%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP322_1 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:37:41 AM UTC 2026
% Result : Theorem 19.58s 5.75s
% Output : Refutation 20.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 495
% Syntax : Number of formulae : 992 ( 299 unt; 0 typ; 0 def)
% Number of atoms : 2742 ( 847 equ; 0 cnn)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 12805 ( 293 ~; 58 |; 697 &;10762 @)
% ( 139 <=>; 856 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 8 avg)
% Number of types : 18 ( 17 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 42 ( 39 usr; 21 con; 0-3 aty)
% Number of variables : 2404 ( 0 ^;2380 !; 24 ?;2404 :)
% Comments :
%------------------------------------------------------------------------------
thf('B_bool_fun_b_bool_fun_fun$_type',type,
'B_bool_fun_b_bool_fun_fun$': $tType ).
thf('B_bool_fun_b_bool_fun_bool_fun_fun$_type',type,
'B_bool_fun_b_bool_fun_bool_fun_fun$': $tType ).
thf('B_bool_fun_bool_fun$_type',type,
'B_bool_fun_bool_fun$': $tType ).
thf('B$_type',type,
'B$': $tType ).
thf('B_bool_fun_b_set_fun$_type',type,
'B_bool_fun_b_set_fun$': $tType ).
thf('B_set_b_set_bool_fun_fun$_type',type,
'B_set_b_set_bool_fun_fun$': $tType ).
thf('B_bool_fun_b_bool_fun_b_bool_fun_fun_fun$_type',type,
'B_bool_fun_b_bool_fun_b_bool_fun_fun_fun$': $tType ).
thf(tlbool_type,type,
tlbool: $tType ).
thf('B_set_b_set_b_set_fun_fun$_type',type,
'B_set_b_set_b_set_fun_fun$': $tType ).
thf('B_b_bool_fun_fun$_type',type,
'B_b_bool_fun_fun$': $tType ).
thf('B_set$_type',type,
'B_set$': $tType ).
thf('B_set_b_bool_fun_fun$_type',type,
'B_set_b_bool_fun_fun$': $tType ).
thf('B_set_bool_fun$_type',type,
'B_set_bool_fun$': $tType ).
thf('Bool_bool_fun$_type',type,
'Bool_bool_fun$': $tType ).
thf('B_set_b_set_fun$_type',type,
'B_set_b_set_fun$': $tType ).
thf('B_bool_fun$_type',type,
'B_bool_fun$': $tType ).
thf('Bool_bool_bool_fun_fun$_type',type,
'Bool_bool_bool_fun_fun$': $tType ).
thf('fun_app$i_decl',type,
'fun_app$i': 'B_set_bool_fun$' > 'B_set$' > $o ).
thf('less_eq$a_decl',type,
'less_eq$a': 'B_bool_fun_b_bool_fun_bool_fun_fun$' ).
thf('bot$a_decl',type,
'bot$a': $o ).
thf('top$a_decl',type,
'top$a': $o ).
thf('a$_decl',type,
'a$': 'B$' ).
thf('fun_app$b_decl',type,
'fun_app$b': 'B_set_b_set_fun$' > 'B_set$' > 'B_set$' ).
thf('semilattice_neutr$b_decl',type,
'semilattice_neutr$b': 'B_set_b_set_b_set_fun_fun$' > 'B_set$' > $o ).
thf('collect$_decl',type,
'collect$': 'B_bool_fun_b_set_fun$' ).
thf('member$_decl',type,
'member$': 'B$' > 'B_set$' > $o ).
thf('top$b_decl',type,
'top$b': 'B_bool_fun$' ).
thf('uminus$_decl',type,
'uminus$': 'B_set_b_set_fun$' ).
thf('fun_app$j_decl',type,
'fun_app$j': 'B_set_b_set_bool_fun_fun$' > 'B_set$' > 'B_set_bool_fun$' ).
thf('fun_app$a_decl',type,
'fun_app$a': 'B_set_b_bool_fun_fun$' > 'B_set$' > 'B_bool_fun$' ).
thf('fun_app$c_decl',type,
'fun_app$c': 'B_set_b_set_b_set_fun_fun$' > 'B_set$' > 'B_set_b_set_fun$' ).
thf('is_empty$_decl',type,
'is_empty$': 'B_set$' > $o ).
thf('insert$_decl',type,
'insert$': 'B$' > 'B_set_b_set_fun$' ).
thf('fun_app$m_decl',type,
'fun_app$m': 'B_bool_fun_b_bool_fun_bool_fun_fun$' > 'B_bool_fun$' > 'B_bool_fun_bool_fun$' ).
thf('top$_decl',type,
'top$': 'B_set$' ).
thf(tltrue_decl,type,
tltrue: tlbool ).
thf('minus$_decl',type,
'minus$': 'B_set_b_set_b_set_fun_fun$' ).
thf('remove$_decl',type,
'remove$': 'B$' > 'B_set_b_set_fun$' ).
thf('is_singleton$_decl',type,
'is_singleton$': 'B_set$' > $o ).
thf('less$_decl',type,
'less$': 'B_set_b_set_bool_fun_fun$' ).
thf('fun_app$k_decl',type,
'fun_app$k': 'B_b_bool_fun_fun$' > 'B$' > 'B_bool_fun$' ).
thf('sup$_decl',type,
'sup$': 'B_set_b_set_b_set_fun_fun$' ).
thf('pairwise$_decl',type,
'pairwise$': 'B_b_bool_fun_fun$' > 'B_set$' > $o ).
thf('uu$_decl',type,
'uu$': 'B_set_b_bool_fun_fun$' ).
thf('bot$b_decl',type,
'bot$b': 'B_bool_fun$' ).
thf('inf$a_decl',type,
'inf$a': 'B_set_b_set_b_set_fun_fun$' ).
thf('the_elem$_decl',type,
'the_elem$': 'B_set$' > 'B$' ).
thf('bot$_decl',type,
'bot$': 'B_set$' ).
thf('b$_decl',type,
'b$': 'B$' ).
thf('less$a_decl',type,
'less$a': 'B_bool_fun_b_bool_fun_bool_fun_fun$' ).
thf('less_eq$_decl',type,
'less_eq$': 'B_set_b_set_bool_fun_fun$' ).
thf('ordering_top$a_decl',type,
'ordering_top$a': 'B_set_b_set_bool_fun_fun$' > 'B_set_b_set_bool_fun_fun$' > 'B_set$' > $o ).
thf('fun_app$_decl',type,
'fun_app$': 'B_bool_fun$' > 'B$' > $o ).
thf('fun_app$l_decl',type,
'fun_app$l': 'B_bool_fun_bool_fun$' > 'B_bool_fun$' > $o ).
thf('ordering_top_axioms$_decl',type,
'ordering_top_axioms$': 'B_set_b_set_bool_fun_fun$' > 'B_set$' > $o ).
thf('fun_app$d_decl',type,
'fun_app$d': 'B_bool_fun_b_set_fun$' > 'B_bool_fun$' > 'B_set$' ).
thf(31,axiom,
! [A: 'B_bool_fun$'] : ( A @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom184) ).
thf(645,plain,
! [A: 'B_bool_fun$'] : ( A @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(195,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom249) ).
thf(1411,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(267,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( A @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom347) ).
thf(1767,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( A @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(129,axiom,
! [A: 'B_set$'] : ( A @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom185) ).
thf(1105,plain,
! [A: 'B_set$'] : ( A @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(85,axiom,
! [A: 'B_bool_fun$',B: 'B_set_b_bool_fun_fun$',C: 'B_set$',D: 'B_set$'] :
( ( ! [E: 'B_set$',F: 'B_set$'] :
( ( F @ ( E @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( F @ ( B @ 'fun_app$a' ) @ ( E @ ( B @ 'fun_app$a' ) @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
& ( D @ ( C @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( A
= ( C @ ( B @ 'fun_app$a' ) ) ) )
=> ( D @ ( B @ 'fun_app$a' ) @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom431) ).
thf(893,plain,
! [A: 'B_bool_fun$',B: 'B_set_b_bool_fun_fun$',C: 'B_set$',D: 'B_set$'] :
( ( ! [E: 'B_set$',F: 'B_set$'] :
( ( F @ ( E @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( F @ ( B @ 'fun_app$a' ) @ ( E @ ( B @ 'fun_app$a' ) @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
& ( D @ ( C @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( A
= ( C @ ( B @ 'fun_app$a' ) ) ) )
=> ( D @ ( B @ 'fun_app$a' ) @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(434,axiom,
! [A: 'B_set$'] :
( ( A @ ( A @ ( 'uminus$' @ 'fun_app$b' ) @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'bot$' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom632) ).
thf(2595,plain,
! [A: 'B_set$'] :
( ( A @ ( A @ ( 'uminus$' @ 'fun_app$b' ) @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'bot$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(276,axiom,
! [A: 'B_set$'] :
( ( 'bot$' @ ( A @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom11) ).
thf(1818,plain,
! [A: 'B_set$'] :
( ( 'bot$' @ ( A @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(366,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( ( A @ ( C @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( B @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom353) ).
thf(2280,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( ( A @ ( C @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( B @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(440,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( A @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom306) ).
thf(2612,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( A @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(114,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( 'uminus$' @ 'fun_app$b' ) @ ( A @ ( 'uminus$' @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
<=> ( A @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom380) ).
thf(1024,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( B @ ( 'uminus$' @ 'fun_app$b' ) @ ( A @ ( 'uminus$' @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( B @ ( 'uminus$' @ 'fun_app$b' ) @ ( A @ ( 'uminus$' @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( A @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(208,axiom,
! [A: 'B$',B: tlbool] :
( ( ( B = tltrue )
& ( A @ ( 'top$b' @ 'fun_app$' ) ) )
<=> ( B = tltrue ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom176) ).
thf(1469,plain,
! [A: 'B$',B: tlbool] :
( ( ( B = tltrue )
=> ( ( B = tltrue )
& ( A @ ( 'top$b' @ 'fun_app$' ) ) ) )
& ( ( ( B = tltrue )
& ( A @ ( 'top$b' @ 'fun_app$' ) ) )
=> ( B = tltrue ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(471,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( A @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom595) ).
thf(2744,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( A @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(278,axiom,
'bot$' != 'top$',
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom60) ).
thf(1823,plain,
'bot$' != 'top$',
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(370,axiom,
! [A: 'B_set$'] :
( ( A @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom115) ).
thf(2306,plain,
! [A: 'B_set$'] :
( ( A @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(55,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$',C: 'B_bool_fun$'] :
( ( ( A @ ( C @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( B @ ( C @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom419) ).
thf(760,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$',C: 'B_bool_fun$'] :
( ( ( A @ ( C @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( B @ ( C @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(379,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( A @ ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom598) ).
thf(2336,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( A @ ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(206,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( A = B )
<=> ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom239) ).
thf(1454,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(87,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set_b_bool_fun_fun$',D: 'B_bool_fun$'] :
( ( ! [E: 'B_set$',F: 'B_set$'] :
( ( F @ ( E @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( F @ ( C @ 'fun_app$a' ) @ ( E @ ( C @ 'fun_app$a' ) @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
& ( D @ ( B @ ( C @ 'fun_app$a' ) @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$a' ) @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom445) ).
thf(909,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set_b_bool_fun_fun$',D: 'B_bool_fun$'] :
( ( ! [E: 'B_set$',F: 'B_set$'] :
( ( F @ ( E @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( F @ ( C @ 'fun_app$a' ) @ ( E @ ( C @ 'fun_app$a' ) @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
& ( D @ ( B @ ( C @ 'fun_app$a' ) @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$a' ) @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(27,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ~ ( A @ ( B @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom474) ).
thf(628,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ~ ( A @ ( B @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(403,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( A @ ( B @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom591) ).
thf(2463,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( A @ ( B @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(298,axiom,
! [A: 'B_set$'] :
( ( 'top$' @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'top$' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom82) ).
thf(1899,plain,
! [A: 'B_set$'] :
( ( 'top$' @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'top$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(302,axiom,
! [A: 'B_set$'] :
( ( A @ ( 'uminus$' @ 'fun_app$b' ) )
= ( A @ ( 'top$' @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom564) ).
thf(1924,plain,
! [A: 'B_set$'] :
( ( A @ ( 'uminus$' @ 'fun_app$b' ) )
= ( A @ ( 'top$' @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(48,axiom,
! [A: 'B_bool_fun$'] : ( A @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom186) ).
thf(730,plain,
! [A: 'B_bool_fun$'] : ( A @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(388,axiom,
! [A: 'B_set$'] :
( ( A @ ( 'bot$' @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom100) ).
thf(2395,plain,
! [A: 'B_set$'] :
( ( A @ ( 'bot$' @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(455,axiom,
! [A: 'B_set$'] :
( ( 'bot$' @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'bot$' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom604) ).
thf(2676,plain,
! [A: 'B_set$'] :
( ( 'bot$' @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'bot$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(336,axiom,
! [A: 'B_set$',B: 'B$'] :
( ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( 'uminus$' @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
<=> ~ ( A @ ( B @ 'member$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom368) ).
thf(2099,plain,
! [A: 'B_set$',B: 'B$'] :
( ( ~ ( A @ ( B @ 'member$' ) )
=> ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( 'uminus$' @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( 'uminus$' @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ~ ( A @ ( B @ 'member$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(220,axiom,
! [A: 'B_set$'] :
( ( 'top$' @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'top$' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom69) ).
thf(1533,plain,
! [A: 'B_set$'] :
( ( 'top$' @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'top$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(287,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( C @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom546) ).
thf(1855,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( C @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(332,axiom,
! [A: 'B_set$'] :
( ( A != 'bot$' )
<=> ( A @ ( 'bot$' @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom531) ).
thf(2077,plain,
! [A: 'B_set$'] :
( ( ( A @ ( 'bot$' @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( A != 'bot$' ) )
& ( ( A != 'bot$' )
=> ( A @ ( 'bot$' @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(139,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( A @ ( C @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( B @ ( C @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom499) ).
thf(1158,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( A @ ( C @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( B @ ( C @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(371,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( B @ ( A @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( B @ ( A @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom25) ).
thf(2309,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( B @ ( A @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( B @ ( A @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(56,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$',C: 'B_bool_fun_b_set_fun$',D: 'B_set$'] :
( ( ! [E: 'B_bool_fun$',F: 'B_bool_fun$'] :
( ( F @ ( E @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( F @ ( C @ 'fun_app$d' ) @ ( E @ ( C @ 'fun_app$d' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( B @ ( C @ 'fun_app$d' ) )
= D )
& ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$d' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom221) ).
thf(762,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$',C: 'B_bool_fun_b_set_fun$',D: 'B_set$'] :
( ( ! [E: 'B_bool_fun$',F: 'B_bool_fun$'] :
( ( F @ ( E @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( F @ ( C @ 'fun_app$d' ) @ ( E @ ( C @ 'fun_app$d' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( B @ ( C @ 'fun_app$d' ) )
= D )
& ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$d' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(443,axiom,
! [A: 'B_set$'] :
( ! [B: 'B$'] : ( A @ ( B @ 'member$' ) )
=> ( 'top$' = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom34) ).
thf(2622,plain,
! [A: 'B_set$'] :
( ! [B: 'B$'] : ( A @ ( B @ 'member$' ) )
=> ( 'top$' = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(121,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( B = C )
& ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( C @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom412) ).
thf(1068,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( B = C )
& ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( C @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(479,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( 'top$'
= ( B @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) ) )
<=> ( ( B = 'top$' )
& ( A = 'top$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom616) ).
thf(2776,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( ( B = 'top$' )
& ( A = 'top$' ) )
=> ( 'top$'
= ( B @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ) )
& ( ( 'top$'
= ( B @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) ) )
=> ( ( B = 'top$' )
& ( A = 'top$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(275,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( B @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'top$' )
<=> ( ( B = 'top$' )
& ( A = 'top$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom614) ).
thf(1808,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( ( B = 'top$' )
& ( A = 'top$' ) )
=> ( ( B @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'top$' ) )
& ( ( ( B @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'top$' )
=> ( ( B = 'top$' )
& ( A = 'top$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(6,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ~ ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
<=> ( ( A = B )
| ~ ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom476) ).
thf(511,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( ( ( A = B )
| ~ ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ~ ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
& ( ~ ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( ( A = B )
| ~ ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(384,axiom,
! [A: 'B$',B: 'B_set$',C: 'B$'] :
( ( ~ ( B @ ( A @ 'member$' ) )
=> ( A = C ) )
=> ( B @ ( C @ 'insert$' @ 'fun_app$b' ) @ ( A @ 'member$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom22) ).
thf(2380,plain,
! [A: 'B$',B: 'B_set$',C: 'B$'] :
( ( ~ ( B @ ( A @ 'member$' ) )
=> ( A = C ) )
=> ( B @ ( C @ 'insert$' @ 'fun_app$b' ) @ ( A @ 'member$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(25,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
<=> ( ( A = B )
| ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom508) ).
thf(614,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( ( ( A = B )
| ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
& ( ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( ( A = B )
| ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(249,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
<=> ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( C @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom191) ).
thf(1692,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( C @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( C @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(37,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
<=> ( ( A != B )
& ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom486) ).
thf(677,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( ( ( A != B )
& ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
& ( ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( ( A != B )
& ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(232,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom45) ).
thf(1608,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(438,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom119) ).
thf(2607,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(258,axiom,
! [A: 'B_set$'] :
( ( 'bot$' @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom67) ).
thf(1735,plain,
! [A: 'B_set$'] :
( ( 'bot$' @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(399,axiom,
! [A: 'B_set$'] :
( ( A @ ( 'uminus$' @ 'fun_app$b' ) @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'bot$' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom633) ).
thf(2448,plain,
! [A: 'B_set$'] :
( ( A @ ( 'uminus$' @ 'fun_app$b' ) @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'bot$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(67,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$',C: 'B_bool_fun$'] :
( ( ( C @ ( B @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( A = B ) )
=> ( C @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom409) ).
thf(814,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$',C: 'B_bool_fun$'] :
( ( ( C @ ( B @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( A = B ) )
=> ( C @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(405,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( A @ ( B @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'bot$' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom631) ).
thf(2476,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( A @ ( B @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'bot$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(270,axiom,
! [A: 'B_set$',B: 'B$',C: 'B_set$'] :
( ( ( C @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'bot$' )
<=> ( ( ( C @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'bot$' )
& ~ ( A @ ( B @ 'member$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom626) ).
thf(1788,plain,
! [A: 'B_set$',B: 'B$',C: 'B_set$'] :
( ( ( ( ( C @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'bot$' )
& ~ ( A @ ( B @ 'member$' ) ) )
=> ( ( C @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'bot$' ) )
& ( ( ( C @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'bot$' )
=> ( ( ( C @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'bot$' )
& ~ ( A @ ( B @ 'member$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(198,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ~ ( A @ ( B @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
<=> $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom458) ).
thf(1426,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ~ ( A @ ( B @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(264,axiom,
'top$' @ ( 'less$' @ ( 'less_eq$' @ 'ordering_top$a' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom569) ).
thf(1756,plain,
'top$' @ ( 'less$' @ ( 'less_eq$' @ 'ordering_top$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(8,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$',C: 'B_bool_fun$'] :
( ( ( A @ ( C @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( B @ ( C @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom498) ).
thf(533,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$',C: 'B_bool_fun$'] :
( ( ( A @ ( C @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( B @ ( C @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(266,axiom,
! [A: 'B$',B: 'B_set$'] :
( ( ! [C: 'B_set$'] :
( ( ~ ( C @ ( A @ 'member$' ) )
& ( B
= ( C @ ( A @ 'insert$' @ 'fun_app$b' ) ) ) )
=> $false )
& ( B @ ( A @ 'member$' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom40) ).
thf(1761,plain,
! [A: 'B$',B: 'B_set$'] :
~ ( ! [C: 'B_set$'] :
~ ( ~ ( C @ ( A @ 'member$' ) )
& ( B
= ( C @ ( A @ 'insert$' @ 'fun_app$b' ) ) ) )
& ( B @ ( A @ 'member$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(88,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( ( A @ ( B @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom427) ).
thf(913,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
~ ( ( A @ ( B @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(152,axiom,
! [A: 'B_set_b_set_bool_fun_fun$',B: 'B_set_b_set_bool_fun_fun$',C: 'B_set$',D: 'B_set$'] :
( ( ( D @ ( C @ ( A @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( C @ ( B @ ( A @ 'ordering_top$a' ) ) ) )
=> ( D = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom574) ).
thf(1222,plain,
! [A: 'B_set_b_set_bool_fun_fun$',B: 'B_set_b_set_bool_fun_fun$',C: 'B_set$',D: 'B_set$'] :
( ( ( D @ ( C @ ( A @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( C @ ( B @ ( A @ 'ordering_top$a' ) ) ) )
=> ( D = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(94,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( A = B )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom211) ).
thf(930,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( A = B )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(260,axiom,
! [A: 'B_set$'] :
( ( A @ ( 'bot$' @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'bot$' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom606) ).
thf(1746,plain,
! [A: 'B_set$'] :
( ( A @ ( 'bot$' @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'bot$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(282,axiom,
! [A: 'B$',B: 'B_set$',C: 'B$'] :
( ( ( B @ ( A @ 'insert$' @ 'fun_app$b' ) )
= ( 'bot$' @ ( C @ 'insert$' @ 'fun_app$b' ) ) )
<=> ( ( 'bot$' @ ( C @ 'insert$' @ 'fun_app$b' ) @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( A = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom198) ).
