TSTP Solution File: ITP367_1 by Leo-III---1.7.10
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ITP367_1 : TPTP v8.1.2. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 07:51:05 EDT 2024
% Result : Theorem 16.08s 4.55s
% Output : Refutation 17.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 701
% Syntax : Number of formulae : 1319 ( 416 unt; 85 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 : 56 ( 56 >; 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$\'': $tType ).
thf('\'member$\'_type',type,
'\'member$\'': '\'A_ltln$\'' > '\'A_ltln_set_bool_fun$\'' ).
thf('\'subformulas_nu$\'_type',type,
'\'subformulas_nu$\'': '\'A_ltln_a_ltln_set_fun$\'' ).
thf('\'sup_fin$a\'_type',type,
'\'sup_fin$a\'': '\'A_ltln_set_set_a_ltln_set_fun$\'' ).
thf('\'bot$\'_type',type,
'\'bot$\'': '\'A_ltln_set_set$\'' ).
thf('\'comp_fun_idem$\'_type',type,
'\'comp_fun_idem$\'': '\'A_ltln_set_set_a_ltln_set_set_a_ltln_set_set_fun_fun$\'' > $o ).
thf('\'inf_fin$a\'_type',type,
'\'inf_fin$a\'': '\'A_ltln_set_set_a_ltln_set_fun$\'' ).
thf('\'fun_app$l\'_type',type,
'\'fun_app$l\'': '\'A_ltln_a_ltln_bool_fun_fun$\'' > '\'A_ltln$\'' > '\'A_ltln_bool_fun$\'' ).
thf('\'bind$c\'_type',type,
'\'bind$c\'': '\'A_ltln_set$\'' > '\'A_ltln_a_ltln_set_fun$\'' > '\'A_ltln_set$\'' ).
thf('\'bot$c\'_type',type,
'\'bot$c\'': '\'A_ltln_bool_fun$\'' ).
thf('\'insert$b\'_type',type,
'\'insert$b\'': '\'A_ltln_a_ltln_set_a_ltln_set_fun_fun$\'' ).
thf('\'disjnt$a\'_type',type,
'\'disjnt$a\'': '\'A_ltln_set_a_ltln_set_bool_fun_fun$\'' ).
thf('\'fun_app$b\'_type',type,
'\'fun_app$b\'': '\'A_ltln_set_set_bool_fun$\'' > '\'A_ltln_set_set$\'' > $o ).
thf('\'x$\'_type',type,
'\'x$\'': '\'A_ltln_set$\'' ).
thf('\'minus$a\'_type',type,
'\'minus$a\'': '\'A_ltln_set_set_a_ltln_set_set_a_ltln_set_set_fun_fun$\'' ).
thf('\'fun_app$a\'_type',type,
'\'fun_app$a\'': '\'A_ltln_set_bool_fun$\'' > '\'A_ltln_set$\'' > $o ).
thf('\'is_singleton$a\'_type',type,
'\'is_singleton$a\'': '\'A_ltln_set_set_bool_fun$\'' ).
thf('\'fun_app$g\'_type',type,
'\'fun_app$g\'': '\'A_ltln_set_a_ltln_set_bool_fun_fun$\'' > '\'A_ltln_set$\'' > '\'A_ltln_set_bool_fun$\'' ).
thf('\'minus$b\'_type',type,
'\'minus$b\'': '\'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$\'' ).
thf('\'less_eq$a\'_type',type,
'\'less_eq$a\'': '\'A_ltln_set_set$\'' > '\'A_ltln_set_set_bool_fun$\'' ).
thf('\'comp_fun_idem$a\'_type',type,
'\'comp_fun_idem$a\'': '\'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$\'' > $o ).
thf('\'bind$\'_type',type,
'\'bind$\'': '\'A_ltln_set$\'' > '\'A_ltln_a_ltln_set_set_fun$\'' > '\'A_ltln_set_set$\'' ).
thf('\'filter$a\'_type',type,
'\'filter$a\'': '\'A_ltln_bool_fun$\'' > '\'A_ltln_set_a_ltln_set_fun$\'' ).
thf('\'comp_fun_idem$b\'_type',type,
'\'comp_fun_idem$b\'': '\'A_ltln_set_a_ltln_set_set_a_ltln_set_set_fun_fun$\'' > $o ).
thf('\'y$\'_type',type,
'\'y$\'': '\'A_ltln_set$\'' ).
thf('\'fun_app$h\'_type',type,
'\'fun_app$h\'': '\'A_ltln_a_ltln_set_fun$\'' > '\'A_ltln$\'' > '\'A_ltln_set$\'' ).
thf('\'subformulas_mu$\'_type',type,
'\'subformulas_mu$\'': '\'A_ltln_a_ltln_set_fun$\'' ).
thf('\'fun_app$i\'_type',type,
'\'fun_app$i\'': '\'A_ltln_set_set_a_ltln_set_fun$\'' > '\'A_ltln_set_set$\'' > '\'A_ltln_set$\'' ).
thf('\'is_empty$a\'_type',type,
'\'is_empty$a\'': '\'A_ltln_set_set_bool_fun$\'' ).
thf('\'fun_app$\'_type',type,
'\'fun_app$\'': '\'A_ltln_bool_fun$\'' > '\'A_ltln$\'' > $o ).
thf('\'fun_app$e\'_type',type,
'\'fun_app$e\'': '\'A_ltln_set_set_a_ltln_set_set_fun$\'' > '\'A_ltln_set_set$\'' > '\'A_ltln_set_set$\'' ).
thf('\'is_singleton$\'_type',type,
'\'is_singleton$\'': '\'A_ltln_set_bool_fun$\'' ).
thf('\'collect$a\'_type',type,
'\'collect$a\'': '\'A_ltln_bool_fun$\'' > '\'A_ltln_set$\'' ).
thf('\'insert$a\'_type',type,
'\'insert$a\'': '\'A_ltln_set_a_ltln_set_set_a_ltln_set_set_fun_fun$\'' ).
thf('\'max$\'_type',type,
'\'max$\'': '\'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$\'' ).
thf('\'uu$\'_type',type,
'\'uu$\'': '\'A_ltln_set_set$\'' > '\'A_ltln_set_bool_fun$\'' ).
thf('\'inf$a\'_type',type,
'\'inf$a\'': '\'A_ltln_set_set_a_ltln_set_set_a_ltln_set_set_fun_fun$\'' ).
thf('\'bind$a\'_type',type,
'\'bind$a\'': '\'A_ltln_set_set$\'' > '\'A_ltln_set_a_ltln_set_fun$\'' > '\'A_ltln_set$\'' ).
thf('\'bind$b\'_type',type,
'\'bind$b\'': '\'A_ltln_set_set$\'' > '\'A_ltln_set_a_ltln_set_set_fun$\'' > '\'A_ltln_set_set$\'' ).
thf('\'inf$\'_type',type,
'\'inf$\'': '\'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$\'' ).
thf('\'fun_app$k\'_type',type,
'\'fun_app$k\'': '\'A_ltln_set_a_ltln_set_set_fun$\'' > '\'A_ltln_set$\'' > '\'A_ltln_set_set$\'' ).
thf('\'fun_app$m\'_type',type,
'\'fun_app$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\'_type',type,
'\'bot$a\'': '\'A_ltln_set$\'' ).
thf('\'fun_app$j\'_type',type,
'\'fun_app$j\'': '\'A_ltln_a_ltln_set_set_fun$\'' > '\'A_ltln$\'' > '\'A_ltln_set_set$\'' ).
thf('\'disjnt$\'_type',type,
'\'disjnt$\'': '\'A_ltln_set_set$\'' > '\'A_ltln_set_set_bool_fun$\'' ).
thf('\'fold$a\'_type',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$\'_type',type,
'\'is_empty$\'': '\'A_ltln_set_bool_fun$\'' ).
thf('\'sup$a\'_type',type,
'\'sup$a\'': '\'A_ltln_set_set_a_ltln_set_set_a_ltln_set_set_fun_fun$\'' ).
thf('\'fun_app$n\'_type',type,
'\'fun_app$n\'': '\'A_ltln_a_ltln_set_a_ltln_set_fun_fun$\'' > '\'A_ltln$\'' > '\'A_ltln_set_a_ltln_set_fun$\'' ).
thf('\'fold$\'_type',type,
'\'fold$\'': '\'A_ltln_a_ltln_set_a_ltln_set_fun_fun$\'' > '\'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$\'' ).
thf('\'the_elem$\'_type',type,
'\'the_elem$\'': '\'A_ltln_set$\'' > '\'A_ltln$\'' ).
thf('\'comp_fun_idem$c\'_type',type,
'\'comp_fun_idem$c\'': '\'A_ltln_a_ltln_set_a_ltln_set_fun_fun$\'' > $o ).
thf('\'bot$d\'_type',type,
'\'bot$d\'': '\'A_ltln_set_bool_fun$\'' ).
thf('\'fun_app$f\'_type',type,
'\'fun_app$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$\'' ).
thf('\'collect$\'_type',type,
'\'collect$\'': '\'A_ltln_set_bool_fun$\'' > '\'A_ltln_set_set$\'' ).
thf('\'sup$\'_type',type,
'\'sup$\'': '\'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$\'' ).
thf('\'less_eq$\'_type',type,
'\'less_eq$\'': '\'A_ltln_set_a_ltln_set_bool_fun_fun$\'' ).
thf('\'the_elem$a\'_type',type,
'\'the_elem$a\'': '\'A_ltln_set_set_a_ltln_set_fun$\'' ).
thf('\'finite$a\'_type',type,
'\'finite$a\'': '\'A_ltln_set_set_bool_fun$\'' ).
thf('\'finite$\'_type',type,
'\'finite$\'': '\'A_ltln_set_bool_fun$\'' ).
thf('\'member$a\'_type',type,
'\'member$a\'': '\'A_ltln_set$\'' > '\'A_ltln_set_set_bool_fun$\'' ).
thf('\'uua$\'_type',type,
'\'uua$\'': '\'A_ltln_set$\'' > '\'A_ltln_bool_fun$\'' ).
thf('\'fun_app$d\'_type',type,
'\'fun_app$d\'': '\'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$\'' > '\'A_ltln_set$\'' > '\'A_ltln_set_a_ltln_set_fun$\'' ).
thf('\'remove$\'_type',type,
'\'remove$\'': '\'A_ltln_a_ltln_set_a_ltln_set_fun_fun$\'' ).
thf('\'filter$\'_type',type,
'\'filter$\'': '\'A_ltln_set_bool_fun$\'' > '\'A_ltln_set_set_a_ltln_set_set_fun$\'' ).
thf('\'phi$\'_type',type,
'\'phi$\'': '\'A_ltln$\'' ).
thf('\'fun_app$c\'_type',type,
'\'fun_app$c\'': '\'A_ltln_set_a_ltln_set_fun$\'' > '\'A_ltln_set$\'' > '\'A_ltln_set$\'' ).
thf(240,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom255) ).
thf(1718,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(441,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom615) ).
thf(2612,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(375,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
<=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom606) ).
thf(2295,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B )
= A ) )
& ( ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B )
= A )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(244,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B )
= '\'bot$\'' )
<=> ( ( A = '\'bot$\'' )
& ( B = '\'bot$\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom116) ).
thf(1729,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B )
= '\'bot$\'' )
=> ( ( A = '\'bot$\'' )
& ( B = '\'bot$\'' ) ) )
& ( ( ( A = '\'bot$\'' )
& ( B = '\'bot$\'' ) )
=> ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B )
= '\'bot$\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(396,axiom,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ C ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom489) ).
thf(2412,plain,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ C ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(269,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ A ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom310) ).
thf(1840,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ A ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(427,axiom,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ B ) ) @ C )
= '\'bot$a\'' )
<=> ( ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ C )
& ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C )
= '\'bot$a\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom530) ).
thf(2544,plain,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ B ) ) @ C )
= '\'bot$a\'' )
=> ( ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ C )
& ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C )
= '\'bot$a\'' ) ) )
& ( ( ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ C )
& ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C )
= '\'bot$a\'' ) )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ B ) ) @ C )
= '\'bot$a\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(105,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ A ) )
=> ( '\'fun_app$b\'' @ '\'finite$a\'' @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom261) ).
thf(1110,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ A ) )
=> ( '\'fun_app$b\'' @ '\'finite$a\'' @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(362,axiom,
! [A: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom290) ).
thf(2250,plain,
! [A: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(8,axiom,
'\'comp_fun_idem$\'' @ '\'sup$a\'',
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom73) ).
thf(645,plain,
'\'comp_fun_idem$\'' @ '\'sup$a\'',
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(67,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ B )
=> ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ C ) ) @ B )
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom482) ).
thf(892,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ B )
=> ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ C ) ) @ B )
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(195,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( A != '\'bot$\'' )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ ( '\'fun_app$i\'' @ '\'inf_fin$a\'' @ A ) )
& ( ! [C: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ A )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ C ) )
=> $false ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom139) ).
thf(1501,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\''] :
~ ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( A != '\'bot$\'' )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ ( '\'fun_app$i\'' @ '\'inf_fin$a\'' @ A ) )
& ~ ! [C: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ A )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(49,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ C ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom311) ).
thf(809,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ C ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(170,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) )
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom15) ).
thf(1369,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) )
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(125,axiom,
! [A: '\'A_ltln_set$\''] :
( ( '\'fun_app$i\'' @ '\'the_elem$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ '\'bot$\'' ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom470) ).
thf(1190,plain,
! [A: '\'A_ltln_set$\''] :
( ( '\'fun_app$i\'' @ '\'the_elem$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ '\'bot$\'' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(382,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ C ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom178) ).
thf(2336,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ C ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(335,axiom,
! [A: '\'A_ltln$\'',B: '\'A_ltln$\'',C: '\'A_ltln$\'',D: '\'A_ltln$\''] :
( ( ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ '\'bot$a\'' ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ D ) @ '\'bot$a\'' ) ) )
<=> ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom425) ).
thf(2109,plain,
! [A: '\'A_ltln$\'',B: '\'A_ltln$\'',C: '\'A_ltln$\'',D: '\'A_ltln$\''] :
( ( ( ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ '\'bot$a\'' ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ D ) @ '\'bot$a\'' ) ) )
=> ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) )
& ( ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ '\'bot$a\'' ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ D ) @ '\'bot$a\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(337,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ '\'finite$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) )
<=> ( ( '\'fun_app$a\'' @ '\'finite$\'' @ A )
& ( '\'fun_app$a\'' @ '\'finite$\'' @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom4) ).
thf(2131,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ '\'finite$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) )
=> ( ( '\'fun_app$a\'' @ '\'finite$\'' @ A )
& ( '\'fun_app$a\'' @ '\'finite$\'' @ B ) ) )
& ( ( ( '\'fun_app$a\'' @ '\'finite$\'' @ A )
& ( '\'fun_app$a\'' @ '\'finite$\'' @ B ) )
=> ( '\'fun_app$a\'' @ '\'finite$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(186,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( A != '\'bot$\'' )
& ( '\'fun_app$b\'' @ '\'finite$a\'' @ B ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ A ) ) @ ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom356) ).
thf(1454,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( A != '\'bot$\'' )
& ( '\'fun_app$b\'' @ '\'finite$a\'' @ B ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ A ) ) @ ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(155,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set_a_ltln_set_fun$\'',C: '\'A_ltln_set_set$\'',D: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$i\'' @ B @ C ) )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ C ) @ D )
& ! [E: '\'A_ltln_set_set$\'',F: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ E ) @ F )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$i\'' @ B @ E ) ) @ ( '\'fun_app$i\'' @ B @ F ) ) ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$i\'' @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom325) ).
thf(1315,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set_a_ltln_set_fun$\'',C: '\'A_ltln_set_set$\'',D: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$i\'' @ B @ C ) )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ C ) @ D )
& ! [E: '\'A_ltln_set_set$\'',F: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ E ) @ F )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$i\'' @ B @ E ) ) @ ( '\'fun_app$i\'' @ B @ F ) ) ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$i\'' @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(272,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_bool_fun$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'filter$\'' @ B ) @ C ) )
<=> ( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ C )
& ( '\'fun_app$a\'' @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom105) ).
thf(1850,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_bool_fun$\'',C: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'filter$\'' @ B ) @ C ) )
=> ( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ C )
& ( '\'fun_app$a\'' @ B @ A ) ) )
& ( ( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ C )
& ( '\'fun_app$a\'' @ B @ A ) )
=> ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'filter$\'' @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(417,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom585) ).
thf(2499,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(15,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ B ) ) @ C )
<=> ( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ C )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom385) ).
thf(666,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ B ) ) @ C )
=> ( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ C )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ C ) ) )
& ( ( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ C )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ C ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ B ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(262,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ) @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom510) ).
thf(1818,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(296,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ C ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom312) ).
thf(1950,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ C ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(206,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ C ) @ B ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ C ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom241) ).
thf(1549,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ C ) @ B ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ C ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(326,axiom,
'\'comp_fun_idem$a\'' @ '\'sup$\'',
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom74) ).
thf(2077,plain,
'\'comp_fun_idem$a\'' @ '\'sup$\'',
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(118,axiom,
! [A: '\'A_ltln_set_set$\''] : ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom173) ).
