TSTP Solution File: SET014^5 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SET014^5 : 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 : n018.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 : Tue Jul 19 02:57:52 EDT 2022

% Result   : Theorem 0.13s 0.37s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   37 (  26 unt;   5 typ;   0 def)
%            Number of atoms       :  136 (  35 equ;   0 cnn)
%            Maximal formula atoms :    2 (   4 avg)
%            Number of connectives :  178 (  22   ~;  27   |;   8   &;  93   @)
%                                         (   0 <=>;  28  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   2 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   15 (  15   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   44 (   0   ^  44   !;   0   ?;  44   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_a,type,
    a: $tType ).

thf(tp_sK1_X,type,
    sK1_X: a > $o ).

thf(tp_sK2_SY6,type,
    sK2_SY6: a > $o ).

thf(tp_sK3_SY11,type,
    sK3_SY11: a > $o ).

thf(tp_sK4_SY17,type,
    sK4_SY17: a ).

thf(1,conjecture,
    ! [X: a > $o,Y: a > $o,Z: a > $o] :
      ( ( ! [Xx: a] :
            ( ( X @ Xx )
           => ( Z @ Xx ) )
        & ! [Xx: a] :
            ( ( Y @ Xx )
           => ( Z @ Xx ) ) )
     => ! [Xx: a] :
          ( ( ( X @ Xx )
            | ( Y @ Xx ) )
         => ( Z @ Xx ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_32_pme) ).

thf(2,negated_conjecture,
    ( ( ! [X: a > $o,Y: a > $o,Z: a > $o] :
          ( ( ! [Xx: a] :
                ( ( X @ Xx )
               => ( Z @ Xx ) )
            & ! [Xx: a] :
                ( ( Y @ Xx )
               => ( Z @ Xx ) ) )
         => ! [Xx: a] :
              ( ( ( X @ Xx )
                | ( Y @ Xx ) )
             => ( Z @ Xx ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ! [X: a > $o,Y: a > $o,Z: a > $o] :
          ( ( ! [Xx: a] :
                ( ( X @ Xx )
               => ( Z @ Xx ) )
            & ! [Xx: a] :
                ( ( Y @ Xx )
               => ( Z @ Xx ) ) )
         => ! [Xx: a] :
              ( ( ( X @ Xx )
                | ( Y @ Xx ) )
             => ( Z @ Xx ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ! [SY6: a > $o,SY7: a > $o] :
          ( ( ! [SY8: a] :
                ( ( sK1_X @ SY8 )
               => ( SY7 @ SY8 ) )
            & ! [Xx: a] :
                ( ( SY6 @ Xx )
               => ( SY7 @ Xx ) ) )
         => ! [SY10: a] :
              ( ( ( sK1_X @ SY10 )
                | ( SY6 @ SY10 ) )
             => ( SY7 @ SY10 ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[3]) ).

thf(5,plain,
    ( ( ! [SY11: a > $o] :
          ( ( ! [SY8: a] :
                ( ( sK1_X @ SY8 )
               => ( SY11 @ SY8 ) )
            & ! [SY13: a] :
                ( ( sK2_SY6 @ SY13 )
               => ( SY11 @ SY13 ) ) )
         => ! [SY14: a] :
              ( ( ( sK1_X @ SY14 )
                | ( sK2_SY6 @ SY14 ) )
             => ( SY11 @ SY14 ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[4]) ).

thf(6,plain,
    ( ( ( ! [SY15: a] :
            ( ( sK1_X @ SY15 )
           => ( sK3_SY11 @ SY15 ) )
        & ! [SY16: a] :
            ( ( sK2_SY6 @ SY16 )
           => ( sK3_SY11 @ SY16 ) ) )
     => ! [SY17: a] :
          ( ( ( sK1_X @ SY17 )
            | ( sK2_SY6 @ SY17 ) )
         => ( sK3_SY11 @ SY17 ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[5]) ).

thf(7,plain,
    ( ( ! [SY15: a] :
          ( ( sK1_X @ SY15 )
         => ( sK3_SY11 @ SY15 ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[6]) ).

thf(8,plain,
    ( ( ! [SY16: a] :
          ( ( sK2_SY6 @ SY16 )
         => ( sK3_SY11 @ SY16 ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[6]) ).

thf(9,plain,
    ( ( ! [SY17: a] :
          ( ( ( sK1_X @ SY17 )
            | ( sK2_SY6 @ SY17 ) )
         => ( sK3_SY11 @ SY17 ) ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[6]) ).

thf(10,plain,
    ( ( ~ ! [SY17: a] :
            ( ( ( sK1_X @ SY17 )
              | ( sK2_SY6 @ SY17 ) )
           => ( sK3_SY11 @ SY17 ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[9]) ).

thf(11,plain,
    ( ( ( ( sK1_X @ sK4_SY17 )
        | ( sK2_SY6 @ sK4_SY17 ) )
      & ~ ( sK3_SY11 @ sK4_SY17 ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[10]) ).

