TSTP Solution File: SWV435^4 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SWV435^4 : TPTP v8.1.0. Released v3.6.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n009.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 : Wed Jul 20 20:12:43 EDT 2022

% Result   : Theorem 0.20s 0.40s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   63
% Syntax   : Number of formulae    :  130 (  54 unt;  35 typ;  24 def)
%            Number of atoms       :  495 ( 149 equ;   0 cnn)
%            Maximal formula atoms :    8 (   5 avg)
%            Number of connectives :  564 (  90   ~; 119   |;   2   &; 352   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :  163 ( 163   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   37 (  34 usr;   5 con; 0-3 aty)
%            Number of variables   :  186 (  41   ^ 141   !;   4   ?; 186   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_individuals,type,
    individuals: $tType ).

thf(tp_a,type,
    a: $i > $o ).

thf(tp_current_world,type,
    current_world: $i ).

thf(tp_icl_and,type,
    icl_and: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(tp_icl_atom,type,
    icl_atom: ( $i > $o ) > $i > $o ).

thf(tp_icl_false,type,
    icl_false: $i > $o ).

thf(tp_icl_impl,type,
    icl_impl: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(tp_icl_or,type,
    icl_or: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(tp_icl_princ,type,
    icl_princ: ( $i > $o ) > $i > $o ).

thf(tp_icl_says,type,
    icl_says: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(tp_icl_true,type,
    icl_true: $i > $o ).

thf(tp_iclval,type,
    iclval: ( $i > $o ) > $o ).

thf(tp_mall,type,
    mall: ( individuals > $i > $o ) > $i > $o ).

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

thf(tp_mbox,type,
    mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).

thf(tp_mcountersatisfiable,type,
    mcountersatisfiable: ( $i > $o ) > $o ).

thf(tp_mdia,type,
    mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).

thf(tp_mexists,type,
    mexists: ( individuals > $i > $o ) > $i > $o ).

thf(tp_mfalse,type,
    mfalse: $i > $o ).

thf(tp_miff,type,
    miff: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(tp_mimpl,type,
    mimpl: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(tp_minvalid,type,
    minvalid: ( $i > $o ) > $o ).

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

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

thf(tp_msatisfiable,type,
    msatisfiable: ( $i > $o ) > $o ).

thf(tp_mtrue,type,
    mtrue: $i > $o ).

thf(tp_mvalid,type,
    mvalid: ( $i > $o ) > $o ).

thf(tp_prop_a,type,
    prop_a: $i > $o ).

thf(tp_prop_b,type,
    prop_b: $i > $o ).

thf(tp_prop_c,type,
    prop_c: $i > $o ).

thf(tp_rel,type,
    rel: $i > $i > $o ).

thf(tp_sK1_SX0,type,
    sK1_SX0: $i ).

thf(tp_sK2_SY10,type,
    sK2_SY10: $i ).

thf(tp_sK3_SY6,type,
    sK3_SY6: ( $i > $o ) > $i > $i ).

thf(tp_sK4_SY9,type,
    sK4_SY9: ( $i > $o ) > $i > $i ).

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

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

thf(icl_false,definition,
    icl_false = mfalse,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',icl_false) ).

thf(icl_impl,definition,
    ( icl_impl
    = ( ^ [A: $i > $o,B: $i > $o] : ( mbox @ rel @ ( mimpl @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',icl_impl) ).

thf(icl_or,definition,
    ( icl_or
    = ( ^ [A: $i > $o,B: $i > $o] : ( mor @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',icl_or) ).

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

thf(icl_says,definition,
    ( icl_says
    = ( ^ [A: $i > $o,S: $i > $o] : ( mbox @ rel @ ( mor @ A @ S ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',icl_says) ).

thf(icl_true,definition,
    icl_true = mtrue,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',icl_true) ).

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

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

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

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

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

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

thf(mfalse,definition,
    ( mfalse
    = ( ^ [X: $i] : $false ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mfalse) ).

