TSTP Solution File: NUM692^1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : NUM692^1 : 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 : n023.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 11:54:18 EDT 2022

% Result   : Theorem 0.13s 0.36s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   50 (  29 unt;   8 typ;   0 def)
%            Number of atoms       :  176 (  47 equ;   0 cnn)
%            Maximal formula atoms :    3 (   4 avg)
%            Number of connectives :  298 (  26   ~;  32   |;   0   &; 232   @)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   3 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :   80 (   0   ^  80   !;   0   ?;  80   :)

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

thf(tp_lessis,type,
    lessis: nat > nat > $o ).

thf(tp_moreis,type,
    moreis: nat > nat > $o ).

thf(tp_ts,type,
    ts: 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] :
      ( ( lessis @ Xx @ Xy )
     => ( moreis @ Xy @ Xx ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz14) ).

thf(2,axiom,
    ! [Xx: nat,Xy: nat,Xz: nat,Xu: nat] :
      ( ( moreis @ Xx @ Xy )
     => ( ( moreis @ Xz @ Xu )
       => ( moreis @ ( ts @ Xx @ Xz ) @ ( ts @ Xy @ Xu ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz23) ).

thf(3,axiom,
    ! [Xx: nat,Xy: nat] :
      ( ( moreis @ Xx @ Xy )
     => ( lessis @ Xy @ Xx ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz13) ).

thf(4,axiom,
    lessis @ z @ u,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',k) ).

thf(5,axiom,
    lessis @ x @ y,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l) ).

thf(6,conjecture,
    lessis @ ( ts @ x @ z ) @ ( ts @ y @ u ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz23a) ).

thf(7,negated_conjecture,
    ( ( lessis @ ( ts @ x @ z ) @ ( ts @ y @ u ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[6]) ).

thf(8,plain,
    ( ( lessis @ ( ts @ x @ z ) @ ( ts @ y @ u ) )
    = $false ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(9,plain,
    ( ( ! [Xx: nat,Xy: nat] :
          ( ( lessis @ Xx @ Xy )
         => ( moreis @ Xy @ Xx ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(10,plain,
    ( ( ! [Xx: nat,Xy: nat,Xz: nat,Xu: nat] :
          ( ( moreis @ Xx @ Xy )
         => ( ( moreis @ Xz @ Xu )
           => ( moreis @ ( ts @ Xx @ Xz ) @ ( ts @ Xy @ Xu ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(11,plain,
    ( ( ! [Xx: nat,Xy: nat] :
          ( ( moreis @ Xx @ Xy )
         => ( lessis @ Xy @ Xx ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(12,plain,
    ( ( lessis @ z @ u )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(13,plain,
    ( ( lessis @ x @ y )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(14,plain,
    ( ( ~ ( lessis @ ( ts @ x @ z ) @ ( ts @ y @ u ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[8]) ).

thf(15,plain,
    ( ( ! [Xx: nat,Xy: nat] :
          ( ~ ( lessis @ Xx @ Xy )
          | ( moreis @ Xy @ Xx ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[9]) ).

thf(16,plain,
    ( ( ! [Xx: nat,Xy: nat] :
          ( ~ ( moreis @ Xx @ Xy )
          | ! [Xz: nat,Xu: nat] :
              ( ~ ( moreis @ Xz @ Xu )
              | ( moreis @ ( ts @ Xx @ Xz ) @ ( ts @ Xy @ Xu ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[10]) ).

thf(17,plain,
    ( ( ! [Xx: nat,Xy: nat] :
          ( ~ ( moreis @ Xx @ Xy )
          | ( lessis @ Xy @ Xx ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[11]) ).

thf(18,plain,
    ( ( lessis @ x @ y )
    = $true ),
    inference(copy,[status(thm)],[13]) ).

thf(19,plain,
    ( ( lessis @ z @ u )
    = $true ),
    inference(copy,[status(thm)],[12]) ).

thf(20,plain,
    ( ( ! [Xx: nat,Xy: nat] :
          ( ~ ( moreis @ Xx @ Xy )
          | ( lessis @ Xy @ Xx ) ) )
    = $true ),
    inference(copy,[status(thm)],[17]) ).

thf(21,plain,
    ( ( ! [Xx: nat,Xy: nat] :
          ( ~ ( moreis @ Xx @ Xy )
          | ! [Xz: nat,Xu: nat] :
              ( ~ ( moreis @ Xz @ Xu )
              | ( moreis @ ( ts @ Xx @ Xz ) @ ( ts @ Xy @ Xu ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[16]) ).

thf(22,plain,
    ( ( ! [Xx: nat,Xy: nat] :
          ( ~ ( lessis @ Xx @ Xy )
          | ( moreis @ Xy @ Xx ) ) )
    = $true ),
    inference(copy,[status(thm)],[15]) ).

thf(23,plain,
    ( ( ~ ( lessis @ ( ts @ x @ z ) @ ( ts @ y @ u ) ) )
    = $true ),
    inference(copy,[status(thm)],[14]) ).

thf(24,plain,
    ! [SV1: nat] :
      ( ( ! [SY8: nat] :
            ( ~ ( moreis @ SV1 @ SY8 )
            | ( lessis @ SY8 @ SV1 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[20]) ).

thf(25,plain,
    ! [SV2: nat] :
      ( ( ! [SY9: nat] :
            ( ~ ( moreis @ SV2 @ SY9 )
            | ! [SY10: nat,SY11: nat] :
                ( ~ ( moreis @ SY10 @ SY11 )
                | ( moreis @ ( ts @ SV2 @ SY10 ) @ ( ts @ SY9 @ SY11 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[21]) ).

