TSTP Solution File: SEU781^2 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SEU781^2 : 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.pFjc76EWgn true

% Computer : n003.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 19:17:34 EDT 2023

% Result   : Theorem 1.16s 0.82s
% Output   : Refutation 1.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   23
% Syntax   : Number of formulae    :   47 (  20 unt;  15 typ;   0 def)
%            Number of atoms       :  150 (   8 equ;   0 cnn)
%            Maximal formula atoms :   16 (   4 avg)
%            Number of connectives :  661 (  57   ~;  50   |;   8   &; 496   @)
%                                         (   0 <=>;  50  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   23 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   21 (  21   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   17 (  15 usr;   8 con; 0-5 aty)
%            Number of variables   :   82 (  15   ^;  63   !;   4   ?;  82   :)

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

thf(sk__8_type,type,
    sk__8: $i ).

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

thf(breln1compset_type,type,
    breln1compset: $i > $i > $i > $i ).

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

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

thf(sk__6_type,type,
    sk__6: $i ).

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

thf(sk__7_type,type,
    sk__7: $i ).

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

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

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

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

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

thf(breln1compE_type,type,
    breln1compE: $o ).

thf(breln1compE,axiom,
    ( breln1compE
    = ( ! [A: $i,R: $i] :
          ( ( breln1 @ A @ R )
         => ! [S: $i] :
              ( ( breln1 @ A @ S )
             => ! [Xx: $i] :
                  ( ( in @ Xx @ A )
                 => ! [Xy: $i] :
                      ( ( in @ Xy @ A )
                     => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
                       => ? [Xz: $i] :
                            ( ( in @ ( kpair @ Xz @ Xy ) @ S )
                            & ( in @ ( kpair @ Xx @ Xz ) @ R )
                            & ( in @ Xz @ A ) ) ) ) ) ) ) ) ) ).

thf('0',plain,
    ( breln1compE
    = ( ! [X4: $i,X6: $i] :
          ( ( breln1 @ X4 @ X6 )
         => ! [X8: $i] :
              ( ( breln1 @ X4 @ X8 )
             => ! [X10: $i] :
                  ( ( in @ X10 @ X4 )
                 => ! [X12: $i] :
                      ( ( in @ X12 @ X4 )
                     => ( ( in @ ( kpair @ X10 @ X12 ) @ ( breln1compset @ X4 @ X6 @ X8 ) )
                       => ? [X14: $i] :
                            ( ( in @ ( kpair @ X14 @ X12 ) @ X8 )
                            & ( in @ ( kpair @ X10 @ X14 ) @ X6 )
                            & ( in @ X14 @ X4 ) ) ) ) ) ) ) ) ),
    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(breln1compEex,conjecture,
    ( breln1compE
   => ! [A: $i,R: $i] :
        ( ( breln1 @ A @ R )
       => ! [S: $i] :
            ( ( breln1 @ A @ S )
           => ! [Xx: $i] :
                ( ( in @ Xx @ A )
               => ! [Xy: $i] :
                    ( ( in @ Xy @ A )
                   => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
                     => ! [Xphi: $o] :
                          ( ! [Xz: $i] :
                              ( ( in @ Xz @ A )
                             => ( ( in @ ( kpair @ Xx @ Xz ) @ R )
                               => ( ( in @ ( kpair @ Xz @ Xy ) @ S )
                                 => Xphi ) ) )
                         => Xphi ) ) ) ) ) ) ) ).

