TSTP Solution File: PHI005^4 by Zipperpin---2.1.9999
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%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : PHI005^4 : TPTP v8.1.2. Released v6.4.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.Rj0tvYFgdU true
% Computer : n004.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 12:58:49 EDT 2023
% Result : Theorem 59.01s 8.27s
% Output : Refutation 59.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 30
% Syntax : Number of formulae : 103 ( 27 unt; 13 typ; 0 def)
% Number of atoms : 346 ( 21 equ; 39 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 973 ( 75 ~; 28 |; 18 &; 691 @)
% ( 0 <=>; 70 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 8 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 212 ( 212 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 11 usr; 6 con; 0-3 aty)
% ( 85 !!; 6 ??; 0 @@+; 0 @@-)
% Number of variables : 330 ( 164 ^; 163 !; 3 ?; 330 :)
% Comments :
%------------------------------------------------------------------------------
thf(qML_i_type,type,
qML_i: $tType ).
thf(qML_mu_type,type,
qML_mu: $tType ).
thf('#l_lift20063_type',type,
'#l_lift20063': qML_mu > qML_i > $o ).
thf(scott_P_type,type,
scott_P: ( qML_mu > qML_i > $o ) > qML_i > $o ).
thf('#sk103_type',type,
'#sk103': ( qML_mu > qML_i > $o ) > ( qML_mu > qML_i > $o ) > qML_i ).
thf('#l_lift20060_type',type,
'#l_lift20060': ( qML_mu > qML_i > $o ) > qML_mu > qML_i > $o ).
thf('#sk316_type',type,
'#sk316': ( qML_mu > qML_i > $o ) > ( qML_mu > qML_i > $o ) > qML_mu ).
thf('#sk118_type',type,
'#sk118': ( qML_mu > qML_i > $o ) > ( qML_mu > qML_i > $o ) > qML_mu ).
thf(scott_G_type,type,
scott_G: qML_mu > qML_i > $o ).
thf('#sk46_type',type,
'#sk46': qML_i ).
thf(scott_ess_QML_mu_type,type,
scott_ess_QML_mu: ( qML_mu > qML_i > $o ) > qML_mu > qML_i > $o ).
thf(scott_NE_QML_mu_type,type,
scott_NE_QML_mu: qML_mu > qML_i > $o ).
thf('#sk301_type',type,
'#sk301': ( qML_mu > qML_i > $o ) > ( qML_mu > qML_i > $o ) > qML_i ).
thf(fact_0_G__def,axiom,
( scott_G
= ( ^ [X: qML_mu,W: qML_i] :
! [Y: qML_mu > qML_i > $o] :
( ( scott_P @ Y @ W )
=> ( Y @ X @ W ) ) ) ) ).
thf(zip_derived_cl0,plain,
( scott_G
= ( ^ [Y0: qML_mu,Y1: qML_i] :
( !!
@ ^ [Y2: qML_mu > qML_i > $o] :
( ( scott_P @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ),
inference(cnf,[status(esa)],[fact_0_G__def]) ).
thf(zip_derived_cl18,plain,
! [X2: qML_mu,X3: qML_i] :
( ( scott_G @ X2 @ X3 )
= ( ^ [Y0: qML_mu,Y1: qML_i] :
( !!
@ ^ [Y2: qML_mu > qML_i > $o] :
( ( scott_P @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ X2
@ X3 ) ),
inference(arg_cong_simpl,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl19,plain,
! [X2: qML_mu,X3: qML_i] :
( ( scott_G @ X2 @ X3 )
= ( !!
@ ^ [Y0: qML_mu > qML_i > $o] :
( ( scott_P @ Y0 @ X3 )
=> ( Y0 @ X2 @ X3 ) ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl18]) ).
thf(fact_6_ess__def,axiom,
( scott_ess_QML_mu
= ( ^ [Phi: qML_mu > qML_i > $o,X: qML_mu,W: qML_i] :
( ! [Y: qML_mu > qML_i > $o] :
( ( Y @ X @ W )
=> ! [V2: qML_i,Z: qML_mu] :
( ( Phi @ Z @ V2 )
=> ( Y @ Z @ V2 ) ) )
& ( Phi @ X @ W ) ) ) ) ).
thf(zip_derived_cl6,plain,
( scott_ess_QML_mu
= ( ^ [Y0: qML_mu > qML_i > $o,Y1: qML_mu,Y2: qML_i] :
( ( !!
@ ^ [Y3: qML_mu > qML_i > $o] :
( ( Y3 @ Y1 @ Y2 )
=> ( !!
@ ^ [Y4: qML_i] :
( !!
