TSTP Solution File: NUM677^1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : NUM677^1 : 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 : n015.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 11:54:06 EDT 2022

% Result   : Theorem 0.22s 0.40s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   38 (  24 unt;   7 typ;   0 def)
%            Number of atoms       :  121 (  53 equ;   0 cnn)
%            Maximal formula atoms :    3 (   3 avg)
%            Number of connectives :  198 (  16   ~;  20   |;   0   &; 158   @)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   3 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   6 usr;   6 con; 0-2 aty)
%            Number of variables   :   58 (   0   ^  58   !;   0   ?;  58   :)

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

thf(tp_more,type,
    more: nat > nat > $o ).

thf(tp_pl,type,
    pl: nat > nat > nat ).

thf(tp_u,type,
    u: nat ).

thf(tp_x,type,
    x: nat ).

thf(tp_y,type,
    y: nat ).

thf(tp_z,type,
    z: nat ).

thf(1,axiom,
    ! [Xx: nat,Xy: nat] :
      ( ( pl @ Xx @ Xy )
      = ( pl @ Xy @ Xx ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz6) ).

thf(2,axiom,
    ! [Xx: nat,Xy: nat,Xz: nat,Xu: nat] :
      ( ( Xx = Xy )
     => ( ( more @ Xz @ Xu )
       => ( more @ ( pl @ Xx @ Xz ) @ ( pl @ Xy @ Xu ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz19g) ).

thf(3,axiom,
    more @ z @ u,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m) ).

thf(4,axiom,
    x = y,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i) ).

thf(5,conjecture,
    more @ ( pl @ z @ x ) @ ( pl @ u @ y ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz19h) ).

thf(6,negated_conjecture,
    ( ( more @ ( pl @ z @ x ) @ ( pl @ u @ y ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[5]) ).

thf(7,plain,
    ( ( more @ ( pl @ z @ x ) @ ( pl @ u @ y ) )
    = $false ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(8,plain,
    ( ( ! [Xx: nat,Xy: nat] :
          ( ( pl @ Xx @ Xy )
          = ( pl @ Xy @ Xx ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(9,plain,
    ( ( ! [Xx: nat,Xy: nat,Xz: nat,Xu: nat] :
          ( ( Xx = Xy )
         => ( ( more @ Xz @ Xu )
           => ( more @ ( pl @ Xx @ Xz ) @ ( pl @ Xy @ Xu ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(10,plain,
    ( ( more @ z @ u )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(11,plain,
    ( ( x = y )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(12,plain,
    ( ( ~ ( more @ ( pl @ z @ x ) @ ( pl @ u @ y ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[7]) ).

thf(13,plain,
    ( ( ! [Xx: nat,Xy: nat] :
          ( ( Xx != Xy )
          | ! [Xz: nat,Xu: nat] :
              ( ~ ( more @ Xz @ Xu )
              | ( more @ ( pl @ Xx @ Xz ) @ ( pl @ Xy @ Xu ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[9]) ).

thf(14,plain,
    ( ( x = y )
    = $true ),
    inference(copy,[status(thm)],[11]) ).

thf(15,plain,
    ( ( more @ z @ u )
    = $true ),
    inference(copy,[status(thm)],[10]) ).

thf(16,plain,
    ( ( ! [Xx: nat,Xy: nat] :
          ( ( Xx != Xy )
          | ! [Xz: nat,Xu: nat] :
              ( ~ ( more @ Xz @ Xu )
              | ( more @ ( pl @ Xx @ Xz ) @ ( pl @ Xy @ Xu ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[13]) ).

thf(17,plain,
    ( ( ! [Xx: nat,Xy: nat] :
          ( ( pl @ Xx @ Xy )
          = ( pl @ Xy @ Xx ) ) )
    = $true ),
    inference(copy,[status(thm)],[8]) ).

thf(18,plain,
    ( ( ~ ( more @ ( pl @ z @ x ) @ ( pl @ u @ y ) ) )
    = $true ),
    inference(copy,[status(thm)],[12]) ).

thf(19,plain,
    ! [SV1: nat] :
      ( ( ! [SY6: nat] :
            ( ( SV1 != SY6 )
            | ! [SY7: nat,SY8: nat] :
                ( ~ ( more @ SY7 @ SY8 )
                | ( more @ ( pl @ SV1 @ SY7 ) @ ( pl @ SY6 @ SY8 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[16]) ).

thf(20,plain,
    ! [SV2: nat] :
      ( ( ! [SY9: nat] :
            ( ( pl @ SV2 @ SY9 )
            = ( pl @ SY9 @ SV2 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[17]) ).

