TSTP Solution File: SEU681^2 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SEU681^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.gk4wOfhUUh true

% Computer : n015.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 19:16:07 EDT 2023

% Result   : Theorem 0.11s 0.52s
% Output   : Refutation 0.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   44 (  12 unt;  14 typ;   0 def)
%            Number of atoms       :  118 (  13 equ;   0 cnn)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  434 (  39   ~;  36   |;   8   &; 315   @)
%                                         (   0 <=>;  36  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   21 (  21   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   16 (  14 usr;   7 con; 0-3 aty)
%            Number of variables   :   96 (   9   ^;  79   !;   8   ?;  96   :)

% Comments : 
%------------------------------------------------------------------------------
thf(sk__8_type,type,
    sk__8: $i > $i > $i > $i ).

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

thf(cartprodmempair1_type,type,
    cartprodmempair1: $o ).

thf(subsetE_type,type,
    subsetE: $o ).

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

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

thf(sk__10_type,type,
    sk__10: $i ).

thf(sk__12_type,type,
    sk__12: $i ).

thf(sk__14_type,type,
    sk__14: $i ).

thf(sk__11_type,type,
    sk__11: $i ).

thf(sk__13_type,type,
    sk__13: $i > $o ).

thf(sk__9_type,type,
    sk__9: $i > $i > $i > $i ).

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

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

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

thf('0',plain,
    ( breln
    = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[breln]) ).

thf('1',plain,
    ( breln
    = ( ^ [V_1: $i,V_2: $i,V_3: $i] : ( subset @ V_3 @ ( cartprod @ V_1 @ V_2 ) ) ) ),
    define([status(thm)]) ).

thf(cartprodmempair1,axiom,
    ( cartprodmempair1
    = ( ! [A: $i,B: $i,Xu: $i] :
          ( ( in @ Xu @ ( cartprod @ A @ B ) )
         => ? [Xx: $i] :
              ( ? [Xy: $i] :
                  ( ( Xu
                    = ( kpair @ Xx @ Xy ) )
                  & ( in @ Xy @ B ) )
              & ( in @ Xx @ A ) ) ) ) ) ).

thf('2',plain,
    ( cartprodmempair1
    = ( ! [X4: $i,X6: $i,X8: $i] :
          ( ( in @ X8 @ ( cartprod @ X4 @ X6 ) )
         => ? [X10: $i] :
              ( ? [X12: $i] :
                  ( ( X8
                    = ( kpair @ X10 @ X12 ) )
                  & ( in @ X12 @ X6 ) )
              & ( in @ X10 @ X4 ) ) ) ) ),
    define([status(thm)]) ).

thf(subsetE,axiom,
    ( subsetE
    = ( ! [A: $i,B: $i,Xx: $i] :
          ( ( subset @ A @ B )
         => ( ( in @ Xx @ A )
           => ( in @ Xx @ B ) ) ) ) ) ).

thf('3',plain,
    ( subsetE
    = ( ! [X4: $i,X6: $i,X8: $i] :
          ( ( subset @ X4 @ X6 )
         => ( ( in @ X8 @ X4 )
           => ( in @ X8 @ X6 ) ) ) ) ),
    define([status(thm)]) ).

thf(brelnall1,conjecture,
    ( subsetE
   => ( cartprodmempair1
     => ! [A: $i,B: $i,R: $i] :
          ( ( breln @ A @ B @ R )
         => ! [Xphi: $i > $o] :
              ( ! [Xx: $i] :
                  ( ( in @ Xx @ A )
                 => ! [Xy: $i] :
                      ( ( in @ Xy @ B )
                     => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
                       => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
             => ! [Xx: $i] :
                  ( ( in @ Xx @ R )
                 => ( Xphi @ Xx ) ) ) ) ) ) ).

thf(zf_stmt_0,conjecture,
    ( ! [X4: $i,X6: $i,X8: $i] :
        ( ( subset @ X4 @ X6 )
       => ( ( in @ X8 @ X4 )
         => ( in @ X8 @ X6 ) ) )
   => ( ! [X10: $i,X12: $i,X14: $i] :
          ( ( in @ X14 @ ( cartprod @ X10 @ X12 ) )
         => ? [X16: $i] :
              ( ? [X18: $i] :
                  ( ( X14
                    = ( kpair @ X16 @ X18 ) )
                  & ( in @ X18 @ X12 ) )
              & ( in @ X16 @ X10 ) ) )
     => ! [X20: $i,X22: $i,X24: $i] :
          ( ( subset @ X24 @ ( cartprod @ X20 @ X22 ) )
         => ! [X26: $i > $o] :
              ( ! [X28: $i] :
                  ( ( in @ X28 @ X20 )
                 => ! [X30: $i] :
                      ( ( in @ X30 @ X22 )
                     => ( ( in @ ( kpair @ X28 @ X30 ) @ X24 )
                       => ( X26 @ ( kpair @ X28 @ X30 ) ) ) ) )
             => ! [X32: $i] :
                  ( ( in @ X32 @ X24 )
                 => ( X26 @ X32 ) ) ) ) ) ) ).