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

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

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

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

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

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

thf(1,axiom,
    ( ( icl_princ @ a )
    = icl_true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).

thf(2,axiom,
    ! [B: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ rel @ B ) @ ( mbox @ rel @ ( mbox @ rel @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',trans_axiom) ).

thf(3,axiom,
    ! [A: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ rel @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',refl_axiom) ).

thf(4,conjecture,
    iclval @ ( icl_says @ ( icl_princ @ a ) @ icl_false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',untrust) ).

thf(5,negated_conjecture,
    ( ( iclval @ ( icl_says @ ( icl_princ @ a ) @ icl_false ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[4]) ).

thf(6,plain,
    ( ( ~ ( iclval @ ( icl_says @ ( icl_princ @ a ) @ icl_false ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[5]) ).

thf(7,plain,
    ( ( ! [A: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ rel @ A ) @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[3]) ).

thf(8,plain,
    ( ( ! [B: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ rel @ B ) @ ( mbox @ rel @ ( mbox @ rel @ B ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2]) ).

thf(9,plain,
    ( ( ( icl_princ @ a )
      = icl_true )
    = $true ),
    inference(copy,[status(thm)],[1]) ).

thf(10,plain,
    ( ( ~ ( iclval @ ( icl_says @ ( icl_princ @ a ) @ icl_false ) ) )
    = $true ),
    inference(copy,[status(thm)],[6]) ).

thf(11,plain,
    ( ( ! [SX0: $i > $o,SX1: $i] :
          ( ~ ! [SX2: $i] :
                ( ~ ( rel @ SX1 @ SX2 )
                | ( SX0 @ SX2 ) )
          | ! [SX2: $i] :
              ( ~ ( rel @ SX1 @ SX2 )
              | ! [SX3: $i] :
                  ( ~ ( rel @ SX2 @ SX3 )
                  | ( SX0 @ SX3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8,icl_and,icl_atom,icl_false,icl_impl,icl_or,icl_princ,icl_says,icl_true,iclval,mall,mand,mbox,mcountersatisfiable,mdia,mexists,mfalse,miff,mimpl,minvalid,mnot,mor,msatisfiable,mtrue,mvalid]) ).

thf(12,plain,
    ( ( ! [SX0: $i > $o,SX1: $i] :
          ( ~ ! [SX2: $i] :
                ( ~ ( rel @ SX1 @ SX2 )
                | ( SX0 @ SX2 ) )
          | ( SX0 @ SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7,icl_and,icl_atom,icl_false,icl_impl,icl_or,icl_princ,icl_says,icl_true,iclval,mall,mand,mbox,mcountersatisfiable,mdia,mexists,mfalse,miff,mimpl,minvalid,mnot,mor,msatisfiable,mtrue,mvalid]) ).

thf(13,plain,
    ( ( a
      = ( ^ [SX0: $i] : $true ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9,icl_and,icl_atom,icl_false,icl_impl,icl_or,icl_princ,icl_says,icl_true,iclval,mall,mand,mbox,mcountersatisfiable,mdia,mexists,mfalse,miff,mimpl,minvalid,mnot,mor,msatisfiable,mtrue,mvalid]) ).

thf(14,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( rel @ SX0 @ SX1 )
            | ( a @ SX1 )
            | $false ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10,icl_and,icl_atom,icl_false,icl_impl,icl_or,icl_princ,icl_says,icl_true,iclval,mall,mand,mbox,mcountersatisfiable,mdia,mexists,mfalse,miff,mimpl,minvalid,mnot,mor,msatisfiable,mtrue,mvalid]) ).

thf(15,plain,
    ! [SV1: $i > $o] :
      ( ( ! [SY0: $i] :
            ( ~ ! [SY1: $i] :
                  ( ~ ( rel @ SY0 @ SY1 )
                  | ( SV1 @ SY1 ) )
            | ! [SY2: $i] :
                ( ~ ( rel @ SY0 @ SY2 )
                | ! [SY3: $i] :
                    ( ~ ( rel @ SY2 @ SY3 )
                    | ( SV1 @ SY3 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11]) ).

thf(16,plain,
    ! [SV2: $i > $o] :
      ( ( ! [SY4: $i] :
            ( ~ ! [SY5: $i] :
                  ( ~ ( rel @ SY4 @ SY5 )
                  | ( SV2 @ SY5 ) )
            | ( SV2 @ SY4 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12]) ).

