TSTP Solution File: LCL873^1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : LCL873^1 : TPTP v8.1.2. Bugfixed v5.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.3NVYpfPk55 true
% Computer : n008.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 09:02:29 EDT 2023
% Result : Theorem 1.46s 0.93s
% Output : Refutation 1.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 52
% Syntax : Number of formulae : 150 ( 38 unt; 21 typ; 0 def)
% Number of atoms : 961 ( 24 equ; 199 cnn)
% Maximal formula atoms : 39 ( 7 avg)
% Number of connectives : 2344 ( 340 ~; 419 |; 19 &;1311 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 151 ( 151 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 21 usr; 10 con; 0-3 aty)
% ( 242 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 419 ( 291 ^; 128 !; 0 ?; 419 :)
% Comments :
%------------------------------------------------------------------------------
thf('#sk10_type',type,
'#sk10': $i ).
thf(meuclidean_type,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(mbox_type,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf('#sk9_type',type,
'#sk9': $i > $o ).
thf(ra_type,type,
ra: $i > $i > $o ).
thf('#sk4_type',type,
'#sk4': $i ).
thf('#sk8_type',type,
'#sk8': $i > $o ).
thf(mreflexive_type,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(mnot_type,type,
mnot: ( $i > $o ) > $i > $o ).
thf(mimplies_type,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf('#form6_type',type,
'#form6': $o ).
thf('#sk2_type',type,
'#sk2': $i > $o ).
thf(rb_type,type,
rb: $i > $i > $o ).
thf('#sk7_type',type,
'#sk7': $i ).
thf('#sk11_type',type,
'#sk11': $i ).
thf('#sk5_type',type,
'#sk5': $i ).
thf('#sk3_type',type,
'#sk3': $i > $o ).
thf(mor_type,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mforall_prop_type,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(mvalid_type,type,
mvalid: ( $i > $o ) > $o ).
thf('#sk1_type',type,
'#sk1': $i ).
thf(mvalid,axiom,
( mvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ) ).
thf('0',plain,
( mvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ),
inference(simplify_rw_rule,[status(thm)],[mvalid]) ).
thf('1',plain,
( mvalid
= ( ^ [V_1: $i > $o] :
! [X4: $i] : ( V_1 @ X4 ) ) ),
define([status(thm)]) ).
thf(mbox,axiom,
( mbox
= ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
! [V: $i] :
( ( Phi @ V )
| ~ ( R @ W @ V ) ) ) ) ).
thf('2',plain,
( mbox
= ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
! [V: $i] :
( ( Phi @ V )
| ~ ( R @ W @ V ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mbox]) ).
thf('3',plain,
( mbox
= ( ^ [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(mforall_prop,axiom,
( mforall_prop
= ( ^ [Phi: ( $i > $o ) > $i > $o,W: $i] :
! [P: $i > $o] : ( Phi @ P @ W ) ) ) ).
thf('4',plain,
( mforall_prop
= ( ^ [Phi: ( $i > $o ) > $i > $o,W: $i] :
! [P: $i > $o] : ( Phi @ P @ W ) ) ),
inference(simplify_rw_rule,[status(thm)],[mforall_prop]) ).
thf('5',plain,
( mforall_prop
= ( ^ [V_1: ( $i > $o ) > $i > $o,V_2: $i] :
! [X4: $i > $o] : ( V_1 @ X4 @ 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('6',plain,
( mor
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
| ( Psi @ W ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mor]) ).
thf('7',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(mnot,axiom,
( mnot
= ( ^ [Phi: $i > $o,W: $i] :
~ ( Phi @ W ) ) ) ).
thf('8',plain,
( mnot
= ( ^ [Phi: $i > $o,W: $i] :
~ ( Phi @ W ) ) ),
inference(simplify_rw_rule,[status(thm)],[mnot]) ).
thf('9',plain,
( mnot
= ( ^ [V_1: $i > $o,V_2: $i] :
~ ( V_1 @ V_2 ) ) ),
define([status(thm)]) ).
thf('10',plain,
( mimplies
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ),
inference(simplify_rw_rule,[status(thm)],[mimplies,'7','9']) ).
thf('11',plain,
( mimplies
= ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mor @ ( mnot @ V_1 ) @ V_2 ) ) ),
define([status(thm)]) ).
thf(conj,conjecture,
( ( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] :
( mforall_prop
@ ^ [B: $i > $o] : ( mimplies @ ( mbox @ rb @ ( mor @ ( mbox @ ra @ A ) @ ( mbox @ rb @ B ) ) ) @ ( mor @ ( mbox @ rb @ A ) @ ( mbox @ rb @ B ) ) ) ) ) )
& ( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] :
( mforall_prop
@ ^ [B: $i > $o] : ( mimplies @ ( mbox @ ra @ ( mor @ ( mbox @ ra @ A ) @ ( mbox @ rb @ B ) ) ) @ ( mor @ ( mbox @ ra @ A ) @ ( mbox @ ra @ B ) ) ) ) ) ) ) ).
