TSTP Solution File: SYO895^9 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SYO895^9 : TPTP v8.1.0. Released v8.1.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n029.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 17:38:15 EDT 2022

% Result   : Theorem 0.14s 0.38s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   25
% Syntax   : Number of formulae    :   57 (  34 unt;  15 typ;   8 def)
%            Number of atoms       :  208 (  46 equ;   0 cnn)
%            Maximal formula atoms :   11 (   4 avg)
%            Number of connectives :  269 (  66   ~;  41   |;   2   &; 157   @)
%                                         (   1 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   2 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   48 (  48   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   17 (  14 usr;   4 con; 0-3 aty)
%            Number of variables   :   49 (  19   ^  28   !;   2   ?;  49   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_mworld,type,
    mworld: $tType ).

thf(tp_mactual,type,
    mactual: mworld ).

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

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

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

thf(tp_mequiv,type,
    mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).

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

thf(tp_mlocal,type,
    mlocal: ( mworld > $o ) > $o ).

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

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

thf(tp_mrel,type,
    mrel: mworld > mworld > $o ).

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

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

thf(tp_sK1_V,type,
    sK1_V: mworld > mworld ).

thf(tp_sK2_SX0,type,
    sK2_SX0: mworld ).

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

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

thf(mdia,definition,
    ( mdia
    = ( ^ [Phi: mworld > $o,W: mworld] :
        ? [V: mworld] :
          ( ( mrel @ W @ V )
          & ( Phi @ V ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia) ).

thf(mequiv,definition,
    ( mequiv
    = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
          ( ( A @ W )
        <=> ( B @ W ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mequiv) ).

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

thf(mlocal,definition,
    ( mlocal
    = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mlocal) ).

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

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

thf(1,axiom,
    ! [W: mworld] :
    ? [V: mworld] : ( mrel @ W @ V ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_serial) ).

thf(2,conjecture,
    mlocal @ ( mimplies @ ( mand @ ( mbox @ p ) @ ( mbox @ q ) ) @ ( mbox @ ( mand @ p @ q ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).

thf(3,negated_conjecture,
    ( ( mlocal @ ( mimplies @ ( mand @ ( mbox @ p ) @ ( mbox @ q ) ) @ ( mbox @ ( mand @ p @ q ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[2]) ).

thf(4,plain,
    ( ( ~ ( mlocal @ ( mimplies @ ( mand @ ( mbox @ p ) @ ( mbox @ q ) ) @ ( mbox @ ( mand @ p @ q ) ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[3]) ).

thf(5,plain,
    ( ( ! [W: mworld] : ( mrel @ W @ ( sK1_V @ W ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1]) ).

thf(6,plain,
    ( ( ! [W: mworld] : ( mrel @ W @ ( sK1_V @ W ) ) )
    = $true ),
    inference(copy,[status(thm)],[5]) ).

thf(7,plain,
    ( ( ~ ( mlocal @ ( mimplies @ ( mand @ ( mbox @ p ) @ ( mbox @ q ) ) @ ( mbox @ ( mand @ p @ q ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[4]) ).

thf(8,plain,
    ( ( ~ ( ~ ~ ( ~ ! [SX0: mworld] :
                      ( ~ ( mrel @ mactual @ SX0 )
                      | ( p @ SX0 ) )
                | ~ ! [SX0: mworld] :
                      ( ~ ( mrel @ mactual @ SX0 )
                      | ( q @ SX0 ) ) )
          | ! [SX0: mworld] :
              ( ~ ( mrel @ mactual @ SX0 )
              | ~ ( ~ ( p @ SX0 )
                  | ~ ( q @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7,mand,mbox,mdia,mequiv,mimplies,mlocal,mnot,mor]) ).

thf(9,plain,
    ! [SV1: mworld] :
      ( ( mrel @ SV1 @ ( sK1_V @ SV1 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6]) ).

thf(10,plain,
    ( ( ~ ~ ( ~ ! [SX0: mworld] :
                  ( ~ ( mrel @ mactual @ SX0 )
                  | ( p @ SX0 ) )
            | ~ ! [SX0: mworld] :
                  ( ~ ( mrel @ mactual @ SX0 )
                  | ( q @ SX0 ) ) )
      | ! [SX0: mworld] :
          ( ~ ( mrel @ mactual @ SX0 )
          | ~ ( ~ ( p @ SX0 )
              | ~ ( q @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[8]) ).

thf(11,plain,
    ( ( ~ ~ ( ~ ! [SX0: mworld] :
                  ( ~ ( mrel @ mactual @ SX0 )
                  | ( p @ SX0 ) )
            | ~ ! [SX0: mworld] :
                  ( ~ ( mrel @ mactual @ SX0 )
                  | ( q @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[10]) ).

thf(12,plain,
    ( ( ! [SX0: mworld] :
          ( ~ ( mrel @ mactual @ SX0 )
          | ~ ( ~ ( p @ SX0 )
              | ~ ( q @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[10]) ).