thf(17,plain,
    ( ( ! [SV3: $i] :
          ( ( a @ SV3 )
          = $true ) )
    = $true ),
    inference(extcnf_equal_pos,[status(thm)],[13]) ).

thf(18,plain,
    ( ( a
      = ( ^ [SX0: $i] : $true ) )
    = $true ),
    inference(extcnf_equal_pos,[status(thm)],[13]) ).

thf(19,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( rel @ SX0 @ SX1 )
          | ( a @ SX1 )
          | $false ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[14]) ).

thf(20,plain,
    ! [SV1: $i > $o,SV4: $i] :
      ( ( ~ ! [SY6: $i] :
              ( ~ ( rel @ SV4 @ SY6 )
              | ( SV1 @ SY6 ) )
        | ! [SY7: $i] :
            ( ~ ( rel @ SV4 @ SY7 )
            | ! [SY3: $i] :
                ( ~ ( rel @ SY7 @ SY3 )
                | ( SV1 @ SY3 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[15]) ).

thf(21,plain,
    ! [SV2: $i > $o,SV5: $i] :
      ( ( ~ ! [SY9: $i] :
              ( ~ ( rel @ SV5 @ SY9 )
              | ( SV2 @ SY9 ) )
        | ( SV2 @ SV5 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[16]) ).

thf(22,plain,
    ! [SV6: $i] :
      ( ( ( a @ SV6 )
        = $true )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[17]) ).

thf(23,plain,
    ( ( ! [SY10: $i] :
          ( ~ ( rel @ sK1_SX0 @ SY10 )
          | ( a @ SY10 )
          | $false ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[19]) ).

thf(24,plain,
    ! [SV1: $i > $o,SV4: $i] :
      ( ( ( ~ ! [SY6: $i] :
                ( ~ ( rel @ SV4 @ SY6 )
                | ( SV1 @ SY6 ) ) )
        = $true )
      | ( ( ! [SY7: $i] :
              ( ~ ( rel @ SV4 @ SY7 )
              | ! [SY3: $i] :
                  ( ~ ( rel @ SY7 @ SY3 )
                  | ( SV1 @ SY3 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[20]) ).

thf(25,plain,
    ! [SV2: $i > $o,SV5: $i] :
      ( ( ( ~ ! [SY9: $i] :
                ( ~ ( rel @ SV5 @ SY9 )
                | ( SV2 @ SY9 ) ) )
        = $true )
      | ( ( SV2 @ SV5 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[21]) ).

thf(26,plain,
    ! [SV6: $i] :
      ( ( ~ ( ( a @ SV6 )
            | $true )
        | ~ ( ~ ( a @ SV6 )
            | ~ $true ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[22]) ).

thf(27,plain,
    ! [SV6: $i] :
      ( ( ( a @ SV6 )
        = $true )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[22]) ).

thf(28,plain,
    ( ( ~ ( rel @ sK1_SX0 @ sK2_SY10 )
      | ( a @ sK2_SY10 )
      | $false )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[23]) ).

thf(29,plain,
    ! [SV1: $i > $o,SV4: $i] :
      ( ( ( ! [SY6: $i] :
              ( ~ ( rel @ SV4 @ SY6 )
              | ( SV1 @ SY6 ) ) )
        = $false )
      | ( ( ! [SY7: $i] :
              ( ~ ( rel @ SV4 @ SY7 )
              | ! [SY3: $i] :
                  ( ~ ( rel @ SY7 @ SY3 )
                  | ( SV1 @ SY3 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[24]) ).

thf(30,plain,
    ! [SV2: $i > $o,SV5: $i] :
      ( ( ( ! [SY9: $i] :
              ( ~ ( rel @ SV5 @ SY9 )
              | ( SV2 @ SY9 ) ) )
        = $false )
      | ( ( SV2 @ SV5 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[25]) ).

thf(31,plain,
    ! [SV6: $i] :
      ( ( ( ~ ( ( a @ SV6 )
              | $true ) )
        = $true )
      | ( ( ~ ( ~ ( a @ SV6 )
              | ~ $true ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[26]) ).

thf(32,plain,
    ( ( ~ ( rel @ sK1_SX0 @ sK2_SY10 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[28]) ).

