 @ SY840 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV25 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[205]) ).

thf(213,plain,
    ! [SV29: $i,SV26: $i] :
      ( ( ( ~ ( irel @ SV26 @ SV29 ) )
        = $true )
      | ( ( f @ SV29 )
        = $true )
      | ( ( irel @ SV26 @ ( sK11_SY647 @ SV26 ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV26 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[206]) ).

thf(214,plain,
    ! [SV31: $i,SV26: $i] :
      ( ( ( ~ ( irel @ SV26 @ SV31 )
          | ( f @ SV31 ) )
        = $true )
      | ( ( a0 @ ( sK11_SY647 @ SV26 ) )
        = $false )
      | ( ( irel @ sK1_SY740 @ SV26 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[207]) ).

thf(215,plain,
    ! [SV30: $i,SV24: $i] :
      ( ( ( ~ ( irel @ ( sK9_SY639 @ SV24 ) @ SV30 ) )
        = $true )
      | ( ( b0 @ SV30 )
        = $true )
      | ( ( ! [SY838: $i] :
              ( ~ ( irel @ SV24 @ SY838 )
              | ( a0 @ SY838 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV24 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[208]) ).

thf(216,plain,
    ! [SV24: $i] :
      ( ( ( ~ ( irel @ ( sK9_SY639 @ SV24 ) @ ( sK10_SY823 @ SV24 ) ) )
        = $false )
      | ( ( ! [SY838: $i] :
              ( ~ ( irel @ SV24 @ SY838 )
              | ( a0 @ SY838 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV24 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[209]) ).

thf(217,plain,
    ! [SV24: $i] :
      ( ( ( ~ ~ ( a1 @ ( sK10_SY823 @ SV24 ) ) )
        = $false )
      | ( ( ! [SY838: $i] :
              ( ~ ( irel @ SV24 @ SY838 )
              | ( a0 @ SY838 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV24 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[209]) ).

thf(218,plain,
    ! [SV28: $i,SV25: $i] :
      ( ( ( irel @ SV25 @ SV28 )
        = $false )
      | ( ( a1 @ SV28 )
        = $true )
      | ( ( irel @ SV25 @ ( sK12_SY643 @ SV25 ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV25 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[210]) ).

thf(219,plain,
    ! [SV25: $i] :
      ( ( ( ! [SY839: $i] :
              ( ~ ( irel @ ( sK12_SY643 @ SV25 ) @ SY839 )
              | ( b1 @ SY839 ) ) )
        = $true )
      | ( ( ! [SY840: $i] :
              ( ~ ( irel @ SV25 @ SY840 )
              | ( a1 @ SY840 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV25 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[211]) ).

thf(220,plain,
    ! [SV25: $i] :
      ( ( ( ~ ( ~ ( irel @ ( sK12_SY643 @ SV25 ) @ ( sK13_SY825 @ SV25 ) )
              | ~ ~ ( b0 @ ( sK13_SY825 @ SV25 ) ) ) )
        = $true )
      | ( ( ! [SY840: $i] :
              ( ~ ( irel @ SV25 @ SY840 )
              | ( a1 @ SY840 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV25 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[212]) ).

thf(221,plain,
    ! [SV29: $i,SV26: $i] :
      ( ( ( irel @ SV26 @ SV29 )
        = $false )
      | ( ( f @ SV29 )
        = $true )
      | ( ( irel @ SV26 @ ( sK11_SY647 @ SV26 ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV26 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[213]) ).

thf(222,plain,
    ! [SV31: $i,SV26: $i] :
      ( ( ( ~ ( irel @ SV26 @ SV31 ) )
        = $true )
      | ( ( f @ SV31 )
        = $true )
      | ( ( a0 @ ( sK11_SY647 @ SV26 ) )
        = $false )
      | ( ( irel @ sK1_SY740 @ SV26 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[214]) ).

thf(223,plain,
    ! [SV30: $i,SV24: $i] :
      ( ( ( irel @ ( sK9_SY639 @ SV24 ) @ SV30 )
        = $false )
      | ( ( b0 @ SV30 )
        = $true )
      | ( ( ! [SY838: $i] :
              ( ~ ( irel @ SV24 @ SY838 )
              | ( a0 @ SY838 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV24 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[215]) ).

thf(224,plain,
    ! [SV24: $i] :
      ( ( ( irel @ ( sK9_SY639 @ SV24 ) @ ( sK10_SY823 @ SV24 ) )
        = $true )
      | ( ( ! [SY838: $i] :
              ( ~ ( irel @ SV24 @ SY838 )
              | ( a0 @ SY838 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV24 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[216]) ).