thf(1835,plain,
! [A: 'B$',B: 'B_set$',C: 'B$'] :
( ( ( ( 'bot$' @ ( C @ 'insert$' @ 'fun_app$b' ) @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( A = C ) )
=> ( ( B @ ( A @ 'insert$' @ 'fun_app$b' ) )
= ( 'bot$' @ ( C @ 'insert$' @ 'fun_app$b' ) ) ) )
& ( ( ( B @ ( A @ 'insert$' @ 'fun_app$b' ) )
= ( 'bot$' @ ( C @ 'insert$' @ 'fun_app$b' ) ) )
=> ( ( 'bot$' @ ( C @ 'insert$' @ 'fun_app$b' ) @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(464,axiom,
( 'top$'
= ( 'top$b' @ ( 'collect$' @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom129) ).
thf(2723,plain,
( 'top$'
= ( 'top$b' @ ( 'collect$' @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(59,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$',C: 'B_bool_fun$'] :
( ( ( C @ ( B @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( C @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom429) ).
thf(782,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$',C: 'B_bool_fun$'] :
( ( ( C @ ( B @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( C @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(240,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( C @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom552) ).
thf(1645,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( C @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(180,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
<=> ( ~ ( A @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom493) ).
thf(1359,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( ~ ( A @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ~ ( A @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(256,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'uminus$' @ 'fun_app$b' ) @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'top$' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom394) ).
thf(1724,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'uminus$' @ 'fun_app$b' ) @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'top$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(181,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ~ ( A @ ( B @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom450) ).
thf(1366,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ~ ( A @ ( B @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(309,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( C @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom51) ).
thf(1967,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( C @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(273,axiom,
! [A: 'B$',B: 'B_set$'] :
( ( B @ ( 'uminus$' @ 'fun_app$b' ) @ ( A @ 'member$' ) )
=> ~ ( B @ ( A @ 'member$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom459) ).
thf(1803,plain,
! [A: 'B$',B: 'B_set$'] :
( ( B @ ( 'uminus$' @ 'fun_app$b' ) @ ( A @ 'member$' ) )
=> ~ ( B @ ( A @ 'member$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(217,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( B @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom587) ).
thf(1518,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( B @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(235,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom629) ).
thf(1623,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(451,axiom,
! [A: 'B_set$'] :
( ( A @ ( A @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'bot$' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom13) ).
thf(2654,plain,
! [A: 'B_set$'] :
( ( A @ ( A @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'bot$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(194,axiom,
! [A: 'B_set$'] : ( A @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom187) ).
thf(1409,plain,
! [A: 'B_set$'] : ( A @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(200,axiom,
! [A: 'B$',B: 'B_bool_fun$'] :
( ( B @ ( 'collect$' @ 'fun_app$d' ) @ ( A @ 'member$' ) )
<=> ( A @ ( B @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom47) ).
thf(1430,plain,
! [A: 'B$',B: 'B_bool_fun$'] :
( ( ( A @ ( B @ 'fun_app$' ) )
=> ( B @ ( 'collect$' @ 'fun_app$d' ) @ ( A @ 'member$' ) ) )
& ( ( B @ ( 'collect$' @ 'fun_app$d' ) @ ( A @ 'member$' ) )
=> ( A @ ( B @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(453,axiom,
! [A: 'B_b_bool_fun_fun$',B: 'B$'] : ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ 'pairwise$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom359) ).
thf(2667,plain,
! [A: 'B_b_bool_fun_fun$',B: 'B$'] : ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ 'pairwise$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(380,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( B @ ( A @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'bot$' )
<=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom358) ).
thf(2339,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( B @ ( A @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'bot$' ) )
& ( ( ( B @ ( A @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'bot$' )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(473,axiom,
! [A: 'B_set$',B: 'B$',C: 'B_set$'] :
( ( C @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( C @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( B @ 'insert$' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom10) ).
thf(2755,plain,
! [A: 'B_set$',B: 'B$',C: 'B_set$'] :
( ( C @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( C @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( B @ 'insert$' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(290,axiom,
! [A: 'B_set$',B: 'B_set$'] : ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom332) ).
thf(1871,plain,
! [A: 'B_set$',B: 'B_set$'] : ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(461,axiom,
! [A: 'B_set$'] :
( ( A != 'top$' )
<=> ( 'top$' @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom535) ).
thf(2708,plain,
! [A: 'B_set$'] :
( ( ( 'top$' @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( A != 'top$' ) )
& ( ( A != 'top$' )
=> ( 'top$' @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(300,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( ( B
= ( A @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) )
=> $false )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom316) ).
thf(1907,plain,
! [A: 'B_set$',B: 'B_set$'] :
~ ( ( B
!= ( A @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(289,axiom,
! [A: 'B$',B: 'B_set$',C: 'B_bool_fun$'] :
( ! [D: 'B$'] :
( ( B @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( D @ 'member$' ) )
=> ( D @ ( C @ 'fun_app$' ) ) )
<=> ( ! [D: 'B$'] :
( ( B @ ( D @ 'member$' ) )
=> ( D @ ( C @ 'fun_app$' ) ) )
& ( A @ ( C @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom159) ).
thf(1860,plain,
! [A: 'B$',B: 'B_set$',C: 'B_bool_fun$'] :
( ( ( ! [D: 'B$'] :
( ( B @ ( D @ 'member$' ) )
=> ( D @ ( C @ 'fun_app$' ) ) )
& ( A @ ( C @ 'fun_app$' ) ) )
=> ! [D: 'B$'] :
( ( B @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( D @ 'member$' ) )
=> ( D @ ( C @ 'fun_app$' ) ) ) )
& ( ! [D: 'B$'] :
( ( B @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( D @ 'member$' ) )
=> ( D @ ( C @ 'fun_app$' ) ) )
=> ( ! [D: 'B$'] :
( ( B @ ( D @ 'member$' ) )
=> ( D @ ( C @ 'fun_app$' ) ) )
& ( A @ ( C @ 'fun_app$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(174,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( C @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom491) ).
thf(1323,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( C @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(364,axiom,
! [A: 'B$'] :
( ( 'bot$' @ ( A @ 'member$' ) )
<=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom18) ).
thf(2274,plain,
! [A: 'B$'] :
~ ( 'bot$' @ ( A @ 'member$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(279,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom304) ).
thf(1826,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(404,axiom,
! [A: 'B$',B: 'B_set$',C: 'B_set$'] :
( ( 'bot$'
= ( C @ ( B @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) ) )
<=> ( ( 'bot$'
= ( C @ ( B @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) ) )
& ~ ( C @ ( A @ 'member$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom627) ).
thf(2466,plain,
! [A: 'B$',B: 'B_set$',C: 'B_set$'] :
( ( ( ( 'bot$'
= ( C @ ( B @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) ) )
& ~ ( C @ ( A @ 'member$' ) ) )
=> ( 'bot$'
= ( C @ ( B @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ) )
& ( ( 'bot$'
= ( C @ ( B @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) ) )
=> ( ( 'bot$'
= ( C @ ( B @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) ) )
& ~ ( C @ ( A @ 'member$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(120,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> $false )
& ( A = B ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom215) ).
thf(1059,plain,
! [A: 'B_set$',B: 'B_set$'] :
~ ( ~ ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(429,axiom,
! [A: 'B$',B: 'B_set$',C: 'B_set$'] :
( ( C @ ( B @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ 'member$' ) )
<=> ( ~ ( C @ ( A @ 'member$' ) )
& ( B @ ( A @ 'member$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom26) ).
thf(2571,plain,
! [A: 'B$',B: 'B_set$',C: 'B_set$'] :
( ( ( ~ ( C @ ( A @ 'member$' ) )
& ( B @ ( A @ 'member$' ) ) )
=> ( C @ ( B @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ 'member$' ) ) )
& ( ( C @ ( B @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ 'member$' ) )
=> ( ~ ( C @ ( A @ 'member$' ) )
& ( B @ ( A @ 'member$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(281,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom630) ).
thf(1832,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(95,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
<=> ( ( A != B )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom540) ).
thf(934,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( ( A != B )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( A != B )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(145,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( A != B ) )
=> ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom517) ).
thf(1191,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( A != B ) )
=> ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(13,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( ~ ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom480) ).
thf(559,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( ( ( A = B )
=> ~ ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
& ( ~ ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(272,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( A @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom138) ).
thf(1800,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( A @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(296,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( C @ ( B @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( C @ ( A @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom72) ).
thf(1892,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( C @ ( B @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( C @ ( A @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(425,axiom,
! [A: 'B_set$'] :
( ( A @ ( 'bot$' @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom127) ).
thf(2552,plain,
! [A: 'B_set$'] :
( ( A @ ( 'bot$' @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(477,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( C @ ( B @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
<=> ( ( C @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom599) ).
thf(2767,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( ( C @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( C @ ( B @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( C @ ( B @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( C @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(101,axiom,
! [A: 'B_set$',B: 'B_b_bool_fun_fun$'] :
( ! [C: 'B$',D: 'B$'] :
( ( ( C != D )
& ( A @ ( D @ 'member$' ) )
& ( A @ ( C @ 'member$' ) ) )
=> ( D @ ( C @ ( B @ 'fun_app$k' ) @ 'fun_app$' ) ) )
=> ( A @ ( B @ 'pairwise$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom213) ).
thf(969,plain,
! [A: 'B_set$',B: 'B_b_bool_fun_fun$'] :
( ! [C: 'B$',D: 'B$'] :
( ( ( C != D )
& ( A @ ( D @ 'member$' ) )
& ( A @ ( C @ 'member$' ) ) )
=> ( D @ ( C @ ( B @ 'fun_app$k' ) @ 'fun_app$' ) ) )
=> ( A @ ( B @ 'pairwise$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(190,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( A = B )
<=> $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom454) ).
thf(1398,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(416,axiom,
! [A: 'B_set$',B: 'B$'] :
( ( A = 'bot$' )
=> ~ ( A @ ( B @ 'member$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom31) ).
thf(2520,plain,
! [A: 'B_set$',B: 'B$'] :
( ( A = 'bot$' )
=> ~ ( A @ ( B @ 'member$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(322,axiom,
! [A: 'B$',B: 'B_set$',C: 'B_set$'] :
( ( ( C @ ( A @ 'member$' ) )
& ( C @ ( B @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ 'member$' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom57) ).
thf(2024,plain,
! [A: 'B$',B: 'B_set$',C: 'B_set$'] :
~ ( ( C @ ( A @ 'member$' ) )
& ( C @ ( B @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ 'member$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(420,axiom,
! [A: 'B$'] : ( 'top$' @ ( A @ 'member$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom19) ).
thf(2533,plain,
! [A: 'B$'] : ( 'top$' @ ( A @ 'member$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(284,axiom,
! [A: 'B_set$',B: 'B_set$'] : ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom350) ).
thf(1847,plain,
! [A: 'B_set$',B: 'B_set$'] : ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(345,axiom,
! [A: 'B_set$'] :
( ( A @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom589) ).
thf(2169,plain,
! [A: 'B_set$'] :
( ( A @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(126,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( 'uminus$' @ 'fun_app$b' ) @ ( A @ ( 'uminus$' @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
<=> ( A @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom385) ).
thf(1087,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( B @ ( 'uminus$' @ 'fun_app$b' ) @ ( A @ ( 'uminus$' @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( B @ ( 'uminus$' @ 'fun_app$b' ) @ ( A @ ( 'uminus$' @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( A @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(111,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( A = B )
| ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom529) ).
thf(1013,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( A = B )
| ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(57,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom423) ).
thf(770,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(210,axiom,
! [A: 'B_set$'] :
( ( A @ ( 'uminus$' @ 'fun_app$b' ) @ ( 'uminus$' @ 'fun_app$b' ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom462) ).
thf(1489,plain,
! [A: 'B_set$'] :
( ( A @ ( 'uminus$' @ 'fun_app$b' ) @ ( 'uminus$' @ 'fun_app$b' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(92,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( A @ ( 'uminus$' @ 'fun_app$b' ) @ ( B @ ( 'uminus$' @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom469) ).
thf(924,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( A @ ( 'uminus$' @ 'fun_app$b' ) @ ( B @ ( 'uminus$' @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(323,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom592) ).
thf(2027,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(184,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom257) ).
thf(1373,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(301,axiom,
! [A: 'B_set$',B: 'B$',C: 'B_set$'] :
( ( C @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
<=> ( ( ~ ( A @ ( B @ 'member$' ) )
=> ( C @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( A @ ( B @ 'member$' ) )
=> ( C @ ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom178) ).
thf(1911,plain,
! [A: 'B_set$',B: 'B$',C: 'B_set$'] :
( ( ( ( ~ ( A @ ( B @ 'member$' ) )
=> ( C @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( A @ ( B @ 'member$' ) )
=> ( C @ ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) )
=> ( C @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( C @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( ~ ( A @ ( B @ 'member$' ) )
=> ( C @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( A @ ( B @ 'member$' ) )
=> ( C @ ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(131,axiom,
! [A: 'B_set$'] :
( ( A @ ( 'uu$' @ 'fun_app$a' ) @ ( 'collect$' @ 'fun_app$d' ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom48) ).
thf(1109,plain,
! [A: 'B_set$'] :
( ( A @ ( 'uu$' @ 'fun_app$a' ) @ ( 'collect$' @ 'fun_app$d' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(400,axiom,
! [A: 'B$'] :
( ( 'top$' @ ( A @ 'member$' ) )
<=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom161) ).
thf(2451,plain,
! [A: 'B$'] : ( 'top$' @ ( A @ 'member$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(177,axiom,
! [A: 'B_b_bool_fun_fun$',B: 'B_set$'] :
( ( B @ ( A @ 'pairwise$' ) )
<=> ! [C: 'B$'] :
( ( B @ ( C @ 'member$' ) )
=> ! [D: 'B$'] :
( ( ( C != D )
& ( B @ ( D @ 'member$' ) ) )
=> ( D @ ( C @ ( A @ 'fun_app$k' ) @ 'fun_app$' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom206) ).
thf(1334,plain,
! [A: 'B_b_bool_fun_fun$',B: 'B_set$'] :
( ( ! [C: 'B$'] :
( ( B @ ( C @ 'member$' ) )
=> ! [D: 'B$'] :
( ( ( C != D )
& ( B @ ( D @ 'member$' ) ) )
=> ( D @ ( C @ ( A @ 'fun_app$k' ) @ 'fun_app$' ) ) ) )
=> ( B @ ( A @ 'pairwise$' ) ) )
& ( ( B @ ( A @ 'pairwise$' ) )
=> ! [C: 'B$'] :
( ( B @ ( C @ 'member$' ) )
=> ! [D: 'B$'] :
( ( ( C != D )
& ( B @ ( D @ 'member$' ) ) )
=> ( D @ ( C @ ( A @ 'fun_app$k' ) @ 'fun_app$' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(248,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( 'top$'
= ( B @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) ) )
<=> ( ( B = 'top$' )
& ( A = 'top$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom622) ).
thf(1682,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( ( B = 'top$' )
& ( A = 'top$' ) )
=> ( 'top$'
= ( B @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ) )
& ( ( 'top$'
= ( B @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) ) )
=> ( ( B = 'top$' )
& ( A = 'top$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(288,axiom,
! [A: 'B_set$'] : ( 'top$' @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom275) ).
thf(1858,plain,
! [A: 'B_set$'] : ( 'top$' @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(361,axiom,
! [A: 'B$',B: 'B$'] :
( ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ 'member$' ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom64) ).
thf(2254,plain,
! [A: 'B$',B: 'B$'] :
( ( ( A = B )
=> ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ 'member$' ) ) )
& ( ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ 'member$' ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(246,axiom,
! [A: 'B$',B: 'B_set$',C: 'B_set$'] :
( ( ( B @ ( C @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ 'member$' ) ) )
=> ( B @ ( C @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom365) ).
thf(1677,plain,
! [A: 'B$',B: 'B_set$',C: 'B_set$'] :
( ( ( B @ ( C @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ 'member$' ) ) )
=> ( B @ ( C @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(378,axiom,
'bot$' @ ( 'sup$' @ 'semilattice_neutr$b' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom183) ).
thf(2335,plain,
'bot$' @ ( 'sup$' @ 'semilattice_neutr$b' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(165,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
<=> ( ( A = B )
| ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom509) ).
thf(1283,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( ( A = B )
| ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( A = B )
| ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(119,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
<=> ! [C: 'B$'] :
( ( A @ ( C @ 'member$' ) )
=> ( B @ ( C @ 'member$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom209) ).
thf(1051,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( ! [C: 'B$'] :
( ( A @ ( C @ 'member$' ) )
=> ( B @ ( C @ 'member$' ) ) )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ! [C: 'B$'] :
( ( A @ ( C @ 'member$' ) )
=> ( B @ ( C @ 'member$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(169,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom505) ).
thf(1302,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(243,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( C @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( C @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom154) ).
thf(1664,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( C @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( C @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(337,axiom,
! [A: 'B_set$'] :
( ( A @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom590) ).
thf(2105,plain,
! [A: 'B_set$'] :
( ( A @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(205,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( A = B )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom229) ).
thf(1450,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( A = B )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(426,axiom,
! [A: 'B$',B: 'B_set$',C: 'B_set$'] :
( ( ( C @ ( B @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'bot$' )
<=> ( ( ( C @ ( B @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'bot$' )
& ~ ( C @ ( A @ 'member$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom628) ).
thf(2555,plain,
! [A: 'B$',B: 'B_set$',C: 'B_set$'] :
( ( ( ( ( C @ ( B @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'bot$' )
& ~ ( C @ ( A @ 'member$' ) ) )
=> ( ( C @ ( B @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'bot$' ) )
& ( ( ( C @ ( B @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'bot$' )
=> ( ( ( C @ ( B @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'bot$' )
& ~ ( C @ ( A @ 'member$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(65,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$',C: 'B_bool_fun_b_set_fun$',D: 'B_set$'] :
( ( ! [E: 'B_bool_fun$',F: 'B_bool_fun$'] :
( ( F @ ( E @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( F @ ( C @ 'fun_app$d' ) @ ( E @ ( C @ 'fun_app$d' ) @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( D @ ( B @ ( C @ 'fun_app$d' ) @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$d' ) @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom446) ).
thf(806,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$',C: 'B_bool_fun_b_set_fun$',D: 'B_set$'] :
( ( ! [E: 'B_bool_fun$',F: 'B_bool_fun$'] :
( ( F @ ( E @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( F @ ( C @ 'fun_app$d' ) @ ( E @ ( C @ 'fun_app$d' ) @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( D @ ( B @ ( C @ 'fun_app$d' ) @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$d' ) @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(38,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom504) ).
thf(687,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(492,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( A @ ( B @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom594) ).
thf(2833,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( A @ ( B @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(407,axiom,
! [A: 'B_set$',B: 'B$',C: 'B_set$'] :
( ( C @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( C @ ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom77) ).
thf(2483,plain,
! [A: 'B_set$',B: 'B$',C: 'B_set$'] :
( ( C @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( C @ ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(294,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( A @ ( B @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom364) ).
thf(1886,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( A @ ( B @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(58,axiom,
! [A: 'B_bool_fun$',B: 'B_set_b_bool_fun_fun$',C: 'B_set$',D: 'B_set$'] :
( ( ! [E: 'B_set$',F: 'B_set$'] :
( ( F @ ( E @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( F @ ( B @ 'fun_app$a' ) @ ( E @ ( B @ 'fun_app$a' ) @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
& ( D @ ( C @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( A
= ( C @ ( B @ 'fun_app$a' ) ) ) )
=> ( D @ ( B @ 'fun_app$a' ) @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom224) ).
thf(774,plain,
! [A: 'B_bool_fun$',B: 'B_set_b_bool_fun_fun$',C: 'B_set$',D: 'B_set$'] :
( ( ! [E: 'B_set$',F: 'B_set$'] :
( ( F @ ( E @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( F @ ( B @ 'fun_app$a' ) @ ( E @ ( B @ 'fun_app$a' ) @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
& ( D @ ( C @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( A
= ( C @ ( B @ 'fun_app$a' ) ) ) )
=> ( D @ ( B @ 'fun_app$a' ) @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(188,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B$'] :
( ( ( A @ ( C @ 'member$' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( B @ ( C @ 'member$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom460) ).
thf(1394,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B$'] :
( ( ( A @ ( C @ 'member$' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( B @ ( C @ 'member$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(475,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( B @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( B @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom586) ).
thf(2762,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( B @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( B @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(122,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom188) ).
thf(1072,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(419,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( C @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( B @ ( A @ ( 'uminus$' @ 'fun_app$b' ) @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'top$' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom561) ).
thf(2530,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( C @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( B @ ( A @ ( 'uminus$' @ 'fun_app$b' ) @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'top$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(105,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( 'uminus$' @ 'fun_app$b' ) @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( A @ ( 'uminus$' @ 'fun_app$b' ) @ ( B @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom464) ).
thf(998,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( 'uminus$' @ 'fun_app$b' ) @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( A @ ( 'uminus$' @ 'fun_app$b' ) @ ( B @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(486,axiom,
! [A: 'B$',B: 'B_set$',C: 'B_set$'] :
( ~ ( B @ ( A @ 'member$' ) )
=> ( ( B @ ( C @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( B @ ( C @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom580) ).
thf(2809,plain,
! [A: 'B$',B: 'B_set$',C: 'B_set$'] :
( ~ ( B @ ( A @ 'member$' ) )
=> ( ( B @ ( C @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( B @ ( C @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(358,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( B @ ( C @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom547) ).
thf(2242,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( B @ ( C @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(483,axiom,
! [A: 'B_set$'] :
( ! [B: 'B$'] :
( ( A @ ( B @ 'member$' ) )
=> $false )
=> ( A = 'bot$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom30) ).