@ ^ [Y5: qML_mu] :
( ( Y0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
& ( Y0 @ Y1 @ Y2 ) ) ) ),
inference(cnf,[status(esa)],[fact_6_ess__def]) ).
thf(zip_derived_cl62,plain,
! [X2: qML_mu > qML_i > $o,X3: qML_mu,X4: qML_i] :
( ( scott_ess_QML_mu @ X2 @ X3 @ X4 )
= ( ^ [Y0: qML_mu > qML_i > $o,Y1: qML_mu,Y2: qML_i] :
( ( !!
@ ^ [Y3: qML_mu > qML_i > $o] :
( ( Y3 @ Y1 @ Y2 )
=> ( !!
@ ^ [Y4: qML_i] :
( !!
@ ^ [Y5: qML_mu] :
( ( Y0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
& ( Y0 @ Y1 @ Y2 ) )
@ X2
@ X3
@ X4 ) ),
inference(arg_cong_simpl,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl63,plain,
! [X2: qML_mu > qML_i > $o,X3: qML_mu,X4: qML_i] :
( ( scott_ess_QML_mu @ X2 @ X3 @ X4 )
= ( ( !!
@ ^ [Y0: qML_mu > qML_i > $o] :
( ( Y0 @ X3 @ X4 )
=> ( !!
@ ^ [Y1: qML_i] :
( !!
@ ^ [Y2: qML_mu] :
( ( X2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( X2 @ X3 @ X4 ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl62]) ).
thf(fact_3_A1b,axiom,
! [W2: qML_i,X2: qML_mu > qML_i > $o] :
( ~ ( scott_P @ X2 @ W2 )
=> ( scott_P
@ ^ [Y: qML_mu,Z: qML_i] :
~ ( X2 @ Y @ Z )
@ W2 ) ) ).
thf(zip_derived_cl3,plain,
( !!
@ ^ [Y0: qML_i] :
( !!
@ ^ [Y1: qML_mu > qML_i > $o] :
( ( (~) @ ( scott_P @ Y1 @ Y0 ) )
=> ( scott_P
@ ^ [Y2: qML_mu,Y3: qML_i] : ( (~) @ ( Y1 @ Y2 @ Y3 ) )
@ Y0 ) ) ) ),
inference(cnf,[status(esa)],[fact_3_A1b]) ).
thf(zip_derived_cl22,plain,
! [X2: qML_i] :
( !!
@ ^ [Y0: qML_mu > qML_i > $o] :
( ( (~) @ ( scott_P @ Y0 @ X2 ) )
=> ( scott_P
@ ^ [Y1: qML_mu,Y2: qML_i] : ( (~) @ ( Y0 @ Y1 @ Y2 ) )
@ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl23,plain,
! [X2: qML_i,X4: qML_mu > qML_i > $o] :
( ( (~) @ ( scott_P @ X4 @ X2 ) )
=> ( scott_P
@ ^ [Y0: qML_mu,Y1: qML_i] : ( (~) @ ( X4 @ Y0 @ Y1 ) )
@ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl26,plain,
! [X2: qML_i,X4: qML_mu > qML_i > $o] :
( ( scott_P @ X4 @ X2 )
| ( scott_P
@ ^ [Y0: qML_mu,Y1: qML_i] : ( (~) @ ( X4 @ Y0 @ Y1 ) )
@ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl23]) ).
thf(fact_2_A4,axiom,
! [W2: qML_i,X2: qML_mu > qML_i > $o] :
( ( scott_P @ X2 @ W2 )
=> ! [X_1: qML_i] : ( scott_P @ X2 @ X_1 ) ) ).
thf(zip_derived_cl2,plain,
( !!
@ ^ [Y0: qML_i] :
( !!
@ ^ [Y1: qML_mu > qML_i > $o] :
( ( scott_P @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: qML_i] : ( scott_P @ Y1 @ Y2 ) ) ) ) ),
inference(cnf,[status(esa)],[fact_2_A4]) ).
thf(zip_derived_cl12,plain,
! [X2: qML_i] :
( !!
@ ^ [Y0: qML_mu > qML_i > $o] :
( ( scott_P @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: qML_i] : ( scott_P @ Y0 @ Y1 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl13,plain,
! [X2: qML_i,X4: qML_mu > qML_i > $o] :
( ( scott_P @ X4 @ X2 )
=> ( !!
@ ^ [Y0: qML_i] : ( scott_P @ X4 @ Y0 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl16,plain,
! [X2: qML_i,X4: qML_mu > qML_i > $o] :
( ~ ( scott_P @ X4 @ X2 )
| ( !!
