TSTP Solution File: SYO001^1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SYO001^1 : TPTP v8.1.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n024.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 17:31:17 EDT 2022

% Result   : Theorem 0.18s 0.37s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   37 (  27 unt;   5 typ;   1 def)
%            Number of atoms       :   89 (  34 equ;   0 cnn)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :  144 (  22   ~;  12   |;   8   &;  79   @)
%                                         (   0 <=>;  23  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   30 (  30   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   5 usr;   5 con; 0-2 aty)
%            Number of variables   :   41 (   2   ^  39   !;   0   ?;  41   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_leibeq,type,
    leibeq: $i > $i > $o ).

thf(tp_sK1_SY0,type,
    sK1_SY0: $i ).

thf(tp_sK2_SY18,type,
    sK2_SY18: $i ).

thf(tp_sK3_SY23,type,
    sK3_SY23: $i ).

thf(tp_sK4_SY29,type,
    sK4_SY29: $i > $o ).

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

thf(1,conjecture,
    ! [X: $i,Y: $i,Z: $i] :
      ( ( ( leibeq @ X @ Y )
        & ( leibeq @ Y @ Z ) )
     => ( leibeq @ X @ Z ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).

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

thf(3,plain,
    ( ( ! [SY0: $i,SY1: $i,SY2: $i] :
          ( ( ! [SY5: $i > $o] :
                ( ( SY5 @ SY0 )
               => ( SY5 @ SY1 ) )
            & ! [SY8: $i > $o] :
                ( ( SY8 @ SY1 )
               => ( SY8 @ SY2 ) ) )
         => ! [SY11: $i > $o] :
              ( ( SY11 @ SY0 )
             => ( SY11 @ SY2 ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2,leibeq]) ).

thf(4,plain,
    ( ( ! [SY18: $i,SY19: $i] :
          ( ( ! [SY20: $i > $o] :
                ( ( SY20 @ sK1_SY0 )
               => ( SY20 @ SY18 ) )
            & ! [SY8: $i > $o] :
                ( ( SY8 @ SY18 )
               => ( SY8 @ SY19 ) ) )
         => ! [SY22: $i > $o] :
              ( ( SY22 @ sK1_SY0 )
             => ( SY22 @ SY19 ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[3]) ).

thf(5,plain,
    ( ( ! [SY23: $i] :
          ( ( ! [SY24: $i > $o] :
                ( ( SY24 @ sK1_SY0 )
               => ( SY24 @ sK2_SY18 ) )
            & ! [SY25: $i > $o] :
                ( ( SY25 @ sK2_SY18 )
               => ( SY25 @ SY23 ) ) )
         => ! [SY22: $i > $o] :
              ( ( SY22 @ sK1_SY0 )
             => ( SY22 @ SY23 ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[4]) ).

thf(6,plain,
    ( ( ( ! [SY24: $i > $o] :
            ( ( SY24 @ sK1_SY0 )
           => ( SY24 @ sK2_SY18 ) )
        & ! [SY28: $i > $o] :
            ( ( SY28 @ sK2_SY18 )
           => ( SY28 @ sK3_SY23 ) ) )
     => ! [SY29: $i > $o] :
          ( ( SY29 @ sK1_SY0 )
         => ( SY29 @ sK3_SY23 ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[5]) ).

thf(7,plain,
    ( ( ! [SY24: $i > $o] :
          ( ( SY24 @ sK1_SY0 )
         => ( SY24 @ sK2_SY18 ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[6]) ).

thf(8,plain,
    ( ( ! [SY28: $i > $o] :
          ( ( SY28 @ sK2_SY18 )
         => ( SY28 @ sK3_SY23 ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[6]) ).

thf(9,plain,
    ( ( ! [SY29: $i > $o] :
          ( ( SY29 @ sK1_SY0 )
         => ( SY29 @ sK3_SY23 ) ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[6]) ).

thf(10,plain,
    ( ( ~ ! [SY29: $i > $o] :
            ( ( SY29 @ sK1_SY0 )
           => ( SY29 @ sK3_SY23 ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[9]) ).

thf(11,plain,
    ( ( ( sK4_SY29 @ sK1_SY0 )
      & ~ ( sK4_SY29 @ sK3_SY23 ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[10]) ).

thf(12,plain,
    ( ( ! [SY24: $i > $o] :
          ( ~ ( SY24 @ sK1_SY0 )
          | ( SY24 @ sK2_SY18 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[7]) ).

thf(13,plain,
    ( ( ! [SY28: $i > $o] :
          ( ~ ( SY28 @ sK2_SY18 )
          | ( SY28 @ sK3_SY23 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[8]) ).