thf(zf_stmt_1,negated_conjecture,
    ~ ( ! [X4: $i,X6: $i,X8: $i] :
          ( ( subset @ X4 @ X6 )
         => ( ( in @ X8 @ X4 )
           => ( in @ X8 @ X6 ) ) )
     => ( ! [X10: $i,X12: $i,X14: $i] :
            ( ( in @ X14 @ ( cartprod @ X10 @ X12 ) )
           => ? [X16: $i] :
                ( ? [X18: $i] :
                    ( ( X14
                      = ( kpair @ X16 @ X18 ) )
                    & ( in @ X18 @ X12 ) )
                & ( in @ X16 @ X10 ) ) )
       => ! [X20: $i,X22: $i,X24: $i] :
            ( ( subset @ X24 @ ( cartprod @ X20 @ X22 ) )
           => ! [X26: $i > $o] :
                ( ! [X28: $i] :
                    ( ( in @ X28 @ X20 )
                   => ! [X30: $i] :
                        ( ( in @ X30 @ X22 )
                       => ( ( in @ ( kpair @ X28 @ X30 ) @ X24 )
                         => ( X26 @ ( kpair @ X28 @ X30 ) ) ) ) )
               => ! [X32: $i] :
                    ( ( in @ X32 @ X24 )
                   => ( X26 @ X32 ) ) ) ) ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl5,plain,
    ! [X5: $i,X6: $i,X7: $i] :
      ( ( in @ ( sk__9 @ X5 @ X6 @ X7 ) @ X6 )
      | ~ ( in @ X5 @ ( cartprod @ X7 @ X6 ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl7,plain,
    ! [X5: $i,X6: $i,X7: $i] :
      ( ( in @ ( sk__8 @ X5 @ X6 @ X7 ) @ X7 )
      | ~ ( in @ X5 @ ( cartprod @ X7 @ X6 ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl6,plain,
    ! [X5: $i,X6: $i,X7: $i] :
      ( ( X5
        = ( kpair @ ( sk__8 @ X5 @ X6 @ X7 ) @ ( sk__9 @ X5 @ X6 @ X7 ) ) )
      | ~ ( in @ X5 @ ( cartprod @ X7 @ X6 ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl6_001,plain,
    ! [X5: $i,X6: $i,X7: $i] :
      ( ( X5
        = ( kpair @ ( sk__8 @ X5 @ X6 @ X7 ) @ ( sk__9 @ X5 @ X6 @ X7 ) ) )
      | ~ ( in @ X5 @ ( cartprod @ X7 @ X6 ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl1,plain,
    ! [X3: $i,X4: $i] :
      ( ~ ( in @ X3 @ sk__11 )
      | ( sk__13 @ ( kpair @ X4 @ X3 ) )
      | ~ ( in @ ( kpair @ X4 @ X3 ) @ sk__12 )
      | ~ ( in @ X4 @ sk__10 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl10,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( sk__13 @ X0 )
      | ~ ( in @ X0 @ ( cartprod @ X1 @ X2 ) )
      | ~ ( in @ ( sk__8 @ X0 @ X2 @ X1 ) @ sk__10 )
      | ~ ( in @ ( kpair @ ( sk__8 @ X0 @ X2 @ X1 ) @ ( sk__9 @ X0 @ X2 @ X1 ) ) @ sk__12 )
      | ~ ( in @ ( sk__9 @ X0 @ X2 @ X1 ) @ sk__11 ) ),
    inference('sup+',[status(thm)],[zip_derived_cl6,zip_derived_cl1]) ).

thf(zip_derived_cl12,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( in @ X0 @ sk__12 )
      | ~ ( in @ X0 @ ( cartprod @ X1 @ X2 ) )
      | ~ ( in @ ( sk__9 @ X0 @ X2 @ X1 ) @ sk__11 )
      | ~ ( in @ ( sk__8 @ X0 @ X2 @ X1 ) @ sk__10 )
      | ~ ( in @ X0 @ ( cartprod @ X1 @ X2 ) )
      | ( sk__13 @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl6,zip_derived_cl10]) ).

