%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP367_1 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n004.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 07:37:45 AM UTC 2026
% Result : Theorem 24.72s 7.17s
% Output : Refutation 26.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 616
% Syntax : Number of formulae : 1234 ( 416 unt; 0 typ; 0 def)
% Number of atoms : 3522 (1109 equ; 0 cnn)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 18027 ( 360 ~; 76 |;1016 &;15379 @)
% ( 148 <=>;1048 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 8 avg)
% Number of types : 20 ( 19 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 68 ( 66 usr; 31 con; 0-2 aty)
% Number of variables : 3136 ( 0 ^;3076 !; 60 ?;3136 :)
% Comments :
%------------------------------------------------------------------------------
thf('A_ltln_set_a_ltln_set_set_fun$_type',type,
'A_ltln_set_a_ltln_set_set_fun$': $tType ).
thf('A_ltln_set_a_ltln_set_set_a_ltln_set_set_fun_fun$_type',type,
'A_ltln_set_a_ltln_set_set_a_ltln_set_set_fun_fun$': $tType ).
thf('A_ltln_set_a_ltln_set_bool_fun_fun$_type',type,
'A_ltln_set_a_ltln_set_bool_fun_fun$': $tType ).
thf('A_ltln_set_bool_fun$_type',type,
'A_ltln_set_bool_fun$': $tType ).
thf('A_ltln_set_set_a_ltln_set_set_a_ltln_set_set_fun_fun$_type',type,
'A_ltln_set_set_a_ltln_set_set_a_ltln_set_set_fun_fun$': $tType ).
thf('A_ltln_set_set_a_ltln_set_fun$_type',type,
'A_ltln_set_set_a_ltln_set_fun$': $tType ).
thf('A_ltln_bool_fun$_type',type,
'A_ltln_bool_fun$': $tType ).
thf('A_ltln_set_set_set$_type',type,
'A_ltln_set_set_set$': $tType ).
thf('A_ltln_set$_type',type,
'A_ltln_set$': $tType ).
thf('A_ltln_set_set_bool_fun$_type',type,
'A_ltln_set_set_bool_fun$': $tType ).
thf('A_ltln$_type',type,
'A_ltln$': $tType ).
thf('A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$_type',type,
'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$': $tType ).
thf('A_ltln_a_ltln_set_a_ltln_set_fun_fun$_type',type,
'A_ltln_a_ltln_set_a_ltln_set_fun_fun$': $tType ).
thf('A_ltln_set_a_ltln_set_fun$_type',type,
'A_ltln_set_a_ltln_set_fun$': $tType ).
thf('A_ltln_a_ltln_set_set_fun$_type',type,
'A_ltln_a_ltln_set_set_fun$': $tType ).
thf('A_ltln_set_set_a_ltln_set_set_fun$_type',type,
'A_ltln_set_set_a_ltln_set_set_fun$': $tType ).
thf('A_ltln_a_ltln_set_fun$_type',type,
'A_ltln_a_ltln_set_fun$': $tType ).
thf('A_ltln_a_ltln_bool_fun_fun$_type',type,
'A_ltln_a_ltln_bool_fun_fun$': $tType ).
thf('A_ltln_set_set$_type',type,
'A_ltln_set_set$': $tType ).
thf('member$_decl',type,
'member$': 'A_ltln$' > 'A_ltln_set_bool_fun$' ).
thf('subformulas_nu$_decl',type,
'subformulas_nu$': 'A_ltln_a_ltln_set_fun$' ).
thf('sup_fin$a_decl',type,
'sup_fin$a': 'A_ltln_set_set_a_ltln_set_fun$' ).
thf('bot$_decl',type,
'bot$': 'A_ltln_set_set$' ).
thf('comp_fun_idem$_decl',type,
'comp_fun_idem$': 'A_ltln_set_set_a_ltln_set_set_a_ltln_set_set_fun_fun$' > $o ).
thf('inf_fin$a_decl',type,
'inf_fin$a': 'A_ltln_set_set_a_ltln_set_fun$' ).
thf('fun_app$l_decl',type,
'fun_app$l': 'A_ltln_a_ltln_bool_fun_fun$' > 'A_ltln$' > 'A_ltln_bool_fun$' ).
thf('bind$c_decl',type,
'bind$c': 'A_ltln_set$' > 'A_ltln_a_ltln_set_fun$' > 'A_ltln_set$' ).
thf('bot$c_decl',type,
'bot$c': 'A_ltln_bool_fun$' ).
thf('insert$b_decl',type,
'insert$b': 'A_ltln_a_ltln_set_a_ltln_set_fun_fun$' ).
thf('disjnt$a_decl',type,
'disjnt$a': 'A_ltln_set_a_ltln_set_bool_fun_fun$' ).
thf('fun_app$b_decl',type,
'fun_app$b': 'A_ltln_set_set_bool_fun$' > 'A_ltln_set_set$' > $o ).
thf('x$_decl',type,
'x$': 'A_ltln_set$' ).
thf('minus$a_decl',type,
'minus$a': 'A_ltln_set_set_a_ltln_set_set_a_ltln_set_set_fun_fun$' ).
thf('fun_app$a_decl',type,
'fun_app$a': 'A_ltln_set_bool_fun$' > 'A_ltln_set$' > $o ).
thf('is_singleton$a_decl',type,
'is_singleton$a': 'A_ltln_set_set_bool_fun$' ).
thf('fun_app$g_decl',type,
'fun_app$g': 'A_ltln_set_a_ltln_set_bool_fun_fun$' > 'A_ltln_set$' > 'A_ltln_set_bool_fun$' ).
thf('minus$b_decl',type,
'minus$b': 'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$' ).
thf('less_eq$a_decl',type,
'less_eq$a': 'A_ltln_set_set$' > 'A_ltln_set_set_bool_fun$' ).
thf('comp_fun_idem$a_decl',type,
'comp_fun_idem$a': 'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$' > $o ).
thf('bind$_decl',type,
'bind$': 'A_ltln_set$' > 'A_ltln_a_ltln_set_set_fun$' > 'A_ltln_set_set$' ).
thf('filter$a_decl',type,
'filter$a': 'A_ltln_bool_fun$' > 'A_ltln_set_a_ltln_set_fun$' ).
thf('comp_fun_idem$b_decl',type,
'comp_fun_idem$b': 'A_ltln_set_a_ltln_set_set_a_ltln_set_set_fun_fun$' > $o ).
thf('y$_decl',type,
'y$': 'A_ltln_set$' ).
thf('fun_app$h_decl',type,
'fun_app$h': 'A_ltln_a_ltln_set_fun$' > 'A_ltln$' > 'A_ltln_set$' ).
thf('subformulas_mu$_decl',type,
'subformulas_mu$': 'A_ltln_a_ltln_set_fun$' ).
thf('fun_app$i_decl',type,
'fun_app$i': 'A_ltln_set_set_a_ltln_set_fun$' > 'A_ltln_set_set$' > 'A_ltln_set$' ).
thf('is_empty$a_decl',type,
'is_empty$a': 'A_ltln_set_set_bool_fun$' ).
thf('fun_app$_decl',type,
'fun_app$': 'A_ltln_bool_fun$' > 'A_ltln$' > $o ).
thf('fun_app$e_decl',type,
'fun_app$e': 'A_ltln_set_set_a_ltln_set_set_fun$' > 'A_ltln_set_set$' > 'A_ltln_set_set$' ).
thf('is_singleton$_decl',type,
'is_singleton$': 'A_ltln_set_bool_fun$' ).
thf('collect$a_decl',type,
'collect$a': 'A_ltln_bool_fun$' > 'A_ltln_set$' ).
thf('insert$a_decl',type,
'insert$a': 'A_ltln_set_a_ltln_set_set_a_ltln_set_set_fun_fun$' ).
thf('max$_decl',type,
'max$': 'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$' ).
thf('uu$_decl',type,
'uu$': 'A_ltln_set_set$' > 'A_ltln_set_bool_fun$' ).
thf('inf$a_decl',type,
'inf$a': 'A_ltln_set_set_a_ltln_set_set_a_ltln_set_set_fun_fun$' ).
thf('bind$a_decl',type,
'bind$a': 'A_ltln_set_set$' > 'A_ltln_set_a_ltln_set_fun$' > 'A_ltln_set$' ).
thf('bind$b_decl',type,
'bind$b': 'A_ltln_set_set$' > 'A_ltln_set_a_ltln_set_set_fun$' > 'A_ltln_set_set$' ).
thf('inf$_decl',type,
'inf$': 'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$' ).
thf('fun_app$k_decl',type,
'fun_app$k': 'A_ltln_set_a_ltln_set_set_fun$' > 'A_ltln_set$' > 'A_ltln_set_set$' ).
thf('fun_app$m_decl',type,
'fun_app$m': 'A_ltln_set_a_ltln_set_set_a_ltln_set_set_fun_fun$' > 'A_ltln_set$' > 'A_ltln_set_set_a_ltln_set_set_fun$' ).
thf('bot$a_decl',type,
'bot$a': 'A_ltln_set$' ).
thf('fun_app$j_decl',type,
'fun_app$j': 'A_ltln_a_ltln_set_set_fun$' > 'A_ltln$' > 'A_ltln_set_set$' ).
thf('disjnt$_decl',type,
'disjnt$': 'A_ltln_set_set$' > 'A_ltln_set_set_bool_fun$' ).
thf('fold$a_decl',type,
'fold$a': 'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$' > 'A_ltln_set$' > 'A_ltln_set_set_a_ltln_set_fun$' ).
thf('is_empty$_decl',type,
'is_empty$': 'A_ltln_set_bool_fun$' ).
thf('sup$a_decl',type,
'sup$a': 'A_ltln_set_set_a_ltln_set_set_a_ltln_set_set_fun_fun$' ).
thf('fun_app$n_decl',type,
'fun_app$n': 'A_ltln_a_ltln_set_a_ltln_set_fun_fun$' > 'A_ltln$' > 'A_ltln_set_a_ltln_set_fun$' ).
thf('fold$_decl',type,
'fold$': 'A_ltln_a_ltln_set_a_ltln_set_fun_fun$' > 'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$' ).
thf('the_elem$_decl',type,
'the_elem$': 'A_ltln_set$' > 'A_ltln$' ).
thf('comp_fun_idem$c_decl',type,
'comp_fun_idem$c': 'A_ltln_a_ltln_set_a_ltln_set_fun_fun$' > $o ).
thf('bot$d_decl',type,
'bot$d': 'A_ltln_set_bool_fun$' ).
thf('fun_app$f_decl',type,
'fun_app$f': 'A_ltln_set_set_a_ltln_set_set_a_ltln_set_set_fun_fun$' > 'A_ltln_set_set$' > 'A_ltln_set_set_a_ltln_set_set_fun$' ).
thf('collect$_decl',type,
'collect$': 'A_ltln_set_bool_fun$' > 'A_ltln_set_set$' ).
thf('sup$_decl',type,
'sup$': 'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$' ).
thf('less_eq$_decl',type,
'less_eq$': 'A_ltln_set_a_ltln_set_bool_fun_fun$' ).
thf('the_elem$a_decl',type,
'the_elem$a': 'A_ltln_set_set_a_ltln_set_fun$' ).
thf('finite$a_decl',type,
'finite$a': 'A_ltln_set_set_bool_fun$' ).
thf('finite$_decl',type,
'finite$': 'A_ltln_set_bool_fun$' ).
thf('member$a_decl',type,
'member$a': 'A_ltln_set$' > 'A_ltln_set_set_bool_fun$' ).
thf('uua$_decl',type,
'uua$': 'A_ltln_set$' > 'A_ltln_bool_fun$' ).
thf('fun_app$d_decl',type,
'fun_app$d': 'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$' > 'A_ltln_set$' > 'A_ltln_set_a_ltln_set_fun$' ).
thf('remove$_decl',type,
'remove$': 'A_ltln_a_ltln_set_a_ltln_set_fun_fun$' ).
thf('filter$_decl',type,
'filter$': 'A_ltln_set_bool_fun$' > 'A_ltln_set_set_a_ltln_set_set_fun$' ).
thf('phi$_decl',type,
'phi$': 'A_ltln$' ).
thf('fun_app$c_decl',type,
'fun_app$c': 'A_ltln_set_a_ltln_set_fun$' > 'A_ltln_set$' > 'A_ltln_set$' ).
thf(7,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ( B @ ( C @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'disjnt$' @ 'fun_app$b' ) ) )
=> ( C @ ( A @ 'disjnt$' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom187) ).
thf(645,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ( B @ ( C @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'disjnt$' @ 'fun_app$b' ) ) )
=> ( C @ ( A @ 'disjnt$' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(328,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( A = B )
=> ( A @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom168) ).
thf(2199,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( A = B )
=> ( A @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(197,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$',C: 'A_ltln_set_set$'] :
( ( ( C @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= 'bot$' )
<=> ( ( ( C @ ( A @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= 'bot$' )
& ~ ( A @ ( B @ 'member$a' @ 'fun_app$b' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom527) ).
thf(1586,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$',C: 'A_ltln_set_set$'] :
( ( ( ( ( C @ ( A @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= 'bot$' )
& ~ ( A @ ( B @ 'member$a' @ 'fun_app$b' ) ) )
=> ( ( C @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= 'bot$' ) )
& ( ( ( C @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= 'bot$' )
=> ( ( ( C @ ( A @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= 'bot$' )
& ~ ( A @ ( B @ 'member$a' @ 'fun_app$b' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(256,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ( C @ ( B @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= 'bot$' )
<=> ( ( ( C @ ( B @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= 'bot$' )
& ~ ( C @ ( A @ 'member$a' @ 'fun_app$b' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom531) ).
thf(1879,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ( ( ( C @ ( B @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= 'bot$' )
& ~ ( C @ ( A @ 'member$a' @ 'fun_app$b' ) ) )
=> ( ( C @ ( B @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= 'bot$' ) )
& ( ( ( C @ ( B @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= 'bot$' )
=> ( ( ( C @ ( B @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= 'bot$' )
& ~ ( C @ ( A @ 'member$a' @ 'fun_app$b' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(155,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set_a_ltln_set_fun$',C: 'A_ltln_set_set$',D: 'A_ltln_set_set$'] :
( ( ! [E: 'A_ltln_set_set$',F: 'A_ltln_set_set$'] :
( ( F @ ( E @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( F @ ( B @ 'fun_app$i' ) @ ( E @ ( B @ 'fun_app$i' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( D @ ( C @ 'less_eq$a' @ 'fun_app$b' ) )
& ( C @ ( B @ 'fun_app$i' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( D @ ( B @ 'fun_app$i' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom325) ).
thf(1369,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set_a_ltln_set_fun$',C: 'A_ltln_set_set$',D: 'A_ltln_set_set$'] :
( ( ! [E: 'A_ltln_set_set$',F: 'A_ltln_set_set$'] :
( ( F @ ( E @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( F @ ( B @ 'fun_app$i' ) @ ( E @ ( B @ 'fun_app$i' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( D @ ( C @ 'less_eq$a' @ 'fun_app$b' ) )
& ( C @ ( B @ 'fun_app$i' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( D @ ( B @ 'fun_app$i' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(175,axiom,
! [A: 'A_ltln_a_ltln_set_fun$'] :
( ( A @ ( 'bot$a' @ 'bind$c' ) )
= 'bot$a' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom134) ).
thf(1454,plain,
! [A: 'A_ltln_a_ltln_set_fun$'] :
( ( A @ ( 'bot$a' @ 'bind$c' ) )
= 'bot$a' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(66,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ~ ( C @ ( A @ 'member$a' @ 'fun_app$b' ) )
& ~ ( B @ ( A @ 'member$a' @ 'fun_app$b' ) ) )
=> ( ( ( B @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) )
= ( C @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) )
<=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom412) ).
thf(909,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ~ ( C @ ( A @ 'member$a' @ 'fun_app$b' ) )
& ~ ( B @ ( A @ 'member$a' @ 'fun_app$b' ) ) )
=> ( ( ( B = C )
=> ( ( B @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) )
= ( C @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) ) )
& ( ( ( B @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) )
= ( C @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(350,axiom,
! [A: 'A_ltln$',B: 'A_ltln_bool_fun$'] :
( ( B @ 'collect$a' @ ( A @ 'member$' @ 'fun_app$a' ) )
<=> ( A @ ( B @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom82) ).
thf(2331,plain,
! [A: 'A_ltln$',B: 'A_ltln_bool_fun$'] :
( ( ( A @ ( B @ 'fun_app$' ) )
=> ( B @ 'collect$a' @ ( A @ 'member$' @ 'fun_app$a' ) ) )
& ( ( B @ 'collect$a' @ ( A @ 'member$' @ 'fun_app$a' ) )
=> ( A @ ( B @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(14,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ~ ( B @ ( A @ 'member$a' @ 'fun_app$b' ) )
=> ( C @ ( A @ 'member$a' @ 'fun_app$b' ) ) )
=> ( B @ ( C @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ 'member$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom5) ).
thf(666,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ~ ( B @ ( A @ 'member$a' @ 'fun_app$b' ) )
=> ( C @ ( A @ 'member$a' @ 'fun_app$b' ) ) )
=> ( B @ ( C @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ 'member$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(191,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( ( A @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom309) ).
thf(1549,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( ( A @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(344,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom254) ).
thf(2306,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(501,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( B @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom581) ).
thf(3053,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( B @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(585,axiom,
! [A: 'A_ltln$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ~ ( B @ ( A @ 'member$' @ 'fun_app$a' ) )
=> ( C @ ( A @ 'member$' @ 'fun_app$a' ) ) )
=> ( B @ ( C @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ 'member$' @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom6) ).
thf(3434,plain,
! [A: 'A_ltln$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ~ ( B @ ( A @ 'member$' @ 'fun_app$a' ) )
=> ( C @ ( A @ 'member$' @ 'fun_app$a' ) ) )
=> ( B @ ( C @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ 'member$' @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(526,axiom,
! [A: 'A_ltln_set$'] :
( ( 'bot$a' @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom113) ).
thf(3167,plain,
! [A: 'A_ltln_set$'] :
( ( 'bot$a' @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(464,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= 'bot$a' )
<=> ( ( B = 'bot$a' )
& ( A = 'bot$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom117) ).
thf(2876,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ( ( B = 'bot$a' )
& ( A = 'bot$a' ) )
=> ( ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= 'bot$a' ) )
& ( ( ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= 'bot$a' )
=> ( ( B = 'bot$a' )
& ( A = 'bot$a' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(126,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( 'finite$a' @ 'fun_app$b' ) )
<=> ( ( B @ ( 'finite$a' @ 'fun_app$b' ) )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom3) ).
thf(1237,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( ( ( B @ ( 'finite$a' @ 'fun_app$b' ) )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( 'finite$a' @ 'fun_app$b' ) ) )
& ( ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( 'finite$a' @ 'fun_app$b' ) )
=> ( ( B @ ( 'finite$a' @ 'fun_app$b' ) )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(575,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( A @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom36) ).
thf(3397,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( A @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(259,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$',D: 'A_ltln_set_set$'] :
( ( ( D @ ( C @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( D @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( C @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ 'less_eq$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom217) ).
thf(1899,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$',D: 'A_ltln_set_set$'] :
( ( ( D @ ( C @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( D @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( C @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ 'less_eq$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(144,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$'] :
( ( 'bot$' @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( ( A
= ( 'bot$' @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) )
| ( A = 'bot$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom457) ).
thf(1315,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$'] :
( ( 'bot$' @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( ( A
= ( 'bot$' @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) )
| ( A = 'bot$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(408,axiom,
! [A: 'A_ltln$',B: 'A_ltln_set$'] :
( ( ! [C: 'A_ltln_set$'] :
( ( ~ ( C @ ( A @ 'member$' @ 'fun_app$a' ) )
& ( B
= ( C @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) ) )
=> $false )
& ( B @ ( A @ 'member$' @ 'fun_app$a' ) ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom413) ).
thf(2595,plain,
! [A: 'A_ltln$',B: 'A_ltln_set$'] :
~ ( ! [C: 'A_ltln_set$'] :
~ ( ~ ( C @ ( A @ 'member$' @ 'fun_app$a' ) )
& ( B
= ( C @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) ) )
& ( B @ ( A @ 'member$' @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(250,axiom,
! [A: 'A_ltln_set_set$'] : ( A @ ( 'bot$' @ 'less_eq$a' @ 'fun_app$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom128) ).
thf(1850,plain,
! [A: 'A_ltln_set_set$'] : ( A @ ( 'bot$' @ 'less_eq$a' @ 'fun_app$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(389,axiom,
! [A: 'A_ltln_set_bool_fun$',B: 'A_ltln_set$'] :
( ( ! [C: 'A_ltln$',D: 'A_ltln_set$'] :
( ( ( D @ ( A @ 'fun_app$a' ) )
& ~ ( D @ ( C @ 'member$' @ 'fun_app$a' ) )
& ( D @ ( 'finite$' @ 'fun_app$a' ) ) )
=> ( D @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ 'fun_app$a' ) ) )
& ( 'bot$a' @ ( A @ 'fun_app$a' ) )
& ! [C: 'A_ltln_set$'] :
( ~ ( C @ ( 'finite$' @ 'fun_app$a' ) )
=> ( C @ ( A @ 'fun_app$a' ) ) ) )
=> ( B @ ( A @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom454) ).
thf(2499,plain,
! [A: 'A_ltln_set_bool_fun$',B: 'A_ltln_set$'] :
( ( ! [C: 'A_ltln$',D: 'A_ltln_set$'] :
( ( ( D @ ( A @ 'fun_app$a' ) )
& ~ ( D @ ( C @ 'member$' @ 'fun_app$a' ) )
& ( D @ ( 'finite$' @ 'fun_app$a' ) ) )
=> ( D @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ 'fun_app$a' ) ) )
& ( 'bot$a' @ ( A @ 'fun_app$a' ) )
& ! [C: 'A_ltln_set$'] :
( ~ ( C @ ( 'finite$' @ 'fun_app$a' ) )
=> ( C @ ( A @ 'fun_app$a' ) ) ) )
=> ( B @ ( A @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(17,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( C @ ( B @ ( 'minus$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ 'member$a' @ 'fun_app$b' ) )
<=> ( ~ ( C @ ( A @ 'member$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'member$a' @ 'fun_app$b' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom516) ).
thf(683,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ( ~ ( C @ ( A @ 'member$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'member$a' @ 'fun_app$b' ) ) )
=> ( C @ ( B @ ( 'minus$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ 'member$a' @ 'fun_app$b' ) ) )
& ( ( C @ ( B @ ( 'minus$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ 'member$a' @ 'fun_app$b' ) )
=> ( ~ ( C @ ( A @ 'member$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'member$a' @ 'fun_app$b' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(186,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( ( B @ ( 'finite$a' @ 'fun_app$b' ) )
& ( A != 'bot$' )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( B @ ( 'sup_fin$a' @ 'fun_app$i' ) @ ( A @ ( 'sup_fin$a' @ 'fun_app$i' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom356) ).
thf(1522,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( ( B @ ( 'finite$a' @ 'fun_app$b' ) )
& ( A != 'bot$' )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( B @ ( 'sup_fin$a' @ 'fun_app$i' ) @ ( A @ ( 'sup_fin$a' @ 'fun_app$i' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(362,axiom,
! [A: 'A_ltln_set$'] : ( A @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom290) ).
thf(2381,plain,
! [A: 'A_ltln_set$'] : ( A @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(298,axiom,
! [A: 'A_ltln_set_bool_fun$',B: 'A_ltln_set$'] :
( ( ! [C: 'A_ltln_set$'] :
( ( C @ ( A @ 'fun_app$a' ) )
=> ? [D: 'A_ltln$'] :
( ( ~ ( 'bot$a' @ ( D @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( C @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'finite$' @ 'fun_app$a' ) )
| ( 'bot$a' @ ( D @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( C @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ 'fun_app$a' ) ) )
& ( C @ ( D @ 'member$' @ 'fun_app$a' ) ) ) )
& ( B @ ( A @ 'fun_app$a' ) ) )
=> ~ ( B @ ( 'finite$' @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom628) ).
thf(2062,plain,
! [A: 'A_ltln_set_bool_fun$',B: 'A_ltln_set$'] :
( ( ! [C: 'A_ltln_set$'] :
( ( C @ ( A @ 'fun_app$a' ) )
=> ? [D: 'A_ltln$'] :
( ( ~ ( 'bot$a' @ ( D @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( C @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'finite$' @ 'fun_app$a' ) )
| ( 'bot$a' @ ( D @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( C @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ 'fun_app$a' ) ) )
& ( C @ ( D @ 'member$' @ 'fun_app$a' ) ) ) )
& ( B @ ( A @ 'fun_app$a' ) ) )
=> ~ ( B @ ( 'finite$' @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(240,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( B @ ( C @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom255) ).
thf(1808,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( B @ ( C @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(406,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom26) ).
thf(2590,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(29,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( A = B )
<=> ( ( A @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom323) ).
thf(741,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( ( ( A @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(58,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( ( ( ( A @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> $false )
& ( A = B ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom158) ).
thf(873,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
~ ( ~ ( ( A @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
& ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(188,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
<=> ( ( A @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom249) ).
thf(1533,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( ( ( A @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= B )
=> ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
& ( ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( ( A @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(16,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( 'finite$a' @ 'fun_app$b' ) )
<=> ( B @ ( 'finite$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom383) ).
thf(677,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$'] :
( ( ( B @ ( 'finite$a' @ 'fun_app$b' ) )
=> ( B @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( 'finite$a' @ 'fun_app$b' ) ) )
& ( ( B @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( 'finite$a' @ 'fun_app$b' ) )
=> ( B @ ( 'finite$a' @ 'fun_app$b' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(573,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
<=> ! [C: 'A_ltln$'] :
( ( A @ ( C @ 'member$' @ 'fun_app$a' ) )
=> ( B @ ( C @ 'member$' @ 'fun_app$a' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom161) ).
thf(3382,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ! [C: 'A_ltln$'] :
( ( A @ ( C @ 'member$' @ 'fun_app$a' ) )
=> ( B @ ( C @ 'member$' @ 'fun_app$a' ) ) )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ! [C: 'A_ltln$'] :
( ( A @ ( C @ 'member$' @ 'fun_app$a' ) )
=> ( B @ ( C @ 'member$' @ 'fun_app$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(356,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( B @ ( C @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom611) ).
thf(2363,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( B @ ( C @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(118,axiom,
! [A: 'A_ltln_set_set$'] : ( A @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom173) ).
thf(1200,plain,
! [A: 'A_ltln_set_set$'] : ( A @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(301,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln$'] :
( ( B @ ( A @ 'uua$' @ 'fun_app$' ) )
<=> ( A @ ( B @ 'member$' @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom0) ).
thf(2077,plain,
! [A: 'A_ltln_set$',B: 'A_ltln$'] :
( ( ( A @ ( B @ 'member$' @ 'fun_app$a' ) )
=> ( B @ ( A @ 'uua$' @ 'fun_app$' ) ) )
& ( ( B @ ( A @ 'uua$' @ 'fun_app$' ) )
=> ( A @ ( B @ 'member$' @ 'fun_app$a' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(345,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( A @ ( B @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= 'bot$a' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom545) ).
thf(2309,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( A @ ( B @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= 'bot$a' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(32,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set_bool_fun$'] :
( ( ! [D: 'A_ltln_set$',E: 'A_ltln_set_set$'] :
( ( ( E @ ( C @ 'fun_app$b' ) )
& ~ ( E @ ( D @ 'member$a' @ 'fun_app$b' ) )
& ( B @ ( E @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( D @ 'member$a' @ 'fun_app$b' ) )
& ( E @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( E @ ( D @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( C @ 'fun_app$b' ) ) )
& ( 'bot$' @ ( C @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( A @ ( C @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom465) ).
thf(762,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set_bool_fun$'] :
( ( ! [D: 'A_ltln_set$',E: 'A_ltln_set_set$'] :
( ( ( E @ ( C @ 'fun_app$b' ) )
& ~ ( E @ ( D @ 'member$a' @ 'fun_app$b' ) )
& ( B @ ( E @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( D @ 'member$a' @ 'fun_app$b' ) )
& ( E @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( E @ ( D @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( C @ 'fun_app$b' ) ) )
& ( 'bot$' @ ( C @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( A @ ( C @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(505,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'finite$' @ 'fun_app$a' ) )
<=> ( C @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'finite$' @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom560) ).
thf(3072,plain,
! [A: 'A_ltln_set$',B: 'A_ltln$',C: 'A_ltln_set$'] :
( ( ( C @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'finite$' @ 'fun_app$a' ) )
=> ( C @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'finite$' @ 'fun_app$a' ) ) )
& ( ( C @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'finite$' @ 'fun_app$a' ) )
=> ( C @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'finite$' @ 'fun_app$a' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(265,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( ( B @ ( 'finite$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( A @ ( 'finite$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom257) ).
thf(1924,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( ( B @ ( 'finite$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( A @ ( 'finite$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(86,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( C @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ 'disjnt$' @ 'fun_app$b' ) )
<=> ( ( C @ ( A @ 'disjnt$' @ 'fun_app$b' ) )
& ( B @ ( A @ 'disjnt$' @ 'fun_app$b' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom77) ).
thf(1005,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ( ( C @ ( A @ 'disjnt$' @ 'fun_app$b' ) )
& ( B @ ( A @ 'disjnt$' @ 'fun_app$b' ) ) )
=> ( C @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ 'disjnt$' @ 'fun_app$b' ) ) )
& ( ( C @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ 'disjnt$' @ 'fun_app$b' ) )
=> ( ( C @ ( A @ 'disjnt$' @ 'fun_app$b' ) )
& ( B @ ( A @ 'disjnt$' @ 'fun_app$b' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(331,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( A @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom564) ).
thf(2210,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( A @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(311,axiom,
! [A: 'A_ltln_set$'] :
( ( A @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom12) ).
thf(2117,plain,
! [A: 'A_ltln_set$'] :
( ( A @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(198,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) )
= ( B @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom375) ).
thf(1596,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) )
= ( B @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(227,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_a_ltln_set_set_fun$'] :
( ( ! [C: 'A_ltln_set$'] :
( ( A @ ( C @ 'member$a' @ 'fun_app$b' ) )
=> ( C @ ( B @ 'fun_app$k' ) @ ( 'finite$a' @ 'fun_app$b' ) ) )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( B @ ( A @ 'bind$b' ) @ ( 'finite$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom88) ).