thf(14,plain,
    ( ( ! [SY28: $i > $o] :
          ( ~ ( SY28 @ sK2_SY18 )
          | ( SY28 @ sK3_SY23 ) ) )
    = $true ),
    inference(copy,[status(thm)],[13]) ).

thf(15,plain,
    ( ( ! [SY24: $i > $o] :
          ( ~ ( SY24 @ sK1_SY0 )
          | ( SY24 @ sK2_SY18 ) ) )
    = $true ),
    inference(copy,[status(thm)],[12]) ).

thf(16,plain,
    ( ( ( sK4_SY29 @ sK1_SY0 )
      & ~ ( sK4_SY29 @ sK3_SY23 ) )
    = $true ),
    inference(copy,[status(thm)],[11]) ).

thf(17,plain,
    ( ( ~ ( ~ ( sK4_SY29 @ sK1_SY0 )
          | ~ ~ ( sK4_SY29 @ sK3_SY23 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[16,leibeq]) ).

thf(18,plain,
    ! [SV1: $i > $o] :
      ( ( ~ ( SV1 @ sK2_SY18 )
        | ( SV1 @ sK3_SY23 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[14]) ).

thf(19,plain,
    ! [SV2: $i > $o] :
      ( ( ~ ( SV2 @ sK1_SY0 )
        | ( SV2 @ sK2_SY18 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[15]) ).

thf(20,plain,
    ( ( ~ ( sK4_SY29 @ sK1_SY0 )
      | ~ ~ ( sK4_SY29 @ sK3_SY23 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[17]) ).

thf(21,plain,
    ! [SV1: $i > $o] :
      ( ( ( ~ ( SV1 @ sK2_SY18 ) )
        = $true )
      | ( ( SV1 @ sK3_SY23 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[18]) ).

thf(22,plain,
    ! [SV2: $i > $o] :
      ( ( ( ~ ( SV2 @ sK1_SY0 ) )
        = $true )
      | ( ( SV2 @ sK2_SY18 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[19]) ).

thf(23,plain,
    ( ( ~ ( sK4_SY29 @ sK1_SY0 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[20]) ).

thf(24,plain,
    ( ( ~ ~ ( sK4_SY29 @ sK3_SY23 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[20]) ).

thf(25,plain,
    ! [SV1: $i > $o] :
      ( ( ( SV1 @ sK2_SY18 )
        = $false )
      | ( ( SV1 @ sK3_SY23 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[21]) ).

thf(26,plain,
    ! [SV2: $i > $o] :
      ( ( ( SV2 @ sK1_SY0 )
        = $false )
      | ( ( SV2 @ sK2_SY18 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[22]) ).

thf(27,plain,
    ( ( sK4_SY29 @ sK1_SY0 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[23]) ).

thf(28,plain,
    ( ( ~ ( sK4_SY29 @ sK3_SY23 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[24]) ).

thf(29,plain,
    ( ( sK4_SY29 @ sK3_SY23 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[28]) ).

thf(30,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[25,29,27,26]) ).

thf(31,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[30]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SYO001^1 : TPTP v8.1.0. Released v3.7.0.
% 0.12/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34  % Computer : n024.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
% 0.18/0.34  % CPULimit : 300
% 0.18/0.34  % WCLimit  : 600
% 0.18/0.34  % DateTime : Sat Jul  9 07:11:43 EDT 2022
% 0.18/0.34  % CPUTime  : 
% 0.18/0.34  
% 0.18/0.34   No.of.Axioms: 0
% 0.18/0.34  
% 0.18/0.34   Length.of.Defs: 150
% 0.18/0.34  
% 0.18/0.34   Contains.Choice.Funs: false
% 0.18/0.34  (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).
% 0.18/0.37  
% 0.18/0.37  ********************************
% 0.18/0.37  *   All subproblems solved!    *
% 0.18/0.37  ********************************
% 0.18/0.37  % SZS status Theorem for /export/starexec/sandbox/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:30,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.18/0.37  
% 0.18/0.37  %**** Beginning of derivation protocol ****
% 0.18/0.37  % SZS output start CNFRefutation
% See solution above
% 0.18/0.37  
% 0.18/0.37  %**** End of derivation protocol ****
% 0.18/0.37  %**** no. of clauses in derivation: 31 ****
% 0.18/0.37  %**** clause counter: 30 ****
% 0.18/0.37  
% 0.18/0.37  % SZS status Theorem for /export/starexec/sandbox/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:30,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------