thf(1158,plain,
! [A: '\'A_ltln_set_set$\''] : ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(18,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\''] : ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom418) ).
thf(683,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\''] : ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(29,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( A = B )
<=> ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom323) ).
thf(730,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( ( A = B )
=> ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ A ) ) )
& ( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(446,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ B ) ) @ B )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom519) ).
thf(2622,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ B ) ) @ B )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(450,axiom,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ C ) ) @ B )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom483) ).
thf(2644,plain,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ C ) ) @ B )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(322,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
<=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom594) ).
thf(2062,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ A )
= A ) )
& ( ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ A )
= A )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(542,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom438) ).
thf(3040,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(361,axiom,
! [A: '\'A_ltln$\''] : ( '\'fun_app$a\'' @ '\'finite$\'' @ ( '\'fun_app$h\'' @ '\'subformulas_nu$\'' @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom288) ).
thf(2248,plain,
! [A: '\'A_ltln$\''] : ( '\'fun_app$a\'' @ '\'finite$\'' @ ( '\'fun_app$h\'' @ '\'subformulas_nu$\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(30,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( A != '\'bot$\'' )
& ! [C: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ A )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ C ) ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ ( '\'fun_app$i\'' @ '\'inf_fin$a\'' @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom141) ).
thf(741,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( A != '\'bot$\'' )
& ! [C: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ A )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ C ) ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ ( '\'fun_app$i\'' @ '\'inf_fin$a\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(129,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ B )
& ! [C: '\'A_ltln_set_set$\''] :
( ( ( B
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ C ) )
& ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ C ) )
=> $false ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom414) ).
thf(1205,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\''] :
~ ( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ B )
& ! [C: '\'A_ltln_set_set$\''] :
~ ( ( B
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ C ) )
& ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(12,axiom,
! [A: '\'A_ltln_set_set$\''] : ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom291) ).
thf(655,plain,
! [A: '\'A_ltln_set_set$\''] : ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(497,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\'',D: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ D ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ C ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom567) ).
thf(2854,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\'',D: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ D ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ C ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(17,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'minus$a\'' @ B ) @ C ) )
<=> ( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ B )
& ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom516) ).
thf(677,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'minus$a\'' @ B ) @ C ) )
=> ( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ B )
& ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ C ) ) )
& ( ( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ B )
& ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ C ) )
=> ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'minus$a\'' @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(183,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( A = B )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom167) ).
thf(1437,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( A = B )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(59,axiom,
'\'comp_fun_idem$c\'' @ '\'insert$b\'',
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom402) ).
thf(861,plain,
'\'comp_fun_idem$c\'' @ '\'insert$b\'',
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(249,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set_a_ltln_set_fun$\'',C: '\'A_ltln_set_set$\'',D: '\'A_ltln_set_set$\''] :
( ( ( A
= ( '\'fun_app$i\'' @ B @ C ) )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ C ) @ D )
& ! [E: '\'A_ltln_set_set$\'',F: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ E ) @ F )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$i\'' @ B @ E ) ) @ ( '\'fun_app$i\'' @ B @ F ) ) ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$i\'' @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom336) ).
thf(1750,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set_a_ltln_set_fun$\'',C: '\'A_ltln_set_set$\'',D: '\'A_ltln_set_set$\''] :
( ( ( A
= ( '\'fun_app$i\'' @ B @ C ) )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ C ) @ D )
& ! [E: '\'A_ltln_set_set$\'',F: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ E ) @ F )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$i\'' @ B @ E ) ) @ ( '\'fun_app$i\'' @ B @ F ) ) ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$i\'' @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(86,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'disjnt$\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ C ) )
<=> ( ( '\'fun_app$b\'' @ ( '\'disjnt$\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'disjnt$\'' @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom77) ).
thf(977,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'disjnt$\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ C ) )
=> ( ( '\'fun_app$b\'' @ ( '\'disjnt$\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'disjnt$\'' @ A ) @ C ) ) )
& ( ( ( '\'fun_app$b\'' @ ( '\'disjnt$\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'disjnt$\'' @ A ) @ C ) )
=> ( '\'fun_app$b\'' @ ( '\'disjnt$\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(217,axiom,
! [A: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( A != '\'bot$\'' ) )
=> ? [B: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ B ) @ A )
& ! [C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ A )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ C ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom194) ).
thf(1596,plain,
! [A: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( A != '\'bot$\'' ) )
=> ? [B: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ B ) @ A )
& ! [C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ A )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ C ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(177,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
<=> ! [C: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ A )
=> ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom171) ).
thf(1406,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
=> ! [C: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ A )
=> ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ B ) ) )
& ( ! [C: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ A )
=> ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ B ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(180,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ B ) @ C ) )
<=> ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom522) ).
thf(1426,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ B ) @ C ) )
=> ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ C ) ) )
& ( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ C ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(440,axiom,
! [A: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ '\'bot$d\'' @ A )
<=> ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ '\'bot$\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom368) ).
thf(2607,plain,
! [A: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ '\'bot$d\'' @ A )
=> ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ '\'bot$\'' ) )
& ( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ '\'bot$\'' )
=> ( '\'fun_app$a\'' @ '\'bot$d\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(471,axiom,
! [A: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ '\'finite$\'' @ A )
<=> ( ( A = '\'bot$a\'' )
| ? [B: '\'A_ltln_set$\'',C: '\'A_ltln$\''] :
( ( A
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ B ) )
& ( '\'fun_app$a\'' @ '\'finite$\'' @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom448) ).
thf(2740,plain,
! [A: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ '\'finite$\'' @ A )
=> ( ( A = '\'bot$a\'' )
| ? [B: '\'A_ltln_set$\'',C: '\'A_ltln$\''] :
( ( A
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ B ) )
& ( '\'fun_app$a\'' @ '\'finite$\'' @ B ) ) ) )
& ( ( ( A = '\'bot$a\'' )
| ? [B: '\'A_ltln_set$\'',C: '\'A_ltln$\''] :
( ( A
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ B ) )
& ( '\'fun_app$a\'' @ '\'finite$\'' @ B ) ) )
=> ( '\'fun_app$a\'' @ '\'finite$\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(45,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ C ) )
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom43) ).
thf(797,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ C ) )
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(516,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ B ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom188) ).
thf(2933,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ B ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(535,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C ) )
<=> ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom521) ).
thf(3004,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C ) )
=> ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ C ) ) )
& ( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ C ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(317,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom563) ).
thf(2035,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(277,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) @ C )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ C ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom573) ).
thf(1867,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) @ C )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ C ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(345,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ B ) @ A ) )
= '\'bot$a\'' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom545) ).
thf(2184,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ B ) @ A ) )
= '\'bot$a\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(412,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) @ C )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom38) ).
thf(2476,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) @ C )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(340,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\'',D: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ D ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ D ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom571) ).
thf(2168,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\'',D: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ D ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ D ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(22,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ) @ C )
& ( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ C )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ C ) )
=> $false ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom205) ).
thf(698,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
~ ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ) @ C )
& ~ ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ C )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(74,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
<=> ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom251) ).
thf(930,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
=> ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B )
= B ) )
& ( ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B )
= B )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(389,axiom,
! [A: '\'A_ltln_set_bool_fun$\'',B: '\'A_ltln_set$\''] :
( ( ! [C: '\'A_ltln_set$\''] :
( ~ ( '\'fun_app$a\'' @ '\'finite$\'' @ C )
=> ( '\'fun_app$a\'' @ A @ C ) )
& ( '\'fun_app$a\'' @ A @ '\'bot$a\'' )
& ! [C: '\'A_ltln$\'',D: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ '\'finite$\'' @ D )
& ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ C ) @ D )
& ( '\'fun_app$a\'' @ A @ D ) )
=> ( '\'fun_app$a\'' @ A @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ D ) ) ) )
=> ( '\'fun_app$a\'' @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom454) ).
thf(2360,plain,
! [A: '\'A_ltln_set_bool_fun$\'',B: '\'A_ltln_set$\''] :
( ( ! [C: '\'A_ltln_set$\''] :
( ~ ( '\'fun_app$a\'' @ '\'finite$\'' @ C )
=> ( '\'fun_app$a\'' @ A @ C ) )
& ( '\'fun_app$a\'' @ A @ '\'bot$a\'' )
& ! [C: '\'A_ltln$\'',D: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ '\'finite$\'' @ D )
& ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ C ) @ D )
& ( '\'fun_app$a\'' @ A @ D ) )
=> ( '\'fun_app$a\'' @ A @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ D ) ) ) )
=> ( '\'fun_app$a\'' @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(255,axiom,
! [A: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom11) ).
thf(1782,plain,
! [A: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(174,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'member$a\'' @ B ) @ A ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom358) ).
thf(1391,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'member$a\'' @ B ) @ A ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(290,axiom,
! [A: '\'A_ltln$\'',B: '\'A_ltln_bool_fun$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'filter$a\'' @ B ) @ C ) )
<=> ( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ C )
& ( '\'fun_app$\'' @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom104) ).
thf(1921,plain,
! [A: '\'A_ltln$\'',B: '\'A_ltln_bool_fun$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'filter$a\'' @ B ) @ C ) )
=> ( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ C )
& ( '\'fun_app$\'' @ B @ A ) ) )
& ( ( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ C )
& ( '\'fun_app$\'' @ B @ A ) )
=> ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'filter$a\'' @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(218,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( A = B )
<=> ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom183) ).
thf(1601,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( ( A = B )
=> ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ A ) ) )
& ( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(259,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\'',D: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ C ) @ D ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ C ) ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom217) ).
thf(1803,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\'',D: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ C ) @ D ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ C ) ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(144,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ '\'bot$\'' ) )
=> ( ( A = '\'bot$\'' )
| ( A
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ '\'bot$\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom457) ).
thf(1265,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ '\'bot$\'' ) )
=> ( ( A = '\'bot$\'' )
| ( A
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ '\'bot$\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(141,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ~ ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
=> ~ ( '\'fun_app$b\'' @ '\'finite$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom21) ).
thf(1254,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ~ ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
=> ~ ( '\'fun_app$b\'' @ '\'finite$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(401,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom507) ).
thf(2432,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(289,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set_a_ltln_set_set_fun$\'',D: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( ( '\'fun_app$k\'' @ C @ B )
= D )
& ! [E: '\'A_ltln_set$\'',F: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ E ) @ F )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$k\'' @ C @ E ) ) @ ( '\'fun_app$k\'' @ C @ F ) ) ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$k\'' @ C @ A ) ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom339) ).
thf(1914,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set_a_ltln_set_set_fun$\'',D: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( ( '\'fun_app$k\'' @ C @ B )
= D )
& ! [E: '\'A_ltln_set$\'',F: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ E ) @ F )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$k\'' @ C @ E ) ) @ ( '\'fun_app$k\'' @ C @ F ) ) ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$k\'' @ C @ A ) ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(594,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ C ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom613) ).
thf(3249,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ C ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(42,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\'',D: '\'A_ltln_set_set$\''] :
( ( A
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ C ) )
=> ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ D ) @ A )
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom65) ).
thf(782,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\'',D: '\'A_ltln_set_set$\''] :
( ( A
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ C ) )
=> ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ D ) @ A )
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(184,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ B )
=> ? [C: '\'A_ltln_set_set$\''] :
( ( B
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ C ) )
& ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom404) ).
thf(1441,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ B )
=> ? [C: '\'A_ltln_set_set$\''] :
( ( B
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ C ) )
& ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(84,axiom,
'\'comp_fun_idem$b\'' @ '\'insert$a\'',
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom401) ).
thf(973,plain,
'\'comp_fun_idem$b\'' @ '\'insert$a\'',
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(551,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ C ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom314) ).
thf(3088,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ C ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(604,axiom,
! [A: '\'A_ltln$\'',B: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ '\'bot$a\'' ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom427) ).
thf(3308,plain,
! [A: '\'A_ltln$\'',B: '\'A_ltln$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ '\'bot$a\'' ) )
=> ( A = B ) )
& ( ( A = B )
=> ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ '\'bot$a\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(293,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ '\'bot$a\'' ) )
<=> ( ( A = '\'bot$a\'' )
| ( A
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ '\'bot$a\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom456) ).
thf(1935,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ '\'bot$a\'' ) )
=> ( ( A = '\'bot$a\'' )
| ( A
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ '\'bot$a\'' ) ) ) )
& ( ( ( A = '\'bot$a\'' )
| ( A
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ '\'bot$a\'' ) ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ '\'bot$a\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(342,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_bool_fun$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ ( '\'collect$\'' @ B ) )
<=> ( '\'fun_app$a\'' @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom81) ).
thf(2173,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_bool_fun$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ ( '\'collect$\'' @ B ) )
=> ( '\'fun_app$a\'' @ B @ A ) )
& ( ( '\'fun_app$a\'' @ B @ A )
=> ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ ( '\'collect$\'' @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(169,axiom,
! [A: '\'A_ltln_set$\''] :
( ( '\'fun_app$i\'' @ '\'inf_fin$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ '\'bot$\'' ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom399) ).
thf(1366,plain,
! [A: '\'A_ltln_set$\''] :
( ( '\'fun_app$i\'' @ '\'inf_fin$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ '\'bot$\'' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(224,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom213) ).
thf(1628,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(596,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
<=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom278) ).
thf(3275,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B )
= B ) )
& ( ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B )
= B )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(151,axiom,
! [A: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ '\'bot$\'' ) @ A )
= '\'bot$\'' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom533) ).
thf(1298,plain,
! [A: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ '\'bot$\'' ) @ A )
= '\'bot$\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(557,axiom,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ B ) @ C ) )
<=> ( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ B )
& ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom517) ).
thf(3116,plain,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ B ) @ C ) )
=> ( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ B )
& ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ C ) ) )
& ( ( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ B )
& ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ C ) )
=> ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(612,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ B ) ) @ C )
<=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom624) ).
thf(3342,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ B ) ) @ C )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) ) )
& ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ B ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(546,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ '\'finite$\'' @ A )
| ( '\'fun_app$a\'' @ '\'finite$\'' @ B ) )
=> ( '\'fun_app$a\'' @ '\'finite$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom479) ).
thf(3061,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ '\'finite$\'' @ A )
| ( '\'fun_app$a\'' @ '\'finite$\'' @ B ) )
=> ( '\'fun_app$a\'' @ '\'finite$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(288,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ~ ( '\'fun_app$a\'' @ '\'finite$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) )
<=> ( ~ ( '\'fun_app$a\'' @ '\'finite$\'' @ A )
| ~ ( '\'fun_app$a\'' @ '\'finite$\'' @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom64) ).
thf(1907,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ~ ( '\'fun_app$a\'' @ '\'finite$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) )
=> ( ~ ( '\'fun_app$a\'' @ '\'finite$\'' @ A )
| ~ ( '\'fun_app$a\'' @ '\'finite$\'' @ B ) ) )
& ( ( ~ ( '\'fun_app$a\'' @ '\'finite$\'' @ A )
| ~ ( '\'fun_app$a\'' @ '\'finite$\'' @ B ) )
=> ~ ( '\'fun_app$a\'' @ '\'finite$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(353,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( A = B )
<=> ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom324) ).
thf(2217,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( A = B )
=> ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ A ) ) )
& ( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(559,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) @ C )
& ( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ C )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ C ) )
=> $false ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom240) ).
thf(3125,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
~ ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) @ C )
& ~ ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ C )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(211,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( '\'fun_app$b\'' @ '\'finite$a\'' @ B ) )
=> ( '\'fun_app$b\'' @ '\'finite$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom19) ).
thf(1577,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( '\'fun_app$b\'' @ '\'finite$a\'' @ B ) )
=> ( '\'fun_app$b\'' @ '\'finite$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(414,axiom,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ B ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ C ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom434) ).
thf(2488,plain,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ B ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ C ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(432,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom274) ).
thf(2571,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(158,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ B )
=> ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ C ) )
<=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom439) ).
thf(1323,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ B )
=> ( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ C ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ C ) )
& ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ C )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(3,axiom,
! [A: '\'A_ltln_bool_fun$\''] :
( ( ( '\'collect$a\'' @ A )
= '\'bot$a\'' )
<=> ! [B: '\'A_ltln$\''] :
~ ( '\'fun_app$\'' @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom96) ).
thf(619,plain,
! [A: '\'A_ltln_bool_fun$\''] :
( ( ( ( '\'collect$a\'' @ A )
= '\'bot$a\'' )
=> ! [B: '\'A_ltln$\''] :
~ ( '\'fun_app$\'' @ A @ B ) )
& ( ! [B: '\'A_ltln$\''] :
~ ( '\'fun_app$\'' @ A @ B )
=> ( ( '\'collect$a\'' @ A )
= '\'bot$a\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(370,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ C ) @ A ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom592) ).
thf(2274,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ C ) @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(23,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ) @ C )
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom37) ).
thf(702,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ) @ C )
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(172,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'disjnt$\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ B ) ) @ C )
<=> ( ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ C )
& ( '\'fun_app$b\'' @ ( '\'disjnt$\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom394) ).