thf(1728,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_a_ltln_set_set_fun$'] :
( ( ! [C: 'A_ltln_set$'] :
( ( A @ ( C @ 'member$a' @ 'fun_app$b' ) )
=> ( C @ ( B @ 'fun_app$k' ) @ ( 'finite$a' @ 'fun_app$b' ) ) )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( B @ ( A @ 'bind$b' ) @ ( 'finite$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(512,axiom,
! [A: 'A_ltln_set$'] :
( ( A @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom492) ).
thf(3108,plain,
! [A: 'A_ltln_set$'] :
( ( A @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(102,axiom,
! [A: 'A_ltln_set_set$'] :
( ( 'bot$' @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom195) ).
thf(1137,plain,
! [A: 'A_ltln_set_set$'] :
( ( 'bot$' @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(423,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom32) ).
thf(2686,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(520,axiom,
! [A: 'A_ltln$'] :
( ( 'bot$a' @ ( A @ 'member$' @ 'fun_app$a' ) )
<=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom92) ).
thf(3135,plain,
! [A: 'A_ltln$'] :
~ ( 'bot$a' @ ( A @ 'member$' @ 'fun_app$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(568,axiom,
! [A: 'A_ltln$',B: 'A_ltln$'] :
( ( ( 'bot$a' @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) )
= ( 'bot$a' @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom421) ).
thf(3365,plain,
! [A: 'A_ltln$',B: 'A_ltln$'] :
( ( ( 'bot$a' @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) )
= ( 'bot$a' @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(499,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] : ( B @ ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom618) ).
thf(3044,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] : ( B @ ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(252,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( ( ( B
= ( A @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) )
=> $false )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom225) ).
thf(1867,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
~ ( ( B
!= ( A @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(562,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom511) ).
thf(3338,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(316,axiom,
! [A: 'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ! [D: 'A_ltln_set$',E: 'A_ltln_set$',F: 'A_ltln_set$'] :
( ( ( D @ ( F @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( D @ ( E @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( D @ ( F @ ( E @ ( A @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ! [D: 'A_ltln_set$',E: 'A_ltln_set$'] : ( E @ ( D @ ( A @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( E @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ! [D: 'A_ltln_set$',E: 'A_ltln_set$'] : ( E @ ( D @ ( A @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( D @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( B @ ( A @ 'fun_app$d' ) @ 'fun_app$c' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom230) ).
thf(2141,plain,
! [A: 'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ! [D: 'A_ltln_set$',E: 'A_ltln_set$',F: 'A_ltln_set$'] :
( ( ( D @ ( F @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( D @ ( E @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( D @ ( F @ ( E @ ( A @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ! [D: 'A_ltln_set$',E: 'A_ltln_set$'] : ( E @ ( D @ ( A @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( E @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ! [D: 'A_ltln_set$',E: 'A_ltln_set$'] : ( E @ ( D @ ( A @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( D @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( B @ ( A @ 'fun_app$d' ) @ 'fun_app$c' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(516,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( B @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( C @ ( A @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom188) ).
thf(3121,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( B @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( C @ ( A @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(615,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom509) ).
thf(3577,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(15,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( C @ ( B @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ 'less_eq$a' @ 'fun_app$b' ) )
<=> ( ( C @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
& ( C @ ( A @ 'member$a' @ 'fun_app$b' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom385) ).
thf(670,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ( ( C @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
& ( C @ ( A @ 'member$a' @ 'fun_app$b' ) ) )
=> ( C @ ( B @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ 'less_eq$a' @ 'fun_app$b' ) ) )
& ( ( C @ ( B @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( ( C @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
& ( C @ ( A @ 'member$a' @ 'fun_app$b' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(326,axiom,
'sup$' @ 'comp_fun_idem$a',
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom74) ).
thf(2195,plain,
'sup$' @ 'comp_fun_idem$a',
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(222,axiom,
! [A: 'A_ltln_set_set$'] :
( ( A @ ( 'bot$' @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom120) ).
thf(1705,plain,
! [A: 'A_ltln_set_set$'] :
( ( A @ ( 'bot$' @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(42,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$',D: 'A_ltln_set_set$'] :
( ( A
= ( C @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) )
=> ( ( A @ ( D @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( C @ ( D @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom65) ).
thf(797,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$',D: 'A_ltln_set_set$'] :
( ( A
= ( C @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) )
=> ( ( A @ ( D @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( C @ ( D @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(347,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ! [C: 'A_ltln$'] :
( ( A @ ( C @ 'member$' @ 'fun_app$a' ) )
=> ( B @ ( C @ 'member$' @ 'fun_app$a' ) ) )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom101) ).
thf(2316,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ! [C: 'A_ltln$'] :
( ( A @ ( C @ 'member$' @ 'fun_app$a' ) )
=> ( B @ ( C @ 'member$' @ 'fun_app$a' ) ) )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(383,axiom,
! [A: 'A_ltln$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( B @ ( C @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ~ ( B @ ( A @ 'member$' @ 'fun_app$a' ) ) )
=> ( B @ ( C @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom443) ).
thf(2476,plain,
! [A: 'A_ltln$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( B @ ( C @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ~ ( B @ ( A @ 'member$' @ 'fun_app$a' ) ) )
=> ( B @ ( C @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(413,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln$',C: 'A_ltln_set$'] :
( ( 'bot$a'
= ( C @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) )
<=> ( ( 'bot$a'
= ( C @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) )
& ~ ( A @ ( B @ 'member$' @ 'fun_app$a' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom524) ).
thf(2627,plain,
! [A: 'A_ltln_set$',B: 'A_ltln$',C: 'A_ltln_set$'] :
( ( ( ( 'bot$a'
= ( C @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) )
& ~ ( A @ ( B @ 'member$' @ 'fun_app$a' ) ) )
=> ( 'bot$a'
= ( C @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ) )
& ( ( 'bot$a'
= ( C @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) )
=> ( ( 'bot$a'
= ( C @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) )
& ~ ( A @ ( B @ 'member$' @ 'fun_app$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(184,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ 'member$a' @ 'fun_app$b' ) )
=> ? [C: 'A_ltln_set_set$'] :
( ~ ( C @ ( A @ 'member$a' @ 'fun_app$b' ) )
& ( B
= ( C @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom404) ).
thf(1507,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ 'member$a' @ 'fun_app$b' ) )
=> ? [C: 'A_ltln_set_set$'] :
( ~ ( C @ ( A @ 'member$a' @ 'fun_app$b' ) )
& ( B
= ( C @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(121,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom540) ).
thf(1222,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(355,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln$'] :
( ( A @ ( 'finite$' @ 'fun_app$a' ) )
=> ( A @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( 'finite$' @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom432) ).
thf(2360,plain,
! [A: 'A_ltln_set$',B: 'A_ltln$'] :
( ( A @ ( 'finite$' @ 'fun_app$a' ) )
=> ( A @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( 'finite$' @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(96,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set$'] :
( ( B @ ( A @ 'member$a' @ 'fun_app$b' ) )
=> ( B @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ 'member$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom416) ).
thf(1095,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set$'] :
( ( B @ ( A @ 'member$a' @ 'fun_app$b' ) )
=> ( B @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ 'member$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(333,axiom,
! [A: 'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ! [D: 'A_ltln_set$',E: 'A_ltln_set$',F: 'A_ltln_set$'] :
( ( ( F @ ( D @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( E @ ( D @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( F @ ( E @ ( A @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( D @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ! [D: 'A_ltln_set$',E: 'A_ltln_set$'] : ( E @ ( E @ ( D @ ( A @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ! [D: 'A_ltln_set$',E: 'A_ltln_set$'] : ( D @ ( E @ ( D @ ( A @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( B @ ( A @ 'fun_app$d' ) @ 'fun_app$c' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom607) ).
thf(2216,plain,
! [A: 'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ! [D: 'A_ltln_set$',E: 'A_ltln_set$',F: 'A_ltln_set$'] :
( ( ( F @ ( D @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( E @ ( D @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( F @ ( E @ ( A @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( D @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ! [D: 'A_ltln_set$',E: 'A_ltln_set$'] : ( E @ ( E @ ( D @ ( A @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ! [D: 'A_ltln_set$',E: 'A_ltln_set$'] : ( D @ ( E @ ( D @ ( A @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( B @ ( A @ 'fun_app$d' ) @ 'fun_app$c' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(599,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set_a_ltln_set_fun$',C: 'A_ltln_set$',D: 'A_ltln_set$'] :
( ( ! [E: 'A_ltln_set$',F: 'A_ltln_set$'] :
( ( F @ ( E @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( F @ ( B @ 'fun_app$c' ) @ ( E @ ( B @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( D @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( C @ ( B @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( D @ ( B @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom328) ).
thf(3502,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set_a_ltln_set_fun$',C: 'A_ltln_set$',D: 'A_ltln_set$'] :
( ( ! [E: 'A_ltln_set$',F: 'A_ltln_set$'] :
( ( F @ ( E @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( F @ ( B @ 'fun_app$c' ) @ ( E @ ( B @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( D @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( C @ ( B @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( D @ ( B @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(52,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( B @ ( A @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom502) ).
thf(841,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( B @ ( A @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(508,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom46) ).
thf(3088,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(202,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( A @ ( B @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom498) ).
thf(1613,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( A @ ( B @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(465,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set_a_ltln_set_fun$',D: 'A_ltln_set$'] :
( ( ! [E: 'A_ltln_set$',F: 'A_ltln_set$'] :
( ( F @ ( E @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( F @ ( C @ 'fun_app$c' ) @ ( E @ ( C @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( ( B @ ( C @ 'fun_app$c' ) )
= D )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom342) ).
thf(2886,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set_a_ltln_set_fun$',D: 'A_ltln_set$'] :
( ( ! [E: 'A_ltln_set$',F: 'A_ltln_set$'] :
( ( F @ ( E @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( F @ ( C @ 'fun_app$c' ) @ ( E @ ( C @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( ( B @ ( C @ 'fun_app$c' ) )
= D )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(123,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( B @ ( A @ ( 'minus$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( 'minus$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( B @ ( A @ ( 'minus$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom518) ).
thf(1228,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( B @ ( A @ ( 'minus$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( 'minus$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( B @ ( A @ ( 'minus$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(565,axiom,
! [A: 'A_ltln_set_bool_fun$'] :
( ( 'bot$'
= ( A @ 'collect$' ) )
<=> ! [B: 'A_ltln_set$'] :
~ ( B @ ( A @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom99) ).
thf(3350,plain,
! [A: 'A_ltln_set_bool_fun$'] :
( ( ! [B: 'A_ltln_set$'] :
~ ( B @ ( A @ 'fun_app$a' ) )
=> ( 'bot$'
= ( A @ 'collect$' ) ) )
& ( ( 'bot$'
= ( A @ 'collect$' ) )
=> ! [B: 'A_ltln_set$'] :
~ ( B @ ( A @ 'fun_app$a' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(84,axiom,
'insert$a' @ 'comp_fun_idem$b',
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom401) ).
thf(1001,plain,
'insert$a' @ 'comp_fun_idem$b',
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(610,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( A @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom604) ).
thf(3545,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( A @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(439,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom388) ).
thf(2763,plain,
! [A: 'A_ltln_set$',B: 'A_ltln$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(394,axiom,
! [A: 'A_ltln_set$'] :
( ( A @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom10) ).
thf(2548,plain,
! [A: 'A_ltln_set$'] :
( ( A @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(483,axiom,
! [A: 'A_ltln_set$'] :
( ( 'bot$a' @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom125) ).
thf(2985,plain,
! [A: 'A_ltln_set$'] :
( ( 'bot$a' @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(162,axiom,
! [A: 'A_ltln_set_set$'] :
( ( ( A != 'bot$' )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( A @ ( 'sup_fin$a' @ 'fun_app$i' ) @ ( A @ ( 'inf_fin$a' @ 'fun_app$i' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom350) ).
thf(1391,plain,
! [A: 'A_ltln_set_set$'] :
( ( ( A != 'bot$' )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( A @ ( 'sup_fin$a' @ 'fun_app$i' ) @ ( A @ ( 'inf_fin$a' @ 'fun_app$i' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(210,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$'] :
( ( 'bot$' @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
<=> ( ( A
= ( 'bot$' @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) )
| ( A = 'bot$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom455) ).
thf(1645,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$'] :
( ( ( ( A
= ( 'bot$' @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) )
| ( A = 'bot$' ) )
=> ( 'bot$' @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
& ( ( 'bot$' @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( ( A
= ( 'bot$' @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) )
| ( A = 'bot$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(264,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( A @ ( 'finite$a' @ 'fun_app$b' ) )
=> ( B @ ( A @ ( 'minus$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( 'finite$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom552) ).
thf(1921,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( A @ ( 'finite$a' @ 'fun_app$b' ) )
=> ( B @ ( A @ ( 'minus$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( 'finite$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(368,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom322) ).
thf(2400,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(299,axiom,
! [A: 'A_ltln_set_bool_fun$',B: 'A_ltln_set_bool_fun$'] :
( ( B @ 'collect$' @ ( A @ 'collect$' @ 'less_eq$a' @ 'fun_app$b' ) )
<=> ! [C: 'A_ltln_set$'] :
( ( C @ ( A @ 'fun_app$a' ) )
=> ( C @ ( B @ 'fun_app$a' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom189) ).
thf(2067,plain,
! [A: 'A_ltln_set_bool_fun$',B: 'A_ltln_set_bool_fun$'] :
( ( ! [C: 'A_ltln_set$'] :
( ( C @ ( A @ 'fun_app$a' ) )
=> ( C @ ( B @ 'fun_app$a' ) ) )
=> ( B @ 'collect$' @ ( A @ 'collect$' @ 'less_eq$a' @ 'fun_app$b' ) ) )
& ( ( B @ 'collect$' @ ( A @ 'collect$' @ 'less_eq$a' @ 'fun_app$b' ) )
=> ! [C: 'A_ltln_set$'] :
( ( C @ ( A @ 'fun_app$a' ) )
=> ( C @ ( B @ 'fun_app$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(171,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( 'bot$' @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ 'member$a' @ 'fun_app$b' ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom428) ).
thf(1430,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ( A = B )
=> ( 'bot$' @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ 'member$a' @ 'fun_app$b' ) ) )
& ( ( 'bot$' @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ 'member$a' @ 'fun_app$b' ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(427,axiom,
! [A: 'A_ltln$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( C @ ( B @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= 'bot$a' )
<=> ( ( ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= 'bot$a' )
& ~ ( C @ ( A @ 'member$' @ 'fun_app$a' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom530) ).
thf(2698,plain,
! [A: 'A_ltln$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( ( ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= 'bot$a' )
& ~ ( C @ ( A @ 'member$' @ 'fun_app$a' ) ) )
=> ( ( C @ ( B @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= 'bot$a' ) )
& ( ( ( C @ ( B @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= 'bot$a' )
=> ( ( ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= 'bot$a' )
& ~ ( C @ ( A @ 'member$' @ 'fun_app$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(500,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
<=> ( ( C @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom523) ).
thf(3046,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( ( C @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( C @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(253,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( ~ ( A @ ( 'finite$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ~ ( B @ ( 'finite$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom259) ).
thf(1871,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( ~ ( A @ ( 'finite$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ~ ( B @ ( 'finite$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(428,axiom,
! [A: 'A_ltln_set$'] :
( ( A @ ( 'bot$a' @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= 'bot$a' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom538) ).
thf(2708,plain,
! [A: 'A_ltln_set$'] :
( ( A @ ( 'bot$a' @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= 'bot$a' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(43,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom500) ).
thf(802,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(93,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ( 'bot$' @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) )
= ( C @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) )
<=> ( ( ( C
= ( 'bot$' @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) )
& ( B
= ( 'bot$' @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) ) )
| ( ( C = 'bot$' )
& ( B
= ( 'bot$' @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) ) )
| ( ( C
= ( 'bot$' @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) )
& ( B = 'bot$' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom463) ).
thf(1059,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ( ( ( C
= ( 'bot$' @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) )
& ( B
= ( 'bot$' @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) ) )
| ( ( C = 'bot$' )
& ( B
= ( 'bot$' @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) ) )
| ( ( C
= ( 'bot$' @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) )
& ( B = 'bot$' ) ) )
=> ( ( 'bot$' @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) )
= ( C @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) ) )
& ( ( ( 'bot$' @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) )
= ( C @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) )
=> ( ( ( C
= ( 'bot$' @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) )
& ( B
= ( 'bot$' @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) ) )
| ( ( C = 'bot$' )
& ( B
= ( 'bot$' @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) ) )
| ( ( C
= ( 'bot$' @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) )
& ( B = 'bot$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(419,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ~ ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( B @ ( A @ ( 'max$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ) )
& ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( B @ ( A @ ( 'max$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom634) ).
thf(2654,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ~ ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( B @ ( A @ ( 'max$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ) )
& ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( B @ ( A @ ( 'max$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(207,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= 'bot$' )
<=> ( ( B = 'bot$' )
& ( A = 'bot$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom90) ).
thf(1628,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( ( ( B = 'bot$' )
& ( A = 'bot$' ) )
=> ( ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= 'bot$' ) )
& ( ( ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= 'bot$' )
=> ( ( B = 'bot$' )
& ( A = 'bot$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(25,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set$'] :
( ( ( B @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) )
= ( 'bot$' @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) )
<=> ( ( 'bot$' @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
& ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom395) ).
thf(724,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set$'] :
( ( ( ( 'bot$' @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
& ( A = C ) )
=> ( ( B @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) )
= ( 'bot$' @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) ) )
& ( ( ( B @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) )
= ( 'bot$' @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) )
=> ( ( 'bot$' @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(536,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) )
<=> ( ( C @ ( A @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom78) ).
thf(3204,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( ( C @ ( A @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( C @ ( A @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(587,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$',D: 'A_ltln_set$'] :
( ( A
= ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) )
=> ( ( A @ ( D @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( D @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom66) ).
thf(3442,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$',D: 'A_ltln_set$'] :
( ( A
= ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) )
=> ( ( A @ ( D @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( D @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(547,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( C @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom589) ).
thf(3263,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( C @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(136,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$'] : ( A @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom437) ).
thf(1287,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$'] : ( A @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(539,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom52) ).
thf(3221,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(522,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set_a_ltln_set_fun$',D: 'A_ltln_set$'] :
( ( ! [E: 'A_ltln_set$',F: 'A_ltln_set$'] :
( ( F @ ( E @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( F @ ( C @ 'fun_app$c' ) @ ( E @ ( C @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( D @ ( B @ ( C @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom332) ).
thf(3148,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set_a_ltln_set_fun$',D: 'A_ltln_set$'] :
( ( ! [E: 'A_ltln_set$',F: 'A_ltln_set$'] :
( ( F @ ( E @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( F @ ( C @ 'fun_app$c' ) @ ( E @ ( C @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( D @ ( B @ ( C @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(3,axiom,
! [A: 'A_ltln_bool_fun$'] :
( ( ( A @ 'collect$a' )
= 'bot$a' )
<=> ! [B: 'A_ltln$'] :
~ ( B @ ( A @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom96) ).
thf(619,plain,
! [A: 'A_ltln_bool_fun$'] :
( ( ! [B: 'A_ltln$'] :
~ ( B @ ( A @ 'fun_app$' ) )
=> ( ( A @ 'collect$a' )
= 'bot$a' ) )
& ( ( ( A @ 'collect$a' )
= 'bot$a' )
=> ! [B: 'A_ltln$'] :
~ ( B @ ( A @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(369,axiom,
! [A: 'A_ltln$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom390) ).
thf(2403,plain,
! [A: 'A_ltln$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(128,axiom,
! [A: 'A_ltln_set_set$'] :
( ( 'bot$' @ ( A @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= 'bot$' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom537) ).
thf(1247,plain,
! [A: 'A_ltln_set_set$'] :
( ( 'bot$' @ ( A @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= 'bot$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(359,axiom,
! [A: 'A_ltln_set_bool_fun$',B: 'A_ltln_set_bool_fun$'] :
( ! [C: 'A_ltln_set$'] :
( ( C @ ( A @ 'fun_app$a' ) )
=> ( C @ ( B @ 'fun_app$a' ) ) )
=> ( B @ 'collect$' @ ( A @ 'collect$' @ 'less_eq$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom175) ).
thf(2373,plain,
! [A: 'A_ltln_set_bool_fun$',B: 'A_ltln_set_bool_fun$'] :
( ! [C: 'A_ltln_set$'] :
( ( C @ ( A @ 'fun_app$a' ) )
=> ( C @ ( B @ 'fun_app$a' ) ) )
=> ( B @ 'collect$' @ ( A @ 'collect$' @ 'less_eq$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(33,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ~ ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( 'finite$a' @ 'fun_app$b' ) )
<=> ( ~ ( B @ ( 'finite$a' @ 'fun_app$b' ) )
| ~ ( A @ ( 'finite$a' @ 'fun_app$b' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom63) ).
thf(770,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( ( ~ ( B @ ( 'finite$a' @ 'fun_app$b' ) )
| ~ ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ~ ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( 'finite$a' @ 'fun_app$b' ) ) )
& ( ~ ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( 'finite$a' @ 'fun_app$b' ) )
=> ( ~ ( B @ ( 'finite$a' @ 'fun_app$b' ) )
| ~ ( A @ ( 'finite$a' @ 'fun_app$b' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(98,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$'] :
( ( ( A @ ( B @ 'member$a' @ 'fun_app$b' ) )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ? [C: 'A_ltln_set$'] :
( ! [D: 'A_ltln_set$'] :
( ( ( D @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( A @ ( D @ 'member$a' @ 'fun_app$b' ) ) )
=> ( C = D ) )
& ( C @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( A @ ( C @ 'member$a' @ 'fun_app$b' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom198) ).
thf(1115,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$'] :
( ( ( A @ ( B @ 'member$a' @ 'fun_app$b' ) )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ? [C: 'A_ltln_set$'] :
( ! [D: 'A_ltln_set$'] :
( ( ( D @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( A @ ( D @ 'member$a' @ 'fun_app$b' ) ) )
=> ( C = D ) )
& ( C @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( A @ ( C @ 'member$a' @ 'fun_app$b' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(529,axiom,
! [A: 'A_ltln_set_set$'] :
( ( ! [B: 'A_ltln_set$',C: 'A_ltln_set$'] : ( 'bot$' @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ 'member$a' @ 'fun_app$b' ) )
& ( A != 'bot$' )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( A @ ( A @ ( 'sup_fin$a' @ 'fun_app$i' ) @ 'member$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom372) ).
thf(3180,plain,
! [A: 'A_ltln_set_set$'] :
( ( ! [B: 'A_ltln_set$',C: 'A_ltln_set$'] : ( 'bot$' @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ 'member$a' @ 'fun_app$b' ) )
& ( A != 'bot$' )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( A @ ( A @ ( 'sup_fin$a' @ 'fun_app$i' ) @ 'member$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(365,axiom,
! [A: 'A_ltln$'] : ( A @ ( 'subformulas_mu$' @ 'fun_app$h' ) @ ( 'finite$' @ 'fun_app$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom287) ).
thf(2388,plain,
! [A: 'A_ltln$'] : ( A @ ( 'subformulas_mu$' @ 'fun_app$h' ) @ ( 'finite$' @ 'fun_app$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(154,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$',C: 'A_ltln_set_set$'] :
( ( C @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ 'disjnt$' @ 'fun_app$b' ) )
<=> ( ( C @ ( A @ 'disjnt$' @ 'fun_app$b' ) )
& ~ ( A @ ( B @ 'member$a' @ 'fun_app$b' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom392) ).
thf(1362,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$',C: 'A_ltln_set_set$'] :
( ( ( ( C @ ( A @ 'disjnt$' @ 'fun_app$b' ) )
& ~ ( A @ ( B @ 'member$a' @ 'fun_app$b' ) ) )
=> ( C @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ 'disjnt$' @ 'fun_app$b' ) ) )
& ( ( C @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ 'disjnt$' @ 'fun_app$b' ) )
=> ( ( C @ ( A @ 'disjnt$' @ 'fun_app$b' ) )
& ~ ( A @ ( B @ 'member$a' @ 'fun_app$b' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(276,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom16) ).
thf(1963,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(69,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( 'bot$' @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ 'member$a' @ 'fun_app$b' ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom430) ).
thf(924,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( 'bot$' @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ 'member$a' @ 'fun_app$b' ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(584,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom103) ).
thf(3431,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(213,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( C @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( C @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom39) ).
thf(1664,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( C @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( C @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(225,axiom,
! [A: 'A_ltln_set_set_bool_fun$',B: 'A_ltln_set_set$'] :
( ( ! [C: 'A_ltln_set$',D: 'A_ltln_set_set$'] :
( ( ( D @ ( A @ 'fun_app$b' ) )
& ~ ( D @ ( C @ 'member$a' @ 'fun_app$b' ) )
& ( D @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( D @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ 'fun_app$b' ) ) )
& ( 'bot$' @ ( A @ 'fun_app$b' ) )
& ! [C: 'A_ltln_set_set$'] :
( ~ ( C @ ( 'finite$a' @ 'fun_app$b' ) )
=> ( C @ ( A @ 'fun_app$b' ) ) ) )
=> ( B @ ( A @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom453) ).
thf(1714,plain,
! [A: 'A_ltln_set_set_bool_fun$',B: 'A_ltln_set_set$'] :
( ( ! [C: 'A_ltln_set$',D: 'A_ltln_set_set$'] :
( ( ( D @ ( A @ 'fun_app$b' ) )
& ~ ( D @ ( C @ 'member$a' @ 'fun_app$b' ) )
& ( D @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( D @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ 'fun_app$b' ) ) )
& ( 'bot$' @ ( A @ 'fun_app$b' ) )
& ! [C: 'A_ltln_set_set$'] :
( ~ ( C @ ( 'finite$a' @ 'fun_app$b' ) )
=> ( C @ ( A @ 'fun_app$b' ) ) ) )
=> ( B @ ( A @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(38,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$'] :
( ( ( A @ ( B @ 'member$a' @ 'fun_app$b' ) )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( B @ ( A @ ( 'inf_fin$a' @ 'fun_app$i' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom143) ).
thf(789,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$'] :
( ( ( A @ ( B @ 'member$a' @ 'fun_app$b' ) )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( B @ ( A @ ( 'inf_fin$a' @ 'fun_app$i' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(241,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ( B @ ( C @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( B @ ( C @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ 'less_eq$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom221) ).
thf(1811,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ( B @ ( C @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( B @ ( C @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ 'less_eq$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(156,axiom,
! [A: 'A_ltln_set_set$'] :
( ( 'bot$' @ ( A @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= 'bot$' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom535) ).
thf(1373,plain,
! [A: 'A_ltln_set_set$'] :
( ( 'bot$' @ ( A @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= 'bot$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(446,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( B @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( B @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom519) ).
thf(2782,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( B @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( B @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(89,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ( B = C )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( C @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom307) ).
thf(1040,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ( B = C )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( C @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(338,axiom,
! [A: 'A_ltln_set$'] :
( ( 'bot$a' @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
<=> ( A = 'bot$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom127) ).
thf(2259,plain,
! [A: 'A_ltln_set$'] :
( ( ( A = 'bot$a' )
=> ( 'bot$a' @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( ( 'bot$a' @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( A = 'bot$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(525,axiom,
! [A: 'A_ltln$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( B @ ( A @ 'member$' @ 'fun_app$a' ) )
=> ( ( C @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom491) ).
thf(3163,plain,
! [A: 'A_ltln$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( B @ ( A @ 'member$' @ 'fun_app$a' ) )
=> ( ( C @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(590,axiom,
! [A: 'A_ltln_set$'] :
( ( 'bot$a' @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= 'bot$a' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom534) ).
thf(3453,plain,
! [A: 'A_ltln_set$'] :
( ( 'bot$a' @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= 'bot$a' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(510,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
<=> ! [C: 'A_ltln$'] :
( ( A @ ( C @ 'member$' @ 'fun_app$a' ) )
=> ( B @ ( C @ 'member$' @ 'fun_app$a' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom172) ).
thf(3093,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ! [C: 'A_ltln$'] :
( ( A @ ( C @ 'member$' @ 'fun_app$a' ) )
=> ( B @ ( C @ 'member$' @ 'fun_app$a' ) ) )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ! [C: 'A_ltln$'] :
( ( A @ ( C @ 'member$' @ 'fun_app$a' ) )
=> ( B @ ( C @ 'member$' @ 'fun_app$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(76,axiom,
! [A: 'A_ltln_set_set_a_ltln_set_set_a_ltln_set_set_fun_fun$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ! [D: 'A_ltln_set_set$',E: 'A_ltln_set_set$',F: 'A_ltln_set_set$'] :
( ( ( D @ ( F @ 'less_eq$a' @ 'fun_app$b' ) )
& ( D @ ( E @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( D @ ( F @ ( E @ ( A @ 'fun_app$f' ) @ 'fun_app$e' ) @ 'less_eq$a' @ 'fun_app$b' ) ) )
& ! [D: 'A_ltln_set_set$',E: 'A_ltln_set_set$'] : ( E @ ( D @ ( A @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( E @ 'less_eq$a' @ 'fun_app$b' ) )
& ! [D: 'A_ltln_set_set$',E: 'A_ltln_set_set$'] : ( E @ ( D @ ( A @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( D @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( ( C @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( C @ ( B @ ( A @ 'fun_app$f' ) @ 'fun_app$e' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom229) ).
thf(966,plain,
! [A: 'A_ltln_set_set_a_ltln_set_set_a_ltln_set_set_fun_fun$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ! [D: 'A_ltln_set_set$',E: 'A_ltln_set_set$',F: 'A_ltln_set_set$'] :
( ( ( D @ ( F @ 'less_eq$a' @ 'fun_app$b' ) )
& ( D @ ( E @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( D @ ( F @ ( E @ ( A @ 'fun_app$f' ) @ 'fun_app$e' ) @ 'less_eq$a' @ 'fun_app$b' ) ) )
& ! [D: 'A_ltln_set_set$',E: 'A_ltln_set_set$'] : ( E @ ( D @ ( A @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( E @ 'less_eq$a' @ 'fun_app$b' ) )
& ! [D: 'A_ltln_set_set$',E: 'A_ltln_set_set$'] : ( E @ ( D @ ( A @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( D @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( ( C @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( C @ ( B @ ( A @ 'fun_app$f' ) @ 'fun_app$e' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(135,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( A = B )
=> ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom165) ).
