TSTP Solution File: SYN399+1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SYN399+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n005.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 08:25:58 EDT 2022

% Result   : Theorem 0.19s 0.38s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   61 (  45 unt;   3 typ;   0 def)
%            Number of atoms       :  258 (  68 equ;   0 cnn)
%            Maximal formula atoms :    4 (   4 avg)
%            Number of connectives :  194 (  70   ~;  42   |;   7   &;  60   @)
%                                         (   8 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    1 (   1   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   3 usr;   4 con; 0-2 aty)
%            Number of variables   :   53 (   0   ^  53   !;   0   ?;  53   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_f,type,
    f: $i > $o ).

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

thf(tp_sK1_Y,type,
    sK1_Y: $i ).

thf(1,conjecture,
    ( ! [X: $i] :
        ( ( f @ X )
      <=> p )
   => ( ! [Y: $i] : ( f @ Y )
    <=> p ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',kalish223) ).

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

thf(3,plain,
    ( ( ! [X: $i] :
          ( ( f @ X )
        <=> p )
     => ( ! [Y: $i] : ( f @ Y )
      <=> p ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ! [X: $i] :
          ( ( f @ X )
        <=> p ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(5,plain,
    ( ( ! [Y: $i] : ( f @ Y )
    <=> p )
    = $false ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(6,plain,
    ( ( ! [Y: $i] : ( f @ Y )
     => p )
    = $false ),
    inference(split_conjecture,[split_conjecture(split,[])],[5]) ).

thf(7,plain,
    ( ( p
     => ! [Y: $i] : ( f @ Y ) )
    = $false ),
    inference(split_conjecture,[split_conjecture(split,[])],[5]) ).

thf(8,plain,
    ( ( ~ ( ! [Y: $i] : ( f @ Y )
         => p ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[6]) ).

thf(9,plain,
    ( ( ~ ( p
         => ! [Y: $i] : ( f @ Y ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[7]) ).

thf(10,plain,
    ( ( ! [Y: $i] : ( f @ Y )
      & ~ p )
    = $true ),
    inference(extcnf_combined,[status(esa)],[8]) ).

thf(11,plain,
    ( ( p
      & ~ ( f @ sK1_Y ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[9]) ).

thf(12,plain,
    ( ( ( ! [X: $i] :
            ~ ( f @ X )
        | p )
      & ( ~ p
        | ! [X: $i] : ( f @ X ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[4]) ).

thf(13,plain,
    ( ( ( ! [X: $i] :
            ~ ( f @ X )
        | p )
      & ( ~ p
        | ! [X: $i] : ( f @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[12]) ).

thf(14,plain,
    ( ( ! [Y: $i] : ( f @ Y )
      & ~ p )
    = $true ),
    inference(copy,[status(thm)],[10]) ).

thf(15,plain,
    ( ( ~ ( ~ ! [SX0: $i] : ( f @ SX0 )
          | ~ ~ p ) )
    = $true ),
    inference(unfold_def,[status(thm)],[14]) ).

thf(16,plain,
    ( ( ~ ( ~ ( ! [SX0: $i] :
                  ~ ( f @ SX0 )
              | p )
          | ~ ( ~ p
              | ! [SX0: $i] : ( f @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[13]) ).

thf(17,plain,
    ( ( ~ ! [SX0: $i] : ( f @ SX0 )
      | ~ ~ p )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[15]) ).

thf(18,plain,
    ( ( ~ ( ! [SX0: $i] :
              ~ ( f @ SX0 )
          | p )
      | ~ ( ~ p
          | ! [SX0: $i] : ( f @ SX0 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[16]) ).

thf(19,plain,
    ( ( ~ ! [SX0: $i] : ( f @ SX0 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[17]) ).

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

thf(21,plain,
    ( ( ~ ( ! [SX0: $i] :
              ~ ( f @ SX0 )
          | p ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[18]) ).

thf(22,plain,
    ( ( ~ ( ~ p
          | ! [SX0: $i] : ( f @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[18]) ).

thf(23,plain,
    ( ( ! [SX0: $i] : ( f @ SX0 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[19]) ).

thf(24,plain,
    ( ( ~ p )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[20]) ).

thf(25,plain,
    ( ( ! [SX0: $i] :
          ~ ( f @ SX0 )
      | p )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[21]) ).

thf(26,plain,
    ( ( ~ p
      | ! [SX0: $i] : ( f @ SX0 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[22]) ).

thf(27,plain,
    ! [SV1: $i] :
      ( ( f @ SV1 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[23]) ).

