TSTP Solution File: PHI003^2 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : PHI003^2 : TPTP v8.1.2. Released v6.1.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.ZMoUB8Mt8J true
% Computer : n003.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 Aug 31 12:58:47 EDT 2023
% Result : Theorem 1.46s 0.90s
% Output : Refutation 1.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 34
% Syntax : Number of formulae : 68 ( 26 unt; 14 typ; 0 def)
% Number of atoms : 168 ( 21 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 398 ( 18 ~; 8 |; 16 &; 289 @)
% ( 0 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 136 ( 136 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 13 usr; 5 con; 0-4 aty)
% ( 19 !!; 20 ??; 0 @@+; 0 @@-)
% Number of variables : 144 ( 89 ^; 43 !; 12 ?; 144 :)
% Comments :
%------------------------------------------------------------------------------
thf(mu_type,type,
mu: $tType ).
thf('#sk1_type',type,
'#sk1': $i ).
thf(mdia_type,type,
mdia: ( $i > $o ) > $i > $o ).
thf(mexists_ind_type,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf('#sk2_type',type,
'#sk2': $i > mu > mu > $i > $o ).
thf(rel_type,type,
rel: $i > $i > $o ).
thf(positive_type,type,
positive: ( mu > $i > $o ) > $i > $o ).
thf('#sk70_type',type,
'#sk70': $i > mu ).
thf(mdia_generic_type,type,
mdia_generic: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf('#sk69_type',type,
'#sk69': $i > $i ).
thf(mforall_indset_type,type,
mforall_indset: ( ( mu > $i > $o ) > $i > $o ) > $i > $o ).
thf(mvalid_type,type,
mvalid: ( $i > $o ) > $o ).
thf(god_type,type,
god: mu > $i > $o ).
thf(mimplies_type,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(defD1,axiom,
( god
= ( ^ [X: mu] :
( mforall_indset
@ ^ [Phi: mu > $i > $o] : ( mimplies @ ( positive @ Phi ) @ ( Phi @ X ) ) ) ) ) ).
thf(mforall_indset,axiom,
( mforall_indset
= ( ^ [Phi: ( mu > $i > $o ) > $i > $o,W: $i] :
! [X: mu > $i > $o] : ( Phi @ X @ W ) ) ) ).
thf('0',plain,
( mforall_indset
= ( ^ [Phi: ( mu > $i > $o ) > $i > $o,W: $i] :
! [X: mu > $i > $o] : ( Phi @ X @ W ) ) ),
inference(simplify_rw_rule,[status(thm)],[mforall_indset]) ).
thf('1',plain,
( mforall_indset
= ( ^ [V_1: ( mu > $i > $o ) > $i > $o,V_2: $i] :
! [X4: mu > $i > $o] : ( V_1 @ X4 @ V_2 ) ) ),
define([status(thm)]) ).
thf(mimplies,axiom,
( mimplies
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
=> ( Psi @ W ) ) ) ) ).
thf('2',plain,
( mimplies
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
=> ( Psi @ W ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mimplies]) ).
thf('3',plain,
( mimplies
= ( ^ [V_1: $i > $o,V_2: $i > $o,V_3: $i] :
( ( V_1 @ V_3 )
=> ( V_2 @ V_3 ) ) ) ),
define([status(thm)]) ).
thf('4',plain,
( god
= ( ^ [X: mu] :
( mforall_indset
@ ^ [Phi: mu > $i > $o] : ( mimplies @ ( positive @ Phi ) @ ( Phi @ X ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[defD1,'1','3']) ).
thf('5',plain,
( god
= ( ^ [V_1: mu] :
( mforall_indset
@ ^ [V_2: mu > $i > $o] : ( mimplies @ ( positive @ V_2 ) @ ( V_2 @ 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(mdia,axiom,
( mdia
= ( mdia_generic @ rel ) ) ).
thf(mdia_generic,axiom,
( mdia_generic
= ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
? [V: $i] :
( ( Phi @ V )
& ( R @ W @ V ) ) ) ) ).
thf('8',plain,
( mdia_generic
= ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
? [V: $i] :
( ( Phi @ V )
& ( R @ W @ V ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mdia_generic]) ).
thf('9',plain,
( mdia_generic
= ( ^ [V_1: $i > $i > $o,V_2: $i > $o,V_3: $i] :
? [X4: $i] :
( ( V_2 @ X4 )
& ( V_1 @ V_3 @ X4 ) ) ) ),
define([status(thm)]) ).
thf('10',plain,
( mdia
= ( mdia_generic @ rel ) ),
inference(simplify_rw_rule,[status(thm)],[mdia,'9']) ).
thf('11',plain,
( mdia
= ( mdia_generic @ rel ) ),
define([status(thm)]) ).
thf(mexists_ind,axiom,
( mexists_ind
= ( ^ [Phi: mu > $i > $o,W: $i] :
? [X: mu] : ( Phi @ X @ W ) ) ) ).