thf(zf_stmt_0,conjecture,
( ! [X4: $i,X6: $i > $o,X8: $i > $o] :
( ! [X18: $i] :
( ~ ( rb @ X4 @ X18 )
| ( X8 @ X18 ) )
| ! [X16: $i] :
( ~ ( rb @ X4 @ X16 )
| ( X6 @ X16 ) )
| ~ ! [X10: $i] :
( ~ ( rb @ X4 @ X10 )
| ! [X14: $i] :
( ~ ( rb @ X10 @ X14 )
| ( X8 @ X14 ) )
| ! [X12: $i] :
( ~ ( ra @ X10 @ X12 )
| ( X6 @ X12 ) ) ) )
& ! [X20: $i,X22: $i > $o,X24: $i > $o] :
( ! [X34: $i] :
( ~ ( ra @ X20 @ X34 )
| ( X24 @ X34 ) )
| ! [X32: $i] :
( ~ ( ra @ X20 @ X32 )
| ( X22 @ X32 ) )
| ~ ! [X26: $i] :
( ~ ( ra @ X20 @ X26 )
| ! [X30: $i] :
( ~ ( rb @ X26 @ X30 )
| ( X24 @ X30 ) )
| ! [X28: $i] :
( ~ ( ra @ X26 @ X28 )
| ( X22 @ X28 ) ) ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ( ! [X4: $i,X6: $i > $o,X8: $i > $o] :
( ! [X18: $i] :
( ~ ( rb @ X4 @ X18 )
| ( X8 @ X18 ) )
| ! [X16: $i] :
( ~ ( rb @ X4 @ X16 )
| ( X6 @ X16 ) )
| ~ ! [X10: $i] :
( ~ ( rb @ X4 @ X10 )
| ! [X14: $i] :
( ~ ( rb @ X10 @ X14 )
| ( X8 @ X14 ) )
| ! [X12: $i] :
( ~ ( ra @ X10 @ X12 )
| ( X6 @ X12 ) ) ) )
& ! [X20: $i,X22: $i > $o,X24: $i > $o] :
( ! [X34: $i] :
( ~ ( ra @ X20 @ X34 )
| ( X24 @ X34 ) )
| ! [X32: $i] :
( ~ ( ra @ X20 @ X32 )
| ( X22 @ X32 ) )
| ~ ! [X26: $i] :
( ~ ( ra @ X20 @ X26 )
| ! [X30: $i] :
( ~ ( rb @ X26 @ X30 )
| ( X24 @ X30 ) )
| ! [X28: $i] :
( ~ ( ra @ X26 @ X28 )
| ( X22 @ X28 ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl6,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rb @ Y0 @ Y3 ) )
| ( Y2 @ Y3 ) ) )
| ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rb @ Y0 @ Y3 ) )
| ( Y1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rb @ Y0 @ Y3 ) )
| ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rb @ Y3 @ Y4 ) )
| ( Y2 @ Y4 ) ) )
| ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( ra @ Y3 @ Y4 ) )
| ( Y1 @ Y4 ) ) ) ) ) ) ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( Y2 @ Y3 ) ) )
| ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( Y1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rb @ Y3 @ Y4 ) )
| ( Y2 @ Y4 ) ) )
| ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( ra @ Y3 @ Y4 ) )
| ( Y1 @ Y4 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl59,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rb @ Y0 @ Y3 ) )
| ( Y2 @ Y3 ) ) )
| ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rb @ Y0 @ Y3 ) )
| ( Y1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rb @ Y0 @ Y3 ) )
| ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rb @ Y3 @ Y4 ) )
| ( Y2 @ Y4 ) ) )
| ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( ra @ Y3 @ Y4 ) )
| ( Y1 @ Y4 ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( Y2 @ Y3 ) ) )
| ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( Y1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rb @ Y3 @ Y4 ) )
| ( Y2 @ Y4 ) ) )
| ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( ra @ Y3 @ Y4 ) )
| ( Y1 @ Y4 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl60,plain,
( ~ ( !!
@ ^ [Y0: $i > $o] :
( !!
