TSTP Solution File: SEU668^2 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SEU668^2 : 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.wdpSny6nyT true

% Computer : n016.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 19:15:55 EDT 2023

% Result   : Theorem 1.48s 0.88s
% Output   : Refutation 1.48s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   27
% Syntax   : Number of formulae    :   50 (  25 unt;  17 typ;   0 def)
%            Number of atoms       :  101 (  47 equ;   0 cnn)
%            Maximal formula atoms :   11 (   3 avg)
%            Number of connectives :  315 (   6   ~;   4   |;  24   &; 245   @)
%                                         (   0 <=>;  30  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   23 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   36 (  36   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   20 (  17 usr;  11 con; 0-3 aty)
%                                         (   0  !!;   6  ??;   0 @@+;   0 @@-)
%            Number of variables   :  120 (  29   ^;  81   !;  10   ?; 120   :)

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

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

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

thf(sk__17_type,type,
    sk__17: $i ).

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

thf('#_fresh_sk2_type',type,
    '#_fresh_sk2': $i > $i ).

thf(dsetconstrER_type,type,
    dsetconstrER: $o ).

thf(setukpairinjL_type,type,
    setukpairinjL: $o ).

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

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

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

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

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

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

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

thf(setukpairinjR_type,type,
    setukpairinjR: $o ).

thf('#_fresh_sk1_type',type,
    '#_fresh_sk1': $i > $i ).

thf(dpsetconstr,axiom,
    ( dpsetconstr
    = ( ^ [A: $i,B: $i,Xphi: $i > $i > $o] :
          ( dsetconstr @ ( cartprod @ A @ B )
          @ ^ [Xu: $i] :
            ? [Xx: $i] :
              ( ? [Xy: $i] :
                  ( ( Xu
                    = ( kpair @ Xx @ Xy ) )
                  & ( Xphi @ Xx @ Xy )
                  & ( in @ Xy @ B ) )
              & ( in @ Xx @ A ) ) ) ) ) ).

thf('0',plain,
    ( dpsetconstr
    = ( ^ [A: $i,B: $i,Xphi: $i > $i > $o] :
          ( dsetconstr @ ( cartprod @ A @ B )
          @ ^ [Xu: $i] :
            ? [Xx: $i] :
              ( ? [Xy: $i] :
                  ( ( Xu
                    = ( kpair @ Xx @ Xy ) )
                  & ( Xphi @ Xx @ Xy )
                  & ( in @ Xy @ B ) )
              & ( in @ Xx @ A ) ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[dpsetconstr]) ).

thf('1',plain,
    ( dpsetconstr
    = ( ^ [V_1: $i,V_2: $i,V_3: $i > $i > $o] :
          ( dsetconstr @ ( cartprod @ V_1 @ V_2 )
          @ ^ [V_4: $i] :
            ? [X4: $i] :
              ( ? [X6: $i] :
                  ( ( V_4
                    = ( kpair @ X4 @ X6 ) )
                  & ( V_3 @ X4 @ X6 )
                  & ( in @ X6 @ V_2 ) )
              & ( in @ X4 @ V_1 ) ) ) ) ),
    define([status(thm)]) ).

thf(setukpairinjR,axiom,
    ( setukpairinjR
    = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
          ( ( ( kpair @ Xx @ Xy )
            = ( kpair @ Xz @ Xu ) )
         => ( Xy = Xu ) ) ) ) ).

thf('2',plain,
    ( setukpairinjR
    = ( ! [X4: $i,X6: $i,X8: $i,X10: $i] :
          ( ( ( kpair @ X4 @ X6 )
            = ( kpair @ X8 @ X10 ) )
         => ( X6 = X10 ) ) ) ),
    define([status(thm)]) ).

thf(setukpairinjL,axiom,
    ( setukpairinjL
    = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
          ( ( ( kpair @ Xx @ Xy )
            = ( kpair @ Xz @ Xu ) )
         => ( Xx = Xz ) ) ) ) ).

thf('3',plain,
    ( setukpairinjL
    = ( ! [X4: $i,X6: $i,X8: $i,X10: $i] :
          ( ( ( kpair @ X4 @ X6 )
            = ( kpair @ X8 @ X10 ) )
         => ( X4 = X8 ) ) ) ),
    define([status(thm)]) ).

thf(dsetconstrER,axiom,
    ( dsetconstrER
    = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
          ( ( in @ Xx
            @ ( dsetconstr @ A
              @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
         => ( Xphi @ Xx ) ) ) ) ).

thf('4',plain,
    ( dsetconstrER
    = ( ! [X4: $i,X6: $i > $o,X8: $i] :
          ( ( in @ X8
            @ ( dsetconstr @ X4
              @ ^ [V_1: $i] : ( X6 @ V_1 ) ) )
         => ( X6 @ X8 ) ) ) ),
    define([status(thm)]) ).

thf(dpsetconstrERa,conjecture,
    ( dsetconstrER
   => ( setukpairinjL
     => ( setukpairinjR
       => ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
            ( ( in @ Xx @ A )
           => ! [Xy: $i] :
                ( ( in @ Xy @ B )
               => ( ( in @ ( kpair @ Xx @ Xy )
                    @ ( dpsetconstr @ A @ B
                      @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
                 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ) ).

