TSTP Solution File: SEU650^2 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SEU650^2 : 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 : n013.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 12:13:39 EDT 2022

% Result   : Theorem 0.13s 0.36s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   29 (  21 unt;   5 typ;   1 def)
%            Number of atoms       :   93 (  65 equ;   0 cnn)
%            Maximal formula atoms :    3 (   3 avg)
%            Number of connectives :  262 (  19   ~;   8   |;   2   &; 222   @)
%                                         (   0 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   5 usr;   6 con; 0-2 aty)
%            Number of variables   :   28 (   0   ^  28   !;   0   ?;  28   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_emptyset,type,
    emptyset: $i ).

thf(tp_sK1_Xx,type,
    sK1_Xx: $i ).

thf(tp_sK2_SY6,type,
    sK2_SY6: $i ).

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

thf(tp_setukpairinjR11,type,
    setukpairinjR11: $o ).

thf(setukpairinjR11,definition,
    ( setukpairinjR11
    = ( ! [Xx: $i,Xy: $i] :
          ( ( Xx = Xy )
         => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
            = ( setadjoin @ Xx @ emptyset ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR11) ).

thf(1,conjecture,
    ( setukpairinjR11
   => ! [Xx: $i,Xy: $i] :
        ( ( Xx = Xy )
       => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
          = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR12) ).

thf(2,negated_conjecture,
    ( ( setukpairinjR11
     => ! [Xx: $i,Xy: $i] :
          ( ( Xx = Xy )
         => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
            = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ! [Xx: $i,Xy: $i] :
          ( ( Xx = Xy )
         => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
            = ( setadjoin @ Xx @ emptyset ) ) )
     => ! [Xx: $i,Xy: $i] :
          ( ( Xx = Xy )
         => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
            = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2,setukpairinjR11]) ).

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

thf(5,plain,
    ( ( ! [Xx: $i,Xy: $i] :
          ( ( Xx = Xy )
         => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
            = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[3]) ).

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

thf(7,plain,
    ( ( ( sK1_Xx = sK2_SY6 )
      & ( ( setadjoin @ ( setadjoin @ sK1_Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_Xx @ ( setadjoin @ sK2_SY6 @ emptyset ) ) @ emptyset ) )
       != ( setadjoin @ ( setadjoin @ sK1_Xx @ emptyset ) @ emptyset ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[6]) ).

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

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

thf(10,plain,
    ( ( ( sK1_Xx = sK2_SY6 )
      & ( ( setadjoin @ ( setadjoin @ sK1_Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_Xx @ ( setadjoin @ sK2_SY6 @ emptyset ) ) @ emptyset ) )
       != ( setadjoin @ ( setadjoin @ sK1_Xx @ emptyset ) @ emptyset ) ) )
    = $true ),
    inference(copy,[status(thm)],[7]) ).

thf(11,plain,
    ( ( ~ ( ( sK1_Xx != sK2_SY6 )
          | ~ ( ( ( setadjoin @ ( setadjoin @ sK1_Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_Xx @ ( setadjoin @ sK2_SY6 @ emptyset ) ) @ emptyset ) )
               != ( setadjoin @ ( setadjoin @ sK1_Xx @ emptyset ) @ emptyset ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10,setukpairinjR11]) ).

thf(12,plain,
    ! [SV1: $i] :
      ( ( ! [SY7: $i] :
            ( ( SV1 != SY7 )
            | ( ( setadjoin @ SV1 @ ( setadjoin @ SY7 @ emptyset ) )
              = ( setadjoin @ SV1 @ emptyset ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[9]) ).

thf(13,plain,
    ( ( ( sK1_Xx != sK2_SY6 )
      | ~ ( ( ( setadjoin @ ( setadjoin @ sK1_Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_Xx @ ( setadjoin @ sK2_SY6 @ emptyset ) ) @ emptyset ) )
           != ( setadjoin @ ( setadjoin @ sK1_Xx @ emptyset ) @ emptyset ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[11]) ).

thf(14,plain,
    ! [SV2: $i,SV1: $i] :
      ( ( ( SV1 != SV2 )
        | ( ( setadjoin @ SV1 @ ( setadjoin @ SV2 @ emptyset ) )
          = ( setadjoin @ SV1 @ emptyset ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12]) ).

thf(15,plain,
    ( ( ( sK1_Xx != sK2_SY6 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[13]) ).

thf(16,plain,
    ( ( ~ ( ( ( setadjoin @ ( setadjoin @ sK1_Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_Xx @ ( setadjoin @ sK2_SY6 @ emptyset ) ) @ emptyset ) )
           != ( setadjoin @ ( setadjoin @ sK1_Xx @ emptyset ) @ emptyset ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[13]) ).

thf(17,plain,
    ! [SV2: $i,SV1: $i] :
      ( ( ( ( SV1 != SV2 ) )
        = $true )
      | ( ( ( setadjoin @ SV1 @ ( setadjoin @ SV2 @ emptyset ) )
          = ( setadjoin @ SV1 @ emptyset ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[14]) ).

thf(18,plain,
    ( ( sK1_Xx = sK2_SY6 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[15]) ).

thf(19,plain,
    ( ( ( ( setadjoin @ ( setadjoin @ sK1_Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_Xx @ ( setadjoin @ sK2_SY6 @ emptyset ) ) @ emptyset ) )
       != ( setadjoin @ ( setadjoin @ sK1_Xx @ emptyset ) @ emptyset ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[16]) ).

thf(20,plain,
    ! [SV2: $i,SV1: $i] :
      ( ( ( SV1 = SV2 )
        = $false )
      | ( ( ( setadjoin @ SV1 @ ( setadjoin @ SV2 @ emptyset ) )
          = ( setadjoin @ SV1 @ emptyset ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[17]) ).

thf(21,plain,
    ( ( ( setadjoin @ ( setadjoin @ sK1_Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_Xx @ ( setadjoin @ sK2_SY6 @ emptyset ) ) @ emptyset ) )
      = ( setadjoin @ ( setadjoin @ sK1_Xx @ emptyset ) @ emptyset ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[19]) ).

thf(22,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[18,21,20]) ).

thf(23,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[22]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11  % Problem  : SEU650^2 : TPTP v8.1.0. Released v3.7.0.
% 0.09/0.12  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33  % Computer : n013.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 : Mon Jun 20 09:07:59 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.13/0.34  
% 0.13/0.34   No.of.Axioms: 0
% 0.13/0.34  
% 0.13/0.34   Length.of.Defs: 235
% 0.13/0.34  
% 0.13/0.34   Contains.Choice.Funs: false
% 0.13/0.34  (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).
% 0.13/0.36  
% 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/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:22,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: 23 ****
% 0.13/0.36  %**** clause counter: 22 ****
% 0.13/0.36  
% 0.13/0.36  % 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:22,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------