thf(1379,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'disjnt$\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ B ) ) @ C )
=> ( ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ C )
& ( '\'fun_app$b\'' @ ( '\'disjnt$\'' @ B ) @ C ) ) )
& ( ( ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ C )
& ( '\'fun_app$b\'' @ ( '\'disjnt$\'' @ B ) @ C ) )
=> ( '\'fun_app$b\'' @ ( '\'disjnt$\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ B ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(114,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom506) ).
thf(1147,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(583,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom575) ).
thf(3216,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(246,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'minus$a\'' @ B ) @ A ) )
= '\'bot$\'' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom544) ).
thf(1741,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'minus$a\'' @ B ) @ A ) )
= '\'bot$\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(292,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( A = B )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom334) ).
thf(1931,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( A = B )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(226,axiom,
! [A: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ '\'bot$\'' )
<=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom93) ).
thf(1641,plain,
! [A: '\'A_ltln_set$\''] :
~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ '\'bot$\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(252,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( ( B
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ A ) )
=> $false ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom225) ).
thf(1773,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
~ ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( B
!= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(134,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ B )
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ '\'bot$\'' ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom459) ).
thf(1232,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ B )
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ '\'bot$\'' ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(271,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set_a_ltln_set_set_fun$\'',D: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$k\'' @ C @ B ) ) @ D )
& ! [E: '\'A_ltln_set$\'',F: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ E ) @ F )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$k\'' @ C @ E ) ) @ ( '\'fun_app$k\'' @ C @ F ) ) ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$k\'' @ C @ A ) ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom329) ).
thf(1847,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set_a_ltln_set_set_fun$\'',D: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$k\'' @ C @ B ) ) @ D )
& ! [E: '\'A_ltln_set$\'',F: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ E ) @ F )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$k\'' @ C @ E ) ) @ ( '\'fun_app$k\'' @ C @ F ) ) ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$k\'' @ C @ A ) ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(5,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( A != '\'bot$\'' )
& ( '\'fun_app$b\'' @ '\'finite$a\'' @ B ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$i\'' @ '\'inf_fin$a\'' @ B ) ) @ ( '\'fun_app$i\'' @ '\'inf_fin$a\'' @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom145) ).
thf(638,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( A != '\'bot$\'' )
& ( '\'fun_app$b\'' @ '\'finite$a\'' @ B ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$i\'' @ '\'inf_fin$a\'' @ B ) ) @ ( '\'fun_app$i\'' @ '\'inf_fin$a\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(58,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( ( A = B )
& ( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ A ) )
=> $false ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom158) ).
thf(853,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
~ ( ( A = B )
& ~ ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(409,axiom,
! [A: '\'A_ltln_set_bool_fun$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ A @ '\'bot$a\'' )
& ( ~ ( '\'fun_app$a\'' @ '\'finite$\'' @ B )
=> ( '\'fun_app$a\'' @ A @ B ) )
& ! [C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ '\'finite$\'' @ C )
& ( C != '\'bot$a\'' )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ B )
& ! [D: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ D ) @ C )
=> ( '\'fun_app$a\'' @ A @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ C ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ D ) @ '\'bot$a\'' ) ) ) ) )
=> ( '\'fun_app$a\'' @ A @ C ) ) )
=> ( '\'fun_app$a\'' @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom632) ).
thf(2456,plain,
! [A: '\'A_ltln_set_bool_fun$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ A @ '\'bot$a\'' )
& ( ~ ( '\'fun_app$a\'' @ '\'finite$\'' @ B )
=> ( '\'fun_app$a\'' @ A @ B ) )
& ! [C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ '\'finite$\'' @ C )
& ( C != '\'bot$a\'' )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ B )
& ! [D: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ D ) @ C )
=> ( '\'fun_app$a\'' @ A @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ C ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ D ) @ '\'bot$a\'' ) ) ) ) )
=> ( '\'fun_app$a\'' @ A @ C ) ) )
=> ( '\'fun_app$a\'' @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(343,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ B ) @ A )
& ( A != '\'bot$\'' ) )
=> ( ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ A ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom374) ).
thf(2178,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ B ) @ A )
& ( A != '\'bot$\'' ) )
=> ( ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ A ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(608,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom234) ).
thf(3322,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(532,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ C ) ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom620) ).
thf(2996,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ C ) ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(477,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\'',D: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ D ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ C ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom218) ).
thf(2782,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\'',D: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ D ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ C ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(506,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ C ) )
<=> ( ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ B ) @ A )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom391) ).
thf(2893,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ C ) )
=> ( ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ B ) @ A )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ A ) @ C ) ) )
& ( ( ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ B ) @ A )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ A ) @ C ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(366,axiom,
! [A: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ '\'is_empty$\'' @ A )
<=> ( A = '\'bot$a\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom347) ).
thf(2259,plain,
! [A: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ '\'is_empty$\'' @ A )
=> ( A = '\'bot$a\'' ) )
& ( ( A = '\'bot$a\'' )
=> ( '\'fun_app$a\'' @ '\'is_empty$\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(452,axiom,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ B )
=> ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom60) ).
thf(2650,plain,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ B )
=> ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(9,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ C ) @ B ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ C ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom207) ).
thf(646,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ C ) @ B ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ C ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(236,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ B ) @ C ) )
<=> ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom480) ).
thf(1682,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ B ) @ C ) )
=> ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ C ) ) )
& ( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ C ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(276,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom16) ).
thf(1864,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(514,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\'',D: '\'A_ltln_set$\''] :
( ( A
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ D )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom68) ).
thf(2925,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\'',D: '\'A_ltln_set$\''] :
( ( A
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ D )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(75,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ '\'bot$\'' )
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ '\'bot$\'' ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom422) ).
thf(937,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ '\'bot$\'' )
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ '\'bot$\'' ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(566,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_a_ltln_set_fun$\''] :
( ( ( '\'fun_app$a\'' @ '\'finite$\'' @ A )
& ! [C: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ C ) @ A )
=> ( '\'fun_app$a\'' @ '\'finite$\'' @ ( '\'fun_app$h\'' @ B @ C ) ) ) )
=> ( '\'fun_app$a\'' @ '\'finite$\'' @ ( '\'bind$c\'' @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom89) ).
thf(3152,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_a_ltln_set_fun$\''] :
( ( ( '\'fun_app$a\'' @ '\'finite$\'' @ A )
& ! [C: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ C ) @ A )
=> ( '\'fun_app$a\'' @ '\'finite$\'' @ ( '\'fun_app$h\'' @ B @ C ) ) ) )
=> ( '\'fun_app$a\'' @ '\'finite$\'' @ ( '\'bind$c\'' @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(314,axiom,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ B ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ C ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom556) ).
thf(2017,plain,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ B ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ C ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(33,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ~ ( '\'fun_app$b\'' @ '\'finite$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) )
<=> ( ~ ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
| ~ ( '\'fun_app$b\'' @ '\'finite$a\'' @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom63) ).
thf(756,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( ~ ( '\'fun_app$b\'' @ '\'finite$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) )
=> ( ~ ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
| ~ ( '\'fun_app$b\'' @ '\'finite$a\'' @ B ) ) )
& ( ( ~ ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
| ~ ( '\'fun_app$b\'' @ '\'finite$a\'' @ B ) )
=> ~ ( '\'fun_app$b\'' @ '\'finite$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(232,axiom,
! [A: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
<=> ( ( A = '\'bot$\'' )
| ? [B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set$\''] :
( ( A
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ B ) )
& ( '\'fun_app$b\'' @ '\'finite$a\'' @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom447) ).
thf(1664,plain,
! [A: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
=> ( ( A = '\'bot$\'' )
| ? [B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set$\''] :
( ( A
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ B ) )
& ( '\'fun_app$b\'' @ '\'finite$a\'' @ B ) ) ) )
& ( ( ( A = '\'bot$\'' )
| ? [B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set$\''] :
( ( A
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ B ) )
& ( '\'fun_app$b\'' @ '\'finite$a\'' @ B ) ) )
=> ( '\'fun_app$b\'' @ '\'finite$a\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(239,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( A = B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ C ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom305) ).
thf(1714,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( A = B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ C ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(316,axiom,
! [A: '\'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ! [D: '\'A_ltln_set$\'',E: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ D ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ A @ D ) @ E ) )
& ! [D: '\'A_ltln_set$\'',E: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ E ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ A @ D ) @ E ) )
& ! [D: '\'A_ltln_set$\'',E: '\'A_ltln_set$\'',F: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ E ) @ D )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ F ) @ D ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ A @ E ) @ F ) ) @ D ) ) )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom230) ).
thf(2027,plain,
! [A: '\'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ! [D: '\'A_ltln_set$\'',E: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ D ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ A @ D ) @ E ) )
& ! [D: '\'A_ltln_set$\'',E: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ E ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ A @ D ) @ E ) )
& ! [D: '\'A_ltln_set$\'',E: '\'A_ltln_set$\'',F: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ E ) @ D )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ F ) @ D ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ A @ E ) @ F ) ) @ D ) ) )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(408,axiom,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ B )
& ! [C: '\'A_ltln_set$\''] :
( ( ( B
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ C ) )
& ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ C ) )
=> $false ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom413) ).
thf(2451,plain,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\''] :
~ ( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ B )
& ! [C: '\'A_ltln_set$\''] :
~ ( ( B
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ C ) )
& ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(357,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( ( A
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) )
=> $false ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom609) ).
thf(2236,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
~ ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( A
!= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(374,axiom,
! [A: '\'A_ltln$\'',B: '\'A_ltln$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ C ) )
& ( ( A = B )
=> $false )
& ( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ C )
=> $false ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom419) ).
thf(2291,plain,
! [A: '\'A_ltln$\'',B: '\'A_ltln$\'',C: '\'A_ltln_set$\''] :
~ ( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ C ) )
& ( A != B )
& ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(364,axiom,
! [A: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ '\'bot$a\'' )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom196) ).
thf(2254,plain,
! [A: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ '\'bot$a\'' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(600,axiom,
! [A: '\'A_ltln_set$\''] :
( ! [B: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ B ) @ A )
=> $false )
=> ( A = '\'bot$a\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom156) ).
thf(3290,plain,
! [A: '\'A_ltln_set$\''] :
( ! [B: '\'A_ltln$\''] :
~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ B ) @ A )
=> ( A = '\'bot$a\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(48,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom512) ).
thf(806,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(553,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom566) ).
thf(3093,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(35,axiom,
! [A: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'minus$a\'' @ '\'bot$\'' ) @ A )
= '\'bot$\'' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom548) ).
thf(766,plain,
! [A: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'minus$a\'' @ '\'bot$\'' ) @ A )
= '\'bot$\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(270,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( B = C ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom308) ).
thf(1843,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( B = C ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(403,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom603) ).
thf(2437,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(282,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom28) ).
thf(1886,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(338,axiom,
! [A: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ '\'bot$a\'' )
<=> ( A = '\'bot$a\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom127) ).
thf(2137,plain,
! [A: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ '\'bot$a\'' )
=> ( A = '\'bot$a\'' ) )
& ( ( A = '\'bot$a\'' )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ '\'bot$a\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(166,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\''] :
( ( A = '\'bot$\'' )
=> ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom155) ).
thf(1351,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\''] :
( ( A = '\'bot$\'' )
=> ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(610,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom604) ).
thf(3327,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(198,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ B ) )
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom375) ).
thf(1521,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ B ) )
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(504,axiom,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ C ) ) @ B )
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom485) ).
thf(2884,plain,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ C ) ) @ B )
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(209,axiom,
! [A: '\'A_ltln_a_ltln_set_set_fun$\''] :
( ( '\'bind$\'' @ '\'bot$a\'' @ A )
= '\'bot$\'' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom135) ).
thf(1564,plain,
! [A: '\'A_ltln_a_ltln_set_set_fun$\''] :
( ( '\'bind$\'' @ '\'bot$a\'' @ A )
= '\'bot$\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(64,axiom,
! [A: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ '\'bot$\'' )
<=> ( A = '\'bot$\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom299) ).
thf(877,plain,
! [A: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ '\'bot$\'' )
=> ( A = '\'bot$\'' ) )
& ( ( A = '\'bot$\'' )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ '\'bot$\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(20,axiom,
! [A: '\'A_ltln_set$\''] :
( ( '\'collect$a\'' @ ( '\'uua$\'' @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom84) ).
thf(692,plain,
! [A: '\'A_ltln_set$\''] :
( ( '\'collect$a\'' @ ( '\'uua$\'' @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(222,axiom,
! [A: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ '\'bot$\'' ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom120) ).
thf(1622,plain,
! [A: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ '\'bot$\'' ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(38,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'member$a\'' @ B ) @ A ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$i\'' @ '\'inf_fin$a\'' @ A ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom143) ).
thf(774,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'member$a\'' @ B ) @ A ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$i\'' @ '\'inf_fin$a\'' @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(591,axiom,
'\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ '\'y$\'' ) @ ( '\'fun_app$h\'' @ '\'subformulas_nu$\'' @ '\'phi$\'' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom69) ).
thf(3243,plain,
'\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ '\'y$\'' ) @ ( '\'fun_app$h\'' @ '\'subformulas_nu$\'' @ '\'phi$\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(484,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) @ C )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ C ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom584) ).
thf(2809,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) @ C )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ C ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(164,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ C ) )
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom25) ).
thf(1345,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ C ) )
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(481,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) @ C )
& ( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ C )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ C ) )
=> $false ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom206) ).
thf(2799,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
~ ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) @ C )
& ~ ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ C )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(555,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_bool_fun$\''] :
( ! [D: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ D ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) )
=> ( '\'fun_app$\'' @ C @ D ) )
<=> ( ! [D: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ D ) @ A )
=> ( '\'fun_app$\'' @ C @ D ) )
& ! [D: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ D ) @ B )
=> ( '\'fun_app$\'' @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom54) ).
thf(3097,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_bool_fun$\''] :
( ( ! [D: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ D ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) )
=> ( '\'fun_app$\'' @ C @ D ) )
=> ( ! [D: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ D ) @ A )
=> ( '\'fun_app$\'' @ C @ D ) )
& ! [D: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ D ) @ B )
=> ( '\'fun_app$\'' @ C @ D ) ) ) )
& ( ( ! [D: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ D ) @ A )
=> ( '\'fun_app$\'' @ C @ D ) )
& ! [D: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ D ) @ B )
=> ( '\'fun_app$\'' @ C @ D ) ) )
=> ! [D: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ D ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) )
=> ( '\'fun_app$\'' @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(587,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\'',D: '\'A_ltln_set$\''] :
( ( A
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ D ) @ A )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom66) ).
thf(3229,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\'',D: '\'A_ltln_set$\''] :
( ( A
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ D ) @ A )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(350,axiom,
! [A: '\'A_ltln$\'',B: '\'A_ltln_bool_fun$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ ( '\'collect$a\'' @ B ) )
<=> ( '\'fun_app$\'' @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom82) ).
thf(2204,plain,
! [A: '\'A_ltln$\'',B: '\'A_ltln_bool_fun$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ ( '\'collect$a\'' @ B ) )
=> ( '\'fun_app$\'' @ B @ A ) )
& ( ( '\'fun_app$\'' @ B @ A )
=> ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ ( '\'collect$a\'' @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(238,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set$\'',D: '\'A_ltln_set_set$\''] :
( ( ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ B )
& ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ D ) )
=> ( ( ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ B )
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ D ) )
<=> ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: '\'A_ltln_set_set$\''] :
( ( B
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ E ) )
& ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ E )
& ( D
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ E ) )
& ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom408) ).
thf(1691,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set$\'',D: '\'A_ltln_set_set$\''] :
( ( ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ B )
& ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ D ) )
=> ( ( ( ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ B )
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ D ) )
=> ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: '\'A_ltln_set_set$\''] :
( ( B
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ E ) )
& ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ E )
& ( D
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ E ) )
& ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ E ) ) ) ) )
& ( ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: '\'A_ltln_set_set$\''] :
( ( B
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ E ) )
& ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ E )
& ( D
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ E ) )
& ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ E ) ) ) )
=> ( ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ B )
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(433,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom238) ).
thf(2574,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(572,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'member$a\'' @ B ) @ A ) )
=> ( ( ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'minus$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ '\'bot$\'' ) )
= '\'bot$\'' )
=> ( ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ A )
= B ) )
& ( ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'minus$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ '\'bot$\'' ) )
!= '\'bot$\'' )
=> ( ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ A )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'minus$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ '\'bot$\'' ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom474) ).
thf(3169,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'member$a\'' @ B ) @ A ) )
=> ( ( ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'minus$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ '\'bot$\'' ) )
= '\'bot$\'' )
=> ( ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ A )
= B ) )
& ( ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'minus$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ '\'bot$\'' ) )
!= '\'bot$\'' )
=> ( ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ A )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'minus$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ '\'bot$\'' ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(127,axiom,
! [A: '\'A_ltln_set_a_ltln_set_set_fun$\''] :
( ( '\'bind$b\'' @ '\'bot$\'' @ A )
= '\'bot$\'' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom137) ).
thf(1199,plain,
! [A: '\'A_ltln_set_a_ltln_set_set_fun$\''] :
( ( '\'bind$b\'' @ '\'bot$\'' @ A )
= '\'bot$\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(116,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ A ) )
=> ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom152) ).
thf(1153,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ A ) )
=> ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(163,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
<=> ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom223) ).