thf(1283,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( A = B )
=> ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(289,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set_a_ltln_set_set_fun$',D: 'A_ltln_set_set$'] :
( ( ! [E: 'A_ltln_set$',F: 'A_ltln_set$'] :
( ( F @ ( E @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( F @ ( C @ 'fun_app$k' ) @ ( E @ ( C @ 'fun_app$k' ) @ 'less_eq$a' @ 'fun_app$b' ) ) )
& ( ( B @ ( C @ 'fun_app$k' ) )
= D )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$k' ) @ 'less_eq$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom339) ).
thf(2017,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set_a_ltln_set_set_fun$',D: 'A_ltln_set_set$'] :
( ( ! [E: 'A_ltln_set$',F: 'A_ltln_set$'] :
( ( F @ ( E @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( F @ ( C @ 'fun_app$k' ) @ ( E @ ( C @ 'fun_app$k' ) @ 'less_eq$a' @ 'fun_app$b' ) ) )
& ( ( B @ ( C @ 'fun_app$k' ) )
= D )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$k' ) @ 'less_eq$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(379,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
<=> ( ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom224) ).
thf(2456,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ( ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= B )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(287,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] : ( A @ ( B @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom570) ).
thf(2007,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] : ( A @ ( B @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(586,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ! [D: 'A_ltln_set$',E: 'A_ltln_set$',F: 'A_ltln_set$'] :
( ( F @ ( E @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( D @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( F @ ( D @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( E @ ( D @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) )
=> ( ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom586) ).
thf(3438,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ! [D: 'A_ltln_set$',E: 'A_ltln_set$',F: 'A_ltln_set$'] :
( ( F @ ( E @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( D @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( F @ ( D @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( E @ ( D @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) )
=> ( ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(604,axiom,
! [A: 'A_ltln$',B: 'A_ltln$'] :
( ( 'bot$a' @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ 'member$' @ 'fun_app$a' ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom427) ).
thf(3525,plain,
! [A: 'A_ltln$',B: 'A_ltln$'] :
( ( ( A = B )
=> ( 'bot$a' @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ 'member$' @ 'fun_app$a' ) ) )
& ( ( 'bot$a' @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ 'member$' @ 'fun_app$a' ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(614,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
<=> ( ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom595) ).
thf(3569,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ( ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(217,axiom,
! [A: 'A_ltln_set_set$'] :
( ( ( A != 'bot$' )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ? [B: 'A_ltln_set$'] :
( ! [C: 'A_ltln_set$'] :
( ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( A @ ( C @ 'member$a' @ 'fun_app$b' ) ) )
=> ( B = C ) )
& ( A @ ( B @ 'member$a' @ 'fun_app$b' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom194) ).
thf(1677,plain,
! [A: 'A_ltln_set_set$'] :
( ( ( A != 'bot$' )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ? [B: 'A_ltln_set$'] :
( ! [C: 'A_ltln_set$'] :
( ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( A @ ( C @ 'member$a' @ 'fun_app$b' ) ) )
=> ( B = C ) )
& ( A @ ( B @ 'member$a' @ 'fun_app$b' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(393,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set_a_ltln_set_fun$',C: 'A_ltln_set$',D: 'A_ltln_set$'] :
( ( ! [E: 'A_ltln_set$',F: 'A_ltln_set$'] :
( ( F @ ( E @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( F @ ( B @ 'fun_app$c' ) @ ( E @ ( B @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( D @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( A
= ( C @ ( B @ 'fun_app$c' ) ) ) )
=> ( D @ ( B @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom338) ).
thf(2540,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set_a_ltln_set_fun$',C: 'A_ltln_set$',D: 'A_ltln_set$'] :
( ( ! [E: 'A_ltln_set$',F: 'A_ltln_set$'] :
( ( F @ ( E @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( F @ ( B @ 'fun_app$c' ) @ ( E @ ( B @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( D @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( A
= ( C @ ( B @ 'fun_app$c' ) ) ) )
=> ( D @ ( B @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(443,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( A @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( B @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom320) ).
thf(2777,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( A @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( B @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(523,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( 'bot$a'
= ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) )
<=> ( ( B = 'bot$a' )
& ( A = 'bot$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom115) ).
thf(3152,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ( ( B = 'bot$a' )
& ( A = 'bot$a' ) )
=> ( 'bot$a'
= ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ) )
& ( ( 'bot$a'
= ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) )
=> ( ( B = 'bot$a' )
& ( A = 'bot$a' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(79,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( A @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom47) ).
thf(981,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( A @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(504,axiom,
! [A: 'A_ltln$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( B @ ( A @ 'member$' @ 'fun_app$a' ) )
=> ( ( B @ ( C @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( B @ ( C @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom485) ).
thf(3068,plain,
! [A: 'A_ltln$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( B @ ( A @ 'member$' @ 'fun_app$a' ) )
=> ( ( B @ ( C @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( B @ ( C @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(532,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] : ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( C @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom620) ).
thf(3189,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] : ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( C @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(26,axiom,
( 'bot$'
= ( 'bot$d' @ 'collect$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom302) ).
thf(734,plain,
( 'bot$'
= ( 'bot$d' @ 'collect$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(498,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set_bool_fun$'] :
( ( ! [D: 'A_ltln$',E: 'A_ltln_set$'] :
( ( ( E @ ( C @ 'fun_app$a' ) )
& ~ ( E @ ( D @ 'member$' @ 'fun_app$a' ) )
& ( B @ ( E @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( D @ 'member$' @ 'fun_app$a' ) )
& ( E @ ( 'finite$' @ 'fun_app$a' ) ) )
=> ( E @ ( D @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( C @ 'fun_app$a' ) ) )
& ( 'bot$a' @ ( C @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( A @ ( 'finite$' @ 'fun_app$a' ) ) )
=> ( A @ ( C @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom466) ).
thf(3036,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set_bool_fun$'] :
( ( ! [D: 'A_ltln$',E: 'A_ltln_set$'] :
( ( ( E @ ( C @ 'fun_app$a' ) )
& ~ ( E @ ( D @ 'member$' @ 'fun_app$a' ) )
& ( B @ ( E @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( D @ 'member$' @ 'fun_app$a' ) )
& ( E @ ( 'finite$' @ 'fun_app$a' ) ) )
=> ( E @ ( D @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( C @ 'fun_app$a' ) ) )
& ( 'bot$a' @ ( C @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( A @ ( 'finite$' @ 'fun_app$a' ) ) )
=> ( A @ ( C @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(165,axiom,
! [A: 'A_ltln_set$'] :
( ( 'bot$' @ ( A @ 'member$a' @ 'fun_app$b' ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom149) ).
thf(1405,plain,
! [A: 'A_ltln_set$'] :
~ ( 'bot$' @ ( A @ 'member$a' @ 'fun_app$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(537,axiom,
! [A: 'A_ltln_set$'] :
( ( A @ ( 'bot$a' @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= 'bot$a' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom549) ).
thf(3211,plain,
! [A: 'A_ltln_set$'] :
( ( A @ ( 'bot$a' @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= 'bot$a' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(482,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom583) ).
thf(2982,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(601,axiom,
! [A: 'A_ltln_set$'] : ( A @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom174) ).
thf(3510,plain,
! [A: 'A_ltln_set$'] : ( A @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(19,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set_a_ltln_set_fun$',D: 'A_ltln_set$'] :
( ( ! [E: 'A_ltln_set_set$',F: 'A_ltln_set_set$'] :
( ( F @ ( E @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( F @ ( C @ 'fun_app$i' ) @ ( E @ ( C @ 'fun_app$i' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( ( B @ ( C @ 'fun_app$i' ) )
= D )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$i' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom340) ).
thf(692,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set_a_ltln_set_fun$',D: 'A_ltln_set$'] :
( ( ! [E: 'A_ltln_set_set$',F: 'A_ltln_set_set$'] :
( ( F @ ( E @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( F @ ( C @ 'fun_app$i' ) @ ( E @ ( C @ 'fun_app$i' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( ( B @ ( C @ 'fun_app$i' ) )
= D )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$i' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(580,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( B @ ( A @ ( C @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom610) ).
thf(3421,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( B @ ( A @ ( C @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(205,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set_a_ltln_set_set_fun$',D: 'A_ltln_set_set$'] :
( ( ! [E: 'A_ltln_set_set$',F: 'A_ltln_set_set$'] :
( ( F @ ( E @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( F @ ( C @ 'fun_app$e' ) @ ( E @ ( C @ 'fun_app$e' ) @ 'less_eq$a' @ 'fun_app$b' ) ) )
& ( D @ ( B @ ( C @ 'fun_app$e' ) @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$e' ) @ 'less_eq$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom331) ).
thf(1622,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set_a_ltln_set_set_fun$',D: 'A_ltln_set_set$'] :
( ( ! [E: 'A_ltln_set_set$',F: 'A_ltln_set_set$'] :
( ( F @ ( E @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( F @ ( C @ 'fun_app$e' ) @ ( E @ ( C @ 'fun_app$e' ) @ 'less_eq$a' @ 'fun_app$b' ) ) )
& ( D @ ( B @ ( C @ 'fun_app$e' ) @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$e' ) @ 'less_eq$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(374,axiom,
! [A: 'A_ltln$',B: 'A_ltln$',C: 'A_ltln_set$'] :
( ( ( ( C @ ( A @ 'member$' @ 'fun_app$a' ) )
=> $false )
& ( ( A = B )
=> $false )
& ( C @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ 'member$' @ 'fun_app$a' ) ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom419) ).
thf(2424,plain,
! [A: 'A_ltln$',B: 'A_ltln$',C: 'A_ltln_set$'] :
~ ( ~ ( C @ ( A @ 'member$' @ 'fun_app$a' ) )
& ( A != B )
& ( C @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ 'member$' @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(163,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
<=> ( ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom223) ).
thf(1394,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( ( ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= B )
=> ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
& ( ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(441,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] : ( B @ ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom615) ).
thf(2772,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] : ( B @ ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(449,axiom,
! [A: 'A_ltln_set_bool_fun$'] :
( ( ( A @ 'collect$' )
= 'bot$' )
<=> ! [B: 'A_ltln_set$'] :
~ ( B @ ( A @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom97) ).
thf(2799,plain,
! [A: 'A_ltln_set_bool_fun$'] :
( ( ! [B: 'A_ltln_set$'] :
~ ( B @ ( A @ 'fun_app$a' ) )
=> ( ( A @ 'collect$' )
= 'bot$' ) )
& ( ( ( A @ 'collect$' )
= 'bot$' )
=> ! [B: 'A_ltln_set$'] :
~ ( B @ ( A @ 'fun_app$a' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(415,axiom,
! [A: 'A_ltln_set$'] :
( ( A @ ( A @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) )
<=> ( A = 'bot$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom132) ).
thf(2639,plain,
! [A: 'A_ltln_set$'] :
( ( ( A = 'bot$a' )
=> ( A @ ( A @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( ( A @ ( A @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( A = 'bot$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(68,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set_set$'] :
( ( ( ( C @ ( A @ 'member$a' @ 'fun_app$b' ) )
=> $false )
& ( ( A = B )
=> $false )
& ( C @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ 'member$a' @ 'fun_app$b' ) ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom420) ).
thf(920,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set_set$'] :
~ ( ~ ( C @ ( A @ 'member$a' @ 'fun_app$b' ) )
& ( A != B )
& ( C @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ 'member$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(470,axiom,
! [A: 'A_ltln_set$'] :
( ( 'bot$a' @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom547) ).
thf(2910,plain,
! [A: 'A_ltln_set$'] :
( ( 'bot$a' @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(613,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] : ( A @ ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom616) ).
thf(3567,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] : ( A @ ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(172,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( C @ ( B @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ 'disjnt$' @ 'fun_app$b' ) )
<=> ( ( C @ ( B @ 'disjnt$' @ 'fun_app$b' ) )
& ~ ( C @ ( A @ 'member$a' @ 'fun_app$b' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom394) ).
thf(1438,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ( ( C @ ( B @ 'disjnt$' @ 'fun_app$b' ) )
& ~ ( C @ ( A @ 'member$a' @ 'fun_app$b' ) ) )
=> ( C @ ( B @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ 'disjnt$' @ 'fun_app$b' ) ) )
& ( ( C @ ( B @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ 'disjnt$' @ 'fun_app$b' ) )
=> ( ( C @ ( B @ 'disjnt$' @ 'fun_app$b' ) )
& ~ ( C @ ( A @ 'member$a' @ 'fun_app$b' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(142,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$'] :
( ( ( A @ ( B @ 'member$a' @ 'fun_app$b' ) )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ? [C: 'A_ltln_set$'] :
( ! [D: 'A_ltln_set$'] :
( ( ( C @ ( D @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( A @ ( D @ 'member$a' @ 'fun_app$b' ) ) )
=> ( C = D ) )
& ( B @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( A @ ( C @ 'member$a' @ 'fun_app$b' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom200) ).
thf(1306,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$'] :
( ( ( A @ ( B @ 'member$a' @ 'fun_app$b' ) )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ? [C: 'A_ltln_set$'] :
( ! [D: 'A_ltln_set$'] :
( ( ( C @ ( D @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( A @ ( D @ 'member$a' @ 'fun_app$b' ) ) )
=> ( C = D ) )
& ( B @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( A @ ( C @ 'member$a' @ 'fun_app$b' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(320,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( A = B )
<=> ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom184) ).
thf(2164,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(531,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom24) ).
thf(3186,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(557,axiom,
! [A: 'A_ltln$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ 'member$' @ 'fun_app$a' ) )
<=> ( ~ ( C @ ( A @ 'member$' @ 'fun_app$a' ) )
& ( B @ ( A @ 'member$' @ 'fun_app$a' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom517) ).
thf(3318,plain,
! [A: 'A_ltln$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( ~ ( C @ ( A @ 'member$' @ 'fun_app$a' ) )
& ( B @ ( A @ 'member$' @ 'fun_app$a' ) ) )
=> ( C @ ( B @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ 'member$' @ 'fun_app$a' ) ) )
& ( ( C @ ( B @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ 'member$' @ 'fun_app$a' ) )
=> ( ~ ( C @ ( A @ 'member$' @ 'fun_app$a' ) )
& ( B @ ( A @ 'member$' @ 'fun_app$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(285,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ( ( B
= ( A @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) )
=> $false )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom226) ).
thf(2000,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
~ ( ( B
!= ( A @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(579,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( A @ ( B @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom625) ).
thf(3418,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( A @ ( B @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(91,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set$'] :
( ( ( A @ ( C @ 'member$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( B @ ( C @ 'member$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom150) ).
thf(1047,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set$'] :
( ( ( A @ ( C @ 'member$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( B @ ( C @ 'member$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(589,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( B @ ( A @ ( 'max$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom636) ).
thf(3450,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( B @ ( A @ ( 'max$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(593,axiom,
! [A: 'A_ltln$',B: 'A_ltln$'] :
( ( 'bot$a' @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ 'member$' @ 'fun_app$a' ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom429) ).
thf(3459,plain,
! [A: 'A_ltln$',B: 'A_ltln$'] :
( ( 'bot$a' @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ 'member$' @ 'fun_app$a' ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(262,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom510) ).
thf(1915,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(223,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom542) ).
thf(1708,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(302,axiom,
! [A: 'A_ltln$',B: 'A_ltln_set$',C: 'A_ltln$'] :
( ( B @ ( A @ 'member$' @ 'fun_app$a' ) )
=> ( B @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ 'member$' @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom415) ).
thf(2083,plain,
! [A: 'A_ltln$',B: 'A_ltln_set$',C: 'A_ltln$'] :
( ( B @ ( A @ 'member$' @ 'fun_app$a' ) )
=> ( B @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ 'member$' @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(388,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( A
= ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) )
=> ( A @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom228) ).
thf(2496,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( A
= ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) )
=> ( A @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(235,axiom,
! [A: 'A_ltln_set_set$'] : ( A @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom289) ).
thf(1768,plain,
! [A: 'A_ltln_set_set$'] : ( A @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(24,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set_set$'] :
( ( C @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ 'member$a' @ 'fun_app$b' ) )
<=> ( ( C @ ( A @ 'member$a' @ 'fun_app$b' ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom378) ).
thf(714,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set_set$'] :
( ( ( ( C @ ( A @ 'member$a' @ 'fun_app$b' ) )
| ( A = B ) )
=> ( C @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ 'member$a' @ 'fun_app$b' ) ) )
& ( ( C @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ 'member$a' @ 'fun_app$b' ) )
=> ( ( C @ ( A @ 'member$a' @ 'fun_app$b' ) )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(371,axiom,
! [A: 'A_ltln_bool_fun$',B: 'A_ltln_bool_fun$'] :
( ( B @ 'collect$a' @ ( A @ 'collect$a' @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
<=> ! [C: 'A_ltln$'] :
( ( C @ ( A @ 'fun_app$' ) )
=> ( C @ ( B @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom190) ).
thf(2409,plain,
! [A: 'A_ltln_bool_fun$',B: 'A_ltln_bool_fun$'] :
( ( ! [C: 'A_ltln$'] :
( ( C @ ( A @ 'fun_app$' ) )
=> ( C @ ( B @ 'fun_app$' ) ) )
=> ( B @ 'collect$a' @ ( A @ 'collect$a' @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( ( B @ 'collect$a' @ ( A @ 'collect$a' @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ! [C: 'A_ltln$'] :
( ( C @ ( A @ 'fun_app$' ) )
=> ( C @ ( B @ 'fun_app$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(160,axiom,
! [A: 'A_ltln_set$'] : ( 'bot$' @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( 'is_singleton$a' @ 'fun_app$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom472) ).
thf(1387,plain,
! [A: 'A_ltln_set$'] : ( 'bot$' @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( 'is_singleton$a' @ 'fun_app$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(62,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ( B @ ( C @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'member$a' @ 'fun_app$b' ) ) )
=> ( B @ ( C @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ 'less_eq$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom433) ).
thf(894,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ( B @ ( C @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'member$a' @ 'fun_app$b' ) ) )
=> ( B @ ( C @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ 'less_eq$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(49,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ( C @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( C @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom311) ).
thf(825,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ( C @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( C @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(34,axiom,
! [A: 'A_ltln_set_set$'] :
( ( A @ ( A @ ( 'minus$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= 'bot$' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom550) ).
thf(778,plain,
! [A: 'A_ltln_set_set$'] :
( ( A @ ( A @ ( 'minus$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= 'bot$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(73,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set$'] :
( ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( B @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom435) ).
thf(952,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set$'] :
( ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( B @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(153,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ! [D: 'A_ltln_set_set$',E: 'A_ltln_set_set$'] :
( ( ( A
= ( E @ ( D @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) )
& ( C @ ( E @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( D @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> $false )
& ( C @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom275) ).
thf(1355,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
~ ( ! [D: 'A_ltln_set_set$',E: 'A_ltln_set_set$'] :
~ ( ( A
= ( E @ ( D @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) )
& ( C @ ( E @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( D @ 'less_eq$a' @ 'fun_app$b' ) ) )
& ( C @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(232,axiom,
! [A: 'A_ltln_set_set$'] :
( ( A @ ( 'finite$a' @ 'fun_app$b' ) )
<=> ( ? [B: 'A_ltln_set_set$',C: 'A_ltln_set$'] :
( ( B @ ( 'finite$a' @ 'fun_app$b' ) )
& ( A
= ( B @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) ) )
| ( A = 'bot$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom447) ).
thf(1751,plain,
! [A: 'A_ltln_set_set$'] :
( ( ( ? [B: 'A_ltln_set_set$',C: 'A_ltln_set$'] :
( ( B @ ( 'finite$a' @ 'fun_app$b' ) )
& ( A
= ( B @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) ) )
| ( A = 'bot$' ) )
=> ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
& ( ( A @ ( 'finite$a' @ 'fun_app$b' ) )
=> ( ? [B: 'A_ltln_set_set$',C: 'A_ltln_set$'] :
( ( B @ ( 'finite$a' @ 'fun_app$b' ) )
& ( A
= ( B @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) ) )
| ( A = 'bot$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(543,axiom,
! [A: 'A_ltln$',B: 'A_ltln_set$'] :
( ( B @ ( A @ 'member$' @ 'fun_app$a' ) )
=> ( ( B @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom409) ).
thf(3239,plain,
! [A: 'A_ltln$',B: 'A_ltln_set$'] :
( ( B @ ( A @ 'member$' @ 'fun_app$a' ) )
=> ( ( B @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(570,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] : ( A @ ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom617) ).
thf(3371,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] : ( A @ ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(291,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_bool_fun$',D: 'A_ltln_bool_fun$'] :
( ( ! [E: 'A_ltln$'] :
( ( ( E @ ( C @ 'fun_app$' ) )
& ( A @ ( E @ 'member$' @ 'fun_app$a' ) ) )
=> ( E @ ( D @ 'fun_app$' ) ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( D @ 'collect$a' @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( C @ 'collect$a' @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom561) ).
thf(2032,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_bool_fun$',D: 'A_ltln_bool_fun$'] :
( ( ! [E: 'A_ltln$'] :
( ( ( E @ ( C @ 'fun_app$' ) )
& ( A @ ( E @ 'member$' @ 'fun_app$a' ) ) )
=> ( E @ ( D @ 'fun_app$' ) ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( D @ 'collect$a' @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( C @ 'collect$a' @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(409,axiom,
! [A: 'A_ltln_set_bool_fun$',B: 'A_ltln_set$'] :
( ( ! [C: 'A_ltln_set$'] :
( ( ! [D: 'A_ltln$'] :
( ( C @ ( D @ 'member$' @ 'fun_app$a' ) )
=> ( 'bot$a' @ ( D @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( C @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ 'fun_app$a' ) ) )
& ( B @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( C != 'bot$a' )
& ( C @ ( 'finite$' @ 'fun_app$a' ) ) )
=> ( C @ ( A @ 'fun_app$a' ) ) )
& ( ~ ( B @ ( 'finite$' @ 'fun_app$a' ) )
=> ( B @ ( A @ 'fun_app$a' ) ) )
& ( 'bot$a' @ ( A @ 'fun_app$a' ) ) )
=> ( B @ ( A @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom632) ).
thf(2601,plain,
! [A: 'A_ltln_set_bool_fun$',B: 'A_ltln_set$'] :
( ( ! [C: 'A_ltln_set$'] :
( ( ! [D: 'A_ltln$'] :
( ( C @ ( D @ 'member$' @ 'fun_app$a' ) )
=> ( 'bot$a' @ ( D @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( C @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ 'fun_app$a' ) ) )
& ( B @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( C != 'bot$a' )
& ( C @ ( 'finite$' @ 'fun_app$a' ) ) )
=> ( C @ ( A @ 'fun_app$a' ) ) )
& ( ~ ( B @ ( 'finite$' @ 'fun_app$a' ) )
=> ( B @ ( A @ 'fun_app$a' ) ) )
& ( 'bot$a' @ ( A @ 'fun_app$a' ) ) )
=> ( B @ ( A @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(375,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
<=> ( ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom606) ).
thf(2428,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ( ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(204,axiom,
! [A: 'A_ltln_set_a_ltln_set_fun$'] :
( ( A @ ( 'bot$' @ 'bind$a' ) )
= 'bot$a' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom136) ).
thf(1619,plain,
! [A: 'A_ltln_set_a_ltln_set_fun$'] :
( ( A @ ( 'bot$' @ 'bind$a' ) )
= 'bot$a' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(317,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom563) ).
thf(2150,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(477,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$',D: 'A_ltln_set$'] :
( ( ( D @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( D @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( C @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom218) ).
thf(2958,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$',D: 'A_ltln_set$'] :
( ( ( D @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( D @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( C @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(67,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ~ ( B @ ( A @ 'member$a' @ 'fun_app$b' ) )
=> ( ( B @ ( C @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( B @ ( C @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom482) ).
thf(916,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ~ ( B @ ( A @ 'member$a' @ 'fun_app$b' ) )
=> ( ( B @ ( C @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( B @ ( C @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(200,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( C @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom253) ).
thf(1602,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( C @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(193,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( C @ ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ 'disjnt$' @ 'fun_app$b' ) )
<=> ( ( C @ ( B @ 'disjnt$' @ 'fun_app$b' ) )
& ( C @ ( A @ 'disjnt$' @ 'fun_app$b' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom79) ).
thf(1555,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ( ( C @ ( B @ 'disjnt$' @ 'fun_app$b' ) )
& ( C @ ( A @ 'disjnt$' @ 'fun_app$b' ) ) )
=> ( C @ ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ 'disjnt$' @ 'fun_app$b' ) ) )
& ( ( C @ ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ 'disjnt$' @ 'fun_app$b' ) )
=> ( ( C @ ( B @ 'disjnt$' @ 'fun_app$b' ) )
& ( C @ ( A @ 'disjnt$' @ 'fun_app$b' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(598,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( A @ ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom505) ).
thf(3499,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( A @ ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(176,axiom,
! [A: 'A_ltln_bool_fun$',B: 'A_ltln_bool_fun$'] :
( ! [C: 'A_ltln$'] :
( ( C @ ( A @ 'fun_app$' ) )
<=> ( C @ ( B @ 'fun_app$' ) ) )
=> ( ( A @ 'collect$a' )
= ( B @ 'collect$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom85) ).
thf(1457,plain,
! [A: 'A_ltln_bool_fun$',B: 'A_ltln_bool_fun$'] :
( ! [C: 'A_ltln$'] :
( ( ( C @ ( B @ 'fun_app$' ) )
=> ( C @ ( A @ 'fun_app$' ) ) )
& ( ( C @ ( A @ 'fun_app$' ) )
=> ( C @ ( B @ 'fun_app$' ) ) ) )
=> ( ( A @ 'collect$a' )
= ( B @ 'collect$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(322,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
<=> ( ( A @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom594) ).
thf(2179,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ( ( A @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( A @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(108,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set_bool_fun$'] :
( ( ! [C: 'A_ltln_set$',D: 'A_ltln_set_set$'] :
( ( ( D @ ( B @ 'fun_app$b' ) )
& ~ ( D @ ( C @ 'member$a' @ 'fun_app$b' ) )
& ( D @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( D @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( B @ 'fun_app$b' ) ) )
& ( 'bot$' @ ( B @ 'fun_app$b' ) )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( A @ ( B @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom449) ).
thf(1159,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set_bool_fun$'] :
( ( ! [C: 'A_ltln_set$',D: 'A_ltln_set_set$'] :
( ( ( D @ ( B @ 'fun_app$b' ) )
& ~ ( D @ ( C @ 'member$a' @ 'fun_app$b' ) )
& ( D @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( D @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( B @ 'fun_app$b' ) ) )
& ( 'bot$' @ ( B @ 'fun_app$b' ) )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( A @ ( B @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(247,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( C @ ( B @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( C @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom389) ).
thf(1836,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( C @ ( B @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( C @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(332,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( B @ ( C @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom256) ).
thf(2213,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( B @ ( C @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(116,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set$'] :
( ( ( A @ ( C @ 'member$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( B @ ( C @ 'member$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom152) ).
thf(1195,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set$'] :
( ( ( A @ ( C @ 'member$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( B @ ( C @ 'member$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(436,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
<=> ( ( ~ ( A @ ( B @ 'member$' @ 'fun_app$a' ) )
=> ( C @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( ( A @ ( B @ 'member$' @ 'fun_app$a' ) )
=> ( C @ ( 'bot$a' @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom631) ).
thf(2741,plain,
! [A: 'A_ltln_set$',B: 'A_ltln$',C: 'A_ltln_set$'] :
( ( ( ( ~ ( A @ ( B @ 'member$' @ 'fun_app$a' ) )
=> ( C @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( ( A @ ( B @ 'member$' @ 'fun_app$a' ) )
=> ( C @ ( 'bot$a' @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ) )
=> ( C @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( ( C @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( ~ ( A @ ( B @ 'member$' @ 'fun_app$a' ) )
=> ( C @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( ( A @ ( B @ 'member$' @ 'fun_app$a' ) )
=> ( C @ ( 'bot$a' @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(335,axiom,
! [A: 'A_ltln$',B: 'A_ltln$',C: 'A_ltln$',D: 'A_ltln$'] :
( ( ( 'bot$a' @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) )
= ( 'bot$a' @ ( D @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) )
<=> ( ( ( B = C )
& ( A = D ) )
| ( ( B = D )
& ( A = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom425) ).
thf(2228,plain,
! [A: 'A_ltln$',B: 'A_ltln$',C: 'A_ltln$',D: 'A_ltln$'] :
( ( ( ( ( B = C )
& ( A = D ) )
| ( ( B = D )
& ( A = C ) ) )
=> ( ( 'bot$a' @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) )
= ( 'bot$a' @ ( D @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) ) )
& ( ( ( 'bot$a' @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) )
= ( 'bot$a' @ ( D @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) )
=> ( ( ( B = C )
& ( A = D ) )
| ( ( B = D )
& ( A = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(309,axiom,
! [A: 'A_ltln$'] :
( ( 'bot$a' @ ( A @ 'member$' @ 'fun_app$a' ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom148) ).
thf(2112,plain,
! [A: 'A_ltln$'] :
~ ( 'bot$a' @ ( A @ 'member$' @ 'fun_app$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(229,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ( A @ ( C @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'disjnt$' @ 'fun_app$b' ) ) )
=> ( B @ ( C @ 'disjnt$' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom185) ).
thf(1740,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ( A @ ( C @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'disjnt$' @ 'fun_app$b' ) ) )
=> ( B @ ( C @ 'disjnt$' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(87,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set$'] :
( ( ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( 'bot$' @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) )
<=> ( ( ( B
= ( 'bot$' @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) )
& ( A
= ( 'bot$' @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) ) )
| ( ( B = 'bot$' )
& ( A
= ( 'bot$' @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) ) )
| ( ( B
= ( 'bot$' @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) )
& ( A = 'bot$' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom461) ).