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rb @ '#sk1' @ Y2 ) )
| ( Y1 @ Y2 ) ) )
| ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rb @ '#sk1' @ Y2 ) )
| ( Y0 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rb @ '#sk1' @ Y2 ) )
| ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rb @ Y2 @ Y3 ) )
| ( Y1 @ Y3 ) ) )
| ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y2 @ Y3 ) )
| ( Y0 @ Y3 ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( Y2 @ Y3 ) ) )
| ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( Y1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rb @ Y3 @ Y4 ) )
| ( Y2 @ Y4 ) ) )
| ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( ra @ Y3 @ Y4 ) )
| ( Y1 @ Y4 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl59]) ).
thf(zip_derived_cl61,plain,
( ~ ( !!
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rb @ '#sk1' @ Y1 ) )
| ( Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rb @ '#sk1' @ Y1 ) )
| ( '#sk2' @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rb @ '#sk1' @ Y1 ) )
| ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rb @ Y1 @ Y2 ) )
| ( Y0 @ Y2 ) ) )
| ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( ra @ Y1 @ Y2 ) )
| ( '#sk2' @ Y2 ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( Y2 @ Y3 ) ) )
| ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( Y1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rb @ Y3 @ Y4 ) )
| ( Y2 @ Y4 ) ) )
| ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( ra @ Y3 @ Y4 ) )
| ( Y1 @ Y4 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl60]) ).
thf(zip_derived_cl62,plain,
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rb @ '#sk1' @ Y0 ) )
| ( '#sk3' @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rb @ '#sk1' @ Y0 ) )
| ( '#sk2' @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rb @ '#sk1' @ Y0 ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rb @ Y0 @ Y1 ) )
| ( '#sk3' @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( ra @ Y0 @ Y1 ) )
| ( '#sk2' @ Y1 ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( Y2 @ Y3 ) ) )
| ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( Y1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rb @ Y3 @ Y4 ) )
| ( Y2 @ Y4 ) ) )
| ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( ra @ Y3 @ Y4 ) )
| ( Y1 @ Y4 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl61]) ).
thf(zip_derived_cl64,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rb @ '#sk1' @ Y0 ) )
| ( '#sk2' @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( Y2 @ Y3 ) ) )
| ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( Y1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rb @ Y3 @ Y4 ) )
| ( Y2 @ Y4 ) ) )
| ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( ra @ Y3 @ Y4 ) )
| ( Y1 @ Y4 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl62]) ).
thf(zip_derived_cl67,plain,
( ~ ( ( (~) @ ( rb @ '#sk1' @ '#sk5' ) )
| ( '#sk2' @ '#sk5' ) )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( Y2 @ Y3 ) ) )
| ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( Y1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rb @ Y3 @ Y4 ) )
| ( Y2 @ Y4 ) ) )
| ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( ra @ Y3 @ Y4 ) )
| ( Y1 @ Y4 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl64]) ).
thf(zip_derived_cl71,plain,
( '#form6'
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( Y2 @ Y3 ) ) )
| ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( Y1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rb @ Y3 @ Y4 ) )
| ( Y2 @ Y4 ) ) )
| ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( ra @ Y3 @ Y4 ) )
| ( Y1 @ Y4 ) ) ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl72,plain,
( ~ ( !!
@ ^ [Y0: $i > $o] :
( !!
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( ra @ '#sk7' @ Y2 ) )
| ( Y1 @ Y2 ) ) )
| ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( ra @ '#sk7' @ Y2 ) )
| ( Y0 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( ra @ '#sk7' @ Y2 ) )
| ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rb @ Y2 @ Y3 ) )
| ( Y1 @ Y3 ) ) )
| ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y2 @ Y3 ) )
| ( Y0 @ Y3 ) ) ) ) ) ) ) ) )
| '#form6' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl71]) ).
thf(zip_derived_cl79,plain,
( ~ ( !!
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( ra @ '#sk7' @ Y1 ) )
| ( Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( ra @ '#sk7' @ Y1 ) )
| ( '#sk8' @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( ra @ '#sk7' @ Y1 ) )
| ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rb @ Y1 @ Y2 ) )
| ( Y0 @ Y2 ) ) )
| ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( ra @ Y1 @ Y2 ) )
| ( '#sk8' @ Y2 ) ) ) ) ) ) ) )
| '#form6' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl72]) ).
thf(zip_derived_cl81,plain,
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( ra @ '#sk7' @ Y0 ) )
| ( '#sk9' @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( ra @ '#sk7' @ Y0 ) )
| ( '#sk8' @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( ra @ '#sk7' @ Y0 ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rb @ Y0 @ Y1 ) )
| ( '#sk9' @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( ra @ Y0 @ Y1 ) )
| ( '#sk8' @ Y1 ) ) ) ) ) ) )
| '#form6' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl79]) ).
thf(zip_derived_cl83,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( ra @ '#sk7' @ Y0 ) )
| ( '#sk9' @ Y0 ) ) )
| '#form6' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl81]) ).