thf(zip_derived_cl14,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( sk__13 @ X0 )
      | ~ ( in @ ( sk__8 @ X0 @ X2 @ X1 ) @ sk__10 )
      | ~ ( in @ ( sk__9 @ X0 @ X2 @ X1 ) @ sk__11 )
      | ~ ( in @ X0 @ ( cartprod @ X1 @ X2 ) )
      | ~ ( in @ X0 @ sk__12 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl12]) ).

thf(zip_derived_cl16,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X1 @ ( cartprod @ sk__10 @ X0 ) )
      | ~ ( in @ X1 @ sk__12 )
      | ~ ( in @ X1 @ ( cartprod @ sk__10 @ X0 ) )
      | ~ ( in @ ( sk__9 @ X1 @ X0 @ sk__10 ) @ sk__11 )
      | ( sk__13 @ X1 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl7,zip_derived_cl14]) ).

thf(zip_derived_cl18,plain,
    ! [X0: $i,X1: $i] :
      ( ( sk__13 @ X1 )
      | ~ ( in @ ( sk__9 @ X1 @ X0 @ sk__10 ) @ sk__11 )
      | ~ ( in @ X1 @ sk__12 )
      | ~ ( in @ X1 @ ( cartprod @ sk__10 @ X0 ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl16]) ).

thf(zip_derived_cl20,plain,
    ! [X0: $i] :
      ( ~ ( in @ X0 @ ( cartprod @ sk__10 @ sk__11 ) )
      | ~ ( in @ X0 @ ( cartprod @ sk__10 @ sk__11 ) )
      | ~ ( in @ X0 @ sk__12 )
      | ( sk__13 @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl5,zip_derived_cl18]) ).

thf(zip_derived_cl22,plain,
    ! [X0: $i] :
      ( ( sk__13 @ X0 )
      | ~ ( in @ X0 @ sk__12 )
      | ~ ( in @ X0 @ ( cartprod @ sk__10 @ sk__11 ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl20]) ).

thf(zip_derived_cl4,plain,
    subset @ sk__12 @ ( cartprod @ sk__10 @ sk__11 ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl0,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( subset @ X0 @ X1 )
      | ( in @ X2 @ X1 )
      | ~ ( in @ X2 @ X0 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl8,plain,
    ! [X0: $i] :
      ( ~ ( in @ X0 @ sk__12 )
      | ( in @ X0 @ ( cartprod @ sk__10 @ sk__11 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl4,zip_derived_cl0]) ).

thf(zip_derived_cl24,plain,
    ! [X0: $i] :
      ( ~ ( in @ X0 @ sk__12 )
      | ( sk__13 @ X0 ) ),
    inference(clc,[status(thm)],[zip_derived_cl22,zip_derived_cl8]) ).

thf(zip_derived_cl2,plain,
    ~ ( sk__13 @ sk__14 ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl25,plain,
    ~ ( in @ sk__14 @ sk__12 ),
    inference('sup-',[status(thm)],[zip_derived_cl24,zip_derived_cl2]) ).

thf(zip_derived_cl3,plain,
    in @ sk__14 @ sk__12,
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl27,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl25,zip_derived_cl3]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07  % Problem  : SEU681^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.08  % Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.gk4wOfhUUh true
% 0.07/0.26  % Computer : n015.cluster.edu
% 0.07/0.26  % Model    : x86_64 x86_64
% 0.07/0.26  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26  % Memory   : 8042.1875MB
% 0.07/0.26  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26  % CPULimit : 300
% 0.07/0.26  % WCLimit  : 300
% 0.07/0.26  % DateTime : Wed Aug 23 13:15:04 EDT 2023
% 0.07/0.26  % CPUTime  : 
% 0.07/0.26  % Running portfolio for 300 s
% 0.07/0.26  % File         : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.26  % Number of cores: 8
% 0.07/0.26  % Python version: Python 3.6.8
% 0.07/0.27  % Running in HO mode
% 0.11/0.42  % Total configuration time : 828
% 0.11/0.42  % Estimated wc time : 1656
% 0.11/0.42  % Estimated cpu time (8 cpus) : 207.0
% 0.11/0.48  % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.11/0.48  % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.11/0.49  % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.11/0.50  % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.11/0.50  % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.11/0.51  % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.11/0.51  % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.11/0.51  % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 0.11/0.52  % Solved by lams/40_c.s.sh.
% 0.11/0.52  % done 14 iterations in 0.018s
% 0.11/0.52  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 0.11/0.52  % SZS output start Refutation
% See solution above
% 0.11/0.52  
% 0.11/0.52  
% 0.11/0.52  % Terminating...
% 0.11/0.63  % Runner terminated.
% 0.11/0.64  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------