@ ^ [Y0: qML_i] : ( scott_P @ X4 @ Y0 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl17,plain,
! [X2: qML_i,X4: qML_mu > qML_i > $o,X6: qML_i] :
( ( scott_P @ X4 @ X6 )
| ~ ( scott_P @ X4 @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl203,plain,
! [X0: qML_i,X1: qML_mu > qML_i > $o,X2: qML_i] :
( ( scott_P
@ ^ [Y0: qML_mu,Y1: qML_i] : ( (~) @ ( X1 @ Y0 @ Y1 ) )
@ X0 )
| ( scott_P @ X1 @ X2 ) ),
inference('sup-',[status(thm)],[zip_derived_cl26,zip_derived_cl17]) ).
thf(zip_derived_cl26_001,plain,
! [X2: qML_i,X4: qML_mu > qML_i > $o] :
( ( scott_P @ X4 @ X2 )
| ( scott_P
@ ^ [Y0: qML_mu,Y1: qML_i] : ( (~) @ ( X4 @ Y0 @ Y1 ) )
@ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl5834,plain,
! [X4: qML_mu > qML_i > $o,X5: qML_mu,X6: qML_i] :
( ( '#l_lift20060' @ X4 @ X5 @ X6 )
= ( (~) @ ( X4 @ X5 @ X6 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl5862,plain,
! [X0: qML_i,X1: qML_mu > qML_i > $o,X2: qML_i] :
( ( scott_P @ ( '#l_lift20060' @ X1 ) @ X0 )
| ( scott_P @ X1 @ X2 ) ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl203,zip_derived_cl5834]) ).
thf(zip_derived_cl19_002,plain,
! [X2: qML_mu,X3: qML_i] :
( ( scott_G @ X2 @ X3 )
= ( !!
@ ^ [Y0: qML_mu > qML_i > $o] :
( ( scott_P @ Y0 @ X3 )
=> ( Y0 @ X2 @ X3 ) ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl199,plain,
! [X2: qML_mu,X3: qML_i] :
( ~ ( scott_G @ X2 @ X3 )
| ( !!
@ ^ [Y0: qML_mu > qML_i > $o] :
( ( scott_P @ Y0 @ X3 )
=> ( Y0 @ X2 @ X3 ) ) ) ),
inference(eq_elim,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl209,plain,
! [X2: qML_mu,X3: qML_i,X5: qML_mu > qML_i > $o] :
( ( ( scott_P @ X5 @ X3 )
=> ( X5 @ X2 @ X3 ) )
| ~ ( scott_G @ X2 @ X3 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl199]) ).
thf(zip_derived_cl210,plain,
! [X0: qML_mu > qML_i > $o,X1: qML_i,X2: qML_mu] :
( ( ( scott_P
@ ^ [Y0: qML_mu,Y1: qML_i] : ( (~) @ ( X0 @ Y0 @ Y1 ) )
@ X1 )
=> ( (~) @ ( X0 @ X2 @ X1 ) ) )
| ~ ( scott_G @ X2 @ X1 ) ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl209]) ).
thf(zip_derived_cl3218,plain,
! [X0: qML_mu > qML_i > $o,X1: qML_i,X2: qML_mu] :
( ~ ( scott_P
@ ^ [Y0: qML_mu,Y1: qML_i] : ( (~) @ ( X0 @ Y0 @ Y1 ) )
@ X1 )
| ~ ( X0 @ X2 @ X1 )
| ~ ( scott_G @ X2 @ X1 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl210]) ).
thf(zip_derived_cl5834_003,plain,
! [X4: qML_mu > qML_i > $o,X5: qML_mu,X6: qML_i] :
( ( '#l_lift20060' @ X4 @ X5 @ X6 )
= ( (~) @ ( X4 @ X5 @ X6 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl5864,plain,
! [X0: qML_mu > qML_i > $o,X1: qML_i,X2: qML_mu] :
( ~ ( scott_P @ ( '#l_lift20060' @ X0 ) @ X1 )
| ~ ( X0 @ X2 @ X1 )
| ~ ( scott_G @ X2 @ X1 ) ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl3218,zip_derived_cl5834]) ).
thf(fact_4_A2,axiom,
! [W2: qML_i,X2: qML_mu > qML_i > $o,Xa: qML_mu > qML_i > $o] :
( ( ! [V: qML_i,Xb: qML_mu] :
( ( X2 @ Xb @ V )
=> ( Xa @ Xb @ V ) )
& ( scott_P @ X2 @ W2 ) )
=> ( scott_P @ Xa @ W2 ) ) ).
thf(zip_derived_cl4,plain,
( !!
@ ^ [Y0: qML_i] :
( !!
@ ^ [Y1: qML_mu > qML_i > $o] :
( !!