thf(zip_derived_cl87,plain,
( ~ ( ( (~) @ ( ra @ '#sk7' @ '#sk10' ) )
| ( '#sk9' @ '#sk10' ) )
| '#form6' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl83]) ).
thf(zip_derived_cl92,plain,
( ~ ( '#sk9' @ '#sk10' )
| '#form6' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl87]) ).
thf(zip_derived_cl67_001,plain,
( ~ ( ( (~) @ ( rb @ '#sk1' @ '#sk5' ) )
| ( '#sk2' @ '#sk5' ) )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( Y2 @ Y3 ) ) )
| ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( Y1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rb @ Y3 @ Y4 ) )
| ( Y2 @ Y4 ) ) )
| ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( ra @ Y3 @ Y4 ) )
| ( Y1 @ Y4 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl64]) ).
thf(zip_derived_cl71_002,plain,
( '#form6'
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( Y2 @ Y3 ) ) )
| ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( Y1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rb @ Y3 @ Y4 ) )
| ( Y2 @ Y4 ) ) )
| ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( ra @ Y3 @ Y4 ) )
| ( Y1 @ Y4 ) ) ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl73,plain,
( ~ '#form6'
| ~ ( ( (~) @ ( rb @ '#sk1' @ '#sk5' ) )
| ( '#sk2' @ '#sk5' ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl67,zip_derived_cl71]) ).
thf(zip_derived_cl77,plain,
( ( rb @ '#sk1' @ '#sk5' )
| ~ '#form6' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl73]) ).
thf(zip_derived_cl63,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rb @ '#sk1' @ Y0 ) )
| ( '#sk3' @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( Y2 @ Y3 ) ) )
| ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( Y1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rb @ Y3 @ Y4 ) )
| ( Y2 @ Y4 ) ) )
| ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( ra @ Y3 @ Y4 ) )
| ( Y1 @ Y4 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl62]) ).
thf(zip_derived_cl66,plain,
( ~ ( ( (~) @ ( rb @ '#sk1' @ '#sk4' ) )
| ( '#sk3' @ '#sk4' ) )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( Y2 @ Y3 ) ) )
| ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( Y1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rb @ Y3 @ Y4 ) )
| ( Y2 @ Y4 ) ) )
| ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( ra @ Y3 @ Y4 ) )
| ( Y1 @ Y4 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl63]) ).
thf(zip_derived_cl69,plain,
( ( rb @ '#sk1' @ '#sk4' )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( Y2 @ Y3 ) ) )
| ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( Y1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rb @ Y3 @ Y4 ) )
| ( Y2 @ Y4 ) ) )
| ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( ra @ Y3 @ Y4 ) )
| ( Y1 @ Y4 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl66]) ).
thf(zip_derived_cl71_003,plain,
( '#form6'
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( Y2 @ Y3 ) ) )
| ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( Y1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rb @ Y3 @ Y4 ) )
| ( Y2 @ Y4 ) ) )
| ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( ra @ Y3 @ Y4 ) )
| ( Y1 @ Y4 ) ) ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl75,plain,
( ~ '#form6'
| ( rb @ '#sk1' @ '#sk4' ) ),
inference(renaming,[status(thm)],[zip_derived_cl69,zip_derived_cl71]) ).
thf(meuclidean,axiom,
( meuclidean
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ( R @ T @ U ) ) ) ) ).
thf('12',plain,
( meuclidean
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ( R @ T @ U ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[meuclidean]) ).
thf('13',plain,
( meuclidean
= ( ^ [V_1: $i > $i > $o] :
! [X4: $i,X6: $i,X8: $i] :
( ( ( V_1 @ X4 @ X6 )
& ( V_1 @ X4 @ X8 ) )
=> ( V_1 @ X6 @ X8 ) ) ) ),
define([status(thm)]) ).
thf(ax6,axiom,
meuclidean @ rb ).
thf(zf_stmt_2,axiom,
! [X4: $i,X6: $i,X8: $i] :
( ( ( rb @ X4 @ X8 )
& ( rb @ X4 @ X6 ) )
=> ( rb @ X6 @ X8 ) ) ).
thf(zip_derived_cl5,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( rb @ Y0 @ Y2 )
& ( rb @ Y0 @ Y1 ) )
=> ( rb @ Y1 @ Y2 ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_2]) ).
thf(zip_derived_cl47,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( ( rb @ X2 @ Y1 )
& ( rb @ X2 @ Y0 ) )
=> ( rb @ Y0 @ Y1 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl48,plain,
! [X2: $i,X4: $i] :
( !!
