TSTP Solution File: SYO363^5 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SYO363^5 : 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 : n019.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 17:33:35 EDT 2022

% Result   : Theorem 0.20s 0.46s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   38 (  29 unt;   8 typ;   0 def)
%            Number of atoms       :   97 (  52 equ;   0 cnn)
%            Maximal formula atoms :    2 (   3 avg)
%            Number of connectives :  143 (  14   ~;   2   |;   5   &; 114   @)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   29 (  29   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   31 (   0   ^  31   !;   0   ?;  31   :)

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

thf(tp_f,type,
    f: ( a > a ) > a > a ).

thf(tp_g,type,
    g: ( a > a ) > a > a ).

thf(tp_h,type,
    h: a > a ).

thf(tp_j,type,
    j: a > a ).

thf(tp_sK1_Xq,type,
    sK1_Xq: ( a > a ) > $o ).

thf(tp_sK2_E,type,
    sK2_E: a ).

thf(tp_sK3_E,type,
    sK3_E: a ).

thf(1,conjecture,
    ( ( ! [X: a > a,Y: a] :
          ( ( f @ X @ Y )
          = ( g @ X @ Y ) )
      & ! [Z: a] :
          ( ( h @ Z )
          = ( j @ Z ) ) )
   => ! [Xq: ( a > a ) > $o] :
        ( ( Xq @ ( f @ h ) )
       => ( Xq @ ( g @ j ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cEDEC2_pme) ).

thf(2,negated_conjecture,
    ( ( ( ! [X: a > a,Y: a] :
            ( ( f @ X @ Y )
            = ( g @ X @ Y ) )
        & ! [Z: a] :
            ( ( h @ Z )
            = ( j @ Z ) ) )
     => ! [Xq: ( a > a ) > $o] :
          ( ( Xq @ ( f @ h ) )
         => ( Xq @ ( g @ j ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ( ! [X: a > a,Y: a] :
            ( ( f @ X @ Y )
            = ( g @ X @ Y ) )
        & ! [Z: a] :
            ( ( h @ Z )
            = ( j @ Z ) ) )
     => ! [Xq: ( a > a ) > $o] :
          ( ( Xq @ ( f @ h ) )
         => ( Xq @ ( g @ j ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ! [X: a > a,Y: a] :
          ( ( f @ X @ Y )
          = ( g @ X @ Y ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(5,plain,
    ( ( ! [Z: a] :
          ( ( h @ Z )
          = ( j @ Z ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(6,plain,
    ( ( ! [Xq: ( a > a ) > $o] :
          ( ( Xq @ ( f @ h ) )
         => ( Xq @ ( g @ j ) ) ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(7,plain,
    ( ( ~ ! [Xq: ( a > a ) > $o] :
            ( ( Xq @ ( f @ h ) )
           => ( Xq @ ( g @ j ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[6]) ).

thf(8,plain,
    ( ( ( sK1_Xq @ ( f @ h ) )
      & ~ ( sK1_Xq @ ( g @ j ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[7]) ).

thf(9,plain,
    ( ( ! [Z: a] :
          ( ( h @ Z )
          = ( j @ Z ) ) )
    = $true ),
    inference(copy,[status(thm)],[5]) ).

thf(10,plain,
    ( ( ! [X: a > a,Y: a] :
          ( ( f @ X @ Y )
          = ( g @ X @ Y ) ) )
    = $true ),
    inference(copy,[status(thm)],[4]) ).

thf(11,plain,
    ( ( ( sK1_Xq @ ( f @ h ) )
      & ~ ( sK1_Xq @ ( g @ j ) ) )
    = $true ),
    inference(copy,[status(thm)],[8]) ).

thf(12,plain,
    ( ( ~ ( ~ ( sK1_Xq @ ( f @ h ) )
          | ~ ~ ( sK1_Xq @ ( g @ j ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11]) ).

thf(13,plain,
    ! [SV1: a] :
      ( ( ( h @ SV1 )
        = ( j @ SV1 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[9]) ).

thf(14,plain,
    ! [SV2: a > a] :
      ( ( ! [SY4: a] :
            ( ( f @ SV2 @ SY4 )
            = ( g @ SV2 @ SY4 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10]) ).