@ ^ [Y2: qML_mu > qML_i > $o] :
( ( ( !!
@ ^ [Y3: qML_i] :
( !!
@ ^ [Y4: qML_mu] :
( ( Y1 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( scott_P @ Y1 @ Y0 ) )
=> ( scott_P @ Y2 @ Y0 ) ) ) ) ),
inference(cnf,[status(esa)],[fact_4_A2]) ).
thf(zip_derived_cl64,plain,
! [X2: qML_i] :
( !!
@ ^ [Y0: qML_mu > qML_i > $o] :
( !!
@ ^ [Y1: qML_mu > qML_i > $o] :
( ( ( !!
@ ^ [Y2: qML_i] :
( !!
@ ^ [Y3: qML_mu] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( scott_P @ Y0 @ X2 ) )
=> ( scott_P @ Y1 @ X2 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl65,plain,
! [X2: qML_i,X4: qML_mu > qML_i > $o] :
( !!
@ ^ [Y0: qML_mu > qML_i > $o] :
( ( ( !!
@ ^ [Y1: qML_i] :
( !!
@ ^ [Y2: qML_mu] :
( ( X4 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( scott_P @ X4 @ X2 ) )
=> ( scott_P @ Y0 @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl64]) ).
thf(zip_derived_cl67,plain,
! [X0: qML_i] :
( !!
@ ^ [Y0: qML_mu > qML_i > $o] :
( ( ( !!
@ ^ [Y1: qML_i] :
( !!
@ ^ [Y2: qML_mu] :
( ( scott_NE_QML_mu @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( scott_P @ scott_NE_QML_mu @ X0 ) )
=> ( scott_P @ Y0 @ X0 ) ) ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl65]) ).
thf(zip_derived_cl83,plain,
! [X0: qML_i,X2: qML_mu > qML_i > $o] :
( ( ( !!
@ ^ [Y0: qML_i] :
( !!
@ ^ [Y1: qML_mu] :
( ( scott_NE_QML_mu @ Y1 @ Y0 )
=> ( X2 @ Y1 @ Y0 ) ) ) )
& ( scott_P @ scott_NE_QML_mu @ X0 ) )
=> ( scott_P @ X2 @ X0 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl67]) ).
thf(zip_derived_cl84,plain,
! [X0: qML_i,X1: qML_mu > qML_i > $o] :
( ( ( !!
@ ^ [Y0: qML_i] :
( !!
@ ^ [Y1: qML_mu] :
( ( scott_NE_QML_mu @ Y1 @ Y0 )
=> ( (~) @ ( X1 @ Y1 @ Y0 ) ) ) ) )
& ( scott_P @ scott_NE_QML_mu @ X0 ) )
=> ( scott_P
@ ^ [Y0: qML_mu,Y1: qML_i] : ( (~) @ ( X1 @ Y0 @ Y1 ) )
@ X0 ) ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl83]) ).
thf(fact_5_A5,axiom,
! [X_1: qML_i] : ( scott_P @ scott_NE_QML_mu @ X_1 ) ).
thf(zip_derived_cl5,plain,
( !!
@ ^ [Y0: qML_i] : ( scott_P @ scott_NE_QML_mu @ Y0 ) ),
inference(cnf,[status(esa)],[fact_5_A5]) ).
thf(zip_derived_cl11,plain,
! [X2: qML_i] : ( scott_P @ scott_NE_QML_mu @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl117,plain,
! [X0: qML_i,X1: qML_mu > qML_i > $o] :
( ( ( !!
@ ^ [Y0: qML_i] :
( !!
@ ^ [Y1: qML_mu] :
( ( scott_NE_QML_mu @ Y1 @ Y0 )
=> ( (~) @ ( X1 @ Y1 @ Y0 ) ) ) ) )
& $true )
=> ( scott_P
@ ^ [Y0: qML_mu,Y1: qML_i] : ( (~) @ ( X1 @ Y0 @ Y1 ) )
@ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl84,zip_derived_cl11]) ).
thf(zip_derived_cl118,plain,
! [X0: qML_i,X1: qML_mu > qML_i > $o] :
( ( !!
@ ^ [Y0: qML_i] :
( !!
@ ^ [Y1: qML_mu] :
( ( scott_NE_QML_mu @ Y1 @ Y0 )
=> ( (~) @ ( X1 @ Y1 @ Y0 ) ) ) ) )
=> ( scott_P
@ ^ [Y0: qML_mu,Y1: qML_i] : ( (~) @ ( X1 @ Y0 @ Y1 ) )
@ X0 ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl117]) ).
thf(zip_derived_cl119,plain,
! [X0: qML_i,X1: qML_mu > qML_i > $o] :
( ~ ( !!
