TSTP Solution File: SEU689^2 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SEU689^2 : 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.wwVLARskNe true

% Computer : n001.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 19:16:14 EDT 2023

% Result   : Theorem 8.64s 1.71s
% Output   : Refutation 8.64s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   49 (  15 unt;  14 typ;   0 def)
%            Number of atoms       :  141 (   7 equ;   0 cnn)
%            Maximal formula atoms :   15 (   4 avg)
%            Number of connectives :  597 (  35   ~;  41   |;   0   &; 465   @)
%                                         (   0 <=>;  56  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   9 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   35 (  35   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   16 (  14 usr;   7 con; 0-4 aty)
%            Number of variables   :  127 (  29   ^;  98   !;   0   ?; 127   :)

% Comments : 
%------------------------------------------------------------------------------
thf(sk__12_type,type,
    sk__12: $i ).

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

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

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

thf(subsetI1_type,type,
    subsetI1: $o ).

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

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

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

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

thf(sk__16_type,type,
    sk__16: $i > $i > $i ).

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

thf(sk__15_type,type,
    sk__15: $i ).

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

thf(brelnall1_type,type,
    brelnall1: $o ).

thf(brelnall1,axiom,
    ( brelnall1
    = ( ! [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('0',plain,
    ( brelnall1
    = ( ! [X4: $i,X6: $i,X8: $i] :
          ( ( breln @ X4 @ X6 @ X8 )
         => ! [X10: $i > $o] :
              ( ! [X12: $i] :
                  ( ( in @ X12 @ X4 )
                 => ! [X14: $i] :
                      ( ( in @ X14 @ X6 )
                     => ( ( in @ ( kpair @ X12 @ X14 ) @ X8 )
                       => ( X10 @ ( kpair @ X12 @ X14 ) ) ) ) )
             => ! [X16: $i] :
                  ( ( in @ X16 @ X8 )
                 => ( X10 @ X16 ) ) ) ) ) ),
    define([status(thm)]) ).

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(subsetI1,axiom,
    ( subsetI1
    = ( ! [A: $i,B: $i] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( in @ Xx @ B ) )
         => ( subset @ A @ B ) ) ) ) ).

thf('3',plain,
    ( subsetI1
    = ( ! [X4: $i,X6: $i] :
          ( ! [X8: $i] :
              ( ( in @ X8 @ X4 )
             => ( in @ X8 @ X6 ) )
         => ( subset @ X4 @ X6 ) ) ) ),
    define([status(thm)]) ).

thf(subbreln,conjecture,
    ( subsetI1
   => ( brelnall1
     => ! [A: $i,B: $i,R: $i] :
          ( ( breln @ A @ B @ R )
         => ! [S: $i] :
              ( ( breln @ A @ B @ S )
             => ( ! [Xx: $i] :
                    ( ( in @ Xx @ A )
                   => ! [Xy: $i] :
                        ( ( in @ Xy @ B )
                       => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
                         => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
               => ( subset @ R @ S ) ) ) ) ) ) ).

thf(zf_stmt_0,conjecture,
    ( ! [X4: $i,X6: $i] :
        ( ! [X8: $i] :
            ( ( in @ X8 @ X4 )
           => ( in @ X8 @ X6 ) )
       => ( subset @ X4 @ X6 ) )
   => ( ! [X10: $i,X12: $i,X14: $i] :
          ( ( subset @ X14 @ ( cartprod @ X10 @ X12 ) )
         => ! [X16: $i > $o] :
              ( ! [X18: $i] :
                  ( ( in @ X18 @ X10 )
                 => ! [X20: $i] :
                      ( ( in @ X20 @ X12 )
                     => ( ( in @ ( kpair @ X18 @ X20 ) @ X14 )
                       => ( X16 @ ( kpair @ X18 @ X20 ) ) ) ) )
             => ! [X22: $i] :
                  ( ( in @ X22 @ X14 )
                 => ( X16 @ X22 ) ) ) )
     => ! [X24: $i,X26: $i,X28: $i] :
          ( ( subset @ X28 @ ( cartprod @ X24 @ X26 ) )
         => ! [X30: $i] :
              ( ( subset @ X30 @ ( cartprod @ X24 @ X26 ) )
             => ( ! [X32: $i] :
                    ( ( in @ X32 @ X24 )
                   => ! [X34: $i] :
                        ( ( in @ X34 @ X26 )
                       => ( ( in @ ( kpair @ X32 @ X34 ) @ X28 )
                         => ( in @ ( kpair @ X32 @ X34 ) @ X30 ) ) ) )
               => ( subset @ X28 @ X30 ) ) ) ) ) ) ).