thf(2799,plain,
! [A: 'B_set$'] :
( ! [B: 'B$'] :
~ ( A @ ( B @ 'member$' ) )
=> ( A = 'bot$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(448,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$',D: 'B_set$'] :
( ( ( D @ ( C @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( D @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( C @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom324) ).
thf(2639,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$',D: 'B_set$'] :
( ( ( D @ ( C @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( D @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( C @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(308,axiom,
! [A: 'B$',B: 'B_set$',C: 'B$',D: 'B_set$'] :
( ( ~ ( D @ ( C @ 'member$' ) )
& ~ ( B @ ( A @ 'member$' ) ) )
=> ( ( ( B @ ( A @ 'insert$' @ 'fun_app$b' ) )
= ( D @ ( C @ 'insert$' @ 'fun_app$b' ) ) )
<=> ( ( ( A != C )
=> ? [E: 'B_set$'] :
( ~ ( E @ ( A @ 'member$' ) )
& ( D
= ( E @ ( A @ 'insert$' @ 'fun_app$b' ) ) )
& ~ ( E @ ( C @ 'member$' ) )
& ( B
= ( E @ ( C @ 'insert$' @ 'fun_app$b' ) ) ) ) )
& ( ( A = C )
=> ( B = D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom37) ).
thf(1943,plain,
! [A: 'B$',B: 'B_set$',C: 'B$',D: 'B_set$'] :
( ( ~ ( D @ ( C @ 'member$' ) )
& ~ ( B @ ( A @ 'member$' ) ) )
=> ( ( ( ( ( A != C )
=> ? [E: 'B_set$'] :
( ~ ( E @ ( A @ 'member$' ) )
& ( D
= ( E @ ( A @ 'insert$' @ 'fun_app$b' ) ) )
& ~ ( E @ ( C @ 'member$' ) )
& ( B
= ( E @ ( C @ 'insert$' @ 'fun_app$b' ) ) ) ) )
& ( ( A = C )
=> ( B = D ) ) )
=> ( ( B @ ( A @ 'insert$' @ 'fun_app$b' ) )
= ( D @ ( C @ 'insert$' @ 'fun_app$b' ) ) ) )
& ( ( ( B @ ( A @ 'insert$' @ 'fun_app$b' ) )
= ( D @ ( C @ 'insert$' @ 'fun_app$b' ) ) )
=> ( ( ( A != C )
=> ? [E: 'B_set$'] :
( ~ ( E @ ( A @ 'member$' ) )
& ( D
= ( E @ ( A @ 'insert$' @ 'fun_app$b' ) ) )
& ~ ( E @ ( C @ 'member$' ) )
& ( B
= ( E @ ( C @ 'insert$' @ 'fun_app$b' ) ) ) ) )
& ( ( A = C )
=> ( B = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(149,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
<=> ( ~ ( A @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom543) ).
thf(1201,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( ~ ( A @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ~ ( A @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(387,axiom,
! [A: 'B_set$'] :
( ( A @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom117) ).
thf(2392,plain,
! [A: 'B_set$'] :
( ( A @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(218,axiom,
! [A: 'B$',B: 'B_set$',C: 'B_set$'] :
( ( ~ ( C @ ( A @ 'member$' ) )
& ~ ( B @ ( A @ 'member$' ) ) )
=> ( ( ( B @ ( A @ 'insert$' @ 'fun_app$b' ) )
= ( C @ ( A @ 'insert$' @ 'fun_app$b' ) ) )
<=> ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom39) ).
thf(1521,plain,
! [A: 'B$',B: 'B_set$',C: 'B_set$'] :
( ( ~ ( C @ ( A @ 'member$' ) )
& ~ ( B @ ( A @ 'member$' ) ) )
=> ( ( ( B = C )
=> ( ( B @ ( A @ 'insert$' @ 'fun_app$b' ) )
= ( C @ ( A @ 'insert$' @ 'fun_app$b' ) ) ) )
& ( ( ( B @ ( A @ 'insert$' @ 'fun_app$b' ) )
= ( C @ ( A @ 'insert$' @ 'fun_app$b' ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(90,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ~ ( A @ ( B @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom475) ).
thf(920,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ~ ( A @ ( B @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(450,axiom,
! [A: 'B_bool_fun$'] :
( ( ( A @ ( 'collect$' @ 'fun_app$d' ) )
= 'bot$' )
<=> ! [B: 'B$'] :
~ ( B @ ( A @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom16) ).
thf(2646,plain,
! [A: 'B_bool_fun$'] :
( ( ! [B: 'B$'] :
~ ( B @ ( A @ 'fun_app$' ) )
=> ( ( A @ ( 'collect$' @ 'fun_app$d' ) )
= 'bot$' ) )
& ( ( ( A @ ( 'collect$' @ 'fun_app$d' ) )
= 'bot$' )
=> ! [B: 'B$'] :
~ ( B @ ( A @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(148,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( C @ ( B @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( C @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom519) ).
thf(1199,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( C @ ( B @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( C @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(66,axiom,
! [A: 'B_bool_fun$',B: 'B_set_b_bool_fun_fun$',C: 'B_set$',D: 'B_set$'] :
( ( ! [E: 'B_set$',F: 'B_set$'] :
( ( F @ ( E @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( F @ ( B @ 'fun_app$a' ) @ ( E @ ( B @ 'fun_app$a' ) @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
& ( D @ ( C @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( C @ ( B @ 'fun_app$a' ) @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( D @ ( B @ 'fun_app$a' ) @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom523) ).
thf(810,plain,
! [A: 'B_bool_fun$',B: 'B_set_b_bool_fun_fun$',C: 'B_set$',D: 'B_set$'] :
( ( ! [E: 'B_set$',F: 'B_set$'] :
( ( F @ ( E @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( F @ ( B @ 'fun_app$a' ) @ ( E @ ( B @ 'fun_app$a' ) @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
& ( D @ ( C @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( C @ ( B @ 'fun_app$a' ) @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( D @ ( B @ 'fun_app$a' ) @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(469,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$',D: 'B_set$'] :
( ( A
= ( C @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) )
=> ( ( D @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( D @ ( C @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom148) ).
thf(2737,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$',D: 'B_set$'] :
( ( A
= ( C @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) )
=> ( ( D @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( D @ ( C @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(369,axiom,
! [A: 'B$',B: 'B$',C: 'B_set$'] :
( ( C @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ 'member$' ) )
<=> ( ( C @ ( A @ 'member$' ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom21) ).
thf(2296,plain,
! [A: 'B$',B: 'B$',C: 'B_set$'] :
( ( ( ( C @ ( A @ 'member$' ) )
| ( A = B ) )
=> ( C @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ 'member$' ) ) )
& ( ( C @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ 'member$' ) )
=> ( ( C @ ( A @ 'member$' ) )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(449,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$',D: 'B_set$'] :
( ( A
= ( C @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) )
=> ( ( A @ ( D @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( C @ ( D @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom150) ).
thf(2641,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$',D: 'B_set$'] :
( ( A
= ( C @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) )
=> ( ( A @ ( D @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( C @ ( D @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(316,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set_b_set_fun$',D: 'B_set$'] :
( ( ! [E: 'B_set$',F: 'B_set$'] :
( ( F @ ( E @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( F @ ( C @ 'fun_app$b' ) @ ( E @ ( C @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( D @ ( B @ ( C @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom233) ).
thf(2000,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set_b_set_fun$',D: 'B_set$'] :
( ( ! [E: 'B_set$',F: 'B_set$'] :
( ( F @ ( E @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( F @ ( C @ 'fun_app$b' ) @ ( E @ ( C @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( D @ ( B @ ( C @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(64,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set_b_bool_fun_fun$',D: 'B_bool_fun$'] :
( ( ! [E: 'B_set$',F: 'B_set$'] :
( ( F @ ( E @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( F @ ( C @ 'fun_app$a' ) @ ( E @ ( C @ 'fun_app$a' ) @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
& ( ( B @ ( C @ 'fun_app$a' ) )
= D )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$a' ) @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom220) ).
thf(798,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set_b_bool_fun_fun$',D: 'B_bool_fun$'] :
( ( ! [E: 'B_set$',F: 'B_set$'] :
( ( F @ ( E @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( F @ ( C @ 'fun_app$a' ) @ ( E @ ( C @ 'fun_app$a' ) @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
& ( ( B @ ( C @ 'fun_app$a' ) )
= D )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$a' ) @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(436,axiom,
! [A: 'B_set$'] :
( ( 'top$' @ ( A @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'bot$' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom4) ).
thf(2601,plain,
! [A: 'B_set$'] :
( ( 'top$' @ ( A @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'bot$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(70,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set_b_bool_fun_fun$',D: 'B_bool_fun$'] :
( ( ! [E: 'B_set$',F: 'B_set$'] :
( ( F @ ( E @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( F @ ( C @ 'fun_app$a' ) @ ( E @ ( C @ 'fun_app$a' ) @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
& ( ( B @ ( C @ 'fun_app$a' ) )
= D )
& ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$a' ) @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom435) ).
thf(825,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set_b_bool_fun_fun$',D: 'B_bool_fun$'] :
( ( ! [E: 'B_set$',F: 'B_set$'] :
( ( F @ ( E @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( F @ ( C @ 'fun_app$a' ) @ ( E @ ( C @ 'fun_app$a' ) @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
& ( ( B @ ( C @ 'fun_app$a' ) )
= D )
& ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$a' ) @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(228,axiom,
! [A: 'B$',B: 'B_set$',C: 'B_set$'] :
( ( C @ ( B @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( C @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ 'insert$' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom9) ).
thf(1570,plain,
! [A: 'B$',B: 'B_set$',C: 'B_set$'] :
( ( C @ ( B @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( C @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ 'insert$' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(213,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
<=> ( B
= ( A @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom298) ).
thf(1502,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( B
= ( A @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( B
= ( A @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(28,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( ( A @ ( B @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom248) ).
thf(630,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( ( A @ ( B @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(418,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( B @ ( C @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( B @ ( C @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom351) ).
thf(2528,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( B @ ( C @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( B @ ( C @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(319,axiom,
! [A: 'B$',B: 'B_set$',C: 'B_set$'] :
( ( B @ ( A @ 'member$' ) )
=> ( ( B @ ( C @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( B @ ( C @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ 'insert$' @ 'fun_app$b' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom581) ).
thf(2015,plain,
! [A: 'B$',B: 'B_set$',C: 'B_set$'] :
( ( B @ ( A @ 'member$' ) )
=> ( ( B @ ( C @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( B @ ( C @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ 'insert$' @ 'fun_app$b' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(460,axiom,
! [A: 'B_set$'] :
( ( 'bot$' @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'bot$' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom608) ).
thf(2705,plain,
! [A: 'B_set$'] :
( ( 'bot$' @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'bot$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(363,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( 'bot$'
= ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) )
<=> ( ( B = 'bot$' )
& ( A = 'bot$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom97) ).
thf(2264,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( ( B = 'bot$' )
& ( A = 'bot$' ) )
=> ( 'bot$'
= ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ) )
& ( ( 'bot$'
= ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) )
=> ( ( B = 'bot$' )
& ( A = 'bot$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(230,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B$'] :
( ( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( 'bot$' @ ( C @ 'insert$' @ 'fun_app$b' ) ) )
<=> ( ( ( B
= ( 'bot$' @ ( C @ 'insert$' @ 'fun_app$b' ) ) )
& ( A
= ( 'bot$' @ ( C @ 'insert$' @ 'fun_app$b' ) ) ) )
| ( ( B = 'bot$' )
& ( A
= ( 'bot$' @ ( C @ 'insert$' @ 'fun_app$b' ) ) ) )
| ( ( B
= ( 'bot$' @ ( C @ 'insert$' @ 'fun_app$b' ) ) )
& ( A = 'bot$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom74) ).
thf(1580,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B$'] :
( ( ( ( ( B
= ( 'bot$' @ ( C @ 'insert$' @ 'fun_app$b' ) ) )
& ( A
= ( 'bot$' @ ( C @ 'insert$' @ 'fun_app$b' ) ) ) )
| ( ( B = 'bot$' )
& ( A
= ( 'bot$' @ ( C @ 'insert$' @ 'fun_app$b' ) ) ) )
| ( ( B
= ( 'bot$' @ ( C @ 'insert$' @ 'fun_app$b' ) ) )
& ( A = 'bot$' ) ) )
=> ( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( 'bot$' @ ( C @ 'insert$' @ 'fun_app$b' ) ) ) )
& ( ( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( 'bot$' @ ( C @ 'insert$' @ 'fun_app$b' ) ) )
=> ( ( ( B
= ( 'bot$' @ ( C @ 'insert$' @ 'fun_app$b' ) ) )
& ( A
= ( 'bot$' @ ( C @ 'insert$' @ 'fun_app$b' ) ) ) )
| ( ( B = 'bot$' )
& ( A
= ( 'bot$' @ ( C @ 'insert$' @ 'fun_app$b' ) ) ) )
| ( ( B
= ( 'bot$' @ ( C @ 'insert$' @ 'fun_app$b' ) ) )
& ( A = 'bot$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(365,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( A @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom146) ).
thf(2277,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( A @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(19,axiom,
! [A: 'B_bool_fun$'] :
( ( A @ ( 'top$b' @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( A = 'top$b' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom280) ).
thf(598,plain,
! [A: 'B_bool_fun$'] :
( ( A @ ( 'top$b' @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( A = 'top$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(342,axiom,
! [A: 'B$',B: 'B_set$',C: 'B$'] :
( ( B @ ( A @ 'member$' ) )
=> ( B @ ( C @ 'insert$' @ 'fun_app$b' ) @ ( A @ 'member$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom41) ).
thf(2147,plain,
! [A: 'B$',B: 'B_set$',C: 'B$'] :
( ( B @ ( A @ 'member$' ) )
=> ( B @ ( C @ 'insert$' @ 'fun_app$b' ) @ ( A @ 'member$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(343,axiom,
! [A: 'B_set$',B: 'B_set$'] : ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom338) ).
thf(2150,plain,
! [A: 'B_set$',B: 'B_set$'] : ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(183,axiom,
! [A: 'B_b_bool_fun_fun$',B: 'B_set$',C: 'B$',D: 'B$'] :
( ( ( C != D )
& ( B @ ( D @ 'member$' ) )
& ( B @ ( C @ 'member$' ) )
& ( B @ ( A @ 'pairwise$' ) ) )
=> ( D @ ( C @ ( A @ 'fun_app$k' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom214) ).
thf(1370,plain,
! [A: 'B_b_bool_fun_fun$',B: 'B_set$',C: 'B$',D: 'B$'] :
( ( ( C != D )
& ( B @ ( D @ 'member$' ) )
& ( B @ ( C @ 'member$' ) )
& ( B @ ( A @ 'pairwise$' ) ) )
=> ( D @ ( C @ ( A @ 'fun_app$k' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(116,axiom,
! [A: 'B$'] :
( ( A @ ( 'bot$b' @ 'fun_app$' ) )
<=> 'bot$a' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom163) ).
thf(1032,plain,
! [A: 'B$'] :
( ( 'bot$a'
=> ( A @ ( 'bot$b' @ 'fun_app$' ) ) )
& ( ( A @ ( 'bot$b' @ 'fun_app$' ) )
=> 'bot$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(445,axiom,
! [A: 'B$',B: 'B_set$'] :
( ( B @ ( A @ 'member$' ) )
=> ? [C: 'B_set$'] :
( ~ ( C @ ( A @ 'member$' ) )
& ( B
= ( C @ ( A @ 'insert$' @ 'fun_app$b' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom35) ).
thf(2628,plain,
! [A: 'B$',B: 'B_set$'] :
( ( B @ ( A @ 'member$' ) )
=> ? [C: 'B_set$'] :
( ~ ( C @ ( A @ 'member$' ) )
& ( B
= ( C @ ( A @ 'insert$' @ 'fun_app$b' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(427,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( C @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( C @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom152) ).
thf(2565,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( C @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( C @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(330,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( B @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( B @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom585) ).
thf(2068,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( B @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( B @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(349,axiom,
! [A: 'B_set$'] :
( ( A @ ( 'uminus$' @ 'fun_app$b' ) @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'top$' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom562) ).
thf(2200,plain,
! [A: 'B_set$'] :
( ( A @ ( 'uminus$' @ 'fun_app$b' ) @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'top$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(242,axiom,
! [A: 'B$',B: 'B_set$',C: 'B_set$'] :
( ( ~ ( C @ ( A @ 'member$' ) )
=> ( ( C @ ( B @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( C @ ( B @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ 'insert$' @ 'fun_app$b' ) ) ) )
& ( ( C @ ( A @ 'member$' ) )
=> ( ( C @ ( B @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( C @ ( B @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom71) ).
thf(1656,plain,
! [A: 'B$',B: 'B_set$',C: 'B_set$'] :
( ( ~ ( C @ ( A @ 'member$' ) )
=> ( ( C @ ( B @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( C @ ( B @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ 'insert$' @ 'fun_app$b' ) ) ) )
& ( ( C @ ( A @ 'member$' ) )
=> ( ( C @ ( B @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( C @ ( B @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(124,axiom,
! [A: 'B$'] :
( ( A @ ( 'top$b' @ 'fun_app$' ) )
<=> 'top$a' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom162) ).
thf(1079,plain,
! [A: 'B$'] :
( ( 'top$a'
=> ( A @ ( 'top$b' @ 'fun_app$' ) ) )
& ( ( A @ ( 'top$b' @ 'fun_app$' ) )
=> 'top$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(193,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B$'] :
( ( ( A @ ( C @ 'member$' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( B @ ( C @ 'member$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom217) ).
thf(1407,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B$'] :
( ( ( A @ ( C @ 'member$' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( B @ ( C @ 'member$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(43,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom506) ).
thf(710,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(229,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( C @ ( B @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
<=> ( ( C @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom579) ).
thf(1573,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( ( C @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( C @ ( B @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( C @ ( B @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( C @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(89,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom421) ).
thf(916,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(398,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( A @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom144) ).
thf(2445,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( A @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(474,axiom,
! [A: 'B$',B: 'B_set$',C: 'B_set$'] :
( ~ ( B @ ( A @ 'member$' ) )
=> ( ( C @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( B @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( C @ ( B @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom7) ).
thf(2758,plain,
! [A: 'B$',B: 'B_set$',C: 'B_set$'] :
( ~ ( B @ ( A @ 'member$' ) )
=> ( ( C @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( B @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( C @ ( B @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(14,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
<=> ( ~ ( A @ ( B @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom502) ).
thf(566,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( ( ~ ( A @ ( B @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
& ( ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( ~ ( A @ ( B @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(225,axiom,
( ( 'top$' @ ( 'uminus$' @ 'fun_app$b' ) )
= 'bot$' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom555) ).
thf(1555,plain,
( ( 'top$' @ ( 'uminus$' @ 'fun_app$b' ) )
= 'bot$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(377,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( B @ ( A @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom6) ).
thf(2332,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( B @ ( A @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(490,axiom,
'a$' = 'b$',
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom2) ).
thf(2826,plain,
'a$' = 'b$',
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(167,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( C @ ( B @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( A = B ) )
=> ( C @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom410) ).
thf(1296,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( C @ ( B @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( A = B ) )
=> ( C @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(36,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( A = B )
<=> ( ( A @ ( B @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom262) ).
thf(665,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( ( ( A @ ( B @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( B @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(191,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom513) ).
thf(1402,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(359,axiom,
! [A: 'B$'] :
( ( A @ ( 'top$b' @ 'fun_app$' ) )
<=> ( 'top$' @ ( A @ 'member$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom173) ).
thf(2245,plain,
! [A: 'B$'] :
( ( ( 'top$' @ ( A @ 'member$' ) )
=> ( A @ ( 'top$b' @ 'fun_app$' ) ) )
& ( ( A @ ( 'top$b' @ 'fun_app$' ) )
=> ( 'top$' @ ( A @ 'member$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(313,axiom,
! [A: 'B_set$',B: 'B$',C: 'B_set$'] :
( ( 'bot$'
= ( C @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) ) )
<=> ( ( 'bot$'
= ( C @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) ) )
& ~ ( A @ ( B @ 'member$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom625) ).
thf(1983,plain,
! [A: 'B_set$',B: 'B$',C: 'B_set$'] :
( ( ( ( 'bot$'
= ( C @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) ) )
& ~ ( A @ ( B @ 'member$' ) ) )
=> ( 'bot$'
= ( C @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ) )
& ( ( 'bot$'
= ( C @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) ) )
=> ( ( 'bot$'
= ( C @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) ) )
& ~ ( A @ ( B @ 'member$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(494,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( B @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'top$' )
<=> ( ( B = 'top$' )
& ( A = 'top$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom578) ).
thf(2840,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( ( B = 'top$' )
& ( A = 'top$' ) )
=> ( ( B @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'top$' ) )
& ( ( ( B @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'top$' )
=> ( ( B = 'top$' )
& ( A = 'top$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(176,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( 'uminus$' @ 'fun_app$b' ) @ ( A @ ( 'uminus$' @ 'fun_app$b' ) @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
<=> ( A @ ( B @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom382) ).
thf(1328,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( A @ ( B @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( B @ ( 'uminus$' @ 'fun_app$b' ) @ ( A @ ( 'uminus$' @ 'fun_app$b' ) @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( B @ ( 'uminus$' @ 'fun_app$b' ) @ ( A @ ( 'uminus$' @ 'fun_app$b' ) @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( A @ ( B @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(78,axiom,
! [A: 'B_bool_fun$'] :
~ ( A @ ( 'top$b' @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom536) ).
