TSTP Solution File: SYO572^7 by Zipperpin---2.1.9999
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%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SYO572^7 : 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.xTMOFvOhMG true
% Computer : n025.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 : Fri Sep 1 05:52:07 EDT 2023
% Result : Theorem 0.21s 0.74s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 35
% Syntax : Number of formulae : 57 ( 33 unt; 15 typ; 0 def)
% Number of atoms : 122 ( 24 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 204 ( 29 ~; 19 |; 1 &; 147 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 72 ( 72 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 3 con; 0-3 aty)
% Number of variables : 82 ( 47 ^; 34 !; 1 ?; 82 :)
% Comments :
%------------------------------------------------------------------------------
thf(mu_type,type,
mu: $tType ).
thf(sk__9_type,type,
sk__9: $i ).
thf(f_type,type,
f: mu > $i > $o ).
thf(rel_s4_type,type,
rel_s4: $i > $i > $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(sk__8_type,type,
sk__8: $i ).
thf(sk__type,type,
sk_: $i > mu ).
thf(mexists_ind_type,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(mimplies_type,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mdia_s4_type,type,
mdia_s4: ( $i > $o ) > $i > $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(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,
! [X0: $i] : ( exists_in_world @ ( sk_ @ X0 ) @ X0 ),
inference(cnf,[status(esa)],[nonempty_ax]) ).
thf(cumulative_ax,axiom,
! [X: mu,V: $i,W: $i] :
( ( ( exists_in_world @ X @ V )
& ( rel_s4 @ V @ W ) )
=> ( exists_in_world @ X @ W ) ) ).
thf(zip_derived_cl3,plain,
! [X0: mu,X1: $i,X2: $i] :
( ~ ( exists_in_world @ X0 @ X1 )
| ~ ( rel_s4 @ X1 @ X2 )
| ( exists_in_world @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[cumulative_ax]) ).
thf(zip_derived_cl25,plain,
! [X0: $i,X1: $i] :
( ( exists_in_world @ ( sk_ @ X0 ) @ X1 )
| ~ ( rel_s4 @ X0 @ X1 ) ),
inference('sup-',[status(thm)],[zip_derived_cl0,zip_derived_cl3]) ).
thf(mdia_s4,axiom,
( mdia_s4
= ( ^ [Phi: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ Phi ) ) ) ) ) ).
thf(mbox_s4,axiom,
( mbox_s4
= ( ^ [Phi: $i > $o,W: $i] :
! [V: $i] :
( ( Phi @ V )
| ~ ( rel_s4 @ W @ V ) ) ) ) ).
thf('0',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('1',plain,
( mbox_s4
= ( ^ [V_1: $i > $o,V_2: $i] :
! [X4: $i] :
( ( V_1 @ X4 )
| ~ ( rel_s4 @ 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_s4
= ( ^ [Phi: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ Phi ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mdia_s4,'1','3']) ).
thf('5',plain,
( mdia_s4
= ( ^ [V_1: $i > $o] : ( mnot @ ( mbox_s4 @ ( 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(mexists_ind,axiom,
( mexists_ind
= ( ^ [Phi: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X: mu] : ( mnot @ ( Phi @ X ) ) ) ) ) ) ).
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('10',plain,
( mexists_ind
= ( ^ [Phi: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X: mu] : ( mnot @ ( Phi @ X ) ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mexists_ind,'9','3']) ).
thf('11',plain,
( mexists_ind
= ( ^ [V_1: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [V_2: mu] : ( mnot @ ( V_1 @ 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('12',plain,
( mor
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
| ( Psi @ W ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mor]) ).
thf('13',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('14',plain,
( mimplies
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ),
inference(simplify_rw_rule,[status(thm)],[mimplies,'13','3']) ).
thf('15',plain,
( mimplies
= ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mor @ ( mnot @ V_1 ) @ V_2 ) ) ),
define([status(thm)]) ).