thf(33,plain,
    ( ( ( a @ sK2_SY10 )
      | $false )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[28]) ).

thf(34,plain,
    ! [SV1: $i > $o,SV4: $i] :
      ( ( ( ~ ( rel @ SV4 @ ( sK3_SY6 @ SV1 @ SV4 ) )
          | ( SV1 @ ( sK3_SY6 @ SV1 @ SV4 ) ) )
        = $false )
      | ( ( ! [SY7: $i] :
              ( ~ ( rel @ SV4 @ SY7 )
              | ! [SY3: $i] :
                  ( ~ ( rel @ SY7 @ SY3 )
                  | ( SV1 @ SY3 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[29]) ).

thf(35,plain,
    ! [SV2: $i > $o,SV5: $i] :
      ( ( ( ~ ( rel @ SV5 @ ( sK4_SY9 @ SV2 @ SV5 ) )
          | ( SV2 @ ( sK4_SY9 @ SV2 @ SV5 ) ) )
        = $false )
      | ( ( SV2 @ SV5 )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[30]) ).

thf(36,plain,
    ! [SV6: $i] :
      ( ( ( ( a @ SV6 )
          | $true )
        = $false )
      | ( ( ~ ( ~ ( a @ SV6 )
              | ~ $true ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[31]) ).

thf(37,plain,
    ( ( rel @ sK1_SX0 @ sK2_SY10 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[32]) ).

thf(38,plain,
    ( ( a @ sK2_SY10 )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[33]) ).

thf(39,plain,
    $false = $false,
    inference(extcnf_or_neg,[status(thm)],[33]) ).

thf(40,plain,
    ! [SV1: $i > $o,SV4: $i] :
      ( ( ( ~ ( rel @ SV4 @ ( sK3_SY6 @ SV1 @ SV4 ) ) )
        = $false )
      | ( ( ! [SY7: $i] :
              ( ~ ( rel @ SV4 @ SY7 )
              | ! [SY3: $i] :
                  ( ~ ( rel @ SY7 @ SY3 )
                  | ( SV1 @ SY3 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[34]) ).

thf(41,plain,
    ! [SV4: $i,SV1: $i > $o] :
      ( ( ( SV1 @ ( sK3_SY6 @ SV1 @ SV4 ) )
        = $false )
      | ( ( ! [SY7: $i] :
              ( ~ ( rel @ SV4 @ SY7 )
              | ! [SY3: $i] :
                  ( ~ ( rel @ SY7 @ SY3 )
                  | ( SV1 @ SY3 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[34]) ).

thf(42,plain,
    ! [SV2: $i > $o,SV5: $i] :
      ( ( ( ~ ( rel @ SV5 @ ( sK4_SY9 @ SV2 @ SV5 ) ) )
        = $false )
      | ( ( SV2 @ SV5 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[35]) ).

thf(43,plain,
    ! [SV5: $i,SV2: $i > $o] :
      ( ( ( SV2 @ ( sK4_SY9 @ SV2 @ SV5 ) )
        = $false )
      | ( ( SV2 @ SV5 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[35]) ).

thf(44,plain,
    ! [SV6: $i] :
      ( ( ( a @ SV6 )
        = $false )
      | ( ( ~ ( ~ ( a @ SV6 )
              | ~ $true ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[36]) ).

thf(45,plain,
    ! [SV6: $i] :
      ( ( $true = $false )
      | ( ( ~ ( ~ ( a @ SV6 )
              | ~ $true ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[36]) ).

thf(46,plain,
    ! [SV1: $i > $o,SV4: $i] :
      ( ( ( rel @ SV4 @ ( sK3_SY6 @ SV1 @ SV4 ) )
        = $true )
      | ( ( ! [SY7: $i] :
              ( ~ ( rel @ SV4 @ SY7 )
              | ! [SY3: $i] :
                  ( ~ ( rel @ SY7 @ SY3 )
                  | ( SV1 @ SY3 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[40]) ).

