%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SET002^7 : TPTP v8.1.2. Released v5.5.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.WxFLJ8vSOM true

% Computer : n017.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 16:11:34 EDT 2023

% Result   : Theorem 1.45s 0.82s
% Output   : Refutation 1.45s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   28
% Syntax   : Number of formulae    :   44 (  22 unt;  12 typ;   0 def)
%            Number of atoms       :   77 (  15 equ;   0 cnn)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  158 (  15   ~;  10   |;   0   &; 125   @)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   53 (  53   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  11 usr;   3 con; 0-3 aty)
%            Number of variables   :   54 (  34   ^;  20   !;   0   ?;  54   :)

% Comments : 
%------------------------------------------------------------------------------
thf(mu_type,type,
    mu: $tType ).

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

thf(sk__7_type,type,
    sk__7: mu ).

thf(mforall_ind_type,type,
    mforall_ind: ( mu > $i > $o ) > $i > $o ).

thf(mnot_type,type,
    mnot: ( $i > $o ) > $i > $o ).

thf(mor_type,type,
    mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(mimplies_type,type,
    mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(union_type,type,
    union: mu > mu > mu ).

thf(exists_in_world_type,type,
    exists_in_world: mu > $i > $o ).

thf(qmltpeq_type,type,
    qmltpeq: mu > mu > $i > $o ).

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

thf(mvalid_type,type,
    mvalid: ( $i > $o ) > $o ).

thf(mvalid,axiom,
    ( mvalid
    = ( ^ [Phi: $i > $o] :
        ! [W: $i] : ( Phi @ W ) ) ) ).

thf('0',plain,
    ( mvalid
    = ( ^ [Phi: $i > $o] :
        ! [W: $i] : ( Phi @ W ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mvalid]) ).

thf('1',plain,
    ( mvalid
    = ( ^ [V_1: $i > $o] :
        ! [X4: $i] : ( V_1 @ X4 ) ) ),
    define([status(thm)]) ).

thf(mforall_ind,axiom,
    ( mforall_ind
    = ( ^ [Phi: mu > $i > $o,W: $i] :
        ! [X: mu] :
          ( ( exists_in_world @ X @ W )
         => ( Phi @ X @ W ) ) ) ) ).

thf('2',plain,
    ( mforall_ind
    = ( ^ [Phi: mu > $i > $o,W: $i] :
        ! [X: mu] :
          ( ( exists_in_world @ X @ W )
         => ( Phi @ X @ W ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mforall_ind]) ).

thf('3',plain,
    ( mforall_ind
    = ( ^ [V_1: mu > $i > $o,V_2: $i] :
        ! [X4: mu] :
          ( ( exists_in_world @ X4 @ V_2 )
         => ( V_1 @ X4 @ V_2 ) ) ) ),
    define([status(thm)]) ).

thf(reflexivity_of_subset,axiom,
    ( mvalid
    @ ( mforall_ind
      @ ^ [B: mu] : ( subset @ B @ B ) ) ) ).

thf(zf_stmt_0,axiom,
    ! [X4: $i,X6: mu] :
      ( ( exists_in_world @ X6 @ X4 )
     => ( subset @ X6 @ X6 @ X4 ) ) ).

thf(zip_derived_cl26,plain,
    ! [X0: mu,X1: $i] :
      ( ( subset @ X0 @ X0 @ X1 )
      | ~ ( exists_in_world @ X0 @ X1 ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(mimplies,axiom,
    ( mimplies
    = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ) ).

thf(mor,axiom,
    ( mor
    = ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
          ( ( Phi @ W )
          | ( Psi @ W ) ) ) ) ).

thf('4',plain,
    ( mor
    = ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
          ( ( Phi @ W )
          | ( Psi @ W ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mor]) ).

thf('5',plain,
    ( mor
    = ( ^ [V_1: $i > $o,V_2: $i > $o,V_3: $i] :
          ( ( V_1 @ V_3 )
          | ( V_2 @ V_3 ) ) ) ),
    define([status(thm)]) ).

thf(mnot,axiom,
    ( mnot
    = ( ^ [Phi: $i > $o,W: $i] :
          ~ ( Phi @ W ) ) ) ).

thf('6',plain,
    ( mnot
    = ( ^ [Phi: $i > $o,W: $i] :
          ~ ( Phi @ W ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mnot]) ).

thf('7',plain,
    ( mnot
    = ( ^ [V_1: $i > $o,V_2: $i] :
          ~ ( V_1 @ V_2 ) ) ),
    define([status(thm)]) ).

thf('8',plain,
    ( mimplies
    = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mimplies,'5','7']) ).

thf('9',plain,
    ( mimplies
    = ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mor @ ( mnot @ V_1 ) @ V_2 ) ) ),
    define([status(thm)]) ).