thf(869,plain,
! [A: 'B_bool_fun$'] :
~ ( A @ ( 'top$b' @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(24,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$',C: 'B_bool_fun$'] :
( ( ( B = C )
& ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( C @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom258) ).
thf(610,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$',C: 'B_bool_fun$'] :
( ( ( B = C )
& ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( C @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(3,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( ( A @ ( B @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom218) ).
thf(499,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( ( ( B = A )
=> ( A @ ( B @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
& ( ( A @ ( B @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(310,axiom,
( ( 'top$' @ ( 'uminus$' @ 'fun_app$b' ) )
= 'bot$' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom388) ).
thf(1970,plain,
( ( 'top$' @ ( 'uminus$' @ 'fun_app$b' ) )
= 'bot$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(154,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( C @ ( B @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( C @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom461) ).
thf(1227,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( C @ ( B @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( C @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(136,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
<=> ( ~ ( A @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom483) ).
thf(1138,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( ~ ( A @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ~ ( A @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(254,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ? [C: 'B$'] : ( A @ ( B @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( C @ 'member$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom554) ).
thf(1719,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ? [C: 'B$'] : ( A @ ( B @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( C @ 'member$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(227,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( C @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom328) ).
thf(1567,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( C @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(402,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( A @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom548) ).
thf(2460,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( A @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(82,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( ( B = A )
<=> $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom455) ).
thf(884,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(140,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( C @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom542) ).
thf(1160,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( C @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(372,axiom,
! [A: 'B_set$'] :
~ ( A @ ( 'top$' @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom537) ).
thf(2312,plain,
! [A: 'B_set$'] :
~ ( A @ ( 'top$' @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(306,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( B @ ( C @ 'insert$' @ 'fun_app$b' ) @ ( A @ ( C @ 'insert$' @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom344) ).
thf(1937,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( B @ ( C @ 'insert$' @ 'fun_app$b' ) @ ( A @ ( C @ 'insert$' @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(346,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'uminus$' @ 'fun_app$b' ) )
= ( B @ ( A @ ( 'uminus$' @ 'fun_app$b' ) @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom404) ).
thf(2172,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'uminus$' @ 'fun_app$b' ) )
= ( B @ ( A @ ( 'uminus$' @ 'fun_app$b' ) @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(295,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'uminus$' @ 'fun_app$b' ) @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'top$' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom397) ).
thf(1889,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'uminus$' @ 'fun_app$b' ) @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'top$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(86,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$',C: 'B_bool_fun_b_set_fun$',D: 'B_set$'] :
( ( ! [E: 'B_bool_fun$',F: 'B_bool_fun$'] :
( ( F @ ( E @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( F @ ( C @ 'fun_app$d' ) @ ( E @ ( C @ 'fun_app$d' ) @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( B @ ( C @ 'fun_app$d' ) )
= D )
& ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$d' ) @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom436) ).
thf(901,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$',C: 'B_bool_fun_b_set_fun$',D: 'B_set$'] :
( ( ! [E: 'B_bool_fun$',F: 'B_bool_fun$'] :
( ( F @ ( E @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( F @ ( C @ 'fun_app$d' ) @ ( E @ ( C @ 'fun_app$d' ) @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( B @ ( C @ 'fun_app$d' ) )
= D )
& ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$d' ) @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(123,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ! [C: 'B$'] :
( ( C @ ( A @ 'fun_app$' ) )
=> ( C @ ( B @ 'fun_app$' ) ) )
=> ( B @ ( 'collect$' @ 'fun_app$d' ) @ ( A @ ( 'collect$' @ 'fun_app$d' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom207) ).
thf(1075,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ! [C: 'B$'] :
( ( C @ ( A @ 'fun_app$' ) )
=> ( C @ ( B @ 'fun_app$' ) ) )
=> ( B @ ( 'collect$' @ 'fun_app$d' ) @ ( A @ ( 'collect$' @ 'fun_app$d' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(196,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom541) ).
thf(1414,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(357,axiom,
! [A: 'B$'] : ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( A @ 'member$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom28) ).
thf(2240,plain,
! [A: 'B$'] : ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( A @ 'member$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(338,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set_b_set_fun$',D: 'B_set$'] :
( ( ! [E: 'B_set$',F: 'B_set$'] :
( ( F @ ( E @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( F @ ( C @ 'fun_app$b' ) @ ( E @ ( C @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( B @ ( C @ 'fun_app$b' ) )
= D )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom223) ).
thf(2108,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set_b_set_fun$',D: 'B_set$'] :
( ( ! [E: 'B_set$',F: 'B_set$'] :
( ( F @ ( E @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( F @ ( C @ 'fun_app$b' ) @ ( E @ ( C @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( B @ ( C @ 'fun_app$b' ) )
= D )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(327,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$',D: 'B_set$'] :
( ( ( D @ ( C @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( C @ ( B @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( D @ ( A @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom355) ).
thf(2038,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$',D: 'B_set$'] :
( ( ( D @ ( C @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( C @ ( B @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( D @ ( A @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(204,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set_b_set_fun$',D: 'B_set$'] :
( ( ! [E: 'B_set$',F: 'B_set$'] :
( ( F @ ( E @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( F @ ( C @ 'fun_app$b' ) @ ( E @ ( C @ 'fun_app$b' ) @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( D @ ( B @ ( C @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$b' ) @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom528) ).
thf(1446,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set_b_set_fun$',D: 'B_set$'] :
( ( ! [E: 'B_set$',F: 'B_set$'] :
( ( F @ ( E @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( F @ ( C @ 'fun_app$b' ) @ ( E @ ( C @ 'fun_app$b' ) @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( D @ ( B @ ( C @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$b' ) @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(112,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( A @ ( B @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom426) ).
thf(1016,plain,
! [A: 'B_set$',B: 'B_set$'] :
~ ( ( A @ ( B @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(333,axiom,
! [A: 'B_set$'] : ( 'top$' @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom283) ).
thf(2085,plain,
! [A: 'B_set$'] : ( 'top$' @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(138,axiom,
! [A: 'B_set$'] :
~ ( A @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom440) ).
thf(1155,plain,
! [A: 'B_set$'] :
~ ( A @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(11,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
<=> ( ( A = B )
| ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom484) ).
thf(547,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( ( ( A = B )
| ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
& ( ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( ( A = B )
| ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(72,axiom,
! [A: 'B_set$',B: 'B_bool_fun_b_set_fun$',C: 'B_bool_fun$',D: 'B_bool_fun$'] :
( ( ! [E: 'B_bool_fun$',F: 'B_bool_fun$'] :
( ( F @ ( E @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( F @ ( B @ 'fun_app$d' ) @ ( E @ ( B @ 'fun_app$d' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( D @ ( C @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( A
= ( C @ ( B @ 'fun_app$d' ) ) ) )
=> ( D @ ( B @ 'fun_app$d' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom225) ).
thf(837,plain,
! [A: 'B_set$',B: 'B_bool_fun_b_set_fun$',C: 'B_bool_fun$',D: 'B_bool_fun$'] :
( ( ! [E: 'B_bool_fun$',F: 'B_bool_fun$'] :
( ( F @ ( E @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( F @ ( B @ 'fun_app$d' ) @ ( E @ ( B @ 'fun_app$d' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( D @ ( C @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( A
= ( C @ ( B @ 'fun_app$d' ) ) ) )
=> ( D @ ( B @ 'fun_app$d' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(32,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
<=> ( ~ ( A @ ( B @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom482) ).
thf(647,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( ( ~ ( A @ ( B @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
& ( ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( ~ ( A @ ( B @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(435,axiom,
! [A: 'B$',B: 'B_set$'] :
( ( B @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( A @ 'insert$' @ 'fun_app$b' ) )
= ( B @ ( A @ 'insert$' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom20) ).
thf(2598,plain,
! [A: 'B$',B: 'B_set$'] :
( ( B @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( A @ 'insert$' @ 'fun_app$b' ) )
= ( B @ ( A @ 'insert$' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(33,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$',C: 'B_bool_fun$'] :
( ( ( C @ ( B @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( C @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom254) ).
thf(654,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$',C: 'B_bool_fun$'] :
( ( ( C @ ( B @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( C @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(224,axiom,
! [A: 'B_set$'] :
( ( A @ ( 'top$' @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'top$' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom91) ).
thf(1552,plain,
! [A: 'B_set$'] :
( ( A @ ( 'top$' @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'top$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(431,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( C @ ( B @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
<=> ( ( C @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom600) ).
thf(2581,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( ( C @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( C @ ( B @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( C @ ( B @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( C @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(413,axiom,
! [A: 'B_set$',B: 'B$',C: 'B_set$'] :
( ( C @ ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( C @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom179) ).
thf(2505,plain,
! [A: 'B_set$',B: 'B$',C: 'B_set$'] :
( ( C @ ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( C @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(410,axiom,
! [A: 'B$',B: 'B$',C: 'B_set$'] :
( ( C @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ 'insert$' @ 'fun_app$b' ) )
= ( C @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( B @ 'insert$' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom36) ).
thf(2497,plain,
! [A: 'B$',B: 'B$',C: 'B_set$'] :
( ( C @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ 'insert$' @ 'fun_app$b' ) )
= ( C @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( B @ 'insert$' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(458,axiom,
! [A: 'B_b_bool_fun_fun$'] : ( 'bot$' @ ( A @ 'pairwise$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom282) ).
thf(2697,plain,
! [A: 'B_b_bool_fun_fun$'] : ( 'bot$' @ ( A @ 'pairwise$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(22,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( ( A @ ( B @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom256) ).
thf(605,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( ( A @ ( B @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(383,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'bot$' )
<=> ( ( B = 'bot$' )
& ( A = 'bot$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom14) ).
thf(2370,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( ( B = 'bot$' )
& ( A = 'bot$' ) )
=> ( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'bot$' ) )
& ( ( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'bot$' )
=> ( ( B = 'bot$' )
& ( A = 'bot$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(222,axiom,
! [A: 'B_set$',B: 'B_set_b_set_fun$',C: 'B_set$',D: 'B_set$'] :
( ( ! [E: 'B_set$',F: 'B_set$'] :
( ( F @ ( E @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( F @ ( B @ 'fun_app$b' ) @ ( E @ ( B @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( D @ ( C @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( A
= ( C @ ( B @ 'fun_app$b' ) ) ) )
=> ( D @ ( B @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom227) ).
thf(1539,plain,
! [A: 'B_set$',B: 'B_set_b_set_fun$',C: 'B_set$',D: 'B_set$'] :
( ( ! [E: 'B_set$',F: 'B_set$'] :
( ( F @ ( E @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( F @ ( B @ 'fun_app$b' ) @ ( E @ ( B @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( D @ ( C @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( A
= ( C @ ( B @ 'fun_app$b' ) ) ) )
=> ( D @ ( B @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(493,axiom,
! [A: 'B$',B: 'B$',C: 'B_set$'] :
( ( ( ( C @ ( A @ 'member$' ) )
=> $false )
& ( ( A = B )
=> $false )
& ( C @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ 'member$' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom43) ).
thf(2836,plain,
! [A: 'B$',B: 'B$',C: 'B_set$'] :
~ ( ~ ( C @ ( A @ 'member$' ) )
& ( A != B )
& ( C @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ 'member$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(187,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( A = B )
<=> ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom203) ).
thf(1382,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(161,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( A @ ( C @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( B @ ( C @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom420) ).
thf(1266,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( A @ ( C @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( B @ ( C @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(156,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
<=> ( ( B = A )
| ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom495) ).
thf(1231,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( ( B = A )
| ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( B = A )
| ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(107,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( 'uminus$' @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( A @ ( 'uminus$' @ 'fun_app$b' ) @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom471) ).
thf(1002,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( 'uminus$' @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( A @ ( 'uminus$' @ 'fun_app$b' ) @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(286,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom121) ).
thf(1852,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(487,axiom,
! [A: 'B_set$'] :
( ( A @ 'is_singleton$' )
<=> ? [B: 'B$'] :
( A
= ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$b' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom171) ).
thf(2813,plain,
! [A: 'B_set$'] :
( ( ? [B: 'B$'] :
( A
= ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$b' ) ) )
=> ( A @ 'is_singleton$' ) )
& ( ( A @ 'is_singleton$' )
=> ? [B: 'B$'] :
( A
= ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$b' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(481,axiom,
! [A: 'B_set$'] :
( ( 'bot$' @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( A = 'bot$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom272) ).
thf(2788,plain,
! [A: 'B_set$'] :
( ( 'bot$' @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( A = 'bot$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(350,axiom,
! [A: 'B$'] :
( ( 'top$' @ ( A @ 'insert$' @ 'fun_app$b' ) )
= 'top$' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom66) ).
thf(2203,plain,
! [A: 'B$'] :
( ( 'top$' @ ( A @ 'insert$' @ 'fun_app$b' ) )
= 'top$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(29,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
<=> ( ( A != B )
& ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom510) ).
thf(633,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( ( ( A != B )
& ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
& ( ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( ( A != B )
& ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(5,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( A != B ) )
=> ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom516) ).
thf(508,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( A != B ) )
=> ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(207,axiom,
! [A: 'B_set_b_set_bool_fun_fun$',B: 'B_set_b_set_bool_fun_fun$',C: 'B_set$',D: 'B_set$'] :
( ( C @ ( B @ ( A @ 'ordering_top$a' ) ) )
=> ~ ( D @ ( C @ ( B @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom571) ).
thf(1466,plain,
! [A: 'B_set_b_set_bool_fun_fun$',B: 'B_set_b_set_bool_fun_fun$',C: 'B_set$',D: 'B_set$'] :
( ( C @ ( B @ ( A @ 'ordering_top$a' ) ) )
=> ~ ( D @ ( C @ ( B @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(297,axiom,
! [A: 'B$',B: 'B_set$',C: 'B_set$'] :
( ( ~ ( B @ ( A @ 'member$' ) )
=> ( C @ ( A @ 'member$' ) ) )
=> ( B @ ( C @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ 'member$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom24) ).
thf(1895,plain,
! [A: 'B$',B: 'B_set$',C: 'B_set$'] :
( ( ~ ( B @ ( A @ 'member$' ) )
=> ( C @ ( A @ 'member$' ) ) )
=> ( B @ ( C @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ 'member$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(98,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
<=> ( ( A != B )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom487) ).
thf(953,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( ( A != B )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( A != B )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(93,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom406) ).
thf(926,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(157,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
<=> ( ~ ( A @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom503) ).
thf(1241,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( ~ ( A @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ~ ( A @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(423,axiom,
! [A: 'B_set$'] :
( ( 'top$' @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'top$' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom88) ).
thf(2546,plain,
! [A: 'B_set$'] :
( ( 'top$' @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'top$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(216,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( C @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom136) ).
thf(1515,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( C @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(354,axiom,
( 'bot$'
= ( 'bot$b' @ ( 'collect$' @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom128) ).
thf(2221,plain,
( 'bot$'
= ( 'bot$b' @ ( 'collect$' @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(63,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$',C: tlbool] :
( ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( ( ( A @ ( B @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( C = tltrue ) )
<=> $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom451) ).
thf(794,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$',C: tlbool] :
( ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( ( A @ ( B @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( C = tltrue ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(18,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( A = B )
<=> ( ( A @ ( B @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom238) ).
thf(586,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( ( ( A @ ( B @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( B @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(395,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
<=> ( ( A @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom292) ).
thf(2423,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( ( A @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= B )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( A @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(83,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$',C: 'B_bool_fun$'] :
( ( ( C @ ( B @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( C @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom417) ).
thf(888,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$',C: 'B_bool_fun$'] :
( ( ( C @ ( B @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( C @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(341,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( B @ ( C @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom326) ).
thf(2144,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( B @ ( C @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(241,axiom,
! [A: 'B_set$'] :
( ( A @ ( 'top$' @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
<=> ( A = 'top$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom278) ).
thf(1648,plain,
! [A: 'B_set$'] :
( ( ( A = 'top$' )
=> ( A @ ( 'top$' @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( A @ ( 'top$' @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( A = 'top$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(263,axiom,
! [A: 'B_set$',B: 'B_set$'] : ( A @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom330) ).
thf(1754,plain,
! [A: 'B_set$',B: 'B_set$'] : ( A @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(325,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( C @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom140) ).
thf(2033,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( C @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(303,axiom,
! [A: 'B_set$'] :
( ( A @ ( 'bot$' @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom68) ).
thf(1927,plain,
! [A: 'B_set$'] :
( ( A @ ( 'bot$' @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(468,axiom,
! [A: 'B_set$'] :
( ( A @ ( A @ ( 'uminus$' @ 'fun_app$b' ) @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'top$' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom563) ).
thf(2734,plain,
! [A: 'B_set$'] :
( ( A @ ( A @ ( 'uminus$' @ 'fun_app$b' ) @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'top$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(15,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( ( A != B )
& ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom514) ).
thf(573,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( ( A != B )
& ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(39,axiom,
! [A: 'B_bool_fun$'] : ( A @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom369) ).
thf(689,plain,
! [A: 'B_bool_fun$'] : ( A @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(20,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$',C: 'B_bool_fun$'] :
( ( ( A @ ( C @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( B @ ( C @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom500) ).
thf(601,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$',C: 'B_bool_fun$'] :
( ( ( A @ ( C @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( B @ ( C @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(100,axiom,
! [A: 'B_b_bool_fun_fun$',B: 'B_set$',C: 'B_b_bool_fun_fun$',D: 'B_set$'] :
( ( ( B @ ( D @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ! [E: 'B$',F: 'B$'] :
( ( F @ ( E @ ( A @ 'fun_app$k' ) @ 'fun_app$' ) )
=> ( F @ ( E @ ( C @ 'fun_app$k' ) @ 'fun_app$' ) ) )
& ( B @ ( A @ 'pairwise$' ) ) )
=> ( D @ ( C @ 'pairwise$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom204) ).
thf(965,plain,
! [A: 'B_b_bool_fun_fun$',B: 'B_set$',C: 'B_b_bool_fun_fun$',D: 'B_set$'] :
( ( ( B @ ( D @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ! [E: 'B$',F: 'B$'] :
( ( F @ ( E @ ( A @ 'fun_app$k' ) @ 'fun_app$' ) )
=> ( F @ ( E @ ( C @ 'fun_app$k' ) @ 'fun_app$' ) ) )
& ( B @ ( A @ 'pairwise$' ) ) )
=> ( D @ ( C @ 'pairwise$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(257,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( A @ ( 'uminus$' @ 'fun_app$b' ) )
= ( B @ ( 'uminus$' @ 'fun_app$b' ) ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom378) ).
thf(1727,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( A = B )
=> ( ( A @ ( 'uminus$' @ 'fun_app$b' ) )
= ( B @ ( 'uminus$' @ 'fun_app$b' ) ) ) )
& ( ( ( A @ ( 'uminus$' @ 'fun_app$b' ) )
= ( B @ ( 'uminus$' @ 'fun_app$b' ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(214,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( B @ ( C @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( B @ ( C @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom320) ).
thf(1510,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( B @ ( C @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( B @ ( C @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(109,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( A @ ( C @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( B @ ( C @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom501) ).
thf(1007,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( A @ ( C @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( B @ ( C @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(482,axiom,
! [A: 'B_set$',B: 'B_set_b_set_fun$',C: 'B_set$',D: 'B_set$'] :
( ( ! [E: 'B_set$',F: 'B_set$'] :
( ( F @ ( E @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( F @ ( B @ 'fun_app$b' ) @ ( E @ ( B @ 'fun_app$b' ) @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( D @ ( C @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( A
= ( C @ ( B @ 'fun_app$b' ) ) ) )
=> ( D @ ( B @ 'fun_app$b' ) @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom434) ).
thf(2791,plain,
! [A: 'B_set$',B: 'B_set_b_set_fun$',C: 'B_set$',D: 'B_set$'] :
( ( ! [E: 'B_set$',F: 'B_set$'] :
( ( F @ ( E @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( F @ ( B @ 'fun_app$b' ) @ ( E @ ( B @ 'fun_app$b' ) @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( D @ ( C @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( A
= ( C @ ( B @ 'fun_app$b' ) ) ) )
=> ( D @ ( B @ 'fun_app$b' ) @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(409,axiom,
! [A: 'B_set$'] :
( ( 'bot$' @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
<=> ( A = 'bot$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom195) ).
thf(2489,plain,
! [A: 'B_set$'] :
( ( ( A = 'bot$' )
=> ( 'bot$' @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( 'bot$' @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( A = 'bot$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(262,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$',D: 'B_set$'] :
( ( ( D @ ( C @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( D @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( C @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom352) ).
thf(1752,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$',D: 'B_set$'] :
( ( ( D @ ( C @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( D @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( C @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(428,axiom,
! [A: 'B_set$'] :
( ( A @ ( A @ ( 'uminus$' @ 'fun_app$b' ) @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'top$' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom400) ).
thf(2568,plain,
! [A: 'B_set$'] :
( ( A @ ( A @ ( 'uminus$' @ 'fun_app$b' ) @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'top$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(17,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ~ ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom478) ).
thf(579,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ~ ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( ( ( A = B )
=> ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
& ( ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(485,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( B @ ( C @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom286) ).
thf(2806,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( B @ ( C @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(462,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set_b_set_fun$',D: 'B_set$'] :
( ( ! [E: 'B_set$',F: 'B_set$'] :
( ( F @ ( E @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( F @ ( C @ 'fun_app$b' ) @ ( E @ ( C @ 'fun_app$b' ) @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( D @ ( B @ ( C @ 'fun_app$b' ) @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$b' ) @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom448) ).