thf('12',plain,
( mexists_ind
= ( ^ [Phi: mu > $i > $o,W: $i] :
? [X: mu] : ( Phi @ X @ W ) ) ),
inference(simplify_rw_rule,[status(thm)],[mexists_ind]) ).
thf('13',plain,
( mexists_ind
= ( ^ [V_1: mu > $i > $o,V_2: $i] :
? [X4: mu] : ( V_1 @ X4 @ V_2 ) ) ),
define([status(thm)]) ).
thf(corC,conjecture,
( mvalid
@ ( mdia
@ ( mexists_ind
@ ^ [X: mu] : ( god @ X ) ) ) ) ).
thf(zf_stmt_0,conjecture,
! [X4: $i] :
? [X6: $i] :
( ( rel @ X4 @ X6 )
& ? [X8: mu] :
! [X10: mu > $i > $o] :
( ( positive @ X10 @ X6 )
=> ( X10 @ X8 @ X6 ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ! [X4: $i] :
? [X6: $i] :
( ( rel @ X4 @ X6 )
& ? [X8: mu] :
! [X10: mu > $i > $o] :
( ( positive @ X10 @ X6 )
=> ( X10 @ X8 @ X6 ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl2,plain,
~ ( !!
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
& ( ??
@ ^ [Y2: mu] :
( !!
@ ^ [Y3: mu > $i > $o] :
( ( positive @ Y3 @ Y1 )
=> ( Y3 @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl3,plain,
~ ( ??
@ ^ [Y0: $i] :
( ( rel @ '#sk1' @ Y0 )
& ( ??
@ ^ [Y1: mu] :
( !!
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl4,plain,
! [X2: $i] :
~ ( ( rel @ '#sk1' @ X2 )
& ( ??
@ ^ [Y0: mu] :
( !!
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ X2 )
=> ( Y1 @ Y0 @ X2 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl5,plain,
! [X2: $i] :
( ~ ( rel @ '#sk1' @ X2 )
| ~ ( ??
@ ^ [Y0: mu] :
( !!
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ X2 )
=> ( Y1 @ Y0 @ X2 ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl6,plain,
! [X2: $i,X4: mu] :
( ~ ( !!
@ ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ X2 )
=> ( Y0 @ X4 @ X2 ) ) )
| ~ ( rel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl7,plain,
! [X2: $i,X4: mu] :
( ~ ( ( positive @ ( '#sk2' @ X2 @ X4 ) @ X2 )
=> ( '#sk2' @ X2 @ X4 @ X4 @ X2 ) )
| ~ ( rel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl8,plain,
! [X2: $i,X4: mu] :
( ( positive @ ( '#sk2' @ X2 @ X4 ) @ X2 )
| ~ ( rel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl7]) ).
thf(thmT1,axiom,
( mvalid
@ ( mforall_indset
@ ^ [Phi: mu > $i > $o] :
( mimplies @ ( positive @ Phi )
@ ( mdia
@ ( mexists_ind
@ ^ [X: mu] : ( Phi @ X ) ) ) ) ) ) ).
thf(zf_stmt_2,axiom,
! [X4: $i,X6: mu > $i > $o] :
( ( positive @ X6 @ X4 )
=> ? [X8: $i] :
( ( rel @ X4 @ X8 )
& ? [X10: mu] : ( X6 @ X10 @ X8 ) ) ) ).
thf(zip_derived_cl1,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ Y0 )
=> ( ??
@ ^ [Y2: $i] :
( ( rel @ Y0 @ Y2 )
& ( ??
@ ^ [Y3: mu] : ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_2]) ).
thf(zip_derived_cl15,plain,
! [X2: $i] :
( !!
@ ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ X2 )
=> ( ??
@ ^ [Y1: $i] :
( ( rel @ X2 @ Y1 )
& ( ??
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl16,plain,
! [X2: $i,X4: mu > $i > $o] :
( ( positive @ X4 @ X2 )
=> ( ??
@ ^ [Y0: $i] :
( ( rel @ X2 @ Y0 )
& ( ??
@ ^ [Y1: mu] : ( X4 @ Y1 @ Y0 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl17,plain,
! [X0: $i] :
( ( positive
@ ^ [Y0: mu,Y1: $i] :
( !!
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ X0 )
=> ( ??
@ ^ [Y0: $i] :
( ( rel @ X0 @ Y0 )
& ( ??
@ ^ [Y1: mu] :
( !!
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl16]) ).
thf(axA3,axiom,
mvalid @ ( positive @ god ) ).
thf(zf_stmt_3,axiom,
! [X4: $i] :
( positive
@ ^ [V_1: mu,V_2: $i] :
! [X6: mu > $i > $o] :
( ( positive @ X6 @ V_2 )
=> ( X6 @ V_1 @ V_2 ) )
@ X4 ) ).
thf(zip_derived_cl0,plain,
( !!
