TSTP Solution File: SEU674^2 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SEU674^2 : 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.jFQD6wHS4F true

% Computer : n031.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 19:16:01 EDT 2023

% Result   : Theorem 0.22s 0.77s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   34
% Syntax   : Number of formulae    :   59 (  24 unt;  20 typ;   0 def)
%            Number of atoms       :  162 (  27 equ;   0 cnn)
%            Maximal formula atoms :   16 (   4 avg)
%            Number of connectives :  571 (  23   ~;  22   |;  14   &; 488   @)
%                                         (   0 <=>;  24  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   35 (  35   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   22 (  20 usr;   7 con; 0-4 aty)
%            Number of variables   :  137 (  77   ^;  53   !;   7   ?; 137   :)

% Comments : 
%------------------------------------------------------------------------------
thf(dsetconstr_type,type,
    dsetconstr: $i > ( $i > $o ) > $i ).

thf(ex1_type,type,
    ex1: $i > ( $i > $o ) > $o ).

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

thf(singleton_type,type,
    singleton: $i > $o ).

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

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

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

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

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

thf(func_type,type,
    func: $i > $i > $i > $o ).

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

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

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

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

thf(setunion_type,type,
    setunion: $i > $i ).

thf(emptyset_type,type,
    emptyset: $i ).

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

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

thf(apProp_type,type,
    apProp: $o ).

thf(ap_type,type,
    ap: $i > $i > $i > $i > $i ).

thf(ap,axiom,
    ( ap
    = ( ^ [A: $i,B: $i,Xf: $i,Xx: $i] :
          ( setunion
          @ ( dsetconstr @ B
            @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ).

thf('0',plain,
    ( ap
    = ( ^ [A: $i,B: $i,Xf: $i,Xx: $i] :
          ( setunion
          @ ( dsetconstr @ B
            @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[ap]) ).

thf('1',plain,
    ( ap
    = ( ^ [V_1: $i,V_2: $i,V_3: $i,V_4: $i] :
          ( setunion
          @ ( dsetconstr @ V_2
            @ ^ [V_5: $i] : ( in @ ( kpair @ V_4 @ V_5 ) @ V_3 ) ) ) ) ),
    define([status(thm)]) ).

thf(apProp,axiom,
    ( apProp
    = ( ! [A: $i,B: $i,Xf: $i] :
          ( ( func @ A @ B @ Xf )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( in
                @ ( setunion
                  @ ( dsetconstr @ B
                    @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
                @ B ) ) ) ) ) ).

thf('2',plain,
    ( apProp
    = ( ! [X4: $i,X6: $i,X8: $i] :
          ( ( func @ X4 @ X6 @ X8 )
         => ! [X10: $i] :
              ( ( in @ X10 @ X4 )
             => ( in
                @ ( setunion
                  @ ( dsetconstr @ X6
                    @ ^ [V_1: $i] : ( in @ ( kpair @ X10 @ V_1 ) @ X8 ) ) )
                @ X6 ) ) ) ) ),
    define([status(thm)]) ).

thf(func,axiom,
    ( func
    = ( ^ [A: $i,B: $i,R: $i] :
          ( ( breln @ A @ B @ R )
          & ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( ex1 @ B
                @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ).

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

thf('3',plain,
    ( breln
    = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[breln]) ).

thf('4',plain,
    ( breln
    = ( ^ [V_1: $i,V_2: $i,V_3: $i] : ( subset @ V_3 @ ( cartprod @ V_1 @ V_2 ) ) ) ),
    define([status(thm)]) ).

thf(ex1,axiom,
    ( ex1
    = ( ^ [A: $i,Xphi: $i > $o] :
          ( singleton
          @ ( dsetconstr @ A
            @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).

thf(singleton,axiom,
    ( singleton
    = ( ^ [A: $i] :
        ? [Xx: $i] :
          ( ( A
            = ( setadjoin @ Xx @ emptyset ) )
          & ( in @ Xx @ A ) ) ) ) ).

thf('5',plain,
    ( singleton
    = ( ^ [A: $i] :
        ? [Xx: $i] :
          ( ( A
            = ( setadjoin @ Xx @ emptyset ) )
          & ( in @ Xx @ A ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[singleton]) ).

thf('6',plain,
    ( singleton
    = ( ^ [V_1: $i] :
        ? [X4: $i] :
          ( ( V_1
            = ( setadjoin @ X4 @ emptyset ) )
          & ( in @ X4 @ V_1 ) ) ) ),
    define([status(thm)]) ).