thf(1012,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set$'] :
( ( ( ( ( B
= ( 'bot$' @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) )
& ( A
= ( 'bot$' @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) ) )
| ( ( B = 'bot$' )
& ( A
= ( 'bot$' @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) ) )
| ( ( B
= ( 'bot$' @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) )
& ( A = 'bot$' ) ) )
=> ( ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( 'bot$' @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) ) )
& ( ( ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( 'bot$' @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) )
=> ( ( ( B
= ( 'bot$' @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) )
& ( A
= ( 'bot$' @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) ) )
| ( ( B = 'bot$' )
& ( A
= ( 'bot$' @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) ) )
| ( ( B
= ( 'bot$' @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) )
& ( A = 'bot$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(533,axiom,
! [A: 'A_ltln_set$'] :
( ( A @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom50) ).
thf(3191,plain,
! [A: 'A_ltln_set$'] :
( ( A @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(380,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) )
<=> ! [C: 'A_ltln$'] :
~ ( ( B @ ( C @ 'member$' @ 'fun_app$a' ) )
& ( A @ ( C @ 'member$' @ 'fun_app$a' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom162) ).
thf(2464,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ! [C: 'A_ltln$'] :
~ ( ( B @ ( C @ 'member$' @ 'fun_app$a' ) )
& ( A @ ( C @ 'member$' @ 'fun_app$a' ) ) )
=> ( B @ ( A @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( ( B @ ( A @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ! [C: 'A_ltln$'] :
~ ( ( B @ ( C @ 'member$' @ 'fun_app$a' ) )
& ( A @ ( C @ 'member$' @ 'fun_app$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(577,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ( B @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= 'bot$a' )
<=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom559) ).
thf(3403,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( B @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= 'bot$a' ) )
& ( ( ( B @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= 'bot$a' )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(399,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
<=> ( ( A @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom250) ).
thf(2565,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ( ( A @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= B )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( A @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(120,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( A = B )
<=> ( ( A @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom303) ).
thf(1210,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( ( ( A @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(211,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( ( B @ ( 'finite$a' @ 'fun_app$b' ) )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( 'finite$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom19) ).
thf(1656,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( ( B @ ( 'finite$a' @ 'fun_app$b' ) )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( 'finite$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(164,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( C @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( C @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom25) ).
thf(1402,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( C @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( C @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(281,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom605) ).
thf(1983,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(310,axiom,
! [A: 'A_ltln$',B: 'A_ltln_set$'] : ( B @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ 'member$' @ 'fun_app$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom417) ).
thf(2115,plain,
! [A: 'A_ltln$',B: 'A_ltln_set$'] : ( B @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ 'member$' @ 'fun_app$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(307,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln$'] :
( ( ( A @ ( C @ 'member$' @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( B @ ( C @ 'member$' @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom151) ).
thf(2100,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln$'] :
( ( ( A @ ( C @ 'member$' @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( B @ ( C @ 'member$' @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(239,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ( C @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
& ( A = B ) )
=> ( C @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom305) ).
thf(1804,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ( C @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
& ( A = B ) )
=> ( C @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(458,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom344) ).
thf(2841,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( ( B = A )
=> ( A @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(99,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( ( B @ ( 'finite$a' @ 'fun_app$b' ) )
| ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( B @ ( A @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( 'finite$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom478) ).
thf(1121,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( ( B @ ( 'finite$a' @ 'fun_app$b' ) )
| ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( B @ ( A @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( 'finite$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(431,axiom,
! [A: 'A_ltln$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ~ ( C @ ( A @ 'member$' @ 'fun_app$a' ) )
& ( B @ ( A @ 'member$' @ 'fun_app$a' ) ) )
=> ( C @ ( B @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ 'member$' @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom515) ).
thf(2726,plain,
! [A: 'A_ltln$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ~ ( C @ ( A @ 'member$' @ 'fun_app$a' ) )
& ( B @ ( A @ 'member$' @ 'fun_app$a' ) ) )
=> ( C @ ( B @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ 'member$' @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(506,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) )
<=> ( ( C @ ( A @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ~ ( A @ ( B @ 'member$' @ 'fun_app$a' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom391) ).
thf(3078,plain,
! [A: 'A_ltln_set$',B: 'A_ltln$',C: 'A_ltln_set$'] :
( ( ( ( C @ ( A @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ~ ( A @ ( B @ 'member$' @ 'fun_app$a' ) ) )
=> ( C @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( ( C @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( C @ ( A @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ~ ( A @ ( B @ 'member$' @ 'fun_app$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(542,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln$'] : ( A @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom438) ).
thf(3237,plain,
! [A: 'A_ltln_set$',B: 'A_ltln$'] : ( A @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(336,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
<=> ( ( C @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom481) ).
thf(2245,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( ( C @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( C @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(151,axiom,
! [A: 'A_ltln_set_set$'] :
( ( A @ ( 'bot$' @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= 'bot$' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom533) ).
thf(1350,plain,
! [A: 'A_ltln_set_set$'] :
( ( A @ ( 'bot$' @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= 'bot$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(125,axiom,
! [A: 'A_ltln_set$'] :
( ( 'bot$' @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( 'the_elem$a' @ 'fun_app$i' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom470) ).
thf(1234,plain,
! [A: 'A_ltln_set$'] :
( ( 'bot$' @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( 'the_elem$a' @ 'fun_app$i' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(189,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ( C @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( C @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom313) ).
thf(1541,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ( C @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( C @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(360,axiom,
! [A: 'A_ltln_set$'] : ( A @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom292) ).
thf(2377,plain,
! [A: 'A_ltln_set$'] : ( A @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(10,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) )
!= 'bot$' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom424) ).
thf(650,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) )
!= 'bot$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(72,axiom,
! [A: 'A_ltln_set_set$'] :
( ~ ( A @ ( 'finite$a' @ 'fun_app$b' ) )
=> ( A != 'bot$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom281) ).
thf(948,plain,
! [A: 'A_ltln_set_set$'] :
( ~ ( A @ ( 'finite$a' @ 'fun_app$b' ) )
=> ( A != 'bot$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(425,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( B @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom442) ).
thf(2692,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( B @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(181,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$',D: 'A_ltln_set_set$'] :
( ( ( D @ ( C @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( D @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( C @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ 'less_eq$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom263) ).
thf(1498,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$',D: 'A_ltln_set_set$'] :
( ( ( D @ ( C @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( D @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( C @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ 'less_eq$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(461,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_a_ltln_set_fun$'] :
( ( ! [C: 'A_ltln_set$'] :
( ( A @ ( C @ 'member$a' @ 'fun_app$b' ) )
=> ( C @ ( B @ 'fun_app$c' ) @ ( 'finite$' @ 'fun_app$a' ) ) )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( B @ ( A @ 'bind$a' ) @ ( 'finite$' @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom87) ).
thf(2858,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_a_ltln_set_fun$'] :
( ( ! [C: 'A_ltln_set$'] :
( ( A @ ( C @ 'member$a' @ 'fun_app$b' ) )
=> ( C @ ( B @ 'fun_app$c' ) @ ( 'finite$' @ 'fun_app$a' ) ) )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( B @ ( A @ 'bind$a' ) @ ( 'finite$' @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(392,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( B @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom558) ).
thf(2537,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( B @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(492,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln$',C: 'A_ltln_set$'] :
( ( C @ ( 'bot$a' @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( C @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom630) ).
thf(3018,plain,
! [A: 'A_ltln_set$',B: 'A_ltln$',C: 'A_ltln_set$'] :
( ( C @ ( 'bot$a' @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( C @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(56,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$'] :
( ( ! [C: 'A_ltln_set$'] :
( ( A @ ( C @ 'member$a' @ 'fun_app$b' ) )
=> ( B @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( A != 'bot$' )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( B @ ( A @ ( 'sup_fin$a' @ 'fun_app$i' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom364) ).
thf(857,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$'] :
( ( ! [C: 'A_ltln_set$'] :
( ( A @ ( C @ 'member$a' @ 'fun_app$b' ) )
=> ( B @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( A != 'bot$' )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( B @ ( A @ ( 'sup_fin$a' @ 'fun_app$i' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(218,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( A = B )
<=> ( ( A @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom183) ).
thf(1683,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( ( ( A @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(138,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ( C @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( C @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom177) ).
thf(1292,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ( C @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( C @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(269,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom310) ).
thf(1937,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(583,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom575) ).
thf(3428,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(534,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( A @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom30) ).
thf(3194,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( A @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(395,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom34) ).
thf(2551,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(421,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( A = B )
<=> ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( A @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom316) ).
thf(2666,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( A @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( A @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(257,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
<=> ( ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom277) ).
thf(1889,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( ( ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= B )
=> ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
& ( ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(553,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] : ( A @ ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom566) ).
thf(3294,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] : ( A @ ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(22,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ( ( ( C @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
& ( C @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> $false )
& ( C @ ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom205) ).
thf(706,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
~ ( ~ ( ( C @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
& ( C @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
& ( C @ ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ 'less_eq$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(488,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] : ( A @ ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom597) ).
thf(3000,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] : ( A @ ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(349,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
<=> ( ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom252) ).
thf(2323,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ( ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= B )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(30,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$'] :
( ( ! [C: 'A_ltln_set$'] :
( ( A @ ( C @ 'member$a' @ 'fun_app$b' ) )
=> ( C @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( A != 'bot$' )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( A @ ( 'inf_fin$a' @ 'fun_app$i' ) @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom141) ).
thf(753,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$'] :
( ( ! [C: 'A_ltln_set$'] :
( ( A @ ( C @ 'member$a' @ 'fun_app$b' ) )
=> ( C @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( A != 'bot$' )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( A @ ( 'inf_fin$a' @ 'fun_app$i' ) @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(398,axiom,
! [A: 'A_ltln_bool_fun$',B: 'A_ltln_bool_fun$'] :
( ! [C: 'A_ltln$'] :
( ( C @ ( A @ 'fun_app$' ) )
=> ( C @ ( B @ 'fun_app$' ) ) )
=> ( B @ 'collect$a' @ ( A @ 'collect$a' @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom176) ).
thf(2561,plain,
! [A: 'A_ltln_bool_fun$',B: 'A_ltln_bool_fun$'] :
( ! [C: 'A_ltln$'] :
( ( C @ ( A @ 'fun_app$' ) )
=> ( C @ ( B @ 'fun_app$' ) ) )
=> ( B @ 'collect$a' @ ( A @ 'collect$a' @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(169,axiom,
! [A: 'A_ltln_set$'] :
( ( 'bot$' @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( 'inf_fin$a' @ 'fun_app$i' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom399) ).
thf(1424,plain,
! [A: 'A_ltln_set$'] :
( ( 'bot$' @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( 'inf_fin$a' @ 'fun_app$i' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(346,axiom,
! [A: 'A_ltln_set$'] :
( ~ ( A @ ( 'finite$' @ 'fun_app$a' ) )
=> ( A != 'bot$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom282) ).
thf(2312,plain,
! [A: 'A_ltln_set$'] :
( ~ ( A @ ( 'finite$' @ 'fun_app$a' ) )
=> ( A != 'bot$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(327,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( A @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom602) ).
thf(2196,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( A @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(249,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set_a_ltln_set_fun$',C: 'A_ltln_set_set$',D: 'A_ltln_set_set$'] :
( ( ! [E: 'A_ltln_set_set$',F: 'A_ltln_set_set$'] :
( ( F @ ( E @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( F @ ( B @ 'fun_app$i' ) @ ( E @ ( B @ 'fun_app$i' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( D @ ( C @ 'less_eq$a' @ 'fun_app$b' ) )
& ( A
= ( C @ ( B @ 'fun_app$i' ) ) ) )
=> ( D @ ( B @ 'fun_app$i' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom336) ).
thf(1842,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set_a_ltln_set_fun$',C: 'A_ltln_set_set$',D: 'A_ltln_set_set$'] :
( ( ! [E: 'A_ltln_set_set$',F: 'A_ltln_set_set$'] :
( ( F @ ( E @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( F @ ( B @ 'fun_app$i' ) @ ( E @ ( B @ 'fun_app$i' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( D @ ( C @ 'less_eq$a' @ 'fun_app$b' ) )
& ( A
= ( C @ ( B @ 'fun_app$i' ) ) ) )
=> ( D @ ( B @ 'fun_app$i' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(381,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] : ( A @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom212) ).
thf(2472,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] : ( A @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(417,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom585) ).
thf(2649,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(544,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_bool_fun$'] :
( ? [D: 'A_ltln$'] :
( ( D @ ( C @ 'fun_app$' ) )
& ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( D @ 'member$' @ 'fun_app$a' ) ) )
<=> ( ? [D: 'A_ltln$'] :
( ( D @ ( C @ 'fun_app$' ) )
& ( B @ ( D @ 'member$' @ 'fun_app$a' ) ) )
| ? [D: 'A_ltln$'] :
( ( D @ ( C @ 'fun_app$' ) )
& ( A @ ( D @ 'member$' @ 'fun_app$a' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom56) ).
thf(3242,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_bool_fun$'] :
( ( ( ? [D: 'A_ltln$'] :
( ( D @ ( C @ 'fun_app$' ) )
& ( B @ ( D @ 'member$' @ 'fun_app$a' ) ) )
| ? [D: 'A_ltln$'] :
( ( D @ ( C @ 'fun_app$' ) )
& ( A @ ( D @ 'member$' @ 'fun_app$a' ) ) ) )
=> ? [D: 'A_ltln$'] :
( ( D @ ( C @ 'fun_app$' ) )
& ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( D @ 'member$' @ 'fun_app$a' ) ) ) )
& ( ? [D: 'A_ltln$'] :
( ( D @ ( C @ 'fun_app$' ) )
& ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( D @ 'member$' @ 'fun_app$a' ) ) )
=> ( ? [D: 'A_ltln$'] :
( ( D @ ( C @ 'fun_app$' ) )
& ( B @ ( D @ 'member$' @ 'fun_app$a' ) ) )
| ? [D: 'A_ltln$'] :
( ( D @ ( C @ 'fun_app$' ) )
& ( A @ ( D @ 'member$' @ 'fun_app$a' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(479,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$',D: 'A_ltln_set$'] :
( ( ( D @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( D @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( C @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom612) ).
thf(2968,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$',D: 'A_ltln_set$'] :
( ( ( D @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( D @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( C @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(8,axiom,
'sup$a' @ 'comp_fun_idem$',
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom73) ).
thf(647,plain,
'sup$a' @ 'comp_fun_idem$',
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(106,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( C @ ( B @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
<=> ( ( C @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom520) ).
thf(1150,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ( ( C @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( C @ ( B @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
& ( ( C @ ( B @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( ( C @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(518,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set_bool_fun$'] :
( ( ! [C: 'A_ltln$',D: 'A_ltln_set$'] :
( ( ( D @ ( B @ 'fun_app$a' ) )
& ( D @ ( C @ 'member$' @ 'fun_app$a' ) )
& ( D @ ( 'finite$' @ 'fun_app$a' ) ) )
=> ( 'bot$a' @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( D @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( B @ 'fun_app$a' ) ) )
& ( A @ ( B @ 'fun_app$a' ) )
& ( A @ ( 'finite$' @ 'fun_app$a' ) ) )
=> ( 'bot$a' @ ( B @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom627) ).
thf(3126,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set_bool_fun$'] :
( ( ! [C: 'A_ltln$',D: 'A_ltln_set$'] :
( ( ( D @ ( B @ 'fun_app$a' ) )
& ( D @ ( C @ 'member$' @ 'fun_app$a' ) )
& ( D @ ( 'finite$' @ 'fun_app$a' ) ) )
=> ( 'bot$a' @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( D @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( B @ 'fun_app$a' ) ) )
& ( A @ ( B @ 'fun_app$a' ) )
& ( A @ ( 'finite$' @ 'fun_app$a' ) ) )
=> ( 'bot$a' @ ( B @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(11,axiom,
! [A: 'A_ltln_set_set$'] :
( ( 'bot$' @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom285) ).
thf(654,plain,
! [A: 'A_ltln_set_set$'] :
( ( 'bot$' @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(192,axiom,
! [A: 'A_ltln_set_set$'] :
( ( A @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom9) ).
thf(1552,plain,
! [A: 'A_ltln_set_set$'] :
( ( A @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(115,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( C @ ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( C @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom31) ).
thf(1192,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( C @ ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( C @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(403,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom603) ).
thf(2581,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(608,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom234) ).
thf(3540,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(462,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( A = B )
<=> ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom304) ).
thf(2862,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(560,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( A @ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom513) ).
thf(3333,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( A @ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(503,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_a_ltln_set_set_fun$'] :
( ( ! [C: 'A_ltln$'] :
( ( A @ ( C @ 'member$' @ 'fun_app$a' ) )
=> ( C @ ( B @ 'fun_app$j' ) @ ( 'finite$a' @ 'fun_app$b' ) ) )
& ( A @ ( 'finite$' @ 'fun_app$a' ) ) )
=> ( B @ ( A @ 'bind$' ) @ ( 'finite$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom86) ).
thf(3064,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_a_ltln_set_set_fun$'] :
( ( ! [C: 'A_ltln$'] :
( ( A @ ( C @ 'member$' @ 'fun_app$a' ) )
=> ( C @ ( B @ 'fun_app$j' ) @ ( 'finite$a' @ 'fun_app$b' ) ) )
& ( A @ ( 'finite$' @ 'fun_app$a' ) ) )
=> ( B @ ( A @ 'bind$' ) @ ( 'finite$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(438,axiom,
! [A: 'A_ltln_set$'] :
( ( ! [B: 'A_ltln_set$',C: 'A_ltln$'] :
( ( ( B @ ( 'finite$' @ 'fun_app$a' ) )
& ( A
= ( B @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) ) )
=> $false )
& ( ( A = 'bot$a' )
=> $false )
& ( A @ ( 'finite$' @ 'fun_app$a' ) ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom446) ).
thf(2756,plain,
! [A: 'A_ltln_set$'] :
~ ( ! [B: 'A_ltln_set$',C: 'A_ltln$'] :
~ ( ( B @ ( 'finite$' @ 'fun_app$a' ) )
& ( A
= ( B @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) ) )
& ( A != 'bot$a' )
& ( A @ ( 'finite$' @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(524,axiom,
'phi$' @ ( 'subformulas_mu$' @ 'fun_app$h' ) @ ( 'x$' @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom70) ).
thf(3162,plain,
'phi$' @ ( 'subformulas_mu$' @ 'fun_app$h' ) @ ( 'x$' @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(318,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_a_ltln_set_set_fun$',C: 'A_ltln_set$',D: 'A_ltln_set$'] :
( ( ! [E: 'A_ltln_set$',F: 'A_ltln_set$'] :
( ( F @ ( E @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( F @ ( B @ 'fun_app$k' ) @ ( E @ ( B @ 'fun_app$k' ) @ 'less_eq$a' @ 'fun_app$b' ) ) )
& ( D @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( A
= ( C @ ( B @ 'fun_app$k' ) ) ) )
=> ( D @ ( B @ 'fun_app$k' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom335) ).
thf(2153,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_a_ltln_set_set_fun$',C: 'A_ltln_set$',D: 'A_ltln_set$'] :
( ( ! [E: 'A_ltln_set$',F: 'A_ltln_set$'] :
( ( F @ ( E @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( F @ ( B @ 'fun_app$k' ) @ ( E @ ( B @ 'fun_app$k' ) @ 'less_eq$a' @ 'fun_app$b' ) ) )
& ( D @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( A
= ( C @ ( B @ 'fun_app$k' ) ) ) )
=> ( D @ ( B @ 'fun_app$k' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(124,axiom,
! [A: 'A_ltln_set_set$'] :
( ( A @ ( 'bot$' @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom110) ).
thf(1231,plain,
! [A: 'A_ltln_set_set$'] :
( ( A @ ( 'bot$' @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(80,axiom,
! [A: 'A_ltln_set_set$'] :
( ( 'bot$' @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
<=> ( A = 'bot$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom126) ).
thf(984,plain,
! [A: 'A_ltln_set_set$'] :
( ( ( A = 'bot$' )
=> ( 'bot$' @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
& ( ( 'bot$' @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( A = 'bot$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(574,axiom,
! [A: 'A_ltln$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) )
<=> ( ( C @ ( B @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ~ ( C @ ( A @ 'member$' @ 'fun_app$a' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom393) ).
thf(3390,plain,
! [A: 'A_ltln$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( ( C @ ( B @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ~ ( C @ ( A @ 'member$' @ 'fun_app$a' ) ) )
=> ( C @ ( B @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( ( C @ ( B @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( C @ ( B @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ~ ( C @ ( A @ 'member$' @ 'fun_app$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(85,axiom,
! [A: 'A_ltln_set_set$'] :
( ! [B: 'A_ltln_set$'] :
( ( A @ ( B @ 'member$a' @ 'fun_app$b' ) )
=> $false )
=> ( 'bot$' @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom293) ).
thf(1002,plain,
! [A: 'A_ltln_set_set$'] :
( ! [B: 'A_ltln_set$'] :
~ ( A @ ( B @ 'member$a' @ 'fun_app$b' ) )
=> ( 'bot$' @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(251,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_bool_fun$'] :
( ? [D: 'A_ltln_set$'] :
( ( D @ ( C @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( D @ 'member$a' @ 'fun_app$b' ) ) )
<=> ( ? [D: 'A_ltln_set$'] :
( ( D @ ( C @ 'fun_app$a' ) )
& ( B @ ( D @ 'member$a' @ 'fun_app$b' ) ) )
| ? [D: 'A_ltln_set$'] :
( ( D @ ( C @ 'fun_app$a' ) )
& ( A @ ( D @ 'member$a' @ 'fun_app$b' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom55) ).
thf(1852,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_bool_fun$'] :
( ( ( ? [D: 'A_ltln_set$'] :
( ( D @ ( C @ 'fun_app$a' ) )
& ( B @ ( D @ 'member$a' @ 'fun_app$b' ) ) )
| ? [D: 'A_ltln_set$'] :
( ( D @ ( C @ 'fun_app$a' ) )
& ( A @ ( D @ 'member$a' @ 'fun_app$b' ) ) ) )
=> ? [D: 'A_ltln_set$'] :
( ( D @ ( C @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( D @ 'member$a' @ 'fun_app$b' ) ) ) )
& ( ? [D: 'A_ltln_set$'] :
( ( D @ ( C @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( D @ 'member$a' @ 'fun_app$b' ) ) )
=> ( ? [D: 'A_ltln_set$'] :
( ( D @ ( C @ 'fun_app$a' ) )
& ( B @ ( D @ 'member$a' @ 'fun_app$b' ) ) )
| ? [D: 'A_ltln_set$'] :
( ( D @ ( C @ 'fun_app$a' ) )
& ( A @ ( D @ 'member$a' @ 'fun_app$b' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(452,axiom,
! [A: 'A_ltln$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( B @ ( A @ 'member$' @ 'fun_app$a' ) )
=> ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ 'member$' @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom60) ).
thf(2813,plain,
! [A: 'A_ltln$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( B @ ( A @ 'member$' @ 'fun_app$a' ) )
=> ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ 'member$' @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(440,axiom,
! [A: 'A_ltln_set$'] :
( ( A @ ( 'bot$d' @ 'fun_app$a' ) )
<=> ( 'bot$' @ ( A @ 'member$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom368) ).
thf(2766,plain,
! [A: 'A_ltln_set$'] :
( ( ( 'bot$' @ ( A @ 'member$a' @ 'fun_app$b' ) )
=> ( A @ ( 'bot$d' @ 'fun_app$a' ) ) )
& ( ( A @ ( 'bot$d' @ 'fun_app$a' ) )
=> ( 'bot$' @ ( A @ 'member$a' @ 'fun_app$b' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(294,axiom,
! [A: 'A_ltln_set$'] : ( 'bot$a' @ ( A @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom181) ).
thf(2052,plain,
! [A: 'A_ltln_set$'] : ( 'bot$a' @ ( A @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(199,axiom,
! [A: 'A_ltln_set_set$'] :
( ( 'bot$' @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom112) ).
thf(1599,plain,
! [A: 'A_ltln_set_set$'] :
( ( 'bot$' @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(358,axiom,
! [A: 'A_ltln$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) )
= ( B @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom376) ).
thf(2370,plain,
! [A: 'A_ltln$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) )
= ( B @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(187,axiom,
! [A: 'A_ltln_bool_fun$'] :
( ( 'bot$a'
= ( A @ 'collect$a' ) )
<=> ! [B: 'A_ltln$'] :
~ ( B @ ( A @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom98) ).
thf(1525,plain,
! [A: 'A_ltln_bool_fun$'] :
( ( ! [B: 'A_ltln$'] :
~ ( B @ ( A @ 'fun_app$' ) )
=> ( 'bot$a'
= ( A @ 'collect$a' ) ) )
& ( ( 'bot$a'
= ( A @ 'collect$a' ) )
=> ! [B: 'A_ltln$'] :
~ ( B @ ( A @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(148,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( B @ ( C @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom215) ).
thf(1333,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( B @ ( C @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(145,axiom,
! [A: 'A_ltln_set_set$'] :
( ( 'bot$' @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom124) ).
thf(1318,plain,
! [A: 'A_ltln_set_set$'] :
( ( 'bot$' @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(472,axiom,
! [A: 'A_ltln$',B: 'A_ltln$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ 'member$' @ 'fun_app$a' ) )
<=> ( ( C @ ( A @ 'member$' @ 'fun_app$a' ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom377) ).
thf(2926,plain,
! [A: 'A_ltln$',B: 'A_ltln$',C: 'A_ltln_set$'] :
( ( ( ( C @ ( A @ 'member$' @ 'fun_app$a' ) )
| ( A = B ) )
=> ( C @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ 'member$' @ 'fun_app$a' ) ) )
& ( ( C @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ 'member$' @ 'fun_app$a' ) )
=> ( ( C @ ( A @ 'member$' @ 'fun_app$a' ) )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(44,axiom,
! [A: 'A_ltln_set_set$'] :
( ( A @ ( 'is_empty$a' @ 'fun_app$b' ) )
<=> ( A = 'bot$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom348) ).
thf(805,plain,
! [A: 'A_ltln_set_set$'] :
( ( ( A = 'bot$' )
=> ( A @ ( 'is_empty$a' @ 'fun_app$b' ) ) )
& ( ( A @ ( 'is_empty$a' @ 'fun_app$b' ) )
=> ( A = 'bot$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(530,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( B @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom579) ).
thf(3183,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( B @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(219,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( B @ ( A @ 'member$a' @ 'fun_app$b' ) )
=> ( ( B @ ( C @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( B @ ( C @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom484) ).
thf(1695,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( B @ ( A @ 'member$a' @ 'fun_app$b' ) )
=> ( ( B @ ( C @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( B @ ( C @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(12,axiom,
! [A: 'A_ltln_set_set$'] : ( A @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom291) ).
thf(657,plain,
! [A: 'A_ltln_set_set$'] : ( A @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(296,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( C @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom312) ).
thf(2057,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( C @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(110,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] : ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom209) ).
thf(1170,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] : ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(411,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set_bool_fun$'] :
( ( ! [D: 'A_ltln$',E: 'A_ltln_set$'] :
( ( ( E @ ( C @ 'fun_app$a' ) )
& ~ ( E @ ( D @ 'member$' @ 'fun_app$a' ) )
& ( B @ ( D @ 'member$' @ 'fun_app$a' ) )
& ( E @ ( 'finite$' @ 'fun_app$a' ) ) )
=> ( E @ ( D @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( C @ 'fun_app$a' ) ) )
& ( 'bot$a' @ ( C @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( A @ ( 'finite$' @ 'fun_app$a' ) ) )
=> ( A @ ( C @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom468) ).
thf(2617,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set_bool_fun$'] :
( ( ! [D: 'A_ltln$',E: 'A_ltln_set$'] :
( ( ( E @ ( C @ 'fun_app$a' ) )
& ~ ( E @ ( D @ 'member$' @ 'fun_app$a' ) )
& ( B @ ( D @ 'member$' @ 'fun_app$a' ) )
& ( E @ ( 'finite$' @ 'fun_app$a' ) ) )
=> ( E @ ( D @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( C @ 'fun_app$a' ) ) )
& ( 'bot$a' @ ( C @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( A @ ( 'finite$' @ 'fun_app$a' ) ) )
=> ( A @ ( C @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(420,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_a_ltln_set_set_fun$',C: 'A_ltln_set$',D: 'A_ltln_set$'] :
( ( ! [E: 'A_ltln_set$',F: 'A_ltln_set$'] :
( ( F @ ( E @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( F @ ( B @ 'fun_app$k' ) @ ( E @ ( B @ 'fun_app$k' ) @ 'less_eq$a' @ 'fun_app$b' ) ) )
& ( D @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( C @ ( B @ 'fun_app$k' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( D @ ( B @ 'fun_app$k' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom326) ).
thf(2662,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_a_ltln_set_set_fun$',C: 'A_ltln_set$',D: 'A_ltln_set$'] :
( ( ! [E: 'A_ltln_set$',F: 'A_ltln_set$'] :
( ( F @ ( E @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( F @ ( B @ 'fun_app$k' ) @ ( E @ ( B @ 'fun_app$k' ) @ 'less_eq$a' @ 'fun_app$b' ) ) )
& ( D @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( C @ ( B @ 'fun_app$k' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( D @ ( B @ 'fun_app$k' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(40,axiom,
'bot$' @ ( 'finite$a' @ 'fun_app$b' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom279) ).
thf(794,plain,
'bot$' @ ( 'finite$a' @ 'fun_app$b' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(228,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
<=> ! [C: 'A_ltln_set$'] :
( ( A @ ( C @ 'member$a' @ 'fun_app$b' ) )
=> ( B @ ( C @ 'member$a' @ 'fun_app$b' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom160) ).
thf(1732,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( ! [C: 'A_ltln_set$'] :
( ( A @ ( C @ 'member$a' @ 'fun_app$b' ) )
=> ( B @ ( C @ 'member$a' @ 'fun_app$b' ) ) )
=> ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
& ( ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
=> ! [C: 'A_ltln_set$'] :
( ( A @ ( C @ 'member$a' @ 'fun_app$b' ) )
=> ( B @ ( C @ 'member$a' @ 'fun_app$b' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(119,axiom,
! [A: 'A_ltln_set_set$'] :
( ! [B: 'A_ltln_set$'] :
~ ( A @ ( B @ 'member$a' @ 'fun_app$b' ) )
<=> ( A = 'bot$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom95) ).