thf(225,plain,
    ! [SV24: $i] :
      ( ( ( ~ ( a1 @ ( sK10_SY823 @ SV24 ) ) )
        = $true )
      | ( ( ! [SY838: $i] :
              ( ~ ( irel @ SV24 @ SY838 )
              | ( a0 @ SY838 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV24 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[217]) ).

thf(226,plain,
    ! [SV32: $i,SV25: $i] :
      ( ( ( ~ ( irel @ ( sK12_SY643 @ SV25 ) @ SV32 )
          | ( b1 @ SV32 ) )
        = $true )
      | ( ( ! [SY840: $i] :
              ( ~ ( irel @ SV25 @ SY840 )
              | ( a1 @ SY840 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV25 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[219]) ).

thf(227,plain,
    ! [SV25: $i] :
      ( ( ( ~ ( irel @ ( sK12_SY643 @ SV25 ) @ ( sK13_SY825 @ SV25 ) )
          | ~ ~ ( b0 @ ( sK13_SY825 @ SV25 ) ) )
        = $false )
      | ( ( ! [SY840: $i] :
              ( ~ ( irel @ SV25 @ SY840 )
              | ( a1 @ SY840 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV25 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[220]) ).

thf(228,plain,
    ! [SV31: $i,SV26: $i] :
      ( ( ( irel @ SV26 @ SV31 )
        = $false )
      | ( ( f @ SV31 )
        = $true )
      | ( ( a0 @ ( sK11_SY647 @ SV26 ) )
        = $false )
      | ( ( irel @ sK1_SY740 @ SV26 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[222]) ).

thf(229,plain,
    ! [SV30: $i,SV33: $i,SV24: $i] :
      ( ( ( ~ ( irel @ SV24 @ SV33 )
          | ( a0 @ SV33 ) )
        = $true )
      | ( ( b0 @ SV30 )
        = $true )
      | ( ( irel @ ( sK9_SY639 @ SV24 ) @ SV30 )
        = $false )
      | ( ( irel @ sK1_SY740 @ SV24 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[223]) ).

thf(230,plain,
    ! [SV34: $i,SV24: $i] :
      ( ( ( ~ ( irel @ SV24 @ SV34 )
          | ( a0 @ SV34 ) )
        = $true )
      | ( ( irel @ ( sK9_SY639 @ SV24 ) @ ( sK10_SY823 @ SV24 ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV24 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[224]) ).

thf(231,plain,
    ! [SV24: $i] :
      ( ( ( a1 @ ( sK10_SY823 @ SV24 ) )
        = $false )
      | ( ( ! [SY838: $i] :
              ( ~ ( irel @ SV24 @ SY838 )
              | ( a0 @ SY838 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV24 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[225]) ).

thf(232,plain,
    ! [SV32: $i,SV25: $i] :
      ( ( ( ~ ( irel @ ( sK12_SY643 @ SV25 ) @ SV32 ) )
        = $true )
      | ( ( b1 @ SV32 )
        = $true )
      | ( ( ! [SY840: $i] :
              ( ~ ( irel @ SV25 @ SY840 )
              | ( a1 @ SY840 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV25 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[226]) ).

thf(233,plain,
    ! [SV25: $i] :
      ( ( ( ~ ( irel @ ( sK12_SY643 @ SV25 ) @ ( sK13_SY825 @ SV25 ) ) )
        = $false )
      | ( ( ! [SY840: $i] :
              ( ~ ( irel @ SV25 @ SY840 )
              | ( a1 @ SY840 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV25 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[227]) ).

thf(234,plain,
    ! [SV25: $i] :
      ( ( ( ~ ~ ( b0 @ ( sK13_SY825 @ SV25 ) ) )
        = $false )
      | ( ( ! [SY840: $i] :
              ( ~ ( irel @ SV25 @ SY840 )
              | ( a1 @ SY840 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV25 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[227]) ).

thf(235,plain,
    ! [SV30: $i,SV33: $i,SV24: $i] :
      ( ( ( ~ ( irel @ SV24 @ SV33 ) )
        = $true )
      | ( ( a0 @ SV33 )
        = $true )
      | ( ( b0 @ SV30 )
        = $true )
      | ( ( irel @ ( sK9_SY639 @ SV24 ) @ SV30 )
        = $false )
      | ( ( irel @ sK1_SY740 @ SV24 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[229]) ).