thf(1338,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
=> ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B )
= B ) )
& ( ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B )
= B )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(606,axiom,
! [A: '\'A_ltln$\''] : ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ '\'bot$a\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom381) ).
thf(3318,plain,
! [A: '\'A_ltln$\''] : ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ '\'bot$a\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(470,axiom,
! [A: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ '\'bot$a\'' )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom547) ).
thf(2737,plain,
! [A: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ '\'bot$a\'' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(455,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) @ C )
<=> ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ C )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom131) ).
thf(2660,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) @ C )
=> ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ C )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ C ) ) )
& ( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ C )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ C ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(509,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom248) ).
thf(2905,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(25,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ B )
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ '\'bot$\'' ) )
<=> ( ( A = C )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ '\'bot$\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom395) ).
thf(714,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set$\''] :
( ( ( ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ B )
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ '\'bot$\'' ) )
=> ( ( A = C )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ '\'bot$\'' ) ) ) )
& ( ( ( A = C )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ '\'bot$\'' ) ) )
=> ( ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ B )
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ '\'bot$\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(476,axiom,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln$\''] :
( ( ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ B )
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ '\'bot$a\'' ) )
<=> ( ( A = C )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ '\'bot$a\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom396) ).
thf(2773,plain,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln$\''] :
( ( ( ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ B )
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ '\'bot$a\'' ) )
=> ( ( A = C )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ '\'bot$a\'' ) ) ) )
& ( ( ( A = C )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ '\'bot$a\'' ) ) )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ B )
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ '\'bot$a\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(309,axiom,
! [A: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ '\'bot$a\'' )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom148) ).
thf(2000,plain,
! [A: '\'A_ltln$\''] :
~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ '\'bot$a\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(395,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) @ C )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom34) ).
thf(2409,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) @ C )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(242,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set_a_ltln_set_set_fun$\'',C: '\'A_ltln_set_set$\'',D: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$e\'' @ B @ C ) )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ C ) @ D )
& ! [E: '\'A_ltln_set_set$\'',F: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ E ) @ F )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$e\'' @ B @ E ) ) @ ( '\'fun_app$e\'' @ B @ F ) ) ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$e\'' @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom327) ).
thf(1723,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set_a_ltln_set_set_fun$\'',C: '\'A_ltln_set_set$\'',D: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$e\'' @ B @ C ) )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ C ) @ D )
& ! [E: '\'A_ltln_set_set$\'',F: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ E ) @ F )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$e\'' @ B @ E ) ) @ ( '\'fun_app$e\'' @ B @ F ) ) ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$e\'' @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(80,axiom,
! [A: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ '\'bot$\'' )
<=> ( A = '\'bot$\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom126) ).
thf(957,plain,
! [A: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ '\'bot$\'' )
=> ( A = '\'bot$\'' ) )
& ( ( A = '\'bot$\'' )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ '\'bot$\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(31,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
=> ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom233) ).
thf(746,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
=> ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(426,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ '\'finite$\'' @ A )
=> ( '\'fun_app$a\'' @ '\'finite$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom553) ).
thf(2541,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ '\'finite$\'' @ A )
=> ( '\'fun_app$a\'' @ '\'finite$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(437,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ~ ( '\'fun_app$a\'' @ '\'finite$\'' @ A ) )
=> ~ ( '\'fun_app$a\'' @ '\'finite$\'' @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom260) ).
thf(2596,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ~ ( '\'fun_app$a\'' @ '\'finite$\'' @ A ) )
=> ~ ( '\'fun_app$a\'' @ '\'finite$\'' @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(371,axiom,
! [A: '\'A_ltln_bool_fun$\'',B: '\'A_ltln_bool_fun$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'collect$a\'' @ A ) ) @ ( '\'collect$a\'' @ B ) )
<=> ! [C: '\'A_ltln$\''] :
( ( '\'fun_app$\'' @ A @ C )
=> ( '\'fun_app$\'' @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom190) ).
thf(2277,plain,
! [A: '\'A_ltln_bool_fun$\'',B: '\'A_ltln_bool_fun$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'collect$a\'' @ A ) ) @ ( '\'collect$a\'' @ B ) )
=> ! [C: '\'A_ltln$\''] :
( ( '\'fun_app$\'' @ A @ C )
=> ( '\'fun_app$\'' @ B @ C ) ) )
& ( ! [C: '\'A_ltln$\''] :
( ( '\'fun_app$\'' @ A @ C )
=> ( '\'fun_app$\'' @ B @ C ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'collect$a\'' @ A ) ) @ ( '\'collect$a\'' @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(60,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set_a_ltln_set_set_fun$\'',D: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( ( '\'fun_app$e\'' @ C @ B )
= D )
& ! [E: '\'A_ltln_set_set$\'',F: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ E ) @ F )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$e\'' @ C @ E ) ) @ ( '\'fun_app$e\'' @ C @ F ) ) ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$e\'' @ C @ A ) ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom341) ).
thf(862,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set_a_ltln_set_set_fun$\'',D: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( ( '\'fun_app$e\'' @ C @ B )
= D )
& ! [E: '\'A_ltln_set_set$\'',F: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ E ) @ F )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$e\'' @ C @ E ) ) @ ( '\'fun_app$e\'' @ C @ F ) ) ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$e\'' @ C @ A ) ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(233,axiom,
! [A: '\'A_ltln_set_set$\''] : ( '\'fun_app$b\'' @ ( '\'disjnt$\'' @ '\'bot$\'' ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom180) ).
thf(1676,plain,
! [A: '\'A_ltln_set_set$\''] : ( '\'fun_app$b\'' @ ( '\'disjnt$\'' @ '\'bot$\'' ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(562,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom511) ).
thf(3134,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(51,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ '\'bot$\'' )
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ C ) )
<=> ( ( B = A )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ C ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ '\'bot$\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom397) ).
thf(815,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ '\'bot$\'' )
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ C ) )
=> ( ( B = A )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ C ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ '\'bot$\'' ) ) ) )
& ( ( ( B = A )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ C ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ '\'bot$\'' ) ) )
=> ( ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ '\'bot$\'' )
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(392,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ B ) ) @ B )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom558) ).
thf(2396,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ B ) ) @ B )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(313,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ C ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom562) ).
thf(2015,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ C ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(264,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
=> ( '\'fun_app$b\'' @ '\'finite$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'minus$a\'' @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom552) ).
thf(1824,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
=> ( '\'fun_app$b\'' @ '\'finite$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'minus$a\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(221,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ C ) )
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom405) ).
thf(1619,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ C ) )
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(281,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom605) ).
thf(1883,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(208,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( A = B )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom333) ).
thf(1560,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( A = B )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(571,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ B ) @ A ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom557) ).
thf(3166,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ B ) @ A ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(268,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom216) ).
thf(1837,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(457,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ '\'finite$\'' @ A )
=> ( ( '\'fun_app$a\'' @ '\'finite$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ B ) @ A ) )
<=> ( '\'fun_app$a\'' @ '\'finite$\'' @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom555) ).
thf(2670,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ '\'finite$\'' @ A )
=> ( ( ( '\'fun_app$a\'' @ '\'finite$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ B ) @ A ) )
=> ( '\'fun_app$a\'' @ '\'finite$\'' @ B ) )
& ( ( '\'fun_app$a\'' @ '\'finite$\'' @ B )
=> ( '\'fun_app$a\'' @ '\'finite$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(121,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom540) ).
thf(1178,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(187,axiom,
! [A: '\'A_ltln_bool_fun$\''] :
( ( '\'bot$a\''
= ( '\'collect$a\'' @ A ) )
<=> ! [B: '\'A_ltln$\''] :
~ ( '\'fun_app$\'' @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom98) ).
thf(1457,plain,
! [A: '\'A_ltln_bool_fun$\''] :
( ( ( '\'bot$a\''
= ( '\'collect$a\'' @ A ) )
=> ! [B: '\'A_ltln$\''] :
~ ( '\'fun_app$\'' @ A @ B ) )
& ( ! [B: '\'A_ltln$\''] :
~ ( '\'fun_app$\'' @ A @ B )
=> ( '\'bot$a\''
= ( '\'collect$a\'' @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(344,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom254) ).
thf(2181,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(380,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ A ) @ B )
<=> ! [C: '\'A_ltln$\''] :
~ ( ( '\'fun_app$a\'' @ ( '\'member$\'' @ C ) @ A )
& ( '\'fun_app$a\'' @ ( '\'member$\'' @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom162) ).
thf(2327,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ A ) @ B )
=> ! [C: '\'A_ltln$\''] :
~ ( ( '\'fun_app$a\'' @ ( '\'member$\'' @ C ) @ A )
& ( '\'fun_app$a\'' @ ( '\'member$\'' @ C ) @ B ) ) )
& ( ! [C: '\'A_ltln$\''] :
~ ( ( '\'fun_app$a\'' @ ( '\'member$\'' @ C ) @ A )
& ( '\'fun_app$a\'' @ ( '\'member$\'' @ C ) @ B ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(540,axiom,
! [A: '\'A_ltln$\''] :
( ( '\'the_elem$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ '\'bot$a\'' ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom469) ).
thf(3028,plain,
! [A: '\'A_ltln$\''] :
( ( '\'the_elem$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ '\'bot$a\'' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(354,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom565) ).
thf(2228,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(85,axiom,
! [A: '\'A_ltln_set_set$\''] :
( ! [B: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ B ) @ A )
=> $false )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ '\'bot$\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom293) ).
thf(974,plain,
! [A: '\'A_ltln_set_set$\''] :
( ! [B: '\'A_ltln_set$\''] :
~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ B ) @ A )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ '\'bot$\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(475,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ! [D: '\'A_ltln_set$\'',E: '\'A_ltln_set$\'',F: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ D ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ E ) @ F ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ D ) @ E ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ D ) @ F ) ) )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom587) ).
thf(2769,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ! [D: '\'A_ltln_set$\'',E: '\'A_ltln_set$\'',F: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ D ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ E ) @ F ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ D ) @ E ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ D ) @ F ) ) )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(453,axiom,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ B )
=> ? [C: '\'A_ltln_set$\''] :
( ( B
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ C ) )
& ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom403) ).
thf(2653,plain,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ B )
=> ? [C: '\'A_ltln_set$\''] :
( ( B
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ C ) )
& ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(597,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ B ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ C ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom266) ).
thf(3282,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ B ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ C ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(522,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set_a_ltln_set_fun$\'',D: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ C @ B ) ) @ D )
& ! [E: '\'A_ltln_set$\'',F: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ E ) @ F )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ C @ E ) ) @ ( '\'fun_app$c\'' @ C @ F ) ) ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ C @ A ) ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom332) ).
thf(2958,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set_a_ltln_set_fun$\'',D: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ C @ B ) ) @ D )
& ! [E: '\'A_ltln_set$\'',F: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ E ) @ F )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ C @ E ) ) @ ( '\'fun_app$c\'' @ C @ F ) ) ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ C @ A ) ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(301,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln$\''] :
( ( '\'fun_app$\'' @ ( '\'uua$\'' @ A ) @ B )
<=> ( '\'fun_app$a\'' @ ( '\'member$\'' @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom0) ).
thf(1968,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln$\''] :
( ( ( '\'fun_app$\'' @ ( '\'uua$\'' @ A ) @ B )
=> ( '\'fun_app$a\'' @ ( '\'member$\'' @ B ) @ A ) )
& ( ( '\'fun_app$a\'' @ ( '\'member$\'' @ B ) @ A )
=> ( '\'fun_app$\'' @ ( '\'uua$\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(552,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom543) ).
thf(3090,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(430,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C ) )
& ( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ C ) )
=> $false ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom601) ).
thf(2565,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
~ ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C ) )
& ~ ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(563,axiom,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ B )
=> ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ C ) )
<=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom440) ).
thf(3137,plain,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ B )
=> ( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ C ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ C ) )
& ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ C )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(614,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
<=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom595) ).
thf(3349,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B )
= A ) )
& ( ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B )
= A )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(130,axiom,
! [A: '\'A_ltln_set_set$\''] : ( '\'fun_app$b\'' @ ( '\'disjnt$\'' @ A ) @ '\'bot$\'' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom182) ).
thf(1210,plain,
! [A: '\'A_ltln_set_set$\''] : ( '\'fun_app$b\'' @ ( '\'disjnt$\'' @ A ) @ '\'bot$\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(230,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
=> ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom271) ).
thf(1656,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
=> ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(100,axiom,
! [A: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'disjnt$\'' @ A ) @ A )
<=> ( A = '\'bot$\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom133) ).
thf(1089,plain,
! [A: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'disjnt$\'' @ A ) @ A )
=> ( A = '\'bot$\'' ) )
& ( ( A = '\'bot$\'' )
=> ( '\'fun_app$b\'' @ ( '\'disjnt$\'' @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(77,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
=> ( '\'fun_app$b\'' @ '\'finite$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom431) ).
thf(948,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
=> ( '\'fun_app$b\'' @ '\'finite$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(159,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
=> ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom273) ).
thf(1328,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
=> ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(434,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( A = B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ C ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom306) ).
thf(2577,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( A = B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ C ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(214,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ B )
=> ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom57) ).
thf(1587,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ B )
=> ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(101,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set_a_ltln_set_fun$\'',D: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$i\'' @ C @ B ) ) @ D )
& ! [E: '\'A_ltln_set_set$\'',F: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ E ) @ F )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$i\'' @ C @ E ) ) @ ( '\'fun_app$i\'' @ C @ F ) ) ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$i\'' @ C @ A ) ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom330) ).
thf(1096,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set_a_ltln_set_fun$\'',D: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$i\'' @ C @ B ) ) @ D )
& ! [E: '\'A_ltln_set_set$\'',F: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ E ) @ F )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$i\'' @ C @ E ) ) @ ( '\'fun_app$i\'' @ C @ F ) ) ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$i\'' @ C @ A ) ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(203,axiom,
! [A: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ '\'bot$\'' ) @ A )
= '\'bot$\'' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom539) ).
thf(1540,plain,
! [A: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ '\'bot$\'' ) @ A )
= '\'bot$\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(467,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'member$a\'' @ B ) @ A ) )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$i\'' @ '\'inf_fin$a\'' @ A ) ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom76) ).
thf(2724,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'member$a\'' @ B ) @ A ) )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$i\'' @ '\'inf_fin$a\'' @ A ) ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(61,axiom,
! [A: '\'A_ltln_set_set$\''] :
( ( '\'collect$\'' @ ( '\'uu$\'' @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom83) ).
thf(869,plain,
! [A: '\'A_ltln_set_set$\''] :
( ( '\'collect$\'' @ ( '\'uu$\'' @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(589,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'max$\'' @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom636) ).
thf(3237,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'max$\'' @ A ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(107,axiom,
( '\'bot$a\''
= ( '\'collect$a\'' @ '\'bot$c\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom301) ).
thf(1118,plain,
( '\'bot$a\''
= ( '\'collect$a\'' @ '\'bot$c\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(368,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ A ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom322) ).
thf(2268,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ A ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(534,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom30) ).
thf(3001,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(63,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ) @ C )
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom33) ).
thf(874,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ) @ C )
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(493,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ) @ C )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ C ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom582) ).
thf(2840,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ) @ C )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ C ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(558,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom214) ).
thf(3122,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(520,axiom,
! [A: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ '\'bot$a\'' )
<=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom92) ).
thf(2946,plain,
! [A: '\'A_ltln$\''] :
~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ '\'bot$a\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(530,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ B ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom579) ).
thf(2990,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ B ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(257,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
<=> ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom277) ).
thf(1794,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
=> ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B )
= B ) )
& ( ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B )
= B )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(91,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ A ) )
=> ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom150) ).
thf(1017,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ A ) )
=> ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(273,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C ) ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ C ) @ A ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom576) ).
thf(1856,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C ) ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ C ) @ A ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(27,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ A ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom321) ).
thf(725,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ A ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(210,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ '\'bot$\'' ) )
<=> ( ( A = '\'bot$\'' )
| ( A
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ '\'bot$\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom455) ).
thf(1567,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ '\'bot$\'' ) )
=> ( ( A = '\'bot$\'' )
| ( A
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ '\'bot$\'' ) ) ) )
& ( ( ( A = '\'bot$\'' )
| ( A
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ '\'bot$\'' ) ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ '\'bot$\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(65,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] : ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom247) ).
thf(884,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] : ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(119,axiom,
! [A: '\'A_ltln_set_set$\''] :
( ! [B: '\'A_ltln_set$\''] :
~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ B ) @ A )
<=> ( A = '\'bot$\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom95) ).
thf(1160,plain,
! [A: '\'A_ltln_set_set$\''] :
( ( ! [B: '\'A_ltln_set$\''] :
~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ B ) @ A )
=> ( A = '\'bot$\'' ) )
& ( ( A = '\'bot$\'' )
=> ! [B: '\'A_ltln_set$\''] :
~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(93,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ '\'bot$\'' )
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ C ) )
<=> ( ( ( B = '\'bot$\'' )
& ( C
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ '\'bot$\'' ) ) )
| ( ( B
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ '\'bot$\'' ) )
& ( C = '\'bot$\'' ) )
| ( ( B
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ '\'bot$\'' ) )
& ( C
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ '\'bot$\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom463) ).
