%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SET925^7 : TPTP v9.2.0. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.4mX7fnMHDj true
% Computer : n022.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 04:53:10 PM UTC 2025
% Result : Theorem 25.66s 3.85s
% Output : Refutation 25.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 26
% Syntax : Number of formulae : 41 ( 29 unt; 0 typ; 0 def)
% Number of atoms : 249 ( 27 equ; 26 cnn)
% Maximal formula atoms : 38 ( 6 avg)
% Number of connectives : 586 ( 73 ~; 61 |; 5 &; 403 @)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 6 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 45 ( 45 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 16 usr; 4 con; 0-3 aty)
% ( 26 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 136 ( 78 ^; 58 !; 0 ?; 136 :)
% Comments :
%------------------------------------------------------------------------------
thf(mu_type,type,
mu: $tType ).
thf(rel_s4_type,type,
rel_s4: $i > $i > $o ).
thf(mreflexive_type,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(mforall_ind_type,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(set_difference_type,type,
set_difference: mu > mu > 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(empty_set_type,type,
empty_set: mu ).
thf(mtransitive_type,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(mbox_s4_type,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(exists_in_world_type,type,
exists_in_world: mu > $i > $o ).
thf(qmltpeq_type,type,
qmltpeq: mu > mu > $i > $o ).
thf(singleton_type,type,
singleton: mu > mu ).
thf(mand_type,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(in_type,type,
in: mu > mu > $i > $o ).
thf(mvalid_type,type,
mvalid: ( $i > $o ) > $o ).
thf(mreflexive,axiom,
( mreflexive
= ( ^ [R: $i > $i > $o] :
! [S: $i] : ( R @ S @ S ) ) ) ).
thf('0',plain,
( mreflexive
= ( ^ [R: $i > $i > $o] :
! [S: $i] : ( R @ S @ S ) ) ),
inference(simplify_rw_rule,[status(thm)],[mreflexive]) ).
thf('1',plain,
( mreflexive
= ( ^ [V_1: $i > $i > $o] :
! [X4: $i] : ( V_1 @ X4 @ X4 ) ) ),
define([status(thm)]) ).
thf(a1,axiom,
mreflexive @ rel_s4 ).
thf(zf_stmt_0,axiom,
! [X4: $i] : ( rel_s4 @ X4 @ X4 ) ).
thf(zip_derived_cl1,plain,
( !!
@ ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(mtransitive,axiom,
( mtransitive
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ T @ U ) )
=> ( R @ S @ U ) ) ) ) ).
thf('2',plain,
( mtransitive
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ T @ U ) )
=> ( R @ S @ U ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mtransitive]) ).
thf('3',plain,
( mtransitive
= ( ^ [V_1: $i > $i > $o] :
! [X4: $i,X6: $i,X8: $i] :
( ( ( V_1 @ X4 @ X6 )
& ( V_1 @ X6 @ X8 ) )
=> ( V_1 @ X4 @ X8 ) ) ) ),
define([status(thm)]) ).
thf(a2,axiom,
mtransitive @ rel_s4 ).
thf(zf_stmt_1,axiom,
! [X4: $i,X6: $i,X8: $i] :
( ( ( rel_s4 @ X6 @ X8 )
& ( rel_s4 @ X4 @ X6 ) )
=> ( rel_s4 @ X4 @ X8 ) ) ).
thf(zip_derived_cl2,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( rel_s4 @ Y1 @ Y2 )
& ( rel_s4 @ Y0 @ Y1 ) )
=> ( rel_s4 @ Y0 @ Y2 ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(mbox_s4,axiom,
( mbox_s4
= ( ^ [Phi: $i > $o,W: $i] :
! [V: $i] :
( ( Phi @ V )
| ~ ( rel_s4 @ W @ V ) ) ) ) ).
thf('4',plain,
( mbox_s4
= ( ^ [Phi: $i > $o,W: $i] :
! [V: $i] :
( ( Phi @ V )
| ~ ( rel_s4 @ W @ V ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mbox_s4]) ).
thf('5',plain,
( mbox_s4
= ( ^ [V_1: $i > $o,V_2: $i] :
! [X4: $i] :
( ( V_1 @ X4 )
| ~ ( rel_s4 @ V_2 @ X4 ) ) ) ),
define([status(thm)]) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ) ).
thf('6',plain,
( mvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ),
inference(simplify_rw_rule,[status(thm)],[mvalid]) ).
thf('7',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('8',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('9',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(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('10',plain,
( mor
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
| ( Psi @ W ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mor]) ).