thf(236,plain,
    ! [SV34: $i,SV24: $i] :
      ( ( ( ~ ( irel @ SV24 @ SV34 ) )
        = $true )
      | ( ( a0 @ SV34 )
        = $true )
      | ( ( irel @ ( sK9_SY639 @ SV24 ) @ ( sK10_SY823 @ SV24 ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV24 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[230]) ).

thf(237,plain,
    ! [SV35: $i,SV24: $i] :
      ( ( ( ~ ( irel @ SV24 @ SV35 )
          | ( a0 @ SV35 ) )
        = $true )
      | ( ( a1 @ ( sK10_SY823 @ SV24 ) )
        = $false )
      | ( ( irel @ sK1_SY740 @ SV24 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[231]) ).

thf(238,plain,
    ! [SV32: $i,SV25: $i] :
      ( ( ( irel @ ( sK12_SY643 @ SV25 ) @ SV32 )
        = $false )
      | ( ( b1 @ SV32 )
        = $true )
      | ( ( ! [SY840: $i] :
              ( ~ ( irel @ SV25 @ SY840 )
              | ( a1 @ SY840 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV25 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[232]) ).

thf(239,plain,
    ! [SV25: $i] :
      ( ( ( irel @ ( sK12_SY643 @ SV25 ) @ ( sK13_SY825 @ SV25 ) )
        = $true )
      | ( ( ! [SY840: $i] :
              ( ~ ( irel @ SV25 @ SY840 )
              | ( a1 @ SY840 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV25 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[233]) ).

thf(240,plain,
    ! [SV25: $i] :
      ( ( ( ~ ( b0 @ ( sK13_SY825 @ SV25 ) ) )
        = $true )
      | ( ( ! [SY840: $i] :
              ( ~ ( irel @ SV25 @ SY840 )
              | ( a1 @ SY840 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV25 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[234]) ).

thf(241,plain,
    ! [SV30: $i,SV33: $i,SV24: $i] :
      ( ( ( irel @ SV24 @ SV33 )
        = $false )
      | ( ( a0 @ SV33 )
        = $true )
      | ( ( b0 @ SV30 )
        = $true )
      | ( ( irel @ ( sK9_SY639 @ SV24 ) @ SV30 )
        = $false )
      | ( ( irel @ sK1_SY740 @ SV24 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[235]) ).

thf(242,plain,
    ! [SV34: $i,SV24: $i] :
      ( ( ( irel @ SV24 @ SV34 )
        = $false )
      | ( ( a0 @ SV34 )
        = $true )
      | ( ( irel @ ( sK9_SY639 @ SV24 ) @ ( sK10_SY823 @ SV24 ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV24 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[236]) ).

thf(243,plain,
    ! [SV35: $i,SV24: $i] :
      ( ( ( ~ ( irel @ SV24 @ SV35 ) )
        = $true )
      | ( ( a0 @ SV35 )
        = $true )
      | ( ( a1 @ ( sK10_SY823 @ SV24 ) )
        = $false )
      | ( ( irel @ sK1_SY740 @ SV24 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[237]) ).

thf(244,plain,
    ! [SV32: $i,SV36: $i,SV25: $i] :
      ( ( ( ~ ( irel @ SV25 @ SV36 )
          | ( a1 @ SV36 ) )
        = $true )
      | ( ( b1 @ SV32 )
        = $true )
      | ( ( irel @ ( sK12_SY643 @ SV25 ) @ SV32 )
        = $false )
      | ( ( irel @ sK1_SY740 @ SV25 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[238]) ).

thf(245,plain,
    ! [SV37: $i,SV25: $i] :
      ( ( ( ~ ( irel @ SV25 @ SV37 )
          | ( a1 @ SV37 ) )
        = $true )
      | ( ( irel @ ( sK12_SY643 @ SV25 ) @ ( sK13_SY825 @ SV25 ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV25 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[239]) ).

thf(246,plain,
    ! [SV25: $i] :
      ( ( ( b0 @ ( sK13_SY825 @ SV25 ) )
        = $false )
      | ( ( ! [SY840: $i] :
              ( ~ ( irel @ SV25 @ SY840 )
              | ( a1 @ SY840 ) ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV25 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[240]) ).

thf(247,plain,
    ! [SV35: $i,SV24: $i] :
      ( ( ( irel @ SV24 @ SV35 )
        = $false )
      | ( ( a0 @ SV35 )
        = $true )
      | ( ( a1 @ ( sK10_SY823 @ SV24 ) )
        = $false )
      | ( ( irel @ sK1_SY740 @ SV24 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[243]) ).

