TSTP Solution File: HEN003-5 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : HEN003-5 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n004.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 : Sat Jul 16 12:57:14 EDT 2022

% Result   : Unsatisfiable 0.18s 0.38s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   46 (  37 unt;   4 typ;   0 def)
%            Number of atoms       :  142 (  94 equ;   0 cnn)
%            Maximal formula atoms :    3 (   3 avg)
%            Number of connectives :  200 (  22   ~;  20   |;   0   &; 158   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   4 usr;   5 con; 0-2 aty)
%            Number of variables   :   56 (   0   ^  56   !;   0   ?;  56   :)

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

thf(tp_divide,type,
    divide: $i > $i > $i ).

thf(tp_identity,type,
    identity: $i ).

thf(tp_zero,type,
    zero: $i ).

thf(1,axiom,
    ! [X: $i] :
      ( ( divide @ X @ identity )
      = zero ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_is_largest) ).

thf(2,axiom,
    ! [X: $i,Y: $i] :
      ( ( ( divide @ X @ Y )
       != zero )
      | ( ( divide @ Y @ X )
       != zero )
      | ( X = Y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',divide_and_equal) ).

thf(3,axiom,
    ! [X: $i] :
      ( ( divide @ zero @ X )
      = zero ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_is_smallest) ).

thf(4,axiom,
    ! [X: $i,Z: $i,Y: $i] :
      ( ( divide @ ( divide @ ( divide @ X @ Z ) @ ( divide @ Y @ Z ) ) @ ( divide @ ( divide @ X @ Y ) @ Z ) )
      = zero ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_property) ).

thf(5,axiom,
    ! [X: $i,Y: $i] :
      ( ( divide @ ( divide @ X @ Y ) @ X )
      = zero ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_smaller_than_numerator) ).

thf(6,conjecture,
    $false,
    file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).

thf(7,negated_conjecture,
    $false = $false,
    inference(negate_conjecture,[status(cth)],[6]) ).

thf(8,negated_conjecture,
    ( divide @ a @ a )
 != zero,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_x_divide_x_is_zero) ).

thf(9,plain,
    $false = $false,
    inference(unfold_def,[status(thm)],[7]) ).

thf(10,plain,
    ( ( ! [X: $i] :
          ( ( divide @ X @ identity )
          = zero ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(11,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( ( divide @ X @ Y )
           != zero )
          | ( ( divide @ Y @ X )
           != zero )
          | ( X = Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(12,plain,
    ( ( ! [X: $i] :
          ( ( divide @ zero @ X )
          = zero ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(13,plain,
    ( ( ! [X: $i,Z: $i,Y: $i] :
          ( ( divide @ ( divide @ ( divide @ X @ Z ) @ ( divide @ Y @ Z ) ) @ ( divide @ ( divide @ X @ Y ) @ Z ) )
          = zero ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(14,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( divide @ ( divide @ X @ Y ) @ X )
          = zero ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(15,plain,
    ( ( ( ( divide @ a @ a )
       != zero ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8]) ).

thf(16,plain,
    ( ( ~ $false )
    = $true ),
    inference(polarity_switch,[status(thm)],[9]) ).

thf(17,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( ( divide @ X @ Y )
           != zero )
          | ( ( divide @ Y @ X )
           != zero )
          | ( X = Y ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[11]) ).

thf(18,plain,
    ( ( ( ( divide @ a @ a )
       != zero ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[15]) ).

thf(19,plain,
    ( ( ( ( divide @ a @ a )
       != zero ) )
    = $true ),
    inference(copy,[status(thm)],[18]) ).

thf(20,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( divide @ ( divide @ X @ Y ) @ X )
          = zero ) )
    = $true ),
    inference(copy,[status(thm)],[14]) ).

thf(21,plain,
    ( ( ! [X: $i,Z: $i,Y: $i] :
          ( ( divide @ ( divide @ ( divide @ X @ Z ) @ ( divide @ Y @ Z ) ) @ ( divide @ ( divide @ X @ Y ) @ Z ) )
          = zero ) )
    = $true ),
    inference(copy,[status(thm)],[13]) ).

thf(22,plain,
    ( ( ! [X: $i] :
          ( ( divide @ zero @ X )
          = zero ) )
    = $true ),
    inference(copy,[status(thm)],[12]) ).

thf(23,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( ( divide @ X @ Y )
           != zero )
          | ( ( divide @ Y @ X )
           != zero )
          | ( X = Y ) ) )
    = $true ),
    inference(copy,[status(thm)],[17]) ).

thf(24,plain,
    ( ( ! [X: $i] :
          ( ( divide @ X @ identity )
          = zero ) )
    = $true ),
    inference(copy,[status(thm)],[10]) ).

thf(25,plain,
    ( ( ~ $false )
    = $true ),
    inference(copy,[status(thm)],[16]) ).

thf(26,plain,
    ( ( ( divide @ a @ a )
      = zero )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[19]) ).