thf(1202,plain,
! [A: 'A_ltln_set_set$'] :
( ( ( A = 'bot$' )
=> ! [B: 'A_ltln_set$'] :
~ ( A @ ( B @ 'member$a' @ 'fun_app$b' ) ) )
& ( ! [B: 'A_ltln_set$'] :
~ ( A @ ( B @ 'member$a' @ 'fun_app$b' ) )
=> ( A = 'bot$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(329,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom503) ).
thf(2203,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(448,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set_bool_fun$'] :
( ( ! [C: 'A_ltln$',D: 'A_ltln_set$'] :
( ( ( D @ ( B @ 'fun_app$a' ) )
& ~ ( D @ ( C @ 'member$' @ 'fun_app$a' ) )
& ( D @ ( 'finite$' @ 'fun_app$a' ) ) )
=> ( D @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( B @ 'fun_app$a' ) ) )
& ( 'bot$a' @ ( B @ 'fun_app$a' ) )
& ( A @ ( 'finite$' @ 'fun_app$a' ) ) )
=> ( A @ ( B @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom450) ).
thf(2793,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set_bool_fun$'] :
( ( ! [C: 'A_ltln$',D: 'A_ltln_set$'] :
( ( ( D @ ( B @ 'fun_app$a' ) )
& ~ ( D @ ( C @ 'member$' @ 'fun_app$a' ) )
& ( D @ ( 'finite$' @ 'fun_app$a' ) ) )
=> ( D @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( B @ 'fun_app$a' ) ) )
& ( 'bot$a' @ ( B @ 'fun_app$a' ) )
& ( A @ ( 'finite$' @ 'fun_app$a' ) ) )
=> ( A @ ( B @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(304,axiom,
! [A: 'A_ltln$',B: 'A_ltln_set$',C: 'A_ltln$'] :
( ( ~ ( B @ ( A @ 'member$' @ 'fun_app$a' ) )
=> ( A = C ) )
=> ( B @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ 'member$' @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom379) ).
thf(2089,plain,
! [A: 'A_ltln$',B: 'A_ltln_set$',C: 'A_ltln$'] :
( ( ~ ( B @ ( A @ 'member$' @ 'fun_app$a' ) )
=> ( A = C ) )
=> ( B @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ 'member$' @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(324,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( A @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom236) ).
thf(2189,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( A @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(203,axiom,
! [A: 'A_ltln_set_set$'] :
( ( A @ ( 'bot$' @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= 'bot$' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom539) ).
thf(1616,plain,
! [A: 'A_ltln_set_set$'] :
( ( A @ ( 'bot$' @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= 'bot$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(473,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln$'] :
( ( A = 'bot$a' )
=> ~ ( A @ ( B @ 'member$' @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom154) ).
thf(2936,plain,
! [A: 'A_ltln_set$',B: 'A_ltln$'] :
( ( A = 'bot$a' )
=> ~ ( A @ ( B @ 'member$' @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(321,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( C @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom572) ).
thf(2176,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( C @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(340,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$',D: 'A_ltln_set$'] :
( ( ( D @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( C @ ( B @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( D @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom571) ).
thf(2292,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$',D: 'A_ltln_set$'] :
( ( ( D @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( C @ ( B @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( D @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(566,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_a_ltln_set_fun$'] :
( ( ! [C: 'A_ltln$'] :
( ( A @ ( C @ 'member$' @ 'fun_app$a' ) )
=> ( C @ ( B @ 'fun_app$h' ) @ ( 'finite$' @ 'fun_app$a' ) ) )
& ( A @ ( 'finite$' @ 'fun_app$a' ) ) )
=> ( B @ ( A @ 'bind$c' ) @ ( 'finite$' @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom89) ).
thf(3358,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_a_ltln_set_fun$'] :
( ( ! [C: 'A_ltln$'] :
( ( A @ ( C @ 'member$' @ 'fun_app$a' ) )
=> ( C @ ( B @ 'fun_app$h' ) @ ( 'finite$' @ 'fun_app$a' ) ) )
& ( A @ ( 'finite$' @ 'fun_app$a' ) ) )
=> ( B @ ( A @ 'bind$c' ) @ ( 'finite$' @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(545,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( C @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom600) ).
thf(3257,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( C @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(474,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( C @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom588) ).
thf(2941,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( C @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(266,axiom,
! [A: 'A_ltln_set$'] :
( ( A @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= 'bot$a' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom551) ).
thf(1927,plain,
! [A: 'A_ltln_set$'] :
( ( A @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= 'bot$a' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(551,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( C @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom314) ).
thf(3289,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( C @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(466,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] : ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom268) ).
thf(2894,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] : ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(1,conjecture,
'y$' @ ( 'x$' @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'finite$' @ 'fun_app$a' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture2) ).
thf(2,negated_conjecture,
~ ( 'y$' @ ( 'x$' @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'finite$' @ 'fun_app$a' ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(618,plain,
~ ( 'y$' @ ( 'x$' @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'finite$' @ 'fun_app$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(233,axiom,
! [A: 'A_ltln_set_set$'] : ( A @ ( 'bot$' @ 'disjnt$' @ 'fun_app$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom180) ).
thf(1764,plain,
! [A: 'A_ltln_set_set$'] : ( A @ ( 'bot$' @ 'disjnt$' @ 'fun_app$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(140,axiom,
! [A: 'A_ltln_set$'] : ( 'bot$' @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ 'member$a' @ 'fun_app$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom382) ).
thf(1301,plain,
! [A: 'A_ltln_set$'] : ( 'bot$' @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ 'member$a' @ 'fun_app$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(434,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( A = B ) )
=> ( C @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom306) ).
thf(2734,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( A = B ) )
=> ( C @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(513,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( B @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( B @ ( C @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom222) ).
thf(3111,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( B @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( B @ ( C @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(549,axiom,
! [A: 'A_ltln$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( B @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom487) ).
thf(3274,plain,
! [A: 'A_ltln$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( B @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(606,axiom,
! [A: 'A_ltln$'] : ( 'bot$a' @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ 'member$' @ 'fun_app$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom381) ).
thf(3536,plain,
! [A: 'A_ltln$'] : ( 'bot$a' @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ 'member$' @ 'fun_app$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(47,axiom,
! [A: 'A_ltln_set_set$'] :
( ( A @ ( 'bot$' @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom283) ).
thf(819,plain,
! [A: 'A_ltln_set_set$'] :
( ( A @ ( 'bot$' @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(77,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$'] :
( ( A @ ( 'finite$a' @ 'fun_app$b' ) )
=> ( A @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( 'finite$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom431) ).
thf(975,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$'] :
( ( A @ ( 'finite$a' @ 'fun_app$b' ) )
=> ( A @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( 'finite$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(246,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( A @ ( B @ ( 'minus$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= 'bot$' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom544) ).
thf(1833,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( A @ ( B @ ( 'minus$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= 'bot$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(480,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ! [D: 'A_ltln_set$',E: 'A_ltln_set$'] :
( ( ( A
= ( E @ ( D @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) )
& ( C @ ( E @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( D @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> $false )
& ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom276) ).
thf(2970,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
~ ( ! [D: 'A_ltln_set$',E: 'A_ltln_set$'] :
~ ( ( A
= ( E @ ( D @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) )
& ( C @ ( E @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( D @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(334,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( B @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom436) ).
thf(2225,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( B @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(161,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] : ( A @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom201) ).
thf(1389,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] : ( A @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(100,axiom,
! [A: 'A_ltln_set_set$'] :
( ( A @ ( A @ 'disjnt$' @ 'fun_app$b' ) )
<=> ( A = 'bot$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom133) ).
thf(1125,plain,
! [A: 'A_ltln_set_set$'] :
( ( ( A = 'bot$' )
=> ( A @ ( A @ 'disjnt$' @ 'fun_app$b' ) ) )
& ( ( A @ ( A @ 'disjnt$' @ 'fun_app$b' ) )
=> ( A = 'bot$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(548,axiom,
! [A: 'A_ltln$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ 'member$' @ 'fun_app$a' ) )
<=> ( ( C @ ( A @ 'member$' @ 'fun_app$a' ) )
| ( B @ ( A @ 'member$' @ 'fun_app$a' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom8) ).
thf(3266,plain,
! [A: 'A_ltln$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( ( C @ ( A @ 'member$' @ 'fun_app$a' ) )
| ( B @ ( A @ 'member$' @ 'fun_app$a' ) ) )
=> ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ 'member$' @ 'fun_app$a' ) ) )
& ( ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ 'member$' @ 'fun_app$a' ) )
=> ( ( C @ ( A @ 'member$' @ 'fun_app$a' ) )
| ( B @ ( A @ 'member$' @ 'fun_app$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(23,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( C @ ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( C @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom37) ).
thf(711,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( C @ ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( C @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(485,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom496) ).
thf(2991,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(367,axiom,
! [A: 'A_ltln_set$'] : ( A @ ( 'bot$a' @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom346) ).
thf(2398,plain,
! [A: 'A_ltln_set$'] : ( A @ ( 'bot$a' @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(315,axiom,
! [A: 'A_ltln$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
<=> ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( C @ ( A @ 'member$' @ 'fun_app$a' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom386) ).
thf(2134,plain,
! [A: 'A_ltln$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( C @ ( A @ 'member$' @ 'fun_app$a' ) ) )
=> ( C @ ( B @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( ( C @ ( B @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( C @ ( A @ 'member$' @ 'fun_app$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(426,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( A @ ( 'finite$' @ 'fun_app$a' ) )
=> ( B @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'finite$' @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom553) ).
thf(2695,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( A @ ( 'finite$' @ 'fun_app$a' ) )
=> ( B @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'finite$' @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(130,axiom,
! [A: 'A_ltln_set_set$'] : ( 'bot$' @ ( A @ 'disjnt$' @ 'fun_app$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom182) ).
thf(1256,plain,
! [A: 'A_ltln_set_set$'] : ( 'bot$' @ ( A @ 'disjnt$' @ 'fun_app$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(319,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( B @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom578) ).
thf(2161,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( B @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(183,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( A = B )
=> ( A @ ( B @ 'less_eq$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom167) ).
thf(1503,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( A = B )
=> ( A @ ( B @ 'less_eq$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(494,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( A @ ( 'finite$' @ 'fun_app$a' ) )
=> ( ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( A @ ( B @ ( 'insert$b' @ 'fold$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom637) ).
thf(3023,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( A @ ( 'finite$' @ 'fun_app$a' ) )
=> ( ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( A @ ( B @ ( 'insert$b' @ 'fold$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(515,axiom,
! [A: 'A_ltln$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) )
= ( B @ ( 'bot$a' @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom460) ).
thf(3118,plain,
! [A: 'A_ltln$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) )
= ( B @ ( 'bot$a' @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(143,axiom,
! [A: 'A_ltln_set_set$'] :
( ( 'bot$' @ ( A @ ( 'minus$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom546) ).
thf(1312,plain,
! [A: 'A_ltln_set_set$'] :
( ( 'bot$' @ ( A @ ( 'minus$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(435,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( ( A @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B != 'bot$' )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( ( A @ ( 'sup_fin$a' @ 'fun_app$i' ) @ ( B @ ( 'sup_fin$a' @ 'fun_app$i' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( A @ ( 'sup_fin$a' @ 'fun_app$i' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom354) ).
thf(2738,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( ( A @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B != 'bot$' )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( ( A @ ( 'sup_fin$a' @ 'fun_app$i' ) @ ( B @ ( 'sup_fin$a' @ 'fun_app$i' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( A @ ( 'sup_fin$a' @ 'fun_app$i' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(489,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$'] :
( ( ( A != 'bot$' )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( ( A @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( 'sup_fin$a' @ 'fun_app$i' ) )
= ( A @ ( 'sup_fin$a' @ 'fun_app$i' ) @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom370) ).
thf(3002,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$'] :
( ( ( A != 'bot$' )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( ( A @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( 'sup_fin$a' @ 'fun_app$i' ) )
= ( A @ ( 'sup_fin$a' @ 'fun_app$i' ) @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(517,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( A @ ( B @ ( 'max$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom635) ).
thf(3123,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( A @ ( B @ ( 'max$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(258,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ~ ( C @ ( A @ 'member$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'member$a' @ 'fun_app$b' ) ) )
=> ( C @ ( B @ ( 'minus$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ 'member$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom514) ).
thf(1897,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ~ ( C @ ( A @ 'member$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'member$a' @ 'fun_app$b' ) ) )
=> ( C @ ( B @ ( 'minus$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ 'member$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(131,axiom,
! [A: 'A_ltln_set_set$'] :
( ? [B: 'A_ltln_set$'] : ( A @ ( B @ 'member$a' @ 'fun_app$b' ) )
<=> ( A != 'bot$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom170) ).
thf(1258,plain,
! [A: 'A_ltln_set_set$'] :
( ( ( A != 'bot$' )
=> ? [B: 'A_ltln_set$'] : ( A @ ( B @ 'member$a' @ 'fun_app$b' ) ) )
& ( ? [B: 'A_ltln_set$'] : ( A @ ( B @ 'member$a' @ 'fun_app$b' ) )
=> ( A != 'bot$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(208,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( A = B )
=> ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom333) ).
thf(1638,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( A = B )
=> ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(527,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) )
<=> ( ( C @ ( B @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( C @ ( A @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom80) ).
thf(3170,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( ( C @ ( B @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( C @ ( A @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( C @ ( B @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( C @ ( A @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(509,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] : ( A @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom248) ).
thf(3091,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] : ( A @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(382,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( C @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom178) ).
thf(2474,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( C @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(400,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( A @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom499) ).
thf(2573,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( A @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(354,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] : ( B @ ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom565) ).
thf(2358,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] : ( B @ ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(390,axiom,
! [A: 'A_ltln$',B: 'A_ltln_set$',C: 'A_ltln$',D: 'A_ltln_set$'] :
( ( ~ ( D @ ( C @ 'member$' @ 'fun_app$a' ) )
& ~ ( B @ ( A @ 'member$' @ 'fun_app$a' ) ) )
=> ( ( ( B @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) )
= ( D @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) )
<=> ( ( ( A != C )
=> ? [E: 'A_ltln_set$'] :
( ~ ( E @ ( A @ 'member$' @ 'fun_app$a' ) )
& ( D
= ( E @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) )
& ~ ( E @ ( C @ 'member$' @ 'fun_app$a' ) )
& ( B
= ( E @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) ) ) )
& ( ( A = C )
=> ( B = D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom407) ).
thf(2510,plain,
! [A: 'A_ltln$',B: 'A_ltln_set$',C: 'A_ltln$',D: 'A_ltln_set$'] :
( ( ~ ( D @ ( C @ 'member$' @ 'fun_app$a' ) )
& ~ ( B @ ( A @ 'member$' @ 'fun_app$a' ) ) )
=> ( ( ( ( ( A != C )
=> ? [E: 'A_ltln_set$'] :
( ~ ( E @ ( A @ 'member$' @ 'fun_app$a' ) )
& ( D
= ( E @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) )
& ~ ( E @ ( C @ 'member$' @ 'fun_app$a' ) )
& ( B
= ( E @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) ) ) )
& ( ( A = C )
=> ( B = D ) ) )
=> ( ( B @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) )
= ( D @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) ) )
& ( ( ( B @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) )
= ( D @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) )
=> ( ( ( A != C )
=> ? [E: 'A_ltln_set$'] :
( ~ ( E @ ( A @ 'member$' @ 'fun_app$a' ) )
& ( D
= ( E @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) )
& ~ ( E @ ( C @ 'member$' @ 'fun_app$a' ) )
& ( B
= ( E @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) ) ) )
& ( ( A = C )
=> ( B = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(353,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( A = B )
<=> ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom324) ).
thf(2346,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(511,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
<=> ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( C @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom109) ).
thf(3101,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( C @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( C @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(430,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( ( ( C @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> $false )
& ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom601) ).
thf(2721,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
~ ( ~ ( ( C @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(51,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set_set$'] :
( ( ( 'bot$' @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) )
= ( C @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) )
<=> ( ( 'bot$' @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( C @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom397) ).
thf(831,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set_set$'] :
( ( ( ( 'bot$' @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( C @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B = A ) )
=> ( ( 'bot$' @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) )
= ( C @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) ) )
& ( ( ( 'bot$' @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) )
= ( C @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) )
=> ( ( 'bot$' @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( C @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(166,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$'] :
( ( A = 'bot$' )
=> ~ ( A @ ( B @ 'member$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom155) ).
thf(1408,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$'] :
( ( A = 'bot$' )
=> ~ ( A @ ( B @ 'member$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(384,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( ( A @ ( C @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( B @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom569) ).
thf(2478,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( ( A @ ( C @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( B @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(387,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom40) ).
thf(2493,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(195,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$'] :
( ( ( ! [C: 'A_ltln_set$'] :
( ( A @ ( C @ 'member$a' @ 'fun_app$b' ) )
=> ( C @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> $false )
& ( A @ ( 'inf_fin$a' @ 'fun_app$i' ) @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( A != 'bot$' )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom139) ).
thf(1574,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$'] :
~ ( ~ ! [C: 'A_ltln_set$'] :
( ( A @ ( C @ 'member$a' @ 'fun_app$b' ) )
=> ( C @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( A @ ( 'inf_fin$a' @ 'fun_app$i' ) @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( A != 'bot$' )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(27,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( ( A @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom321) ).
thf(736,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( ( A @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(306,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom318) ).
thf(2097,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(82,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ( ( C @ ( A @ 'member$a' @ 'fun_app$b' ) )
=> $false )
& ( ( B @ ( A @ 'member$a' @ 'fun_app$b' ) )
=> $false )
& ( C @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ 'member$a' @ 'fun_app$b' ) ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom61) ).
thf(996,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
~ ( ~ ( C @ ( A @ 'member$a' @ 'fun_app$b' ) )
& ~ ( B @ ( A @ 'member$a' @ 'fun_app$b' ) )
& ( C @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ 'member$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(535,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
<=> ( ( C @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom521) ).
thf(3197,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( ( C @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( C @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(521,axiom,
! [A: 'A_ltln$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( 'bot$a'
= ( C @ ( B @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) )
<=> ( ( 'bot$a'
= ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) )
& ~ ( C @ ( A @ 'member$' @ 'fun_app$a' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom528) ).
thf(3138,plain,
! [A: 'A_ltln$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( ( 'bot$a'
= ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) )
& ~ ( C @ ( A @ 'member$' @ 'fun_app$a' ) ) )
=> ( 'bot$a'
= ( C @ ( B @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ) )
& ( ( 'bot$a'
= ( C @ ( B @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) )
=> ( ( 'bot$a'
= ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) )
& ~ ( C @ ( A @ 'member$' @ 'fun_app$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(467,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$'] :
( ( ( A @ ( B @ 'member$a' @ 'fun_app$b' ) )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( ( B @ ( A @ ( 'inf_fin$a' @ 'fun_app$i' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom76) ).
thf(2896,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$'] :
( ( ( A @ ( B @ 'member$a' @ 'fun_app$b' ) )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( ( B @ ( A @ ( 'inf_fin$a' @ 'fun_app$i' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(157,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ( B @ ( C @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( B @ ( C @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ 'less_eq$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom265) ).
thf(1376,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ( B @ ( C @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( B @ ( C @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ 'less_eq$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(278,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom590) ).
thf(1969,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(363,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] : ( B @ ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom596) ).
thf(2383,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] : ( B @ ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(412,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom38) ).
thf(2624,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(36,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] : ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom203) ).
thf(784,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] : ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(414,axiom,
! [A: 'A_ltln$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( B @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ 'member$' @ 'fun_app$a' ) ) )
=> ( B @ ( C @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom434) ).
thf(2637,plain,
! [A: 'A_ltln$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( B @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ 'member$' @ 'fun_app$a' ) ) )
=> ( B @ ( C @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(442,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( A @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom48) ).
thf(2774,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( A @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(603,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= 'bot$a' )
<=> ( ( B = 'bot$a' )
& ( A = 'bot$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom91) ).
thf(3515,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ( ( B = 'bot$a' )
& ( A = 'bot$a' ) )
=> ( ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= 'bot$a' ) )
& ( ( ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= 'bot$a' )
=> ( ( B = 'bot$a' )
& ( A = 'bot$a' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(57,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$',C: 'A_ltln_set_set$'] :
( ( 'bot$'
= ( C @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) )
<=> ( ( 'bot$'
= ( C @ ( A @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) )
& ~ ( A @ ( B @ 'member$a' @ 'fun_app$b' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom525) ).
thf(863,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$',C: 'A_ltln_set_set$'] :
( ( ( ( 'bot$'
= ( C @ ( A @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) )
& ~ ( A @ ( B @ 'member$a' @ 'fun_app$b' ) ) )
=> ( 'bot$'
= ( C @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) ) )
& ( ( 'bot$'
= ( C @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) )
=> ( ( 'bot$'
= ( C @ ( A @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) )
& ~ ( A @ ( B @ 'member$a' @ 'fun_app$b' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(112,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$'] :
( ( ( A != 'bot$' )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( ( A @ ( 'inf_fin$a' @ 'fun_app$i' ) @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
<=> ! [C: 'A_ltln_set$'] :
( ( A @ ( C @ 'member$a' @ 'fun_app$b' ) )
=> ( C @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom147) ).
thf(1175,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$'] :
( ( ( A != 'bot$' )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( ( ! [C: 'A_ltln_set$'] :
( ( A @ ( C @ 'member$a' @ 'fun_app$b' ) )
=> ( C @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( A @ ( 'inf_fin$a' @ 'fun_app$i' ) @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( ( A @ ( 'inf_fin$a' @ 'fun_app$i' ) @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ! [C: 'A_ltln_set$'] :
( ( A @ ( C @ 'member$a' @ 'fun_app$b' ) )
=> ( C @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(455,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
<=> ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( C @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom131) ).
thf(2824,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( C @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( C @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(290,axiom,
! [A: 'A_ltln$',B: 'A_ltln_bool_fun$',C: 'A_ltln_set$'] :
( ( C @ ( B @ 'filter$a' @ 'fun_app$c' ) @ ( A @ 'member$' @ 'fun_app$a' ) )
<=> ( ( A @ ( B @ 'fun_app$' ) )
& ( C @ ( A @ 'member$' @ 'fun_app$a' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom104) ).
thf(2025,plain,
! [A: 'A_ltln$',B: 'A_ltln_bool_fun$',C: 'A_ltln_set$'] :
( ( ( ( A @ ( B @ 'fun_app$' ) )
& ( C @ ( A @ 'member$' @ 'fun_app$a' ) ) )
=> ( C @ ( B @ 'filter$a' @ 'fun_app$c' ) @ ( A @ 'member$' @ 'fun_app$a' ) ) )
& ( ( C @ ( B @ 'filter$a' @ 'fun_app$c' ) @ ( A @ 'member$' @ 'fun_app$a' ) )
=> ( ( A @ ( B @ 'fun_app$' ) )
& ( C @ ( A @ 'member$' @ 'fun_app$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(46,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( B @ ( A @ 'member$a' @ 'fun_app$b' ) )
=> ( C @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ 'member$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom59) ).
thf(816,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( B @ ( A @ 'member$a' @ 'fun_app$b' ) )
=> ( C @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ 'member$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(378,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( 'bot$a'
= ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) )
<=> ( ( B = 'bot$a' )
& ( A = 'bot$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom123) ).
thf(2446,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ( ( B = 'bot$a' )
& ( A = 'bot$a' ) )
=> ( 'bot$a'
= ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ) )
& ( ( 'bot$a'
= ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) )
=> ( ( B = 'bot$a' )
& ( A = 'bot$a' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(20,axiom,
! [A: 'A_ltln_set$'] :
( ( A @ 'uua$' @ 'collect$a' )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom84) ).
thf(700,plain,
! [A: 'A_ltln_set$'] :
( ( A @ 'uua$' @ 'collect$a' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(497,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$',D: 'A_ltln_set$'] :
( ( ( D @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( D @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( C @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom567) ).
thf(3034,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$',D: 'A_ltln_set$'] :
( ( ( D @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( D @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( C @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(617,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ~ ( B @ ( 'finite$' @ 'fun_app$a' ) )
& ( A @ ( 'finite$' @ 'fun_app$a' ) ) )
=> ~ ( A @ ( B @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'finite$' @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom568) ).
thf(3583,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ~ ( B @ ( 'finite$' @ 'fun_app$a' ) )
& ( A @ ( 'finite$' @ 'fun_app$a' ) ) )
=> ~ ( A @ ( B @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'finite$' @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(416,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] : ( C @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom619) ).
thf(2647,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] : ( C @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(337,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'finite$' @ 'fun_app$a' ) )
<=> ( ( B @ ( 'finite$' @ 'fun_app$a' ) )
& ( A @ ( 'finite$' @ 'fun_app$a' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom4) ).
thf(2252,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ( ( B @ ( 'finite$' @ 'fun_app$a' ) )
& ( A @ ( 'finite$' @ 'fun_app$a' ) ) )
=> ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'finite$' @ 'fun_app$a' ) ) )
& ( ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'finite$' @ 'fun_app$a' ) )
=> ( ( B @ ( 'finite$' @ 'fun_app$a' ) )
& ( A @ ( 'finite$' @ 'fun_app$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(244,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= 'bot$' )
<=> ( ( B = 'bot$' )
& ( A = 'bot$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom116) ).
thf(1820,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( ( ( B = 'bot$' )
& ( A = 'bot$' ) )
=> ( ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= 'bot$' ) )
& ( ( ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= 'bot$' )
=> ( ( B = 'bot$' )
& ( A = 'bot$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(591,axiom,
'phi$' @ ( 'subformulas_nu$' @ 'fun_app$h' ) @ ( 'y$' @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom69) ).
thf(3456,plain,
'phi$' @ ( 'subformulas_nu$' @ 'fun_app$h' ) @ ( 'y$' @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(214,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( B @ ( A @ 'member$a' @ 'fun_app$b' ) )
=> ( B @ ( C @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ 'member$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom57) ).
thf(1667,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( B @ ( A @ 'member$a' @ 'fun_app$b' ) )
=> ( B @ ( C @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ 'member$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(150,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$'] :
( ( ( A != 'bot$' )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( ( B @ ( A @ ( 'sup_fin$a' @ 'fun_app$i' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
<=> ! [C: 'A_ltln_set$'] :
( ( A @ ( C @ 'member$a' @ 'fun_app$b' ) )
=> ( B @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom366) ).
thf(1339,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$'] :
( ( ( A != 'bot$' )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( ( ! [C: 'A_ltln_set$'] :
( ( A @ ( C @ 'member$a' @ 'fun_app$b' ) )
=> ( B @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( B @ ( A @ ( 'sup_fin$a' @ 'fun_app$i' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( ( B @ ( A @ ( 'sup_fin$a' @ 'fun_app$i' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ! [C: 'A_ltln_set$'] :
( ( A @ ( C @ 'member$a' @ 'fun_app$b' ) )
=> ( B @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(495,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom580) ).
thf(3027,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(445,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln$'] :
( ( ( A @ ( C @ 'member$' @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( B @ ( C @ 'member$' @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom153) ).
thf(2780,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln$'] :
( ( ( A @ ( C @ 'member$' @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( B @ ( C @ 'member$' @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(339,axiom,
! [A: 'A_ltln$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( 'bot$a' @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) )
= ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) )
<=> ( ( ( C
= ( 'bot$a' @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) )
& ( B
= ( 'bot$a' @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) ) )
| ( ( C = 'bot$a' )
& ( B
= ( 'bot$a' @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) ) )
| ( ( C
= ( 'bot$a' @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) )
& ( B = 'bot$a' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom464) ).
thf(2267,plain,
! [A: 'A_ltln$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( ( ( C
= ( 'bot$a' @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) )
& ( B
= ( 'bot$a' @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) ) )
| ( ( C = 'bot$a' )
& ( B
= ( 'bot$a' @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) ) )
| ( ( C
= ( 'bot$a' @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) )
& ( B = 'bot$a' ) ) )
=> ( ( 'bot$a' @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) )
= ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ) )
& ( ( ( 'bot$a' @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) )
= ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) )
=> ( ( ( C
= ( 'bot$a' @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) )
& ( B
= ( 'bot$a' @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) ) )
| ( ( C = 'bot$a' )
& ( B
= ( 'bot$a' @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) ) )
| ( ( C
= ( 'bot$a' @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) )
& ( B = 'bot$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(447,axiom,
! [A: 'A_ltln_set$'] :
( ! [B: 'A_ltln$'] :
~ ( A @ ( B @ 'member$' @ 'fun_app$a' ) )
<=> ( A = 'bot$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom94) ).
thf(2785,plain,
! [A: 'A_ltln_set$'] :
( ( ( A = 'bot$a' )
=> ! [B: 'A_ltln$'] :
~ ( A @ ( B @ 'member$' @ 'fun_app$a' ) ) )
& ( ! [B: 'A_ltln$'] :
~ ( A @ ( B @ 'member$' @ 'fun_app$a' ) )
=> ( A = 'bot$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(407,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] : ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom204) ).
thf(2593,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] : ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(490,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ( B @ ( 'finite$' @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( A @ ( 'finite$' @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom258) ).
thf(3006,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ( B @ ( 'finite$' @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( A @ ( 'finite$' @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(555,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_bool_fun$'] :
( ! [D: 'A_ltln$'] :
( ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( D @ 'member$' @ 'fun_app$a' ) )
=> ( D @ ( C @ 'fun_app$' ) ) )
<=> ( ! [D: 'A_ltln$'] :
( ( B @ ( D @ 'member$' @ 'fun_app$a' ) )
=> ( D @ ( C @ 'fun_app$' ) ) )
& ! [D: 'A_ltln$'] :
( ( A @ ( D @ 'member$' @ 'fun_app$a' ) )
=> ( D @ ( C @ 'fun_app$' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom54) ).