thf(2716,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set_b_set_fun$',D: 'B_set$'] :
( ( ! [E: 'B_set$',F: 'B_set$'] :
( ( F @ ( E @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( F @ ( C @ 'fun_app$b' ) @ ( E @ ( C @ 'fun_app$b' ) @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( D @ ( B @ ( C @ 'fun_app$b' ) @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$b' ) @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(10,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$',C: 'B_bool_fun$'] :
( ( ( C @ ( B @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( C @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom252) ).
thf(545,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$',C: 'B_bool_fun$'] :
( ( ( C @ ( B @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( C @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(356,axiom,
! [A: 'B_b_bool_fun_fun$',B: 'B$',C: 'B_set$'] :
( ( C @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ 'pairwise$' ) )
<=> ( ( C @ ( A @ 'pairwise$' ) )
& ! [D: 'B$'] :
( ( ( D != B )
& ( C @ ( D @ 'member$' ) ) )
=> ( ( B @ ( D @ ( A @ 'fun_app$k' ) @ 'fun_app$' ) )
& ( D @ ( B @ ( A @ 'fun_app$k' ) @ 'fun_app$' ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom284) ).
thf(2225,plain,
! [A: 'B_b_bool_fun_fun$',B: 'B$',C: 'B_set$'] :
( ( ( ( C @ ( A @ 'pairwise$' ) )
& ! [D: 'B$'] :
( ( ( D != B )
& ( C @ ( D @ 'member$' ) ) )
=> ( ( B @ ( D @ ( A @ 'fun_app$k' ) @ 'fun_app$' ) )
& ( D @ ( B @ ( A @ 'fun_app$k' ) @ 'fun_app$' ) ) ) ) )
=> ( C @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ 'pairwise$' ) ) )
& ( ( C @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ 'pairwise$' ) )
=> ( ( C @ ( A @ 'pairwise$' ) )
& ! [D: 'B$'] :
( ( ( D != B )
& ( C @ ( D @ 'member$' ) ) )
=> ( ( B @ ( D @ ( A @ 'fun_app$k' ) @ 'fun_app$' ) )
& ( D @ ( B @ ( A @ 'fun_app$k' ) @ 'fun_app$' ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(49,axiom,
! [A: 'B_set$',B: 'B_bool_fun_b_set_fun$',C: 'B_bool_fun$',D: 'B_bool_fun$'] :
( ( ! [E: 'B_bool_fun$',F: 'B_bool_fun$'] :
( ( F @ ( E @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( F @ ( B @ 'fun_app$d' ) @ ( E @ ( B @ 'fun_app$d' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( D @ ( C @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( C @ ( B @ 'fun_app$d' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( D @ ( B @ 'fun_app$d' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom234) ).
thf(732,plain,
! [A: 'B_set$',B: 'B_bool_fun_b_set_fun$',C: 'B_bool_fun$',D: 'B_bool_fun$'] :
( ( ! [E: 'B_bool_fun$',F: 'B_bool_fun$'] :
( ( F @ ( E @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( F @ ( B @ 'fun_app$d' ) @ ( E @ ( B @ 'fun_app$d' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( D @ ( C @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( C @ ( B @ 'fun_app$d' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( D @ ( B @ 'fun_app$d' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(293,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$',D: 'B_set$'] :
( ( ( D @ ( C @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( D @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( C @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom322) ).
thf(1884,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$',D: 'B_set$'] :
( ( ( D @ ( C @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( D @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( C @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(417,axiom,
! [A: 'B$',B: 'B_set$'] :
( ( B @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( 'uminus$' @ 'fun_app$b' ) )
= ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( B @ ( 'uminus$' @ 'fun_app$b' ) @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom567) ).
thf(2525,plain,
! [A: 'B$',B: 'B_set$'] :
( ( B @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( 'uminus$' @ 'fun_app$b' ) )
= ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( B @ ( 'uminus$' @ 'fun_app$b' ) @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(452,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'bot$' )
<=> ( ( B = 'bot$' )
& ( A = 'bot$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom103) ).
thf(2657,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( ( B = 'bot$' )
& ( A = 'bot$' ) )
=> ( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'bot$' ) )
& ( ( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'bot$' )
=> ( ( B = 'bot$' )
& ( A = 'bot$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(251,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( 'bot$'
= ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) )
<=> ( ( B = 'bot$' )
& ( A = 'bot$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom109) ).
thf(1701,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( ( B = 'bot$' )
& ( A = 'bot$' ) )
=> ( 'bot$'
= ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ) )
& ( ( 'bot$'
= ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) )
=> ( ( B = 'bot$' )
& ( A = 'bot$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(389,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom549) ).
thf(2398,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(199,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'uminus$' @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( A @ ( B @ ( 'uminus$' @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom473) ).
thf(1428,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'uminus$' @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( A @ ( B @ ( 'uminus$' @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(245,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'top$' )
<=> ( B @ ( A @ ( 'uminus$' @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom566) ).
thf(1669,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( B @ ( A @ ( 'uminus$' @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'top$' ) )
& ( ( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'top$' )
=> ( B @ ( A @ ( 'uminus$' @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(368,axiom,
! [A: 'B$',B: 'B$'] :
( ( ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$b' ) )
= ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$b' ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom61) ).
thf(2293,plain,
! [A: 'B$',B: 'B$'] :
( ( ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$b' ) )
= ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$b' ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(61,axiom,
! [A: 'B_bool_fun$'] :
~ ( A @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom439) ).
thf(787,plain,
! [A: 'B_bool_fun$'] :
~ ( A @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(130,axiom,
! [A: 'B_set$'] : ( A @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom208) ).
thf(1107,plain,
! [A: 'B_set$'] : ( A @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(315,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( C @ ( A @ ( 'uminus$' @ 'fun_app$b' ) @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'top$' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom559) ).
thf(1997,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( C @ ( A @ ( 'uminus$' @ 'fun_app$b' ) @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'top$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(397,axiom,
! [A: 'B$',B: 'B_set$'] :
( ( B @ ( A @ 'member$' ) )
=> ( ( B @ ( A @ 'insert$' @ 'fun_app$b' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom38) ).
thf(2442,plain,
! [A: 'B$',B: 'B_set$'] :
( ( B @ ( A @ 'member$' ) )
=> ( ( B @ ( A @ 'insert$' @ 'fun_app$b' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(97,axiom,
! [A: 'B$'] :
( ( A @ ( 'bot$b' @ 'fun_app$' ) )
<=> 'bot$a' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom170) ).
thf(947,plain,
! [A: 'B$'] :
( ( 'bot$a'
=> ( A @ ( 'bot$b' @ 'fun_app$' ) ) )
& ( ( A @ ( 'bot$b' @ 'fun_app$' ) )
=> 'bot$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(179,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( A @ ( B @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom428) ).
thf(1356,plain,
! [A: 'B_set$',B: 'B_set$'] :
~ ( ( A @ ( B @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(415,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( B @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'top$' )
<=> ( ( B = 'top$' )
& ( A = 'top$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom618) ).
thf(2510,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( ( B = 'top$' )
& ( A = 'top$' ) )
=> ( ( B @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'top$' ) )
& ( ( ( B @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'top$' )
=> ( ( B = 'top$' )
& ( A = 'top$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(146,axiom,
! [A: 'B_set_b_set_bool_fun_fun$',B: 'B_set_b_set_bool_fun_fun$',C: 'B_set$',D: 'B_set$'] :
( ( C @ ( B @ ( A @ 'ordering_top$a' ) ) )
=> ( C @ ( D @ ( A @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom570) ).
thf(1194,plain,
! [A: 'B_set_b_set_bool_fun_fun$',B: 'B_set_b_set_bool_fun_fun$',C: 'B_set$',D: 'B_set$'] :
( ( C @ ( B @ ( A @ 'ordering_top$a' ) ) )
=> ( C @ ( D @ ( A @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(340,axiom,
! [A: 'B$',B: 'B_set$',C: 'B_set$'] :
( ( ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$b' ) )
= ( C @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) )
<=> ( ( ( C
= ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$b' ) ) )
& ( B
= ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$b' ) ) ) )
| ( ( C = 'bot$' )
& ( B
= ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$b' ) ) ) )
| ( ( C
= ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$b' ) ) )
& ( B = 'bot$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom73) ).
thf(2119,plain,
! [A: 'B$',B: 'B_set$',C: 'B_set$'] :
( ( ( ( ( C
= ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$b' ) ) )
& ( B
= ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$b' ) ) ) )
| ( ( C = 'bot$' )
& ( B
= ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$b' ) ) ) )
| ( ( C
= ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$b' ) ) )
& ( B = 'bot$' ) ) )
=> ( ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$b' ) )
= ( C @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ) )
& ( ( ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$b' ) )
= ( C @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) )
=> ( ( ( C
= ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$b' ) ) )
& ( B
= ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$b' ) ) ) )
| ( ( C = 'bot$' )
& ( B
= ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$b' ) ) ) )
| ( ( C
= ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$b' ) ) )
& ( B = 'bot$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(456,axiom,
! [A: 'B$',B: 'B$',C: 'B_set$'] :
( ( C @ ( B @ 'remove$' @ 'fun_app$b' ) @ ( A @ 'member$' ) )
<=> ( ( A != B )
& ( C @ ( A @ 'member$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom167) ).
thf(2679,plain,
! [A: 'B$',B: 'B$',C: 'B_set$'] :
( ( ( ( A != B )
& ( C @ ( A @ 'member$' ) ) )
=> ( C @ ( B @ 'remove$' @ 'fun_app$b' ) @ ( A @ 'member$' ) ) )
& ( ( C @ ( B @ 'remove$' @ 'fun_app$b' ) @ ( A @ 'member$' ) )
=> ( ( A != B )
& ( C @ ( A @ 'member$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(60,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( ( A @ ( B @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom407) ).
thf(784,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
~ ( ( A @ ( B @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(478,axiom,
! [A: 'B_set$'] : ( A @ ( 'bot$' @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom266) ).
thf(2774,plain,
! [A: 'B_set$'] : ( A @ ( 'bot$' @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(50,axiom,
! [A: 'B_bool_fun$'] :
( ( A != 'top$b' )
<=> ( 'top$b' @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom534) ).
thf(736,plain,
! [A: 'B_bool_fun$'] :
( ( ( 'top$b' @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( A != 'top$b' ) )
& ( ( A != 'top$b' )
=> ( 'top$b' @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(104,axiom,
! [A: 'B_set_b_set_bool_fun_fun$',B: 'B_set_b_set_bool_fun_fun$',C: 'B_set$',D: 'B_set$'] :
( ( C @ ( B @ ( A @ 'ordering_top$a' ) ) )
=> ( ( D != C )
<=> ( C @ ( D @ ( B @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom573) ).
thf(990,plain,
! [A: 'B_set_b_set_bool_fun_fun$',B: 'B_set_b_set_bool_fun_fun$',C: 'B_set$',D: 'B_set$'] :
( ( C @ ( B @ ( A @ 'ordering_top$a' ) ) )
=> ( ( ( C @ ( D @ ( B @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( D != C ) )
& ( ( D != C )
=> ( C @ ( D @ ( B @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(211,axiom,
! [A: 'B$',B: 'B_set$'] :
( ( B @ ( A @ 'insert$' @ 'fun_app$b' ) )
= ( B @ ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom75) ).
thf(1492,plain,
! [A: 'B$',B: 'B_set$'] :
( ( B @ ( A @ 'insert$' @ 'fun_app$b' ) )
= ( B @ ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(454,axiom,
! [A: 'B$',B: 'B_set$',C: 'B_set$'] :
( ( C @ ( B @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
<=> ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( C @ ( A @ 'member$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom196) ).
thf(2669,plain,
! [A: 'B$',B: 'B_set$',C: 'B_set$'] :
( ( ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( C @ ( A @ 'member$' ) ) )
=> ( C @ ( B @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( C @ ( B @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( C @ ( A @ 'member$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(339,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( A
= ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) )
=> ( A @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom314) ).
thf(2116,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( A
= ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) )
=> ( A @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(81,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( ( A = B )
<=> $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom453) ).
thf(880,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(133,axiom,
! [A: 'B_set_b_set_bool_fun_fun$',B: 'B_set_b_set_bool_fun_fun$',C: 'B_set$',D: 'B_set$'] :
( ( C @ ( B @ ( A @ 'ordering_top$a' ) ) )
=> ( ( D @ ( C @ ( A @ 'fun_app$j' ) @ 'fun_app$i' ) )
<=> ( D = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom572) ).
thf(1122,plain,
! [A: 'B_set_b_set_bool_fun_fun$',B: 'B_set_b_set_bool_fun_fun$',C: 'B_set$',D: 'B_set$'] :
( ( C @ ( B @ ( A @ 'ordering_top$a' ) ) )
=> ( ( ( D = C )
=> ( D @ ( C @ ( A @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( D @ ( C @ ( A @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( D = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(185,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( B = A )
<=> $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom456) ).
thf(1376,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(171,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ~ ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom481) ).
thf(1307,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( ( A = B )
=> ~ ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ~ ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(470,axiom,
? [A: 'B$'] : ( 'top$' @ ( A @ 'member$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom33) ).
thf(2742,plain,
? [A: 'B$'] : ( 'top$' @ ( A @ 'member$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(226,axiom,
! [A: 'B$',B: 'B$',C: 'B_set$'] :
( ( ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$b' ) )
= ( C @ ( B @ 'insert$' @ 'fun_app$b' ) ) )
<=> ( ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( C @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom199) ).
thf(1557,plain,
! [A: 'B$',B: 'B$',C: 'B_set$'] :
( ( ( ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( C @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B = A ) )
=> ( ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$b' ) )
= ( C @ ( B @ 'insert$' @ 'fun_app$b' ) ) ) )
& ( ( ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$b' ) )
= ( C @ ( B @ 'insert$' @ 'fun_app$b' ) ) )
=> ( ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( C @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(314,axiom,
! [A: 'B_set$',B: 'B_set_b_set_fun$',C: 'B_set$',D: 'B_set$'] :
( ( ! [E: 'B_set$',F: 'B_set$'] :
( ( F @ ( E @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( F @ ( B @ 'fun_app$b' ) @ ( E @ ( B @ 'fun_app$b' ) @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( D @ ( C @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( C @ ( B @ 'fun_app$b' ) @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( D @ ( B @ 'fun_app$b' ) @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom444) ).
thf(1993,plain,
! [A: 'B_set$',B: 'B_set_b_set_fun$',C: 'B_set$',D: 'B_set$'] :
( ( ! [E: 'B_set$',F: 'B_set$'] :
( ( F @ ( E @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( F @ ( B @ 'fun_app$b' ) @ ( E @ ( B @ 'fun_app$b' ) @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( D @ ( C @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( C @ ( B @ 'fun_app$b' ) @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( D @ ( B @ 'fun_app$b' ) @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(277,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( B @ ( C @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( B @ ( C @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom334) ).
thf(1821,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( B @ ( C @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( B @ ( C @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(74,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( ( A @ ( B @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom413) ).
thf(848,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
~ ( ( A @ ( B @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(166,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom245) ).
thf(1293,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(376,axiom,
! [A: 'B$',B: 'B_set$',C: 'B_set$'] :
( ( C @ ( B @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ 'member$' ) )
=> ( B @ ( A @ 'member$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom58) ).
thf(2329,plain,
! [A: 'B$',B: 'B_set$',C: 'B_set$'] :
( ( C @ ( B @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ 'member$' ) )
=> ( B @ ( A @ 'member$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(84,axiom,
! [A: 'B_bool_fun$'] :
~ ( A @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom415) ).
thf(890,plain,
! [A: 'B_bool_fun$'] :
~ ( A @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(244,axiom,
! [A: 'B$',B: 'B_set$',C: 'B_set$'] :
( ( ~ ( C @ ( A @ 'member$' ) )
& ( B @ ( A @ 'member$' ) ) )
=> ( C @ ( B @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ 'member$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom27) ).
thf(1667,plain,
! [A: 'B$',B: 'B_set$',C: 'B_set$'] :
( ( ~ ( C @ ( A @ 'member$' ) )
& ( B @ ( A @ 'member$' ) ) )
=> ( C @ ( B @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ 'member$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(54,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( ~ ( A @ ( B @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
<=> $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom457) ).
thf(758,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ~ ( A @ ( B @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(439,axiom,
! [A: 'B_set$',B: 'B_set$'] : ( A @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom349) ).
thf(2610,plain,
! [A: 'B_set$',B: 'B_set$'] : ( A @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(9,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
<=> ( ( B = A )
| ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom494) ).
thf(535,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( ( ( B = A )
| ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
& ( ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( ( B = A )
| ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(444,axiom,
! [A: 'B$'] :
( ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$b' ) @ 'the_elem$' )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom160) ).
thf(2625,plain,
! [A: 'B$'] :
( ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$b' ) @ 'the_elem$' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(141,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
<=> ( ( A != B )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom511) ).
thf(1162,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( ( A != B )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( A != B )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(46,axiom,
! [A: 'B_bool_fun$'] : ( 'top$b' @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom274) ).
thf(726,plain,
! [A: 'B_bool_fun$'] : ( 'top$b' @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(393,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
<=> ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( C @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom193) ).
thf(2410,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( C @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( C @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(175,axiom,
! [A: 'B_set$'] :
( ! [B: 'B$'] :
( ( A @ ( B @ 'member$' ) )
=> $false )
=> ( 'bot$' @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom366) ).
thf(1325,plain,
! [A: 'B_set$'] :
( ! [B: 'B$'] :
~ ( A @ ( B @ 'member$' ) )
=> ( 'bot$' @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(132,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
<=> ( ( A = B )
| ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom545) ).
thf(1112,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( ( A = B )
| ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( A = B )
| ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(430,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( C @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom142) ).
thf(2578,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( C @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(7,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( A = B )
<=> ( ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( A @ ( B @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom250) ).
thf(521,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( ( ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( A @ ( B @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( A @ ( B @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(189,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B$'] :
( ( ( A @ ( C @ 'member$' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( B @ ( C @ 'member$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom216) ).
thf(1396,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B$'] :
( ( ( A @ ( C @ 'member$' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( B @ ( C @ 'member$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(353,axiom,
! [A: 'B_set_b_set_b_set_fun_fun$',B: 'B_set$',C: 'B_set$'] :
( ( ! [D: 'B_set$',E: 'B_set$',F: 'B_set$'] :
( ( ( D @ ( F @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( D @ ( E @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( D @ ( F @ ( E @ ( A @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ! [D: 'B_set$',E: 'B_set$'] : ( E @ ( D @ ( A @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( E @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ! [D: 'B_set$',E: 'B_set$'] : ( E @ ( D @ ( A @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( D @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( ( C @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( C @ ( B @ ( A @ 'fun_app$c' ) @ 'fun_app$b' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom312) ).
thf(2212,plain,
! [A: 'B_set_b_set_b_set_fun_fun$',B: 'B_set$',C: 'B_set$'] :
( ( ! [D: 'B_set$',E: 'B_set$',F: 'B_set$'] :
( ( ( D @ ( F @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( D @ ( E @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( D @ ( F @ ( E @ ( A @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ! [D: 'B_set$',E: 'B_set$'] : ( E @ ( D @ ( A @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( E @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ! [D: 'B_set$',E: 'B_set$'] : ( E @ ( D @ ( A @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( D @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( ( C @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( C @ ( B @ ( A @ 'fun_app$c' ) @ 'fun_app$b' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(476,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( B @ ( C @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( B @ ( C @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom300) ).
thf(2765,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( B @ ( C @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( B @ ( C @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(219,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( C @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> $false )
& ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom336) ).
thf(1528,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
~ ( ~ ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( C @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(23,axiom,
! [A: 'B_bool_fun$'] : ( A @ ( 'bot$b' @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom265) ).
thf(608,plain,
! [A: 'B_bool_fun$'] : ( A @ ( 'bot$b' @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(106,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom507) ).
thf(1000,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(446,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( A @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom46) ).
thf(2633,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( A @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(421,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( B @ ( A @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'bot$' )
<=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom200) ).
thf(2535,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( B @ ( A @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'bot$' ) )
& ( ( ( B @ ( A @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'bot$' )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(159,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( A = B )
<=> ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( A @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom251) ).
thf(1250,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( A @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( A @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(75,axiom,
! [A: 'B_bool_fun$'] :
( ( A != 'bot$b' )
<=> ( A @ ( 'bot$b' @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom530) ).
thf(851,plain,
! [A: 'B_bool_fun$'] :
( ( ( A @ ( 'bot$b' @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( A != 'bot$b' ) )
& ( ( A != 'bot$b' )
=> ( A @ ( 'bot$b' @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(91,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( C @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom205) ).
thf(922,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( C @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(274,axiom,
! [A: 'B_set$'] :
( ( A @ ( 'top$' @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom610) ).
thf(1805,plain,
! [A: 'B_set$'] :
( ( A @ ( 'top$' @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(465,axiom,
! [A: 'B_set$'] :
( ( 'bot$' @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom94) ).
thf(2725,plain,
! [A: 'B_set$'] :
( ( 'bot$' @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(390,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom308) ).
thf(2401,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(250,axiom,
! [A: 'B$'] : ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$b' ) @ 'is_singleton$' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom164) ).
thf(1699,plain,
! [A: 'B$'] : ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$b' ) @ 'is_singleton$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(236,axiom,
! [A: 'B_set$'] :
( ( A @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom50) ).
thf(1626,plain,
! [A: 'B_set$'] :
( ( A @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(150,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set_b_set_fun$',D: 'B_set$'] :
( ( ! [E: 'B_set$',F: 'B_set$'] :
( ( F @ ( E @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( F @ ( C @ 'fun_app$b' ) @ ( E @ ( C @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( D @ ( B @ ( C @ 'fun_app$b' ) @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$b' ) @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom526) ).