thf(27,plain,
    ! [SV1: $i] :
      ( ( ! [SY9: $i] :
            ( ( divide @ ( divide @ SV1 @ SY9 ) @ SV1 )
            = zero ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[20]) ).

thf(28,plain,
    ! [SV2: $i] :
      ( ( ! [SY10: $i,SY11: $i] :
            ( ( divide @ ( divide @ ( divide @ SV2 @ SY10 ) @ ( divide @ SY11 @ SY10 ) ) @ ( divide @ ( divide @ SV2 @ SY11 ) @ SY10 ) )
            = zero ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[21]) ).

thf(29,plain,
    ! [SV3: $i] :
      ( ( ( divide @ zero @ SV3 )
        = zero )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[22]) ).

thf(30,plain,
    ! [SV4: $i] :
      ( ( ! [SY12: $i] :
            ( ( ( divide @ SV4 @ SY12 )
             != zero )
            | ( ( divide @ SY12 @ SV4 )
             != zero )
            | ( SV4 = SY12 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[23]) ).

thf(31,plain,
    ! [SV5: $i] :
      ( ( ( divide @ SV5 @ identity )
        = zero )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[24]) ).

thf(32,plain,
    $false = $false,
    inference(extcnf_not_pos,[status(thm)],[25]) ).

thf(33,plain,
    ! [SV6: $i,SV1: $i] :
      ( ( ( divide @ ( divide @ SV1 @ SV6 ) @ SV1 )
        = zero )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[27]) ).

thf(34,plain,
    ! [SV7: $i,SV2: $i] :
      ( ( ! [SY13: $i] :
            ( ( divide @ ( divide @ ( divide @ SV2 @ SV7 ) @ ( divide @ SY13 @ SV7 ) ) @ ( divide @ ( divide @ SV2 @ SY13 ) @ SV7 ) )
            = zero ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[28]) ).

thf(35,plain,
    ! [SV8: $i,SV4: $i] :
      ( ( ( ( divide @ SV4 @ SV8 )
         != zero )
        | ( ( divide @ SV8 @ SV4 )
         != zero )
        | ( SV4 = SV8 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[30]) ).

thf(36,plain,
    ! [SV9: $i,SV7: $i,SV2: $i] :
      ( ( ( divide @ ( divide @ ( divide @ SV2 @ SV7 ) @ ( divide @ SV9 @ SV7 ) ) @ ( divide @ ( divide @ SV2 @ SV9 ) @ SV7 ) )
        = zero )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[34]) ).

thf(37,plain,
    ! [SV8: $i,SV4: $i] :
      ( ( ( ( ( divide @ SV4 @ SV8 )
           != zero ) )
        = $true )
      | ( ( ( ( divide @ SV8 @ SV4 )
           != zero )
          | ( SV4 = SV8 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[35]) ).

thf(38,plain,
    ! [SV8: $i,SV4: $i] :
      ( ( ( ( divide @ SV4 @ SV8 )
          = zero )
        = $false )
      | ( ( ( ( divide @ SV8 @ SV4 )
           != zero )
          | ( SV4 = SV8 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[37]) ).

thf(39,plain,
    ! [SV4: $i,SV8: $i] :
      ( ( ( ( ( divide @ SV8 @ SV4 )
           != zero ) )
        = $true )
      | ( ( SV4 = SV8 )
        = $true )
      | ( ( ( divide @ SV4 @ SV8 )
          = zero )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[38]) ).

thf(40,plain,
    ! [SV4: $i,SV8: $i] :
      ( ( ( ( divide @ SV8 @ SV4 )
          = zero )
        = $false )
      | ( ( SV4 = SV8 )
        = $true )
      | ( ( ( divide @ SV4 @ SV8 )
          = zero )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[39]) ).

thf(41,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[26,40,36,33,32,31,29]) ).

thf(42,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[41]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : HEN003-5 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.12  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33  % Computer : n004.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 : Fri Jul  1 14:34:38 EDT 2022
% 0.18/0.33  % CPUTime  : 
% 0.18/0.34  
% 0.18/0.34   No.of.Axioms: 6
% 0.18/0.34  
% 0.18/0.34   Length.of.Defs: 0
% 0.18/0.34  
% 0.18/0.34   Contains.Choice.Funs: false
% 0.18/0.34  (rf:0,axioms:6,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:8,loop_count:0,foatp_calls:0,translation:fof_full).
% 0.18/0.38  
% 0.18/0.38  ********************************
% 0.18/0.38  *   All subproblems solved!    *
% 0.18/0.38  ********************************
% 0.18/0.38  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:6,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:41,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.18/0.38  
% 0.18/0.38  %**** Beginning of derivation protocol ****
% 0.18/0.38  % SZS output start CNFRefutation
% See solution above
% 0.18/0.38  
% 0.18/0.38  %**** End of derivation protocol ****
% 0.18/0.38  %**** no. of clauses in derivation: 42 ****
% 0.18/0.38  %**** clause counter: 41 ****
% 0.18/0.38  
% 0.18/0.38  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:6,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:41,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------