thf(3298,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_bool_fun$'] :
( ( ( ! [D: 'A_ltln$'] :
( ( B @ ( D @ 'member$' @ 'fun_app$a' ) )
=> ( D @ ( C @ 'fun_app$' ) ) )
& ! [D: 'A_ltln$'] :
( ( A @ ( D @ 'member$' @ 'fun_app$a' ) )
=> ( D @ ( C @ 'fun_app$' ) ) ) )
=> ! [D: 'A_ltln$'] :
( ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( D @ 'member$' @ 'fun_app$a' ) )
=> ( D @ ( C @ 'fun_app$' ) ) ) )
& ( ! [D: 'A_ltln$'] :
( ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( D @ 'member$' @ 'fun_app$a' ) )
=> ( D @ ( C @ 'fun_app$' ) ) )
=> ( ! [D: 'A_ltln$'] :
( ( B @ ( D @ 'member$' @ 'fun_app$a' ) )
=> ( D @ ( C @ 'fun_app$' ) ) )
& ! [D: 'A_ltln$'] :
( ( A @ ( D @ 'member$' @ 'fun_app$a' ) )
=> ( D @ ( C @ 'fun_app$' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(463,axiom,
! [A: 'A_ltln_set$'] : ( A @ ( 'bot$a' @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom129) ).
thf(2874,plain,
! [A: 'A_ltln_set$'] : ( A @ ( 'bot$a' @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(300,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] : ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom246) ).
thf(2075,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] : ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(220,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( A @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom29) ).
thf(1699,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( A @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(173,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( ( A @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom343) ).
thf(1445,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( ( ( B = A )
=> ( A @ ( B @ 'less_eq$a' @ 'fun_app$b' ) ) )
& ( ( A @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(303,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( B @ ( C @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom593) ).
thf(2086,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( B @ ( C @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(60,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set_a_ltln_set_set_fun$',D: 'A_ltln_set_set$'] :
( ( ! [E: 'A_ltln_set_set$',F: 'A_ltln_set_set$'] :
( ( F @ ( E @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( F @ ( C @ 'fun_app$e' ) @ ( E @ ( C @ 'fun_app$e' ) @ 'less_eq$a' @ 'fun_app$b' ) ) )
& ( ( B @ ( C @ 'fun_app$e' ) )
= D )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$e' ) @ 'less_eq$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom341) ).
thf(883,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set_a_ltln_set_set_fun$',D: 'A_ltln_set_set$'] :
( ( ! [E: 'A_ltln_set_set$',F: 'A_ltln_set_set$'] :
( ( F @ ( E @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( F @ ( C @ 'fun_app$e' ) @ ( E @ ( C @ 'fun_app$e' ) @ 'less_eq$a' @ 'fun_app$b' ) ) )
& ( ( B @ ( C @ 'fun_app$e' ) )
= D )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$e' ) @ 'less_eq$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(558,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom214) ).
thf(3325,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(343,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$'] :
( ( ( A != 'bot$' )
& ~ ( A @ ( B @ 'member$a' @ 'fun_app$b' ) )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( ( A @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( 'sup_fin$a' @ 'fun_app$i' ) )
= ( A @ ( 'sup_fin$a' @ 'fun_app$i' ) @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom374) ).
thf(2303,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$'] :
( ( ( A != 'bot$' )
& ~ ( A @ ( B @ 'member$a' @ 'fun_app$b' ) )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( ( A @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( 'sup_fin$a' @ 'fun_app$i' ) )
= ( A @ ( 'sup_fin$a' @ 'fun_app$i' ) @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(194,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( A = B )
<=> ( ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
& ( A @ ( B @ 'less_eq$a' @ 'fun_app$b' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom315) ).
thf(1562,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( ( ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
& ( A @ ( B @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
& ( A @ ( B @ 'less_eq$a' @ 'fun_app$b' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(50,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$'] :
( ( ( ! [C: 'A_ltln_set$'] :
( ( A @ ( C @ 'member$a' @ 'fun_app$b' ) )
=> ( B @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> $false )
& ( B @ ( A @ ( 'sup_fin$a' @ 'fun_app$i' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( A != 'bot$' )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom362) ).
thf(827,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$'] :
~ ( ~ ! [C: 'A_ltln_set$'] :
( ( A @ ( C @ 'member$a' @ 'fun_app$b' ) )
=> ( B @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( B @ ( A @ ( 'sup_fin$a' @ 'fun_app$i' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( A != 'bot$' )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(457,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( A @ ( 'finite$' @ 'fun_app$a' ) )
=> ( ( A @ ( B @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'finite$' @ 'fun_app$a' ) )
<=> ( B @ ( 'finite$' @ 'fun_app$a' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom555) ).
thf(2835,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( A @ ( 'finite$' @ 'fun_app$a' ) )
=> ( ( ( B @ ( 'finite$' @ 'fun_app$a' ) )
=> ( A @ ( B @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'finite$' @ 'fun_app$a' ) ) )
& ( ( A @ ( B @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'finite$' @ 'fun_app$a' ) )
=> ( B @ ( 'finite$' @ 'fun_app$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(90,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( ( A @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom102) ).
thf(1044,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( ( A @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(385,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( A @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom232) ).
thf(2481,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( A @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(366,axiom,
! [A: 'A_ltln_set$'] :
( ( A @ ( 'is_empty$' @ 'fun_app$a' ) )
<=> ( A = 'bot$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom347) ).
thf(2390,plain,
! [A: 'A_ltln_set$'] :
( ( ( A = 'bot$a' )
=> ( A @ ( 'is_empty$' @ 'fun_app$a' ) ) )
& ( ( A @ ( 'is_empty$' @ 'fun_app$a' ) )
=> ( A = 'bot$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(129,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$'] :
( ( ! [C: 'A_ltln_set_set$'] :
( ( ~ ( C @ ( A @ 'member$a' @ 'fun_app$b' ) )
& ( B
= ( C @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) ) )
=> $false )
& ( B @ ( A @ 'member$a' @ 'fun_app$b' ) ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom414) ).
thf(1250,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$'] :
~ ( ! [C: 'A_ltln_set_set$'] :
~ ( ~ ( C @ ( A @ 'member$a' @ 'fun_app$b' ) )
& ( B
= ( C @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) ) )
& ( B @ ( A @ 'member$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(602,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom541) ).
thf(3512,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(54,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom17) ).
thf(851,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(167,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
<=> ( B
= ( A @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom243) ).
thf(1413,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( ( B
= ( A @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) )
=> ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
& ( ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( B
= ( A @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(453,axiom,
! [A: 'A_ltln$',B: 'A_ltln_set$'] :
( ( B @ ( A @ 'member$' @ 'fun_app$a' ) )
=> ? [C: 'A_ltln_set$'] :
( ~ ( C @ ( A @ 'member$' @ 'fun_app$a' ) )
& ( B
= ( C @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom403) ).
thf(2816,plain,
! [A: 'A_ltln$',B: 'A_ltln_set$'] :
( ( B @ ( A @ 'member$' @ 'fun_app$a' ) )
=> ? [C: 'A_ltln_set$'] :
( ~ ( C @ ( A @ 'member$' @ 'fun_app$a' ) )
& ( B
= ( C @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(254,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_bool_fun$'] :
( ( A @ ( 'finite$a' @ 'fun_app$b' ) )
=> ( A @ ( B @ 'filter$' @ 'fun_app$e' ) @ ( 'finite$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom71) ).
thf(1873,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_bool_fun$'] :
( ( A @ ( 'finite$a' @ 'fun_app$b' ) )
=> ( A @ ( B @ 'filter$' @ 'fun_app$e' ) @ ( 'finite$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(71,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ~ ( B @ ( A @ 'member$a' @ 'fun_app$b' ) )
=> ( ( C @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( B @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( C @ ( B @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom488) ).
thf(944,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ~ ( B @ ( A @ 'member$a' @ 'fun_app$b' ) )
=> ( ( C @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( B @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( C @ ( B @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(486,axiom,
! [A: 'A_ltln_set$'] :
( ( A @ ( 'bot$a' @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= 'bot$a' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom532) ).
thf(2994,plain,
! [A: 'A_ltln_set$'] :
( ( A @ ( 'bot$a' @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= 'bot$a' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(41,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] : ( A @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom269) ).
thf(795,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] : ( A @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(418,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( C @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom599) ).
thf(2652,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( C @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(133,axiom,
! [A: 'A_ltln_set$'] :
( ! [B: 'A_ltln$'] :
( ( A @ ( B @ 'member$' @ 'fun_app$a' ) )
=> $false )
=> ( 'bot$a' @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom294) ).
thf(1277,plain,
! [A: 'A_ltln_set$'] :
( ! [B: 'A_ltln$'] :
~ ( A @ ( B @ 'member$' @ 'fun_app$a' ) )
=> ( 'bot$a' @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(9,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ( B @ ( C @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( B @ ( C @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ 'less_eq$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom207) ).
thf(648,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ( B @ ( C @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( B @ ( C @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ 'less_eq$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(104,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( C @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( C @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom23) ).
thf(1145,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( C @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( C @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(274,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$'] :
( ( ( A @ ( B @ 'member$a' @ 'fun_app$b' ) )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( ( A @ ( 'sup_fin$a' @ 'fun_app$i' ) @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( A @ ( 'sup_fin$a' @ 'fun_app$i' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom360) ).
thf(1958,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$'] :
( ( ( A @ ( B @ 'member$a' @ 'fun_app$b' ) )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( ( A @ ( 'sup_fin$a' @ 'fun_app$i' ) @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( A @ ( 'sup_fin$a' @ 'fun_app$i' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(468,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$'] :
( ( A @ ( 'finite$a' @ 'fun_app$b' ) )
=> ( ( ( ( 'bot$' @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ ( 'minus$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
!= 'bot$' )
=> ( ( A @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( 'sup_fin$a' @ 'fun_app$i' ) )
= ( 'bot$' @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ ( 'minus$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( 'sup_fin$a' @ 'fun_app$i' ) @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ) )
& ( ( ( 'bot$' @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ ( 'minus$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= 'bot$' )
=> ( ( A @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( 'sup_fin$a' @ 'fun_app$i' ) )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom476) ).
thf(2899,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$'] :
( ( A @ ( 'finite$a' @ 'fun_app$b' ) )
=> ( ( ( ( 'bot$' @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ ( 'minus$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
!= 'bot$' )
=> ( ( A @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( 'sup_fin$a' @ 'fun_app$i' ) )
= ( 'bot$' @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ ( 'minus$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( 'sup_fin$a' @ 'fun_app$i' ) @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ) )
& ( ( ( 'bot$' @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ ( 'minus$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= 'bot$' )
=> ( ( A @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( 'sup_fin$a' @ 'fun_app$i' ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(92,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( 'bot$'
= ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) )
<=> ( ( B = 'bot$' )
& ( A = 'bot$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom114) ).
thf(1049,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( ( ( B = 'bot$' )
& ( A = 'bot$' ) )
=> ( 'bot$'
= ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) ) )
& ( ( 'bot$'
= ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) )
=> ( ( B = 'bot$' )
& ( A = 'bot$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(206,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ( B @ ( C @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( B @ ( C @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ 'less_eq$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom241) ).
thf(1626,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ( B @ ( C @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( B @ ( C @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ 'less_eq$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(491,axiom,
! [A: 'A_ltln_set$'] :
( ? [B: 'A_ltln$'] : ( A @ ( B @ 'member$' @ 'fun_app$a' ) )
<=> ( A != 'bot$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom169) ).
thf(3009,plain,
! [A: 'A_ltln_set$'] :
( ( ( A != 'bot$a' )
=> ? [B: 'A_ltln$'] : ( A @ ( B @ 'member$' @ 'fun_app$a' ) ) )
& ( ? [B: 'A_ltln$'] : ( A @ ( B @ 'member$' @ 'fun_app$a' ) )
=> ( A != 'bot$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(295,axiom,
! [A: 'A_ltln$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( ( C @ ( A @ 'member$' @ 'fun_app$a' ) )
=> $false )
& ( ( B @ ( A @ 'member$' @ 'fun_app$a' ) )
=> $false )
& ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ 'member$' @ 'fun_app$a' ) ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom62) ).
thf(2054,plain,
! [A: 'A_ltln$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
~ ( ~ ( C @ ( A @ 'member$' @ 'fun_app$a' ) )
& ~ ( B @ ( A @ 'member$' @ 'fun_app$a' ) )
& ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ 'member$' @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(272,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set_bool_fun$',C: 'A_ltln_set_set$'] :
( ( C @ ( B @ 'filter$' @ 'fun_app$e' ) @ ( A @ 'member$a' @ 'fun_app$b' ) )
<=> ( ( A @ ( B @ 'fun_app$a' ) )
& ( C @ ( A @ 'member$a' @ 'fun_app$b' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom105) ).
thf(1948,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set_bool_fun$',C: 'A_ltln_set_set$'] :
( ( ( ( A @ ( B @ 'fun_app$a' ) )
& ( C @ ( A @ 'member$a' @ 'fun_app$b' ) ) )
=> ( C @ ( B @ 'filter$' @ 'fun_app$e' ) @ ( A @ 'member$a' @ 'fun_app$b' ) ) )
& ( ( C @ ( B @ 'filter$' @ 'fun_app$e' ) @ ( A @ 'member$a' @ 'fun_app$b' ) )
=> ( ( A @ ( B @ 'fun_app$a' ) )
& ( C @ ( A @ 'member$a' @ 'fun_app$b' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(70,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$',D: 'A_ltln_set$'] :
( ( ( 'bot$' @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) )
= ( 'bot$' @ ( D @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) )
<=> ( ( ( B = C )
& ( A = D ) )
| ( ( B = D )
& ( A = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom426) ).
thf(927,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$',D: 'A_ltln_set$'] :
( ( ( ( ( B = C )
& ( A = D ) )
| ( ( B = D )
& ( A = C ) ) )
=> ( ( 'bot$' @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) )
= ( 'bot$' @ ( D @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) ) )
& ( ( ( 'bot$' @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) )
= ( 'bot$' @ ( D @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) )
=> ( ( ( B = C )
& ( A = D ) )
| ( ( B = D )
& ( A = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(292,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( A = B )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom334) ).
thf(2037,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( A = B )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(481,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( C @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> $false )
& ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom206) ).
thf(2977,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
~ ( ~ ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( C @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(122,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom237) ).
thf(1225,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(325,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom18) ).
thf(2192,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(538,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
<=> ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( C @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom107) ).
thf(3214,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( C @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( C @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(201,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( C @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ 'member$a' @ 'fun_app$b' ) )
<=> ( ( C @ ( A @ 'member$a' @ 'fun_app$b' ) )
| ( B @ ( A @ 'member$a' @ 'fun_app$b' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom7) ).
thf(1605,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ( ( C @ ( A @ 'member$a' @ 'fun_app$b' ) )
| ( B @ ( A @ 'member$a' @ 'fun_app$b' ) ) )
=> ( C @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ 'member$a' @ 'fun_app$b' ) ) )
& ( ( C @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ 'member$a' @ 'fun_app$b' ) )
=> ( ( C @ ( A @ 'member$a' @ 'fun_app$b' ) )
| ( B @ ( A @ 'member$a' @ 'fun_app$b' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(594,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( C @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom613) ).
thf(3462,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( C @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(132,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= 'bot$' )
<=> ( ( B = 'bot$' )
& ( A = 'bot$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom118) ).
thf(1267,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( ( ( B = 'bot$' )
& ( A = 'bot$' ) )
=> ( ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= 'bot$' ) )
& ( ( ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= 'bot$' )
=> ( ( B = 'bot$' )
& ( A = 'bot$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(97,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_bool_fun$'] :
( ! [D: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( D @ 'member$a' @ 'fun_app$b' ) )
=> ( D @ ( C @ 'fun_app$a' ) ) )
<=> ( ! [D: 'A_ltln_set$'] :
( ( B @ ( D @ 'member$a' @ 'fun_app$b' ) )
=> ( D @ ( C @ 'fun_app$a' ) ) )
& ! [D: 'A_ltln_set$'] :
( ( A @ ( D @ 'member$a' @ 'fun_app$b' ) )
=> ( D @ ( C @ 'fun_app$a' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom53) ).
thf(1098,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_bool_fun$'] :
( ( ( ! [D: 'A_ltln_set$'] :
( ( B @ ( D @ 'member$a' @ 'fun_app$b' ) )
=> ( D @ ( C @ 'fun_app$a' ) ) )
& ! [D: 'A_ltln_set$'] :
( ( A @ ( D @ 'member$a' @ 'fun_app$b' ) )
=> ( D @ ( C @ 'fun_app$a' ) ) ) )
=> ! [D: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( D @ 'member$a' @ 'fun_app$b' ) )
=> ( D @ ( C @ 'fun_app$a' ) ) ) )
& ( ! [D: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( D @ 'member$a' @ 'fun_app$b' ) )
=> ( D @ ( C @ 'fun_app$a' ) ) )
=> ( ! [D: 'A_ltln_set$'] :
( ( B @ ( D @ 'member$a' @ 'fun_app$b' ) )
=> ( D @ ( C @ 'fun_app$a' ) ) )
& ! [D: 'A_ltln_set$'] :
( ( A @ ( D @ 'member$a' @ 'fun_app$b' ) )
=> ( D @ ( C @ 'fun_app$a' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(236,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( C @ ( B @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
<=> ( ( C @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom480) ).
thf(1770,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ( ( C @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( C @ ( B @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
& ( ( C @ ( B @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( ( C @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(572,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$'] :
( ( ( A @ ( B @ 'member$a' @ 'fun_app$b' ) )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( ( ( ( 'bot$' @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ ( 'minus$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
!= 'bot$' )
=> ( ( A @ ( 'sup_fin$a' @ 'fun_app$i' ) )
= ( 'bot$' @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ ( 'minus$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( 'sup_fin$a' @ 'fun_app$i' ) @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ) )
& ( ( ( 'bot$' @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ ( 'minus$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= 'bot$' )
=> ( ( A @ ( 'sup_fin$a' @ 'fun_app$i' ) )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom474) ).
thf(3376,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$'] :
( ( ( A @ ( B @ 'member$a' @ 'fun_app$b' ) )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( ( ( ( 'bot$' @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ ( 'minus$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
!= 'bot$' )
=> ( ( A @ ( 'sup_fin$a' @ 'fun_app$i' ) )
= ( 'bot$' @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ ( 'minus$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( 'sup_fin$a' @ 'fun_app$i' ) @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ) )
& ( ( ( 'bot$' @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ ( 'minus$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= 'bot$' )
=> ( ( A @ ( 'sup_fin$a' @ 'fun_app$i' ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(18,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$'] : ( B @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ 'member$a' @ 'fun_app$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom418) ).
thf(690,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$'] : ( B @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ 'member$a' @ 'fun_app$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(556,axiom,
! [A: 'A_ltln_set$'] :
( ( A @ ( 'bot$a' @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom111) ).
thf(3315,plain,
! [A: 'A_ltln_set$'] :
( ( A @ ( 'bot$a' @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(5,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( ( B @ ( 'finite$a' @ 'fun_app$b' ) )
& ( A != 'bot$' )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( A @ ( 'inf_fin$a' @ 'fun_app$i' ) @ ( B @ ( 'inf_fin$a' @ 'fun_app$i' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom145) ).
thf(640,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( ( B @ ( 'finite$a' @ 'fun_app$b' ) )
& ( A != 'bot$' )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( A @ ( 'inf_fin$a' @ 'fun_app$i' ) @ ( B @ ( 'inf_fin$a' @ 'fun_app$i' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(275,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( A @ ( 'finite$' @ 'fun_app$a' ) ) )
=> ( B @ ( 'finite$' @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom262) ).
thf(1961,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( A @ ( 'finite$' @ 'fun_app$a' ) ) )
=> ( B @ ( 'finite$' @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(28,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] : ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom267) ).
thf(739,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] : ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(422,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
<=> ( B
= ( A @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom244) ).
thf(2678,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ( B
= ( A @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( B
= ( A @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(238,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set$',D: 'A_ltln_set_set$'] :
( ( ~ ( D @ ( C @ 'member$a' @ 'fun_app$b' ) )
& ~ ( B @ ( A @ 'member$a' @ 'fun_app$b' ) ) )
=> ( ( ( B @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) )
= ( D @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) )
<=> ( ( ( A != C )
=> ? [E: 'A_ltln_set_set$'] :
( ~ ( E @ ( A @ 'member$a' @ 'fun_app$b' ) )
& ( D
= ( E @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) )
& ~ ( E @ ( C @ 'member$a' @ 'fun_app$b' ) )
& ( B
= ( E @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) ) ) )
& ( ( A = C )
=> ( B = D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom408) ).
thf(1780,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set$',D: 'A_ltln_set_set$'] :
( ( ~ ( D @ ( C @ 'member$a' @ 'fun_app$b' ) )
& ~ ( B @ ( A @ 'member$a' @ 'fun_app$b' ) ) )
=> ( ( ( ( ( A != C )
=> ? [E: 'A_ltln_set_set$'] :
( ~ ( E @ ( A @ 'member$a' @ 'fun_app$b' ) )
& ( D
= ( E @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) )
& ~ ( E @ ( C @ 'member$a' @ 'fun_app$b' ) )
& ( B
= ( E @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) ) ) )
& ( ( A = C )
=> ( B = D ) ) )
=> ( ( B @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) )
= ( D @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) ) )
& ( ( ( B @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) )
= ( D @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) )
=> ( ( ( A != C )
=> ? [E: 'A_ltln_set_set$'] :
( ~ ( E @ ( A @ 'member$a' @ 'fun_app$b' ) )
& ( D
= ( E @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) )
& ~ ( E @ ( C @ 'member$a' @ 'fun_app$b' ) )
& ( B
= ( E @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) ) ) )
& ( ( A = C )
=> ( B = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(454,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln$'] :
( ~ ( A @ ( 'finite$' @ 'fun_app$a' ) )
=> ~ ( 'bot$a' @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'finite$' @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom629) ).
thf(2821,plain,
! [A: 'A_ltln_set$',B: 'A_ltln$'] :
( ~ ( A @ ( 'finite$' @ 'fun_app$a' ) )
=> ~ ( 'bot$a' @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'finite$' @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(460,axiom,
! [A: 'A_ltln_set$'] :
( ( 'bot$a' @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
<=> ( A = 'bot$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom300) ).
thf(2850,plain,
! [A: 'A_ltln_set$'] :
( ( ( A = 'bot$a' )
=> ( 'bot$a' @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( ( 'bot$a' @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( A = 'bot$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(179,axiom,
! [A: 'A_ltln_set_set$'] :
( ( ! [B: 'A_ltln_set_set$',C: 'A_ltln_set$'] :
( ( ( B @ ( 'finite$a' @ 'fun_app$b' ) )
& ( A
= ( B @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) ) )
=> $false )
& ( ( A = 'bot$' )
=> $false )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom445) ).
thf(1484,plain,
! [A: 'A_ltln_set_set$'] :
~ ( ! [B: 'A_ltln_set_set$',C: 'A_ltln_set$'] :
~ ( ( B @ ( 'finite$a' @ 'fun_app$b' ) )
& ( A
= ( B @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) ) )
& ( A != 'bot$' )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(456,axiom,
! [A: 'A_ltln$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) )
!= 'bot$a' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom423) ).
thf(2831,plain,
! [A: 'A_ltln$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) )
!= 'bot$a' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(424,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom497) ).
thf(2689,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(224,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( C @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom213) ).
thf(1711,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( C @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(39,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( A @ ( B @ ( A @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom504) ).
thf(791,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( A @ ( B @ ( A @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(113,axiom,
! [A: 'A_ltln_set_set$'] :
( ( 'bot$' @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( A = 'bot$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom297) ).
thf(1186,plain,
! [A: 'A_ltln_set_set$'] :
( ( 'bot$' @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( A = 'bot$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(351,axiom,
! [A: 'A_ltln$',B: 'A_ltln$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) )
= ( C @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom406) ).
thf(2337,plain,
! [A: 'A_ltln$',B: 'A_ltln$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) )
= ( C @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(245,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$',C: 'A_ltln_set_set$'] :
( ( C @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( C @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom387) ).
thf(1830,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$',C: 'A_ltln_set_set$'] :
( ( C @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( C @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(260,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ( A @ ( C @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( B @ ( C @ 'less_eq$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom319) ).
thf(1901,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ( A @ ( C @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( B @ ( C @ 'less_eq$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(212,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set$'] :
( ( ~ ( B @ ( A @ 'member$a' @ 'fun_app$b' ) )
=> ( A = C ) )
=> ( B @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ 'member$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom380) ).
thf(1658,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set$'] :
( ( ~ ( B @ ( A @ 'member$a' @ 'fun_app$b' ) )
=> ( A = C ) )
=> ( B @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ 'member$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(65,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] : ( A @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom247) ).
thf(907,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] : ( A @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(242,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set_a_ltln_set_set_fun$',C: 'A_ltln_set_set$',D: 'A_ltln_set_set$'] :
( ( ! [E: 'A_ltln_set_set$',F: 'A_ltln_set_set$'] :
( ( F @ ( E @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( F @ ( B @ 'fun_app$e' ) @ ( E @ ( B @ 'fun_app$e' ) @ 'less_eq$a' @ 'fun_app$b' ) ) )
& ( D @ ( C @ 'less_eq$a' @ 'fun_app$b' ) )
& ( C @ ( B @ 'fun_app$e' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( D @ ( B @ 'fun_app$e' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom327) ).
thf(1813,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set_a_ltln_set_set_fun$',C: 'A_ltln_set_set$',D: 'A_ltln_set_set$'] :
( ( ! [E: 'A_ltln_set_set$',F: 'A_ltln_set_set$'] :
( ( F @ ( E @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( F @ ( B @ 'fun_app$e' ) @ ( E @ ( B @ 'fun_app$e' ) @ 'less_eq$a' @ 'fun_app$b' ) ) )
& ( D @ ( C @ 'less_eq$a' @ 'fun_app$b' ) )
& ( C @ ( B @ 'fun_app$e' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( D @ ( B @ 'fun_app$e' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(174,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$'] :
( ( ( A @ ( B @ 'member$a' @ 'fun_app$b' ) )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( A @ ( 'sup_fin$a' @ 'fun_app$i' ) @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom358) ).
thf(1452,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$'] :
( ( ( A @ ( B @ 'member$a' @ 'fun_app$b' ) )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( A @ ( 'sup_fin$a' @ 'fun_app$i' ) @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(280,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom44) ).
thf(1980,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(313,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( C @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom562) ).
thf(2128,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( C @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(149,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( C @ ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( C @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom51) ).
thf(1336,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( C @ ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( C @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(6,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ( B @ ( C @ 'disjnt$' @ 'fun_app$b' ) )
& ~ ( B @ ( A @ 'member$a' @ 'fun_app$b' ) ) )
=> ( B @ ( C @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ 'disjnt$' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom444) ).
thf(643,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ( B @ ( C @ 'disjnt$' @ 'fun_app$b' ) )
& ~ ( B @ ( A @ 'member$a' @ 'fun_app$b' ) ) )
=> ( B @ ( C @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ 'disjnt$' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(402,axiom,
! [A: 'A_ltln_set$'] : ( A @ ( 'bot$a' @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom179) ).
thf(2579,plain,
! [A: 'A_ltln_set$'] : ( A @ ( 'bot$a' @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(215,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ! [C: 'A_ltln_set$'] :
( ( A @ ( C @ 'member$a' @ 'fun_app$b' ) )
=> ( B @ ( C @ 'member$a' @ 'fun_app$b' ) ) )
=> ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom100) ).
thf(1670,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ! [C: 'A_ltln_set$'] :
( ( A @ ( C @ 'member$a' @ 'fun_app$b' ) )
=> ( B @ ( C @ 'member$a' @ 'fun_app$b' ) ) )
=> ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(432,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( A @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom274) ).
thf(2728,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( A @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(450,axiom,
! [A: 'A_ltln$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ~ ( B @ ( A @ 'member$' @ 'fun_app$a' ) )
=> ( ( B @ ( C @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( B @ ( C @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom483) ).
thf(2807,plain,
! [A: 'A_ltln$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ~ ( B @ ( A @ 'member$' @ 'fun_app$a' ) )
=> ( ( B @ ( C @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( B @ ( C @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(459,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$',D: 'A_ltln_set$'] :
( ( ( D @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( D @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( C @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom220) ).
thf(2848,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$',D: 'A_ltln_set$'] :
( ( ( D @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( D @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( C @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(404,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom272) ).
thf(2584,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(268,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( B @ ( C @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom216) ).
thf(1934,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( B @ ( C @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(476,axiom,
! [A: 'A_ltln$',B: 'A_ltln_set$',C: 'A_ltln$'] :
( ( ( B @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) )
= ( 'bot$a' @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) )
<=> ( ( 'bot$a' @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom396) ).
thf(2948,plain,
! [A: 'A_ltln$',B: 'A_ltln_set$',C: 'A_ltln$'] :
( ( ( ( 'bot$a' @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( A = C ) )
=> ( ( B @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) )
= ( 'bot$a' @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) ) )
& ( ( ( B @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) )
= ( 'bot$a' @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) )
=> ( ( 'bot$a' @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(190,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( A @ ( 'finite$a' @ 'fun_app$b' ) )
=> ( ( A @ ( B @ ( 'minus$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( 'finite$a' @ 'fun_app$b' ) )
<=> ( B @ ( 'finite$a' @ 'fun_app$b' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom554) ).
thf(1543,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( A @ ( 'finite$a' @ 'fun_app$b' ) )
=> ( ( ( B @ ( 'finite$a' @ 'fun_app$b' ) )
=> ( A @ ( B @ ( 'minus$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( 'finite$a' @ 'fun_app$b' ) ) )
& ( ( A @ ( B @ ( 'minus$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( 'finite$a' @ 'fun_app$b' ) )
=> ( B @ ( 'finite$a' @ 'fun_app$b' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(234,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] : ( A @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom211) ).
thf(1766,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] : ( A @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(397,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ~ ( A @ ( 'finite$' @ 'fun_app$a' ) )
=> ~ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'finite$' @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom22) ).
thf(2558,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ~ ( A @ ( 'finite$' @ 'fun_app$a' ) )
=> ~ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'finite$' @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(21,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom45) ).
thf(703,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(221,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set_set$'] :
( ( C @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) )
= ( C @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom405) ).
thf(1702,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set_set$'] :
( ( C @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) )
= ( C @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(361,axiom,
! [A: 'A_ltln$'] : ( A @ ( 'subformulas_nu$' @ 'fun_app$h' ) @ ( 'finite$' @ 'fun_app$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom288) ).