thf(zf_stmt_1,negated_conjecture,
    ~ ( ! [X4: $i,X6: $i] :
          ( ! [X8: $i] :
              ( ( in @ X8 @ X4 )
             => ( in @ X8 @ X6 ) )
         => ( subset @ X4 @ X6 ) )
     => ( ! [X10: $i,X12: $i,X14: $i] :
            ( ( subset @ X14 @ ( cartprod @ X10 @ X12 ) )
           => ! [X16: $i > $o] :
                ( ! [X18: $i] :
                    ( ( in @ X18 @ X10 )
                   => ! [X20: $i] :
                        ( ( in @ X20 @ X12 )
                       => ( ( in @ ( kpair @ X18 @ X20 ) @ X14 )
                         => ( X16 @ ( kpair @ X18 @ X20 ) ) ) ) )
               => ! [X22: $i] :
                    ( ( in @ X22 @ X14 )
                   => ( X16 @ X22 ) ) ) )
       => ! [X24: $i,X26: $i,X28: $i] :
            ( ( subset @ X28 @ ( cartprod @ X24 @ X26 ) )
           => ! [X30: $i] :
                ( ( subset @ X30 @ ( cartprod @ X24 @ X26 ) )
               => ( ! [X32: $i] :
                      ( ( in @ X32 @ X24 )
                     => ! [X34: $i] :
                          ( ( in @ X34 @ X26 )
                         => ( ( in @ ( kpair @ X32 @ X34 ) @ X28 )
                           => ( in @ ( kpair @ X32 @ X34 ) @ X30 ) ) ) )
                 => ( subset @ X28 @ X30 ) ) ) ) ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl3,plain,
    ~ ( subset @ sk__14 @ sk__15 ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl1,plain,
    ! [X0: $i,X1: $i] :
      ( ( subset @ X0 @ X1 )
      | ( in @ ( sk__16 @ X1 @ X0 ) @ X0 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl4,plain,
    ! [X2: $i,X3: $i] :
      ( ~ ( in @ X2 @ sk__13 )
      | ( in @ ( kpair @ X3 @ X2 ) @ sk__15 )
      | ~ ( in @ ( kpair @ X3 @ X2 ) @ sk__14 )
      | ~ ( in @ X3 @ sk__12 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl5,plain,
    subset @ sk__14 @ ( cartprod @ sk__12 @ sk__13 ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl7,plain,
    ! [X4: $i > $o,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ~ ( X4 @ ( kpair @ ( sk__10 @ X4 @ X5 @ X6 @ X7 ) @ ( sk__11 @ X4 @ X5 @ X6 @ X7 ) ) )
      | ( X4 @ X8 )
      | ~ ( in @ X8 @ X5 )
      | ~ ( subset @ X5 @ ( cartprod @ X7 @ X6 ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl59,plain,
    ! [X0: $i,X1: $i > $o] :
      ( ~ ( in @ X0 @ sk__14 )
      | ( X1 @ X0 )
      | ~ ( X1 @ ( kpair @ ( sk__10 @ X1 @ sk__14 @ sk__13 @ sk__12 ) @ ( sk__11 @ X1 @ sk__14 @ sk__13 @ sk__12 ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl5,zip_derived_cl7]) ).