thf(1028,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ '\'bot$\'' )
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ C ) )
=> ( ( ( B = '\'bot$\'' )
& ( C
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ '\'bot$\'' ) ) )
| ( ( B
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ '\'bot$\'' ) )
& ( C = '\'bot$\'' ) )
| ( ( B
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ '\'bot$\'' ) )
& ( C
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ '\'bot$\'' ) ) ) ) )
& ( ( ( ( B = '\'bot$\'' )
& ( C
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ '\'bot$\'' ) ) )
| ( ( B
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ '\'bot$\'' ) )
& ( C = '\'bot$\'' ) )
| ( ( B
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ '\'bot$\'' ) )
& ( C
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ '\'bot$\'' ) ) ) )
=> ( ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ '\'bot$\'' )
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(231,axiom,
! [A: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( A != '\'bot$\'' ) )
=> ? [B: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ B ) @ A )
& ! [C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ A )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ B ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom192) ).
thf(1659,plain,
! [A: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( A != '\'bot$\'' ) )
=> ? [B: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ B ) @ A )
& ! [C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ A )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ B ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(491,axiom,
! [A: '\'A_ltln_set$\''] :
( ? [B: '\'A_ltln$\''] : ( '\'fun_app$a\'' @ ( '\'member$\'' @ B ) @ A )
<=> ( A != '\'bot$a\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom169) ).
thf(2830,plain,
! [A: '\'A_ltln_set$\''] :
( ( ? [B: '\'A_ltln$\''] : ( '\'fun_app$a\'' @ ( '\'member$\'' @ B ) @ A )
=> ( A != '\'bot$a\'' ) )
& ( ( A != '\'bot$a\'' )
=> ? [B: '\'A_ltln$\''] : ( '\'fun_app$a\'' @ ( '\'member$\'' @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(398,axiom,
! [A: '\'A_ltln_bool_fun$\'',B: '\'A_ltln_bool_fun$\''] :
( ! [C: '\'A_ltln$\''] :
( ( '\'fun_app$\'' @ A @ C )
=> ( '\'fun_app$\'' @ B @ C ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'collect$a\'' @ A ) ) @ ( '\'collect$a\'' @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom176) ).
thf(2419,plain,
! [A: '\'A_ltln_bool_fun$\'',B: '\'A_ltln_bool_fun$\''] :
( ! [C: '\'A_ltln$\''] :
( ( '\'fun_app$\'' @ A @ C )
=> ( '\'fun_app$\'' @ B @ C ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'collect$a\'' @ A ) ) @ ( '\'collect$a\'' @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(536,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) )
<=> ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom78) ).
thf(3010,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) )
=> ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ A ) @ C ) ) )
& ( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ A ) @ C ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(358,axiom,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ B ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom376) ).
thf(2240,plain,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ B ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(213,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ C ) )
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom39) ).
thf(1584,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ C ) )
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(318,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_a_ltln_set_set_fun$\'',C: '\'A_ltln_set$\'',D: '\'A_ltln_set$\''] :
( ( ( A
= ( '\'fun_app$k\'' @ B @ C ) )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ D )
& ! [E: '\'A_ltln_set$\'',F: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ E ) @ F )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$k\'' @ B @ E ) ) @ ( '\'fun_app$k\'' @ B @ F ) ) ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$k\'' @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom335) ).
thf(2038,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_a_ltln_set_set_fun$\'',C: '\'A_ltln_set$\'',D: '\'A_ltln_set$\''] :
( ( ( A
= ( '\'fun_app$k\'' @ B @ C ) )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ D )
& ! [E: '\'A_ltln_set$\'',F: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ E ) @ F )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$k\'' @ B @ E ) ) @ ( '\'fun_app$k\'' @ B @ F ) ) ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$k\'' @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(329,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ) @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom503) ).
thf(2085,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(456,axiom,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ B )
!= '\'bot$a\'' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom423) ).
thf(2666,plain,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ B )
!= '\'bot$a\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(283,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C ) )
& ( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ C ) )
=> $false ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom614) ).
thf(1889,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
~ ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C ) )
& ~ ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(227,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_a_ltln_set_set_fun$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ! [C: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ A )
=> ( '\'fun_app$b\'' @ '\'finite$a\'' @ ( '\'fun_app$k\'' @ B @ C ) ) ) )
=> ( '\'fun_app$b\'' @ '\'finite$a\'' @ ( '\'bind$b\'' @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom88) ).
thf(1644,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_a_ltln_set_set_fun$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ! [C: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ A )
=> ( '\'fun_app$b\'' @ '\'finite$a\'' @ ( '\'fun_app$k\'' @ B @ C ) ) ) )
=> ( '\'fun_app$b\'' @ '\'finite$a\'' @ ( '\'bind$b\'' @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(219,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ B )
=> ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ C ) ) @ B )
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom484) ).
thf(1612,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ B )
=> ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ C ) ) @ B )
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(527,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) @ C )
<=> ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ A ) @ C )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom80) ).
thf(2978,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) @ C )
=> ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ A ) @ C )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ B ) @ C ) ) )
& ( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ A ) @ C )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ B ) @ C ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(601,axiom,
! [A: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom174) ).
thf(3294,plain,
! [A: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(117,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ B )
=> ( ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom410) ).
thf(1155,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ B )
=> ( ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(247,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ B ) ) @ C )
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom389) ).
thf(1744,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ B ) ) @ C )
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(419,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'max$\'' @ A ) @ B )
= B ) )
& ( ~ ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'max$\'' @ A ) @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom634) ).
thf(2504,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'max$\'' @ A ) @ B )
= B ) )
& ( ~ ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'max$\'' @ A ) @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(459,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\'',D: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ D ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ C ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom220) ).
thf(2681,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\'',D: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ D ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ C ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(201,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ C ) )
<=> ( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ B )
| ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom7) ).
thf(1530,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ C ) )
=> ( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ B )
| ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ C ) ) )
& ( ( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ B )
| ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ C ) )
=> ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(111,axiom,
! [A: '\'A_ltln_set$\''] :
( ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ '\'bot$\'' ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom400) ).
thf(1131,plain,
! [A: '\'A_ltln_set$\''] :
( ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ '\'bot$\'' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(359,axiom,
! [A: '\'A_ltln_set_bool_fun$\'',B: '\'A_ltln_set_bool_fun$\''] :
( ! [C: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ A @ C )
=> ( '\'fun_app$a\'' @ B @ C ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'collect$\'' @ A ) ) @ ( '\'collect$\'' @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom175) ).
thf(2243,plain,
! [A: '\'A_ltln_set_bool_fun$\'',B: '\'A_ltln_set_bool_fun$\''] :
( ! [C: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ A @ C )
=> ( '\'fun_app$a\'' @ B @ C ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'collect$\'' @ A ) ) @ ( '\'collect$\'' @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(295,axiom,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) )
& ( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ B )
=> $false )
& ( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ C )
=> $false ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom62) ).
thf(1947,plain,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
~ ( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) )
& ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ B )
& ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(305,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\'',D: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ D ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ C ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom264) ).
thf(1984,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\'',D: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ D ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ C ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(547,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) @ C )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ C ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom589) ).
thf(3064,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) @ C )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ C ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(390,axiom,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln$\'',D: '\'A_ltln_set$\''] :
( ( ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ B )
& ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ C ) @ D ) )
=> ( ( ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ B )
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ D ) )
<=> ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: '\'A_ltln_set$\''] :
( ( B
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ E ) )
& ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ C ) @ E )
& ( D
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ E ) )
& ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom407) ).
thf(2370,plain,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln$\'',D: '\'A_ltln_set$\''] :
( ( ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ B )
& ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ C ) @ D ) )
=> ( ( ( ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ B )
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ D ) )
=> ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: '\'A_ltln_set$\''] :
( ( B
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ E ) )
& ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ C ) @ E )
& ( D
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ E ) )
& ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ E ) ) ) ) )
& ( ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: '\'A_ltln_set$\''] :
( ( B
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ E ) )
& ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ C ) @ E )
& ( D
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ E ) )
& ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ E ) ) ) )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ B )
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(336,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C ) )
<=> ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom481) ).
thf(2125,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C ) )
=> ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ C ) ) )
& ( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ C ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(102,axiom,
! [A: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ '\'bot$\'' )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom195) ).
thf(1099,plain,
! [A: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ '\'bot$\'' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(115,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ) @ C )
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom31) ).
thf(1150,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ) @ C )
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(191,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ A ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom309) ).
thf(1478,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ A ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(438,axiom,
! [A: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ '\'finite$\'' @ A )
& ( ( A = '\'bot$a\'' )
=> $false )
& ! [B: '\'A_ltln_set$\'',C: '\'A_ltln$\''] :
( ( ( A
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ B ) )
& ( '\'fun_app$a\'' @ '\'finite$\'' @ B ) )
=> $false ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom446) ).
thf(2598,plain,
! [A: '\'A_ltln_set$\''] :
~ ( ( '\'fun_app$a\'' @ '\'finite$\'' @ A )
& ( A != '\'bot$a\'' )
& ! [B: '\'A_ltln_set$\'',C: '\'A_ltln$\''] :
~ ( ( A
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ B ) )
& ( '\'fun_app$a\'' @ '\'finite$\'' @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(545,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ C ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom600) ).
thf(3059,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ C ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(435,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( B != '\'bot$\'' )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ A ) )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ B ) ) @ ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ A ) )
= ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom354) ).
thf(2581,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( B != '\'bot$\'' )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ A ) )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ B ) ) @ ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ A ) )
= ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(410,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'uu$\'' @ A ) @ B )
<=> ( '\'fun_app$b\'' @ ( '\'member$a\'' @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom1) ).
thf(2465,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'uu$\'' @ A ) @ B )
=> ( '\'fun_app$b\'' @ ( '\'member$a\'' @ B ) @ A ) )
& ( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ B ) @ A )
=> ( '\'fun_app$a\'' @ ( '\'uu$\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(585,axiom,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ B )
=> ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ C ) )
=> ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom6) ).
thf(3222,plain,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ B )
=> ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ C ) )
=> ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(416,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C ) ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom619) ).
thf(2497,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C ) ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(474,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ) @ C )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ C ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom588) ).
thf(2766,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ) @ C )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ C ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(139,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ) @ C )
<=> ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ C )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom108) ).
thf(1246,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ) @ C )
=> ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ C )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ C ) ) )
& ( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ C )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ C ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(304,axiom,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln$\''] :
( ( ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ B )
=> ( A = C ) )
=> ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom379) ).
thf(1979,plain,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln$\''] :
( ( ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ B )
=> ( A = C ) )
=> ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(40,axiom,
'\'fun_app$b\'' @ '\'finite$a\'' @ '\'bot$\'',
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom279) ).
thf(779,plain,
'\'fun_app$b\'' @ '\'finite$a\'' @ '\'bot$\'',
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(549,axiom,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ B ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ C ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom487) ).
thf(3074,plain,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ B ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ C ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(251,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_bool_fun$\''] :
( ? [D: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ D ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) )
& ( '\'fun_app$a\'' @ C @ D ) )
<=> ( ? [D: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ D ) @ A )
& ( '\'fun_app$a\'' @ C @ D ) )
| ? [D: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ D ) @ B )
& ( '\'fun_app$a\'' @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom55) ).
thf(1759,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_bool_fun$\''] :
( ( ? [D: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ D ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) )
& ( '\'fun_app$a\'' @ C @ D ) )
=> ( ? [D: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ D ) @ A )
& ( '\'fun_app$a\'' @ C @ D ) )
| ? [D: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ D ) @ B )
& ( '\'fun_app$a\'' @ C @ D ) ) ) )
& ( ( ? [D: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ D ) @ A )
& ( '\'fun_app$a\'' @ C @ D ) )
| ? [D: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ D ) @ B )
& ( '\'fun_app$a\'' @ C @ D ) ) )
=> ? [D: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ D ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) )
& ( '\'fun_app$a\'' @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(175,axiom,
! [A: '\'A_ltln_a_ltln_set_fun$\''] :
( ( '\'bind$c\'' @ '\'bot$a\'' @ A )
= '\'bot$a\'' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom134) ).
thf(1393,plain,
! [A: '\'A_ltln_a_ltln_set_fun$\''] :
( ( '\'bind$c\'' @ '\'bot$a\'' @ A )
= '\'bot$a\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(161,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] : ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom201) ).
thf(1333,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] : ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(182,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
=> ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom231) ).
thf(1434,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
=> ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(128,axiom,
! [A: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ A ) @ '\'bot$\'' )
= '\'bot$\'' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom537) ).
thf(1202,plain,
! [A: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ A ) @ '\'bot$\'' )
= '\'bot$\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(254,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_bool_fun$\''] :
( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
=> ( '\'fun_app$b\'' @ '\'finite$a\'' @ ( '\'fun_app$e\'' @ ( '\'filter$\'' @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom71) ).
thf(1779,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_bool_fun$\''] :
( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
=> ( '\'fun_app$b\'' @ '\'finite$a\'' @ ( '\'fun_app$e\'' @ ( '\'filter$\'' @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(13,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ) @ C )
<=> ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ C )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom130) ).
thf(657,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ) @ C )
=> ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ C )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ C ) ) )
& ( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ C )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ C ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(120,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( A = B )
<=> ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom303) ).
thf(1167,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( ( A = B )
=> ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ A ) ) )
& ( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(220,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B )
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom29) ).
thf(1616,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B )
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(443,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ A ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom320) ).
thf(2617,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ A ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(383,axiom,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ C ) @ B ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ C ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom443) ).
thf(2338,plain,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ C ) @ B ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ C ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(308,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B )
= '\'bot$a\'' )
<=> ( ( A = '\'bot$a\'' )
& ( B = '\'bot$a\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom119) ).
thf(1991,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B )
= '\'bot$a\'' )
=> ( ( A = '\'bot$a\'' )
& ( B = '\'bot$a\'' ) ) )
& ( ( ( A = '\'bot$a\'' )
& ( B = '\'bot$a\'' ) )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B )
= '\'bot$a\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(156,axiom,
! [A: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ A ) @ '\'bot$\'' )
= '\'bot$\'' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom535) ).
thf(1318,plain,
! [A: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ A ) @ '\'bot$\'' )
= '\'bot$\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(99,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
| ( '\'fun_app$b\'' @ '\'finite$a\'' @ B ) )
=> ( '\'fun_app$b\'' @ '\'finite$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom478) ).
thf(1086,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
| ( '\'fun_app$b\'' @ '\'finite$a\'' @ B ) )
=> ( '\'fun_app$b\'' @ '\'finite$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(586,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ! [D: '\'A_ltln_set$\'',E: '\'A_ltln_set$\'',F: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ D ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ E ) @ F ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ D ) @ E ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ D ) @ F ) ) )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom586) ).
thf(3225,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ! [D: '\'A_ltln_set$\'',E: '\'A_ltln_set$\'',F: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ D ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ E ) @ F ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ D ) @ E ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ D ) @ F ) ) )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(137,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ A ) ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom441) ).
thf(1241,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ A ) ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(473,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln$\''] :
( ( A = '\'bot$a\'' )
=> ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom154) ).
thf(2761,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln$\''] :
( ( A = '\'bot$a\'' )
=> ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(124,axiom,
! [A: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ '\'bot$\'' ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom110) ).
thf(1187,plain,
! [A: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ '\'bot$\'' ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(404,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom272) ).
thf(2440,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(480,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) )
& ! [D: '\'A_ltln_set$\'',E: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ D ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ E ) @ C )
& ( A
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ D ) @ E ) ) )
=> $false ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom276) ).
thf(2793,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
~ ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) )
& ! [D: '\'A_ltln_set$\'',E: '\'A_ltln_set$\''] :
~ ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ D ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ E ) @ C )
& ( A
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ D ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(576,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom494) ).
thf(3190,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(339,axiom,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ '\'bot$a\'' )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) )
<=> ( ( ( B = '\'bot$a\'' )
& ( C
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ '\'bot$a\'' ) ) )
| ( ( B
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ '\'bot$a\'' ) )
& ( C = '\'bot$a\'' ) )
| ( ( B
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ '\'bot$a\'' ) )
& ( C
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ '\'bot$a\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom464) ).
thf(2144,plain,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ '\'bot$a\'' )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) )
=> ( ( ( B = '\'bot$a\'' )
& ( C
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ '\'bot$a\'' ) ) )
| ( ( B
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ '\'bot$a\'' ) )
& ( C = '\'bot$a\'' ) )
| ( ( B
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ '\'bot$a\'' ) )
& ( C
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ '\'bot$a\'' ) ) ) ) )
& ( ( ( ( B = '\'bot$a\'' )
& ( C
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ '\'bot$a\'' ) ) )
| ( ( B
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ '\'bot$a\'' ) )
& ( C = '\'bot$a\'' ) )
| ( ( B
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ '\'bot$a\'' ) )
& ( C
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ '\'bot$a\'' ) ) ) )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ '\'bot$a\'' )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(1,conjecture,
'\'fun_app$a\'' @ '\'finite$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ '\'x$\'' ) @ '\'y$\'' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture2) ).