thf(2379,plain,
! [A: 'A_ltln$'] : ( A @ ( 'subformulas_nu$' @ 'fun_app$h' ) @ ( 'finite$' @ 'fun_app$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(152,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] : ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom245) ).
thf(1353,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] : ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(273,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( A @ ( C @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( A @ ( C @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom576) ).
thf(1955,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( A @ ( C @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( A @ ( C @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(279,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set_bool_fun$'] :
( ( ! [C: 'A_ltln_set$'] :
( ( ! [D: 'A_ltln$'] :
( ( C @ ( D @ 'member$' @ 'fun_app$a' ) )
=> ( 'bot$a' @ ( D @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( C @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( B @ 'fun_app$a' ) ) )
& ( A @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( C != 'bot$a' )
& ( C @ ( 'finite$' @ 'fun_app$a' ) ) )
=> ( C @ ( B @ 'fun_app$a' ) ) )
& ( 'bot$a' @ ( B @ 'fun_app$a' ) )
& ( A @ ( 'finite$' @ 'fun_app$a' ) ) )
=> ( A @ ( B @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom633) ).
thf(1972,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set_bool_fun$'] :
( ( ! [C: 'A_ltln_set$'] :
( ( ! [D: 'A_ltln$'] :
( ( C @ ( D @ 'member$' @ 'fun_app$a' ) )
=> ( 'bot$a' @ ( D @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( C @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( B @ 'fun_app$a' ) ) )
& ( A @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( C != 'bot$a' )
& ( C @ ( 'finite$' @ 'fun_app$a' ) ) )
=> ( C @ ( B @ 'fun_app$a' ) ) )
& ( 'bot$a' @ ( B @ 'fun_app$a' ) )
& ( A @ ( 'finite$' @ 'fun_app$a' ) ) )
=> ( A @ ( B @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(348,axiom,
! [A: 'A_ltln_set$'] :
( ( 'bot$a' @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( A = 'bot$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom298) ).
thf(2320,plain,
! [A: 'A_ltln_set$'] :
( ( 'bot$a' @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( A = 'bot$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(429,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln$',C: 'A_ltln_set$'] :
( ( ( C @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= 'bot$a' )
<=> ( ( ( C @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= 'bot$a' )
& ~ ( A @ ( B @ 'member$' @ 'fun_app$a' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom526) ).
thf(2711,plain,
! [A: 'A_ltln_set$',B: 'A_ltln$',C: 'A_ltln_set$'] :
( ( ( ( ( C @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= 'bot$a' )
& ~ ( A @ ( B @ 'member$' @ 'fun_app$a' ) ) )
=> ( ( C @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= 'bot$a' ) )
& ( ( ( C @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= 'bot$a' )
=> ( ( ( C @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= 'bot$a' )
& ~ ( A @ ( B @ 'member$' @ 'fun_app$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(540,axiom,
! [A: 'A_ltln$'] :
( ( 'bot$a' @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ 'the_elem$' )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom469) ).
thf(3224,plain,
! [A: 'A_ltln$'] :
( ( 'bot$a' @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ 'the_elem$' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(170,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom15) ).
thf(1427,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(78,axiom,
! [A: 'A_ltln_set_set$'] :
( ( A @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom49) ).
thf(978,plain,
! [A: 'A_ltln_set_set$'] :
( ( A @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(103,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$',D: 'A_ltln_set_set$'] :
( ( A
= ( C @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) )
=> ( ( D @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( D @ ( C @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom67) ).
thf(1140,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$',D: 'A_ltln_set_set$'] :
( ( A
= ( C @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) )
=> ( ( D @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( D @ ( C @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(270,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( B = C )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( C @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom308) ).
thf(1940,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( B = C )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( C @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(248,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( ( A @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom235) ).
thf(1839,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( ( A @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(4,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_a_ltln_set_bool_fun_fun$'] :
( ( ! [C: 'A_ltln_set$'] :
( ( A @ ( C @ 'member$a' @ 'fun_app$b' ) )
=> ? [D: 'A_ltln_set$'] :
( ( D @ ( C @ ( B @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( A @ ( D @ 'member$a' @ 'fun_app$b' ) ) ) )
& ! [C: 'A_ltln_set$',D: 'A_ltln_set$',E: 'A_ltln_set$'] :
( ( ( E @ ( D @ ( B @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( D @ ( C @ ( B @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( E @ ( C @ ( B @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ! [C: 'A_ltln_set$'] :
~ ( C @ ( C @ ( B @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( A = 'bot$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom295) ).
thf(627,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_a_ltln_set_bool_fun_fun$'] :
( ( ! [C: 'A_ltln_set$'] :
( ( A @ ( C @ 'member$a' @ 'fun_app$b' ) )
=> ? [D: 'A_ltln_set$'] :
( ( D @ ( C @ ( B @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( A @ ( D @ 'member$a' @ 'fun_app$b' ) ) ) )
& ! [C: 'A_ltln_set$',D: 'A_ltln_set$',E: 'A_ltln_set$'] :
( ( ( E @ ( D @ ( B @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( D @ ( C @ ( B @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( E @ ( C @ ( B @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ! [C: 'A_ltln_set$'] :
~ ( C @ ( C @ ( B @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( A = 'bot$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(277,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( C @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom573) ).
thf(1966,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( C @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(611,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_a_ltln_bool_fun_fun$'] :
( ( ! [C: 'A_ltln$'] :
( ( A @ ( C @ 'member$' @ 'fun_app$a' ) )
=> ? [D: 'A_ltln$'] :
( ( D @ ( C @ ( B @ 'fun_app$l' ) @ 'fun_app$' ) )
& ( A @ ( D @ 'member$' @ 'fun_app$a' ) ) ) )
& ! [C: 'A_ltln$',D: 'A_ltln$',E: 'A_ltln$'] :
( ( ( E @ ( D @ ( B @ 'fun_app$l' ) @ 'fun_app$' ) )
& ( D @ ( C @ ( B @ 'fun_app$l' ) @ 'fun_app$' ) ) )
=> ( E @ ( C @ ( B @ 'fun_app$l' ) @ 'fun_app$' ) ) )
& ! [C: 'A_ltln$'] :
~ ( C @ ( C @ ( B @ 'fun_app$l' ) @ 'fun_app$' ) )
& ( A @ ( 'finite$' @ 'fun_app$a' ) ) )
=> ( A = 'bot$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom296) ).
thf(3548,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_a_ltln_bool_fun_fun$'] :
( ( ! [C: 'A_ltln$'] :
( ( A @ ( C @ 'member$' @ 'fun_app$a' ) )
=> ? [D: 'A_ltln$'] :
( ( D @ ( C @ ( B @ 'fun_app$l' ) @ 'fun_app$' ) )
& ( A @ ( D @ 'member$' @ 'fun_app$a' ) ) ) )
& ! [C: 'A_ltln$',D: 'A_ltln$',E: 'A_ltln$'] :
( ( ( E @ ( D @ ( B @ 'fun_app$l' ) @ 'fun_app$' ) )
& ( D @ ( C @ ( B @ 'fun_app$l' ) @ 'fun_app$' ) ) )
=> ( E @ ( C @ ( B @ 'fun_app$l' ) @ 'fun_app$' ) ) )
& ! [C: 'A_ltln$'] :
~ ( C @ ( C @ ( B @ 'fun_app$l' ) @ 'fun_app$' ) )
& ( A @ ( 'finite$' @ 'fun_app$a' ) ) )
=> ( A = 'bot$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(61,axiom,
! [A: 'A_ltln_set_set$'] :
( ( A @ 'uu$' @ 'collect$' )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom83) ).
thf(891,plain,
! [A: 'A_ltln_set_set$'] :
( ( A @ 'uu$' @ 'collect$' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(469,axiom,
! [A: 'A_ltln$'] :
( ( A @ ( 'subformulas_nu$' @ 'fun_app$h' ) @ ( A @ ( 'subformulas_mu$' @ 'fun_app$h' ) @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= 'bot$a' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom626) ).
thf(2907,plain,
! [A: 'A_ltln$'] :
( ( A @ ( 'subformulas_nu$' @ 'fun_app$h' ) @ ( A @ ( 'subformulas_mu$' @ 'fun_app$h' ) @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= 'bot$a' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(168,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom13) ).
thf(1421,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(576,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom494) ).
thf(3400,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(263,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( A @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom27) ).
thf(1918,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( A @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(592,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( A @ ( B @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom164) ).
thf(3457,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( A @ ( B @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(94,axiom,
! [A: 'A_ltln_set_set$'] :
( ! [B: 'A_ltln_set$'] :
( ( A @ ( B @ 'member$a' @ 'fun_app$b' ) )
=> $false )
=> ( A = 'bot$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom157) ).
thf(1084,plain,
! [A: 'A_ltln_set_set$'] :
( ! [B: 'A_ltln_set$'] :
~ ( A @ ( B @ 'member$a' @ 'fun_app$b' ) )
=> ( A = 'bot$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(243,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( C @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( B @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( C @ ( B @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom486) ).
thf(1817,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( C @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( B @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( C @ ( B @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(478,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
<=> ( A
= ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom598) ).
thf(2960,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ( A
= ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( A
= ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(107,axiom,
( 'bot$a'
= ( 'bot$c' @ 'collect$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom301) ).
thf(1157,plain,
( 'bot$a'
= ( 'bot$c' @ 'collect$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(146,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( 'bot$'
= ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) )
<=> ( ( B = 'bot$' )
& ( A = 'bot$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom122) ).
thf(1321,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( ( ( B = 'bot$' )
& ( A = 'bot$' ) )
=> ( 'bot$'
= ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) ) )
& ( ( 'bot$'
= ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) )
=> ( ( B = 'bot$' )
& ( A = 'bot$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(605,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom574) ).
thf(3533,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(588,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom501) ).
thf(3447,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(410,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ 'uu$' @ 'fun_app$a' ) )
<=> ( A @ ( B @ 'member$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom1) ).
thf(2611,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$'] :
( ( ( A @ ( B @ 'member$a' @ 'fun_app$b' ) )
=> ( B @ ( A @ 'uu$' @ 'fun_app$a' ) ) )
& ( ( B @ ( A @ 'uu$' @ 'fun_app$a' ) )
=> ( A @ ( B @ 'member$a' @ 'fun_app$b' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(31,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom233) ).
thf(759,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(487,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom591) ).
thf(2997,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(323,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( A @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( B @ ( C @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom186) ).
thf(2187,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( A @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( B @ ( C @ ( 'disjnt$a' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(114,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( A @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom506) ).
thf(1189,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( A @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(137,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set$'] :
( ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( B @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ 'less_eq$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom441) ).
thf(1289,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set$'] :
( ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( B @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( A @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ 'less_eq$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(502,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( C @ ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) )
<=> ( A @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom623) ).
thf(3056,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( A @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( C @ ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ) )
& ( ( ( C @ ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) )
=> ( A @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(53,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( C @ ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ 'less_eq$a' @ 'fun_app$b' ) )
<=> ( ( C @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
& ( C @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom106) ).
thf(844,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ( ( C @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
& ( C @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( C @ ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ 'less_eq$a' @ 'fun_app$b' ) ) )
& ( ( C @ ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( ( C @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
& ( C @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(377,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_bool_fun$'] :
( ( A @ ( 'finite$' @ 'fun_app$a' ) )
=> ( A @ ( B @ 'filter$a' @ 'fun_app$c' ) @ ( 'finite$' @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom72) ).
thf(2443,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_bool_fun$'] :
( ( A @ ( 'finite$' @ 'fun_app$a' ) )
=> ( A @ ( B @ 'filter$a' @ 'fun_app$c' ) @ ( 'finite$' @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(75,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ( 'bot$' @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) )
= ( 'bot$' @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom422) ).
thf(963,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ( 'bot$' @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) )
= ( 'bot$' @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(178,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set_a_ltln_set_set_fun$',C: 'A_ltln_set_set$',D: 'A_ltln_set_set$'] :
( ( ! [E: 'A_ltln_set_set$',F: 'A_ltln_set_set$'] :
( ( F @ ( E @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( F @ ( B @ 'fun_app$e' ) @ ( E @ ( B @ 'fun_app$e' ) @ 'less_eq$a' @ 'fun_app$b' ) ) )
& ( D @ ( C @ 'less_eq$a' @ 'fun_app$b' ) )
& ( A
= ( C @ ( B @ 'fun_app$e' ) ) ) )
=> ( D @ ( B @ 'fun_app$e' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom337) ).
thf(1476,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set_a_ltln_set_set_fun$',C: 'A_ltln_set_set$',D: 'A_ltln_set_set$'] :
( ( ! [E: 'A_ltln_set_set$',F: 'A_ltln_set_set$'] :
( ( F @ ( E @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( F @ ( B @ 'fun_app$e' ) @ ( E @ ( B @ 'fun_app$e' ) @ 'less_eq$a' @ 'fun_app$b' ) ) )
& ( D @ ( C @ 'less_eq$a' @ 'fun_app$b' ) )
& ( A
= ( C @ ( B @ 'fun_app$e' ) ) ) )
=> ( D @ ( B @ 'fun_app$e' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(63,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( C @ ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( C @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom33) ).
thf(896,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( C @ ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( C @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(216,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( ( A @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom317) ).
thf(1674,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( ( A @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(396,axiom,
! [A: 'A_ltln$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ~ ( B @ ( A @ 'member$' @ 'fun_app$a' ) )
=> ( ( C @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom489) ).
thf(2554,plain,
! [A: 'A_ltln$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ~ ( B @ ( A @ 'member$' @ 'fun_app$a' ) )
=> ( ( C @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(561,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] : ( A @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom202) ).
thf(3336,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] : ( A @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(231,axiom,
! [A: 'A_ltln_set_set$'] :
( ( ( A != 'bot$' )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ? [B: 'A_ltln_set$'] :
( ! [C: 'A_ltln_set$'] :
( ( ( B @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( A @ ( C @ 'member$a' @ 'fun_app$b' ) ) )
=> ( B = C ) )
& ( A @ ( B @ 'member$a' @ 'fun_app$b' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom192) ).
thf(1745,plain,
! [A: 'A_ltln_set_set$'] :
( ( ( A != 'bot$' )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ? [B: 'A_ltln_set$'] :
( ! [C: 'A_ltln_set$'] :
( ( ( B @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( A @ ( C @ 'member$a' @ 'fun_app$b' ) ) )
=> ( B = C ) )
& ( A @ ( B @ 'member$a' @ 'fun_app$b' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(612,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
<=> ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom624) ).
thf(3561,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( C @ ( B @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( ( C @ ( B @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(127,axiom,
! [A: 'A_ltln_set_a_ltln_set_set_fun$'] :
( ( A @ ( 'bot$' @ 'bind$b' ) )
= 'bot$' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom137) ).
thf(1244,plain,
! [A: 'A_ltln_set_a_ltln_set_set_fun$'] :
( ( A @ ( 'bot$' @ 'bind$b' ) )
= 'bot$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(314,axiom,
! [A: 'A_ltln$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ~ ( B @ ( A @ 'member$' @ 'fun_app$a' ) )
=> ( ( C @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( B @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( B @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom556) ).
thf(2130,plain,
! [A: 'A_ltln$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ~ ( B @ ( A @ 'member$' @ 'fun_app$a' ) )
=> ( ( C @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( B @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( B @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(35,axiom,
! [A: 'A_ltln_set_set$'] :
( ( A @ ( 'bot$' @ ( 'minus$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= 'bot$' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom548) ).
thf(781,plain,
! [A: 'A_ltln_set_set$'] :
( ( A @ ( 'bot$' @ ( 'minus$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= 'bot$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(507,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln$'] :
( ( 'bot$a' @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( A
= ( 'bot$a' @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) )
| ( A = 'bot$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom458) ).
thf(3085,plain,
! [A: 'A_ltln_set$',B: 'A_ltln$'] :
( ( 'bot$a' @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( A
= ( 'bot$a' @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) )
| ( A = 'bot$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(45,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( C @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( C @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom43) ).
thf(813,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( C @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( C @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(484,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( C @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom584) ).
thf(2988,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( C @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(261,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set_bool_fun$'] :
( ( ! [C: 'A_ltln_set$',D: 'A_ltln_set_set$'] :
( ( ( D @ ( B @ 'fun_app$b' ) )
& ~ ( D @ ( C @ 'member$a' @ 'fun_app$b' ) )
& ( D != 'bot$' )
& ( D @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( D @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( B @ 'fun_app$b' ) ) )
& ! [C: 'A_ltln_set$'] : ( 'bot$' @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( B @ 'fun_app$b' ) )
& ( A != 'bot$' )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( A @ ( B @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom451) ).
thf(1903,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set_bool_fun$'] :
( ( ! [C: 'A_ltln_set$',D: 'A_ltln_set_set$'] :
( ( ( D @ ( B @ 'fun_app$b' ) )
& ~ ( D @ ( C @ 'member$a' @ 'fun_app$b' ) )
& ( D != 'bot$' )
& ( D @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( D @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( B @ 'fun_app$b' ) ) )
& ! [C: 'A_ltln_set$'] : ( 'bot$' @ ( C @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( B @ 'fun_app$b' ) )
& ( A != 'bot$' )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( A @ ( B @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(370,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( B @ ( A @ ( C @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom592) ).
thf(2406,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( B @ ( A @ ( C @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(451,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( B @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( B @ ( C @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom208) ).
thf(2811,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( B @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( B @ ( C @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(286,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom14) ).
thf(2004,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(37,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( A @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom35) ).
thf(786,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( A @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(569,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( A
= ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom608) ).
thf(3368,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( A
= ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(475,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ! [D: 'A_ltln_set$',E: 'A_ltln_set$',F: 'A_ltln_set$'] :
( ( F @ ( E @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( D @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( F @ ( D @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( E @ ( D @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) )
=> ( ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom587) ).
thf(2944,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ! [D: 'A_ltln_set$',E: 'A_ltln_set$',F: 'A_ltln_set$'] :
( ( F @ ( E @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( D @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( F @ ( D @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( E @ ( D @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) )
=> ( ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(288,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ~ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'finite$' @ 'fun_app$a' ) )
<=> ( ~ ( B @ ( 'finite$' @ 'fun_app$a' ) )
| ~ ( A @ ( 'finite$' @ 'fun_app$a' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom64) ).
thf(2009,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ( ~ ( B @ ( 'finite$' @ 'fun_app$a' ) )
| ~ ( A @ ( 'finite$' @ 'fun_app$a' ) ) )
=> ~ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'finite$' @ 'fun_app$a' ) ) )
& ( ~ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'finite$' @ 'fun_app$a' ) )
=> ( ~ ( B @ ( 'finite$' @ 'fun_app$a' ) )
| ~ ( A @ ( 'finite$' @ 'fun_app$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(180,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( C @ ( B @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
<=> ( ( C @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom522) ).
thf(1491,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ( ( C @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( C @ ( B @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
& ( ( C @ ( B @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( ( C @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(293,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln$'] :
( ( 'bot$a' @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
<=> ( ( A
= ( 'bot$a' @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) )
| ( A = 'bot$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom456) ).
thf(2041,plain,
! [A: 'A_ltln_set$',B: 'A_ltln$'] :
( ( ( ( A
= ( 'bot$a' @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) )
| ( A = 'bot$a' ) )
=> ( 'bot$a' @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( ( 'bot$a' @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( A
= ( 'bot$a' @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) )
| ( A = 'bot$a' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(597,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( B @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( B @ ( C @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom266) ).
thf(3497,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( B @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( B @ ( C @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(237,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom508) ).
thf(1777,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(139,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( C @ ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ 'less_eq$a' @ 'fun_app$b' ) )
<=> ( ( C @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
& ( C @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom108) ).
thf(1294,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ( ( C @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
& ( C @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( C @ ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ 'less_eq$a' @ 'fun_app$b' ) ) )
& ( ( C @ ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( ( C @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
& ( C @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(401,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( A @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom507) ).
thf(2576,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( A @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(64,axiom,
! [A: 'A_ltln_set_set$'] :
( ( 'bot$' @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
<=> ( A = 'bot$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom299) ).
thf(899,plain,
! [A: 'A_ltln_set_set$'] :
( ( ( A = 'bot$' )
=> ( 'bot$' @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
& ( ( 'bot$' @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( A = 'bot$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(312,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ( B @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= 'bot$a' )
<=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom621) ).
thf(2120,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( B @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= 'bot$a' ) )
& ( ( ( B @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= 'bot$a' )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(305,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$',D: 'A_ltln_set$'] :
( ( ( D @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( D @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( C @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom264) ).
thf(2095,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$',D: 'A_ltln_set$'] :
( ( ( D @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( D @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( C @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(341,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( B @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( C @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom577) ).
thf(2294,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( B @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( C @ ( A @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(284,axiom,
! [A: 'A_ltln$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( 'finite$' @ 'fun_app$a' ) )
<=> ( B @ ( 'finite$' @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom384) ).
thf(1994,plain,
! [A: 'A_ltln$',B: 'A_ltln_set$'] :
( ( ( B @ ( 'finite$' @ 'fun_app$a' ) )
=> ( B @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( 'finite$' @ 'fun_app$a' ) ) )
& ( ( B @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( 'finite$' @ 'fun_app$a' ) )
=> ( B @ ( 'finite$' @ 'fun_app$a' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(444,axiom,
'bot$a' @ ( 'finite$' @ 'fun_app$a' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom280) ).
thf(2779,plain,
'bot$a' @ ( 'finite$' @ 'fun_app$a' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(373,axiom,
! [A: 'A_ltln_set$'] :
( ( 'bot$a' @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom286) ).
thf(2421,plain,
! [A: 'A_ltln_set$'] :
( ( 'bot$a' @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(101,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set_a_ltln_set_fun$',D: 'A_ltln_set$'] :
( ( ! [E: 'A_ltln_set_set$',F: 'A_ltln_set_set$'] :
( ( F @ ( E @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( F @ ( C @ 'fun_app$i' ) @ ( E @ ( C @ 'fun_app$i' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( D @ ( B @ ( C @ 'fun_app$i' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$i' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom330) ).
thf(1133,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set_a_ltln_set_fun$',D: 'A_ltln_set$'] :
( ( ! [E: 'A_ltln_set_set$',F: 'A_ltln_set_set$'] :
( ( F @ ( E @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( F @ ( C @ 'fun_app$i' ) @ ( E @ ( C @ 'fun_app$i' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( D @ ( B @ ( C @ 'fun_app$i' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$i' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(83,axiom,
! [A: 'A_ltln_set_set$'] : ( A @ ( 'bot$' @ 'less_eq$a' @ 'fun_app$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom345) ).
thf(999,plain,
! [A: 'A_ltln_set_set$'] : ( A @ ( 'bot$' @ 'less_eq$a' @ 'fun_app$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(185,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( 'bot$'
= ( C @ ( B @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) )
<=> ( ( 'bot$'
= ( C @ ( B @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) )
& ~ ( C @ ( A @ 'member$a' @ 'fun_app$b' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom529) ).
thf(1512,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ( ( 'bot$'
= ( C @ ( B @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) )
& ~ ( C @ ( A @ 'member$a' @ 'fun_app$b' ) ) )
=> ( 'bot$'
= ( C @ ( B @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) ) )
& ( ( 'bot$'
= ( C @ ( B @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) )
=> ( ( 'bot$'
= ( C @ ( B @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) )
& ~ ( C @ ( A @ 'member$a' @ 'fun_app$b' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(196,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ 'disjnt$' @ 'fun_app$b' ) )
<=> ! [C: 'A_ltln_set$'] :
~ ( ( B @ ( C @ 'member$a' @ 'fun_app$b' ) )
& ( A @ ( C @ 'member$a' @ 'fun_app$b' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom163) ).
thf(1578,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( ! [C: 'A_ltln_set$'] :
~ ( ( B @ ( C @ 'member$a' @ 'fun_app$b' ) )
& ( A @ ( C @ 'member$a' @ 'fun_app$b' ) ) )
=> ( B @ ( A @ 'disjnt$' @ 'fun_app$b' ) ) )
& ( ( B @ ( A @ 'disjnt$' @ 'fun_app$b' ) )
=> ! [C: 'A_ltln_set$'] :
~ ( ( B @ ( C @ 'member$a' @ 'fun_app$b' ) )
& ( A @ ( C @ 'member$a' @ 'fun_app$b' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(364,axiom,
! [A: 'A_ltln_set$'] :
( ( 'bot$a' @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom196) ).
thf(2385,plain,
! [A: 'A_ltln_set$'] :
( ( 'bot$a' @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(391,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom42) ).
thf(2534,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(552,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom543) ).
thf(3291,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(405,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( ( B != 'bot$' )
& ( B @ ( 'finite$a' @ 'fun_app$b' ) )
& ( A != 'bot$' )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( 'sup_fin$a' @ 'fun_app$i' ) )
= ( B @ ( 'sup_fin$a' @ 'fun_app$i' ) @ ( A @ ( 'sup_fin$a' @ 'fun_app$i' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom352) ).
thf(2587,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( ( B != 'bot$' )
& ( B @ ( 'finite$a' @ 'fun_app$b' ) )
& ( A != 'bot$' )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( 'sup_fin$a' @ 'fun_app$i' ) )
= ( B @ ( 'sup_fin$a' @ 'fun_app$i' ) @ ( A @ ( 'sup_fin$a' @ 'fun_app$i' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(255,axiom,
! [A: 'A_ltln_set_set$'] :
( ( A @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom11) ).
thf(1876,plain,
! [A: 'A_ltln_set_set$'] :
( ( A @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(105,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( ( A @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( B @ ( 'finite$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom261) ).
thf(1148,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( ( A @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( B @ ( 'finite$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(519,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom495) ).
thf(3132,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(209,axiom,
! [A: 'A_ltln_a_ltln_set_set_fun$'] :
( ( A @ ( 'bot$a' @ 'bind$' ) )
= 'bot$' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom135) ).
thf(1642,plain,
! [A: 'A_ltln_a_ltln_set_set_fun$'] :
( ( A @ ( 'bot$a' @ 'bind$' ) )
= 'bot$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(308,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= 'bot$a' )
<=> ( ( B = 'bot$a' )
& ( A = 'bot$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom119) ).
thf(2102,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ( ( B = 'bot$a' )
& ( A = 'bot$a' ) )
=> ( ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= 'bot$a' ) )
& ( ( ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= 'bot$a' )
=> ( ( B = 'bot$a' )
& ( A = 'bot$a' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(226,axiom,
! [A: 'A_ltln_set$'] :
( ( 'bot$' @ ( A @ 'member$a' @ 'fun_app$b' ) )
<=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom93) ).
thf(1725,plain,
! [A: 'A_ltln_set$'] :
~ ( 'bot$' @ ( A @ 'member$a' @ 'fun_app$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(134,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) )
= ( B @ ( 'bot$' @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom459) ).
thf(1280,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) )
= ( B @ ( 'bot$' @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(571,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( A @ ( B @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom557) ).
thf(3373,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( A @ ( B @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(595,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln$'] :
( ( ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( 'bot$a' @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) )
<=> ( ( ( B
= ( 'bot$a' @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) )
& ( A
= ( 'bot$a' @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) ) )
| ( ( B = 'bot$a' )
& ( A
= ( 'bot$a' @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) ) )
| ( ( B
= ( 'bot$a' @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) )
& ( A = 'bot$a' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom462) ).
thf(3464,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln$'] :
( ( ( ( ( B
= ( 'bot$a' @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) )
& ( A
= ( 'bot$a' @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) ) )
| ( ( B = 'bot$a' )
& ( A
= ( 'bot$a' @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) ) )
| ( ( B
= ( 'bot$a' @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) )
& ( A = 'bot$a' ) ) )
=> ( ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( 'bot$a' @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) ) )
& ( ( ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( 'bot$a' @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) )
=> ( ( ( B
= ( 'bot$a' @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) )
& ( A
= ( 'bot$a' @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) ) )
| ( ( B = 'bot$a' )
& ( A
= ( 'bot$a' @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) ) )
| ( ( B
= ( 'bot$a' @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) )
& ( A = 'bot$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(55,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom41) ).
thf(854,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(141,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ~ ( A @ ( 'finite$a' @ 'fun_app$b' ) )
=> ~ ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( 'finite$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom21) ).
thf(1303,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ~ ( A @ ( 'finite$a' @ 'fun_app$b' ) )
=> ~ ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( 'finite$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(282,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( A @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom28) ).
thf(1986,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( A @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(559,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( C @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> $false )
& ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom240) ).
thf(3328,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
~ ( ~ ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( C @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( C @ ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(283,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( ( ( C @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> $false )
& ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom614) ).
thf(1989,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
~ ( ~ ( ( C @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( C @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(528,axiom,
! [A: 'A_ltln_set$'] :
( ( A @ ( 'bot$a' @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom284) ).
thf(3177,plain,
! [A: 'A_ltln_set$'] :
( ( A @ ( 'bot$a' @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(357,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ( ( A
= ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) )
=> $false )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom609) ).
thf(2366,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
~ ( ( A
!= ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(117,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ 'member$a' @ 'fun_app$b' ) )
=> ( ( B @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom410) ).
thf(1197,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ 'member$a' @ 'fun_app$b' ) )
=> ( ( B @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(471,axiom,
! [A: 'A_ltln_set$'] :
( ( A @ ( 'finite$' @ 'fun_app$a' ) )
<=> ( ? [B: 'A_ltln_set$',C: 'A_ltln$'] :
( ( B @ ( 'finite$' @ 'fun_app$a' ) )
& ( A
= ( B @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) ) )
| ( A = 'bot$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom448) ).
thf(2913,plain,
! [A: 'A_ltln_set$'] :
( ( ( ? [B: 'A_ltln_set$',C: 'A_ltln$'] :
( ( B @ ( 'finite$' @ 'fun_app$a' ) )
& ( A
= ( B @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) ) )
| ( A = 'bot$a' ) )
=> ( A @ ( 'finite$' @ 'fun_app$a' ) ) )
& ( ( A @ ( 'finite$' @ 'fun_app$a' ) )
=> ( ? [B: 'A_ltln_set$',C: 'A_ltln$'] :
( ( B @ ( 'finite$' @ 'fun_app$a' ) )
& ( A
= ( B @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) ) )
| ( A = 'bot$a' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(582,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ( B @ ( 'finite$' @ 'fun_app$a' ) )
& ( A @ ( 'finite$' @ 'fun_app$a' ) ) )
=> ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'finite$' @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom20) ).