thf(zf_stmt_0,conjecture,
    ( ! [X4: $i,X6: $i] :
        ( ( subset @ X6 @ ( cartprod @ X4 @ X4 ) )
       => ! [X8: $i] :
            ( ( subset @ X8 @ ( cartprod @ X4 @ X4 ) )
           => ! [X10: $i] :
                ( ( in @ X10 @ X4 )
               => ! [X12: $i] :
                    ( ( in @ X12 @ X4 )
                   => ( ( in @ ( kpair @ X10 @ X12 ) @ ( breln1compset @ X4 @ X6 @ X8 ) )
                     => ? [X14: $i] :
                          ( ( in @ ( kpair @ X14 @ X12 ) @ X8 )
                          & ( in @ ( kpair @ X10 @ X14 ) @ X6 )
                          & ( in @ X14 @ X4 ) ) ) ) ) ) )
   => ! [X16: $i,X18: $i] :
        ( ( subset @ X18 @ ( cartprod @ X16 @ X16 ) )
       => ! [X20: $i] :
            ( ( subset @ X20 @ ( cartprod @ X16 @ X16 ) )
           => ! [X22: $i] :
                ( ( in @ X22 @ X16 )
               => ! [X24: $i] :
                    ( ( in @ X24 @ X16 )
                   => ( ( in @ ( kpair @ X22 @ X24 ) @ ( breln1compset @ X16 @ X18 @ X20 ) )
                     => ! [X26: $o] :
                          ( ! [X28: $i] :
                              ( ( in @ X28 @ X16 )
                             => ( ( in @ ( kpair @ X22 @ X28 ) @ X18 )
                               => ( ( in @ ( kpair @ X28 @ X24 ) @ X20 )
                                 => X26 ) ) )
                         => X26 ) ) ) ) ) ) ) ).

thf(zf_stmt_1,negated_conjecture,
    ~ ( ! [X4: $i,X6: $i] :
          ( ( subset @ X6 @ ( cartprod @ X4 @ X4 ) )
         => ! [X8: $i] :
              ( ( subset @ X8 @ ( cartprod @ X4 @ X4 ) )
             => ! [X10: $i] :
                  ( ( in @ X10 @ X4 )
                 => ! [X12: $i] :
                      ( ( in @ X12 @ X4 )
                     => ( ( in @ ( kpair @ X10 @ X12 ) @ ( breln1compset @ X4 @ X6 @ X8 ) )
                       => ? [X14: $i] :
                            ( ( in @ ( kpair @ X14 @ X12 ) @ X8 )
                            & ( in @ ( kpair @ X10 @ X14 ) @ X6 )
                            & ( in @ X14 @ X4 ) ) ) ) ) ) )
     => ! [X16: $i,X18: $i] :
          ( ( subset @ X18 @ ( cartprod @ X16 @ X16 ) )
         => ! [X20: $i] :
              ( ( subset @ X20 @ ( cartprod @ X16 @ X16 ) )
             => ! [X22: $i] :
                  ( ( in @ X22 @ X16 )
                 => ! [X24: $i] :
                      ( ( in @ X24 @ X16 )
                     => ( ( in @ ( kpair @ X22 @ X24 ) @ ( breln1compset @ X16 @ X18 @ X20 ) )
                       => ! [X26: $o] :
                            ( ! [X28: $i] :
                                ( ( in @ X28 @ X16 )
                               => ( ( in @ ( kpair @ X22 @ X28 ) @ X18 )
                                 => ( ( in @ ( kpair @ X28 @ X24 ) @ X20 )
                                   => X26 ) ) )
                           => X26 ) ) ) ) ) ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl2,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ~ ( subset @ X0 @ ( cartprod @ X1 @ X1 ) )
      | ~ ( in @ X2 @ X1 )
      | ( in @ ( sk__12 @ X2 @ X3 @ X0 @ X4 @ X1 ) @ X1 )
      | ~ ( in @ ( kpair @ X3 @ X2 ) @ ( breln1compset @ X1 @ X4 @ X0 ) )
      | ~ ( in @ X3 @ X1 )
      | ~ ( subset @ X4 @ ( cartprod @ X1 @ X1 ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl1,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ~ ( subset @ X0 @ ( cartprod @ X1 @ X1 ) )
      | ~ ( in @ X2 @ X1 )
      | ( in @ ( kpair @ X3 @ ( sk__12 @ X2 @ X3 @ X0 @ X4 @ X1 ) ) @ X4 )
      | ~ ( in @ ( kpair @ X3 @ X2 ) @ ( breln1compset @ X1 @ X4 @ X0 ) )
      | ~ ( in @ X3 @ X1 )
      | ~ ( subset @ X4 @ ( cartprod @ X1 @ X1 ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl0,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ~ ( subset @ X0 @ ( cartprod @ X1 @ X1 ) )
      | ~ ( in @ X2 @ X1 )
      | ( in @ ( kpair @ ( sk__12 @ X2 @ X3 @ X0 @ X4 @ X1 ) @ X2 ) @ X0 )
      | ~ ( in @ ( kpair @ X3 @ X2 ) @ ( breln1compset @ X1 @ X4 @ X0 ) )
      | ~ ( in @ X3 @ X1 )
      | ~ ( subset @ X4 @ ( cartprod @ X1 @ X1 ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl6,plain,
    ! [X5: $i] :
      ( sk__11
      | ~ ( in @ X5 @ sk__6 )
      | ~ ( in @ ( kpair @ X5 @ sk__10 ) @ sk__8 )
      | ~ ( in @ ( kpair @ sk__9 @ X5 ) @ sk__7 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl5,plain,
    ~ sk__11,
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl10,plain,
    ! [X5: $i] :
      ( ~ ( in @ X5 @ sk__6 )
      | ~ ( in @ ( kpair @ X5 @ sk__10 ) @ sk__8 )
      | ~ ( in @ ( kpair @ sk__9 @ X5 ) @ sk__7 ) ),
    inference(demod,[status(thm)],[zip_derived_cl6,zip_derived_cl5]) ).