thf(26,plain,
    ! [SV3: nat] :
      ( ( ! [SY12: nat] :
            ( ~ ( lessis @ SV3 @ SY12 )
            | ( moreis @ SY12 @ SV3 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[22]) ).

thf(27,plain,
    ( ( lessis @ ( ts @ x @ z ) @ ( ts @ y @ u ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[23]) ).

thf(28,plain,
    ! [SV4: nat,SV1: nat] :
      ( ( ~ ( moreis @ SV1 @ SV4 )
        | ( lessis @ SV4 @ SV1 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[24]) ).

thf(29,plain,
    ! [SV5: nat,SV2: nat] :
      ( ( ~ ( moreis @ SV2 @ SV5 )
        | ! [SY13: nat,SY14: nat] :
            ( ~ ( moreis @ SY13 @ SY14 )
            | ( moreis @ ( ts @ SV2 @ SY13 ) @ ( ts @ SV5 @ SY14 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[25]) ).

thf(30,plain,
    ! [SV6: nat,SV3: nat] :
      ( ( ~ ( lessis @ SV3 @ SV6 )
        | ( moreis @ SV6 @ SV3 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[26]) ).

thf(31,plain,
    ! [SV4: nat,SV1: nat] :
      ( ( ( ~ ( moreis @ SV1 @ SV4 ) )
        = $true )
      | ( ( lessis @ SV4 @ SV1 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[28]) ).

thf(32,plain,
    ! [SV5: nat,SV2: nat] :
      ( ( ( ~ ( moreis @ SV2 @ SV5 ) )
        = $true )
      | ( ( ! [SY13: nat,SY14: nat] :
              ( ~ ( moreis @ SY13 @ SY14 )
              | ( moreis @ ( ts @ SV2 @ SY13 ) @ ( ts @ SV5 @ SY14 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[29]) ).

thf(33,plain,
    ! [SV6: nat,SV3: nat] :
      ( ( ( ~ ( lessis @ SV3 @ SV6 ) )
        = $true )
      | ( ( moreis @ SV6 @ SV3 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[30]) ).

thf(34,plain,
    ! [SV4: nat,SV1: nat] :
      ( ( ( moreis @ SV1 @ SV4 )
        = $false )
      | ( ( lessis @ SV4 @ SV1 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[31]) ).

thf(35,plain,
    ! [SV5: nat,SV2: nat] :
      ( ( ( moreis @ SV2 @ SV5 )
        = $false )
      | ( ( ! [SY13: nat,SY14: nat] :
              ( ~ ( moreis @ SY13 @ SY14 )
              | ( moreis @ ( ts @ SV2 @ SY13 ) @ ( ts @ SV5 @ SY14 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[32]) ).

thf(36,plain,
    ! [SV6: nat,SV3: nat] :
      ( ( ( lessis @ SV3 @ SV6 )
        = $false )
      | ( ( moreis @ SV6 @ SV3 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[33]) ).

thf(37,plain,
    ! [SV5: nat,SV2: nat,SV7: nat] :
      ( ( ( ! [SY15: nat] :
              ( ~ ( moreis @ SV7 @ SY15 )
              | ( moreis @ ( ts @ SV2 @ SV7 ) @ ( ts @ SV5 @ SY15 ) ) ) )
        = $true )
      | ( ( moreis @ SV2 @ SV5 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[35]) ).

thf(38,plain,
    ! [SV5: nat,SV2: nat,SV8: nat,SV7: nat] :
      ( ( ( ~ ( moreis @ SV7 @ SV8 )
          | ( moreis @ ( ts @ SV2 @ SV7 ) @ ( ts @ SV5 @ SV8 ) ) )
        = $true )
      | ( ( moreis @ SV2 @ SV5 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[37]) ).

thf(39,plain,
    ! [SV5: nat,SV2: nat,SV8: nat,SV7: nat] :
      ( ( ( ~ ( moreis @ SV7 @ SV8 ) )
        = $true )
      | ( ( moreis @ ( ts @ SV2 @ SV7 ) @ ( ts @ SV5 @ SV8 ) )
        = $true )
      | ( ( moreis @ SV2 @ SV5 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[38]) ).

thf(40,plain,
    ! [SV5: nat,SV2: nat,SV8: nat,SV7: nat] :
      ( ( ( moreis @ SV7 @ SV8 )
        = $false )
      | ( ( moreis @ ( ts @ SV2 @ SV7 ) @ ( ts @ SV5 @ SV8 ) )
        = $true )
      | ( ( moreis @ SV2 @ SV5 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[39]) ).

thf(41,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[18,40,36,34,27,19]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : NUM692^1 : TPTP v8.1.0. Released v3.7.0.
% 0.06/0.12  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33  % Computer : n023.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Fri Jul  8 02:45:56 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.13/0.34  
% 0.13/0.34   No.of.Axioms: 5
% 0.13/0.34  
% 0.13/0.34   Length.of.Defs: 0
% 0.13/0.34  
% 0.13/0.34   Contains.Choice.Funs: false
% 0.13/0.34  (rf:0,axioms:5,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:7,loop_count:0,foatp_calls:0,translation:fof_full).
% 0.13/0.36  
% 0.13/0.36  ********************************
% 0.13/0.36  *   All subproblems solved!    *
% 0.13/0.36  ********************************
% 0.13/0.36  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:5,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:41,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.13/0.36  
% 0.13/0.36  %**** Beginning of derivation protocol ****
% 0.13/0.36  % SZS output start CNFRefutation
% See solution above
% 0.13/0.36  
% 0.13/0.36  %**** End of derivation protocol ****
% 0.13/0.36  %**** no. of clauses in derivation: 42 ****
% 0.13/0.36  %**** clause counter: 41 ****
% 0.13/0.36  
% 0.13/0.36  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:5,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:41,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------