@ ^ [Y0: qML_i] :
( !!
@ ^ [Y1: qML_mu] :
( ( scott_NE_QML_mu @ Y1 @ Y0 )
=> ( (~) @ ( X1 @ Y1 @ Y0 ) ) ) ) )
| ( scott_P
@ ^ [Y0: qML_mu,Y1: qML_i] : ( (~) @ ( X1 @ Y0 @ Y1 ) )
@ X0 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl118]) ).
thf(zip_derived_cl120,plain,
! [X0: qML_i,X1: qML_mu > qML_i > $o] :
( ~ ( !!
@ ^ [Y0: qML_mu] :
( ( scott_NE_QML_mu @ Y0 @ ( '#sk301' @ X1 @ scott_NE_QML_mu ) )
=> ( (~) @ ( X1 @ Y0 @ ( '#sk301' @ X1 @ scott_NE_QML_mu ) ) ) ) )
| ( scott_P
@ ^ [Y0: qML_mu,Y1: qML_i] : ( (~) @ ( X1 @ Y0 @ Y1 ) )
@ X0 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl119]) ).
thf(zip_derived_cl121,plain,
! [X0: qML_i,X1: qML_mu > qML_i > $o] :
( ~ ( ( scott_NE_QML_mu @ ( '#sk316' @ X1 @ scott_NE_QML_mu ) @ ( '#sk301' @ X1 @ scott_NE_QML_mu ) )
=> ( (~) @ ( X1 @ ( '#sk316' @ X1 @ scott_NE_QML_mu ) @ ( '#sk301' @ X1 @ scott_NE_QML_mu ) ) ) )
| ( scott_P
@ ^ [Y0: qML_mu,Y1: qML_i] : ( (~) @ ( X1 @ Y0 @ Y1 ) )
@ X0 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl120]) ).
thf(zip_derived_cl122,plain,
! [X0: qML_i,X1: qML_mu > qML_i > $o] :
( ( scott_NE_QML_mu @ ( '#sk316' @ X1 @ scott_NE_QML_mu ) @ ( '#sk301' @ X1 @ scott_NE_QML_mu ) )
| ( scott_P
@ ^ [Y0: qML_mu,Y1: qML_i] : ( (~) @ ( X1 @ Y0 @ Y1 ) )
@ X0 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl121]) ).
thf(zip_derived_cl5834_004,plain,
! [X4: qML_mu > qML_i > $o,X5: qML_mu,X6: qML_i] :
( ( '#l_lift20060' @ X4 @ X5 @ X6 )
= ( (~) @ ( X4 @ X5 @ X6 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl5842,plain,
! [X0: qML_i,X1: qML_mu > qML_i > $o] :
( ( scott_NE_QML_mu @ ( '#sk316' @ X1 @ scott_NE_QML_mu ) @ ( '#sk301' @ X1 @ scott_NE_QML_mu ) )
| ( scott_P @ ( '#l_lift20060' @ X1 ) @ X0 ) ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl122,zip_derived_cl5834]) ).
thf(zip_derived_cl123,plain,
! [X0: qML_i,X1: qML_mu > qML_i > $o] :
( ( X1 @ ( '#sk316' @ X1 @ scott_NE_QML_mu ) @ ( '#sk301' @ X1 @ scott_NE_QML_mu ) )
| ( scott_P
@ ^ [Y0: qML_mu,Y1: qML_i] : ( (~) @ ( X1 @ Y0 @ Y1 ) )
@ X0 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl121]) ).
thf(zip_derived_cl5834_005,plain,
! [X4: qML_mu > qML_i > $o,X5: qML_mu,X6: qML_i] :
( ( '#l_lift20060' @ X4 @ X5 @ X6 )
= ( (~) @ ( X4 @ X5 @ X6 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl5843,plain,
! [X0: qML_i,X1: qML_mu > qML_i > $o] :
( ( X1 @ ( '#sk316' @ X1 @ scott_NE_QML_mu ) @ ( '#sk301' @ X1 @ scott_NE_QML_mu ) )
| ( scott_P @ ( '#l_lift20060' @ X1 ) @ X0 ) ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl123,zip_derived_cl5834]) ).
thf(fact_8_NE__def,axiom,
( scott_NE_QML_mu
= ( ^ [X: qML_mu,W: qML_i] :
! [Y: qML_mu > qML_i > $o] :
( ( scott_ess_QML_mu @ Y @ X @ W )
=> ! [V2: qML_i] :
? [Z: qML_mu] : ( Y @ Z @ V2 ) ) ) ) ).
thf(zip_derived_cl8,plain,
( scott_NE_QML_mu
= ( ^ [Y0: qML_mu,Y1: qML_i] :
( !!
