%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SYO396^1 : TPTP v9.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.bbL5Xf6VKC true
% Computer : n027.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 05:07:23 PM UTC 2025
% Result : Theorem 0.59s 0.77s
% Output : Refutation 0.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 18
% Syntax : Number of formulae : 29 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 148 ( 24 equ; 15 cnn)
% Maximal formula atoms : 30 ( 5 avg)
% Number of connectives : 234 ( 53 ~; 33 |; 0 &; 143 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 36 ( 36 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 10 usr; 3 con; 0-3 aty)
% ( 5 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 66 ( 50 ^; 16 !; 0 ?; 66 :)
% Comments :
%------------------------------------------------------------------------------
thf(rel_k_type,type,
rel_k: $i > $i > $o ).
thf(mand_type,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mnot_type,type,
mnot: ( $i > $o ) > $i > $o ).
thf(mimplies_type,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(p_type,type,
p: $i > $o ).
thf(mdia_k_type,type,
mdia_k: ( $i > $o ) > $i > $o ).
thf(mbox_k_type,type,
mbox_k: ( $i > $o ) > $i > $o ).
thf(mequiv_type,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mor_type,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mvalid_type,type,
mvalid: ( $i > $o ) > $o ).
thf(mdia_k,axiom,
( mdia_k
= ( ^ [Phi: $i > $o] : ( mnot @ ( mbox_k @ ( mnot @ Phi ) ) ) ) ) ).
thf(mbox_k,axiom,
( mbox_k
= ( ^ [Phi: $i > $o,W: $i] :
! [V: $i] :
( ( Phi @ V )
| ~ ( rel_k @ W @ V ) ) ) ) ).
thf('0',plain,
( mbox_k
= ( ^ [Phi: $i > $o,W: $i] :
! [V: $i] :
( ( Phi @ V )
| ~ ( rel_k @ W @ V ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mbox_k]) ).
thf('1',plain,
( mbox_k
= ( ^ [V_1: $i > $o,V_2: $i] :
! [X4: $i] :
( ( V_1 @ X4 )
| ~ ( rel_k @ V_2 @ X4 ) ) ) ),
define([status(thm)]) ).
thf(mnot,axiom,
( mnot
= ( ^ [Phi: $i > $o,W: $i] :
~ ( Phi @ W ) ) ) ).
thf('2',plain,
( mnot
= ( ^ [Phi: $i > $o,W: $i] :
~ ( Phi @ W ) ) ),
inference(simplify_rw_rule,[status(thm)],[mnot]) ).
thf('3',plain,
( mnot
= ( ^ [V_1: $i > $o,V_2: $i] :
~ ( V_1 @ V_2 ) ) ),
define([status(thm)]) ).
thf('4',plain,
( mdia_k
= ( ^ [Phi: $i > $o] : ( mnot @ ( mbox_k @ ( mnot @ Phi ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mdia_k,'1','3']) ).
thf('5',plain,
( mdia_k
= ( ^ [V_1: $i > $o] : ( mnot @ ( mbox_k @ ( mnot @ V_1 ) ) ) ) ),
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(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('8',plain,
( mor
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
| ( Psi @ W ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mor]) ).
thf('9',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('10',plain,
( mimplies
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ),
inference(simplify_rw_rule,[status(thm)],[mimplies,'9','3']) ).
thf('11',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('12',plain,
( mand
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mand,'9','3']) ).
thf('13',plain,
( mand
= ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mnot @ ( mor @ ( mnot @ V_1 ) @ ( mnot @ V_2 ) ) ) ) ),
define([status(thm)]) ).
thf('14',plain,
( mequiv
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mequiv,'11','13','9','3']) ).
thf('15',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(prove,conjecture,
mvalid @ ( mequiv @ ( mbox_k @ ( mimplies @ p @ ( mnot @ p ) ) ) @ ( mnot @ ( mdia_k @ p ) ) ) ).
thf(zf_stmt_0,conjecture,
! [X4: $i] :
~ ( ~ ( ! [X12: $i] :
( ~ ( rel_k @ X4 @ X12 )
| ~ ( p @ X12 )
| ~ ( p @ X12 ) )
| ~ ! [X10: $i] :
( ~ ( rel_k @ X4 @ X10 )
| ~ ( p @ X10 ) ) )
| ~ ( ! [X8: $i] :
( ~ ( rel_k @ X4 @ X8 )
| ~ ( p @ X8 ) )
| ~ ! [X6: $i] :
( ~ ( rel_k @ X4 @ X6 )
| ~ ( p @ X6 )
| ~ ( p @ X6 ) ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ! [X4: $i] :
~ ( ~ ( ! [X12: $i] :
( ~ ( rel_k @ X4 @ X12 )
| ~ ( p @ X12 )
| ~ ( p @ X12 ) )
| ~ ! [X10: $i] :
( ~ ( rel_k @ X4 @ X10 )
| ~ ( p @ X10 ) ) )
| ~ ( ! [X8: $i] :
( ~ ( rel_k @ X4 @ X8 )
| ~ ( p @ X8 ) )
| ~ ! [X6: $i] :
( ~ ( rel_k @ X4 @ X6 )
| ~ ( p @ X6 )
| ~ ( p @ X6 ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl0,plain,
~ ( !!
@ ^ [Y0: $i] :
( (~)
@ ( ( (~)
@ ( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_k @ Y0 @ Y1 ) )
| ( (~) @ ( p @ Y1 ) )
| ( (~) @ ( p @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_k @ Y0 @ Y1 ) )
| ( (~) @ ( p @ Y1 ) ) ) ) ) ) )
| ( (~)
@ ( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_k @ Y0 @ Y1 ) )
| ( (~) @ ( p @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_k @ Y0 @ Y1 ) )
| ( (~) @ ( p @ Y1 ) )
| ( (~) @ ( p @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl1,plain,
$false,
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYO396^1 : TPTP v9.2.0. Released v4.0.0.
% 0.06/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.bbL5Xf6VKC true
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Oct 1 17:58:53 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Running portfolio for 300 s
% 0.13/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in HO mode
% 0.55/0.67 % Total configuration time : 828
% 0.55/0.67 % Estimated wc time : 1656
% 0.55/0.67 % Estimated cpu time (8 cpus) : 207.0
% 0.57/0.72 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.57/0.73 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.59/0.75 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.59/0.76 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.59/0.76 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.59/0.76 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.59/0.77 % Solved by lams/35_full_unif4.sh.
% 0.59/0.77 % done 0 iterations in 0.014s
% 0.59/0.77 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 0.59/0.77 % SZS output start Refutation
% See solution above
% 0.59/0.77
% 0.59/0.77
% 0.59/0.77 % Terminating...
% 1.88/0.85 % Runner terminated.
% 1.88/0.86 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------