%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SYN052^7 : 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.baB1eOXuk9 true
% Computer : n024.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 05:03:51 PM UTC 2025
% Result : Theorem 28.08s 4.23s
% Output : Refutation 28.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 26
% Syntax : Number of formulae : 42 ( 30 unt; 0 typ; 0 def)
% Number of atoms : 271 ( 27 equ; 27 cnn)
% Maximal formula atoms : 74 ( 6 avg)
% Number of connectives : 578 ( 89 ~; 75 |; 7 &; 359 @)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 45 ( 45 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 13 usr; 4 con; 0-3 aty)
% ( 28 !!; 1 ??; 0 @@+; 0 @@-)
% Number of variables : 150 ( 80 ^; 69 !; 1 ?; 150 :)
% Comments :
%------------------------------------------------------------------------------
thf(mu_type,type,
mu: $tType ).
thf(p_type,type,
p: $i > $o ).
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(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(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(mand_type,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(big_f_type,type,
big_f: mu > $i > $o ).
thf(mvalid_type,type,
mvalid: ( $i > $o ) > $o ).
thf(nonempty_ax,axiom,
! [V: $i] :
? [X: mu] : ( exists_in_world @ X @ V ) ).
thf(zip_derived_cl0,plain,
( !!
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: mu] : ( exists_in_world @ Y1 @ Y0 ) ) ),
inference(cnf,[status(esa)],[nonempty_ax]) ).
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(cumulative_ax,axiom,
! [X: mu,V: $i,W: $i] :
( ( ( rel_s4 @ V @ W )
& ( exists_in_world @ X @ V ) )
=> ( exists_in_world @ X @ W ) ) ).
thf(zip_derived_cl3,plain,
( !!
@ ^ [Y0: mu] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( rel_s4 @ Y1 @ Y2 )
& ( exists_in_world @ Y0 @ Y1 ) )
=> ( exists_in_world @ Y0 @ Y2 ) ) ) ) ),
inference(cnf,[status(esa)],[cumulative_ax]) ).
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(pel22,conjecture,
( mvalid
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X: mu] : ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ p ) @ ( mbox_s4 @ ( big_f @ X ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( big_f @ X ) ) @ ( mbox_s4 @ p ) ) ) ) ) )
@ ( mand
@ ( mbox_s4
@ ( mimplies @ ( mbox_s4 @ p )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X1: mu] : ( mbox_s4 @ ( big_f @ X1 ) ) ) ) ) )
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X1: mu] : ( mbox_s4 @ ( big_f @ X1 ) ) ) )
@ ( mbox_s4 @ p ) ) ) ) ) ) ) ).
thf(zf_stmt_2,conjecture,
! [X4: $i,X6: $i] :
( ~ ( rel_s4 @ X4 @ X6 )
| ~ ( ~ ! [X34: $i] :
( ~ ( rel_s4 @ X6 @ X34 )
| ! [X42: $i] :
( ~ ( rel_s4 @ X34 @ X42 )
| ( p @ X42 ) )
| ~ ! [X36: $i] :
( ~ ( rel_s4 @ X34 @ X36 )
| ! [X38: mu] :
( ( exists_in_world @ X38 @ X36 )
=> ! [X40: $i] :
( ~ ( rel_s4 @ X36 @ X40 )
| ( big_f @ X38 @ X40 ) ) ) ) )
| ~ ! [X24: $i] :
( ~ ( rel_s4 @ X6 @ X24 )
| ! [X28: $i] :
( ~ ( rel_s4 @ X24 @ X28 )
| ! [X30: mu] :
( ( exists_in_world @ X30 @ X28 )
=> ! [X32: $i] :
( ~ ( rel_s4 @ X28 @ X32 )
| ( big_f @ X30 @ X32 ) ) ) )
| ~ ! [X26: $i] :
( ~ ( rel_s4 @ X24 @ X26 )
| ( p @ X26 ) ) ) )
| ~ ! [X8: $i] :
( ~ ( rel_s4 @ X6 @ X8 )
| ! [X10: mu] :
( ( exists_in_world @ X10 @ X8 )
=> ~ ( ~ ! [X18: $i] :
( ~ ( rel_s4 @ X8 @ X18 )
| ! [X22: $i] :
( ~ ( rel_s4 @ X18 @ X22 )
| ( p @ X22 ) )
| ~ ! [X20: $i] :
( ~ ( rel_s4 @ X18 @ X20 )
| ( big_f @ X10 @ X20 ) ) )
| ~ ! [X12: $i] :
( ~ ( rel_s4 @ X8 @ X12 )
| ! [X16: $i] :
( ~ ( rel_s4 @ X12 @ X16 )
| ( big_f @ X10 @ X16 ) )
| ~ ! [X14: $i] :
( ~ ( rel_s4 @ X12 @ X14 )
| ( p @ X14 ) ) ) ) ) ) ) ).
