TSTP Solution File: SYO433^1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SYO433^1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.jn9DWsSB64 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 : Fri Sep 1 05:51:09 EDT 2023
% Result : Theorem 0.71s 0.84s
% Output : Refutation 0.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 34
% Syntax : Number of formulae : 75 ( 33 unt; 14 typ; 0 def)
% Number of atoms : 250 ( 24 equ; 34 cnn)
% Maximal formula atoms : 22 ( 4 avg)
% Number of connectives : 506 ( 87 ~; 63 |; 9 &; 318 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 70 ( 70 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 14 usr; 5 con; 0-3 aty)
% ( 21 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 112 ( 63 ^; 49 !; 0 ?; 112 :)
% Comments :
%------------------------------------------------------------------------------
thf(q_type,type,
q: $i > $o ).
thf(rel_s4_type,type,
rel_s4: $i > $i > $o ).
thf(mand_type,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mnot_type,type,
mnot: ( $i > $o ) > $i > $o ).
thf('#sk2_type',type,
'#sk2': $i ).
thf(mimplies_type,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf('#sk1_type',type,
'#sk1': $i ).
thf(p_type,type,
p: $i > $o ).
thf(mdia_s4_type,type,
mdia_s4: ( $i > $o ) > $i > $o ).
thf('#sk3_type',type,
'#sk3': $i > $i ).
thf(mtransitive_type,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(mbox_s4_type,type,
mbox_s4: ( $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_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(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(prove,conjecture,
mvalid @ ( mimplies @ ( mand @ ( mdia_s4 @ p ) @ ( mbox_s4 @ q ) ) @ ( mdia_s4 @ ( mand @ p @ ( mbox_s4 @ q ) ) ) ) ).
thf(zf_stmt_0,conjecture,
! [X4: $i] :
( ~ ! [X10: $i] :
( ~ ( rel_s4 @ X4 @ X10 )
| ~ ( p @ X10 )
| ~ ! [X12: $i] :
( ~ ( rel_s4 @ X10 @ X12 )
| ( q @ X12 ) ) )
| ! [X6: $i] :
( ~ ( rel_s4 @ X4 @ X6 )
| ~ ( p @ X6 ) )
| ~ ! [X8: $i] :
( ~ ( rel_s4 @ X4 @ X8 )
| ( q @ X8 ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ! [X4: $i] :
( ~ ! [X10: $i] :
( ~ ( rel_s4 @ X4 @ X10 )
| ~ ( p @ X10 )
| ~ ! [X12: $i] :
( ~ ( rel_s4 @ X10 @ X12 )
| ( q @ X12 ) ) )
| ! [X6: $i] :
( ~ ( rel_s4 @ X4 @ X6 )
| ~ ( p @ X6 ) )
| ~ ! [X8: $i] :
( ~ ( rel_s4 @ X4 @ X8 )
| ( q @ X8 ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl2,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( (~) @ ( p @ Y1 ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( q @ Y2 ) ) ) ) ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( (~) @ ( p @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( q @ Y1 ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl17,plain,
~ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( q @ Y1 ) ) ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk1' @ Y0 ) )
| ( q @ Y0 ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl19,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl22,plain,
~ ( ( (~) @ ( rel_s4 @ '#sk1' @ '#sk2' ) )
| ( (~) @ ( p @ '#sk2' ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl26,plain,
p @ '#sk2',
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl18,plain,
( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( q @ Y1 ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl21,plain,
! [X2: $i] :
( ( (~) @ ( rel_s4 @ '#sk1' @ X2 ) )
| ( (~) @ ( p @ X2 ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X2 @ Y0 ) )
| ( q @ Y0 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl24,plain,
! [X2: $i] :
( ~ ( rel_s4 @ '#sk1' @ X2 )
| ~ ( p @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X2 @ Y0 ) )
| ( q @ Y0 ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl28,plain,
! [X2: $i] :
( ~ ( ( (~) @ ( rel_s4 @ X2 @ ( '#sk3' @ X2 ) ) )
| ( q @ ( '#sk3' @ X2 ) ) )
| ~ ( p @ X2 )
| ~ ( rel_s4 @ '#sk1' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl30,plain,
! [X2: $i] :
( ~ ( q @ ( '#sk3' @ X2 ) )
| ~ ( rel_s4 @ '#sk1' @ X2 )
| ~ ( p @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl20,plain,
( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk1' @ Y0 ) )
| ( q @ Y0 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl23,plain,
! [X2: $i] :
( ( (~) @ ( rel_s4 @ '#sk1' @ X2 ) )
| ( q @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl27,plain,
! [X2: $i] :
( ~ ( rel_s4 @ '#sk1' @ X2 )
| ( q @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl35,plain,
! [X0: $i] :
( ~ ( p @ X0 )
| ~ ( rel_s4 @ '#sk1' @ X0 )
| ~ ( rel_s4 @ '#sk1' @ ( '#sk3' @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl30,zip_derived_cl27]) ).