thf(3426,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ( B @ ( 'finite$' @ 'fun_app$a' ) )
& ( A @ ( 'finite$' @ 'fun_app$a' ) ) )
=> ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'finite$' @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(496,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( A @ ( 'finite$' @ 'fun_app$a' ) )
=> ( ( A @ ( B @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( A @ ( B @ ( 'remove$' @ 'fold$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom638) ).
thf(3030,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( A @ ( 'finite$' @ 'fun_app$a' ) )
=> ( ( A @ ( B @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( A @ ( B @ ( 'remove$' @ 'fold$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(581,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] : ( A @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom270) ).
thf(3424,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] : ( A @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(230,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom271) ).
thf(1742,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(564,axiom,
! [A: 'A_ltln$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( B @ ( A @ 'member$' @ 'fun_app$a' ) )
=> ( B @ ( C @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ 'member$' @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom58) ).
thf(3347,plain,
! [A: 'A_ltln$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( B @ ( A @ 'member$' @ 'fun_app$a' ) )
=> ( B @ ( C @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ 'member$' @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(550,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set_bool_fun$'] :
( ( ! [C: 'A_ltln$',D: 'A_ltln_set$'] :
( ( ( D @ ( B @ 'fun_app$a' ) )
& ~ ( D @ ( C @ 'member$' @ 'fun_app$a' ) )
& ( D != 'bot$a' )
& ( D @ ( 'finite$' @ 'fun_app$a' ) ) )
=> ( D @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( B @ 'fun_app$a' ) ) )
& ! [C: 'A_ltln$'] : ( 'bot$a' @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( B @ 'fun_app$a' ) )
& ( A != 'bot$a' )
& ( A @ ( 'finite$' @ 'fun_app$a' ) ) )
=> ( A @ ( B @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom452) ).
thf(3277,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set_bool_fun$'] :
( ( ! [C: 'A_ltln$',D: 'A_ltln_set$'] :
( ( ( D @ ( B @ 'fun_app$a' ) )
& ~ ( D @ ( C @ 'member$' @ 'fun_app$a' ) )
& ( D != 'bot$a' )
& ( D @ ( 'finite$' @ 'fun_app$a' ) ) )
=> ( D @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( B @ 'fun_app$a' ) ) )
& ! [C: 'A_ltln$'] : ( 'bot$a' @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( B @ 'fun_app$a' ) )
& ( A != 'bot$a' )
& ( A @ ( 'finite$' @ 'fun_app$a' ) ) )
=> ( A @ ( B @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(111,axiom,
! [A: 'A_ltln_set$'] :
( ( 'bot$' @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( 'sup_fin$a' @ 'fun_app$i' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom400) ).
thf(1172,plain,
! [A: 'A_ltln_set$'] :
( ( 'bot$' @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( 'sup_fin$a' @ 'fun_app$i' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(372,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$'] :
( ( A @ ( 'finite$a' @ 'fun_app$b' ) )
=> ( ( A @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( 'sup_fin$a' @ 'fun_app$i' ) )
= ( A @ ( B @ ( 'sup$' @ 'fold$a' ) @ 'fun_app$i' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom639) ).
thf(2417,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$'] :
( ( A @ ( 'finite$a' @ 'fun_app$b' ) )
=> ( ( A @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( 'sup_fin$a' @ 'fun_app$i' ) )
= ( A @ ( B @ ( 'sup$' @ 'fold$a' ) @ 'fun_app$i' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(352,axiom,
! [A: 'A_ltln$'] :
( ( A @ ( 'bot$c' @ 'fun_app$' ) )
<=> ( 'bot$a' @ ( A @ 'member$' @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom367) ).
thf(2340,plain,
! [A: 'A_ltln$'] :
( ( ( 'bot$a' @ ( A @ 'member$' @ 'fun_app$a' ) )
=> ( A @ ( 'bot$c' @ 'fun_app$' ) ) )
& ( ( A @ ( 'bot$c' @ 'fun_app$' ) )
=> ( 'bot$a' @ ( A @ 'member$' @ 'fun_app$a' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(109,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ( ( ( C @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
& ( C @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> $false )
& ( C @ ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom239) ).
thf(1165,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
~ ( ~ ( ( C @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
& ( C @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
& ( C @ ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ 'less_eq$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(600,axiom,
! [A: 'A_ltln_set$'] :
( ! [B: 'A_ltln$'] :
( ( A @ ( B @ 'member$' @ 'fun_app$a' ) )
=> $false )
=> ( A = 'bot$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom156) ).
thf(3506,plain,
! [A: 'A_ltln_set$'] :
( ! [B: 'A_ltln$'] :
~ ( A @ ( B @ 'member$' @ 'fun_app$a' ) )
=> ( A = 'bot$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(74,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
<=> ( ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom251) ).
thf(955,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( ( ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= B )
=> ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
& ( ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(267,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$'] :
( ( ( A != 'bot$' )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( ( A @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( 'inf_fin$a' @ 'fun_app$i' ) )
= ( A @ ( 'inf_fin$a' @ 'fun_app$i' ) @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom477) ).
thf(1930,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set$'] :
( ( ( A != 'bot$' )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( ( A @ ( B @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( 'inf_fin$a' @ 'fun_app$i' ) )
= ( A @ ( 'inf_fin$a' @ 'fun_app$i' ) @ ( B @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(609,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] : ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom210) ).
thf(3543,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] : ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(158,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ~ ( B @ ( A @ 'member$a' @ 'fun_app$b' ) )
=> ( ( C @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
<=> ( C @ ( B @ 'less_eq$a' @ 'fun_app$b' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom439) ).
thf(1378,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ~ ( B @ ( A @ 'member$a' @ 'fun_app$b' ) )
=> ( ( ( C @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( C @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( B @ 'less_eq$a' @ 'fun_app$b' ) ) )
& ( ( C @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( C @ ( B @ 'less_eq$a' @ 'fun_app$b' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(546,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ( B @ ( 'finite$' @ 'fun_app$a' ) )
| ( A @ ( 'finite$' @ 'fun_app$a' ) ) )
=> ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'finite$' @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom479) ).
thf(3259,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ( B @ ( 'finite$' @ 'fun_app$a' ) )
| ( A @ ( 'finite$' @ 'fun_app$a' ) ) )
=> ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'finite$' @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(48,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( A @ ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom512) ).
thf(822,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( A @ ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(607,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( B @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( B @ ( C @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom242) ).
thf(3538,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ( B @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( B @ ( C @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(514,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$',D: 'A_ltln_set$'] :
( ( A
= ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) )
=> ( ( D @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( D @ ( C @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom68) ).
thf(3113,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$',D: 'A_ltln_set$'] :
( ( A
= ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) )
=> ( ( D @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( D @ ( C @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(386,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ( ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> $false )
& ( A = B ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom159) ).
thf(2484,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
~ ( ~ ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(563,axiom,
! [A: 'A_ltln$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ~ ( B @ ( A @ 'member$' @ 'fun_app$a' ) )
=> ( ( C @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
<=> ( C @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom440) ).
thf(3341,plain,
! [A: 'A_ltln$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ~ ( B @ ( A @ 'member$' @ 'fun_app$a' ) )
=> ( ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( C @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( ( C @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( C @ ( B @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(567,axiom,
! [A: 'A_ltln_set$'] :
( ( A @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom493) ).
thf(3362,plain,
! [A: 'A_ltln_set$'] :
( ( A @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(433,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom238) ).
thf(2731,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(159,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( ( A @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom273) ).
thf(1384,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( ( A @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(578,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln$',D: 'A_ltln_set$'] :
( ( D @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( B @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
<=> ( ~ ( A @ ( C @ 'member$' @ 'fun_app$a' ) )
& ( D @ ( B @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom622) ).
thf(3411,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln$',D: 'A_ltln_set$'] :
( ( ( ~ ( A @ ( C @ 'member$' @ 'fun_app$a' ) )
& ( D @ ( B @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( D @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( B @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( ( D @ ( C @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( B @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ~ ( A @ ( C @ 'member$' @ 'fun_app$a' ) )
& ( D @ ( B @ ( 'minus$b' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(596,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
<=> ( ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom278) ).
thf(3489,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ( ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= B )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
& ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( ( B @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(81,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( B @ ( A @ 'member$a' @ 'fun_app$b' ) )
=> ( ( C @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( B @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( C @ ( B @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom490) ).
thf(992,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( B @ ( A @ 'member$a' @ 'fun_app$b' ) )
=> ( ( C @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( B @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= ( C @ ( B @ ( 'inf$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( A @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(182,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( ( A @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom231) ).
thf(1500,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( ( A @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(493,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( C @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom582) ).
thf(3020,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( C @ ( B @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= ( C @ ( B @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( C @ ( A @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(147,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$',D: 'A_ltln_set_set$'] :
( ( ( D @ ( C @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( D @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( C @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ 'less_eq$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom219) ).
thf(1331,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$',D: 'A_ltln_set_set$'] :
( ( ( D @ ( C @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( D @ ( B @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ ( C @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ 'less_eq$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(437,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ~ ( A @ ( 'finite$' @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ~ ( B @ ( 'finite$' @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom260) ).
thf(2754,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( ~ ( A @ ( 'finite$' @ 'fun_app$a' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ~ ( B @ ( 'finite$' @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(616,axiom,
! [A: 'A_ltln_set$'] :
( ( A @ ( 'bot$a' @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom121) ).
thf(3580,plain,
! [A: 'A_ltln_set$'] :
( ( A @ ( 'bot$a' @ ( 'sup$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(330,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( A = B )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom166) ).
thf(2206,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$'] :
( ( A = B )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(13,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( C @ ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ 'less_eq$a' @ 'fun_app$b' ) )
<=> ( ( C @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
& ( C @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom130) ).
thf(659,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set$'] :
( ( ( ( C @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
& ( C @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
=> ( C @ ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ 'less_eq$a' @ 'fun_app$b' ) ) )
& ( ( C @ ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) @ 'less_eq$a' @ 'fun_app$b' ) )
=> ( ( C @ ( B @ 'less_eq$a' @ 'fun_app$b' ) )
& ( C @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(376,axiom,
! [A: 'A_ltln$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ~ ( C @ ( A @ 'member$' @ 'fun_app$a' ) )
& ~ ( B @ ( A @ 'member$' @ 'fun_app$a' ) ) )
=> ( ( ( B @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) )
= ( C @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) )
<=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom411) ).
thf(2436,plain,
! [A: 'A_ltln$',B: 'A_ltln_set$',C: 'A_ltln_set$'] :
( ( ~ ( C @ ( A @ 'member$' @ 'fun_app$a' ) )
& ~ ( B @ ( A @ 'member$' @ 'fun_app$a' ) ) )
=> ( ( ( B = C )
=> ( ( B @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) )
= ( C @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) ) )
& ( ( ( B @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) )
= ( C @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(297,axiom,
! [A: 'A_ltln_set$'] :
( ( 'bot$a' @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= 'bot$a' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom536) ).
thf(2059,plain,
! [A: 'A_ltln_set$'] :
( ( 'bot$a' @ ( A @ ( 'inf$' @ 'fun_app$d' ) @ 'fun_app$c' ) )
= 'bot$a' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(95,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set_bool_fun$'] :
( ( ! [D: 'A_ltln_set$',E: 'A_ltln_set_set$'] :
( ( ( E @ ( C @ 'fun_app$b' ) )
& ~ ( E @ ( D @ 'member$a' @ 'fun_app$b' ) )
& ( B @ ( D @ 'member$a' @ 'fun_app$b' ) )
& ( E @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( E @ ( D @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( C @ 'fun_app$b' ) ) )
& ( 'bot$' @ ( C @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( A @ ( C @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom467) ).
thf(1088,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$',C: 'A_ltln_set_set_bool_fun$'] :
( ( ! [D: 'A_ltln_set$',E: 'A_ltln_set_set$'] :
( ( ( E @ ( C @ 'fun_app$b' ) )
& ~ ( E @ ( D @ 'member$a' @ 'fun_app$b' ) )
& ( B @ ( D @ 'member$a' @ 'fun_app$b' ) )
& ( E @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( E @ ( D @ ( 'insert$a' @ 'fun_app$m' ) @ 'fun_app$e' ) @ ( C @ 'fun_app$b' ) ) )
& ( 'bot$' @ ( C @ 'fun_app$b' ) )
& ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
& ( A @ ( 'finite$a' @ 'fun_app$b' ) ) )
=> ( A @ ( C @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(177,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
<=> ! [C: 'A_ltln_set$'] :
( ( A @ ( C @ 'member$a' @ 'fun_app$b' ) )
=> ( B @ ( C @ 'member$a' @ 'fun_app$b' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom171) ).
thf(1468,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( ! [C: 'A_ltln_set$'] :
( ( A @ ( C @ 'member$a' @ 'fun_app$b' ) )
=> ( B @ ( C @ 'member$a' @ 'fun_app$b' ) ) )
=> ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) ) )
& ( ( B @ ( A @ 'less_eq$a' @ 'fun_app$b' ) )
=> ! [C: 'A_ltln_set$'] :
( ( A @ ( C @ 'member$a' @ 'fun_app$b' ) )
=> ( B @ ( C @ 'member$a' @ 'fun_app$b' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(554,axiom,
! [A: 'A_ltln$'] : ( 'bot$a' @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( 'is_singleton$' @ 'fun_app$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom471) ).
thf(3296,plain,
! [A: 'A_ltln$'] : ( 'bot$a' @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( 'is_singleton$' @ 'fun_app$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(59,axiom,
'insert$b' @ 'comp_fun_idem$c',
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom402) ).
thf(882,plain,
'insert$b' @ 'comp_fun_idem$c',
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(541,axiom,
! [A: 'A_ltln$',B: 'A_ltln$',C: 'A_ltln_set$'] :
( ( ( 'bot$a' @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) )
= ( C @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) )
<=> ( ( 'bot$a' @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom398) ).
thf(3227,plain,
! [A: 'A_ltln$',B: 'A_ltln$',C: 'A_ltln_set$'] :
( ( ( ( 'bot$a' @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B = A ) )
=> ( ( 'bot$a' @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) )
= ( C @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) ) )
& ( ( ( 'bot$a' @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) )
= ( C @ ( B @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) ) )
=> ( ( 'bot$a' @ ( A @ ( 'insert$b' @ 'fun_app$n' ) @ 'fun_app$c' ) @ ( C @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
& ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(271,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set_a_ltln_set_set_fun$',D: 'A_ltln_set_set$'] :
( ( ! [E: 'A_ltln_set$',F: 'A_ltln_set$'] :
( ( F @ ( E @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( F @ ( C @ 'fun_app$k' ) @ ( E @ ( C @ 'fun_app$k' ) @ 'less_eq$a' @ 'fun_app$b' ) ) )
& ( D @ ( B @ ( C @ 'fun_app$k' ) @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$k' ) @ 'less_eq$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom329) ).
thf(1944,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set$',C: 'A_ltln_set_a_ltln_set_set_fun$',D: 'A_ltln_set_set$'] :
( ( ! [E: 'A_ltln_set$',F: 'A_ltln_set$'] :
( ( F @ ( E @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) )
=> ( F @ ( C @ 'fun_app$k' ) @ ( E @ ( C @ 'fun_app$k' ) @ 'less_eq$a' @ 'fun_app$b' ) ) )
& ( D @ ( B @ ( C @ 'fun_app$k' ) @ 'less_eq$a' @ 'fun_app$b' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$g' ) @ 'fun_app$a' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$k' ) @ 'less_eq$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(88,axiom,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( A
= ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) )
=> ( A @ ( B @ 'less_eq$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom227) ).
thf(1037,plain,
! [A: 'A_ltln_set_set$',B: 'A_ltln_set_set$'] :
( ( A
= ( B @ ( A @ ( 'sup$a' @ 'fun_app$f' ) @ 'fun_app$e' ) ) )
=> ( A @ ( B @ 'less_eq$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(342,axiom,
! [A: 'A_ltln_set$',B: 'A_ltln_set_bool_fun$'] :
( ( B @ 'collect$' @ ( A @ 'member$a' @ 'fun_app$b' ) )
<=> ( A @ ( B @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom81) ).
thf(2297,plain,
! [A: 'A_ltln_set$',B: 'A_ltln_set_bool_fun$'] :
( ( ( A @ ( B @ 'fun_app$a' ) )
=> ( B @ 'collect$' @ ( A @ 'member$a' @ 'fun_app$b' ) ) )
& ( ( B @ 'collect$' @ ( A @ 'member$a' @ 'fun_app$b' ) )
=> ( A @ ( B @ 'fun_app$a' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(3967,plain,
$false,
inference(e,[status(thm)],[645,2199,1586,1879,1369,1454,909,2331,666,1549,2306,3053,3434,3167,2876,1237,3397,1899,1315,2595,1850,2499,683,1522,2381,2062,1808,2590,741,873,1533,677,3382,2363,1200,2077,2309,762,3072,1924,1005,2210,2117,1596,1728,3108,1137,2686,3135,3365,3044,1867,3338,2141,3121,3577,670,2195,1705,797,2316,2476,2627,1507,1222,2360,1095,2216,3502,841,3088,1613,2886,1228,3350,1001,3545,2763,2548,2985,1391,1645,1921,2400,2067,1430,2698,3046,1871,2708,802,1059,2654,1628,724,3204,3442,3263,1287,3221,3148,619,2403,1247,2373,770,1115,3180,2388,1362,1963,924,3431,1664,1714,789,1811,1373,2782,1040,2259,3163,3453,3093,966,1283,2017,2456,2007,3438,3525,3569,1677,2540,2777,3152,981,3068,3189,734,3036,1405,3211,2982,3510,692,3421,1622,2424,1394,2772,2799,2639,920,2910,3567,1438,1306,2164,3186,3318,2000,3418,1047,3450,3459,1915,1708,2083,2496,1768,714,2409,1387,894,825,778,952,1355,1751,3239,3371,2032,2601,2428,1619,2150,2958,916,1602,1555,3499,1457,2179,1159,1836,2213,1195,2741,2228,2112,1740,1012,3191,2464,3403,2565,1210,1656,1402,1983,2115,2100,1804,2841,1121,2726,3078,3237,2245,1350,1234,1541,2377,650,948,2692,1498,2858,2537,3018,857,1683,1292,1937,3428,3194,2551,2666,1889,3294,706,3000,2323,753,2561,1424,2312,2196,1842,2472,2649,3242,2968,647,1150,3126,654,1552,1192,2581,3540,2862,3333,3064,2756,3162,2153,1231,984,3390,1002,1852,2813,2766,2052,1599,2370,1525,1333,1318,2926,805,3183,1695,657,2057,1170,2617,2662,794,1732,1202,2203,2793,2089,2189,1616,2936,2176,2292,3358,3257,2941,1927,3289,2894,618,1764,1301,2734,3111,3274,3536,819,975,1833,2970,2225,1389,1125,3266,711,2991,2398,2134,2695,1256,2161,1503,3023,3118,1312,2738,3002,3123,1897,1258,1638,3170,3091,2474,2573,2358,2510,2346,3101,2721,831,1408,2478,2493,1574,736,2097,996,3197,3138,2896,1376,1969,2383,2624,784,2637,2774,3515,863,1175,2824,2025,816,2446,700,3034,3583,2647,2252,1820,3456,1667,1339,3027,2780,2267,2785,2593,3006,3298,2874,2075,1699,1445,2086,883,3325,2303,1562,827,2835,1044,2481,2390,1250,3512,851,1413,2816,1873,944,2994,795,2652,1277,648,1145,1958,2899,1049,1626,3009,2054,1948,927,2037,2977,1225,2192,3214,1605,3462,1267,1098,1770,3376,690,3315,640,1961,739,2678,1780,2821,2850,1484,2831,2689,1711,791,1186,2337,1830,1901,1658,907,1813,1452,1980,2128,1336,643,2579,1670,2728,2807,2848,2584,1934,2948,1543,1766,2558,703,1702,2379,1353,1955,1972,2320,2711,3224,1427,978,1140,1940,1839,627,1966,3548,891,2907,1421,3400,1918,3457,1084,1817,2960,1157,1321,3533,3447,2611,759,2997,2187,1189,1289,3056,844,2443,963,1476,896,1674,2554,3336,1745,3561,1244,2130,781,3085,813,2988,1903,2406,2811,2004,786,3368,2944,2009,1491,2041,3497,1777,1294,2576,899,2120,2095,2294,1994,2779,2421,1133,999,1512,1578,2385,2534,3291,2587,1876,1148,3132,1642,2102,1725,1280,3373,3464,854,1303,1986,3328,1989,3177,2366,1197,2913,3426,3030,3424,1742,3347,3277,1172,2417,2340,1165,3506,955,1930,3543,1378,3259,822,3538,3113,2484,3341,3362,2731,1384,3411,3489,992,1500,3020,1331,2754,3580,2206,659,2436,2059,1088,1468,3296,882,3227,1944,1037,2297]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP367_1 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.13/0.41 % Computer : n004.cluster.edu
% 0.13/0.41 % Model : x86_64 x86_64
% 0.13/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.41 % Memory : 8046.5625MB
% 0.13/0.41 % OS : Linux 6.8.0-71-generic
% 0.13/0.41 % CPULimit : 300
% 0.13/0.41 % WCLimit : 300
% 0.13/0.41 % DateTime : Fri Sep 25 19:09:06 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.86/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 3.32/1.63 % [INFO] Parsing done (639ms).
% 3.32/1.64 % [INFO] Running in sequential loop mode.
% 4.41/2.03 % [INFO] eprover registered as external prover.
% 4.41/2.04 % [INFO] Scanning for conjecture ...
% 4.76/2.28 % [INFO] Found a conjecture (or negated_conjecture) and 639 axioms. Running axiom selection ...
% 6.10/2.51 % [INFO] Axiom selection finished. Selected 615 axioms (removed 24 axioms).
% 7.43/2.93 % [INFO] Problem is typed first-order (TPTP TFF).
% 7.43/2.96 % [INFO] Type checking passed.
% 7.43/2.96 % [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 ...
% 24.72/7.16 % External prover 'e' found a proof!
% 24.72/7.16 % [INFO] Killing All external provers ...
% 24.72/7.16 % Time passed: 6604ms (effective reasoning time: 5512ms)
% 24.72/7.16 % 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)>
% 24.72/7.16 % Axioms used in derivation (615): axiom326, axiom32, axiom635, axiom260, axiom280, axiom127, axiom626, axiom315, axiom546, axiom116, axiom527, axiom611, axiom452, axiom491, axiom241, axiom28, axiom76, axiom273, axiom61, axiom230, axiom100, axiom6, axiom564, axiom503, axiom553, axiom54, axiom549, axiom480, axiom396, axiom25, axiom404, axiom14, axiom474, axiom333, axiom221, axiom295, axiom485, axiom214, axiom516, axiom322, axiom307, axiom496, axiom311, axiom284, axiom423, axiom65, axiom575, axiom36, axiom203, axiom169, axiom622, axiom531, axiom291, axiom441, axiom507, axiom430, axiom600, axiom50, axiom158, axiom131, axiom10, axiom386, axiom580, axiom344, axiom508, axiom392, axiom597, axiom337, axiom119, axiom210, axiom407, axiom17, axiom401, axiom397, axiom460, axiom354, axiom587, axiom477, axiom467, axiom257, axiom579, axiom22, axiom619, axiom412, axiom147, axiom524, axiom434, axiom341, axiom504, axiom173, axiom638, axiom109, axiom348, axiom184, axiom376, axiom172, axiom535, axiom266, axiom445, axiom42, axiom513, axiom239, axiom300, axiom350, axiom561, axiom329, axiom372, axiom195, axiom162, axiom583, axiom358, axiom161, axiom632, axiom616, axiom542, axiom123, axiom246, axiom592, axiom383, axiom605, axiom134, axiom33, axiom150, axiom104, axiom456, axiom87, axiom572, axiom11, axiom568, axiom130, axiom557, axiom235, axiom98, axiom225, axiom520, axiom39, axiom608, axiom499, axiom330, axiom418, axiom484, axiom112, axiom304, axiom488, axiom251, axiom64, axiom578, axiom530, axiom636, axiom179, axiom283, axiom126, axiom539, axiom427, axiom625, axiom591, axiom59, axiom247, axiom48, axiom217, axiom343, axiom27, axiom352, axiom411, axiom294, axiom314, axiom289, axiom437, axiom601, axiom236, axiom151, axiom115, axiom623, axiom94, axiom83, axiom336, axiom308, axiom321, axiom35, axiom78, axiom24, axiom278, axiom272, axiom228, axiom405, axiom5, axiom101, axiom455, axiom121, axiom132, axiom56, axiom466, axiom137, axiom563, axiom206, axiom318, axiom416, axiom60, axiom631, axiom0, axiom574, axiom490, axiom240, axiom290, axiom13, axiom53, axiom433, axiom143, axiom489, axiom545, axiom108, axiom395, axiom387, axiom16, axiom459, axiom400, axiom517, axiom258, axiom325, axiom448, axiom552, axiom385, axiom478, axiom157, axiom90, axiom168, axiom528, axiom332, axiom9, axiom303, axiom612, axiom366, axiom207, axiom494, axiom538, axiom133, axiom80, axiom97, axiom567, axiom192, axiom586, axiom422, axiom185, axiom472, axiom202, axiom252, axiom391, axiom604, axiom263, axiom415, axiom589, axiom254, axiom444, axiom82, axiom45, axiom541, axiom360, axiom398, axiom382, axiom483, axiom229, axiom174, axiom556, axiom639, axiom319, axiom347, axiom180, axiom67, axiom213, axiom534, axiom450, axiom196, axiom523, axiom232, axiom615, axiom629, axiom243, axiom426, axiom72, axiom461, axiom463, axiom310, axiom449, axiom438, axiom267, axiom89, axiom512, axiom224, axiom122, axiom38, axiom419, axiom377, axiom500, axiom91, axiom1, axiom105, axiom218, axiom86, axiom163, axiom408, axiom111, axiom120, axiom297, axiom447, axiom52, axiom156, axiom511, axiom279, axiom12, axiom390, axiom37, axiom331, axiom212, axiom602, axiom432, axiom223, axiom571, axiom501, axiom342, axiom381, axiom34, axiom630, axiom544, axiom152, axiom425, axiom167, axiom607, axiom454, axiom205, axiom364, axiom628, axiom79, axiom190, axiom573, axiom443, axiom96, axiom149, axiom189, axiom375, axiom394, axiom23, axiom560, axiom93, axiom595, axiom562, axiom41, axiom227, axiom182, axiom476, axiom216, axiom409, axiom286, axiom313, axiom618, axiom118, axiom275, axiom63, axiom19, axiom458, axiom613, axiom102, axiom8, axiom410, axiom320, axiom30, axiom370, axiom201, axiom178, axiom428, axiom479, axiom259, axiom74, axiom276, axiom451, axiom570, axiom85, axiom509, axiom233, axiom220, axiom598, axiom302, axiom367, axiom378, axiom57, axiom599, axiom566, axiom145, axiom471, axiom506, axiom186, axiom497, axiom164, axiom374, axiom614, axiom440, axiom581, axiom282, axiom271, axiom287, axiom4, axiom255, axiom153, axiom324, axiom71, axiom462, axiom15, axiom129, axiom114, axiom244, axiom620, axiom594, axiom136, axiom414, axiom106, axiom533, axiom170, axiom181, axiom403, axiom522, axiom436, axiom482, axiom555, axiom486, axiom346, axiom262, axiom68, axiom335, axiom268, axiom293, axiom175, axiom237, axiom26, axiom219, axiom493, axiom356, axiom298, axiom439, axiom634, axiom469, axiom110, axiom125, axiom603, axiom49, axiom577, axiom46, axiom585, axiom248, axiom421, axiom590, axiom547, axiom18, axiom338, axiom242, axiom379, axiom88, axiom558, axiom510, axiom389, axiom226, axiom166, axiom526, axiom559, axiom457, axiom521, axiom442, axiom327, axiom92, axiom399, axiom66, axiom345, axiom464, axiom204, axiom296, axiom569, axiom141, axiom215, axiom576, axiom596, axiom274, axiom117, axiom393, axiom621, axiom44, axiom222, axiom323, axiom446, axiom84, axiom554, axiom269, axiom453, axiom81, axiom502, axiom103, axiom7, axiom515, axiom231, axiom306, axiom155, axiom495, axiom253, axiom249, axiom368, axiom550, axiom565, axiom429, axiom99, axiom148, axiom128, axiom316, axiom285, axiom540, axiom537, axiom183, axiom301, axiom211, axiom29, axiom532, axiom177, axiom31, axiom380, axiom188, axiom264, axiom431, axiom208, axiom20, axiom588, axiom627, axiom159, axiom487, axiom609, axiom519, axiom402, axiom384, axiom551, axiom73, axiom107, axiom417, axiom339, axiom154, axiom40, axiom265, axiom165, axiom47, axiom518, axiom270, axiom113, axiom176, axiom171, axiom3, axiom305, axiom187, axiom288, axiom69, axiom317, axiom135, axiom277, axiom536, axiom198, axiom529, axiom55, axiom584, axiom281, axiom424, axiom633, axiom593, axiom245, axiom435, axiom312, axiom95, axiom70, axiom238, axiom617, axiom465, axiom543, axiom299, axiom261, axiom413, axiom256, axiom334, axiom160, axiom582, axiom514, axiom43, axiom481, axiom124, axiom505, axiom606, axiom77, axiom406, axiom388, axiom637, axiom420, axiom62, axiom498, axiom209, axiom21, axiom328, axiom139, axiom200, axiom250, axiom292, axiom525, axiom234, axiom362, axiom51, axiom548, axiom309, axiom610, axiom470, axiom468, axiom492, axiom58, axiom624, axiom340, axiom194
% 24.72/7.16 % No. of inferences in proof: 1234
% 24.72/7.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 6604 ms resp. 5512 ms w/o parsing
% 26.79/7.68 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 26.79/7.69 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------