thf(zip_derived_cl11,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( subset @ X1 @ ( cartprod @ X0 @ X0 ) )
      | ~ ( in @ X2 @ X0 )
      | ~ ( in @ ( kpair @ X2 @ sk__10 ) @ ( breln1compset @ X0 @ X1 @ sk__8 ) )
      | ~ ( in @ sk__10 @ X0 )
      | ~ ( subset @ sk__8 @ ( cartprod @ X0 @ X0 ) )
      | ~ ( in @ ( kpair @ sk__9 @ ( sk__12 @ sk__10 @ X2 @ sk__8 @ X1 @ X0 ) ) @ sk__7 )
      | ~ ( in @ ( sk__12 @ sk__10 @ X2 @ sk__8 @ X1 @ X0 ) @ sk__6 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl0,zip_derived_cl10]) ).

thf(zip_derived_cl23,plain,
    ! [X0: $i] :
      ( ~ ( subset @ sk__7 @ ( cartprod @ X0 @ X0 ) )
      | ~ ( in @ sk__9 @ X0 )
      | ~ ( in @ ( kpair @ sk__9 @ sk__10 ) @ ( breln1compset @ X0 @ sk__7 @ sk__8 ) )
      | ~ ( in @ sk__10 @ X0 )
      | ~ ( subset @ sk__8 @ ( cartprod @ X0 @ X0 ) )
      | ~ ( in @ ( sk__12 @ sk__10 @ sk__9 @ sk__8 @ sk__7 @ X0 ) @ sk__6 )
      | ~ ( subset @ sk__8 @ ( cartprod @ X0 @ X0 ) )
      | ~ ( in @ sk__10 @ X0 )
      | ~ ( in @ ( kpair @ sk__9 @ sk__10 ) @ ( breln1compset @ X0 @ sk__7 @ sk__8 ) )
      | ~ ( in @ sk__9 @ X0 )
      | ~ ( subset @ sk__7 @ ( cartprod @ X0 @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl1,zip_derived_cl11]) ).

thf(zip_derived_cl25,plain,
    ! [X0: $i] :
      ( ~ ( in @ ( sk__12 @ sk__10 @ sk__9 @ sk__8 @ sk__7 @ X0 ) @ sk__6 )
      | ~ ( subset @ sk__8 @ ( cartprod @ X0 @ X0 ) )
      | ~ ( in @ sk__10 @ X0 )
      | ~ ( in @ ( kpair @ sk__9 @ sk__10 ) @ ( breln1compset @ X0 @ sk__7 @ sk__8 ) )
      | ~ ( in @ sk__9 @ X0 )
      | ~ ( subset @ sk__7 @ ( cartprod @ X0 @ X0 ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl23]) ).