thf(1208,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set_b_set_fun$',D: 'B_set$'] :
( ( ! [E: 'B_set$',F: 'B_set$'] :
( ( F @ ( E @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( F @ ( C @ 'fun_app$b' ) @ ( E @ ( C @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( D @ ( B @ ( C @ 'fun_app$b' ) @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$b' ) @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(96,axiom,
! [A: 'B_set$'] :
~ ( A @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom416) ).
thf(944,plain,
! [A: 'B_set$'] :
~ ( A @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(374,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( B @ ( C @ 'insert$' @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom341) ).
thf(2318,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( B @ ( C @ 'insert$' @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(35,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$',C: 'B_bool_fun$'] :
( ( ( C @ ( B @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( C @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom520) ).
thf(663,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$',C: 'B_bool_fun$'] :
( ( ( C @ ( B @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( C @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(135,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom422) ).
thf(1134,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(137,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
<=> ( ( A = B )
| ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom485) ).
thf(1145,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( ( A = B )
| ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( A = B )
| ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(118,axiom,
! [A: 'B$'] : ( A @ ( 'top$b' @ 'fun_app$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom166) ).
thf(1049,plain,
! [A: 'B$'] : ( A @ ( 'top$b' @ 'fun_app$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(170,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( A != B )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom515) ).
thf(1304,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( A != B )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(291,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
<=> ( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom318) ).
thf(1873,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= B )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(283,axiom,
! [A: 'B$',B: 'B_set$'] : ( B @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( A @ 'member$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom42) ).
thf(1845,plain,
! [A: 'B$',B: 'B_set$'] : ( B @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( A @ 'member$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(223,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( ( ( C @ ( B @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( C @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> $false )
& ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom550) ).
thf(1547,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
~ ( ~ ( ( C @ ( B @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( C @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(271,axiom,
! [A: 'B_set$',B: 'B_set$'] : ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom296) ).
thf(1798,plain,
! [A: 'B_set$',B: 'B_set$'] : ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(79,axiom,
! [A: 'B_bool_fun$',B: 'B_set_b_bool_fun_fun$',C: 'B_set$',D: 'B_set$'] :
( ( ! [E: 'B_set$',F: 'B_set$'] :
( ( F @ ( E @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( F @ ( B @ 'fun_app$a' ) @ ( E @ ( B @ 'fun_app$a' ) @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
& ( D @ ( C @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( C @ ( B @ 'fun_app$a' ) @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( D @ ( B @ 'fun_app$a' ) @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom442) ).
thf(872,plain,
! [A: 'B_bool_fun$',B: 'B_set_b_bool_fun_fun$',C: 'B_set$',D: 'B_set$'] :
( ( ! [E: 'B_set$',F: 'B_set$'] :
( ( F @ ( E @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( F @ ( B @ 'fun_app$a' ) @ ( E @ ( B @ 'fun_app$a' ) @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
& ( D @ ( C @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( C @ ( B @ 'fun_app$a' ) @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( D @ ( B @ 'fun_app$a' ) @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(233,axiom,
! [A: 'B$',B: 'B_set$',C: 'B_set$'] :
( ( B @ ( A @ 'member$' ) )
=> ( B @ ( C @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ 'member$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom54) ).
thf(1611,plain,
! [A: 'B$',B: 'B_set$',C: 'B_set$'] :
( ( B @ ( A @ 'member$' ) )
=> ( B @ ( C @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ 'member$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(348,axiom,
! [A: 'B_set$'] :
( ! [B: 'B$'] :
~ ( A @ ( B @ 'member$' ) )
<=> ( A = 'bot$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom17) ).
thf(2192,plain,
! [A: 'B_set$'] :
( ( ( A = 'bot$' )
=> ! [B: 'B$'] :
~ ( A @ ( B @ 'member$' ) ) )
& ( ! [B: 'B$'] :
~ ( A @ ( B @ 'member$' ) )
=> ( A = 'bot$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(318,axiom,
! [A: 'B_set$'] :
( ( 'top$' @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom624) ).
thf(2012,plain,
! [A: 'B_set$'] :
( ( 'top$' @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(488,axiom,
! [A: 'B_set$',B: 'B$'] : ( A @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom342) ).
thf(2821,plain,
! [A: 'B_set$',B: 'B$'] : ( A @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(463,axiom,
! [A: 'B$',B: 'B_set$'] :
( ~ ( B @ ( A @ 'member$' ) )
=> ( ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( B @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom76) ).
thf(2720,plain,
! [A: 'B$',B: 'B_set$'] :
( ~ ( B @ ( A @ 'member$' ) )
=> ( ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( B @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(495,axiom,
! [A: 'B_set$'] :
( ( A @ ( 'top$' @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'top$' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom70) ).
thf(2850,plain,
! [A: 'B_set$'] :
( ( A @ ( 'top$' @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'top$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(457,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( A @ ( 'uminus$' @ 'fun_app$b' ) )
= ( B @ ( 'uminus$' @ 'fun_app$b' ) ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom374) ).
thf(2689,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( A = B )
=> ( ( A @ ( 'uminus$' @ 'fun_app$b' ) )
= ( B @ ( 'uminus$' @ 'fun_app$b' ) ) ) )
& ( ( ( A @ ( 'uminus$' @ 'fun_app$b' ) )
= ( B @ ( 'uminus$' @ 'fun_app$b' ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(44,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$',C: 'B_bool_fun$'] :
( ( ( C @ ( B @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( A = B ) )
=> ( C @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom260) ).
thf(712,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$',C: 'B_bool_fun$'] :
( ( ( C @ ( B @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( A = B ) )
=> ( C @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(12,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom512) ).
thf(557,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(268,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ! [D: 'B_set$',E: 'B_set$'] :
( ( ( A
= ( E @ ( D @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) )
& ( C @ ( E @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( D @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> $false )
& ( C @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom346) ).
thf(1770,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
~ ( ! [D: 'B_set$',E: 'B_set$'] :
~ ( ( A
= ( E @ ( D @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) )
& ( C @ ( E @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( D @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( C @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(153,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( A @ ( C @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( B @ ( C @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom247) ).
thf(1225,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( A @ ( C @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( B @ ( C @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(329,axiom,
! [A: 'B_bool_fun$'] :
( ( 'bot$'
= ( A @ ( 'collect$' @ 'fun_app$d' ) ) )
<=> ! [B: 'B$'] :
~ ( B @ ( A @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom15) ).
thf(2060,plain,
! [A: 'B_bool_fun$'] :
( ( ! [B: 'B$'] :
~ ( B @ ( A @ 'fun_app$' ) )
=> ( 'bot$'
= ( A @ ( 'collect$' @ 'fun_app$d' ) ) ) )
& ( ( 'bot$'
= ( A @ ( 'collect$' @ 'fun_app$d' ) ) )
=> ! [B: 'B$'] :
~ ( B @ ( A @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(42,axiom,
! [A: 'B_bool_fun$'] :
( ( 'bot$b' @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( A = 'bot$b' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom271) ).
thf(707,plain,
! [A: 'B_bool_fun$'] :
( ( 'bot$b' @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( A = 'bot$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(231,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom123) ).
thf(1605,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(432,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( B @ ( C @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom553) ).
thf(2588,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( B @ ( C @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(182,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( C @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom521) ).
thf(1368,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( C @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(347,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_bool_fun$'] :
( ! [D: 'B$'] :
( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( D @ 'member$' ) )
=> ( D @ ( C @ 'fun_app$' ) ) )
<=> ( ! [D: 'B$'] :
( ( B @ ( D @ 'member$' ) )
=> ( D @ ( C @ 'fun_app$' ) ) )
& ! [D: 'B$'] :
( ( A @ ( D @ 'member$' ) )
=> ( D @ ( C @ 'fun_app$' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom52) ).
thf(2175,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_bool_fun$'] :
( ( ( ! [D: 'B$'] :
( ( B @ ( D @ 'member$' ) )
=> ( D @ ( C @ 'fun_app$' ) ) )
& ! [D: 'B$'] :
( ( A @ ( D @ 'member$' ) )
=> ( D @ ( C @ 'fun_app$' ) ) ) )
=> ! [D: 'B$'] :
( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( D @ 'member$' ) )
=> ( D @ ( C @ 'fun_app$' ) ) ) )
& ( ! [D: 'B$'] :
( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( D @ 'member$' ) )
=> ( D @ ( C @ 'fun_app$' ) ) )
=> ( ! [D: 'B$'] :
( ( B @ ( D @ 'member$' ) )
=> ( D @ ( C @ 'fun_app$' ) ) )
& ! [D: 'B$'] :
( ( A @ ( D @ 'member$' ) )
=> ( D @ ( C @ 'fun_app$' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(392,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( B @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom588) ).
thf(2407,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( B @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(385,axiom,
! [A: 'B$',B: 'B_set$'] :
( ( B @ ( A @ 'remove$' @ 'fun_app$b' ) )
= ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( B @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom165) ).
thf(2386,plain,
! [A: 'B$',B: 'B_set$'] :
( ( B @ ( A @ 'remove$' @ 'fun_app$b' ) )
= ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( B @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(168,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( A @ ( 'uminus$' @ 'fun_app$b' ) @ ( B @ ( 'uminus$' @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom384) ).
thf(1300,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( A @ ( 'uminus$' @ 'fun_app$b' ) @ ( B @ ( 'uminus$' @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(144,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( A @ ( B @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom408) ).
thf(1188,plain,
! [A: 'B_set$',B: 'B_set$'] :
~ ( ( A @ ( B @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(117,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ! [C: 'B$'] :
( ( C @ ( A @ 'fun_app$' ) )
<=> ( C @ ( B @ 'fun_app$' ) ) )
=> ( ( A @ ( 'collect$' @ 'fun_app$d' ) )
= ( B @ ( 'collect$' @ 'fun_app$d' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom49) ).
thf(1038,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ! [C: 'B$'] :
( ( ( C @ ( B @ 'fun_app$' ) )
=> ( C @ ( A @ 'fun_app$' ) ) )
& ( ( C @ ( A @ 'fun_app$' ) )
=> ( C @ ( B @ 'fun_app$' ) ) ) )
=> ( ( A @ ( 'collect$' @ 'fun_app$d' ) )
= ( B @ ( 'collect$' @ 'fun_app$d' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(160,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( A = B )
=> ( A @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom210) ).
thf(1262,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( A = B )
=> ( A @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(312,axiom,
! [A: 'B_set$'] :
( ( A @ ( 'top$' @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( A = 'top$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom281) ).
thf(1980,plain,
! [A: 'B_set$'] :
( ( A @ ( 'top$' @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( A = 'top$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(408,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom596) ).
thf(2486,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(247,axiom,
! [A: 'B$',B: 'B_set$'] :
( ( B @ ( A @ 'member$' ) )
=> ( ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( B @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ 'insert$' @ 'fun_app$b' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom78) ).
thf(1679,plain,
! [A: 'B$',B: 'B_set$'] :
( ( B @ ( A @ 'member$' ) )
=> ( ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( B @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ 'insert$' @ 'fun_app$b' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(134,axiom,
! [A: 'B_set$',B: 'B_set_b_set_fun$',C: 'B_set$',D: 'B_set$'] :
( ( ! [E: 'B_set$',F: 'B_set$'] :
( ( F @ ( E @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( F @ ( B @ 'fun_app$b' ) @ ( E @ ( B @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( D @ ( C @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( C @ ( B @ 'fun_app$b' ) @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( D @ ( B @ 'fun_app$b' ) @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom527) ).
thf(1130,plain,
! [A: 'B_set$',B: 'B_set_b_set_fun$',C: 'B_set$',D: 'B_set$'] :
( ( ! [E: 'B_set$',F: 'B_set$'] :
( ( F @ ( E @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( F @ ( B @ 'fun_app$b' ) @ ( E @ ( B @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( D @ ( C @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( C @ ( B @ 'fun_app$b' ) @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( D @ ( B @ 'fun_app$b' ) @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(259,axiom,
! [A: 'B_set$'] :
( ( A @ 'is_singleton$' )
<=> ( A
= ( 'bot$' @ ( A @ 'the_elem$' @ 'insert$' @ 'fun_app$b' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom168) ).
thf(1738,plain,
! [A: 'B_set$'] :
( ( ( A
= ( 'bot$' @ ( A @ 'the_elem$' @ 'insert$' @ 'fun_app$b' ) ) )
=> ( A @ 'is_singleton$' ) )
& ( ( A @ 'is_singleton$' )
=> ( A
= ( 'bot$' @ ( A @ 'the_elem$' @ 'insert$' @ 'fun_app$b' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(30,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$',C: 'B_bool_fun$'] :
( ( ( C @ ( B @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( C @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom518) ).
thf(643,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$',C: 'B_bool_fun$'] :
( ( ( C @ ( B @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( C @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(252,axiom,
( ( 'bot$' @ ( 'uminus$' @ 'fun_app$b' ) )
= 'top$' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom556) ).
thf(1711,plain,
( ( 'bot$' @ ( 'uminus$' @ 'fun_app$b' ) )
= 'top$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(472,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set_b_set_fun$',D: 'B_set$'] :
( ( ! [E: 'B_set$',F: 'B_set$'] :
( ( F @ ( E @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( F @ ( C @ 'fun_app$b' ) @ ( E @ ( C @ 'fun_app$b' ) @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( B @ ( C @ 'fun_app$b' ) )
= D )
& ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$b' ) @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom438) ).
thf(2747,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set_b_set_fun$',D: 'B_set$'] :
( ( ! [E: 'B_set$',F: 'B_set$'] :
( ( F @ ( E @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( F @ ( C @ 'fun_app$b' ) @ ( E @ ( C @ 'fun_app$b' ) @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( B @ ( C @ 'fun_app$b' ) )
= D )
& ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$b' ) @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(125,axiom,
! [A: 'B_b_bool_fun_fun$',B: 'B_set$',C: 'B_set$'] :
( ( ( B @ ( C @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ 'pairwise$' ) ) )
=> ( C @ ( A @ 'pairwise$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom202) ).
thf(1085,plain,
! [A: 'B_b_bool_fun_fun$',B: 'B_set$',C: 'B_set$'] :
( ( ( B @ ( C @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ 'pairwise$' ) ) )
=> ( C @ ( A @ 'pairwise$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(16,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( ( A @ ( B @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom244) ).
thf(576,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( ( A @ ( B @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(192,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( A @ ( B @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom414) ).
thf(1404,plain,
! [A: 'B_set$',B: 'B_set$'] :
~ ( ( A @ ( B @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(305,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( B @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom593) ).
thf(1934,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( B @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(285,axiom,
! [A: 'B$',B: 'B_set$'] :
( ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( B @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ 'insert$' @ 'fun_app$b' ) )
= ( B @ ( A @ 'insert$' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom3) ).
thf(1849,plain,
! [A: 'B$',B: 'B_set$'] :
( ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( B @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ 'insert$' @ 'fun_app$b' ) )
= ( B @ ( A @ 'insert$' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(221,axiom,
! [A: 'B_set$'] :
( ( 'bot$' @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom158) ).
thf(1536,plain,
! [A: 'B_set$'] :
( ( 'bot$' @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(34,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
<=> ( ~ ( A @ ( B @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom492) ).
thf(656,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( ( ~ ( A @ ( B @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
& ( ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( ~ ( A @ ( B @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(422,axiom,
! [A: 'B_set$'] :
( ( A @ ( 'bot$' @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'bot$' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom602) ).
thf(2543,plain,
! [A: 'B_set$'] :
( ( A @ ( 'bot$' @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'bot$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(311,axiom,
! [A: 'B_set$'] :
( ( 'bot$' @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
<=> ( A = 'bot$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom269) ).
thf(1972,plain,
! [A: 'B_set$'] :
( ( ( A = 'bot$' )
=> ( 'bot$' @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( 'bot$' @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( A = 'bot$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(261,axiom,
! [A: 'B_set$'] :
~ ( 'bot$' @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom538) ).
thf(1749,plain,
! [A: 'B_set$'] :
~ ( 'bot$' @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(103,axiom,
! [A: tlbool,B: 'B$'] :
( ( ( B @ ( 'top$b' @ 'fun_app$' ) )
& ( A = tltrue ) )
<=> ( A = tltrue ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom175) ).
thf(978,plain,
! [A: tlbool,B: 'B$'] :
( ( ( A = tltrue )
=> ( ( B @ ( 'top$b' @ 'fun_app$' ) )
& ( A = tltrue ) ) )
& ( ( ( B @ ( 'top$b' @ 'fun_app$' ) )
& ( A = tltrue ) )
=> ( A = tltrue ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(76,axiom,
! [A: 'B_set$',B: 'B_bool_fun_b_set_fun$',C: 'B_bool_fun$',D: 'B_bool_fun$'] :
( ( ! [E: 'B_bool_fun$',F: 'B_bool_fun$'] :
( ( F @ ( E @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( F @ ( B @ 'fun_app$d' ) @ ( E @ ( B @ 'fun_app$d' ) @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( D @ ( C @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( A
= ( C @ ( B @ 'fun_app$d' ) ) ) )
=> ( D @ ( B @ 'fun_app$d' ) @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom432) ).
thf(859,plain,
! [A: 'B_set$',B: 'B_bool_fun_b_set_fun$',C: 'B_bool_fun$',D: 'B_bool_fun$'] :
( ( ! [E: 'B_bool_fun$',F: 'B_bool_fun$'] :
( ( F @ ( E @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( F @ ( B @ 'fun_app$d' ) @ ( E @ ( B @ 'fun_app$d' ) @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( D @ ( C @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( A
= ( C @ ( B @ 'fun_app$d' ) ) ) )
=> ( D @ ( B @ 'fun_app$d' ) @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(411,axiom,
! [A: 'B_set$'] : ( A @ ( 'bot$' @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom194) ).
thf(2500,plain,
! [A: 'B_set$'] : ( A @ ( 'bot$' @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(51,axiom,
! [A: 'B_set$',B: 'B_bool_fun_b_set_fun$',C: 'B_bool_fun$',D: 'B_bool_fun$'] :
( ( ! [E: 'B_bool_fun$',F: 'B_bool_fun$'] :
( ( F @ ( E @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( F @ ( B @ 'fun_app$d' ) @ ( E @ ( B @ 'fun_app$d' ) @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( D @ ( C @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( C @ ( B @ 'fun_app$d' ) @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( D @ ( B @ 'fun_app$d' ) @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom441) ).
thf(744,plain,
! [A: 'B_set$',B: 'B_bool_fun_b_set_fun$',C: 'B_bool_fun$',D: 'B_bool_fun$'] :
( ( ! [E: 'B_bool_fun$',F: 'B_bool_fun$'] :
( ( F @ ( E @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( F @ ( B @ 'fun_app$d' ) @ ( E @ ( B @ 'fun_app$d' ) @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( D @ ( C @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( C @ ( B @ 'fun_app$d' ) @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( D @ ( B @ 'fun_app$d' ) @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(466,axiom,
! [A: 'B$',B: 'B$'] :
( ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ 'member$' ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom65) ).
thf(2728,plain,
! [A: 'B$',B: 'B$'] :
( ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ 'member$' ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(324,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom132) ).
thf(2030,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(292,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( C @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( C @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom134) ).
thf(1881,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( C @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( C @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(163,axiom,
! [A: 'B_set$',B: 'B_bool_fun_b_set_fun$',C: 'B_bool_fun$',D: 'B_bool_fun$'] :
( ( ! [E: 'B_bool_fun$',F: 'B_bool_fun$'] :
( ( F @ ( E @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( F @ ( B @ 'fun_app$d' ) @ ( E @ ( B @ 'fun_app$d' ) @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( D @ ( C @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( C @ ( B @ 'fun_app$d' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( D @ ( B @ 'fun_app$d' ) @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom522) ).
thf(1272,plain,
! [A: 'B_set$',B: 'B_bool_fun_b_set_fun$',C: 'B_bool_fun$',D: 'B_bool_fun$'] :
( ( ! [E: 'B_bool_fun$',F: 'B_bool_fun$'] :
( ( F @ ( E @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( F @ ( B @ 'fun_app$d' ) @ ( E @ ( B @ 'fun_app$d' ) @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( D @ ( C @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( C @ ( B @ 'fun_app$d' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( D @ ( B @ 'fun_app$d' ) @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(1,conjecture,
( 'top$'
= ( 'bot$' @ ( 'a$' @ 'insert$' @ 'fun_app$b' ) @ ( 'bot$' @ ( 'a$' @ 'insert$' @ 'fun_app$b' ) @ ( 'top$' @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture1) ).
thf(2,negated_conjecture,
( 'top$'
!= ( 'bot$' @ ( 'a$' @ 'insert$' @ 'fun_app$b' ) @ ( 'bot$' @ ( 'a$' @ 'insert$' @ 'fun_app$b' ) @ ( 'top$' @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(497,plain,
( 'top$'
!= ( 'bot$' @ ( 'a$' @ 'insert$' @ 'fun_app$b' ) @ ( 'bot$' @ ( 'a$' @ 'insert$' @ 'fun_app$b' ) @ ( 'top$' @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(80,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$',C: 'B_bool_fun$'] :
( ( ( B = C )
& ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( C @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom411) ).
thf(876,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$',C: 'B_bool_fun$'] :
( ( ( B = C )
& ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( C @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(307,axiom,
! [A: 'B_set$',B: 'B$',C: 'B_set$'] :
( ( C @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( C @ ( A @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom79) ).
