TSTP Solution File: SEU858^5 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SEU858^5 : 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 : n020.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 : Tue Jul 19 12:15:25 EDT 2022

% Result   : Theorem 0.12s 0.37s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   21 (  15 unt;   2 typ;   0 def)
%            Number of atoms       :   91 (  31 equ;   0 cnn)
%            Maximal formula atoms :    3 (   4 avg)
%            Number of connectives :   83 (   6   ~;  17   |;   4   &;  47   @)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   2 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   19 (  19   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   1 usr;   2 con; 0-2 aty)
%            Number of variables   :   50 (  25   ^  25   !;   0   ?;  50   :)

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

thf(tp_sK1_Xw,type,
    sK1_Xw: ( a > $o ) > $o ).

thf(1,conjecture,
    ! [Xw: ( a > $o ) > $o] :
      ( ( ( Xw
          @ ^ [Xx: a] : $false )
        & ! [Xr: a > $o,Xx: a] :
            ( ( Xw @ Xr )
           => ( Xw
              @ ^ [Xt: a] :
                  ( ( Xr @ Xt )
                  | ( Xt = Xx ) ) ) ) )
     => ( Xw
        @ ^ [Xx: a] : $false ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM163_pme) ).

thf(2,negated_conjecture,
    ( ( ! [Xw: ( a > $o ) > $o] :
          ( ( ( Xw
              @ ^ [Xx: a] : $false )
            & ! [Xr: a > $o,Xx: a] :
                ( ( Xw @ Xr )
               => ( Xw
                  @ ^ [Xt: a] :
                      ( ( Xr @ Xt )
                      | ( Xt = Xx ) ) ) ) )
         => ( Xw
            @ ^ [Xx: a] : $false ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ! [Xw: ( a > $o ) > $o] :
          ( ( ( Xw
              @ ^ [Xx: a] : $false )
            & ! [Xr: a > $o,Xx: a] :
                ( ( Xw @ Xr )
               => ( Xw
                  @ ^ [Xt: a] :
                      ( ( Xr @ Xt )
                      | ( Xt = Xx ) ) ) ) )
         => ( Xw
            @ ^ [Xx: a] : $false ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ( ( sK1_Xw
          @ ^ [Xx: a] : $false )
        & ! [SY7: a > $o,SY8: a] :
            ( ( sK1_Xw @ SY7 )
           => ( sK1_Xw
              @ ^ [Xt: a] :
                  ( ( SY7 @ Xt )
                  | ( Xt = SY8 ) ) ) ) )
     => ( sK1_Xw
        @ ^ [Xx: a] : $false ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[3]) ).

thf(5,plain,
    ( ( sK1_Xw
      @ ^ [Xx: a] : $false )
    = $true ),
    inference(standard_cnf,[status(thm)],[4]) ).

thf(6,plain,
    ( ( ! [SY7: a > $o,SY8: a] :
          ( ( sK1_Xw @ SY7 )
         => ( sK1_Xw
            @ ^ [Xt: a] :
                ( ( SY7 @ Xt )
                | ( Xt = SY8 ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[4]) ).

thf(7,plain,
    ( ( sK1_Xw
      @ ^ [Xx: a] : $false )
    = $false ),
    inference(standard_cnf,[status(thm)],[4]) ).

thf(8,plain,
    ( ( ~ ( sK1_Xw
          @ ^ [Xx: a] : $false ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[7]) ).

thf(9,plain,
    ( ( ! [SY7: a > $o] :
          ( ~ ( sK1_Xw @ SY7 )
          | ! [SY8: a] :
              ( sK1_Xw
              @ ^ [Xt: a] :
                  ( ( SY7 @ Xt )
                  | ( Xt = SY8 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[6]) ).

thf(10,plain,
    ( ( ! [SY7: a > $o] :
          ( ~ ( sK1_Xw @ SY7 )
          | ! [SY8: a] :
              ( sK1_Xw
              @ ^ [Xt: a] :
                  ( ( SY7 @ Xt )
                  | ( Xt = SY8 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[9]) ).

thf(11,plain,
    ( ( sK1_Xw
      @ ^ [Xx: a] : $false )
    = $true ),
    inference(copy,[status(thm)],[5]) ).

thf(12,plain,
    ( ( ~ ( sK1_Xw
          @ ^ [Xx: a] : $false ) )
    = $true ),
    inference(copy,[status(thm)],[8]) ).

thf(13,plain,
    ! [SV1: a > $o] :
      ( ( ~ ( sK1_Xw @ SV1 )
        | ! [SY11: a] :
            ( sK1_Xw
            @ ^ [SY12: a] :
                ( ( SV1 @ SY12 )
                | ( SY12 = SY11 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10]) ).

thf(14,plain,
    ( ( sK1_Xw
      @ ^ [Xx: a] : $false )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[12]) ).

thf(15,plain,
    ! [SV1: a > $o] :
      ( ( ( ~ ( sK1_Xw @ SV1 ) )
        = $true )
      | ( ( ! [SY11: a] :
              ( sK1_Xw
              @ ^ [SY12: a] :
                  ( ( SV1 @ SY12 )
                  | ( SY12 = SY11 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[13]) ).

thf(16,plain,
    ! [SV1: a > $o] :
      ( ( ( sK1_Xw @ SV1 )
        = $false )
      | ( ( ! [SY11: a] :
              ( sK1_Xw
              @ ^ [SY12: a] :
                  ( ( SV1 @ SY12 )
                  | ( SY12 = SY11 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[15]) ).

thf(17,plain,
    ! [SV2: a,SV1: a > $o] :
      ( ( ( sK1_Xw
          @ ^ [SY13: a] :
              ( ( SV1 @ SY13 )
              | ( SY13 = SV2 ) ) )
        = $true )
      | ( ( sK1_Xw @ SV1 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[16]) ).

thf(18,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[11,17,14]) ).

thf(19,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[18]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU858^5 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34  % Computer : n020.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Sun Jun 19 23:14:48 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.35  
% 0.12/0.35   No.of.Axioms: 0
% 0.12/0.35  
% 0.12/0.35   Length.of.Defs: 0
% 0.12/0.35  
% 0.12/0.35   Contains.Choice.Funs: false
% 0.12/0.35  (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)
% 0.12/0.37  ********************************
% 0.12/0.37  *   All subproblems solved!    *
% 0.12/0.37  ********************************
% 0.12/0.37  % 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:18,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.12/0.37  
% 0.12/0.37  %**** Beginning of derivation protocol ****
% 0.12/0.37  % SZS output start CNFRefutation
% See solution above
% 0.12/0.37  
% 0.12/0.37  %**** End of derivation protocol ****
% 0.12/0.37  %**** no. of clauses in derivation: 19 ****
% 0.12/0.37  %**** clause counter: 18 ****
% 0.12/0.37  
% 0.12/0.37  % 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:18,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------