@ ^ [Y0: $i] :
( ( ( rb @ X2 @ Y0 )
& ( rb @ X2 @ X4 ) )
=> ( rb @ X4 @ Y0 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl47]) ).
thf(zip_derived_cl49,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( rb @ X2 @ X6 )
& ( rb @ X2 @ X4 ) )
=> ( rb @ X4 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl48]) ).
thf(zip_derived_cl50,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( ( rb @ X2 @ X6 )
& ( rb @ X2 @ X4 ) )
| ( rb @ X4 @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl49]) ).
thf(zip_derived_cl51,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( rb @ X2 @ X6 )
| ~ ( rb @ X2 @ X4 )
| ( rb @ X4 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl50]) ).
thf(zip_derived_cl101,plain,
! [X0: $i] :
( ~ '#form6'
| ( rb @ X0 @ '#sk4' )
| ~ ( rb @ '#sk1' @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl75,zip_derived_cl51]) ).
thf(zip_derived_cl125,plain,
( ~ '#form6'
| ( rb @ '#sk5' @ '#sk4' )
| ~ '#form6' ),
inference('sup-',[status(thm)],[zip_derived_cl77,zip_derived_cl101]) ).
thf(zip_derived_cl131,plain,
( ( rb @ '#sk5' @ '#sk4' )
| ~ '#form6' ),
inference(simplify,[status(thm)],[zip_derived_cl125]) ).
thf(zip_derived_cl77_004,plain,
( ( rb @ '#sk1' @ '#sk5' )
| ~ '#form6' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl73]) ).
thf(mreflexive,axiom,
( mreflexive
= ( ^ [R: $i > $i > $o] :
! [S: $i] : ( R @ S @ S ) ) ) ).
thf('14',plain,
( mreflexive
= ( ^ [R: $i > $i > $o] :
! [S: $i] : ( R @ S @ S ) ) ),
inference(simplify_rw_rule,[status(thm)],[mreflexive]) ).
thf('15',plain,
( mreflexive
= ( ^ [V_1: $i > $i > $o] :
! [X4: $i] : ( V_1 @ X4 @ X4 ) ) ),
define([status(thm)]) ).
thf(ax1,axiom,
mreflexive @ ra ).
thf(zf_stmt_3,axiom,
! [X4: $i] : ( ra @ X4 @ X4 ) ).
thf(zip_derived_cl0,plain,
( !!
@ ^ [Y0: $i] : ( ra @ Y0 @ Y0 ) ),
inference(cnf,[status(esa)],[zf_stmt_3]) ).
thf(zip_derived_cl7,plain,
! [X2: $i] : ( ra @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl65,plain,
( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rb @ '#sk1' @ Y0 ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rb @ Y0 @ Y1 ) )
| ( '#sk3' @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( ra @ Y0 @ Y1 ) )
| ( '#sk2' @ Y1 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( Y2 @ Y3 ) ) )
| ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( Y1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rb @ Y3 @ Y4 ) )
| ( Y2 @ Y4 ) ) )
| ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( ra @ Y3 @ Y4 ) )
| ( Y1 @ Y4 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl62]) ).
thf(zip_derived_cl68,plain,
! [X2: $i] :
( ( (~) @ ( rb @ '#sk1' @ X2 ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rb @ X2 @ Y0 ) )
| ( '#sk3' @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( ra @ X2 @ Y0 ) )
| ( '#sk2' @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( Y2 @ Y3 ) ) )
| ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( Y1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rb @ Y3 @ Y4 ) )
| ( Y2 @ Y4 ) ) )
| ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( ra @ Y3 @ Y4 ) )
| ( Y1 @ Y4 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl65]) ).
thf(zip_derived_cl71_005,plain,
( '#form6'
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( Y2 @ Y3 ) ) )
| ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( Y1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rb @ Y3 @ Y4 ) )
| ( Y2 @ Y4 ) ) )
| ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( ra @ Y3 @ Y4 ) )
| ( Y1 @ Y4 ) ) ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl74,plain,
! [X2: $i] :
( ~ '#form6'
| ( (~) @ ( rb @ '#sk1' @ X2 ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rb @ X2 @ Y0 ) )
| ( '#sk3' @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( ra @ X2 @ Y0 ) )
| ( '#sk2' @ Y0 ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl68,zip_derived_cl71]) ).
thf(zip_derived_cl80,plain,
! [X2: $i] :
( ~ ( rb @ '#sk1' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rb @ X2 @ Y0 ) )
| ( '#sk3' @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( ra @ X2 @ Y0 ) )
| ( '#sk2' @ Y0 ) ) )
| ~ '#form6' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl74]) ).
thf(zip_derived_cl82,plain,
! [X2: $i,X4: $i] :
( ( (~) @ ( rb @ X2 @ X4 ) )
| ( '#sk3' @ X4 )
| ~ '#form6'
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( ra @ X2 @ Y0 ) )
| ( '#sk2' @ Y0 ) ) )
| ~ ( rb @ '#sk1' @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl80]) ).
