%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SET062^7 : TPTP v9.2.0. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.jZZ6zr3eUi true
% Computer : n005.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 Oct 2 04:51:23 PM UTC 2025
% Result : Theorem 0.58s 0.91s
% Output : Refutation 0.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 21
% Syntax : Number of formulae : 46 ( 32 unt; 0 typ; 0 def)
% Number of atoms : 135 ( 21 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 284 ( 23 ~; 21 |; 0 &; 230 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 36 ( 36 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 4 con; 0-3 aty)
% Number of variables : 77 ( 47 ^; 30 !; 0 ?; 77 :)
% Comments :
%------------------------------------------------------------------------------
thf(mu_type,type,
mu: $tType ).
thf(empty_set_type,type,
empty_set: mu ).
thf(sk__4_type,type,
sk__4: $i ).
thf(mforall_ind_type,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(sk__3_type,type,
sk__3: mu > mu > $i > mu ).
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(subset_type,type,
subset: mu > mu > $i > $o ).
thf(exists_in_world_type,type,
exists_in_world: mu > $i > $o ).
thf(mequiv_type,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(sk__5_type,type,
sk__5: mu ).
thf(mand_type,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(member_type,type,
member: mu > mu > $i > $o ).
thf(mvalid_type,type,
mvalid: ( $i > $o ) > $o ).
thf(existence_of_empty_set_ax,axiom,
! [V: $i] : ( exists_in_world @ empty_set @ V ) ).
thf(zip_derived_cl2,plain,
! [X0: $i] : ( exists_in_world @ empty_set @ X0 ),
inference(cnf,[status(esa)],[existence_of_empty_set_ax]) ).
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(thI15,conjecture,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] : ( subset @ empty_set @ A ) ) ) ).
thf(zf_stmt_0,conjecture,
! [X4: $i,X6: mu] :
( ( exists_in_world @ X6 @ X4 )
=> ( subset @ empty_set @ X6 @ X4 ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ! [X4: $i,X6: mu] :
( ( exists_in_world @ X6 @ X4 )
=> ( subset @ empty_set @ X6 @ X4 ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl29,plain,
exists_in_world @ sk__5 @ sk__4,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(mequiv,axiom,
( mequiv
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) ) ) ).
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(mand,axiom,
( mand
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) ) ) ).
thf('10',plain,
( mand
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mand,'5','7']) ).
thf('11',plain,
( mand
= ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mnot @ ( mor @ ( mnot @ V_1 ) @ ( mnot @ V_2 ) ) ) ) ),
define([status(thm)]) ).
thf('12',plain,
( mequiv
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mequiv,'9','11','5','7']) ).
thf('13',plain,
( mequiv
= ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mand @ ( mimplies @ V_1 @ V_2 ) @ ( mimplies @ V_2 @ V_1 ) ) ) ),
define([status(thm)]) ).
thf(subset,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mequiv @ ( subset @ A @ B )
@ ( mforall_ind
@ ^ [X: mu] : ( mimplies @ ( member @ X @ A ) @ ( member @ X @ B ) ) ) ) ) ) ) ).
thf(zf_stmt_2,axiom,
! [X4: $i,X6: mu] :
( ( exists_in_world @ X6 @ X4 )
=> ! [X8: mu] :
( ( exists_in_world @ X8 @ X4 )
=> ~ ( ~ ( ~ ( subset @ X6 @ X8 @ X4 )
| ! [X10: mu] :
( ( exists_in_world @ X10 @ X4 )
=> ( ~ ( member @ X10 @ X6 @ X4 )
| ( member @ X10 @ X8 @ X4 ) ) ) )
| ~ ( ~ ! [X12: mu] :
( ( exists_in_world @ X12 @ X4 )
=> ( ~ ( member @ X12 @ X6 @ X4 )
| ( member @ X12 @ X8 @ X4 ) ) )
| ( subset @ X6 @ X8 @ X4 ) ) ) ) ) ).
thf(zip_derived_cl14,plain,
! [X0: mu,X1: $i,X2: mu] :
( ~ ( exists_in_world @ X0 @ X1 )
| ( subset @ X2 @ X0 @ X1 )
| ( member @ ( sk__3 @ X0 @ X2 @ X1 ) @ X2 @ X1 )
| ~ ( exists_in_world @ X2 @ X1 ) ),
inference(cnf,[status(esa)],[zf_stmt_2]) ).
thf(zip_derived_cl455,plain,
! [X0: mu] :
( ~ ( exists_in_world @ X0 @ sk__4 )
| ( member @ ( sk__3 @ sk__5 @ X0 @ sk__4 ) @ X0 @ sk__4 )
| ( subset @ X0 @ sk__5 @ sk__4 ) ),
inference('sup-',[status(thm)],[zip_derived_cl29,zip_derived_cl14]) ).
