TSTP Solution File: SEV413^5 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SEV413^5 : 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 : n008.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 17:36:36 EDT 2022

% Result   : Theorem 0.19s 0.38s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   43 (  34 unt;   4 typ;   0 def)
%            Number of atoms       :  169 (  41 equ;   0 cnn)
%            Maximal formula atoms :    8 (   4 avg)
%            Number of connectives :  167 (  35   ~;  17   |;   8   &;  84   @)
%                                         (   0 <=>;  23  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   4 usr;   4 con; 0-2 aty)
%            Number of variables   :   29 (   0   ^  29   !;   0   ?;  29   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_cA,type,
    cA: $i > $o ).

thf(tp_cB,type,
    cB: $i > $o ).

thf(tp_sK1_Xx,type,
    sK1_Xx: $i ).

thf(tp_sK2_Xx,type,
    sK2_Xx: $i ).

thf(1,conjecture,
    ( ( ! [Xx: $i] :
          ( ( cA @ Xx )
         => ( cB @ Xx ) )
      | ! [Xx: $i] :
          ( ( cA @ Xx )
         => ( cB @ Xx ) ) )
   => ( ! [Xx: $i] :
          ( ( cA @ Xx )
         => ( cB @ Xx ) )
      & ! [Xx: $i] :
          ( ( cA @ Xx )
         => ( cB @ Xx ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cDUAL_EG5_pme) ).

thf(2,negated_conjecture,
    ( ( ( ! [Xx: $i] :
            ( ( cA @ Xx )
           => ( cB @ Xx ) )
        | ! [Xx: $i] :
            ( ( cA @ Xx )
           => ( cB @ Xx ) ) )
     => ( ! [Xx: $i] :
            ( ( cA @ Xx )
           => ( cB @ Xx ) )
        & ! [Xx: $i] :
            ( ( cA @ Xx )
           => ( cB @ Xx ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ( ! [Xx: $i] :
            ( ( cA @ Xx )
           => ( cB @ Xx ) )
        | ! [Xx: $i] :
            ( ( cA @ Xx )
           => ( cB @ Xx ) ) )
     => ( ! [Xx: $i] :
            ( ( cA @ Xx )
           => ( cB @ Xx ) )
        & ! [Xx: $i] :
            ( ( cA @ Xx )
           => ( cB @ Xx ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ! [Xx: $i] :
          ( ( cA @ Xx )
         => ( cB @ Xx ) )
      | ! [Xx: $i] :
          ( ( cA @ Xx )
         => ( cB @ Xx ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(5,plain,
    ( ( ! [Xx: $i] :
          ( ( cA @ Xx )
         => ( cB @ Xx ) )
      & ! [Xx: $i] :
          ( ( cA @ Xx )
         => ( cB @ Xx ) ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(6,plain,
    ( ( ! [Xx: $i] :
          ( ( cA @ Xx )
         => ( cB @ Xx ) ) )
    = $false ),
    inference(split_conjecture,[split_conjecture(split,[])],[5]) ).

thf(7,plain,
    ( ( ! [Xx: $i] :
          ( ( cA @ Xx )
         => ( cB @ Xx ) ) )
    = $false ),
    inference(split_conjecture,[split_conjecture(split,[])],[5]) ).

thf(8,plain,
    ( ( ~ ! [Xx: $i] :
            ( ( cA @ Xx )
           => ( cB @ Xx ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[6]) ).

thf(9,plain,
    ( ( ~ ! [Xx: $i] :
            ( ( cA @ Xx )
           => ( cB @ Xx ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[7]) ).

thf(10,plain,
    ( ( ( cA @ sK1_Xx )
      & ~ ( cB @ sK1_Xx ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[8]) ).

thf(11,plain,
    ( ( ( cA @ sK2_Xx )
      & ~ ( cB @ sK2_Xx ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[9]) ).

thf(12,plain,
    ( ( ! [Xx: $i] :
          ( ~ ( cA @ Xx )
          | ( cB @ Xx ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[4]) ).

thf(13,plain,
    ( ( ! [Xx: $i] :
          ( ~ ( cA @ Xx )
          | ( cB @ Xx ) ) )
    = $true ),
    inference(copy,[status(thm)],[12]) ).