thf(28,plain,
    p = $false,
    inference(extcnf_not_pos,[status(thm)],[24]) ).

thf(29,plain,
    ( ( ( ! [SX0: $i] :
            ~ ( f @ SX0 ) )
      = $true )
    | ( p = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[25]) ).

thf(30,plain,
    ( ( ( ~ p )
      = $true )
    | ( ( ! [SX0: $i] : ( f @ SX0 ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[26]) ).

thf(31,plain,
    ! [SV2: $i] :
      ( ( ( ~ ( f @ SV2 ) )
        = $true )
      | ( p = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[29]) ).

thf(32,plain,
    ( ( p = $false )
    | ( ( ! [SX0: $i] : ( f @ SX0 ) )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[30]) ).

thf(33,plain,
    ! [SV2: $i] :
      ( ( ( f @ SV2 )
        = $false )
      | ( p = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[31]) ).

thf(34,plain,
    ! [SV3: $i] :
      ( ( ( f @ SV3 )
        = $true )
      | ( p = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[32]) ).

thf(35,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[27,34,33,28]) ).

thf(36,plain,
    ( ( ( ! [X: $i] :
            ~ ( f @ X )
        | p )
      & ( ~ p
        | ! [X: $i] : ( f @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[12]) ).

thf(37,plain,
    ( ( p
      & ~ ( f @ sK1_Y ) )
    = $true ),
    inference(copy,[status(thm)],[11]) ).

thf(38,plain,
    ( ( ~ ( ~ ( ! [SX0: $i] :
                  ~ ( f @ SX0 )
              | p )
          | ~ ( ~ p
              | ! [SX0: $i] : ( f @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[36]) ).

thf(39,plain,
    ( ( ~ ( ~ p
          | ~ ~ ( f @ sK1_Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[37]) ).

thf(40,plain,
    ( ( ~ ( ! [SX0: $i] :
              ~ ( f @ SX0 )
          | p )
      | ~ ( ~ p
          | ! [SX0: $i] : ( f @ SX0 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[38]) ).

thf(41,plain,
    ( ( ~ p
      | ~ ~ ( f @ sK1_Y ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[39]) ).

thf(42,plain,
    ( ( ~ ( ! [SX0: $i] :
              ~ ( f @ SX0 )
          | p ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[40]) ).

thf(43,plain,
    ( ( ~ ( ~ p
          | ! [SX0: $i] : ( f @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[40]) ).

thf(44,plain,
    ( ( ~ p )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[41]) ).

thf(45,plain,
    ( ( ~ ~ ( f @ sK1_Y ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[41]) ).

thf(46,plain,
    ( ( ! [SX0: $i] :
          ~ ( f @ SX0 )
      | p )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[42]) ).

thf(47,plain,
    ( ( ~ p
      | ! [SX0: $i] : ( f @ SX0 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[43]) ).

thf(48,plain,
    p = $true,
    inference(extcnf_not_neg,[status(thm)],[44]) ).

thf(49,plain,
    ( ( ~ ( f @ sK1_Y ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[45]) ).

thf(50,plain,
    ( ( ( ! [SX0: $i] :
            ~ ( f @ SX0 ) )
      = $true )
    | ( p = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[46]) ).

thf(51,plain,
    ( ( ( ~ p )
      = $true )
    | ( ( ! [SX0: $i] : ( f @ SX0 ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[47]) ).

thf(52,plain,
    ( ( f @ sK1_Y )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[49]) ).

thf(53,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( f @ SV4 ) )
        = $true )
      | ( p = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[50]) ).

thf(54,plain,
    ( ( p = $false )
    | ( ( ! [SX0: $i] : ( f @ SX0 ) )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[51]) ).

thf(55,plain,
    ! [SV4: $i] :
      ( ( ( f @ SV4 )
        = $false )
      | ( p = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[53]) ).

thf(56,plain,
    ! [SV5: $i] :
      ( ( ( f @ SV5 )
        = $true )
      | ( p = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[54]) ).

thf(57,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[48,56,55,52]) ).

thf(58,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[57,35]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SYN399+1 : TPTP v8.1.0. Released v2.0.0.
% 0.06/0.12  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33  % Computer : n005.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 : Mon Jul 11 13:59:51 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:600,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/sandbox/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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:57,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: 58 ****
% 0.19/0.38  %**** clause counter: 57 ****
% 0.19/0.38  
% 0.19/0.38  % SZS status Theorem for /export/starexec/sandbox/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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:57,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------