thf('7',plain,
    ( ex1
    = ( ^ [A: $i,Xphi: $i > $o] :
          ( singleton
          @ ( dsetconstr @ A
            @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[ex1,'6']) ).

thf('8',plain,
    ( ex1
    = ( ^ [V_1: $i,V_2: $i > $o] :
          ( singleton
          @ ( dsetconstr @ V_1
            @ ^ [V_3: $i] : ( V_2 @ V_3 ) ) ) ) ),
    define([status(thm)]) ).

thf('9',plain,
    ( func
    = ( ^ [A: $i,B: $i,R: $i] :
          ( ( breln @ A @ B @ R )
          & ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( ex1 @ B
                @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[func,'4','8','6']) ).

thf('10',plain,
    ( func
    = ( ^ [V_1: $i,V_2: $i,V_3: $i] :
          ( ( breln @ V_1 @ V_2 @ V_3 )
          & ! [X4: $i] :
              ( ( in @ X4 @ V_1 )
             => ( ex1 @ V_2
                @ ^ [V_4: $i] : ( in @ ( kpair @ X4 @ V_4 ) @ V_3 ) ) ) ) ) ),
    define([status(thm)]) ).

thf(app,conjecture,
    ( apProp
   => ! [A: $i,B: $i,Xf: $i] :
        ( ( func @ A @ B @ Xf )
       => ! [Xx: $i] :
            ( ( in @ Xx @ A )
           => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ).

thf(zf_stmt_0,conjecture,
    ( ! [X4: $i,X6: $i,X8: $i] :
        ( ( ( subset @ X8 @ ( cartprod @ X4 @ X6 ) )
          & ! [X10: $i] :
              ( ( in @ X10 @ X4 )
             => ? [X12: $i] :
                  ( ( ( dsetconstr @ X6
                      @ ^ [V_1: $i] : ( in @ ( kpair @ X10 @ V_1 ) @ X8 ) )
                    = ( setadjoin @ X12 @ emptyset ) )
                  & ( in @ X12
                    @ ( dsetconstr @ X6
                      @ ^ [V_2: $i] : ( in @ ( kpair @ X10 @ V_2 ) @ X8 ) ) ) ) ) )
       => ! [X14: $i] :
            ( ( in @ X14 @ X4 )
           => ( in
              @ ( setunion
                @ ( dsetconstr @ X6
                  @ ^ [V_3: $i] : ( in @ ( kpair @ X14 @ V_3 ) @ X8 ) ) )
              @ X6 ) ) )
   => ! [X16: $i,X18: $i,X20: $i] :
        ( ( ( subset @ X20 @ ( cartprod @ X16 @ X18 ) )
          & ! [X22: $i] :
              ( ( in @ X22 @ X16 )
             => ? [X24: $i] :
                  ( ( ( dsetconstr @ X18
                      @ ^ [V_4: $i] : ( in @ ( kpair @ X22 @ V_4 ) @ X20 ) )
                    = ( setadjoin @ X24 @ emptyset ) )
                  & ( in @ X24
                    @ ( dsetconstr @ X18
                      @ ^ [V_5: $i] : ( in @ ( kpair @ X22 @ V_5 ) @ X20 ) ) ) ) ) )
       => ! [X26: $i] :
            ( ( in @ X26 @ X16 )
           => ( in
              @ ( setunion
                @ ( dsetconstr @ X18
                  @ ^ [V_6: $i] : ( in @ ( kpair @ X26 @ V_6 ) @ X20 ) ) )
              @ X18 ) ) ) ) ).