@ ^ [Y2: qML_mu > qML_i > $o] :
( ( scott_ess_QML_mu @ Y2 @ Y0 @ Y1 )
=> ( !!
@ ^ [Y3: qML_i] :
( ??
@ ^ [Y4: qML_mu] : ( Y2 @ Y4 @ Y3 ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[fact_8_NE__def]) ).
thf(zip_derived_cl20,plain,
! [X2: qML_mu,X3: qML_i] :
( ( scott_NE_QML_mu @ X2 @ X3 )
= ( ^ [Y0: qML_mu,Y1: qML_i] :
( !!
@ ^ [Y2: qML_mu > qML_i > $o] :
( ( scott_ess_QML_mu @ Y2 @ Y0 @ Y1 )
=> ( !!
@ ^ [Y3: qML_i] :
( ??
@ ^ [Y4: qML_mu] : ( Y2 @ Y4 @ Y3 ) ) ) ) )
@ X2
@ X3 ) ),
inference(arg_cong_simpl,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl21,plain,
! [X2: qML_mu,X3: qML_i] :
( ( scott_NE_QML_mu @ X2 @ X3 )
= ( !!
@ ^ [Y0: qML_mu > qML_i > $o] :
( ( scott_ess_QML_mu @ Y0 @ X2 @ X3 )
=> ( !!
@ ^ [Y1: qML_i] :
( ??
@ ^ [Y2: qML_mu] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl20]) ).
thf(fact_1_A3,axiom,
! [X_1: qML_i] : ( scott_P @ scott_G @ X_1 ) ).
thf(zip_derived_cl1,plain,
( !!
@ ^ [Y0: qML_i] : ( scott_P @ scott_G @ Y0 ) ),
inference(cnf,[status(esa)],[fact_1_A3]) ).
thf(zip_derived_cl10,plain,
! [X2: qML_i] : ( scott_P @ scott_G @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl65_006,plain,
! [X2: qML_i,X4: qML_mu > qML_i > $o] :
( !!
@ ^ [Y0: qML_mu > qML_i > $o] :
( ( ( !!
@ ^ [Y1: qML_i] :
( !!
@ ^ [Y2: qML_mu] :
( ( X4 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( scott_P @ X4 @ X2 ) )
=> ( scott_P @ Y0 @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl64]) ).
thf(zip_derived_cl68,plain,
! [X0: qML_i] :
( !!
@ ^ [Y0: qML_mu > qML_i > $o] :
( ( ( !!
@ ^ [Y1: qML_i] :
( !!
@ ^ [Y2: qML_mu] :
( ( scott_G @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( scott_P @ scott_G @ X0 ) )
=> ( scott_P @ Y0 @ X0 ) ) ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl65]) ).
thf(zip_derived_cl97,plain,
! [X0: qML_i,X2: qML_mu > qML_i > $o] :
( ( ( !!
@ ^ [Y0: qML_i] :
( !!
@ ^ [Y1: qML_mu] :
( ( scott_G @ Y1 @ Y0 )
=> ( X2 @ Y1 @ Y0 ) ) ) )
& ( scott_P @ scott_G @ X0 ) )
=> ( scott_P @ X2 @ X0 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl68]) ).
thf(zip_derived_cl10_007,plain,
! [X2: qML_i] : ( scott_P @ scott_G @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl101,plain,
! [X0: qML_i,X2: qML_mu > qML_i > $o] :
( ( ( !!
@ ^ [Y0: qML_i] :
( !!
@ ^ [Y1: qML_mu] :
( ( scott_G @ Y1 @ Y0 )
=> ( X2 @ Y1 @ Y0 ) ) ) )
& $true )
=> ( scott_P @ X2 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl97,zip_derived_cl10]) ).
thf(zip_derived_cl102,plain,
! [X0: qML_i,X2: qML_mu > qML_i > $o] :
( ( !!
@ ^ [Y0: qML_i] :
( !!
@ ^ [Y1: qML_mu] :
( ( scott_G @ Y1 @ Y0 )
=> ( X2 @ Y1 @ Y0 ) ) ) )
=> ( scott_P @ X2 @ X0 ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl101]) ).
thf(zip_derived_cl103,plain,
! [X0: qML_i,X2: qML_mu > qML_i > $o] :
( ~ ( !!
@ ^ [Y0: qML_i] :
( !!
@ ^ [Y1: qML_mu] :
( ( scott_G @ Y1 @ Y0 )
=> ( X2 @ Y1 @ Y0 ) ) ) )
| ( scott_P @ X2 @ X0 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl102]) ).
thf(zip_derived_cl104,plain,
! [X0: qML_i,X2: qML_mu > qML_i > $o] :
( ~ ( !!