thf(zip_derived_cl86,plain,
! [X2: $i,X4: $i] :
( ~ ( rb @ X2 @ X4 )
| ( '#sk3' @ X4 )
| ~ ( rb @ '#sk1' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( ra @ X2 @ Y0 ) )
| ( '#sk2' @ Y0 ) ) )
| ~ '#form6' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl82]) ).
thf(zip_derived_cl90,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( (~) @ ( ra @ X2 @ X6 ) )
| ( '#sk2' @ X6 )
| ~ '#form6'
| ~ ( rb @ '#sk1' @ X2 )
| ( '#sk3' @ X4 )
| ~ ( rb @ X2 @ X4 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl86]) ).
thf(zip_derived_cl96,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( ra @ X2 @ X6 )
| ( '#sk2' @ X6 )
| ~ ( rb @ X2 @ X4 )
| ( '#sk3' @ X4 )
| ~ ( rb @ '#sk1' @ X2 )
| ~ '#form6' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl90]) ).
thf(zip_derived_cl211,plain,
! [X0: $i,X1: $i] :
( ~ '#form6'
| ~ ( rb @ '#sk1' @ X0 )
| ( '#sk3' @ X1 )
| ~ ( rb @ X0 @ X1 )
| ( '#sk2' @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl7,zip_derived_cl96]) ).
thf(zip_derived_cl441,plain,
! [X0: $i] :
( ~ '#form6'
| ( '#sk2' @ '#sk5' )
| ~ ( rb @ '#sk5' @ X0 )
| ( '#sk3' @ X0 )
| ~ '#form6' ),
inference('sup-',[status(thm)],[zip_derived_cl77,zip_derived_cl211]) ).
thf(zip_derived_cl450,plain,
! [X0: $i] :
( ( '#sk3' @ X0 )
| ~ ( rb @ '#sk5' @ X0 )
| ( '#sk2' @ '#sk5' )
| ~ '#form6' ),
inference(simplify,[status(thm)],[zip_derived_cl441]) ).
thf(zip_derived_cl78,plain,
( ~ ( '#sk2' @ '#sk5' )
| ~ '#form6' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl73]) ).
thf(zip_derived_cl521,plain,
! [X0: $i] :
( ~ '#form6'
| ~ ( rb @ '#sk5' @ X0 )
| ( '#sk3' @ X0 ) ),
inference(clc,[status(thm)],[zip_derived_cl450,zip_derived_cl78]) ).
thf(zip_derived_cl525,plain,
( ~ '#form6'
| ( '#sk3' @ '#sk4' )
| ~ '#form6' ),
inference('sup-',[status(thm)],[zip_derived_cl131,zip_derived_cl521]) ).
thf(zip_derived_cl534,plain,
( ( '#sk3' @ '#sk4' )
| ~ '#form6' ),
inference(simplify,[status(thm)],[zip_derived_cl525]) ).
thf(zip_derived_cl70,plain,
( ~ ( '#sk3' @ '#sk4' )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( Y2 @ Y3 ) ) )
| ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( Y1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rb @ Y3 @ Y4 ) )
| ( Y2 @ Y4 ) ) )
| ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( ra @ Y3 @ Y4 ) )
| ( Y1 @ Y4 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl66]) ).
thf(zip_derived_cl71_006,plain,
( '#form6'
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( Y2 @ Y3 ) ) )
| ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( Y1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( ra @ Y0 @ Y3 ) )
| ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rb @ Y3 @ Y4 ) )
| ( Y2 @ Y4 ) ) )
| ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( ra @ Y3 @ Y4 ) )
| ( Y1 @ Y4 ) ) ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl76,plain,
( ~ '#form6'
| ~ ( '#sk3' @ '#sk4' ) ),
inference(renaming,[status(thm)],[zip_derived_cl70,zip_derived_cl71]) ).
thf(zip_derived_cl542,plain,
~ '#form6',
inference(clc,[status(thm)],[zip_derived_cl534,zip_derived_cl76]) ).
thf(zip_derived_cl544,plain,
~ ( '#sk9' @ '#sk10' ),
inference(demod,[status(thm)],[zip_derived_cl92,zip_derived_cl542]) ).
thf(zip_derived_cl84,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( ra @ '#sk7' @ Y0 ) )
| ( '#sk8' @ Y0 ) ) )
| '#form6' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl81]) ).
thf(zip_derived_cl88,plain,
( ~ ( ( (~) @ ( ra @ '#sk7' @ '#sk11' ) )
| ( '#sk8' @ '#sk11' ) )
| '#form6' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl84]) ).
