TSTP Solution File: SEU775^2 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SEU775^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.5m5JsEDUoE true

% Computer : n010.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  : 300s
% DateTime : Thu Aug 31 19:17:27 EDT 2023

% Result   : Theorem 0.21s 0.77s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   37 (  16 unt;  11 typ;   0 def)
%            Number of atoms       :   73 (  12 equ;   0 cnn)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  260 (   7   ~;   0   |;   0   &; 226   @)
%                                         (   0 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   38 (  38   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  11 usr;   5 con; 0-3 aty)
%                                         (  14  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :   76 (  53   ^;  23   !;   0   ?;  76   :)

% Comments : 
%------------------------------------------------------------------------------
thf(breln_type,type,
    breln: $i > $i > $i > $o ).

thf(in_type,type,
    in: $i > $i > $o ).

thf(dpsetconstr_type,type,
    dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).

thf(kpair_type,type,
    kpair: $i > $i > $i ).

thf(breln1_type,type,
    breln1: $i > $i > $o ).

thf('#sk1_type',type,
    '#sk1': $i ).

thf(cartprod_type,type,
    cartprod: $i > $i > $i ).

thf(subset_type,type,
    subset: $i > $i > $o ).

thf('#sk2_type',type,
    '#sk2': $i ).

thf(breln1invset_type,type,
    breln1invset: $i > $i > $i ).

thf(setOfPairsIsBReln1_type,type,
    setOfPairsIsBReln1: $o ).

thf(setOfPairsIsBReln1,axiom,
    ( setOfPairsIsBReln1
    = ( ! [A: $i,Xphi: $i > $i > $o] :
          ( breln1 @ A
          @ ( dpsetconstr @ A @ A
            @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).

thf('0',plain,
    ( setOfPairsIsBReln1
    = ( ! [X4: $i,X6: $i > $i > $o] :
          ( breln1 @ X4
          @ ( dpsetconstr @ X4 @ X4
            @ ^ [V_1: $i,V_2: $i] : ( X6 @ V_1 @ V_2 ) ) ) ) ),
    define([status(thm)]) ).

thf(breln1,axiom,
    ( breln1
    = ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ) ).

thf(breln,axiom,
    ( breln
    = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).

thf('1',plain,
    ( breln
    = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[breln]) ).

thf('2',plain,
    ( breln
    = ( ^ [V_1: $i,V_2: $i,V_3: $i] : ( subset @ V_3 @ ( cartprod @ V_1 @ V_2 ) ) ) ),
    define([status(thm)]) ).

thf('3',plain,
    ( breln1
    = ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ),
    inference(simplify_rw_rule,[status(thm)],[breln1,'2']) ).

thf('4',plain,
    ( breln1
    = ( ^ [V_1: $i,V_2: $i] : ( breln @ V_1 @ V_1 @ V_2 ) ) ),
    define([status(thm)]) ).

thf(breln1invprop,conjecture,
    ( setOfPairsIsBReln1
   => ! [A: $i,R: $i] :
        ( ( breln1 @ A @ R )
       => ( breln1 @ A @ ( breln1invset @ A @ R ) ) ) ) ).

thf(zf_stmt_0,conjecture,
    ( ! [X4: $i,X6: $i > $i > $o] :
        ( subset
        @ ( dpsetconstr @ X4 @ X4
          @ ^ [V_1: $i,V_2: $i] : ( X6 @ V_1 @ V_2 ) )
        @ ( cartprod @ X4 @ X4 ) )
   => ! [X8: $i,X10: $i] :
        ( ( subset @ X10 @ ( cartprod @ X8 @ X8 ) )
       => ( subset @ ( breln1invset @ X8 @ X10 ) @ ( cartprod @ X8 @ X8 ) ) ) ) ).

thf(zf_stmt_1,negated_conjecture,
    ~ ( ! [X4: $i,X6: $i > $i > $o] :
          ( subset
          @ ( dpsetconstr @ X4 @ X4
            @ ^ [V_1: $i,V_2: $i] : ( X6 @ V_1 @ V_2 ) )
          @ ( cartprod @ X4 @ X4 ) )
     => ! [X8: $i,X10: $i] :
          ( ( subset @ X10 @ ( cartprod @ X8 @ X8 ) )
         => ( subset @ ( breln1invset @ X8 @ X10 ) @ ( cartprod @ X8 @ X8 ) ) ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl1,plain,
    ~ ( ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i > $i > $o] :
                ( subset
                @ ( dpsetconstr @ Y0 @ Y0
                  @ ^ [Y2: $i,Y3: $i] : ( Y1 @ Y2 @ Y3 ) )
                @ ( cartprod @ Y0 @ Y0 ) ) ) )
     => ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( ( subset @ Y1 @ ( cartprod @ Y0 @ Y0 ) )
               => ( subset @ ( breln1invset @ Y0 @ Y1 ) @ ( cartprod @ Y0 @ Y0 ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl8,plain,
    ~ ( ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i > $i > $o] : ( subset @ ( dpsetconstr @ Y0 @ Y0 @ Y1 ) @ ( cartprod @ Y0 @ Y0 ) ) ) )
     => ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( ( subset @ Y1 @ ( cartprod @ Y0 @ Y0 ) )
               => ( subset @ ( breln1invset @ Y0 @ Y1 ) @ ( cartprod @ Y0 @ Y0 ) ) ) ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl1]) ).