thf(248,plain,
    ! [SV32: $i,SV36: $i,SV25: $i] :
      ( ( ( ~ ( irel @ SV25 @ SV36 ) )
        = $true )
      | ( ( a1 @ SV36 )
        = $true )
      | ( ( b1 @ SV32 )
        = $true )
      | ( ( irel @ ( sK12_SY643 @ SV25 ) @ SV32 )
        = $false )
      | ( ( irel @ sK1_SY740 @ SV25 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[244]) ).

thf(249,plain,
    ! [SV37: $i,SV25: $i] :
      ( ( ( ~ ( irel @ SV25 @ SV37 ) )
        = $true )
      | ( ( a1 @ SV37 )
        = $true )
      | ( ( irel @ ( sK12_SY643 @ SV25 ) @ ( sK13_SY825 @ SV25 ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV25 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[245]) ).

thf(250,plain,
    ! [SV38: $i,SV25: $i] :
      ( ( ( ~ ( irel @ SV25 @ SV38 )
          | ( a1 @ SV38 ) )
        = $true )
      | ( ( b0 @ ( sK13_SY825 @ SV25 ) )
        = $false )
      | ( ( irel @ sK1_SY740 @ SV25 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[246]) ).

thf(251,plain,
    ! [SV32: $i,SV36: $i,SV25: $i] :
      ( ( ( irel @ SV25 @ SV36 )
        = $false )
      | ( ( a1 @ SV36 )
        = $true )
      | ( ( b1 @ SV32 )
        = $true )
      | ( ( irel @ ( sK12_SY643 @ SV25 ) @ SV32 )
        = $false )
      | ( ( irel @ sK1_SY740 @ SV25 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[248]) ).

thf(252,plain,
    ! [SV37: $i,SV25: $i] :
      ( ( ( irel @ SV25 @ SV37 )
        = $false )
      | ( ( a1 @ SV37 )
        = $true )
      | ( ( irel @ ( sK12_SY643 @ SV25 ) @ ( sK13_SY825 @ SV25 ) )
        = $true )
      | ( ( irel @ sK1_SY740 @ SV25 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[249]) ).

thf(253,plain,
    ! [SV38: $i,SV25: $i] :
      ( ( ( ~ ( irel @ SV25 @ SV38 ) )
        = $true )
      | ( ( a1 @ SV38 )
        = $true )
      | ( ( b0 @ ( sK13_SY825 @ SV25 ) )
        = $false )
      | ( ( irel @ sK1_SY740 @ SV25 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[250]) ).

thf(254,plain,
    ! [SV38: $i,SV25: $i] :
      ( ( ( irel @ SV25 @ SV38 )
        = $false )
      | ( ( a1 @ SV38 )
        = $true )
      | ( ( b0 @ ( sK13_SY825 @ SV25 ) )
        = $false )
      | ( ( irel @ sK1_SY740 @ SV25 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[253]) ).

thf(255,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[140,254,252,251,247,242,241,228,221,218,201,165,162,160]) ).

thf(256,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[255,135]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SYO069^4.001 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33  % Computer : n004.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 : Fri Jul  8 18:32:52 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: 2734
% 0.12/0.34  
% 0.12/0.34   Contains.Choice.Funs: false
% 0.12/0.35  (rf:0,axioms:2,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:4,loop_count:0,foatp_calls:0,translation:fof_full).........................................................................................eprover: CPU time limit exceeded, terminating
% 25.52/25.74  ..........eprover: CPU time limit exceeded, terminating
% 51.22/51.43  .......eprover: CPU time limit exceeded, terminating
% 76.67/76.86  .
% 76.67/76.86  (rf:0,axioms:2,ps:3,u:3,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:4,loop_count:0,foatp_calls:0,translation:fof_full)............................
% 77.11/77.37  
% 77.11/77.37  ********************************
% 77.11/77.37  *   All subproblems solved!    *
% 77.11/77.37  ********************************
% 77.11/77.37  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,ps:3,u:3,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:255,loop_count:0,foatp_calls:1,translation:fof_full)
% 77.11/77.38  
% 77.11/77.38  %**** Beginning of derivation protocol ****
% 77.11/77.38  % SZS output start CNFRefutation
% See solution above
% 77.11/77.38  
% 77.11/77.38  %**** End of derivation protocol ****
% 77.11/77.38  %**** no. of clauses in derivation: 256 ****
% 77.11/77.38  %**** clause counter: 255 ****
% 77.11/77.38  
% 77.11/77.38  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,ps:3,u:3,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:255,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------