thf(47,plain,
    ! [SV1: $i > $o,SV7: $i,SV4: $i] :
      ( ( ( ~ ( rel @ SV4 @ SV7 )
          | ! [SY11: $i] :
              ( ~ ( rel @ SV7 @ SY11 )
              | ( SV1 @ SY11 ) ) )
        = $true )
      | ( ( SV1 @ ( sK3_SY6 @ SV1 @ SV4 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[41]) ).

thf(48,plain,
    ! [SV2: $i > $o,SV5: $i] :
      ( ( ( rel @ SV5 @ ( sK4_SY9 @ SV2 @ SV5 ) )
        = $true )
      | ( ( SV2 @ SV5 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[42]) ).

thf(49,plain,
    ! [SV6: $i] :
      ( ( ( ~ ( a @ SV6 )
          | ~ $true )
        = $false )
      | ( ( a @ SV6 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[44]) ).

thf(50,plain,
    ! [SV6: $i] :
      ( ( ( ~ ( a @ SV6 )
          | ~ $true )
        = $false )
      | ( $true = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[45]) ).

thf(51,plain,
    ! [SV1: $i > $o,SV8: $i,SV4: $i] :
      ( ( ( ~ ( rel @ SV4 @ SV8 )
          | ! [SY12: $i] :
              ( ~ ( rel @ SV8 @ SY12 )
              | ( SV1 @ SY12 ) ) )
        = $true )
      | ( ( rel @ SV4 @ ( sK3_SY6 @ SV1 @ SV4 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[46]) ).

thf(52,plain,
    ! [SV1: $i > $o,SV7: $i,SV4: $i] :
      ( ( ( ~ ( rel @ SV4 @ SV7 ) )
        = $true )
      | ( ( ! [SY11: $i] :
              ( ~ ( rel @ SV7 @ SY11 )
              | ( SV1 @ SY11 ) ) )
        = $true )
      | ( ( SV1 @ ( sK3_SY6 @ SV1 @ SV4 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[47]) ).

thf(53,plain,
    ! [SV6: $i] :
      ( ( ( ~ ( a @ SV6 ) )
        = $false )
      | ( ( a @ SV6 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[49]) ).

thf(54,plain,
    ! [SV6: $i] :
      ( ( ( ~ $true )
        = $false )
      | ( ( a @ SV6 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[49]) ).

thf(55,plain,
    ! [SV6: $i] :
      ( ( ( ~ ( a @ SV6 ) )
        = $false )
      | ( $true = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[50]) ).

thf(56,plain,
    ( ( ( ~ $true )
      = $false )
    | ( $true = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[50]) ).

thf(57,plain,
    ! [SV1: $i > $o,SV8: $i,SV4: $i] :
      ( ( ( ~ ( rel @ SV4 @ SV8 ) )
        = $true )
      | ( ( ! [SY12: $i] :
              ( ~ ( rel @ SV8 @ SY12 )
              | ( SV1 @ SY12 ) ) )
        = $true )
      | ( ( rel @ SV4 @ ( sK3_SY6 @ SV1 @ SV4 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[51]) ).

thf(58,plain,
    ! [SV1: $i > $o,SV7: $i,SV4: $i] :
      ( ( ( rel @ SV4 @ SV7 )
        = $false )
      | ( ( ! [SY11: $i] :
              ( ~ ( rel @ SV7 @ SY11 )
              | ( SV1 @ SY11 ) ) )
        = $true )
      | ( ( SV1 @ ( sK3_SY6 @ SV1 @ SV4 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[52]) ).

thf(59,plain,
    ! [SV6: $i] :
      ( ( ( a @ SV6 )
        = $true )
      | ( ( a @ SV6 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[53]) ).

thf(60,plain,
    ! [SV6: $i] :
      ( ( $true = $true )
      | ( ( a @ SV6 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[54]) ).

thf(61,plain,
    ! [SV6: $i] :
      ( ( ( a @ SV6 )
        = $true )
      | ( $true = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[55]) ).

thf(62,plain,
    ( ( $true = $true )
    | ( $true = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[56]) ).

thf(63,plain,
    ! [SV1: $i > $o,SV8: $i,SV4: $i] :
      ( ( ( rel @ SV4 @ SV8 )
        = $false )
      | ( ( ! [SY12: $i] :
              ( ~ ( rel @ SV8 @ SY12 )
              | ( SV1 @ SY12 ) ) )
        = $true )
      | ( ( rel @ SV4 @ ( sK3_SY6 @ SV1 @ SV4 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[57]) ).