thf(zf_stmt_1,negated_conjecture,
    ~ ( ! [X4: $i,X6: $i,X8: $i] :
          ( ( ( subset @ X8 @ ( cartprod @ X4 @ X6 ) )
            & ! [X10: $i] :
                ( ( in @ X10 @ X4 )
               => ? [X12: $i] :
                    ( ( ( dsetconstr @ X6
                        @ ^ [V_1: $i] : ( in @ ( kpair @ X10 @ V_1 ) @ X8 ) )
                      = ( setadjoin @ X12 @ emptyset ) )
                    & ( in @ X12
                      @ ( dsetconstr @ X6
                        @ ^ [V_2: $i] : ( in @ ( kpair @ X10 @ V_2 ) @ X8 ) ) ) ) ) )
         => ! [X14: $i] :
              ( ( in @ X14 @ X4 )
             => ( in
                @ ( setunion
                  @ ( dsetconstr @ X6
                    @ ^ [V_3: $i] : ( in @ ( kpair @ X14 @ V_3 ) @ X8 ) ) )
                @ X6 ) ) )
     => ! [X16: $i,X18: $i,X20: $i] :
          ( ( ( subset @ X20 @ ( cartprod @ X16 @ X18 ) )
            & ! [X22: $i] :
                ( ( in @ X22 @ X16 )
               => ? [X24: $i] :
                    ( ( ( dsetconstr @ X18
                        @ ^ [V_4: $i] : ( in @ ( kpair @ X22 @ V_4 ) @ X20 ) )
                      = ( setadjoin @ X24 @ emptyset ) )
                    & ( in @ X24
                      @ ( dsetconstr @ X18
                        @ ^ [V_5: $i] : ( in @ ( kpair @ X22 @ V_5 ) @ X20 ) ) ) ) ) )
         => ! [X26: $i] :
              ( ( in @ X26 @ X16 )
             => ( in
                @ ( setunion
                  @ ( dsetconstr @ X18
                    @ ^ [V_6: $i] : ( in @ ( kpair @ X26 @ V_6 ) @ X20 ) ) )
                @ X18 ) ) ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl2,plain,
    in @ sk__9 @ sk__6,
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl6,plain,
    subset @ sk__8 @ ( cartprod @ sk__6 @ sk__7 ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl1,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ ( in @ X0 @ X1 )
      | ( in
        @ ( setunion
          @ ( dsetconstr @ X2
            @ ^ [Y0: $i] : ( in @ ( kpair @ X0 @ Y0 ) @ X3 ) ) )
        @ X2 )
      | ( in @ ( sk__11 @ X3 @ X2 @ X1 ) @ X1 )
      | ~ ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl15,plain,
    ! [X0: $i] :
      ( ( in @ ( sk__11 @ sk__8 @ sk__7 @ sk__6 ) @ sk__6 )
      | ( in
        @ ( setunion
          @ ( dsetconstr @ sk__7
            @ ^ [Y0: $i] : ( in @ ( kpair @ X0 @ Y0 ) @ sk__8 ) ) )
        @ sk__7 )
      | ~ ( in @ X0 @ sk__6 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl6,zip_derived_cl1]) ).

thf(zip_derived_cl17,plain,
    ( ( in
      @ ( setunion
        @ ( dsetconstr @ sk__7
          @ ^ [Y0: $i] : ( in @ ( kpair @ sk__9 @ Y0 ) @ sk__8 ) ) )
      @ sk__7 )
    | ( in @ ( sk__11 @ sk__8 @ sk__7 @ sk__6 ) @ sk__6 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl2,zip_derived_cl15]) ).

thf(zip_derived_cl3,plain,
    ~ ( in
      @ ( setunion
        @ ( dsetconstr @ sk__7
          @ ^ [Y0: $i] : ( in @ ( kpair @ sk__9 @ Y0 ) @ sk__8 ) ) )
      @ sk__7 ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl21,plain,
    in @ ( sk__11 @ sk__8 @ sk__7 @ sk__6 ) @ sk__6,
    inference(clc,[status(thm)],[zip_derived_cl17,zip_derived_cl3]) ).

thf(zip_derived_cl5,plain,
    ! [X5: $i] :
      ( ( in @ ( sk__10 @ X5 )
        @ ( dsetconstr @ sk__7
          @ ^ [Y0: $i] : ( in @ ( kpair @ X5 @ Y0 ) @ sk__8 ) ) )
      | ~ ( in @ X5 @ sk__6 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl0,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ~ ( in @ X0 @ X1 )
      | ( in
        @ ( setunion
          @ ( dsetconstr @ X2
            @ ^ [Y0: $i] : ( in @ ( kpair @ X0 @ Y0 ) @ X3 ) ) )
        @ X2 )
      | ~ ( in @ X4
          @ ( dsetconstr @ X2
            @ ^ [Y0: $i] : ( in @ ( kpair @ ( sk__11 @ X3 @ X2 @ X1 ) @ Y0 ) @ X3 ) ) )
      | ( ( dsetconstr @ X2
          @ ^ [Y0: $i] : ( in @ ( kpair @ ( sk__11 @ X3 @ X2 @ X1 ) @ Y0 ) @ X3 ) )
       != ( setadjoin @ X4 @ emptyset ) )
      | ~ ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl20,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ ( sk__11 @ sk__8 @ sk__7 @ X0 ) @ sk__6 )
      | ~ ( subset @ sk__8 @ ( cartprod @ X0 @ sk__7 ) )
      | ( ( dsetconstr @ sk__7
          @ ^ [Y0: $i] : ( in @ ( kpair @ ( sk__11 @ sk__8 @ sk__7 @ X0 ) @ Y0 ) @ sk__8 ) )
       != ( setadjoin @ ( sk__10 @ ( sk__11 @ sk__8 @ sk__7 @ X0 ) ) @ emptyset ) )
      | ( in
        @ ( setunion
          @ ( dsetconstr @ sk__7
            @ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sk__8 ) ) )
        @ sk__7 )
      | ~ ( in @ X1 @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl5,zip_derived_cl0]) ).