thf(14,plain,
    ( ( ( cA @ sK1_Xx )
      & ~ ( cB @ sK1_Xx ) )
    = $true ),
    inference(copy,[status(thm)],[10]) ).

thf(15,plain,
    ( ( ~ ( ~ ( cA @ sK1_Xx )
          | ~ ~ ( cB @ sK1_Xx ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[14]) ).

thf(16,plain,
    ! [SV1: $i] :
      ( ( ~ ( cA @ SV1 )
        | ( cB @ SV1 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[13]) ).

thf(17,plain,
    ( ( ~ ( cA @ sK1_Xx )
      | ~ ~ ( cB @ sK1_Xx ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[15]) ).

thf(18,plain,
    ! [SV1: $i] :
      ( ( ( ~ ( cA @ SV1 ) )
        = $true )
      | ( ( cB @ SV1 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[16]) ).

thf(19,plain,
    ( ( ~ ( cA @ sK1_Xx ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[17]) ).

thf(20,plain,
    ( ( ~ ~ ( cB @ sK1_Xx ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[17]) ).

thf(21,plain,
    ! [SV1: $i] :
      ( ( ( cA @ SV1 )
        = $false )
      | ( ( cB @ SV1 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[18]) ).

thf(22,plain,
    ( ( cA @ sK1_Xx )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[19]) ).

thf(23,plain,
    ( ( ~ ( cB @ sK1_Xx ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[20]) ).

thf(24,plain,
    ( ( cB @ sK1_Xx )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[23]) ).

thf(25,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[21,24,22]) ).

thf(26,plain,
    ( ( ! [Xx: $i] :
          ( ~ ( cA @ Xx )
          | ( cB @ Xx ) ) )
    = $true ),
    inference(copy,[status(thm)],[12]) ).

thf(27,plain,
    ( ( ( cA @ sK2_Xx )
      & ~ ( cB @ sK2_Xx ) )
    = $true ),
    inference(copy,[status(thm)],[11]) ).

thf(28,plain,
    ( ( ~ ( ~ ( cA @ sK2_Xx )
          | ~ ~ ( cB @ sK2_Xx ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[27]) ).

thf(29,plain,
    ! [SV2: $i] :
      ( ( ~ ( cA @ SV2 )
        | ( cB @ SV2 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[26]) ).

thf(30,plain,
    ( ( ~ ( cA @ sK2_Xx )
      | ~ ~ ( cB @ sK2_Xx ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[28]) ).

thf(31,plain,
    ! [SV2: $i] :
      ( ( ( ~ ( cA @ SV2 ) )
        = $true )
      | ( ( cB @ SV2 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[29]) ).

thf(32,plain,
    ( ( ~ ( cA @ sK2_Xx ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[30]) ).

thf(33,plain,
    ( ( ~ ~ ( cB @ sK2_Xx ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[30]) ).

thf(34,plain,
    ! [SV2: $i] :
      ( ( ( cA @ SV2 )
        = $false )
      | ( ( cB @ SV2 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[31]) ).

thf(35,plain,
    ( ( cA @ sK2_Xx )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[32]) ).

thf(36,plain,
    ( ( ~ ( cB @ sK2_Xx ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[33]) ).

thf(37,plain,
    ( ( cB @ sK2_Xx )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[36]) ).

thf(38,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[34,37,35]) ).

thf(39,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[38,25]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SEV413^5 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33  % Computer : n008.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 : Tue Jun 28 17:30:53 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  
% 0.12/0.34   No.of.Axioms: 0
% 0.12/0.34  
% 0.12/0.34   Length.of.Defs: 0
% 0.12/0.34  
% 0.12/0.34   Contains.Choice.Funs: false
% 0.12/0.34  (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).
% 0.19/0.38  
% 0.19/0.38  ********************************
% 0.19/0.38  *   All subproblems solved!    *
% 0.19/0.38  ********************************
% 0.19/0.38  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:1,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:38,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.38  
% 0.19/0.38  %**** Beginning of derivation protocol ****
% 0.19/0.38  % SZS output start CNFRefutation
% See solution above
% 0.19/0.38  
% 0.19/0.38  %**** End of derivation protocol ****
% 0.19/0.38  %**** no. of clauses in derivation: 39 ****
% 0.19/0.38  %**** clause counter: 38 ****
% 0.19/0.38  
% 0.19/0.38  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:1,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:38,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------