@ ^ [Y0: qML_mu] :
( ( scott_G @ Y0 @ ( '#sk103' @ scott_G @ X2 ) )
=> ( X2 @ Y0 @ ( '#sk103' @ scott_G @ X2 ) ) ) )
| ( scott_P @ X2 @ X0 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl103]) ).
thf(zip_derived_cl105,plain,
! [X0: qML_i,X2: qML_mu > qML_i > $o] :
( ~ ( ( scott_G @ ( '#sk118' @ scott_G @ X2 ) @ ( '#sk103' @ scott_G @ X2 ) )
=> ( X2 @ ( '#sk118' @ scott_G @ X2 ) @ ( '#sk103' @ scott_G @ X2 ) ) )
| ( scott_P @ X2 @ X0 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl104]) ).
thf(zip_derived_cl107,plain,
! [X0: qML_i,X2: qML_mu > qML_i > $o] :
( ~ ( X2 @ ( '#sk118' @ scott_G @ X2 ) @ ( '#sk103' @ scott_G @ X2 ) )
| ( scott_P @ X2 @ X0 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl105]) ).
thf(fact_7_A1a,axiom,
! [W2: qML_i,X2: qML_mu > qML_i > $o] :
( ( scott_P
@ ^ [Y: qML_mu,Z: qML_i] :
~ ( X2 @ Y @ Z )
@ W2 )
=> ~ ( scott_P @ X2 @ W2 ) ) ).
thf(zip_derived_cl7,plain,
( !!
@ ^ [Y0: qML_i] :
( !!
@ ^ [Y1: qML_mu > qML_i > $o] :
( ( scott_P
@ ^ [Y2: qML_mu,Y3: qML_i] : ( (~) @ ( Y1 @ Y2 @ Y3 ) )
@ Y0 )
=> ( (~) @ ( scott_P @ Y1 @ Y0 ) ) ) ) ),
inference(cnf,[status(esa)],[fact_7_A1a]) ).
thf(zip_derived_cl47,plain,
! [X2: qML_i] :
( !!
@ ^ [Y0: qML_mu > qML_i > $o] :
( ( scott_P
@ ^ [Y1: qML_mu,Y2: qML_i] : ( (~) @ ( Y0 @ Y1 @ Y2 ) )
@ X2 )
=> ( (~) @ ( scott_P @ Y0 @ X2 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl48,plain,
! [X2: qML_i,X4: qML_mu > qML_i > $o] :
( ( scott_P
@ ^ [Y0: qML_mu,Y1: qML_i] : ( (~) @ ( X4 @ Y0 @ Y1 ) )
@ X2 )
=> ( (~) @ ( scott_P @ X4 @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl47]) ).
thf(zip_derived_cl52,plain,
! [X2: qML_i,X4: qML_mu > qML_i > $o] :
( ~ ( scott_P
@ ^ [Y0: qML_mu,Y1: qML_i] : ( (~) @ ( X4 @ Y0 @ Y1 ) )
@ X2 )
| ~ ( scott_P @ X4 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl48]) ).
thf(zip_derived_cl5834_008,plain,
! [X4: qML_mu > qML_i > $o,X5: qML_mu,X6: qML_i] :
( ( '#l_lift20060' @ X4 @ X5 @ X6 )
= ( (~) @ ( X4 @ X5 @ X6 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl5837,plain,
! [X2: qML_i,X4: qML_mu > qML_i > $o] :
( ~ ( scott_P @ ( '#l_lift20060' @ X4 ) @ X2 )
| ~ ( scott_P @ X4 @ X2 ) ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl52,zip_derived_cl5834]) ).
thf(zip_derived_cl5834_009,plain,
! [X4: qML_mu > qML_i > $o,X5: qML_mu,X6: qML_i] :
( ( '#l_lift20060' @ X4 @ X5 @ X6 )
= ( (~) @ ( X4 @ X5 @ X6 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl63_010,plain,
! [X2: qML_mu > qML_i > $o,X3: qML_mu,X4: qML_i] :
( ( scott_ess_QML_mu @ X2 @ X3 @ X4 )
= ( ( !!
@ ^ [Y0: qML_mu > qML_i > $o] :
( ( Y0 @ X3 @ X4 )
=> ( !!
@ ^ [Y1: qML_i] :
( !!
@ ^ [Y2: qML_mu] :
( ( X2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( X2 @ X3 @ X4 ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl62]) ).
thf(zip_derived_cl223,plain,
! [X2: qML_mu > qML_i > $o,X3: qML_mu,X4: qML_i] :
( ~ ( scott_ess_QML_mu @ X2 @ X3 @ X4 )
| ( ( !!
