TSTP Solution File: SEU808^2 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SEU808^2 : 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 : n009.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 12:14:54 EDT 2022

% Result   : Theorem 0.13s 0.39s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   30 (  21 unt;   6 typ;   2 def)
%            Number of atoms       :   90 (  24 equ;   0 cnn)
%            Maximal formula atoms :    3 (   3 avg)
%            Number of connectives :  156 (  18   ~;   7   |;   2   &; 118   @)
%                                         (   0 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   6 usr;   5 con; 0-2 aty)
%            Number of variables   :   14 (   1   ^  13   !;   0   ?;  14   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_in,type,
    in: $i > $i > $o ).

thf(tp_omega,type,
    omega: $i ).

thf(tp_omegaS,type,
    omegaS: $i > $i ).

thf(tp_omegaSAx,type,
    omegaSAx: $o ).

thf(tp_sK1_SY0,type,
    sK1_SY0: $i ).

thf(tp_setadjoin,type,
    setadjoin: $i > $i > $i ).

thf(omegaS,definition,
    ( omegaS
    = ( ^ [Xx: $i] : ( setadjoin @ Xx @ Xx ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaS) ).

thf(omegaSAx,definition,
    ( omegaSAx
    = ( ! [Xx: $i] :
          ( ( in @ Xx @ omega )
         => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaSAx) ).

thf(1,conjecture,
    ( omegaSAx
   => ! [Xx: $i] :
        ( ( in @ Xx @ omega )
       => ( in @ ( omegaS @ Xx ) @ omega ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaSp) ).

thf(2,negated_conjecture,
    ( ( omegaSAx
     => ! [Xx: $i] :
          ( ( in @ Xx @ omega )
         => ( in @ ( omegaS @ Xx ) @ omega ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ! [Xx: $i] :
          ( ( in @ Xx @ omega )
         => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) )
     => ! [SY0: $i] :
          ( ( in @ SY0 @ omega )
         => ( in @ ( setadjoin @ SY0 @ SY0 ) @ omega ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2,omegaS,omegaSAx]) ).

thf(4,plain,
    ( ( ! [Xx: $i] :
          ( ( in @ Xx @ omega )
         => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(5,plain,
    ( ( ! [SY0: $i] :
          ( ( in @ SY0 @ omega )
         => ( in @ ( setadjoin @ SY0 @ SY0 ) @ omega ) ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(6,plain,
    ( ( ~ ! [SY0: $i] :
            ( ( in @ SY0 @ omega )
           => ( in @ ( setadjoin @ SY0 @ SY0 ) @ omega ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[5]) ).

thf(7,plain,
    ( ( ( in @ sK1_SY0 @ omega )
      & ~ ( in @ ( setadjoin @ sK1_SY0 @ sK1_SY0 ) @ omega ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[6]) ).

thf(8,plain,
    ( ( ! [Xx: $i] :
          ( ~ ( in @ Xx @ omega )
          | ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[4]) ).

thf(9,plain,
    ( ( ! [Xx: $i] :
          ( ~ ( in @ Xx @ omega )
          | ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) )
    = $true ),
    inference(copy,[status(thm)],[8]) ).

thf(10,plain,
    ( ( ( in @ sK1_SY0 @ omega )
      & ~ ( in @ ( setadjoin @ sK1_SY0 @ sK1_SY0 ) @ omega ) )
    = $true ),
    inference(copy,[status(thm)],[7]) ).

thf(11,plain,
    ( ( ~ ( ~ ( in @ sK1_SY0 @ omega )
          | ~ ~ ( in @ ( setadjoin @ sK1_SY0 @ sK1_SY0 ) @ omega ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10,omegaS,omegaSAx]) ).

thf(12,plain,
    ! [SV1: $i] :
      ( ( ~ ( in @ SV1 @ omega )
        | ( in @ ( setadjoin @ SV1 @ SV1 ) @ omega ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[9]) ).

thf(13,plain,
    ( ( ~ ( in @ sK1_SY0 @ omega )
      | ~ ~ ( in @ ( setadjoin @ sK1_SY0 @ sK1_SY0 ) @ omega ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[11]) ).

thf(14,plain,
    ! [SV1: $i] :
      ( ( ( ~ ( in @ SV1 @ omega ) )
        = $true )
      | ( ( in @ ( setadjoin @ SV1 @ SV1 ) @ omega )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12]) ).

thf(15,plain,
    ( ( ~ ( in @ sK1_SY0 @ omega ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[13]) ).

thf(16,plain,
    ( ( ~ ~ ( in @ ( setadjoin @ sK1_SY0 @ sK1_SY0 ) @ omega ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[13]) ).

thf(17,plain,
    ! [SV1: $i] :
      ( ( ( in @ SV1 @ omega )
        = $false )
      | ( ( in @ ( setadjoin @ SV1 @ SV1 ) @ omega )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14]) ).

thf(18,plain,
    ( ( in @ sK1_SY0 @ omega )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[15]) ).

thf(19,plain,
    ( ( ~ ( in @ ( setadjoin @ sK1_SY0 @ sK1_SY0 ) @ omega ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[16]) ).

thf(20,plain,
    ( ( in @ ( setadjoin @ sK1_SY0 @ sK1_SY0 ) @ omega )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[19]) ).

thf(21,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[17,20,18]) ).

thf(22,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[21]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SEU808^2 : TPTP v8.1.0. Released v3.7.0.
% 0.07/0.14  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.35  % Computer : n009.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Mon Jun 20 00:21:37 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.36  
% 0.13/0.36   No.of.Axioms: 0
% 0.13/0.36  
% 0.13/0.36   Length.of.Defs: 308
% 0.13/0.36  
% 0.13/0.36   Contains.Choice.Funs: false
% 0.13/0.36  (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)
% 0.13/0.39  ********************************
% 0.13/0.39  *   All subproblems solved!    *
% 0.13/0.39  ********************************
% 0.13/0.39  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:1,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:21,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.13/0.39  
% 0.13/0.39  %**** Beginning of derivation protocol ****
% 0.13/0.39  % SZS output start CNFRefutation
% See solution above
% 0.13/0.39  
% 0.13/0.39  %**** End of derivation protocol ****
% 0.13/0.39  %**** no. of clauses in derivation: 22 ****
% 0.13/0.39  %**** clause counter: 21 ****
% 0.13/0.39  
% 0.13/0.39  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:1,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:21,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------