thf(zf_stmt_3,negated_conjecture,
~ ! [X4: $i,X6: $i] :
( ~ ( rel_s4 @ X4 @ X6 )
| ~ ( ~ ! [X34: $i] :
( ~ ( rel_s4 @ X6 @ X34 )
| ! [X42: $i] :
( ~ ( rel_s4 @ X34 @ X42 )
| ( p @ X42 ) )
| ~ ! [X36: $i] :
( ~ ( rel_s4 @ X34 @ X36 )
| ! [X38: mu] :
( ( exists_in_world @ X38 @ X36 )
=> ! [X40: $i] :
( ~ ( rel_s4 @ X36 @ X40 )
| ( big_f @ X38 @ X40 ) ) ) ) )
| ~ ! [X24: $i] :
( ~ ( rel_s4 @ X6 @ X24 )
| ! [X28: $i] :
( ~ ( rel_s4 @ X24 @ X28 )
| ! [X30: mu] :
( ( exists_in_world @ X30 @ X28 )
=> ! [X32: $i] :
( ~ ( rel_s4 @ X28 @ X32 )
| ( big_f @ X30 @ X32 ) ) ) )
| ~ ! [X26: $i] :
( ~ ( rel_s4 @ X24 @ X26 )
| ( p @ X26 ) ) ) )
| ~ ! [X8: $i] :
( ~ ( rel_s4 @ X6 @ X8 )
| ! [X10: mu] :
( ( exists_in_world @ X10 @ X8 )
=> ~ ( ~ ! [X18: $i] :
( ~ ( rel_s4 @ X8 @ X18 )
| ! [X22: $i] :
( ~ ( rel_s4 @ X18 @ X22 )
| ( p @ X22 ) )
| ~ ! [X20: $i] :
( ~ ( rel_s4 @ X18 @ X20 )
| ( big_f @ X10 @ X20 ) ) )
| ~ ! [X12: $i] :
( ~ ( rel_s4 @ X8 @ X12 )
| ! [X16: $i] :
( ~ ( rel_s4 @ X12 @ X16 )
| ( big_f @ X10 @ X16 ) )
| ~ ! [X14: $i] :
( ~ ( rel_s4 @ X12 @ X14 )
| ( p @ X14 ) ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_2]) ).
thf(zip_derived_cl4,plain,
~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y3 ) )
| ( p @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y3 ) )
| ( !!
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y5 ) )
| ( big_f @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y3 ) )
| ( !!
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y5 ) )
| ( big_f @ Y4 @ Y5 ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y3 ) )
| ( p @ Y3 ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( p @ Y5 ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( big_f @ Y3 @ Y5 ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( big_f @ Y3 @ Y5 ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( p @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_3]) ).
thf(zip_derived_cl2038,plain,
$false,
inference(eprover,[status(thm)],[zip_derived_cl0,zip_derived_cl1,zip_derived_cl3,zip_derived_cl2,zip_derived_cl4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN052^7 : TPTP v9.2.0. Released v5.5.0.
% 0.11/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.baB1eOXuk9 true
% 0.13/0.35 % Computer : n024.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Oct 1 13:44:08 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in HO mode
% 0.61/0.74 % Total configuration time : 828
% 0.61/0.74 % Estimated wc time : 1656
% 0.61/0.74 % Estimated cpu time (8 cpus) : 207.0
% 0.63/0.81 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.63/0.81 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.63/0.83 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.63/0.83 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.63/0.84 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.63/0.84 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.63/0.84 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.63/0.85 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 0.65/0.90 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 0.65/0.99 % /export/starexec/sandbox/solver/bin/lams/35_full_unif.sh running for 56s
% 28.08/4.23 % Solved by lams/15_e_short1.sh.
% 28.08/4.23 % done 282 iterations in 3.325s
% 28.08/4.23 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 28.08/4.23 % SZS output start Refutation
% See solution above
% 28.08/4.23
% 28.08/4.23
% 28.08/4.23 % Terminating...
% 28.36/4.35 % Runner terminated.
% 28.36/4.36 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------