thf(zf_stmt_0,conjecture,
    ( ! [X4: $i,X6: $i > $o,X8: $i] :
        ( ( in @ X8
          @ ( dsetconstr @ X4
            @ ^ [V_1: $i] : ( X6 @ V_1 ) ) )
       => ( X6 @ X8 ) )
   => ( ! [X10: $i,X12: $i,X14: $i,X16: $i] :
          ( ( ( kpair @ X10 @ X12 )
            = ( kpair @ X14 @ X16 ) )
         => ( X10 = X14 ) )
     => ( ! [X18: $i,X20: $i,X22: $i,X24: $i] :
            ( ( ( kpair @ X18 @ X20 )
              = ( kpair @ X22 @ X24 ) )
           => ( X20 = X24 ) )
       => ! [X26: $i,X28: $i,X30: $i > $i > $o,X32: $i] :
            ( ( in @ X32 @ X26 )
           => ! [X34: $i] :
                ( ( in @ X34 @ X28 )
               => ( ( in @ ( kpair @ X32 @ X34 )
                    @ ( dsetconstr @ ( cartprod @ X26 @ X28 )
                      @ ^ [V_2: $i] :
                        ? [X36: $i] :
                          ( ( in @ X36 @ X26 )
                          & ? [X38: $i] :
                              ( ( in @ X38 @ X28 )
                              & ( X30 @ X36 @ X38 )
                              & ( V_2
                                = ( kpair @ X36 @ X38 ) ) ) ) ) )
                 => ( X30 @ X32 @ X34 ) ) ) ) ) ) ) ).

thf(zf_stmt_1,negated_conjecture,
    ~ ( ! [X4: $i,X6: $i > $o,X8: $i] :
          ( ( in @ X8
            @ ( dsetconstr @ X4
              @ ^ [V_1: $i] : ( X6 @ V_1 ) ) )
         => ( X6 @ X8 ) )
     => ( ! [X10: $i,X12: $i,X14: $i,X16: $i] :
            ( ( ( kpair @ X10 @ X12 )
              = ( kpair @ X14 @ X16 ) )
           => ( X10 = X14 ) )
       => ( ! [X18: $i,X20: $i,X22: $i,X24: $i] :
              ( ( ( kpair @ X18 @ X20 )
                = ( kpair @ X22 @ X24 ) )
             => ( X20 = X24 ) )
         => ! [X26: $i,X28: $i,X30: $i > $i > $o,X32: $i] :
              ( ( in @ X32 @ X26 )
             => ! [X34: $i] :
                  ( ( in @ X34 @ X28 )
                 => ( ( in @ ( kpair @ X32 @ X34 )
                      @ ( dsetconstr @ ( cartprod @ X26 @ X28 )
                        @ ^ [V_2: $i] :
                          ? [X36: $i] :
                            ( ( in @ X36 @ X26 )
                            & ? [X38: $i] :
                                ( ( in @ X38 @ X28 )
                                & ( X30 @ X36 @ X38 )
                                & ( V_2
                                  = ( kpair @ X36 @ X38 ) ) ) ) ) )
                   => ( X30 @ X32 @ X34 ) ) ) ) ) ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl0,plain,
    ! [X0: $i > $o,X1: $i,X2: $i] :
      ( ( X0 @ X1 )
      | ~ ( in @ X1
          @ ( dsetconstr @ X2
            @ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl93,plain,
    ! [X0: $i > $o,X1: $i,X2: $i] :
      ( ( X0 @ X1 )
      | ~ ( in @ X1 @ ( dsetconstr @ X2 @ X0 ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl0]) ).

thf(zip_derived_cl4,plain,
    ( in @ ( kpair @ sk__14 @ sk__15 )
    @ ( dsetconstr @ ( cartprod @ sk__11 @ sk__12 )
      @ ^ [Y0: $i] :
          ( ??
          @ ^ [Y1: $i] :
              ( ( in @ Y1 @ sk__11 )
              & ( ??
                @ ^ [Y2: $i] :
                    ( ( in @ Y2 @ sk__12 )
                    & ( sk__13 @ Y1 @ Y2 )
                    & ( Y0
                      = ( kpair @ Y1 @ Y2 ) ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl173,plain,
    ( ^ [Y0: $i] :
        ( ??
        @ ^ [Y1: $i] :
            ( ( in @ Y1 @ sk__11 )
            & ( ??
              @ ^ [Y2: $i] :
                  ( ( in @ Y2 @ sk__12 )
                  & ( sk__13 @ Y1 @ Y2 )
                  & ( Y0
                    = ( kpair @ Y1 @ Y2 ) ) ) ) ) )
    @ ( kpair @ sk__14 @ sk__15 ) ),
    inference('sup+',[status(thm)],[zip_derived_cl93,zip_derived_cl4]) ).