thf(12,plain,
    ( ( ! [SY15: a] :
          ( ~ ( sK1_X @ SY15 )
          | ( sK3_SY11 @ SY15 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[7]) ).

thf(13,plain,
    ( ( ! [SY16: a] :
          ( ~ ( sK2_SY6 @ SY16 )
          | ( sK3_SY11 @ SY16 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[8]) ).

thf(14,plain,
    ( ( ! [SY16: a] :
          ( ~ ( sK2_SY6 @ SY16 )
          | ( sK3_SY11 @ SY16 ) ) )
    = $true ),
    inference(copy,[status(thm)],[13]) ).

thf(15,plain,
    ( ( ! [SY15: a] :
          ( ~ ( sK1_X @ SY15 )
          | ( sK3_SY11 @ SY15 ) ) )
    = $true ),
    inference(copy,[status(thm)],[12]) ).

thf(16,plain,
    ( ( ( ( sK1_X @ sK4_SY17 )
        | ( sK2_SY6 @ sK4_SY17 ) )
      & ~ ( sK3_SY11 @ sK4_SY17 ) )
    = $true ),
    inference(copy,[status(thm)],[11]) ).

thf(17,plain,
    ( ( ~ ( ~ ( ( sK1_X @ sK4_SY17 )
              | ( sK2_SY6 @ sK4_SY17 ) )
          | ~ ~ ( sK3_SY11 @ sK4_SY17 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[16]) ).

thf(18,plain,
    ! [SV1: a] :
      ( ( ~ ( sK2_SY6 @ SV1 )
        | ( sK3_SY11 @ SV1 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[14]) ).

thf(19,plain,
    ! [SV2: a] :
      ( ( ~ ( sK1_X @ SV2 )
        | ( sK3_SY11 @ SV2 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[15]) ).

thf(20,plain,
    ( ( ~ ( ( sK1_X @ sK4_SY17 )
          | ( sK2_SY6 @ sK4_SY17 ) )
      | ~ ~ ( sK3_SY11 @ sK4_SY17 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[17]) ).

thf(21,plain,
    ! [SV1: a] :
      ( ( ( ~ ( sK2_SY6 @ SV1 ) )
        = $true )
      | ( ( sK3_SY11 @ SV1 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[18]) ).

thf(22,plain,
    ! [SV2: a] :
      ( ( ( ~ ( sK1_X @ SV2 ) )
        = $true )
      | ( ( sK3_SY11 @ SV2 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[19]) ).

thf(23,plain,
    ( ( ~ ( ( sK1_X @ sK4_SY17 )
          | ( sK2_SY6 @ sK4_SY17 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[20]) ).

thf(24,plain,
    ( ( ~ ~ ( sK3_SY11 @ sK4_SY17 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[20]) ).

thf(25,plain,
    ! [SV1: a] :
      ( ( ( sK2_SY6 @ SV1 )
        = $false )
      | ( ( sK3_SY11 @ SV1 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[21]) ).

thf(26,plain,
    ! [SV2: a] :
      ( ( ( sK1_X @ SV2 )
        = $false )
      | ( ( sK3_SY11 @ SV2 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[22]) ).

thf(27,plain,
    ( ( ( sK1_X @ sK4_SY17 )
      | ( sK2_SY6 @ sK4_SY17 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[23]) ).

thf(28,plain,
    ( ( ~ ( sK3_SY11 @ sK4_SY17 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[24]) ).

thf(29,plain,
    ( ( ( sK1_X @ sK4_SY17 )
      = $true )
    | ( ( sK2_SY6 @ sK4_SY17 )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[27]) ).

thf(30,plain,
    ( ( sK3_SY11 @ sK4_SY17 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[28]) ).

thf(31,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[25,30,29,26]) ).

thf(32,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[31]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET014^5 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33  % Computer : n018.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Sun Jul 10 00:54:27 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  
% 0.13/0.34   No.of.Axioms: 0
% 0.13/0.34  
% 0.13/0.34   Length.of.Defs: 0
% 0.13/0.34  
% 0.13/0.34   Contains.Choice.Funs: false
% 0.13/0.34  (rf:0,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout: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).
% 0.13/0.37  
% 0.13/0.37  ********************************
% 0.13/0.37  *   All subproblems solved!    *
% 0.13/0.37  ********************************
% 0.13/0.37  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:2,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:31,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.13/0.37  
% 0.13/0.37  %**** Beginning of derivation protocol ****
% 0.13/0.37  % SZS output start CNFRefutation
% See solution above
% 0.13/0.37  
% 0.13/0.37  %**** End of derivation protocol ****
% 0.13/0.37  %**** no. of clauses in derivation: 32 ****
% 0.13/0.37  %**** clause counter: 31 ****
% 0.13/0.37  
% 0.13/0.37  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:2,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:31,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------