thf(zip_derived_cl633,plain,
( ( subset @ empty_set @ sk__5 @ sk__4 )
| ( member @ ( sk__3 @ sk__5 @ empty_set @ sk__4 ) @ empty_set @ sk__4 ) ),
inference('sup-',[status(thm)],[zip_derived_cl2,zip_derived_cl455]) ).
thf(zip_derived_cl30,plain,
~ ( subset @ empty_set @ sk__5 @ sk__4 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl656,plain,
member @ ( sk__3 @ sk__5 @ empty_set @ sk__4 ) @ empty_set @ sk__4,
inference(demod,[status(thm)],[zip_derived_cl633,zip_derived_cl30]) ).
thf(empty_set,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] : ( mnot @ ( member @ X @ empty_set ) ) ) ) ).
thf(zf_stmt_3,axiom,
! [X4: $i,X6: mu] :
( ( exists_in_world @ X6 @ X4 )
=> ~ ( member @ X6 @ empty_set @ X4 ) ) ).
thf(zip_derived_cl25,plain,
! [X0: mu,X1: $i] :
( ~ ( member @ X0 @ empty_set @ X1 )
| ~ ( exists_in_world @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[zf_stmt_3]) ).
thf(zip_derived_cl666,plain,
~ ( exists_in_world @ ( sk__3 @ sk__5 @ empty_set @ sk__4 ) @ sk__4 ),
inference('sup-',[status(thm)],[zip_derived_cl656,zip_derived_cl25]) ).
thf(zip_derived_cl2_001,plain,
! [X0: $i] : ( exists_in_world @ empty_set @ X0 ),
inference(cnf,[status(esa)],[existence_of_empty_set_ax]) ).
thf(zip_derived_cl29_002,plain,
exists_in_world @ sk__5 @ sk__4,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl15,plain,
! [X0: mu,X1: $i,X2: mu] :
( ~ ( exists_in_world @ X0 @ X1 )
| ( subset @ X2 @ X0 @ X1 )
| ( exists_in_world @ ( sk__3 @ X0 @ X2 @ X1 ) @ X1 )
| ~ ( exists_in_world @ X2 @ X1 ) ),
inference(cnf,[status(esa)],[zf_stmt_2]) ).
thf(zip_derived_cl91,plain,
! [X0: mu] :
( ~ ( exists_in_world @ X0 @ sk__4 )
| ( exists_in_world @ ( sk__3 @ sk__5 @ X0 @ sk__4 ) @ sk__4 )
| ( subset @ X0 @ sk__5 @ sk__4 ) ),
inference('sup-',[status(thm)],[zip_derived_cl29,zip_derived_cl15]) ).
thf(zip_derived_cl101,plain,
( ( subset @ empty_set @ sk__5 @ sk__4 )
| ( exists_in_world @ ( sk__3 @ sk__5 @ empty_set @ sk__4 ) @ sk__4 ) ),
inference('sup-',[status(thm)],[zip_derived_cl2,zip_derived_cl91]) ).
thf(zip_derived_cl30_003,plain,
~ ( subset @ empty_set @ sk__5 @ sk__4 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl107,plain,
exists_in_world @ ( sk__3 @ sk__5 @ empty_set @ sk__4 ) @ sk__4,
inference(demod,[status(thm)],[zip_derived_cl101,zip_derived_cl30]) ).
thf(zip_derived_cl670,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl666,zip_derived_cl107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET062^7 : TPTP v9.2.0. Released v5.5.0.
% 0.11/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.jZZ6zr3eUi true
% 0.14/0.34 % Computer : n005.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 : Wed Oct 1 13:00:38 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox/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
% 0.56/0.67 % Total configuration time : 828
% 0.56/0.67 % Estimated wc time : 1656
% 0.56/0.67 % Estimated cpu time (8 cpus) : 207.0
% 0.56/0.71 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.56/0.74 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.56/0.75 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.56/0.75 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.56/0.75 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.56/0.75 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.56/0.75 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.56/0.76 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 0.58/0.81 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 0.58/0.90 % /export/starexec/sandbox/solver/bin/lams/35_full_unif.sh running for 56s
% 0.58/0.91 % Solved by lams/40_c.s.sh.
% 0.58/0.91 % done 103 iterations in 0.177s
% 0.58/0.91 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 0.58/0.91 % SZS output start Refutation
% See solution above
% 0.58/0.91
% 0.58/0.91
% 0.58/0.91 % Terminating...
% 0.59/0.96 % Runner terminated.
% 0.59/0.97 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------