thf(15,plain,
    ( ( ~ ( sK1_Xq @ ( f @ h ) )
      | ~ ~ ( sK1_Xq @ ( g @ j ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[12]) ).

thf(16,plain,
    ! [SV3: a,SV2: a > a] :
      ( ( ( f @ SV2 @ SV3 )
        = ( g @ SV2 @ SV3 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[14]) ).

thf(17,plain,
    ( ( ~ ( sK1_Xq @ ( f @ h ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[15]) ).

thf(18,plain,
    ( ( ~ ~ ( sK1_Xq @ ( g @ j ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[15]) ).

thf(19,plain,
    ( ( sK1_Xq @ ( f @ h ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[17]) ).

thf(20,plain,
    ( ( ~ ( sK1_Xq @ ( g @ j ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[18]) ).

thf(21,plain,
    ( ( sK1_Xq @ ( g @ j ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[20]) ).

thf(22,plain,
    ! [SV4: a] :
      ( ( ( h @ SV4 )
        = ( j @ SV4 ) )
      = $true ),
    inference(rename,[status(thm)],[13]) ).

thf(23,plain,
    ! [SV5: a,SV6: a > a] :
      ( ( ( f @ SV6 @ SV5 )
        = ( g @ SV6 @ SV5 ) )
      = $true ),
    inference(rename,[status(thm)],[16]) ).

thf(26,plain,
    ( ( ( sK1_Xq @ ( g @ j ) )
      = ( sK1_Xq @ ( f @ h ) ) )
    = $false ),
    inference(res,[status(thm)],[21,19]) ).

thf(27,plain,
    ( ( ( g @ j @ sK2_E )
      = ( f @ h @ sK2_E ) )
    = $false ),
    inference(extuni,[status(esa)],[26]) ).

thf(28,plain,
    ! [SV5: a,SV6: a > a] :
      ( ( ( ( g @ j @ sK2_E )
          = ( f @ h @ sK2_E ) )
        = ( ( f @ SV6 @ SV5 )
          = ( g @ SV6 @ SV5 ) ) )
      = $false ),
    inference(res,[status(thm)],[27,23]) ).

thf(33,plain,
    ( ( ( j @ sK3_E )
      = ( h @ sK3_E ) )
    = $false ),
    inference(extuni,[status(esa)],[28:[bind(SV5,$thf( sK2_E )),bind(SV6,$thf( h ))]]) ).

thf(63,plain,
    ! [SV4: a] :
      ( ( ( ( j @ sK3_E )
          = ( h @ sK3_E ) )
        = ( ( h @ SV4 )
          = ( j @ SV4 ) ) )
      = $false ),
    inference(res,[status(thm)],[33,22]) ).

thf(65,plain,
    $false = $true,
    inference(extuni,[status(esa)],[63:[bind(SV4,$thf( sK3_E ))]]) ).

thf(66,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[65]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SYO363^5 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.34  % Computer : n019.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 : Fri Jul  8 20:09:38 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.14/0.35  
% 0.14/0.35   No.of.Axioms: 0
% 0.14/0.35  
% 0.14/0.35   Length.of.Defs: 0
% 0.14/0.35  
% 0.14/0.35   Contains.Choice.Funs: false
% 0.14/0.35  (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)..
% 0.20/0.46  
% 0.20/0.46  ********************************
% 0.20/0.46  *   All subproblems solved!    *
% 0.20/0.46  ********************************
% 0.20/0.46  % 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:65,loop_count:8,foatp_calls:1,translation:fof_full)
% 0.20/0.46  
% 0.20/0.46  %**** Beginning of derivation protocol ****
% 0.20/0.46  % SZS output start CNFRefutation
% See solution above
% 0.20/0.46  
% 0.20/0.46  %**** End of derivation protocol ****
% 0.20/0.46  %**** no. of clauses in derivation: 30 ****
% 0.20/0.46  %**** clause counter: 65 ****
% 0.20/0.46  
% 0.20/0.46  % 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:65,loop_count:8,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------