thf(zip_derived_cl40,plain,
( ~ ( rel_s4 @ '#sk1' @ ( '#sk3' @ '#sk2' ) )
| ~ ( rel_s4 @ '#sk1' @ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl26,zip_derived_cl35]) ).
thf(zip_derived_cl25,plain,
rel_s4 @ '#sk1' @ '#sk2',
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl43,plain,
~ ( rel_s4 @ '#sk1' @ ( '#sk3' @ '#sk2' ) ),
inference(demod,[status(thm)],[zip_derived_cl40,zip_derived_cl25]) ).
thf(zip_derived_cl26_001,plain,
p @ '#sk2',
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl29,plain,
! [X2: $i] :
( ( rel_s4 @ X2 @ ( '#sk3' @ X2 ) )
| ~ ( rel_s4 @ '#sk1' @ X2 )
| ~ ( p @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl47,plain,
( ~ ( rel_s4 @ '#sk1' @ '#sk2' )
| ( rel_s4 @ '#sk2' @ ( '#sk3' @ '#sk2' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl26,zip_derived_cl29]) ).
thf(zip_derived_cl25_002,plain,
rel_s4 @ '#sk1' @ '#sk2',
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl49,plain,
rel_s4 @ '#sk2' @ ( '#sk3' @ '#sk2' ),
inference(demod,[status(thm)],[zip_derived_cl47,zip_derived_cl25]) ).
thf(mtransitive,axiom,
( mtransitive
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ T @ U ) )
=> ( R @ S @ U ) ) ) ) ).
thf('14',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('15',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_2,axiom,
! [X4: $i,X6: $i,X8: $i] :
( ( ( rel_s4 @ X6 @ X8 )
& ( rel_s4 @ X4 @ X6 ) )
=> ( rel_s4 @ X4 @ X8 ) ) ).
thf(zip_derived_cl1,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_2]) ).
thf(zip_derived_cl4,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( ( rel_s4 @ Y0 @ Y1 )
& ( rel_s4 @ X2 @ Y0 ) )
=> ( rel_s4 @ X2 @ Y1 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl5,plain,
! [X2: $i,X4: $i] :
( !!
@ ^ [Y0: $i] :
( ( ( rel_s4 @ X4 @ Y0 )
& ( rel_s4 @ X2 @ X4 ) )
=> ( rel_s4 @ X2 @ Y0 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl6,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( rel_s4 @ X4 @ X6 )
& ( rel_s4 @ X2 @ X4 ) )
=> ( rel_s4 @ X2 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl7,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( ( rel_s4 @ X4 @ X6 )
& ( rel_s4 @ X2 @ X4 ) )
| ( rel_s4 @ X2 @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl8,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( rel_s4 @ X4 @ X6 )
| ~ ( rel_s4 @ X2 @ X4 )
| ( rel_s4 @ X2 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl51,plain,
! [X0: $i] :
( ( rel_s4 @ X0 @ ( '#sk3' @ '#sk2' ) )
| ~ ( rel_s4 @ X0 @ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl49,zip_derived_cl8]) ).
thf(zip_derived_cl55,plain,
~ ( rel_s4 @ '#sk1' @ '#sk2' ),
inference('sup+',[status(thm)],[zip_derived_cl43,zip_derived_cl51]) ).
thf(zip_derived_cl25_003,plain,
rel_s4 @ '#sk1' @ '#sk2',
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl59,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl55,zip_derived_cl25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SYO433^1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.jn9DWsSB64 true
% 0.15/0.36 % Computer : n027.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sat Aug 26 06:04:19 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.15/0.37 % Running portfolio for 300 s
% 0.15/0.37 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.37 % Number of cores: 8
% 0.15/0.37 % Python version: Python 3.6.8
% 0.15/0.37 % Running in HO mode
% 0.23/0.65 % Total configuration time : 828
% 0.23/0.65 % Estimated wc time : 1656
% 0.23/0.65 % Estimated cpu time (8 cpus) : 207.0
% 0.23/0.77 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.23/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.23/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.23/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.23/0.78 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.23/0.79 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.23/0.79 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.71/0.84 % Solved by lams/35_full_unif4.sh.
% 0.71/0.84 % done 18 iterations in 0.028s
% 0.71/0.84 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 0.71/0.84 % SZS output start Refutation
% See solution above
% 0.71/0.84
% 0.71/0.84
% 0.71/0.84 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.71/0.84 % Terminating...
% 0.71/0.87 % Runner terminated.
% 0.71/0.88 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------