thf('11',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('12',plain,
( mnot
= ( ^ [Phi: $i > $o,W: $i] :
~ ( Phi @ W ) ) ),
inference(simplify_rw_rule,[status(thm)],[mnot]) ).
thf('13',plain,
( mnot
= ( ^ [V_1: $i > $o,V_2: $i] :
~ ( V_1 @ V_2 ) ) ),
define([status(thm)]) ).
thf('14',plain,
( mimplies
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ),
inference(simplify_rw_rule,[status(thm)],[mimplies,'11','13']) ).
thf('15',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('16',plain,
( mand
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mand,'11','13']) ).
thf('17',plain,
( mand
= ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mnot @ ( mor @ ( mnot @ V_1 ) @ ( mnot @ V_2 ) ) ) ) ),
define([status(thm)]) ).
thf(t68_zfmisc_1,conjecture,
( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [A: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [B: mu] : ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set ) ) @ ( mbox_s4 @ ( in @ A @ B ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( in @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set ) ) ) ) ) ) ) ) ) ) ).
thf(zf_stmt_2,conjecture,
! [X4: $i,X6: $i] :
( ~ ( rel_s4 @ X4 @ X6 )
| ! [X8: mu] :
( ( exists_in_world @ X8 @ X6 )
=> ! [X10: $i] :
( ~ ( rel_s4 @ X6 @ X10 )
| ! [X12: mu] :
( ( exists_in_world @ X12 @ X10 )
=> ~ ( ~ ! [X20: $i] :
( ~ ( rel_s4 @ X10 @ X20 )
| ! [X24: $i] :
( ~ ( rel_s4 @ X20 @ X24 )
| ( qmltpeq @ ( set_difference @ ( singleton @ X8 ) @ X12 ) @ empty_set @ X24 ) )
| ~ ! [X22: $i] :
( ~ ( rel_s4 @ X20 @ X22 )
| ( in @ X8 @ X12 @ X22 ) ) )
| ~ ! [X14: $i] :
( ~ ( rel_s4 @ X10 @ X14 )
| ! [X18: $i] :
( ~ ( rel_s4 @ X14 @ X18 )
| ( in @ X8 @ X12 @ X18 ) )
| ~ ! [X16: $i] :
( ~ ( rel_s4 @ X14 @ X16 )
| ( qmltpeq @ ( set_difference @ ( singleton @ X8 ) @ X12 ) @ empty_set @ X16 ) ) ) ) ) ) ) ) ).
thf(zf_stmt_3,negated_conjecture,
~ ! [X4: $i,X6: $i] :
( ~ ( rel_s4 @ X4 @ X6 )
| ! [X8: mu] :
( ( exists_in_world @ X8 @ X6 )
=> ! [X10: $i] :
( ~ ( rel_s4 @ X6 @ X10 )
| ! [X12: mu] :
( ( exists_in_world @ X12 @ X10 )
=> ~ ( ~ ! [X20: $i] :
( ~ ( rel_s4 @ X10 @ X20 )
| ! [X24: $i] :
( ~ ( rel_s4 @ X20 @ X24 )
| ( qmltpeq @ ( set_difference @ ( singleton @ X8 ) @ X12 ) @ empty_set @ X24 ) )
| ~ ! [X22: $i] :
( ~ ( rel_s4 @ X20 @ X22 )
| ( in @ X8 @ X12 @ X22 ) ) )
| ~ ! [X14: $i] :
( ~ ( rel_s4 @ X10 @ X14 )
| ! [X18: $i] :
( ~ ( rel_s4 @ X14 @ X18 )
| ( in @ X8 @ X12 @ X18 ) )
| ~ ! [X16: $i] :
( ~ ( rel_s4 @ X14 @ X16 )
| ( qmltpeq @ ( set_difference @ ( singleton @ X8 ) @ X12 ) @ empty_set @ X16 ) ) ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_2]) ).
thf(zip_derived_cl21,plain,
~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y3 ) )
| ( !!
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y5 ) )
| ( !!
@ ^ [Y6: $i] :
( ( (~) @ ( rel_s4 @ Y5 @ Y6 ) )
| ( qmltpeq @ ( set_difference @ ( singleton @ Y2 ) @ Y4 ) @ empty_set @ Y6 ) ) )
| ( (~)
@ ( !!
@ ^ [Y6: $i] :
( ( (~) @ ( rel_s4 @ Y5 @ Y6 ) )
| ( in @ Y2 @ Y4 @ Y6 ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y5 ) )
| ( !!
@ ^ [Y6: $i] :
( ( (~) @ ( rel_s4 @ Y5 @ Y6 ) )
| ( in @ Y2 @ Y4 @ Y6 ) ) )
| ( (~)
@ ( !!