thf(zip_derived_cl916,plain,
    ! [X0: $i] :
      ( ~ ( in
          @ ( sk__10
            @ ^ [Y0: $i] :
                ( in @ Y0
                @ ( ^ [Y1: $i] : sk__15
                  @ Y0 ) )
            @ sk__14
            @ sk__13
            @ sk__12 )
          @ sk__12 )
      | ~ ( in
          @ ( kpair
            @ ( sk__10
              @ ^ [Y0: $i] :
                  ( in @ Y0
                  @ ( ^ [Y1: $i] : sk__15
                    @ Y0 ) )
              @ sk__14
              @ sk__13
              @ sk__12 )
            @ ( sk__11
              @ ^ [Y0: $i] :
                  ( in @ Y0
                  @ ( ^ [Y1: $i] : sk__15
                    @ Y0 ) )
              @ sk__14
              @ sk__13
              @ sk__12 ) )
          @ sk__14 )
      | ~ ( in
          @ ( sk__11
            @ ^ [Y0: $i] :
                ( in @ Y0
                @ ( ^ [Y1: $i] : sk__15
                  @ Y0 ) )
            @ sk__14
            @ sk__13
            @ sk__12 )
          @ sk__13 )
      | ( ^ [Y0: $i] :
            ( in
            @ ( ^ [Y1: $i] : Y1
              @ Y0 )
            @ ( ^ [Y1: $i] : sk__15
              @ Y0 ) )
        @ X0 )
      | ~ ( in @ X0 @ sk__14 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl4,zip_derived_cl59]) ).

thf(zip_derived_cl964,plain,
    ! [X0: $i] :
      ( ~ ( in
          @ ( sk__10
            @ ^ [Y0: $i] : ( in @ Y0 @ sk__15 )
            @ sk__14
            @ sk__13
            @ sk__12 )
          @ sk__12 )
      | ~ ( in
          @ ( kpair
            @ ( sk__10
              @ ^ [Y0: $i] : ( in @ Y0 @ sk__15 )
              @ sk__14
              @ sk__13
              @ sk__12 )
            @ ( sk__11
              @ ^ [Y0: $i] : ( in @ Y0 @ sk__15 )
              @ sk__14
              @ sk__13
              @ sk__12 ) )
          @ sk__14 )
      | ~ ( in
          @ ( sk__11
            @ ^ [Y0: $i] : ( in @ Y0 @ sk__15 )
            @ sk__14
            @ sk__13
            @ sk__12 )
          @ sk__13 )
      | ( in @ X0 @ sk__15 )
      | ~ ( in @ X0 @ sk__14 ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl916]) ).

thf(zip_derived_cl5_001,plain,
    subset @ sk__14 @ ( cartprod @ sk__12 @ sk__13 ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl9,plain,
    ! [X4: $i > $o,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( in @ ( sk__10 @ X4 @ X5 @ X6 @ X7 ) @ X7 )
      | ( X4 @ X8 )
      | ~ ( in @ X8 @ X5 )
      | ~ ( subset @ X5 @ ( cartprod @ X7 @ X6 ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl190,plain,
    ! [X0: $i,X1: $i > $o] :
      ( ~ ( in @ X0 @ sk__14 )
      | ( X1 @ X0 )
      | ( in @ ( sk__10 @ X1 @ sk__14 @ sk__13 @ sk__12 ) @ sk__12 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl5,zip_derived_cl9]) ).

thf(zip_derived_cl1011,plain,
    ! [X0: $i] :
      ( ~ ( in @ X0 @ sk__14 )
      | ( in @ X0 @ sk__15 )
      | ~ ( in
          @ ( sk__11
            @ ^ [Y0: $i] : ( in @ Y0 @ sk__15 )
            @ sk__14
            @ sk__13
            @ sk__12 )
          @ sk__13 )
      | ~ ( in
          @ ( kpair
            @ ( sk__10
              @ ^ [Y0: $i] : ( in @ Y0 @ sk__15 )
              @ sk__14
              @ sk__13
              @ sk__12 )
            @ ( sk__11
              @ ^ [Y0: $i] : ( in @ Y0 @ sk__15 )
              @ sk__14
              @ sk__13
              @ sk__12 ) )
          @ sk__14 ) ),
    inference(clc,[status(thm)],[zip_derived_cl964,zip_derived_cl190]) ).

thf(zip_derived_cl5_002,plain,
    subset @ sk__14 @ ( cartprod @ sk__12 @ sk__13 ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl6,plain,
    ! [X4: $i > $o,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( in @ ( sk__11 @ X4 @ X5 @ X6 @ X7 ) @ X6 )
      | ( X4 @ X8 )
      | ~ ( in @ X8 @ X5 )
      | ~ ( subset @ X5 @ ( cartprod @ X7 @ X6 ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl19,plain,
    ! [X0: $i,X1: $i > $o] :
      ( ~ ( in @ X0 @ sk__14 )
      | ( X1 @ X0 )
      | ( in @ ( sk__11 @ X1 @ sk__14 @ sk__13 @ sk__12 ) @ sk__13 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl5,zip_derived_cl6]) ).

