TSTP Solution File: NUM635^1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : NUM635^1 : 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 : n027.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 : Mon Jul 18 11:53:27 EDT 2022

% Result   : Theorem 0.12s 0.36s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   25 (  18 unt;   4 typ;   0 def)
%            Number of atoms       :   67 (  46 equ;   0 cnn)
%            Maximal formula atoms :    2 (   3 avg)
%            Number of connectives :   50 (  14   ~;   6   |;   0   &;  28   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Number of types       :    1 (   1 usr)
%            Number of type conns  :    1 (   1   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   3 usr;   4 con; 0-2 aty)
%            Number of variables   :   16 (   0   ^  16   !;   0   ?;  16   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_nat,type,
    nat: $tType ).

thf(tp_suc,type,
    suc: nat > nat ).

thf(tp_x,type,
    x: nat ).

thf(tp_y,type,
    y: nat ).

thf(1,axiom,
    ! [Xx: nat,Xy: nat] :
      ( ( ( suc @ Xx )
        = ( suc @ Xy ) )
     => ( Xx = Xy ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).

thf(2,axiom,
    x != y,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',n) ).

thf(3,conjecture,
    ( suc @ x )
 != ( suc @ y ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz1) ).

thf(4,negated_conjecture,
    ( ( ( ( suc @ x )
       != ( suc @ y ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[3]) ).

thf(5,plain,
    ( ( ( ( suc @ x )
       != ( suc @ y ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(6,plain,
    ( ( ! [Xx: nat,Xy: nat] :
          ( ( ( suc @ Xx )
            = ( suc @ Xy ) )
         => ( Xx = Xy ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(7,plain,
    ( ( ( x != y ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(8,plain,
    ( ( ~ ( ( ( suc @ x )
           != ( suc @ y ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[5]) ).

thf(9,plain,
    ( ( ( suc @ x )
      = ( suc @ y ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[8]) ).

thf(10,plain,
    ( ( ! [Xx: nat,Xy: nat] :
          ( ( ( suc @ Xx )
           != ( suc @ Xy ) )
          | ( Xx = Xy ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[6]) ).

thf(11,plain,
    ( ( ( x != y ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[7]) ).

thf(12,plain,
    ( ( ( x != y ) )
    = $true ),
    inference(copy,[status(thm)],[11]) ).

thf(13,plain,
    ( ( ! [Xx: nat,Xy: nat] :
          ( ( ( suc @ Xx )
           != ( suc @ Xy ) )
          | ( Xx = Xy ) ) )
    = $true ),
    inference(copy,[status(thm)],[10]) ).

thf(14,plain,
    ( ( ( suc @ x )
      = ( suc @ y ) )
    = $true ),
    inference(copy,[status(thm)],[9]) ).

thf(15,plain,
    ( ( x = y )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[12]) ).

thf(16,plain,
    ! [SV1: nat] :
      ( ( ! [SY2: nat] :
            ( ( ( suc @ SV1 )
             != ( suc @ SY2 ) )
            | ( SV1 = SY2 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[13]) ).

thf(17,plain,
    ! [SV2: nat,SV1: nat] :
      ( ( ( ( suc @ SV1 )
         != ( suc @ SV2 ) )
        | ( SV1 = SV2 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[16]) ).

thf(18,plain,
    ! [SV2: nat,SV1: nat] :
      ( ( ( ( ( suc @ SV1 )
           != ( suc @ SV2 ) ) )
        = $true )
      | ( ( SV1 = SV2 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[17]) ).

thf(19,plain,
    ! [SV2: nat,SV1: nat] :
      ( ( ( ( suc @ SV1 )
          = ( suc @ SV2 ) )
        = $false )
      | ( ( SV1 = SV2 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[18]) ).

thf(20,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[14,19,15]) ).

thf(21,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[20]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : NUM635^1 : TPTP v8.1.0. Released v3.7.0.
% 0.06/0.12  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33  % Computer : n027.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 : Thu Jul  7 04:21:29 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  
% 0.12/0.34   No.of.Axioms: 2
% 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: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:4,loop_count:0,foatp_calls:0,translation:fof_full)
% 0.12/0.36  ********************************
% 0.12/0.36  *   All subproblems solved!    *
% 0.12/0.36  ********************************
% 0.12/0.36  % 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:20,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.12/0.36  
% 0.12/0.36  %**** Beginning of derivation protocol ****
% 0.12/0.36  % SZS output start CNFRefutation
% See solution above
% 0.12/0.36  
% 0.12/0.36  %**** End of derivation protocol ****
% 0.12/0.36  %**** no. of clauses in derivation: 21 ****
% 0.12/0.36  %**** clause counter: 20 ****
% 0.12/0.36  
% 0.12/0.36  % 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:20,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------