thf(2,negated_conjecture,
~ ( '\'fun_app$a\'' @ '\'finite$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ '\'x$\'' ) @ '\'y$\'' ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(618,plain,
~ ( '\'fun_app$a\'' @ '\'finite$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ '\'x$\'' ) @ '\'y$\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(235,axiom,
! [A: '\'A_ltln_set_set$\''] : ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom289) ).
thf(1680,plain,
! [A: '\'A_ltln_set_set$\''] : ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(543,axiom,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom409) ).
thf(3042,plain,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(52,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ A ) @ B ) ) @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom502) ).
thf(824,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ A ) @ B ) ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(248,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
=> ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom235) ).
thf(1747,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
=> ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(291,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_bool_fun$\'',D: '\'A_ltln_bool_fun$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ! [E: '\'A_ltln$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'member$\'' @ E ) @ A )
& ( '\'fun_app$\'' @ C @ E ) )
=> ( '\'fun_app$\'' @ D @ E ) ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ ( '\'collect$a\'' @ C ) ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ ( '\'collect$a\'' @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom561) ).
thf(1927,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_bool_fun$\'',D: '\'A_ltln_bool_fun$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ! [E: '\'A_ltln$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'member$\'' @ E ) @ A )
& ( '\'fun_app$\'' @ C @ E ) )
=> ( '\'fun_app$\'' @ D @ E ) ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ ( '\'collect$a\'' @ C ) ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ ( '\'collect$a\'' @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(225,axiom,
! [A: '\'A_ltln_set_set_bool_fun$\'',B: '\'A_ltln_set_set$\''] :
( ( ! [C: '\'A_ltln_set_set$\''] :
( ~ ( '\'fun_app$b\'' @ '\'finite$a\'' @ C )
=> ( '\'fun_app$b\'' @ A @ C ) )
& ( '\'fun_app$b\'' @ A @ '\'bot$\'' )
& ! [C: '\'A_ltln_set$\'',D: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ D )
& ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ D )
& ( '\'fun_app$b\'' @ A @ D ) )
=> ( '\'fun_app$b\'' @ A @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ D ) ) ) )
=> ( '\'fun_app$b\'' @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom453) ).
thf(1631,plain,
! [A: '\'A_ltln_set_set_bool_fun$\'',B: '\'A_ltln_set_set$\''] :
( ( ! [C: '\'A_ltln_set_set$\''] :
( ~ ( '\'fun_app$b\'' @ '\'finite$a\'' @ C )
=> ( '\'fun_app$b\'' @ A @ C ) )
& ( '\'fun_app$b\'' @ A @ '\'bot$\'' )
& ! [C: '\'A_ltln_set$\'',D: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ D )
& ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ D )
& ( '\'fun_app$b\'' @ A @ D ) )
=> ( '\'fun_app$b\'' @ A @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ D ) ) ) )
=> ( '\'fun_app$b\'' @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(568,axiom,
! [A: '\'A_ltln$\'',B: '\'A_ltln$\''] :
( ( ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ '\'bot$a\'' )
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ '\'bot$a\'' ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom421) ).
thf(3158,plain,
! [A: '\'A_ltln$\'',B: '\'A_ltln$\''] :
( ( ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ '\'bot$a\'' )
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ '\'bot$a\'' ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(299,axiom,
! [A: '\'A_ltln_set_bool_fun$\'',B: '\'A_ltln_set_bool_fun$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'collect$\'' @ A ) ) @ ( '\'collect$\'' @ B ) )
<=> ! [C: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ A @ C )
=> ( '\'fun_app$a\'' @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom189) ).
thf(1959,plain,
! [A: '\'A_ltln_set_bool_fun$\'',B: '\'A_ltln_set_bool_fun$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'collect$\'' @ A ) ) @ ( '\'collect$\'' @ B ) )
=> ! [C: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ A @ C )
=> ( '\'fun_app$a\'' @ B @ C ) ) )
& ( ! [C: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ A @ C )
=> ( '\'fun_app$a\'' @ B @ C ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'collect$\'' @ A ) ) @ ( '\'collect$\'' @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(429,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ C ) )
= '\'bot$a\'' )
<=> ( ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ B ) @ A )
& ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ C )
= '\'bot$a\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom526) ).
thf(2556,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln$\'',C: '\'A_ltln_set$\''] :
( ( ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ C ) )
= '\'bot$a\'' )
=> ( ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ B ) @ A )
& ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ C )
= '\'bot$a\'' ) ) )
& ( ( ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ B ) @ A )
& ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ C )
= '\'bot$a\'' ) )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ C ) )
= '\'bot$a\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(152,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] : ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom245) ).
thf(1301,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] : ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(469,axiom,
! [A: '\'A_ltln$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ ( '\'fun_app$h\'' @ '\'subformulas_mu$\'' @ A ) ) @ ( '\'fun_app$h\'' @ '\'subformulas_nu$\'' @ A ) )
= '\'bot$a\'' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom626) ).
thf(2734,plain,
! [A: '\'A_ltln$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ ( '\'fun_app$h\'' @ '\'subformulas_mu$\'' @ A ) ) @ ( '\'fun_app$h\'' @ '\'subformulas_nu$\'' @ A ) )
= '\'bot$a\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(575,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom36) ).
thf(3187,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(267,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( A != '\'bot$\'' ) )
=> ( ( '\'fun_app$i\'' @ '\'inf_fin$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ A ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ ( '\'fun_app$i\'' @ '\'inf_fin$a\'' @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom477) ).
thf(1833,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( A != '\'bot$\'' ) )
=> ( ( '\'fun_app$i\'' @ '\'inf_fin$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ A ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ ( '\'fun_app$i\'' @ '\'inf_fin$a\'' @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(468,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
=> ( ( ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'minus$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ '\'bot$\'' ) )
= '\'bot$\'' )
=> ( ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ A ) )
= B ) )
& ( ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'minus$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ '\'bot$\'' ) )
!= '\'bot$\'' )
=> ( ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ A ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'minus$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ '\'bot$\'' ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom476) ).
thf(2727,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
=> ( ( ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'minus$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ '\'bot$\'' ) )
= '\'bot$\'' )
=> ( ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ A ) )
= B ) )
& ( ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'minus$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ '\'bot$\'' ) )
!= '\'bot$\'' )
=> ( ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ A ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'minus$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ '\'bot$\'' ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(109,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ) @ C )
& ( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ C )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ C ) )
=> $false ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom239) ).
thf(1125,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
~ ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ) @ C )
& ~ ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ C )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(391,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom42) ).
thf(2393,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(421,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( A = B )
<=> ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ A )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom316) ).
thf(2514,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( A = B )
=> ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ A )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B ) ) )
& ( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ A )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(483,axiom,
! [A: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ '\'bot$a\'' )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom125) ).
thf(2806,plain,
! [A: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ '\'bot$a\'' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(490,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ '\'finite$\'' @ B ) )
=> ( '\'fun_app$a\'' @ '\'finite$\'' @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom258) ).
thf(2827,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ '\'finite$\'' @ B ) )
=> ( '\'fun_app$a\'' @ '\'finite$\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(524,axiom,
'\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ '\'x$\'' ) @ ( '\'fun_app$h\'' @ '\'subformulas_mu$\'' @ '\'phi$\'' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom70) ).
thf(2970,plain,
'\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ '\'x$\'' ) @ ( '\'fun_app$h\'' @ '\'subformulas_mu$\'' @ '\'phi$\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(88,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( A
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom227) ).
thf(1007,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( A
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(588,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom501) ).
thf(3234,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(320,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( A = B )
<=> ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom184) ).
thf(2048,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( A = B )
=> ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ A ) ) )
& ( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(518,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_bool_fun$\''] :
( ( ( '\'fun_app$a\'' @ '\'finite$\'' @ A )
& ( '\'fun_app$a\'' @ B @ A )
& ! [C: '\'A_ltln$\'',D: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ '\'finite$\'' @ D )
& ( '\'fun_app$a\'' @ ( '\'member$\'' @ C ) @ D )
& ( '\'fun_app$a\'' @ B @ D ) )
=> ( '\'fun_app$a\'' @ B @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ D ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ '\'bot$a\'' ) ) ) ) )
=> ( '\'fun_app$a\'' @ B @ '\'bot$a\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom627) ).
thf(2938,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_bool_fun$\''] :
( ( ( '\'fun_app$a\'' @ '\'finite$\'' @ A )
& ( '\'fun_app$a\'' @ B @ A )
& ! [C: '\'A_ltln$\'',D: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ '\'finite$\'' @ D )
& ( '\'fun_app$a\'' @ ( '\'member$\'' @ C ) @ D )
& ( '\'fun_app$a\'' @ B @ D ) )
=> ( '\'fun_app$a\'' @ B @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ D ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ '\'bot$a\'' ) ) ) ) )
=> ( '\'fun_app$a\'' @ B @ '\'bot$a\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(479,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\'',D: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ D ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ C ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom612) ).
thf(2791,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\'',D: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ D ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ C ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(590,axiom,
! [A: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ '\'bot$a\'' )
= '\'bot$a\'' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom534) ).
thf(3240,plain,
! [A: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ '\'bot$a\'' )
= '\'bot$a\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(422,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
<=> ( B
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom244) ).
thf(2525,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( B
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ A ) ) )
& ( ( B
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ A ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(454,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln$\''] :
( ~ ( '\'fun_app$a\'' @ '\'finite$\'' @ A )
=> ~ ( '\'fun_app$a\'' @ '\'finite$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ '\'bot$a\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom629) ).
thf(2657,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln$\''] :
( ~ ( '\'fun_app$a\'' @ '\'finite$\'' @ A )
=> ~ ( '\'fun_app$a\'' @ '\'finite$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ '\'bot$a\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(6,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'disjnt$\'' @ C ) @ B ) )
=> ( '\'fun_app$b\'' @ ( '\'disjnt$\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ C ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom444) ).
thf(641,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'disjnt$\'' @ C ) @ B ) )
=> ( '\'fun_app$b\'' @ ( '\'disjnt$\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ C ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(43,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ A ) @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom500) ).
thf(787,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ A ) @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(611,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_a_ltln_bool_fun_fun$\''] :
( ( ( '\'fun_app$a\'' @ '\'finite$\'' @ A )
& ! [C: '\'A_ltln$\''] :
~ ( '\'fun_app$\'' @ ( '\'fun_app$l\'' @ B @ C ) @ C )
& ! [C: '\'A_ltln$\'',D: '\'A_ltln$\'',E: '\'A_ltln$\''] :
( ( ( '\'fun_app$\'' @ ( '\'fun_app$l\'' @ B @ C ) @ D )
& ( '\'fun_app$\'' @ ( '\'fun_app$l\'' @ B @ D ) @ E ) )
=> ( '\'fun_app$\'' @ ( '\'fun_app$l\'' @ B @ C ) @ E ) )
& ! [C: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ C ) @ A )
=> ? [D: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ D ) @ A )
& ( '\'fun_app$\'' @ ( '\'fun_app$l\'' @ B @ C ) @ D ) ) ) )
=> ( A = '\'bot$a\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom296) ).
thf(3330,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_a_ltln_bool_fun_fun$\''] :
( ( ( '\'fun_app$a\'' @ '\'finite$\'' @ A )
& ! [C: '\'A_ltln$\''] :
~ ( '\'fun_app$\'' @ ( '\'fun_app$l\'' @ B @ C ) @ C )
& ! [C: '\'A_ltln$\'',D: '\'A_ltln$\'',E: '\'A_ltln$\''] :
( ( ( '\'fun_app$\'' @ ( '\'fun_app$l\'' @ B @ C ) @ D )
& ( '\'fun_app$\'' @ ( '\'fun_app$l\'' @ B @ D ) @ E ) )
=> ( '\'fun_app$\'' @ ( '\'fun_app$l\'' @ B @ C ) @ E ) )
& ! [C: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ C ) @ A )
=> ? [D: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ D ) @ A )
& ( '\'fun_app$\'' @ ( '\'fun_app$l\'' @ B @ C ) @ D ) ) ) )
=> ( A = '\'bot$a\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(517,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'max$\'' @ B ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom635) ).
thf(2935,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'max$\'' @ B ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(104,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ C ) )
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom23) ).
thf(1107,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ C ) )
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(136,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\''] : ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom437) ).
thf(1239,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\''] : ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(464,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B )
= '\'bot$a\'' )
<=> ( ( A = '\'bot$a\'' )
& ( B = '\'bot$a\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom117) ).
thf(2706,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B )
= '\'bot$a\'' )
=> ( ( A = '\'bot$a\'' )
& ( B = '\'bot$a\'' ) ) )
& ( ( ( A = '\'bot$a\'' )
& ( B = '\'bot$a\'' ) )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B )
= '\'bot$a\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(71,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ B )
=> ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ B ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ C ) )
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom488) ).
thf(919,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ B )
=> ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ B ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ C ) )
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(188,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
<=> ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom249) ).
thf(1464,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
=> ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ A )
= B ) )
& ( ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ A )
= B )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(167,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
<=> ( B
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom243) ).
thf(1356,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
=> ( B
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ A ) ) )
& ( ( B
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ A ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(16,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ '\'finite$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ B ) )
<=> ( '\'fun_app$b\'' @ '\'finite$a\'' @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom383) ).
thf(672,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ B ) )
=> ( '\'fun_app$b\'' @ '\'finite$a\'' @ B ) )
& ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ B )
=> ( '\'fun_app$b\'' @ '\'finite$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(146,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'bot$\''
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) )
<=> ( ( A = '\'bot$\'' )
& ( B = '\'bot$\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom122) ).
thf(1271,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( ( '\'bot$\''
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) )
=> ( ( A = '\'bot$\'' )
& ( B = '\'bot$\'' ) ) )
& ( ( ( A = '\'bot$\'' )
& ( B = '\'bot$\'' ) )
=> ( '\'bot$\''
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(377,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_bool_fun$\''] :
( ( '\'fun_app$a\'' @ '\'finite$\'' @ A )
=> ( '\'fun_app$a\'' @ '\'finite$\'' @ ( '\'fun_app$c\'' @ ( '\'filter$a\'' @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom72) ).
thf(2308,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_bool_fun$\''] :
( ( '\'fun_app$a\'' @ '\'finite$\'' @ A )
=> ( '\'fun_app$a\'' @ '\'finite$\'' @ ( '\'fun_app$c\'' @ ( '\'filter$a\'' @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(550,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_bool_fun$\''] :
( ( ( '\'fun_app$a\'' @ '\'finite$\'' @ A )
& ( A != '\'bot$a\'' )
& ! [C: '\'A_ltln$\''] : ( '\'fun_app$a\'' @ B @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ '\'bot$a\'' ) )
& ! [C: '\'A_ltln$\'',D: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ '\'finite$\'' @ D )
& ( D != '\'bot$a\'' )
& ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ C ) @ D )
& ( '\'fun_app$a\'' @ B @ D ) )
=> ( '\'fun_app$a\'' @ B @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ D ) ) ) )
=> ( '\'fun_app$a\'' @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom452) ).
thf(3077,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_bool_fun$\''] :
( ( ( '\'fun_app$a\'' @ '\'finite$\'' @ A )
& ( A != '\'bot$a\'' )
& ! [C: '\'A_ltln$\''] : ( '\'fun_app$a\'' @ B @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ '\'bot$a\'' ) )
& ! [C: '\'A_ltln$\'',D: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ '\'finite$\'' @ D )
& ( D != '\'bot$a\'' )
& ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ C ) @ D )
& ( '\'fun_app$a\'' @ B @ D ) )
=> ( '\'fun_app$a\'' @ B @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ D ) ) ) )
=> ( '\'fun_app$a\'' @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(386,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( A = B )
& ( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ A ) )
=> $false ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom159) ).
thf(2346,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
~ ( ( A = B )
& ~ ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(378,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'bot$a\''
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) )
<=> ( ( A = '\'bot$a\'' )
& ( B = '\'bot$a\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom123) ).
thf(2311,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'bot$a\''
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) )
=> ( ( A = '\'bot$a\'' )
& ( B = '\'bot$a\'' ) ) )
& ( ( ( A = '\'bot$a\'' )
& ( B = '\'bot$a\'' ) )
=> ( '\'bot$a\''
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(69,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ '\'bot$\'' ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom430) ).
thf(900,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ '\'bot$\'' ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(425,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ A ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom442) ).
thf(2538,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ A ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(567,axiom,
! [A: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom493) ).
thf(3155,plain,
! [A: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(529,axiom,
! [A: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( A != '\'bot$\'' )
& ! [B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] : ( '\'fun_app$b\'' @ ( '\'member$a\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ '\'bot$\'' ) ) ) )
=> ( '\'fun_app$b\'' @ ( '\'member$a\'' @ ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ A ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom372) ).
thf(2987,plain,
! [A: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( A != '\'bot$\'' )
& ! [B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] : ( '\'fun_app$b\'' @ ( '\'member$a\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ '\'bot$\'' ) ) ) )
=> ( '\'fun_app$b\'' @ ( '\'member$a\'' @ ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(360,axiom,
! [A: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom292) ).
thf(2246,plain,
! [A: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(113,axiom,
! [A: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ '\'bot$\'' )
=> ( A = '\'bot$\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom297) ).
thf(1144,plain,
! [A: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ '\'bot$\'' )
=> ( A = '\'bot$\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(519,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom495) ).