thf(zip_derived_cl174,plain,
    ( ??
    @ ^ [Y0: $i] :
        ( ( in @ Y0 @ sk__11 )
        & ( ??
          @ ^ [Y1: $i] :
              ( ( in @ Y1 @ sk__12 )
              & ( sk__13 @ Y0 @ Y1 )
              & ( ( kpair @ sk__14 @ sk__15 )
                = ( kpair @ Y0 @ Y1 ) ) ) ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl173]) ).

thf(zip_derived_cl214,plain,
    sk__13 @ sk__16 @ sk__17,
    inference(cnf_otf,[status(thm)],[zip_derived_cl174]) ).

thf(zip_derived_cl213,plain,
    ( ( kpair @ sk__14 @ sk__15 )
    = ( kpair @ sk__16 @ sk__17 ) ),
    inference(cnf_otf,[status(thm)],[zip_derived_cl174]) ).

thf(zip_derived_cl6,plain,
    ! [X7: $i,X8: $i,X9: $i,X10: $i] :
      ( ( X8 = X7 )
      | ( ( kpair @ X8 @ X10 )
       != ( kpair @ X7 @ X9 ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl71,plain,
    ! [X8: $i,X10: $i] :
      ( ( '#_fresh_sk2' @ ( kpair @ X8 @ X10 ) )
      = X8 ),
    inference(inj_rec,[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl240,plain,
    ( ( '#_fresh_sk2' @ ( kpair @ sk__14 @ sk__15 ) )
    = sk__16 ),
    inference('sup+',[status(thm)],[zip_derived_cl213,zip_derived_cl71]) ).

thf(zip_derived_cl71_001,plain,
    ! [X8: $i,X10: $i] :
      ( ( '#_fresh_sk2' @ ( kpair @ X8 @ X10 ) )
      = X8 ),
    inference(inj_rec,[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl260,plain,
    sk__14 = sk__16,
    inference(demod,[status(thm)],[zip_derived_cl240,zip_derived_cl71]) ).

thf(zip_derived_cl266,plain,
    sk__13 @ sk__14 @ sk__17,
    inference(demod,[status(thm)],[zip_derived_cl214,zip_derived_cl260]) ).

thf(zip_derived_cl213_002,plain,
    ( ( kpair @ sk__14 @ sk__15 )
    = ( kpair @ sk__16 @ sk__17 ) ),
    inference(cnf_otf,[status(thm)],[zip_derived_cl174]) ).

thf(zip_derived_cl1,plain,
    ! [X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( X4 = X3 )
      | ( ( kpair @ X6 @ X4 )
       != ( kpair @ X5 @ X3 ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl28,plain,
    ! [X4: $i,X6: $i] :
      ( ( '#_fresh_sk1' @ ( kpair @ X6 @ X4 ) )
      = X4 ),
    inference(inj_rec,[status(thm)],[zip_derived_cl1]) ).

thf(zip_derived_cl243,plain,
    ( ( '#_fresh_sk1' @ ( kpair @ sk__14 @ sk__15 ) )
    = sk__17 ),
    inference('sup+',[status(thm)],[zip_derived_cl213,zip_derived_cl28]) ).

thf(zip_derived_cl28_003,plain,
    ! [X4: $i,X6: $i] :
      ( ( '#_fresh_sk1' @ ( kpair @ X6 @ X4 ) )
      = X4 ),
    inference(inj_rec,[status(thm)],[zip_derived_cl1]) ).

thf(zip_derived_cl261,plain,
    sk__15 = sk__17,
    inference(demod,[status(thm)],[zip_derived_cl243,zip_derived_cl28]) ).

thf(zip_derived_cl3,plain,
    ~ ( sk__13 @ sk__14 @ sk__15 ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl268,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl266,zip_derived_cl261,zip_derived_cl3]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SEU668^2 : 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.wdpSny6nyT true
% 0.17/0.35  % Computer : n016.cluster.edu
% 0.17/0.35  % Model    : x86_64 x86_64
% 0.17/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35  % Memory   : 8042.1875MB
% 0.17/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35  % CPULimit : 300
% 0.17/0.35  % WCLimit  : 300
% 0.17/0.35  % DateTime : Wed Aug 23 21:00:38 EDT 2023
% 0.17/0.35  % CPUTime  : 
% 0.17/0.35  % Running portfolio for 300 s
% 0.17/0.35  % File         : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.36  % Number of cores: 8
% 0.17/0.36  % Python version: Python 3.6.8
% 0.17/0.36  % Running in HO mode
% 0.21/0.69  % Total configuration time : 828
% 0.21/0.69  % Estimated wc time : 1656
% 0.21/0.69  % Estimated cpu time (8 cpus) : 207.0
% 0.21/0.73  % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 1.31/0.77  % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 1.31/0.78  % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 1.31/0.78  % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 1.31/0.79  % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 1.31/0.79  % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 1.31/0.80  % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.31/0.80  % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 1.48/0.88  % Solved by lams/40_c_ic.sh.
% 1.48/0.88  % done 28 iterations in 0.077s
% 1.48/0.88  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 1.48/0.88  % SZS output start Refutation
% See solution above
% 1.48/0.88  
% 1.48/0.88  
% 1.48/0.88  % Terminating...
% 2.14/0.98  % Runner terminated.
% 2.14/0.99  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------