thf(zip_derived_cl27,plain,
    ( ~ ( subset @ sk__7 @ ( cartprod @ sk__6 @ sk__6 ) )
    | ~ ( in @ sk__9 @ sk__6 )
    | ~ ( in @ ( kpair @ sk__9 @ sk__10 ) @ ( breln1compset @ sk__6 @ sk__7 @ sk__8 ) )
    | ~ ( in @ sk__10 @ sk__6 )
    | ~ ( subset @ sk__8 @ ( cartprod @ sk__6 @ sk__6 ) )
    | ~ ( subset @ sk__7 @ ( cartprod @ sk__6 @ sk__6 ) )
    | ~ ( in @ sk__9 @ sk__6 )
    | ~ ( in @ ( kpair @ sk__9 @ sk__10 ) @ ( breln1compset @ sk__6 @ sk__7 @ sk__8 ) )
    | ~ ( in @ sk__10 @ sk__6 )
    | ~ ( subset @ sk__8 @ ( cartprod @ sk__6 @ sk__6 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl2,zip_derived_cl25]) ).

thf(zip_derived_cl9,plain,
    subset @ sk__7 @ ( cartprod @ sk__6 @ sk__6 ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl8,plain,
    in @ sk__9 @ sk__6,
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl7,plain,
    in @ ( kpair @ sk__9 @ sk__10 ) @ ( breln1compset @ sk__6 @ sk__7 @ sk__8 ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl4,plain,
    in @ sk__10 @ sk__6,
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl3,plain,
    subset @ sk__8 @ ( cartprod @ sk__6 @ sk__6 ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl9_001,plain,
    subset @ sk__7 @ ( cartprod @ sk__6 @ sk__6 ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl8_002,plain,
    in @ sk__9 @ sk__6,
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl7_003,plain,
    in @ ( kpair @ sk__9 @ sk__10 ) @ ( breln1compset @ sk__6 @ sk__7 @ sk__8 ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl4_004,plain,
    in @ sk__10 @ sk__6,
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl3_005,plain,
    subset @ sk__8 @ ( cartprod @ sk__6 @ sk__6 ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl29,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl27,zip_derived_cl9,zip_derived_cl8,zip_derived_cl7,zip_derived_cl4,zip_derived_cl3,zip_derived_cl9,zip_derived_cl8,zip_derived_cl7,zip_derived_cl4,zip_derived_cl3]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SEU781^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.14  % Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.pFjc76EWgn true
% 0.15/0.35  % Computer : n003.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Thu Aug 24 01:42:07 EDT 2023
% 0.15/0.35  % CPUTime  : 
% 0.15/0.35  % Running portfolio for 300 s
% 0.15/0.35  % File         : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.35  % Number of cores: 8
% 0.15/0.36  % Python version: Python 3.6.8
% 0.15/0.36  % Running in HO mode
% 0.22/0.67  % Total configuration time : 828
% 0.22/0.67  % Estimated wc time : 1656
% 0.22/0.67  % Estimated cpu time (8 cpus) : 207.0
% 0.22/0.75  % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.22/0.75  % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.22/0.75  % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.22/0.77  % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 1.16/0.77  % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 1.16/0.78  % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.16/0.78  % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 1.16/0.80  % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 1.16/0.82  % Solved by lams/40_c.s.sh.
% 1.16/0.82  % done 21 iterations in 0.038s
% 1.16/0.82  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 1.16/0.82  % SZS output start Refutation
% See solution above
% 1.16/0.82  
% 1.16/0.82  
% 1.16/0.82  % Terminating...
% 1.66/0.86  % Runner terminated.
% 1.66/0.87  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------