thf(2943,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(258,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ B )
& ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ C ) )
=> ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'minus$a\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom514) ).
thf(1801,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ B )
& ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ C ) )
=> ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'minus$a\'' @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(498,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set_bool_fun$\''] :
( ( ( '\'fun_app$a\'' @ '\'finite$\'' @ A )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ C @ '\'bot$a\'' )
& ! [D: '\'A_ltln$\'',E: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ '\'finite$\'' @ E )
& ( '\'fun_app$a\'' @ ( '\'member$\'' @ D ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ E ) @ B )
& ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ D ) @ E )
& ( '\'fun_app$a\'' @ C @ E ) )
=> ( '\'fun_app$a\'' @ C @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ D ) @ E ) ) ) )
=> ( '\'fun_app$a\'' @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom466) ).
thf(2856,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set_bool_fun$\''] :
( ( ( '\'fun_app$a\'' @ '\'finite$\'' @ A )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ C @ '\'bot$a\'' )
& ! [D: '\'A_ltln$\'',E: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ '\'finite$\'' @ E )
& ( '\'fun_app$a\'' @ ( '\'member$\'' @ D ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ E ) @ B )
& ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ D ) @ E )
& ( '\'fun_app$a\'' @ C @ E ) )
=> ( '\'fun_app$a\'' @ C @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ D ) @ E ) ) ) )
=> ( '\'fun_app$a\'' @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(501,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ B ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom581) ).
thf(2871,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ B ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(349,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
<=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom252) ).
thf(2197,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B )
= B ) )
& ( ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B )
= B )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(148,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom215) ).
thf(1282,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(595,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln$\''] :
( ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B )
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ '\'bot$a\'' ) )
<=> ( ( ( A = '\'bot$a\'' )
& ( B
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ '\'bot$a\'' ) ) )
| ( ( A
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ '\'bot$a\'' ) )
& ( B = '\'bot$a\'' ) )
| ( ( A
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ '\'bot$a\'' ) )
& ( B
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ '\'bot$a\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom462) ).
thf(3251,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln$\''] :
( ( ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B )
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ '\'bot$a\'' ) )
=> ( ( ( A = '\'bot$a\'' )
& ( B
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ '\'bot$a\'' ) ) )
| ( ( A
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ '\'bot$a\'' ) )
& ( B = '\'bot$a\'' ) )
| ( ( A
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ '\'bot$a\'' ) )
& ( B
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ '\'bot$a\'' ) ) ) ) )
& ( ( ( ( A = '\'bot$a\'' )
& ( B
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ '\'bot$a\'' ) ) )
| ( ( A
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ '\'bot$a\'' ) )
& ( B = '\'bot$a\'' ) )
| ( ( A
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ '\'bot$a\'' ) )
& ( B
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ '\'bot$a\'' ) ) ) )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B )
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ '\'bot$a\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(449,axiom,
! [A: '\'A_ltln_set_bool_fun$\''] :
( ( ( '\'collect$\'' @ A )
= '\'bot$\'' )
<=> ! [B: '\'A_ltln_set$\''] :
~ ( '\'fun_app$a\'' @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom97) ).
thf(2637,plain,
! [A: '\'A_ltln_set_bool_fun$\''] :
( ( ( ( '\'collect$\'' @ A )
= '\'bot$\'' )
=> ! [B: '\'A_ltln_set$\''] :
~ ( '\'fun_app$a\'' @ A @ B ) )
& ( ! [B: '\'A_ltln_set$\''] :
~ ( '\'fun_app$a\'' @ A @ B )
=> ( ( '\'collect$\'' @ A )
= '\'bot$\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(399,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
<=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom250) ).
thf(2422,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ A )
= B ) )
& ( ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ A )
= B )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(599,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_a_ltln_set_fun$\'',C: '\'A_ltln_set$\'',D: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ B @ C ) )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ D )
& ! [E: '\'A_ltln_set$\'',F: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ E ) @ F )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ B @ E ) ) @ ( '\'fun_app$c\'' @ B @ F ) ) ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom328) ).
thf(3287,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_a_ltln_set_fun$\'',C: '\'A_ltln_set$\'',D: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ B @ C ) )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ D )
& ! [E: '\'A_ltln_set$\'',F: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ E ) @ F )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ B @ E ) ) @ ( '\'fun_app$c\'' @ B @ F ) ) ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(199,axiom,
! [A: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ '\'bot$\'' )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom112) ).
thf(1524,plain,
! [A: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ '\'bot$\'' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(365,axiom,
! [A: '\'A_ltln$\''] : ( '\'fun_app$a\'' @ '\'finite$\'' @ ( '\'fun_app$h\'' @ '\'subformulas_mu$\'' @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom287) ).
thf(2257,plain,
! [A: '\'A_ltln$\''] : ( '\'fun_app$a\'' @ '\'finite$\'' @ ( '\'fun_app$h\'' @ '\'subformulas_mu$\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(372,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
=> ( ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ A ) )
= ( '\'fun_app$i\'' @ ( '\'fold$a\'' @ '\'sup$\'' @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom639) ).
thf(2284,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
=> ( ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ A ) )
= ( '\'fun_app$i\'' @ ( '\'fold$a\'' @ '\'sup$\'' @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(584,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ A ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom103) ).
thf(3219,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ A ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(50,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( A != '\'bot$\'' )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ A ) ) @ B )
& ( ! [C: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ A )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ B ) )
=> $false ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom362) ).
thf(811,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\''] :
~ ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( A != '\'bot$\'' )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ A ) ) @ B )
& ~ ! [C: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ A )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(189,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ C ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom313) ).
thf(1471,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ C ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(263,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B )
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom27) ).
thf(1821,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B )
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(406,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom26) ).
thf(2446,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(275,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ '\'finite$\'' @ A )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ A ) )
=> ( '\'fun_app$a\'' @ '\'finite$\'' @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom262) ).
thf(1862,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ '\'finite$\'' @ A )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ A ) )
=> ( '\'fun_app$a\'' @ '\'finite$\'' @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(513,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ B ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ C ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom222) ).
thf(2923,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ B ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ C ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(4,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_a_ltln_set_bool_fun_fun$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ! [C: '\'A_ltln_set$\''] :
~ ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ B @ C ) @ C )
& ! [C: '\'A_ltln_set$\'',D: '\'A_ltln_set$\'',E: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ B @ C ) @ D )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ B @ D ) @ E ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ B @ C ) @ E ) )
& ! [C: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ A )
=> ? [D: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ D ) @ A )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ B @ C ) @ D ) ) ) )
=> ( A = '\'bot$\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom295) ).
thf(626,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_a_ltln_set_bool_fun_fun$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ! [C: '\'A_ltln_set$\''] :
~ ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ B @ C ) @ C )
& ! [C: '\'A_ltln_set$\'',D: '\'A_ltln_set$\'',E: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ B @ C ) @ D )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ B @ D ) @ E ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ B @ C ) @ E ) )
& ! [C: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ A )
=> ? [D: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ D ) @ A )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ B @ C ) @ D ) ) ) )
=> ( A = '\'bot$\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(36,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] : ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom203) ).
thf(769,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] : ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(363,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom596) ).
thf(2252,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(428,axiom,
! [A: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ '\'bot$a\'' ) @ A )
= '\'bot$a\'' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom538) ).
thf(2553,plain,
! [A: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ '\'bot$a\'' ) @ A )
= '\'bot$a\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(297,axiom,
! [A: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ '\'bot$a\'' )
= '\'bot$a\'' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom536) ).
thf(1952,plain,
! [A: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ '\'bot$a\'' )
= '\'bot$a\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(485,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ) @ B )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom496) ).
thf(2812,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ) @ B )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(448,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_bool_fun$\''] :
( ( ( '\'fun_app$a\'' @ '\'finite$\'' @ A )
& ( '\'fun_app$a\'' @ B @ '\'bot$a\'' )
& ! [C: '\'A_ltln$\'',D: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ '\'finite$\'' @ D )
& ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ C ) @ D )
& ( '\'fun_app$a\'' @ B @ D ) )
=> ( '\'fun_app$a\'' @ B @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ D ) ) ) )
=> ( '\'fun_app$a\'' @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom450) ).
thf(2632,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_bool_fun$\''] :
( ( ( '\'fun_app$a\'' @ '\'finite$\'' @ A )
& ( '\'fun_app$a\'' @ B @ '\'bot$a\'' )
& ! [C: '\'A_ltln$\'',D: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ '\'finite$\'' @ D )
& ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ C ) @ D )
& ( '\'fun_app$a\'' @ B @ D ) )
=> ( '\'fun_app$a\'' @ B @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ D ) ) ) )
=> ( '\'fun_app$a\'' @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(385,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom232) ).
thf(2343,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(447,axiom,
! [A: '\'A_ltln_set$\''] :
( ! [B: '\'A_ltln$\''] :
~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ B ) @ A )
<=> ( A = '\'bot$a\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom94) ).
thf(2625,plain,
! [A: '\'A_ltln_set$\''] :
( ( ! [B: '\'A_ltln$\''] :
~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ B ) @ A )
=> ( A = '\'bot$a\'' ) )
& ( ( A = '\'bot$a\'' )
=> ! [B: '\'A_ltln$\''] :
~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(81,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ B )
=> ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ B ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ C ) )
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom490) ).
thf(964,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ B )
=> ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ B ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ C ) )
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(502,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ) @ C )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) ) )
<=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom623) ).
thf(2874,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ) @ C )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ A ) )
& ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ A )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ) @ C )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(106,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ B ) @ C ) )
<=> ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom520) ).
thf(1112,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ B ) @ C ) )
=> ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ C ) ) )
& ( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ C ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(237,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom508) ).
thf(1688,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(19,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set_a_ltln_set_fun$\'',D: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( ( '\'fun_app$i\'' @ C @ B )
= D )
& ! [E: '\'A_ltln_set_set$\'',F: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ E ) @ F )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$i\'' @ C @ E ) ) @ ( '\'fun_app$i\'' @ C @ F ) ) ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$i\'' @ C @ A ) ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom340) ).
thf(685,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set_a_ltln_set_fun$\'',D: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( ( '\'fun_app$i\'' @ C @ B )
= D )
& ! [E: '\'A_ltln_set_set$\'',F: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ E ) @ F )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$i\'' @ C @ E ) ) @ ( '\'fun_app$i\'' @ C @ F ) ) ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$i\'' @ C @ A ) ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(87,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B )
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ '\'bot$\'' ) )
<=> ( ( ( A = '\'bot$\'' )
& ( B
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ '\'bot$\'' ) ) )
| ( ( A
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ '\'bot$\'' ) )
& ( B = '\'bot$\'' ) )
| ( ( A
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ '\'bot$\'' ) )
& ( B
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ '\'bot$\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom461) ).
thf(983,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set$\''] :
( ( ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B )
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ '\'bot$\'' ) )
=> ( ( ( A = '\'bot$\'' )
& ( B
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ '\'bot$\'' ) ) )
| ( ( A
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ '\'bot$\'' ) )
& ( B = '\'bot$\'' ) )
| ( ( A
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ '\'bot$\'' ) )
& ( B
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ '\'bot$\'' ) ) ) ) )
& ( ( ( ( A = '\'bot$\'' )
& ( B
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ '\'bot$\'' ) ) )
| ( ( A
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ '\'bot$\'' ) )
& ( B = '\'bot$\'' ) )
| ( ( A
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ '\'bot$\'' ) )
& ( B
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ '\'bot$\'' ) ) ) )
=> ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B )
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ '\'bot$\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(176,axiom,
! [A: '\'A_ltln_bool_fun$\'',B: '\'A_ltln_bool_fun$\''] :
( ! [C: '\'A_ltln$\''] :
( ( '\'fun_app$\'' @ A @ C )
<=> ( '\'fun_app$\'' @ B @ C ) )
=> ( ( '\'collect$a\'' @ A )
= ( '\'collect$a\'' @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom85) ).
thf(1396,plain,
! [A: '\'A_ltln_bool_fun$\'',B: '\'A_ltln_bool_fun$\''] :
( ! [C: '\'A_ltln$\''] :
( ( ( '\'fun_app$\'' @ A @ C )
=> ( '\'fun_app$\'' @ B @ C ) )
& ( ( '\'fun_app$\'' @ B @ C )
=> ( '\'fun_app$\'' @ A @ C ) ) )
=> ( ( '\'collect$a\'' @ A )
= ( '\'collect$a\'' @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(352,axiom,
! [A: '\'A_ltln$\''] :
( ( '\'fun_app$\'' @ '\'bot$c\'' @ A )
<=> ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ '\'bot$a\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom367) ).
thf(2212,plain,
! [A: '\'A_ltln$\''] :
( ( ( '\'fun_app$\'' @ '\'bot$c\'' @ A )
=> ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ '\'bot$a\'' ) )
& ( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ '\'bot$a\'' )
=> ( '\'fun_app$\'' @ '\'bot$c\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(53,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ) @ C )
<=> ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ C )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom106) ).
thf(827,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ) @ C )
=> ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ C )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ C ) ) )
& ( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ C )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ C ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(21,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) )
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom45) ).
thf(695,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) )
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(41,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] : ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom269) ).
thf(780,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] : ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(373,axiom,
! [A: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ '\'bot$a\'' )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom286) ).
thf(2288,plain,
! [A: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ '\'bot$a\'' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(537,axiom,
! [A: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ '\'bot$a\'' ) @ A )
= '\'bot$a\'' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom549) ).
thf(3016,plain,
! [A: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ '\'bot$a\'' ) @ A )
= '\'bot$a\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(472,axiom,
! [A: '\'A_ltln$\'',B: '\'A_ltln$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ C ) )
<=> ( ( A = B )
| ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom377) ).
thf(2752,plain,
! [A: '\'A_ltln$\'',B: '\'A_ltln$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ C ) )
=> ( ( A = B )
| ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ C ) ) )
& ( ( ( A = B )
| ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ C ) )
=> ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(424,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ) @ B )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom497) ).
thf(2535,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ) @ B )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(243,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ B ) ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ C ) )
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom486) ).
thf(1726,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ B ) ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ C ) )
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(103,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\'',D: '\'A_ltln_set_set$\''] :
( ( A
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ C ) )
=> ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ D )
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom67) ).
thf(1102,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\'',D: '\'A_ltln_set_set$\''] :
( ( A
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ C ) )
=> ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ D )
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(462,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( A = B )
<=> ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom304) ).
thf(2693,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( A = B )
=> ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ A ) ) )
& ( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(323,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ A ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom186) ).
thf(2069,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ A ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(185,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'bot$\''
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ B ) ) @ C ) )
<=> ( ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ C )
& ( '\'bot$\''
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom529) ).
thf(1445,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( '\'bot$\''
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ B ) ) @ C ) )
=> ( ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ C )
& ( '\'bot$\''
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ B ) @ C ) ) ) )
& ( ( ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ C )
& ( '\'bot$\''
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ B ) @ C ) ) )
=> ( '\'bot$\''
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ B ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(445,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'member$\'' @ C ) @ A ) )
=> ( '\'fun_app$a\'' @ ( '\'member$\'' @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom153) ).
thf(2620,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'member$\'' @ C ) @ A ) )
=> ( '\'fun_app$a\'' @ ( '\'member$\'' @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(609,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom210) ).
thf(3325,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(564,axiom,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ B )
=> ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom58) ).
thf(3142,plain,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ B )
=> ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(528,axiom,
! [A: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ '\'bot$a\'' ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom284) ).
thf(2984,plain,
! [A: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ '\'bot$a\'' ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(302,axiom,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ B )
=> ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom415) ).
thf(1973,plain,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ B )
=> ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(260,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ C ) @ A ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom319) ).
thf(1805,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ C ) @ A ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(442,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom48) ).
thf(2614,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(14,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ B )
=> ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ C ) )
=> ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom5) ).
thf(663,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ B )
=> ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ C ) )
=> ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(73,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom435) ).
thf(927,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(407,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom204) ).
thf(2449,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(507,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ '\'bot$a\'' ) )
=> ( ( A = '\'bot$a\'' )
| ( A
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ '\'bot$a\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom458) ).
thf(2899,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ '\'bot$a\'' ) )
=> ( ( A = '\'bot$a\'' )
| ( A
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ '\'bot$a\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(311,axiom,
! [A: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom12) ).
thf(2005,plain,
! [A: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(178,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set_a_ltln_set_set_fun$\'',C: '\'A_ltln_set_set$\'',D: '\'A_ltln_set_set$\''] :
( ( ( A
= ( '\'fun_app$e\'' @ B @ C ) )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ C ) @ D )
& ! [E: '\'A_ltln_set_set$\'',F: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ E ) @ F )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$e\'' @ B @ E ) ) @ ( '\'fun_app$e\'' @ B @ F ) ) ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$e\'' @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom337) ).
thf(1413,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set_a_ltln_set_set_fun$\'',C: '\'A_ltln_set_set$\'',D: '\'A_ltln_set_set$\''] :
( ( ( A
= ( '\'fun_app$e\'' @ B @ C ) )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ C ) @ D )
& ! [E: '\'A_ltln_set_set$\'',F: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ E ) @ F )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$e\'' @ B @ E ) ) @ ( '\'fun_app$e\'' @ B @ F ) ) ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$e\'' @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(511,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) @ C )
<=> ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ C )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom109) ).
