TSTP Solution File: LCL586^1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : LCL586^1 : 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 : n003.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 : Sun Jul 17 12:24:17 EDT 2022

% Result   : Theorem 0.12s 0.38s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   41
% Syntax   : Number of formulae    :   67 (  38 unt;  25 typ;  15 def)
%            Number of atoms       :  187 (  43 equ;   0 cnn)
%            Maximal formula atoms :   11 (   4 avg)
%            Number of connectives :  241 (  74   ~;  28   |;   2   &; 136   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   1 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   83 (  83   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   27 (  24 usr;   5 con; 0-3 aty)
%            Number of variables   :   55 (  28   ^  23   !;   4   ?;  55   :)

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

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

thf(tp_b,type,
    b: $i > $o ).

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

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_r,type,
    r: $i > $i > $o ).

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

thf(tp_sK2_SY1,type,
    sK2_SY1: $i ).

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,conjecture,
    mvalid @ ( mimpl @ ( mnot @ ( mdia @ r @ a ) ) @ ( mbox @ r @ ( mimpl @ a @ b ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).

thf(2,negated_conjecture,
    ( ( mvalid @ ( mimpl @ ( mnot @ ( mdia @ r @ a ) ) @ ( mbox @ r @ ( mimpl @ a @ b ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ~ ( mvalid @ ( mimpl @ ( mnot @ ( mdia @ r @ a ) ) @ ( mbox @ r @ ( mimpl @ a @ b ) ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ~ ( mvalid @ ( mimpl @ ( mnot @ ( mdia @ r @ a ) ) @ ( mbox @ r @ ( mimpl @ a @ b ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[3]) ).

thf(5,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ~ ~ ! [SX1: $i] :
                      ~ ~ ( ~ ( r @ SX0 @ SX1 )
                          | ~ ( a @ SX1 ) )
            | ! [SX1: $i] :
                ( ~ ( r @ SX0 @ SX1 )
                | ~ ( a @ SX1 )
                | ( b @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4,mall,mand,mbox,mcountersatisfiable,mdia,mexists,mfalse,miff,mimpl,minvalid,mnot,mor,msatisfiable,mtrue,mvalid]) ).

thf(6,plain,
    ( ( ! [SX0: $i] :
          ( ~ ~ ~ ! [SX1: $i] :
                    ~ ~ ( ~ ( r @ SX0 @ SX1 )
                        | ~ ( a @ SX1 ) )
          | ! [SX1: $i] :
              ( ~ ( r @ SX0 @ SX1 )
              | ~ ( a @ SX1 )
              | ( b @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[5]) ).

thf(7,plain,
    ( ( ~ ~ ~ ! [SY0: $i] :
                ~ ~ ( ~ ( r @ sK1_SX0 @ SY0 )
                    | ~ ( a @ SY0 ) )
      | ! [SY1: $i] :
          ( ~ ( r @ sK1_SX0 @ SY1 )
          | ~ ( a @ SY1 )
          | ( b @ SY1 ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[6]) ).

thf(8,plain,
    ( ( ~ ~ ~ ! [SY0: $i] :
                ~ ~ ( ~ ( r @ sK1_SX0 @ SY0 )
                    | ~ ( a @ SY0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7]) ).

thf(9,plain,
    ( ( ! [SY1: $i] :
          ( ~ ( r @ sK1_SX0 @ SY1 )
          | ~ ( a @ SY1 )
          | ( b @ SY1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7]) ).

thf(10,plain,
    ( ( ~ ~ ! [SY0: $i] :
              ~ ~ ( ~ ( r @ sK1_SX0 @ SY0 )
                  | ~ ( a @ SY0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[8]) ).

thf(11,plain,
    ( ( ~ ( r @ sK1_SX0 @ sK2_SY1 )
      | ~ ( a @ sK2_SY1 )
      | ( b @ sK2_SY1 ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[9]) ).

thf(12,plain,
    ( ( ~ ! [SY0: $i] :
            ~ ~ ( ~ ( r @ sK1_SX0 @ SY0 )
                | ~ ( a @ SY0 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[10]) ).

thf(13,plain,
    ( ( ~ ( r @ sK1_SX0 @ sK2_SY1 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[11]) ).

thf(14,plain,
    ( ( ~ ( a @ sK2_SY1 )
      | ( b @ sK2_SY1 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[11]) ).

thf(15,plain,
    ( ( ! [SY0: $i] :
          ~ ~ ( ~ ( r @ sK1_SX0 @ SY0 )
              | ~ ( a @ SY0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[12]) ).

thf(16,plain,
    ( ( r @ sK1_SX0 @ sK2_SY1 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[13]) ).

thf(17,plain,
    ( ( ~ ( a @ sK2_SY1 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[14]) ).

thf(18,plain,
    ( ( b @ sK2_SY1 )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[14]) ).

thf(19,plain,
    ! [SV1: $i] :
      ( ( ~ ~ ( ~ ( r @ sK1_SX0 @ SV1 )
              | ~ ( a @ SV1 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[15]) ).

thf(20,plain,
    ( ( a @ sK2_SY1 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[17]) ).

thf(21,plain,
    ! [SV1: $i] :
      ( ( ~ ( ~ ( r @ sK1_SX0 @ SV1 )
            | ~ ( a @ SV1 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[19]) ).

thf(22,plain,
    ! [SV1: $i] :
      ( ( ~ ( r @ sK1_SX0 @ SV1 )
        | ~ ( a @ SV1 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[21]) ).

thf(23,plain,
    ! [SV1: $i] :
      ( ( ( ~ ( r @ sK1_SX0 @ SV1 ) )
        = $true )
      | ( ( ~ ( a @ SV1 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[22]) ).

thf(24,plain,
    ! [SV1: $i] :
      ( ( ( r @ sK1_SX0 @ SV1 )
        = $false )
      | ( ( ~ ( a @ SV1 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[23]) ).

thf(25,plain,
    ! [SV1: $i] :
      ( ( ( a @ SV1 )
        = $false )
      | ( ( r @ sK1_SX0 @ SV1 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[24]) ).

thf(26,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[16,25,20,18]) ).

thf(27,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[26]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : LCL586^1 : TPTP v8.1.0. Released v3.6.0.
% 0.07/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34  % Computer : n003.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Sun Jul  3 21:26:24 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.35  
% 0.12/0.35   No.of.Axioms: 0
% 0.12/0.35  
% 0.12/0.35   Length.of.Defs: 2203
% 0.12/0.35  
% 0.12/0.35   Contains.Choice.Funs: false
% 0.12/0.35  (rf:0,axioms:0,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:2,loop_count:0,foatp_calls:0,translation:fof_full).
% 0.12/0.38  
% 0.12/0.38  ********************************
% 0.12/0.38  *   All subproblems solved!    *
% 0.12/0.38  ********************************
% 0.12/0.38  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:0,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:26,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.12/0.38  
% 0.12/0.38  %**** Beginning of derivation protocol ****
% 0.12/0.38  % SZS output start CNFRefutation
% See solution above
% 0.12/0.38  
% 0.12/0.38  %**** End of derivation protocol ****
% 0.12/0.38  %**** no. of clauses in derivation: 27 ****
% 0.12/0.38  %**** clause counter: 26 ****
% 0.12/0.38  
% 0.12/0.38  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:0,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:26,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------