thf(zip_derived_cl93,plain,
( ( ra @ '#sk7' @ '#sk11' )
| '#form6' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl88]) ).
thf(zip_derived_cl91,plain,
( ( ra @ '#sk7' @ '#sk10' )
| '#form6' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl87]) ).
thf(ax5,axiom,
meuclidean @ ra ).
thf(zf_stmt_4,axiom,
! [X4: $i,X6: $i,X8: $i] :
( ( ( ra @ X4 @ X8 )
& ( ra @ X4 @ X6 ) )
=> ( ra @ X6 @ X8 ) ) ).
thf(zip_derived_cl4,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( ra @ Y0 @ Y2 )
& ( ra @ Y0 @ Y1 ) )
=> ( ra @ Y1 @ Y2 ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_4]) ).
thf(zip_derived_cl35,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( ( ra @ X2 @ Y1 )
& ( ra @ X2 @ Y0 ) )
=> ( ra @ Y0 @ Y1 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl36,plain,
! [X2: $i,X4: $i] :
( !!
@ ^ [Y0: $i] :
( ( ( ra @ X2 @ Y0 )
& ( ra @ X2 @ X4 ) )
=> ( ra @ X4 @ Y0 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl35]) ).
thf(zip_derived_cl37,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( ra @ X2 @ X6 )
& ( ra @ X2 @ X4 ) )
=> ( ra @ X4 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl38,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( ( ra @ X2 @ X6 )
& ( ra @ X2 @ X4 ) )
| ( ra @ X4 @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl37]) ).
thf(zip_derived_cl39,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( ra @ X2 @ X6 )
| ~ ( ra @ X2 @ X4 )
| ( ra @ X4 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl114,plain,
! [X0: $i] :
( '#form6'
| ( ra @ X0 @ '#sk10' )
| ~ ( ra @ '#sk7' @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl91,zip_derived_cl39]) ).
thf(zip_derived_cl275,plain,
( '#form6'
| ( ra @ '#sk11' @ '#sk10' )
| '#form6' ),
inference('sup-',[status(thm)],[zip_derived_cl93,zip_derived_cl114]) ).
thf(zip_derived_cl281,plain,
( ( ra @ '#sk11' @ '#sk10' )
| '#form6' ),
inference(simplify,[status(thm)],[zip_derived_cl275]) ).
thf(zip_derived_cl7_007,plain,
! [X2: $i] : ( ra @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl39_008,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( ra @ X2 @ X6 )
| ~ ( ra @ X2 @ X4 )
| ( ra @ X4 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl40,plain,
! [X0: $i,X1: $i] :
( ( ra @ X1 @ X0 )
| ~ ( ra @ X0 @ X1 ) ),
inference('sup-',[status(thm)],[zip_derived_cl7,zip_derived_cl39]) ).
thf(zip_derived_cl287,plain,
( '#form6'
| ( ra @ '#sk10' @ '#sk11' ) ),
inference('sup-',[status(thm)],[zip_derived_cl281,zip_derived_cl40]) ).
thf(zip_derived_cl85,plain,
( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( ra @ '#sk7' @ Y0 ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rb @ Y0 @ Y1 ) )
| ( '#sk9' @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( ra @ Y0 @ Y1 ) )
| ( '#sk8' @ Y1 ) ) ) ) )
| '#form6' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl81]) ).
thf(zip_derived_cl89,plain,
! [X2: $i] :
( ( (~) @ ( ra @ '#sk7' @ X2 ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rb @ X2 @ Y0 ) )
| ( '#sk9' @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( ra @ X2 @ Y0 ) )
| ( '#sk8' @ Y0 ) ) )
| '#form6' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl85]) ).
thf(zip_derived_cl95,plain,
! [X2: $i] :
( ~ ( ra @ '#sk7' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rb @ X2 @ Y0 ) )
| ( '#sk9' @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( ra @ X2 @ Y0 ) )
| ( '#sk8' @ Y0 ) ) )
| '#form6' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl89]) ).
thf(zip_derived_cl97,plain,
! [X2: $i,X4: $i] :
( ( (~) @ ( rb @ X2 @ X4 ) )
| ( '#sk9' @ X4 )
| '#form6'
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( ra @ X2 @ Y0 ) )
| ( '#sk8' @ Y0 ) ) )
| ~ ( ra @ '#sk7' @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl95]) ).
thf(zip_derived_cl98,plain,
! [X2: $i,X4: $i] :
( ~ ( rb @ X2 @ X4 )
| ( '#sk9' @ X4 )
| ~ ( ra @ '#sk7' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( ra @ X2 @ Y0 ) )
| ( '#sk8' @ Y0 ) ) )
| '#form6' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl97]) ).