@ ^ [Y0: $i] :
( positive
@ ^ [Y1: mu,Y2: $i] :
( !!
@ ^ [Y3: mu > $i > $o] :
( ( positive @ Y3 @ Y2 )
=> ( Y3 @ Y1 @ Y2 ) ) )
@ Y0 ) ),
inference(cnf,[status(esa)],[zf_stmt_3]) ).
thf(zip_derived_cl10,plain,
! [X2: $i] :
( positive
@ ^ [Y0: mu,Y1: $i] :
( !!
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl40,plain,
! [X0: $i] :
( $true
=> ( ??
@ ^ [Y0: $i] :
( ( rel @ X0 @ Y0 )
& ( ??
@ ^ [Y1: mu] :
( !!
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl17,zip_derived_cl10]) ).
thf(zip_derived_cl41,plain,
! [X0: $i] :
( ??
@ ^ [Y0: $i] :
( ( rel @ X0 @ Y0 )
& ( ??
@ ^ [Y1: mu] :
( !!
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl40]) ).
thf(zip_derived_cl42,plain,
! [X0: $i] :
( ( rel @ X0 @ ( '#sk69' @ X0 ) )
& ( ??
@ ^ [Y0: mu] :
( !!
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ ( '#sk69' @ X0 ) )
=> ( Y1 @ Y0 @ ( '#sk69' @ X0 ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl41]) ).
thf(zip_derived_cl44,plain,
! [X0: $i] :
( ??
@ ^ [Y0: mu] :
( !!
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ ( '#sk69' @ X0 ) )
=> ( Y1 @ Y0 @ ( '#sk69' @ X0 ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl42]) ).
thf(zip_derived_cl45,plain,
! [X0: $i] :
( !!
@ ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ ( '#sk69' @ X0 ) )
=> ( Y0 @ ( '#sk70' @ X0 ) @ ( '#sk69' @ X0 ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl46,plain,
! [X0: $i,X2: mu > $i > $o] :
( ( positive @ X2 @ ( '#sk69' @ X0 ) )
=> ( X2 @ ( '#sk70' @ X0 ) @ ( '#sk69' @ X0 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl49,plain,
! [X0: $i,X2: mu > $i > $o] :
( ~ ( positive @ X2 @ ( '#sk69' @ X0 ) )
| ( X2 @ ( '#sk70' @ X0 ) @ ( '#sk69' @ X0 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl46]) ).
thf(zip_derived_cl51,plain,
! [X0: $i,X1: mu] :
( ~ ( rel @ '#sk1' @ ( '#sk69' @ X0 ) )
| ( '#sk2' @ ( '#sk69' @ X0 ) @ X1 @ ( '#sk70' @ X0 ) @ ( '#sk69' @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl8,zip_derived_cl49]) ).
thf(zip_derived_cl9,plain,
! [X2: $i,X4: mu] :
( ~ ( '#sk2' @ X2 @ X4 @ X4 @ X2 )
| ~ ( rel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl75,plain,
! [X0: $i] :
( ~ ( rel @ '#sk1' @ ( '#sk69' @ X0 ) )
| ~ ( rel @ '#sk1' @ ( '#sk69' @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl51,zip_derived_cl9]) ).
thf(zip_derived_cl77,plain,
! [X0: $i] :
~ ( rel @ '#sk1' @ ( '#sk69' @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl75]) ).
thf(zip_derived_cl43,plain,
! [X0: $i] : ( rel @ X0 @ ( '#sk69' @ X0 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl42]) ).
thf(zip_derived_cl79,plain,
$false,
inference('sup+',[status(thm)],[zip_derived_cl77,zip_derived_cl43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.14 % Problem : PHI003^2 : TPTP v8.1.2. Released v6.1.0.
% 0.14/0.15 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.ZMoUB8Mt8J true
% 0.15/0.36 % Computer : n003.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
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Sun Aug 27 09:00:39 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.15/0.37 % Running portfolio for 300 s
% 0.15/0.37 % File : /export/starexec/sandbox/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
% 0.22/0.70 % Total configuration time : 828
% 0.22/0.70 % Estimated wc time : 1656
% 0.22/0.70 % Estimated cpu time (8 cpus) : 207.0
% 0.22/0.73 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.22/0.77 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.22/0.78 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.22/0.78 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.22/0.78 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.22/0.78 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.22/0.78 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.99/0.83 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 0.99/0.83 % /export/starexec/sandbox/solver/bin/lams/35_full_unif.sh running for 56s
% 0.99/0.83 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 1.46/0.90 % Solved by lams/35_full_unif4.sh.
% 1.46/0.90 % done 14 iterations in 0.109s
% 1.46/0.90 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 1.46/0.90 % SZS output start Refutation
% See solution above
% 1.46/0.91
% 1.46/0.91
% 1.46/0.91 % Terminating...
% 1.68/1.01 % Runner terminated.
% 1.68/1.02 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------