thf(1940,plain,
! [A: 'B_set$',B: 'B$',C: 'B_set$'] :
( ( C @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( C @ ( A @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(73,axiom,
! [A: 'B_bool_fun$'] :
~ ( 'bot$b' @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom532) ).
thf(845,plain,
! [A: 'B_bool_fun$'] :
~ ( 'bot$b' @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(173,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ~ ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom479) ).
thf(1316,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ~ ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( ( A = B )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(406,axiom,
! [A: 'B$',B: 'B_set$',C: 'B_set$'] :
( ( B @ ( A @ 'member$' ) )
=> ( ( B @ ( C @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( B @ ( C @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom8) ).
thf(2479,plain,
! [A: 'B$',B: 'B_set$',C: 'B_set$'] :
( ( B @ ( A @ 'member$' ) )
=> ( ( B @ ( C @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( B @ ( C @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(491,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( C @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> $false )
& ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom302) ).
thf(2828,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
~ ( ~ ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( C @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(102,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( C @ ( B @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( C @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom489) ).
thf(976,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( C @ ( B @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( C @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(381,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_bool_fun$'] :
( ? [D: 'B$'] :
( ( D @ ( C @ 'fun_app$' ) )
& ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( D @ 'member$' ) ) )
<=> ( ? [D: 'B$'] :
( ( D @ ( C @ 'fun_app$' ) )
& ( B @ ( D @ 'member$' ) ) )
| ? [D: 'B$'] :
( ( D @ ( C @ 'fun_app$' ) )
& ( A @ ( D @ 'member$' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom53) ).
thf(2347,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_bool_fun$'] :
( ( ( ? [D: 'B$'] :
( ( D @ ( C @ 'fun_app$' ) )
& ( B @ ( D @ 'member$' ) ) )
| ? [D: 'B$'] :
( ( D @ ( C @ 'fun_app$' ) )
& ( A @ ( D @ 'member$' ) ) ) )
=> ? [D: 'B$'] :
( ( D @ ( C @ 'fun_app$' ) )
& ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( D @ 'member$' ) ) ) )
& ( ? [D: 'B$'] :
( ( D @ ( C @ 'fun_app$' ) )
& ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( D @ 'member$' ) ) )
=> ( ? [D: 'B$'] :
( ( D @ ( C @ 'fun_app$' ) )
& ( B @ ( D @ 'member$' ) ) )
| ? [D: 'B$'] :
( ( D @ ( C @ 'fun_app$' ) )
& ( A @ ( D @ 'member$' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(352,axiom,
! [A: 'B_set$'] :
( ( A @ ( 'uminus$' @ 'fun_app$b' ) @ ( 'uminus$' @ 'fun_app$b' ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom372) ).
thf(2209,plain,
! [A: 'B_set$'] :
( ( A @ ( 'uminus$' @ 'fun_app$b' ) @ ( 'uminus$' @ 'fun_app$b' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(331,axiom,
! [A: 'B$'] :
( ( A @ ( 'bot$b' @ 'fun_app$' ) )
<=> ( 'bot$' @ ( A @ 'member$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom174) ).
thf(2071,plain,
! [A: 'B$'] :
( ( ( 'bot$' @ ( A @ 'member$' ) )
=> ( A @ ( 'bot$b' @ 'fun_app$' ) ) )
& ( ( A @ ( 'bot$b' @ 'fun_app$' ) )
=> ( 'bot$' @ ( A @ 'member$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(41,axiom,
! [A: 'B_bool_fun$'] :
( ( 'bot$b' @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
<=> ( A = 'bot$b' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom268) ).
thf(699,plain,
! [A: 'B_bool_fun$'] :
( ( ( A = 'bot$b' )
=> ( 'bot$b' @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
& ( ( 'bot$b' @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( A = 'bot$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(255,axiom,
! [A: 'B_set$',B: 'B$'] :
( ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( A
= ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$b' ) ) )
| ( A = 'bot$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom361) ).
thf(1721,plain,
! [A: 'B_set$',B: 'B$'] :
( ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( A
= ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$b' ) ) )
| ( A = 'bot$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(99,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( C @ ( B @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( C @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom418) ).
thf(963,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( C @ ( B @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( C @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(52,axiom,
! [A: 'B_bool_fun$',B: 'B_set_b_bool_fun_fun$',C: 'B_set$',D: 'B_set$'] :
( ( ! [E: 'B_set$',F: 'B_set$'] :
( ( F @ ( E @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( F @ ( B @ 'fun_app$a' ) @ ( E @ ( B @ 'fun_app$a' ) @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
& ( D @ ( C @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( C @ ( B @ 'fun_app$a' ) @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( D @ ( B @ 'fun_app$a' ) @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom235) ).
thf(748,plain,
! [A: 'B_bool_fun$',B: 'B_set_b_bool_fun_fun$',C: 'B_set$',D: 'B_set$'] :
( ( ! [E: 'B_set$',F: 'B_set$'] :
( ( F @ ( E @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( F @ ( B @ 'fun_app$a' ) @ ( E @ ( B @ 'fun_app$a' ) @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
& ( D @ ( C @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( C @ ( B @ 'fun_app$a' ) @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( D @ ( B @ 'fun_app$a' ) @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(238,axiom,
! [A: 'B_set$'] :
( ( 'bot$' @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom112) ).
thf(1639,plain,
! [A: 'B_set$'] :
( ( 'bot$' @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(209,axiom,
! [A: 'B_set$'] :
( ( ! [B: 'B$',C: 'B$'] :
( ( ( A @ ( C @ 'member$' ) )
& ( A @ ( B @ 'member$' ) ) )
=> ( B = C ) )
& ( A != 'bot$' ) )
=> ( A @ 'is_singleton$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom169) ).
thf(1481,plain,
! [A: 'B_set$'] :
( ( ! [B: 'B$',C: 'B$'] :
( ( ( A @ ( C @ 'member$' ) )
& ( A @ ( B @ 'member$' ) ) )
=> ( B = C ) )
& ( A != 'bot$' ) )
=> ( A @ 'is_singleton$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(489,axiom,
! [A: 'B$',B: 'B_set$',C: 'B_set$'] :
( ( C @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( B @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( C @ ( B @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ 'insert$' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom582) ).
thf(2823,plain,
! [A: 'B$',B: 'B_set$',C: 'B_set$'] :
( ( C @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( B @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( C @ ( B @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ 'insert$' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(396,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
<=> ( ( B != A )
& ( B
= ( A @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom551) ).
thf(2431,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( ( B != A )
& ( B
= ( A @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ) )
=> ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( B != A )
& ( B
= ( A @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(164,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom219) ).
thf(1276,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( ( B = A )
=> ( A @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(433,axiom,
! [A: 'B_set$'] :
( ( ! [B: 'B$'] :
( ( A
= ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$b' ) ) )
=> $false )
& ( A @ 'is_singleton$' ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom172) ).
thf(2591,plain,
! [A: 'B_set$'] :
~ ( ! [B: 'B$'] :
( A
!= ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$b' ) ) )
& ( A @ 'is_singleton$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(367,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'bot$' )
<=> ( ( B = 'bot$' )
& ( A = 'bot$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom106) ).
thf(2283,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( ( B = 'bot$' )
& ( A = 'bot$' ) )
=> ( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'bot$' ) )
& ( ( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'bot$' )
=> ( ( B = 'bot$' )
& ( A = 'bot$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(386,axiom,
! [A: 'B_set$'] :
( ( A @ ( 'bot$' @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'bot$' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom12) ).
thf(2389,plain,
! [A: 'B_set$'] :
( ( A @ ( 'bot$' @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'bot$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(496,axiom,
! [A: 'B$',B: 'B_set$',C: 'B_set$'] :
( ( C @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ 'member$' ) )
<=> ( ( C @ ( A @ 'member$' ) )
| ( B @ ( A @ 'member$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom23) ).
thf(2853,plain,
! [A: 'B$',B: 'B_set$',C: 'B_set$'] :
( ( ( ( C @ ( A @ 'member$' ) )
| ( B @ ( A @ 'member$' ) ) )
=> ( C @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ 'member$' ) ) )
& ( ( C @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ 'member$' ) )
=> ( ( C @ ( A @ 'member$' ) )
| ( B @ ( A @ 'member$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(360,axiom,
! [A: 'B_set$'] :
( ( A @ ( 'uminus$' @ 'fun_app$b' ) @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'top$' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom403) ).
thf(2251,plain,
! [A: 'B_set$'] :
( ( A @ ( 'uminus$' @ 'fun_app$b' ) @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'top$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(237,axiom,
! [A: 'B_b_bool_fun_fun$',B: 'B_set$'] :
( ( B @ ( A @ 'pairwise$' ) )
<=> ! [C: 'B$'] :
( ( B @ ( C @ 'member$' ) )
=> ! [D: 'B$'] :
( ( 'bot$' @ ( C @ 'insert$' @ 'fun_app$b' ) @ ( B @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( D @ 'member$' ) )
=> ( D @ ( C @ ( A @ 'fun_app$k' ) @ 'fun_app$' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom180) ).
thf(1629,plain,
! [A: 'B_b_bool_fun_fun$',B: 'B_set$'] :
( ( ! [C: 'B$'] :
( ( B @ ( C @ 'member$' ) )
=> ! [D: 'B$'] :
( ( 'bot$' @ ( C @ 'insert$' @ 'fun_app$b' ) @ ( B @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( D @ 'member$' ) )
=> ( D @ ( C @ ( A @ 'fun_app$k' ) @ 'fun_app$' ) ) ) )
=> ( B @ ( A @ 'pairwise$' ) ) )
& ( ( B @ ( A @ 'pairwise$' ) )
=> ! [C: 'B$'] :
( ( B @ ( C @ 'member$' ) )
=> ! [D: 'B$'] :
( ( 'bot$' @ ( C @ 'insert$' @ 'fun_app$b' ) @ ( B @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( D @ 'member$' ) )
=> ( D @ ( C @ ( A @ 'fun_app$k' ) @ 'fun_app$' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(317,axiom,
! [A: 'B_set$'] :
( ( A @ ( 'uminus$' @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
<=> ( A = 'bot$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom557) ).
thf(2004,plain,
! [A: 'B_set$'] :
( ( ( A = 'bot$' )
=> ( A @ ( 'uminus$' @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( A @ ( 'uminus$' @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( A = 'bot$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(344,axiom,
! [A: 'B$',B: 'B$',C: 'B$',D: 'B$'] :
( ( ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ 'insert$' @ 'fun_app$b' ) )
= ( 'bot$' @ ( D @ 'insert$' @ 'fun_app$b' ) @ ( C @ 'insert$' @ 'fun_app$b' ) ) )
<=> ( ( ( B = C )
& ( A = D ) )
| ( ( B = D )
& ( A = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom63) ).
thf(2152,plain,
! [A: 'B$',B: 'B$',C: 'B$',D: 'B$'] :
( ( ( ( ( B = C )
& ( A = D ) )
| ( ( B = D )
& ( A = C ) ) )
=> ( ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ 'insert$' @ 'fun_app$b' ) )
= ( 'bot$' @ ( D @ 'insert$' @ 'fun_app$b' ) @ ( C @ 'insert$' @ 'fun_app$b' ) ) ) )
& ( ( ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ 'insert$' @ 'fun_app$b' ) )
= ( 'bot$' @ ( D @ 'insert$' @ 'fun_app$b' ) @ ( C @ 'insert$' @ 'fun_app$b' ) ) )
=> ( ( ( B = C )
& ( A = D ) )
| ( ( B = D )
& ( A = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(362,axiom,
! [A: 'B_set$',B: 'B_set$'] : ( A @ ( B @ ( A @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom354) ).
thf(2262,plain,
! [A: 'B_set$',B: 'B_set$'] : ( A @ ( B @ ( A @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(115,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( C @ ( B @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( C @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom544) ).
thf(1030,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( C @ ( B @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( C @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(480,axiom,
! [A: 'B_set$',B: 'B_set$'] : ( A @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom294) ).
thf(2786,plain,
! [A: 'B_set$',B: 'B_set$'] : ( A @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(269,axiom,
! [A: 'B_set$',B: 'B$'] :
( ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
<=> ( ( A
= ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$b' ) ) )
| ( A = 'bot$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom360) ).
thf(1777,plain,
! [A: 'B_set$',B: 'B$'] :
( ( ( ( A
= ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$b' ) ) )
| ( A = 'bot$' ) )
=> ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( A
= ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$b' ) ) )
| ( A = 'bot$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(202,axiom,
! [A: 'B_set_b_set_bool_fun_fun$',B: 'B_set_b_set_bool_fun_fun$',C: 'B_set$'] :
( ( C @ ( B @ ( A @ 'ordering_top$a' ) ) )
=> ( C @ ( A @ 'ordering_top_axioms$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom577) ).
thf(1440,plain,
! [A: 'B_set_b_set_bool_fun_fun$',B: 'B_set_b_set_bool_fun_fun$',C: 'B_set$'] :
( ( C @ ( B @ ( A @ 'ordering_top$a' ) ) )
=> ( C @ ( A @ 'ordering_top_axioms$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(382,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
<=> ( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom290) ).
thf(2362,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= B )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(151,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
<=> ( ( B != A )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom497) ).
thf(1212,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( ( B != A )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( B != A )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(335,axiom,
! [A: 'B$',B: 'B_set$',C: 'B_set$'] :
( ( B @ ( A @ 'member$' ) )
=> ( ( C @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( B @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( C @ ( B @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ 'insert$' @ 'fun_app$b' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom584) ).
thf(2095,plain,
! [A: 'B$',B: 'B_set$',C: 'B_set$'] :
( ( B @ ( A @ 'member$' ) )
=> ( ( C @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( B @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( C @ ( B @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ 'insert$' @ 'fun_app$b' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(326,axiom,
( ( 'bot$' @ ( 'uminus$' @ 'fun_app$b' ) )
= 'top$' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom391) ).
thf(2036,plain,
( ( 'bot$' @ ( 'uminus$' @ 'fun_app$b' ) )
= 'top$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(373,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( C @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom288) ).
thf(2315,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( C @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(203,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( B = C )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( C @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom259) ).
thf(1442,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( B = C )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( C @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(320,axiom,
! [A: 'B_set$',B: 'B_set$'] : ( A @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom340) ).
thf(2019,plain,
! [A: 'B_set$',B: 'B_set$'] : ( A @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(45,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
<=> ( ( B != A )
& ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom496) ).
thf(716,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( ( ( B != A )
& ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
& ( ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( ( B != A )
& ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(234,axiom,
! [A: 'B_set$'] :
( ? [B: 'B$'] : ( A @ ( B @ 'member$' ) )
<=> ( A != 'bot$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom29) ).
thf(1614,plain,
! [A: 'B_set$'] :
( ( ( A != 'bot$' )
=> ? [B: 'B$'] : ( A @ ( B @ 'member$' ) ) )
& ( ? [B: 'B$'] : ( A @ ( B @ 'member$' ) )
=> ( A != 'bot$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(178,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( B @ ( 'collect$' @ 'fun_app$d' ) @ ( A @ ( 'collect$' @ 'fun_app$d' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
<=> ! [C: 'B$'] :
( ( C @ ( A @ 'fun_app$' ) )
=> ( C @ ( B @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom201) ).
thf(1348,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( ! [C: 'B$'] :
( ( C @ ( A @ 'fun_app$' ) )
=> ( C @ ( B @ 'fun_app$' ) ) )
=> ( B @ ( 'collect$' @ 'fun_app$d' ) @ ( A @ ( 'collect$' @ 'fun_app$d' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( B @ ( 'collect$' @ 'fun_app$d' ) @ ( A @ ( 'collect$' @ 'fun_app$d' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ! [C: 'B$'] :
( ( C @ ( A @ 'fun_app$' ) )
=> ( C @ ( B @ 'fun_app$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(215,axiom,
! [A: 'B$'] :
( ( 'bot$' @ ( A @ 'member$' ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom32) ).
thf(1512,plain,
! [A: 'B$'] :
~ ( 'bot$' @ ( A @ 'member$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(71,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set_b_bool_fun_fun$',D: 'B_bool_fun$'] :
( ( ! [E: 'B_set$',F: 'B_set$'] :
( ( F @ ( E @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( F @ ( C @ 'fun_app$a' ) @ ( E @ ( C @ 'fun_app$a' ) @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
& ( D @ ( B @ ( C @ 'fun_app$a' ) @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$a' ) @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom230) ).
thf(833,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set_b_bool_fun_fun$',D: 'B_bool_fun$'] :
( ( ! [E: 'B_set$',F: 'B_set$'] :
( ( F @ ( E @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( F @ ( C @ 'fun_app$a' ) @ ( E @ ( C @ 'fun_app$a' ) @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
& ( D @ ( B @ ( C @ 'fun_app$a' ) @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$a' ) @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(128,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
<=> ! [C: 'B$'] :
( ( A @ ( C @ 'member$' ) )
=> ( B @ ( C @ 'member$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom212) ).
thf(1097,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( ! [C: 'B$'] :
( ( A @ ( C @ 'member$' ) )
=> ( B @ ( C @ 'member$' ) ) )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ! [C: 'B$'] :
( ( A @ ( C @ 'member$' ) )
=> ( B @ ( C @ 'member$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(155,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( C @ ( B @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( C @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom430) ).
thf(1229,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( C @ ( B @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( C @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(68,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$',C: 'B_bool_fun_b_set_fun$',D: 'B_set$'] :
( ( ! [E: 'B_bool_fun$',F: 'B_bool_fun$'] :
( ( F @ ( E @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( F @ ( C @ 'fun_app$d' ) @ ( E @ ( C @ 'fun_app$d' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( D @ ( B @ ( C @ 'fun_app$d' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$d' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom231) ).
thf(818,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$',C: 'B_bool_fun_b_set_fun$',D: 'B_set$'] :
( ( ! [E: 'B_bool_fun$',F: 'B_bool_fun$'] :
( ( F @ ( E @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( F @ ( C @ 'fun_app$d' ) @ ( E @ ( C @ 'fun_app$d' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( D @ ( B @ ( C @ 'fun_app$d' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$d' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(21,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$',C: 'B_bool_fun$'] :
( ( ( A @ ( C @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( B @ ( C @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom246) ).
thf(603,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$',C: 'B_bool_fun$'] :
( ( ( A @ ( C @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( B @ ( C @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(239,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom597) ).
thf(1642,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(53,axiom,
! [A: 'B_set$',B: 'B$'] :
( ( B @ ( A @ ( 'uu$' @ 'fun_app$a' ) @ 'fun_app$' ) )
<=> ( A @ ( B @ 'member$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom0) ).
thf(752,plain,
! [A: 'B_set$',B: 'B$'] :
( ( ( A @ ( B @ 'member$' ) )
=> ( B @ ( A @ ( 'uu$' @ 'fun_app$a' ) @ 'fun_app$' ) ) )
& ( ( B @ ( A @ ( 'uu$' @ 'fun_app$a' ) @ 'fun_app$' ) )
=> ( A @ ( B @ 'member$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(186,axiom,
! [A: 'B_set$'] : ( A @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom370) ).
thf(1380,plain,
! [A: 'B_set$'] : ( A @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(437,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( A @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom310) ).
thf(2604,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( A @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(158,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( C @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom255) ).
thf(1248,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( C @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(62,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom405) ).
thf(790,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(77,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ~ ( A @ ( B @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom449) ).
thf(867,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ~ ( A @ ( B @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(265,axiom,
! [A: 'B$',B: 'B_set$',C: 'B_set$'] :
( ~ ( B @ ( A @ 'member$' ) )
=> ( ( C @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( B @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( C @ ( B @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom583) ).
thf(1757,plain,
! [A: 'B$',B: 'B_set$',C: 'B_set$'] :
( ~ ( B @ ( A @ 'member$' ) )
=> ( ( C @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( B @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( C @ ( B @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(447,axiom,
! [A: 'B_set$'] :
( ( A @ ( 'top$' @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'top$' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom85) ).
thf(2636,plain,
! [A: 'B_set$'] :
( ( A @ ( 'top$' @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'top$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(201,axiom,
! [A: 'B_set$',B: 'B_set$',C: tlbool] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( ( A @ ( B @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( C = tltrue ) )
<=> $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom452) ).
thf(1436,plain,
! [A: 'B_set$',B: 'B_set$',C: tlbool] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( A @ ( B @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( C = tltrue ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(172,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'uminus$' @ 'fun_app$b' ) @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( A @ ( B @ ( 'uminus$' @ 'fun_app$b' ) @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom466) ).
thf(1314,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'uminus$' @ 'fun_app$b' ) @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( A @ ( B @ ( 'uminus$' @ 'fun_app$b' ) @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(212,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
<=> ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( C @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom197) ).
thf(1495,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( C @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( C @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(4,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$',C: 'B_bool_fun$'] :
( ( ( C @ ( B @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( C @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom490) ).
thf(506,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$',C: 'B_bool_fun$'] :
( ( ( C @ ( B @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( C @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(147,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( C @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom253) ).
thf(1197,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( C @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(391,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( 'uminus$' @ 'fun_app$b' ) @ ( A @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( B @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom634) ).
thf(2404,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( 'uminus$' @ 'fun_app$b' ) @ ( A @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( B @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(355,axiom,
! [A: 'B$',B: 'B_set$'] :
( ( ( B @ ( A @ 'member$' ) )
=> $false )
=> ( B @ ( 'uminus$' @ 'fun_app$b' ) @ ( A @ 'member$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom376) ).