thf(zip_derived_cl99,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( (~) @ ( ra @ X2 @ X6 ) )
| ( '#sk8' @ X6 )
| '#form6'
| ~ ( ra @ '#sk7' @ X2 )
| ( '#sk9' @ X4 )
| ~ ( rb @ X2 @ X4 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl98]) ).
thf(zip_derived_cl100,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( ra @ X2 @ X6 )
| ( '#sk8' @ X6 )
| ~ ( rb @ X2 @ X4 )
| ( '#sk9' @ X4 )
| ~ ( ra @ '#sk7' @ X2 )
| '#form6' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl99]) ).
thf(zip_derived_cl312,plain,
! [X0: $i] :
( '#form6'
| '#form6'
| ~ ( ra @ '#sk7' @ '#sk10' )
| ( '#sk9' @ X0 )
| ~ ( rb @ '#sk10' @ X0 )
| ( '#sk8' @ '#sk11' ) ),
inference('sup-',[status(thm)],[zip_derived_cl287,zip_derived_cl100]) ).
thf(zip_derived_cl321,plain,
! [X0: $i] :
( ( '#sk8' @ '#sk11' )
| ~ ( rb @ '#sk10' @ X0 )
| ( '#sk9' @ X0 )
| ~ ( ra @ '#sk7' @ '#sk10' )
| '#form6' ),
inference(simplify,[status(thm)],[zip_derived_cl312]) ).
thf(zip_derived_cl94,plain,
( ~ ( '#sk8' @ '#sk11' )
| '#form6' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl88]) ).
thf(zip_derived_cl542_009,plain,
~ '#form6',
inference(clc,[status(thm)],[zip_derived_cl534,zip_derived_cl76]) ).
thf(zip_derived_cl546,plain,
~ ( '#sk8' @ '#sk11' ),
inference(demod,[status(thm)],[zip_derived_cl94,zip_derived_cl542]) ).
thf(zip_derived_cl91_010,plain,
( ( ra @ '#sk7' @ '#sk10' )
| '#form6' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl87]) ).
thf(zip_derived_cl542_011,plain,
~ '#form6',
inference(clc,[status(thm)],[zip_derived_cl534,zip_derived_cl76]) ).
thf(zip_derived_cl543,plain,
ra @ '#sk7' @ '#sk10',
inference(demod,[status(thm)],[zip_derived_cl91,zip_derived_cl542]) ).
thf(zip_derived_cl542_012,plain,
~ '#form6',
inference(clc,[status(thm)],[zip_derived_cl534,zip_derived_cl76]) ).
thf(zip_derived_cl694,plain,
! [X0: $i] :
( ~ ( rb @ '#sk10' @ X0 )
| ( '#sk9' @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl321,zip_derived_cl546,zip_derived_cl543,zip_derived_cl542]) ).
thf(ax2,axiom,
mreflexive @ rb ).
thf(zf_stmt_5,axiom,
! [X4: $i] : ( rb @ X4 @ X4 ) ).
thf(zip_derived_cl1,plain,
( !!
@ ^ [Y0: $i] : ( rb @ Y0 @ Y0 ) ),
inference(cnf,[status(esa)],[zf_stmt_5]) ).
thf(zip_derived_cl8,plain,
! [X2: $i] : ( rb @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl695,plain,
'#sk9' @ '#sk10',
inference('sup+',[status(thm)],[zip_derived_cl694,zip_derived_cl8]) ).
thf(zip_derived_cl699,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl544,zip_derived_cl695]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LCL873^1 : TPTP v8.1.2. Bugfixed v5.0.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.3NVYpfPk55 true
% 0.14/0.35 % Computer : n008.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 25 05:54:17 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % 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
% 0.22/0.66 % Total configuration time : 828
% 0.22/0.66 % Estimated wc time : 1656
% 0.22/0.66 % Estimated cpu time (8 cpus) : 207.0
% 0.22/0.74 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.22/0.74 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.22/0.75 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.22/0.76 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.22/0.76 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.22/0.78 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.22/0.78 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.22/0.80 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 1.20/0.87 % /export/starexec/sandbox/solver/bin/lams/35_full_unif.sh running for 56s
% 1.20/0.88 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 1.46/0.93 % Solved by lams/35_full_unif4.sh.
% 1.46/0.93 % done 364 iterations in 0.141s
% 1.46/0.93 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 1.46/0.93 % SZS output start Refutation
% See solution above
% 1.46/0.93
% 1.46/0.93
% 1.46/0.93 % Terminating...
% 1.46/0.93 % /export/starexec/sandbox/solver/bin/lams/15_old_s4.sh running for 30s
% 2.04/1.11 % Runner terminated.
% 2.04/1.12 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------