@ ^ [Y0: qML_mu > qML_i > $o] :
( ( Y0 @ X3 @ X4 )
=> ( !!
@ ^ [Y1: qML_i] :
( !!
@ ^ [Y2: qML_mu] :
( ( X2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( X2 @ X3 @ X4 ) ) ),
inference(eq_elim,[status(thm)],[zip_derived_cl63]) ).
thf(zip_derived_cl465,plain,
! [X2: qML_mu > qML_i > $o,X3: qML_mu,X4: qML_i] :
( ( X2 @ X3 @ X4 )
| ~ ( scott_ess_QML_mu @ X2 @ X3 @ X4 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl223]) ).
thf(conj_0,conjecture,
! [W3: qML_i,V: qML_i] :
? [X2: qML_mu] : ( scott_G @ X2 @ V ) ).
thf(zf_stmt_0,negated_conjecture,
~ ! [W3: qML_i,V: qML_i] :
? [X2: qML_mu] : ( scott_G @ X2 @ V ),
inference('cnf.neg',[status(esa)],[conj_0]) ).
thf(zip_derived_cl9,plain,
~ ( !!
@ ^ [Y0: qML_i] :
( !!
@ ^ [Y1: qML_i] :
( ??
@ ^ [Y2: qML_mu] : ( scott_G @ Y2 @ Y1 ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl44,plain,
~ ( !!
@ ^ [Y0: qML_i] :
( ??
@ ^ [Y1: qML_mu] : ( scott_G @ Y1 @ Y0 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl45,plain,
~ ( ??
@ ^ [Y0: qML_mu] : ( scott_G @ Y0 @ '#sk46' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl46,plain,
! [X2: qML_mu] :
~ ( scott_G @ X2 @ '#sk46' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl512,plain,
! [X0: qML_mu,X1: qML_i] :
~ ( scott_ess_QML_mu
@ ^ [Y0: qML_mu,Y1: qML_i] :
( scott_G
@ ( ^ [Y2: qML_mu,Y3: qML_i] : Y2
@ Y0
@ Y1 )
@ ( ^ [Y2: qML_mu,Y3: qML_i] : '#sk46'
@ Y0
@ Y1 ) )
@ X0
@ X1 ),
inference('sup-',[status(thm)],[zip_derived_cl465,zip_derived_cl46]) ).
thf(zip_derived_cl556,plain,
! [X0: qML_mu,X1: qML_i] :
~ ( scott_ess_QML_mu
@ ^ [Y0: qML_mu,Y1: qML_i] : ( scott_G @ Y0 @ '#sk46' )
@ X0
@ X1 ),
inference(ho_norm,[status(thm)],[zip_derived_cl512]) ).
thf(zip_derived_cl5856,plain,
! [X2: qML_mu,X3: qML_i] :
( ( '#l_lift20063' @ X2 @ X3 )
= ( scott_G @ X2 @ '#sk46' ) ),
define([status(thm)]) ).
thf(zip_derived_cl46_011,plain,
! [X2: qML_mu] :
~ ( scott_G @ X2 @ '#sk46' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl5865,plain,
$false,
inference(eprover,[status(thm)],[zip_derived_cl19,zip_derived_cl63,zip_derived_cl5862,zip_derived_cl5864,zip_derived_cl5842,zip_derived_cl5843,zip_derived_cl21,zip_derived_cl10,zip_derived_cl107,zip_derived_cl5837,zip_derived_cl5834,zip_derived_cl5856,zip_derived_cl46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : PHI005^4 : TPTP v8.1.2. Released v6.4.0.
% 0.12/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.Rj0tvYFgdU true
% 0.14/0.36 % Computer : n004.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sun Aug 27 08:48:37 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % Running portfolio for 300 s
% 0.14/0.36 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.36 % Number of cores: 8
% 0.14/0.36 % Python version: Python 3.6.8
% 0.14/0.36 % 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
% 1.00/0.77 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 1.00/0.77 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 1.00/0.77 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 1.00/0.77 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 1.00/0.77 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 1.00/0.78 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 1.00/0.78 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.00/0.78 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 59.01/8.27 % Solved by lams/20_acsne_simpl.sh.
% 59.01/8.27 % done 426 iterations in 7.439s
% 59.01/8.27 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 59.01/8.27 % SZS output start Refutation
% See solution above
% 59.01/8.27
% 59.01/8.27
% 60.02/8.28 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 60.02/8.29 % Terminating...
% 60.03/8.42 % Runner terminated.
% 60.07/8.43 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------