@ ^ [Y6: $i] :
( ( (~) @ ( rel_s4 @ Y5 @ Y6 ) )
| ( qmltpeq @ ( set_difference @ ( singleton @ Y2 ) @ Y4 ) @ empty_set @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_3]) ).
thf(l36_zfmisc_1,axiom,
( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [A: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [B: mu] : ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set ) ) @ ( mbox_s4 @ ( in @ A @ B ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( in @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set ) ) ) ) ) ) ) ) ) ) ).
thf(zf_stmt_4,axiom,
! [X4: $i,X6: $i] :
( ~ ( rel_s4 @ X4 @ X6 )
| ! [X8: mu] :
( ( exists_in_world @ X8 @ X6 )
=> ! [X10: $i] :
( ~ ( rel_s4 @ X6 @ X10 )
| ! [X12: mu] :
( ( exists_in_world @ X12 @ X10 )
=> ~ ( ~ ! [X20: $i] :
( ~ ( rel_s4 @ X10 @ X20 )
| ! [X24: $i] :
( ~ ( rel_s4 @ X20 @ X24 )
| ( qmltpeq @ ( set_difference @ ( singleton @ X8 ) @ X12 ) @ empty_set @ X24 ) )
| ~ ! [X22: $i] :
( ~ ( rel_s4 @ X20 @ X22 )
| ( in @ X8 @ X12 @ X22 ) ) )
| ~ ! [X14: $i] :
( ~ ( rel_s4 @ X10 @ X14 )
| ! [X18: $i] :
( ~ ( rel_s4 @ X14 @ X18 )
| ( in @ X8 @ X12 @ X18 ) )
| ~ ! [X16: $i] :
( ~ ( rel_s4 @ X14 @ X16 )
| ( qmltpeq @ ( set_difference @ ( singleton @ X8 ) @ X12 ) @ empty_set @ X16 ) ) ) ) ) ) ) ) ).
thf(zip_derived_cl20,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y3 ) )
| ( !!
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y5 ) )
| ( !!
@ ^ [Y6: $i] :
( ( (~) @ ( rel_s4 @ Y5 @ Y6 ) )
| ( qmltpeq @ ( set_difference @ ( singleton @ Y2 ) @ Y4 ) @ empty_set @ Y6 ) ) )
| ( (~)
@ ( !!
@ ^ [Y6: $i] :
( ( (~) @ ( rel_s4 @ Y5 @ Y6 ) )
| ( in @ Y2 @ Y4 @ Y6 ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y5 ) )
| ( !!
@ ^ [Y6: $i] :
( ( (~) @ ( rel_s4 @ Y5 @ Y6 ) )
| ( in @ Y2 @ Y4 @ Y6 ) ) )
| ( (~)
@ ( !!
@ ^ [Y6: $i] :
( ( (~) @ ( rel_s4 @ Y5 @ Y6 ) )
| ( qmltpeq @ ( set_difference @ ( singleton @ Y2 ) @ Y4 ) @ empty_set @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_4]) ).
thf(zip_derived_cl1748,plain,
$false,
inference(eprover,[status(thm)],[zip_derived_cl1,zip_derived_cl2,zip_derived_cl21,zip_derived_cl20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : SET925^7 : TPTP v9.2.0. Released v5.5.0.
% 0.06/0.11 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.4mX7fnMHDj true
% 0.10/0.31 % Computer : n022.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Wed Oct 1 13:08:53 EDT 2025
% 0.10/0.32 % CPUTime :
% 0.10/0.32 % Running portfolio for 300 s
% 0.10/0.32 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.32 % Number of cores: 8
% 0.10/0.32 % Python version: Python 3.6.8
% 0.10/0.32 % Running in HO mode
% 0.42/0.60 % Total configuration time : 828
% 0.42/0.60 % Estimated wc time : 1656
% 0.42/0.60 % Estimated cpu time (8 cpus) : 207.0
% 0.46/0.67 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.46/0.68 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.46/0.68 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.46/0.68 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.46/0.68 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.46/0.69 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.46/0.69 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.46/0.73 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.47/0.78 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 25.66/3.85 % Solved by lams/15_e_short1.sh.
% 25.66/3.85 % done 293 iterations in 3.130s
% 25.66/3.85 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 25.66/3.85 % SZS output start Refutation
% See solution above
% 25.66/3.86
% 25.66/3.86
% 25.66/3.86 % Terminating...
% 26.32/3.92 % Runner terminated.
% 26.35/3.94 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------