thf(subset_union,axiom,
    ( mvalid
    @ ( mforall_ind
      @ ^ [B: mu] :
          ( mforall_ind
          @ ^ [C: mu] : ( mimplies @ ( subset @ B @ C ) @ ( qmltpeq @ ( union @ B @ C ) @ C ) ) ) ) ) ).

thf(zf_stmt_1,axiom,
    ! [X4: $i,X6: mu] :
      ( ( exists_in_world @ X6 @ X4 )
     => ! [X8: mu] :
          ( ( exists_in_world @ X8 @ X4 )
         => ( ~ ( subset @ X6 @ X8 @ X4 )
            | ( qmltpeq @ ( union @ X6 @ X8 ) @ X8 @ X4 ) ) ) ) ).

thf(zip_derived_cl14,plain,
    ! [X0: mu,X1: $i,X2: mu] :
      ( ~ ( exists_in_world @ X0 @ X1 )
      | ~ ( subset @ X2 @ X0 @ X1 )
      | ( qmltpeq @ ( union @ X2 @ X0 ) @ X0 @ X1 )
      | ~ ( exists_in_world @ X2 @ X1 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(prove_idempotency_of_union,conjecture,
    ( mvalid
    @ ( mforall_ind
      @ ^ [B: mu] : ( qmltpeq @ ( union @ B @ B ) @ B ) ) ) ).

thf(zf_stmt_2,conjecture,
    ! [X4: $i,X6: mu] :
      ( ( exists_in_world @ X6 @ X4 )
     => ( qmltpeq @ ( union @ X6 @ X6 ) @ X6 @ X4 ) ) ).

thf(zf_stmt_3,negated_conjecture,
    ~ ! [X4: $i,X6: mu] :
        ( ( exists_in_world @ X6 @ X4 )
       => ( qmltpeq @ ( union @ X6 @ X6 ) @ X6 @ X4 ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_2]) ).

thf(zip_derived_cl36,plain,
    ~ ( qmltpeq @ ( union @ sk__7 @ sk__7 ) @ sk__7 @ sk__6 ),
    inference(cnf,[status(esa)],[zf_stmt_3]) ).

thf(zip_derived_cl125,plain,
    ( ~ ( exists_in_world @ sk__7 @ sk__6 )
    | ~ ( subset @ sk__7 @ sk__7 @ sk__6 )
    | ~ ( exists_in_world @ sk__7 @ sk__6 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl14,zip_derived_cl36]) ).

thf(zip_derived_cl35,plain,
    exists_in_world @ sk__7 @ sk__6,
    inference(cnf,[status(esa)],[zf_stmt_3]) ).

thf(zip_derived_cl35_001,plain,
    exists_in_world @ sk__7 @ sk__6,
    inference(cnf,[status(esa)],[zf_stmt_3]) ).

thf(zip_derived_cl135,plain,
    ~ ( subset @ sk__7 @ sk__7 @ sk__6 ),
    inference(demod,[status(thm)],[zip_derived_cl125,zip_derived_cl35,zip_derived_cl35]) ).

thf(zip_derived_cl147,plain,
    ~ ( exists_in_world @ sk__7 @ sk__6 ),
    inference('sup-',[status(thm)],[zip_derived_cl26,zip_derived_cl135]) ).

thf(zip_derived_cl35_002,plain,
    exists_in_world @ sk__7 @ sk__6,
    inference(cnf,[status(esa)],[zf_stmt_3]) ).

thf(zip_derived_cl153,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl147,zip_derived_cl35]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SET002^7 : TPTP v8.1.2. Released v5.5.0.
% 0.06/0.13  % Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.WxFLJ8vSOM true
% 0.14/0.34  % Computer : n017.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Sat Aug 26 12:31:11 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.14/0.34  % Running portfolio for 300 s
% 0.14/0.34  % File         : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.34  % Number of cores: 8
% 0.14/0.35  % Python version: Python 3.6.8
% 0.14/0.35  % Running in HO mode
% 0.21/0.61  % Total configuration time : 828
% 0.21/0.61  % Estimated wc time : 1656
% 0.21/0.61  % Estimated cpu time (8 cpus) : 207.0
% 0.21/0.72  % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.21/0.72  % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.21/0.73  % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.21/0.74  % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.21/0.74  % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.21/0.74  % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.21/0.74  % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 0.21/0.74  % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 1.43/0.79  % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 1.45/0.82  % Solved by lams/40_c.s.sh.
% 1.45/0.82  % done 35 iterations in 0.065s
% 1.45/0.82  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 1.45/0.82  % SZS output start Refutation
% See solution above
% 1.45/0.82  
% 1.45/0.82  
% 1.45/0.82  % Terminating...
% 1.93/0.93  % Runner terminated.
% 1.93/0.94  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------