thf(64,plain,
    ! [SV4: $i,SV1: $i > $o,SV9: $i,SV7: $i] :
      ( ( ( ~ ( rel @ SV7 @ SV9 )
          | ( SV1 @ SV9 ) )
        = $true )
      | ( ( rel @ SV4 @ SV7 )
        = $false )
      | ( ( SV1 @ ( sK3_SY6 @ SV1 @ SV4 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[58]) ).

thf(65,plain,
    ! [SV4: $i,SV1: $i > $o,SV10: $i,SV8: $i] :
      ( ( ( ~ ( rel @ SV8 @ SV10 )
          | ( SV1 @ SV10 ) )
        = $true )
      | ( ( rel @ SV4 @ SV8 )
        = $false )
      | ( ( rel @ SV4 @ ( sK3_SY6 @ SV1 @ SV4 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[63]) ).

thf(66,plain,
    ! [SV4: $i,SV1: $i > $o,SV9: $i,SV7: $i] :
      ( ( ( ~ ( rel @ SV7 @ SV9 ) )
        = $true )
      | ( ( SV1 @ SV9 )
        = $true )
      | ( ( rel @ SV4 @ SV7 )
        = $false )
      | ( ( SV1 @ ( sK3_SY6 @ SV1 @ SV4 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[64]) ).

thf(67,plain,
    ! [SV4: $i,SV1: $i > $o,SV10: $i,SV8: $i] :
      ( ( ( ~ ( rel @ SV8 @ SV10 ) )
        = $true )
      | ( ( SV1 @ SV10 )
        = $true )
      | ( ( rel @ SV4 @ SV8 )
        = $false )
      | ( ( rel @ SV4 @ ( sK3_SY6 @ SV1 @ SV4 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[65]) ).

thf(68,plain,
    ! [SV4: $i,SV1: $i > $o,SV9: $i,SV7: $i] :
      ( ( ( rel @ SV7 @ SV9 )
        = $false )
      | ( ( SV1 @ SV9 )
        = $true )
      | ( ( rel @ SV4 @ SV7 )
        = $false )
      | ( ( SV1 @ ( sK3_SY6 @ SV1 @ SV4 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[66]) ).

thf(69,plain,
    ! [SV4: $i,SV1: $i > $o,SV10: $i,SV8: $i] :
      ( ( ( rel @ SV8 @ SV10 )
        = $false )
      | ( ( SV1 @ SV10 )
        = $true )
      | ( ( rel @ SV4 @ SV8 )
        = $false )
      | ( ( rel @ SV4 @ ( sK3_SY6 @ SV1 @ SV4 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[67]) ).

thf(70,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[18,69,68,62,61,60,59,48,43,39,38,37,27]) ).

thf(71,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[70]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SWV435^4 : TPTP v8.1.0. Released v3.6.0.
% 0.12/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34  % Computer : n009.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Tue Jun 14 21:23:23 EDT 2022
% 0.20/0.34  % CPUTime  : 
% 0.20/0.35  
% 0.20/0.35   No.of.Axioms: 3
% 0.20/0.35  
% 0.20/0.35   Length.of.Defs: 3431
% 0.20/0.35  
% 0.20/0.35   Contains.Choice.Funs: false
% 0.20/0.35  (rf:0,axioms:3,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:5,loop_count:0,foatp_calls:0,translation:fof_full)..
% 0.20/0.40  
% 0.20/0.40  ********************************
% 0.20/0.40  *   All subproblems solved!    *
% 0.20/0.40  ********************************
% 0.20/0.40  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:3,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:70,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.20/0.40  
% 0.20/0.40  %**** Beginning of derivation protocol ****
% 0.20/0.40  % SZS output start CNFRefutation
% See solution above
% 0.20/0.40  
% 0.20/0.40  %**** End of derivation protocol ****
% 0.20/0.40  %**** no. of clauses in derivation: 71 ****
% 0.20/0.40  %**** clause counter: 70 ****
% 0.20/0.40  
% 0.20/0.40  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:3,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:70,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------