thf(21,plain,
    ( ( more @ ( pl @ z @ x ) @ ( pl @ u @ y ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[18]) ).

thf(22,plain,
    ! [SV3: nat,SV1: nat] :
      ( ( ( SV1 != SV3 )
        | ! [SY10: nat,SY11: nat] :
            ( ~ ( more @ SY10 @ SY11 )
            | ( more @ ( pl @ SV1 @ SY10 ) @ ( pl @ SV3 @ SY11 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[19]) ).

thf(23,plain,
    ! [SV4: nat,SV2: nat] :
      ( ( ( pl @ SV2 @ SV4 )
        = ( pl @ SV4 @ SV2 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[20]) ).

thf(24,plain,
    ! [SV3: nat,SV1: nat] :
      ( ( ( ( SV1 != SV3 ) )
        = $true )
      | ( ( ! [SY10: nat,SY11: nat] :
              ( ~ ( more @ SY10 @ SY11 )
              | ( more @ ( pl @ SV1 @ SY10 ) @ ( pl @ SV3 @ SY11 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[22]) ).

thf(25,plain,
    ! [SV3: nat,SV1: nat] :
      ( ( ( SV1 = SV3 )
        = $false )
      | ( ( ! [SY10: nat,SY11: nat] :
              ( ~ ( more @ SY10 @ SY11 )
              | ( more @ ( pl @ SV1 @ SY10 ) @ ( pl @ SV3 @ SY11 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[24]) ).

thf(26,plain,
    ! [SV3: nat,SV1: nat,SV5: nat] :
      ( ( ( ! [SY12: nat] :
              ( ~ ( more @ SV5 @ SY12 )
              | ( more @ ( pl @ SV1 @ SV5 ) @ ( pl @ SV3 @ SY12 ) ) ) )
        = $true )
      | ( ( SV1 = SV3 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[25]) ).

thf(27,plain,
    ! [SV3: nat,SV1: nat,SV6: nat,SV5: nat] :
      ( ( ( ~ ( more @ SV5 @ SV6 )
          | ( more @ ( pl @ SV1 @ SV5 ) @ ( pl @ SV3 @ SV6 ) ) )
        = $true )
      | ( ( SV1 = SV3 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[26]) ).

thf(28,plain,
    ! [SV3: nat,SV1: nat,SV6: nat,SV5: nat] :
      ( ( ( ~ ( more @ SV5 @ SV6 ) )
        = $true )
      | ( ( more @ ( pl @ SV1 @ SV5 ) @ ( pl @ SV3 @ SV6 ) )
        = $true )
      | ( ( SV1 = SV3 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[27]) ).

thf(29,plain,
    ! [SV3: nat,SV1: nat,SV6: nat,SV5: nat] :
      ( ( ( more @ SV5 @ SV6 )
        = $false )
      | ( ( more @ ( pl @ SV1 @ SV5 ) @ ( pl @ SV3 @ SV6 ) )
        = $true )
      | ( ( SV1 = SV3 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[28]) ).

thf(30,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[14,29,23,21,15]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem  : NUM677^1 : TPTP v8.1.0. Released v3.7.0.
% 0.08/0.14  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.15/0.36  % Computer : n015.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 600
% 0.15/0.36  % DateTime : Wed Jul  6 05:09:33 EDT 2022
% 0.15/0.36  % CPUTime  : 
% 0.15/0.37  
% 0.15/0.37   No.of.Axioms: 4
% 0.15/0.37  
% 0.15/0.37   Length.of.Defs: 0
% 0.15/0.37  
% 0.15/0.37   Contains.Choice.Funs: false
% 0.15/0.37  (rf:0,axioms:4,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:6,loop_count:0,foatp_calls:0,translation:fof_full).
% 0.22/0.40  
% 0.22/0.40  ********************************
% 0.22/0.40  *   All subproblems solved!    *
% 0.22/0.40  ********************************
% 0.22/0.40  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:4,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)
% 0.22/0.40  
% 0.22/0.40  %**** Beginning of derivation protocol ****
% 0.22/0.40  % SZS output start CNFRefutation
% See solution above
% 0.22/0.40  
% 0.22/0.40  %**** End of derivation protocol ****
% 0.22/0.40  %**** no. of clauses in derivation: 31 ****
% 0.22/0.40  %**** clause counter: 30 ****
% 0.22/0.40  
% 0.22/0.40  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:4,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)
%------------------------------------------------------------------------------