thf(13,plain,
    ( ( ~ ( ~ ! [SX0: mworld] :
                ( ~ ( mrel @ mactual @ SX0 )
                | ( p @ SX0 ) )
          | ~ ! [SX0: mworld] :
                ( ~ ( mrel @ mactual @ SX0 )
                | ( q @ SX0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[11]) ).

thf(14,plain,
    ( ( ~ ( mrel @ mactual @ sK2_SX0 )
      | ~ ( ~ ( p @ sK2_SX0 )
          | ~ ( q @ sK2_SX0 ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[12]) ).

thf(15,plain,
    ( ( ~ ! [SX0: mworld] :
            ( ~ ( mrel @ mactual @ SX0 )
            | ( p @ SX0 ) )
      | ~ ! [SX0: mworld] :
            ( ~ ( mrel @ mactual @ SX0 )
            | ( q @ SX0 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[13]) ).

thf(16,plain,
    ( ( ~ ( mrel @ mactual @ sK2_SX0 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[14]) ).

thf(17,plain,
    ( ( ~ ( ~ ( p @ sK2_SX0 )
          | ~ ( q @ sK2_SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[14]) ).

thf(18,plain,
    ( ( ~ ! [SX0: mworld] :
            ( ~ ( mrel @ mactual @ SX0 )
            | ( p @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[15]) ).

thf(19,plain,
    ( ( ~ ! [SX0: mworld] :
            ( ~ ( mrel @ mactual @ SX0 )
            | ( q @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[15]) ).

thf(20,plain,
    ( ( mrel @ mactual @ sK2_SX0 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[16]) ).

thf(21,plain,
    ( ( ~ ( p @ sK2_SX0 )
      | ~ ( q @ sK2_SX0 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[17]) ).

thf(22,plain,
    ( ( ! [SX0: mworld] :
          ( ~ ( mrel @ mactual @ SX0 )
          | ( p @ SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[18]) ).

thf(23,plain,
    ( ( ! [SX0: mworld] :
          ( ~ ( mrel @ mactual @ SX0 )
          | ( q @ SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[19]) ).

thf(24,plain,
    ( ( ( ~ ( p @ sK2_SX0 ) )
      = $true )
    | ( ( ~ ( q @ sK2_SX0 ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[21]) ).

thf(25,plain,
    ! [SV2: mworld] :
      ( ( ~ ( mrel @ mactual @ SV2 )
        | ( p @ SV2 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[22]) ).

thf(26,plain,
    ! [SV3: mworld] :
      ( ( ~ ( mrel @ mactual @ SV3 )
        | ( q @ SV3 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[23]) ).

thf(27,plain,
    ( ( ( p @ sK2_SX0 )
      = $false )
    | ( ( ~ ( q @ sK2_SX0 ) )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[24]) ).

thf(28,plain,
    ! [SV2: mworld] :
      ( ( ( ~ ( mrel @ mactual @ SV2 ) )
        = $true )
      | ( ( p @ SV2 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[25]) ).

thf(29,plain,
    ! [SV3: mworld] :
      ( ( ( ~ ( mrel @ mactual @ SV3 ) )
        = $true )
      | ( ( q @ SV3 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[26]) ).

thf(30,plain,
    ( ( ( q @ sK2_SX0 )
      = $false )
    | ( ( p @ sK2_SX0 )
      = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[27]) ).

thf(31,plain,
    ! [SV2: mworld] :
      ( ( ( mrel @ mactual @ SV2 )
        = $false )
      | ( ( p @ SV2 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[28]) ).

thf(32,plain,
    ! [SV3: mworld] :
      ( ( ( mrel @ mactual @ SV3 )
        = $false )
      | ( ( q @ SV3 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[29]) ).

thf(33,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[9,32,31,30,20]) ).

thf(34,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[33]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : SYO895^9 : TPTP v8.1.0. Released v8.1.0.
% 0.10/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.34  % Computer : n029.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Sat Jul  9 08:55:30 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.14/0.35  
% 0.14/0.35   No.of.Axioms: 1
% 0.14/0.35  
% 0.14/0.35   Length.of.Defs: 1238
% 0.14/0.35  
% 0.14/0.35   Contains.Choice.Funs: false
% 0.14/0.35  (rf:0,axioms:1,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:3,loop_count:0,foatp_calls:0,translation:fof_full).
% 0.14/0.38  
% 0.14/0.38  ********************************
% 0.14/0.38  *   All subproblems solved!    *
% 0.14/0.38  ********************************
% 0.14/0.38  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,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:33,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.14/0.38  
% 0.14/0.38  %**** Beginning of derivation protocol ****
% 0.14/0.38  % SZS output start CNFRefutation
% See solution above
% 0.14/0.38  
% 0.14/0.38  %**** End of derivation protocol ****
% 0.14/0.38  %**** no. of clauses in derivation: 34 ****
% 0.14/0.38  %**** clause counter: 33 ****
% 0.14/0.38  
% 0.14/0.38  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,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:33,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------