thf(2223,plain,
! [A: 'B$',B: 'B_set$'] :
( ~ ( B @ ( A @ 'member$' ) )
=> ( B @ ( 'uminus$' @ 'fun_app$b' ) @ ( A @ 'member$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(442,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( A @ ( B @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom5) ).
thf(2619,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( A @ ( B @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(328,axiom,
! [A: 'B_set$',B: 'B$',C: 'B_set$'] :
( ( C @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
<=> ( ( ~ ( C @ ( B @ 'member$' ) )
=> ( ( ~ ( A @ ( B @ 'member$' ) )
=> ( C @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( A @ ( B @ 'member$' ) )
=> ( C @ ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ) )
& ( ( C @ ( B @ 'member$' ) )
=> ( C @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom367) ).
thf(2040,plain,
! [A: 'B_set$',B: 'B$',C: 'B_set$'] :
( ( ( ( ~ ( C @ ( B @ 'member$' ) )
=> ( ( ~ ( A @ ( B @ 'member$' ) )
=> ( C @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( A @ ( B @ 'member$' ) )
=> ( C @ ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ) )
& ( ( C @ ( B @ 'member$' ) )
=> ( C @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) )
=> ( C @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( C @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( ~ ( C @ ( B @ 'member$' ) )
=> ( ( ~ ( A @ ( B @ 'member$' ) )
=> ( C @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( A @ ( B @ 'member$' ) )
=> ( C @ ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$b' ) @ ( A @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ) )
& ( ( C @ ( B @ 'member$' ) )
=> ( C @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(321,axiom,
! [A: 'B_set$'] :
( ( 'top$' @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom612) ).
thf(2021,plain,
! [A: 'B_set$'] :
( ( 'top$' @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(424,axiom,
! [A: 'B$',B: 'B_set$',C: 'B_set$'] :
( ( ( ( C @ ( A @ 'member$' ) )
=> $false )
& ( ( B @ ( A @ 'member$' ) )
=> $false )
& ( C @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ 'member$' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom56) ).
thf(2549,plain,
! [A: 'B$',B: 'B_set$',C: 'B_set$'] :
~ ( ~ ( C @ ( A @ 'member$' ) )
& ~ ( B @ ( A @ 'member$' ) )
& ( C @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ 'member$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(142,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( A = B )
<=> ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom263) ).
thf(1172,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(394,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( C @ ( B @ ( A @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
<=> ( C @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom363) ).
thf(2417,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( C @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( C @ ( B @ ( A @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( C @ ( B @ ( A @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( C @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(47,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$',C: 'B_bool_fun$'] :
( ( ( C @ ( B @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( C @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom488) ).
thf(728,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$',C: 'B_bool_fun$'] :
( ( ( C @ ( B @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> ( C @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(412,axiom,
! [A: 'B_set$'] :
( ( A @ ( 'top$' @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom620) ).
thf(2502,plain,
! [A: 'B_set$'] :
( ( A @ ( 'top$' @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(467,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'top$' )
& ( ( B @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'bot$' ) )
=> ( ( A @ ( 'uminus$' @ 'fun_app$b' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom576) ).
thf(2731,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'top$' )
& ( ( B @ ( A @ ( 'inf$a' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= 'bot$' ) )
=> ( ( A @ ( 'uminus$' @ 'fun_app$b' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(280,axiom,
! [A: 'B_set$'] :
~ ( 'bot$' @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom533) ).
thf(1829,plain,
! [A: 'B_set$'] :
~ ( 'bot$' @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(162,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom424) ).
thf(1268,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(484,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom348) ).
thf(2803,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(113,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( ( ~ ( A @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> $false )
& ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom539) ).
thf(1019,plain,
! [A: 'B_set$',B: 'B_set$'] :
~ ( ~ ( ~ ( A @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(253,axiom,
! [A: 'B$',B: 'B_set$'] :
( ( B @ ( 'uminus$' @ 'fun_app$b' ) @ ( A @ 'member$' ) )
<=> ~ ( B @ ( A @ 'member$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom377) ).
thf(1713,plain,
! [A: 'B$',B: 'B_set$'] :
( ( ~ ( B @ ( A @ 'member$' ) )
=> ( B @ ( 'uminus$' @ 'fun_app$b' ) @ ( A @ 'member$' ) ) )
& ( ( B @ ( 'uminus$' @ 'fun_app$b' ) @ ( A @ 'member$' ) )
=> ~ ( B @ ( A @ 'member$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(108,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( A != B )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom383) ).
thf(1004,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( A != B )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(459,axiom,
! [A: 'B$',B: 'B_set$',C: 'B_set$'] :
( ~ ( B @ ( A @ 'member$' ) )
=> ( ( C @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
<=> ( C @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom343) ).
thf(2699,plain,
! [A: 'B$',B: 'B_set$',C: 'B_set$'] :
( ~ ( B @ ( A @ 'member$' ) )
=> ( ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( C @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( C @ ( A @ 'insert$' @ 'fun_app$b' ) @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( C @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(127,axiom,
! [A: 'B_set$',B: 'B_set_b_set_fun$',C: 'B_set$',D: 'B_set$'] :
( ( ! [E: 'B_set$',F: 'B_set$'] :
( ( F @ ( E @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( F @ ( B @ 'fun_app$b' ) @ ( E @ ( B @ 'fun_app$b' ) @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( D @ ( C @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( C @ ( B @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( D @ ( B @ 'fun_app$b' ) @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom525) ).
thf(1093,plain,
! [A: 'B_set$',B: 'B_set_b_set_fun$',C: 'B_set$',D: 'B_set$'] :
( ( ! [E: 'B_set$',F: 'B_set$'] :
( ( F @ ( E @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( F @ ( B @ 'fun_app$b' ) @ ( E @ ( B @ 'fun_app$b' ) @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( D @ ( C @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( C @ ( B @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( D @ ( B @ 'fun_app$b' ) @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(304,axiom,
! [A: 'B_set$',B: 'B_set_b_set_fun$',C: 'B_set$',D: 'B_set$'] :
( ( ! [E: 'B_set$',F: 'B_set$'] :
( ( F @ ( E @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( F @ ( B @ 'fun_app$b' ) @ ( E @ ( B @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( D @ ( C @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( C @ ( B @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( D @ ( B @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom237) ).
thf(1930,plain,
! [A: 'B_set$',B: 'B_set_b_set_fun$',C: 'B_set$',D: 'B_set$'] :
( ( ! [E: 'B_set$',F: 'B_set$'] :
( ( F @ ( E @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( F @ ( B @ 'fun_app$b' ) @ ( E @ ( B @ 'fun_app$b' ) @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( D @ ( C @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( C @ ( B @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( D @ ( B @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(26,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( A = B )
=> ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom228) ).
thf(624,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( A = B )
=> ( B @ ( A @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(69,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ( ( A @ ( B @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom425) ).
thf(822,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
~ ( ( A @ ( B @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
& ( B @ ( A @ ( 'less$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(414,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( C @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( C @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom44) ).
thf(2507,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( C @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= ( C @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(299,axiom,
! [A: 'B$',B: 'B_set$',C: 'B_set$'] :
( ( ( ( ~ ( C @ ( A @ 'member$' ) )
& ( B @ ( A @ 'member$' ) ) )
=> $false )
& ( C @ ( B @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ 'member$' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom59) ).
thf(1902,plain,
! [A: 'B$',B: 'B_set$',C: 'B_set$'] :
~ ( ~ ( ~ ( C @ ( A @ 'member$' ) )
& ( B @ ( A @ 'member$' ) ) )
& ( C @ ( B @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ 'member$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(40,axiom,
! [A: 'B_bool_fun$'] :
( ( A @ ( 'top$b' @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
<=> ( A = 'top$b' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom277) ).
thf(691,plain,
! [A: 'B_bool_fun$'] :
( ( ( A = 'top$b' )
=> ( A @ ( 'top$b' @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) )
& ( ( A @ ( 'top$b' @ ( 'less_eq$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
=> ( A = 'top$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(375,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
<=> ( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom345) ).
thf(2321,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= B )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( B @ ( A @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(110,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ! [C: 'B$'] :
( ( A @ ( C @ 'member$' ) )
=> ( B @ ( C @ 'member$' ) ) )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom189) ).
thf(1009,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ! [C: 'B$'] :
( ( A @ ( C @ 'member$' ) )
=> ( B @ ( C @ 'member$' ) ) )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(351,axiom,
! [A: 'B$',B: 'B_set$',C: 'B_set$'] :
( ( B @ ( A @ 'member$' ) )
=> ( C @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ 'member$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom55) ).
thf(2206,plain,
! [A: 'B$',B: 'B_set$',C: 'B_set$'] :
( ( B @ ( A @ 'member$' ) )
=> ( C @ ( B @ ( 'sup$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ 'member$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(143,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( A = B ) )
=> ( C @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom261) ).
thf(1184,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_set$'] :
( ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
& ( A = B ) )
=> ( C @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(197,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ~ ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
<=> ( ( A = B )
| ~ ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom477) ).
thf(1416,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( ( A = B )
| ~ ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ~ ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ~ ( B @ ( A @ ( 'less$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ( A = B )
| ~ ( B @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(441,axiom,
! [A: 'B$',B: 'B_set$'] :
( ( B @ ( A @ 'insert$' @ 'fun_app$b' ) )
!= 'bot$' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom62) ).
thf(2615,plain,
! [A: 'B$',B: 'B_set$'] :
( ( B @ ( A @ 'insert$' @ 'fun_app$b' ) )
!= 'bot$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(401,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B$',D: 'B_set$'] :
( ( D @ ( C @ 'insert$' @ 'fun_app$b' ) @ ( B @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
<=> ( ~ ( A @ ( C @ 'member$' ) )
& ( D @ ( B @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom362) ).
thf(2453,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B$',D: 'B_set$'] :
( ( ( ~ ( A @ ( C @ 'member$' ) )
& ( D @ ( B @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
=> ( D @ ( C @ 'insert$' @ 'fun_app$b' ) @ ( B @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
& ( ( D @ ( C @ 'insert$' @ 'fun_app$b' ) @ ( B @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
=> ( ~ ( A @ ( C @ 'member$' ) )
& ( D @ ( B @ ( 'minus$' @ 'fun_app$c' ) @ 'fun_app$b' ) @ ( A @ ( 'less_eq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(334,axiom,
! [A: 'B_set$'] :
( ( A @ 'is_empty$' )
<=> ( A = 'bot$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom177) ).
thf(2087,plain,
! [A: 'B_set$'] :
( ( ( A = 'bot$' )
=> ( A @ 'is_empty$' ) )
& ( ( A @ 'is_empty$' )
=> ( A = 'bot$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(2890,plain,
$false,
inference(e,[status(thm)],[645,1411,1767,1105,893,2595,1818,2280,2612,1024,1469,2744,1823,2306,760,2336,1454,909,628,2463,1899,1924,730,2395,2676,2099,1533,1855,2077,1158,2309,762,2622,1068,2776,1808,511,2380,614,1692,677,1608,2607,1735,2448,814,2476,1788,1426,1756,533,1761,913,1222,930,1746,1835,2723,782,1645,1359,1724,1366,1967,1803,1518,1623,2654,1409,1430,2667,2339,2755,1871,2708,1907,1860,1323,2274,1826,2466,1059,2571,1832,934,1191,559,1800,1892,2552,2767,969,1398,2520,2024,2533,1847,2169,1087,1013,770,1489,924,2027,1373,1911,1109,2451,1334,1682,1858,2254,1677,2335,1283,1051,1302,1664,2105,1450,2555,806,687,2833,2483,1886,774,1394,2762,1072,2530,998,2809,2242,2799,2639,1943,1201,2392,1521,920,2646,1199,810,2737,2296,2641,2000,798,2601,825,1570,1502,630,2528,2015,2705,2264,1580,2277,598,2147,2150,1370,1032,2628,2565,2068,2200,1656,1079,1407,710,1573,916,2445,2758,566,1555,2332,2826,1296,665,1402,2245,1983,2840,1328,869,610,499,1970,1227,1138,1719,1567,2460,884,1160,2312,1937,2172,1889,901,1075,1414,2240,2108,2038,1446,1016,2085,1155,547,837,647,2598,654,1552,2581,2505,2497,2697,605,2370,1539,2836,1382,1266,1231,1002,1852,2813,2788,2203,633,508,1466,1895,953,926,1241,2546,1515,2221,794,586,2423,888,2144,1648,1754,2033,1927,2734,573,689,601,965,1727,1510,1007,2791,2489,1752,2568,579,2806,2716,545,2225,732,1884,2525,2657,1701,2398,1428,1669,2293,787,1107,1997,2442,947,1356,2510,1194,2119,2679,784,2774,736,990,1492,2669,2116,880,1122,1376,1307,2742,1557,1993,1821,848,1293,2329,890,1667,758,2610,535,2625,1162,726,2410,1325,1112,2578,521,1396,2212,2765,1528,608,1000,2633,2535,1250,851,922,1805,2725,2401,1699,1626,1208,944,2318,663,1134,1145,1049,1304,1873,1845,1547,1798,872,1611,2192,2012,2821,2720,2850,2689,712,557,1770,1225,2060,707,1605,2588,1368,2175,2407,2386,1300,1188,1038,1262,1980,2486,1679,1130,1738,643,1711,2747,1085,576,1404,1934,1849,1536,656,2543,1972,1749,978,859,2500,744,2728,2030,1881,1272,497,876,1940,845,1316,2479,2828,976,2347,2209,2071,699,1721,963,748,1639,1481,2823,2431,1276,2591,2283,2389,2853,2251,1629,2004,2152,2262,1030,2786,1777,1440,2362,1212,2095,2036,2315,1442,2019,716,1614,1348,1512,833,1097,1229,818,603,1642,752,1380,2604,1248,790,867,1757,2636,1436,1314,1495,506,1197,2404,2223,2619,2040,2021,2549,1172,2417,728,2502,2731,1829,1268,2803,1019,1713,1004,2699,1093,1930,624,822,2507,1902,691,2321,1009,2206,1184,1416,2615,2453,2087]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP322_1 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.14/0.46 % Computer : n013.cluster.edu
% 0.14/0.46 % Model : x86_64 x86_64
% 0.14/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.46 % Memory : 8046.5625MB
% 0.14/0.46 % OS : Linux 6.8.0-71-generic
% 0.14/0.46 % CPULimit : 300
% 0.14/0.46 % WCLimit : 300
% 0.14/0.46 % DateTime : Fri Sep 25 19:06:07 UTC 2026
% 0.14/0.46 % CPUTime :
% 0.14/0.46 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.94/1.06 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.96/1.61 % [INFO] Parsing done (548ms).
% 2.96/1.62 % [INFO] Running in sequential loop mode.
% 3.82/1.82 % [INFO] eprover registered as external prover.
% 3.82/1.83 % [INFO] Scanning for conjecture ...
% 4.22/2.00 % [INFO] Found a conjecture (or negated_conjecture) and 678 axioms. Running axiom selection ...
% 5.53/2.23 % [INFO] Axiom selection finished. Selected 494 axioms (removed 184 axioms).
% 7.21/2.64 % [INFO] Problem is typed first-order (TPTP TFF).
% 7.21/2.66 % [INFO] Type checking passed.
% 7.21/2.67 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 19.58/5.75 % External prover 'e' found a proof!
% 19.58/5.75 % [INFO] Killing All external provers ...
% 19.58/5.75 % Time passed: 5139ms (effective reasoning time: 4126ms)
% 19.58/5.75 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 19.58/5.75 % Axioms used in derivation (494): axiom326, axiom32, axiom260, axiom280, axiom127, axiom626, axiom546, axiom61, axiom527, axiom452, axiom491, axiom28, axiom76, axiom230, axiom100, axiom6, axiom564, axiom503, axiom485, axiom553, axiom54, axiom549, axiom480, axiom25, axiom369, axiom404, axiom14, axiom474, axiom221, axiom214, axiom516, axiom322, axiom496, axiom142, axiom284, axiom423, axiom65, axiom36, axiom203, axiom169, axiom622, axiom531, axiom441, axiom507, axiom430, axiom600, axiom50, axiom158, axiom10, axiom508, axiom597, axiom580, axiom344, axiom138, axiom119, axiom210, axiom407, axiom191, axiom17, axiom257, axiom397, axiom412, axiom460, axiom354, axiom587, axiom477, axiom579, axiom22, axiom434, axiom341, axiom504, axiom173, axiom109, axiom348, axiom184, axiom561, axiom376, axiom172, axiom535, axiom266, axiom445, axiom42, axiom513, axiom239, axiom300, axiom350, axiom372, axiom195, axiom162, axiom583, axiom358, axiom161, axiom632, axiom616, axiom542, axiom123, axiom246, axiom592, axiom383, axiom2, axiom134, axiom456, axiom33, axiom150, axiom572, axiom11, axiom557, axiom235, axiom225, axiom473, axiom39, axiom608, axiom499, axiom330, axiom418, axiom484, axiom112, axiom304, axiom488, axiom520, axiom365, axiom251, axiom64, axiom578, axiom530, axiom283, axiom314, axiom539, axiom427, axiom625, axiom591, axiom59, axiom247, axiom48, axiom217, axiom343, axiom27, axiom352, axiom411, axiom294, axiom179, axiom363, axiom115, axiom94, axiom5, axiom336, axiom308, axiom35, axiom78, axiom24, axiom278, axiom272, axiom228, axiom405, axiom455, axiom475, axiom121, axiom132, axiom56, axiom466, axiom563, axiom290, axiom206, axiom318, axiom60, axiom631, axiom0, axiom574, axiom490, axiom13, axiom53, axiom359, axiom416, axiom489, axiom545, axiom16, axiom459, axiom400, axiom517, axiom258, axiom75, axiom448, axiom552, axiom385, axiom478, axiom168, axiom528, axiom332, axiom9, axiom612, axiom366, axiom207, axiom494, axiom538, axiom567, axiom355, axiom586, axiom422, axiom185, axiom202, axiom252, axiom146, axiom97, axiom391, axiom604, axiom263, axiom415, axiom589, axiom382, axiom254, axiom444, axiom82, axiom45, axiom541, axiom360, axiom483, axiom229, axiom174, axiom556, axiom426, axiom347, axiom180, axiom67, axiom213, axiom534, axiom450, axiom196, axiom523, axiom629, axiom310, axiom72, axiom461, axiom449, axiom224, axiom438, axiom218, axiom512, axiom38, axiom419, axiom377, axiom500, axiom91, axiom163, axiom408, axiom52, axiom511, axiom12, axiom37, axiom212, axiom602, axiom432, axiom223, axiom571, axiom501, axiom342, axiom193, axiom34, axiom630, axiom544, axiom152, axiom425, axiom167, axiom454, axiom573, axiom205, axiom364, axiom628, axiom79, axiom189, axiom394, axiom23, axiom227, axiom595, axiom562, axiom41, axiom476, axiom216, axiom409, axiom286, axiom618, axiom275, axiom63, axiom19, axiom458, axiom8, axiom410, axiom320, axiom30, axiom370, axiom201, axiom178, axiom428, axiom479, axiom259, axiom74, axiom451, axiom570, axiom85, axiom566, axiom509, axiom233, axiom220, axiom598, axiom302, axiom367, axiom378, axiom57, axiom599, axiom471, axiom506, axiom186, axiom497, axiom164, axiom374, axiom324, axiom614, axiom440, axiom581, axiom282, axiom244, axiom271, axiom4, axiom255, axiom71, axiom462, axiom15, axiom129, axiom620, axiom594, axiom136, axiom414, axiom106, axiom533, axiom170, axiom268, axiom403, axiom522, axiom436, axiom482, axiom555, axiom486, axiom346, axiom262, axiom68, axiom175, axiom237, axiom26, axiom493, axiom298, axiom439, axiom634, axiom469, axiom49, axiom577, axiom219, axiom197, axiom46, axiom585, axiom248, axiom421, axiom590, axiom18, axiom338, axiom88, axiom442, axiom510, axiom199, axiom547, axiom166, axiom526, axiom559, axiom457, axiom521, axiom66, axiom345, axiom464, axiom204, axiom296, axiom569, axiom215, axiom576, axiom596, axiom274, axiom117, axiom44, axiom446, axiom554, axiom495, axiom269, axiom453, axiom502, axiom103, axiom7, axiom515, axiom231, axiom306, axiom253, axiom368, axiom183, axiom550, axiom148, axiom128, axiom316, axiom540, axiom537, axiom349, axiom249, axiom211, axiom29, axiom361, axiom429, axiom532, axiom177, axiom31, axiom380, axiom188, axiom431, axiom208, axiom20, axiom588, axiom627, axiom176, axiom159, axiom487, axiom519, axiom384, axiom551, axiom73, axiom417, axiom154, axiom40, axiom265, axiom165, axiom47, axiom518, axiom171, axiom3, axiom187, axiom288, axiom69, axiom277, axiom536, axiom198, axiom529, axiom144, axiom55, axiom70, axiom238, axiom584, axiom281, axiom424, axiom633, axiom593, axiom245, axiom435, axiom312, axiom543, axiom351, axiom505, axiom261, axiom413, axiom256, axiom334, axiom160, axiom582, axiom514, axiom43, axiom481, axiom606, axiom77, axiom406, axiom388, axiom420, axiom610, axiom62, axiom498, axiom209, axiom492, axiom21, axiom200, axiom250, axiom292, axiom525, axiom234, axiom362, axiom51, axiom548, axiom328, axiom140, axiom58, axiom624, axiom340, axiom194, axiom353
% 19.58/5.75 % No. of inferences in proof: 992
% 19.58/5.75 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5139 ms resp. 4126 ms w/o parsing
% 20.92/6.07 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 20.92/6.08 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------