thf(con,conjecture,
( mvalid
@ ( mimplies
@ ( mdia_s4
@ ( mforall_ind
@ ^ [X: mu] : ( f @ X ) ) )
@ ( mexists_ind
@ ^ [X: mu] : ( mdia_s4 @ ( f @ X ) ) ) ) ) ).
thf(zf_stmt_0,conjecture,
! [X4: $i] :
( ! [X6: $i] :
( ~ ! [X8: mu] :
( ( exists_in_world @ X8 @ X6 )
=> ( f @ X8 @ X6 ) )
| ~ ( rel_s4 @ X4 @ X6 ) )
| ~ ! [X10: mu] :
( ( exists_in_world @ X10 @ X4 )
=> ! [X12: $i] :
( ~ ( f @ X10 @ X12 )
| ~ ( rel_s4 @ X4 @ X12 ) ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ! [X4: $i] :
( ! [X6: $i] :
( ~ ! [X8: mu] :
( ( exists_in_world @ X8 @ X6 )
=> ( f @ X8 @ X6 ) )
| ~ ( rel_s4 @ X4 @ X6 ) )
| ~ ! [X10: mu] :
( ( exists_in_world @ X10 @ X4 )
=> ! [X12: $i] :
( ~ ( f @ X10 @ X12 )
| ~ ( rel_s4 @ X4 @ X12 ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl5,plain,
! [X2: mu] :
( ( f @ X2 @ sk__9 )
| ~ ( exists_in_world @ X2 @ sk__9 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl0_001,plain,
! [X0: $i] : ( exists_in_world @ ( sk_ @ X0 ) @ X0 ),
inference(cnf,[status(esa)],[nonempty_ax]) ).
thf(zip_derived_cl6,plain,
rel_s4 @ sk__8 @ sk__9,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl4,plain,
! [X0: $i,X1: mu] :
( ~ ( rel_s4 @ sk__8 @ X0 )
| ~ ( f @ X1 @ X0 )
| ~ ( exists_in_world @ X1 @ sk__8 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl21,plain,
! [X0: mu] :
( ~ ( exists_in_world @ X0 @ sk__8 )
| ~ ( f @ X0 @ sk__9 ) ),
inference('sup-',[status(thm)],[zip_derived_cl6,zip_derived_cl4]) ).
thf(zip_derived_cl33,plain,
~ ( f @ ( sk_ @ sk__8 ) @ sk__9 ),
inference('sup-',[status(thm)],[zip_derived_cl0,zip_derived_cl21]) ).
thf(zip_derived_cl36,plain,
~ ( exists_in_world @ ( sk_ @ sk__8 ) @ sk__9 ),
inference('sup-',[status(thm)],[zip_derived_cl5,zip_derived_cl33]) ).
thf(zip_derived_cl42,plain,
~ ( rel_s4 @ sk__8 @ sk__9 ),
inference('sup-',[status(thm)],[zip_derived_cl25,zip_derived_cl36]) ).
thf(zip_derived_cl6_002,plain,
rel_s4 @ sk__8 @ sk__9,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl44,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl42,zip_derived_cl6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SYO572^7 : TPTP v8.1.2. Released v5.5.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.xTMOFvOhMG true
% 0.14/0.34 % Computer : n025.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 05:19:52 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
% 0.21/0.65 % Total configuration time : 828
% 0.21/0.65 % Estimated wc time : 1656
% 0.21/0.65 % Estimated cpu time (8 cpus) : 207.0
% 0.21/0.70 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.21/0.73 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.21/0.74 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.21/0.74 % Solved by lams/40_c.s.sh.
% 0.21/0.74 % done 18 iterations in 0.022s
% 0.21/0.74 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 0.21/0.74 % SZS output start Refutation
% See solution above
% 0.21/0.74
% 0.21/0.74
% 0.21/0.74 % Terminating...
% 1.48/0.84 % Runner terminated.
% 1.48/0.86 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------