thf(zip_derived_cl1012,plain,
    ! [X0: $i] :
      ( ~ ( in
          @ ( kpair
            @ ( sk__10
              @ ^ [Y0: $i] : ( in @ Y0 @ sk__15 )
              @ sk__14
              @ sk__13
              @ sk__12 )
            @ ( sk__11
              @ ^ [Y0: $i] : ( in @ Y0 @ sk__15 )
              @ sk__14
              @ sk__13
              @ sk__12 ) )
          @ sk__14 )
      | ( in @ X0 @ sk__15 )
      | ~ ( in @ X0 @ sk__14 ) ),
    inference(clc,[status(thm)],[zip_derived_cl1011,zip_derived_cl19]) ).

thf(zip_derived_cl5_003,plain,
    subset @ sk__14 @ ( cartprod @ sk__12 @ sk__13 ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl8,plain,
    ! [X4: $i > $o,X5: $i,X6: $i,X7: $i,X8: $i] :
      ( ( in @ ( kpair @ ( sk__10 @ X4 @ X5 @ X6 @ X7 ) @ ( sk__11 @ X4 @ X5 @ X6 @ X7 ) ) @ X5 )
      | ( X4 @ X8 )
      | ~ ( in @ X8 @ X5 )
      | ~ ( subset @ X5 @ ( cartprod @ X7 @ X6 ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl294,plain,
    ! [X0: $i,X1: $i > $o] :
      ( ~ ( in @ X0 @ sk__14 )
      | ( X1 @ X0 )
      | ( in @ ( kpair @ ( sk__10 @ X1 @ sk__14 @ sk__13 @ sk__12 ) @ ( sk__11 @ X1 @ sk__14 @ sk__13 @ sk__12 ) ) @ sk__14 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl5,zip_derived_cl8]) ).

thf(zip_derived_cl1013,plain,
    ! [X0: $i] :
      ( ~ ( in @ X0 @ sk__14 )
      | ( in @ X0 @ sk__15 ) ),
    inference(clc,[status(thm)],[zip_derived_cl1012,zip_derived_cl294]) ).

thf(zip_derived_cl0,plain,
    ! [X0: $i,X1: $i] :
      ( ( subset @ X0 @ X1 )
      | ~ ( in @ ( sk__16 @ X1 @ X0 ) @ X1 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl1014,plain,
    ! [X0: $i] :
      ( ~ ( in @ ( sk__16 @ sk__15 @ X0 ) @ sk__14 )
      | ( subset @ X0 @ sk__15 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl1013,zip_derived_cl0]) ).

thf(zip_derived_cl1104,plain,
    ( ( subset @ sk__14 @ sk__15 )
    | ( subset @ sk__14 @ sk__15 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl1,zip_derived_cl1014]) ).

thf(zip_derived_cl1140,plain,
    subset @ sk__14 @ sk__15,
    inference(simplify,[status(thm)],[zip_derived_cl1104]) ).

thf(zip_derived_cl1176,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl3,zip_derived_cl1140]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU689^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.wwVLARskNe true
% 0.14/0.35  % Computer : n001.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Wed Aug 23 16:04:09 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.14/0.35  % Running portfolio for 300 s
% 0.14/0.35  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.35  % Number of cores: 8
% 0.14/0.35  % Python version: Python 3.6.8
% 0.14/0.35  % 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
% 0.21/0.74  % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.21/0.74  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.21/0.75  % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.21/0.75  % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.21/0.75  % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.21/0.75  % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.21/0.75  % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.21/0.76  % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 8.64/1.71  % Solved by lams/40_c.s.sh.
% 8.64/1.71  % done 96 iterations in 0.927s
% 8.64/1.71  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 8.64/1.71  % SZS output start Refutation
% See solution above
% 8.64/1.71  
% 8.64/1.71  
% 8.64/1.71  % Terminating...
% 8.64/1.84  % Runner terminated.
% 8.64/1.86  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------