thf(zip_derived_cl10,plain,
    ~ ( !!
      @ ^ [Y0: $i] :
          ( !!
          @ ^ [Y1: $i] :
              ( ( subset @ Y1 @ ( cartprod @ Y0 @ Y0 ) )
             => ( subset @ ( breln1invset @ Y0 @ Y1 ) @ ( cartprod @ Y0 @ Y0 ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl8]) ).

thf(zip_derived_cl12,plain,
    ~ ( !!
      @ ^ [Y0: $i] :
          ( ( subset @ Y0 @ ( cartprod @ '#sk1' @ '#sk1' ) )
         => ( subset @ ( breln1invset @ '#sk1' @ Y0 ) @ ( cartprod @ '#sk1' @ '#sk1' ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl10]) ).

thf(zip_derived_cl15,plain,
    ~ ( ( subset @ '#sk2' @ ( cartprod @ '#sk1' @ '#sk1' ) )
     => ( subset @ ( breln1invset @ '#sk1' @ '#sk2' ) @ ( cartprod @ '#sk1' @ '#sk1' ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl12]) ).

thf(zip_derived_cl17,plain,
    ~ ( subset @ ( breln1invset @ '#sk1' @ '#sk2' ) @ ( cartprod @ '#sk1' @ '#sk1' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15]) ).

thf(breln1invset,axiom,
    ( breln1invset
    = ( ^ [A: $i,R: $i] :
          ( dpsetconstr @ A @ A
          @ ^ [Xx: $i,Xy: $i] : ( in @ ( kpair @ Xy @ Xx ) @ R ) ) ) ) ).

thf(zip_derived_cl0,plain,
    ( breln1invset
    = ( ^ [Y0: $i,Y1: $i] :
          ( dpsetconstr @ Y0 @ Y0
          @ ^ [Y2: $i,Y3: $i] : ( in @ ( kpair @ Y3 @ Y2 ) @ Y1 ) ) ) ),
    inference(cnf,[status(esa)],[breln1invset]) ).

thf(zip_derived_cl3,plain,
    ! [X1: $i,X2: $i] :
      ( ( breln1invset @ X1 @ X2 )
      = ( ^ [Y0: $i,Y1: $i] :
            ( dpsetconstr @ Y0 @ Y0
            @ ^ [Y2: $i,Y3: $i] : ( in @ ( kpair @ Y3 @ Y2 ) @ Y1 ) )
        @ X1
        @ X2 ) ),
    inference(ho_complete_eq,[status(thm)],[zip_derived_cl0]) ).

thf(zip_derived_cl5,plain,
    ! [X1: $i,X2: $i] :
      ( ( breln1invset @ X1 @ X2 )
      = ( dpsetconstr @ X1 @ X1
        @ ^ [Y0: $i,Y1: $i] : ( in @ ( kpair @ Y1 @ Y0 ) @ X2 ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl3]) ).

thf(zip_derived_cl9,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( !!
        @ ^ [Y1: $i > $i > $o] : ( subset @ ( dpsetconstr @ Y0 @ Y0 @ Y1 ) @ ( cartprod @ Y0 @ Y0 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl8]) ).

thf(zip_derived_cl11,plain,
    ! [X2: $i] :
      ( !!
      @ ^ [Y0: $i > $i > $o] : ( subset @ ( dpsetconstr @ X2 @ X2 @ Y0 ) @ ( cartprod @ X2 @ X2 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl9]) ).

thf(zip_derived_cl13,plain,
    ! [X2: $i,X4: $i > $i > $o] : ( subset @ ( dpsetconstr @ X2 @ X2 @ X4 ) @ ( cartprod @ X2 @ X2 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl11]) ).

thf(zip_derived_cl18,plain,
    ! [X0: $i,X1: $i] : ( subset @ ( breln1invset @ X1 @ X0 ) @ ( cartprod @ X1 @ X1 ) ),
    inference('sup+',[status(thm)],[zip_derived_cl5,zip_derived_cl13]) ).

thf(zip_derived_cl19,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl17,zip_derived_cl18]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SEU775^2 : TPTP v8.1.2. Released v3.7.0.
% 0.11/0.13  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.5m5JsEDUoE true
% 0.13/0.34  % Computer : n010.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Wed Aug 23 20:14:36 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  % Running portfolio for 300 s
% 0.13/0.35  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35  % Number of cores: 8
% 0.13/0.35  % Python version: Python 3.6.8
% 0.13/0.35  % Running in HO mode
% 0.21/0.62  % Total configuration time : 828
% 0.21/0.62  % Estimated wc time : 1656
% 0.21/0.62  % Estimated cpu time (8 cpus) : 207.0
% 0.21/0.73  % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.21/0.73  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.21/0.74  % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.21/0.76  % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.21/0.77  % Solved by lams/35_full_unif4.sh.
% 0.21/0.77  % done 7 iterations in 0.013s
% 0.21/0.77  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 0.21/0.77  % SZS output start Refutation
% See solution above
% 0.21/0.77  
% 0.21/0.77  
% 0.21/0.77  % Terminating...
% 1.52/0.84  % Runner terminated.
% 1.52/0.85  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------