thf(zip_derived_cl4,plain,
    ! [X5: $i] :
      ( ( ( dsetconstr @ sk__7
          @ ^ [Y0: $i] : ( in @ ( kpair @ X5 @ Y0 ) @ sk__8 ) )
        = ( setadjoin @ ( sk__10 @ X5 ) @ emptyset ) )
      | ~ ( in @ X5 @ sk__6 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl22,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X1 @ X0 )
      | ( in
        @ ( setunion
          @ ( dsetconstr @ sk__7
            @ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sk__8 ) ) )
        @ sk__7 )
      | ~ ( subset @ sk__8 @ ( cartprod @ X0 @ sk__7 ) )
      | ~ ( in @ ( sk__11 @ sk__8 @ sk__7 @ X0 ) @ sk__6 ) ),
    inference(clc,[status(thm)],[zip_derived_cl20,zip_derived_cl4]) ).

thf(zip_derived_cl23,plain,
    ! [X0: $i] :
      ( ~ ( subset @ sk__8 @ ( cartprod @ sk__6 @ sk__7 ) )
      | ( in
        @ ( setunion
          @ ( dsetconstr @ sk__7
            @ ^ [Y0: $i] : ( in @ ( kpair @ X0 @ Y0 ) @ sk__8 ) ) )
        @ sk__7 )
      | ~ ( in @ X0 @ sk__6 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl21,zip_derived_cl22]) ).

thf(zip_derived_cl6_001,plain,
    subset @ sk__8 @ ( cartprod @ sk__6 @ sk__7 ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl25,plain,
    ! [X0: $i] :
      ( ( in
        @ ( setunion
          @ ( dsetconstr @ sk__7
            @ ^ [Y0: $i] : ( in @ ( kpair @ X0 @ Y0 ) @ sk__8 ) ) )
        @ sk__7 )
      | ~ ( in @ X0 @ sk__6 ) ),
    inference(demod,[status(thm)],[zip_derived_cl23,zip_derived_cl6]) ).

thf(zip_derived_cl3_002,plain,
    ~ ( in
      @ ( setunion
        @ ( dsetconstr @ sk__7
          @ ^ [Y0: $i] : ( in @ ( kpair @ sk__9 @ Y0 ) @ sk__8 ) ) )
      @ sk__7 ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl27,plain,
    ~ ( in @ sk__9 @ sk__6 ),
    inference('sup-',[status(thm)],[zip_derived_cl25,zip_derived_cl3]) ).

thf(zip_derived_cl2_003,plain,
    in @ sk__9 @ sk__6,
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl30,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl27,zip_derived_cl2]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : SEU674^2 : TPTP v8.1.2. Released v3.7.0.
% 0.14/0.14  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.jFQD6wHS4F true
% 0.15/0.36  % Computer : n031.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Wed Aug 23 15:56:20 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 0.15/0.36  % Running portfolio for 300 s
% 0.15/0.36  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.36  % Number of cores: 8
% 0.22/0.36  % Python version: Python 3.6.8
% 0.22/0.36  % Running in HO mode
% 0.22/0.66  % Total configuration time : 828
% 0.22/0.66  % Estimated wc time : 1656
% 0.22/0.66  % Estimated cpu time (8 cpus) : 207.0
% 0.22/0.72  % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.22/0.76  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.22/0.76  % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.22/0.76  % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.22/0.76  % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.22/0.77  % Solved by lams/40_c.s.sh.
% 0.22/0.77  % done 15 iterations in 0.023s
% 0.22/0.77  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 0.22/0.77  % SZS output start Refutation
% See solution above
% 0.22/0.77  
% 0.22/0.77  
% 0.22/0.77  % Terminating...
% 1.63/0.86  % Runner terminated.
% 1.63/0.87  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------