thf(2914,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) @ C )
=> ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ C )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ C ) ) )
& ( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ C )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ C ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(541,axiom,
! [A: '\'A_ltln$\'',B: '\'A_ltln$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ '\'bot$a\'' )
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ C ) )
<=> ( ( B = A )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ '\'bot$a\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom398) ).
thf(3031,plain,
! [A: '\'A_ltln$\'',B: '\'A_ltln$\'',C: '\'A_ltln_set$\''] :
( ( ( ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ '\'bot$a\'' )
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ C ) )
=> ( ( B = A )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ '\'bot$a\'' ) ) ) )
& ( ( ( B = A )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ '\'bot$a\'' ) ) )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ '\'bot$a\'' )
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(279,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_bool_fun$\''] :
( ( ( '\'fun_app$a\'' @ '\'finite$\'' @ A )
& ( '\'fun_app$a\'' @ B @ '\'bot$a\'' )
& ! [C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ '\'finite$\'' @ C )
& ( C != '\'bot$a\'' )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ A )
& ! [D: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ D ) @ C )
=> ( '\'fun_app$a\'' @ B @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ C ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ D ) @ '\'bot$a\'' ) ) ) ) )
=> ( '\'fun_app$a\'' @ B @ C ) ) )
=> ( '\'fun_app$a\'' @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom633) ).
thf(1873,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_bool_fun$\''] :
( ( ( '\'fun_app$a\'' @ '\'finite$\'' @ A )
& ( '\'fun_app$a\'' @ B @ '\'bot$a\'' )
& ! [C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ '\'finite$\'' @ C )
& ( C != '\'bot$a\'' )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ A )
& ! [D: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ D ) @ C )
=> ( '\'fun_app$a\'' @ B @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ C ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ D ) @ '\'bot$a\'' ) ) ) ) )
=> ( '\'fun_app$a\'' @ B @ C ) ) )
=> ( '\'fun_app$a\'' @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(577,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ B )
= '\'bot$a\'' )
<=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom559) ).
thf(3193,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ B )
= '\'bot$a\'' )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B ) )
& ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ B )
= '\'bot$a\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(478,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
<=> ( A
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom598) ).
thf(2784,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( A
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ) )
& ( ( A
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(369,axiom,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ B ) ) @ C )
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom390) ).
thf(2271,plain,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ B ) ) @ C )
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(579,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ B ) @ A ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom625) ).
thf(3206,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ B ) @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(569,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( A
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom608) ).
thf(3161,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( A
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(287,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ B ) ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom570) ).
thf(1905,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ B ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(179,axiom,
! [A: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( ( A = '\'bot$\'' )
=> $false )
& ! [B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set$\''] :
( ( ( A
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ B ) )
& ( '\'fun_app$b\'' @ '\'finite$a\'' @ B ) )
=> $false ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom445) ).
thf(1420,plain,
! [A: '\'A_ltln_set_set$\''] :
~ ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( A != '\'bot$\'' )
& ! [B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set$\''] :
~ ( ( A
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ B ) )
& ( '\'fun_app$b\'' @ '\'finite$a\'' @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(112,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( A != '\'bot$\'' ) )
=> ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ ( '\'fun_app$i\'' @ '\'inf_fin$a\'' @ A ) )
<=> ! [C: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ A )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom147) ).
thf(1134,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( A != '\'bot$\'' ) )
=> ( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ ( '\'fun_app$i\'' @ '\'inf_fin$a\'' @ A ) )
=> ! [C: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ A )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ C ) ) )
& ( ! [C: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ A )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ C ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ ( '\'fun_app$i\'' @ '\'inf_fin$a\'' @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(10,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ B )
!= '\'bot$\'' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom424) ).
thf(648,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ B )
!= '\'bot$\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(98,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'member$a\'' @ B ) @ A ) )
=> ? [C: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ A )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ C )
& ! [D: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ D ) @ A )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ D ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom198) ).
thf(1081,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'member$a\'' @ B ) @ A ) )
=> ? [C: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ A )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ C )
& ! [D: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ D ) @ A )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ D ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(32,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set_bool_fun$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ C @ '\'bot$\'' )
& ! [D: '\'A_ltln_set$\'',E: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ E )
& ( '\'fun_app$b\'' @ ( '\'member$a\'' @ D ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ E ) @ B )
& ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ D ) @ E )
& ( '\'fun_app$b\'' @ C @ E ) )
=> ( '\'fun_app$b\'' @ C @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ D ) @ E ) ) ) )
=> ( '\'fun_app$b\'' @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom465) ).
thf(749,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set_bool_fun$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ C @ '\'bot$\'' )
& ! [D: '\'A_ltln_set$\'',E: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ E )
& ( '\'fun_app$b\'' @ ( '\'member$a\'' @ D ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ E ) @ B )
& ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ D ) @ E )
& ( '\'fun_app$b\'' @ C @ E ) )
=> ( '\'fun_app$b\'' @ C @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ D ) @ E ) ) ) )
=> ( '\'fun_app$b\'' @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(82,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ C ) )
& ( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ B )
=> $false )
& ( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ C )
=> $false ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom61) ).
thf(968,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
~ ( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ C ) )
& ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ B )
& ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(122,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
=> ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom237) ).
thf(1181,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
=> ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(55,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) )
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom41) ).
thf(836,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) )
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(207,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B )
= '\'bot$\'' )
<=> ( ( A = '\'bot$\'' )
& ( B = '\'bot$\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom90) ).
thf(1551,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B )
= '\'bot$\'' )
=> ( ( A = '\'bot$\'' )
& ( B = '\'bot$\'' ) ) )
& ( ( ( A = '\'bot$\'' )
& ( B = '\'bot$\'' ) )
=> ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B )
= '\'bot$\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(39,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ A ) @ B ) ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom504) ).
thf(776,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ A ) @ B ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(465,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set_a_ltln_set_fun$\'',D: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( ( '\'fun_app$c\'' @ C @ B )
= D )
& ! [E: '\'A_ltln_set$\'',F: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ E ) @ F )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ C @ E ) ) @ ( '\'fun_app$c\'' @ C @ F ) ) ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ C @ A ) ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom342) ).
thf(2715,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set_a_ltln_set_fun$\'',D: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( ( '\'fun_app$c\'' @ C @ B )
= D )
& ! [E: '\'A_ltln_set$\'',F: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ E ) @ F )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ C @ E ) ) @ ( '\'fun_app$c\'' @ C @ F ) ) ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ C @ A ) ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(62,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ C ) @ B ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ C ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom433) ).
thf(872,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ C ) @ B ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ C ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(24,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ C ) )
<=> ( ( A = B )
| ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom378) ).
thf(705,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ C ) )
=> ( ( A = B )
| ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ C ) ) )
& ( ( ( A = B )
| ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ C ) )
=> ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(228,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
<=> ! [C: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ A )
=> ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom160) ).
thf(1647,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
=> ! [C: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ A )
=> ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ B ) ) )
& ( ! [C: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ A )
=> ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ B ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(560,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom513) ).
thf(3129,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(505,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ '\'finite$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ C ) ) )
<=> ( '\'fun_app$a\'' @ '\'finite$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom560) ).
thf(2888,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ '\'finite$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ C ) ) )
=> ( '\'fun_app$a\'' @ '\'finite$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ C ) ) )
& ( ( '\'fun_app$a\'' @ '\'finite$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ C ) )
=> ( '\'fun_app$a\'' @ '\'finite$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(499,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom618) ).
thf(2863,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(605,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom574) ).
thf(3315,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(582,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ '\'finite$\'' @ A )
& ( '\'fun_app$a\'' @ '\'finite$\'' @ B ) )
=> ( '\'fun_app$a\'' @ '\'finite$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom20) ).
thf(3214,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ '\'finite$\'' @ A )
& ( '\'fun_app$a\'' @ '\'finite$\'' @ B ) )
=> ( '\'fun_app$a\'' @ '\'finite$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(83,axiom,
! [A: '\'A_ltln_set_set$\''] : ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ '\'bot$\'' ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom345) ).
thf(971,plain,
! [A: '\'A_ltln_set_set$\''] : ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ '\'bot$\'' ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(79,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B )
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom47) ).
thf(954,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B )
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(140,axiom,
! [A: '\'A_ltln_set$\''] : ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ '\'bot$\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom382) ).
thf(1252,plain,
! [A: '\'A_ltln_set$\''] : ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ '\'bot$\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(488,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom597) ).
thf(2821,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(580,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ C ) @ A ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom610) ).
thf(3209,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ C ) @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(496,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ '\'finite$\'' @ A )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ B ) @ A )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ ( '\'fold$\'' @ '\'remove$\'' ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom638) ).
thf(2850,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ '\'finite$\'' @ A )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ B ) @ A )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ ( '\'fold$\'' @ '\'remove$\'' ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(193,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'disjnt$\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ) @ C )
<=> ( ( '\'fun_app$b\'' @ ( '\'disjnt$\'' @ A ) @ C )
& ( '\'fun_app$b\'' @ ( '\'disjnt$\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom79) ).
thf(1484,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'disjnt$\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ) @ C )
=> ( ( '\'fun_app$b\'' @ ( '\'disjnt$\'' @ A ) @ C )
& ( '\'fun_app$b\'' @ ( '\'disjnt$\'' @ B ) @ C ) ) )
& ( ( ( '\'fun_app$b\'' @ ( '\'disjnt$\'' @ A ) @ C )
& ( '\'fun_app$b\'' @ ( '\'disjnt$\'' @ B ) @ C ) )
=> ( '\'fun_app$b\'' @ ( '\'disjnt$\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(538,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) @ C )
<=> ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ C )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom107) ).
thf(3019,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) @ C )
=> ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ C )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ C ) ) )
& ( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ C )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ C ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(331,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom564) ).
thf(2092,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(181,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\'',D: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ C ) @ D ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ C ) ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom263) ).
thf(1432,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\'',D: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ C ) @ D ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ C ) ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(512,axiom,
! [A: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom492) ).
thf(2920,plain,
! [A: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(256,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ B ) ) @ C )
= '\'bot$\'' )
<=> ( ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ C )
& ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ B ) @ C )
= '\'bot$\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom531) ).
thf(1785,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ B ) ) @ C )
= '\'bot$\'' )
=> ( ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ C )
& ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ B ) @ C )
= '\'bot$\'' ) ) )
& ( ( ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ C )
& ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ B ) @ C )
= '\'bot$\'' ) )
=> ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ B ) ) @ C )
= '\'bot$\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(400,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom499) ).
thf(2429,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(266,axiom,
! [A: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ A )
= '\'bot$a\'' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom551) ).
thf(1830,plain,
! [A: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ A )
= '\'bot$a\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(78,axiom,
! [A: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom49) ).
thf(951,plain,
! [A: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(212,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set$\''] :
( ( ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ B )
=> ( A = C ) )
=> ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom380) ).
thf(1579,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set$\''] :
( ( ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ B )
=> ( A = C ) )
=> ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(7,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'disjnt$\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ C ) @ B ) )
=> ( '\'fun_app$b\'' @ ( '\'disjnt$\'' @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom187) ).
thf(643,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'disjnt$\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ C ) @ B ) )
=> ( '\'fun_app$b\'' @ ( '\'disjnt$\'' @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(132,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B )
= '\'bot$\'' )
<=> ( ( A = '\'bot$\'' )
& ( B = '\'bot$\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom118) ).
thf(1220,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B )
= '\'bot$\'' )
=> ( ( A = '\'bot$\'' )
& ( B = '\'bot$\'' ) ) )
& ( ( ( A = '\'bot$\'' )
& ( B = '\'bot$\'' ) )
=> ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B )
= '\'bot$\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(387,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom40) ).
thf(2354,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(431,axiom,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ B )
& ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ C ) )
=> ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom515) ).
thf(2569,plain,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ B )
& ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ C ) )
=> ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(593,axiom,
! [A: '\'A_ltln$\'',B: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ '\'bot$a\'' ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom429) ).
thf(3246,plain,
! [A: '\'A_ltln$\'',B: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ '\'bot$a\'' ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(143,axiom,
! [A: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'minus$a\'' @ A ) @ '\'bot$\'' )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom546) ).
thf(1262,plain,
! [A: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'minus$a\'' @ A ) @ '\'bot$\'' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(135,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( A = B )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom165) ).
thf(1235,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( A = B )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(616,axiom,
! [A: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ '\'bot$a\'' ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom121) ).
thf(3359,plain,
! [A: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ '\'bot$a\'' ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(573,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
<=> ! [C: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ C ) @ A )
=> ( '\'fun_app$a\'' @ ( '\'member$\'' @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom161) ).
thf(3174,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ! [C: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ C ) @ A )
=> ( '\'fun_app$a\'' @ ( '\'member$\'' @ C ) @ B ) ) )
& ( ! [C: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ C ) @ A )
=> ( '\'fun_app$a\'' @ ( '\'member$\'' @ C ) @ B ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(149,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ) @ C )
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom51) ).
thf(1285,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ) @ C )
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(245,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ C ) )
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom387) ).
thf(1738,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ C ) )
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(554,axiom,
! [A: '\'A_ltln$\''] : ( '\'fun_app$a\'' @ '\'is_singleton$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ '\'bot$a\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom471) ).
thf(3095,plain,
! [A: '\'A_ltln$\''] : ( '\'fun_app$a\'' @ '\'is_singleton$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ '\'bot$a\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(458,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ A )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom344) ).
thf(2675,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ A )
=> ( B = A ) )
& ( ( B = A )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(204,axiom,
! [A: '\'A_ltln_set_a_ltln_set_fun$\''] :
( ( '\'bind$a\'' @ '\'bot$\'' @ A )
= '\'bot$a\'' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom136) ).
thf(1543,plain,
! [A: '\'A_ltln_set_a_ltln_set_fun$\''] :
( ( '\'bind$a\'' @ '\'bot$\'' @ A )
= '\'bot$a\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(492,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ '\'bot$a\'' ) ) ) @ C )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom630) ).
thf(2838,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ '\'bot$a\'' ) ) ) @ C )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(615,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom509) ).
thf(3356,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(526,axiom,
! [A: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ '\'bot$a\'' )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom113) ).
thf(2975,plain,
! [A: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ '\'bot$a\'' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(420,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_a_ltln_set_set_fun$\'',C: '\'A_ltln_set$\'',D: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$k\'' @ B @ C ) )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ D )
& ! [E: '\'A_ltln_set$\'',F: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ E ) @ F )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$k\'' @ B @ E ) ) @ ( '\'fun_app$k\'' @ B @ F ) ) ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$k\'' @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom326) ).
thf(2511,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_a_ltln_set_set_fun$\'',C: '\'A_ltln_set$\'',D: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$k\'' @ B @ C ) )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ D )
& ! [E: '\'A_ltln_set$\'',F: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ E ) @ F )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$k\'' @ B @ E ) ) @ ( '\'fun_app$k\'' @ B @ F ) ) ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$k\'' @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(171,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ '\'bot$\'' ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom428) ).
thf(1372,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ '\'bot$\'' ) )
=> ( A = B ) )
& ( ( A = B )
=> ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ '\'bot$\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(367,axiom,
! [A: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ '\'bot$a\'' ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom346) ).
thf(2266,plain,
! [A: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ '\'bot$a\'' ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(436,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ C ) )
<=> ( ( ( '\'fun_app$a\'' @ ( '\'member$\'' @ B ) @ A )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ '\'bot$a\'' ) ) ) @ C ) )
& ( ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ B ) @ A )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom631) ).
thf(2584,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ C ) )
=> ( ( ( '\'fun_app$a\'' @ ( '\'member$\'' @ B ) @ A )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ '\'bot$a\'' ) ) ) @ C ) )
& ( ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ B ) @ A )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ C ) ) ) )
& ( ( ( ( '\'fun_app$a\'' @ ( '\'member$\'' @ B ) @ A )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ '\'bot$a\'' ) ) ) @ C ) )
& ( ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ B ) @ A )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ C ) ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(285,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( ( B
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ A ) )
=> $false ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom226) ).
thf(1898,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
~ ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( B
!= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(142,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'member$a\'' @ B ) @ A ) )
=> ? [C: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ A )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ B )
& ! [D: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ D ) @ A )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ D ) @ C ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom200) ).
thf(1257,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'member$a\'' @ B ) @ A ) )
=> ? [C: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ A )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ B )
& ! [D: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ D ) @ A )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ D ) @ C ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(388,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( A
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom228) ).
thf(2357,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( A
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(298,axiom,
! [A: '\'A_ltln_set_bool_fun$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ A @ B )
& ! [C: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ A @ C )
=> ? [D: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ D ) @ C )
& ( ( '\'fun_app$a\'' @ A @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ C ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ D ) @ '\'bot$a\'' ) ) )
| ~ ( '\'fun_app$a\'' @ '\'finite$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ C ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ D ) @ '\'bot$a\'' ) ) ) ) ) ) )
=> ~ ( '\'fun_app$a\'' @ '\'finite$\'' @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom628) ).
thf(1955,plain,
! [A: '\'A_ltln_set_bool_fun$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ A @ B )
& ! [C: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ A @ C )
=> ? [D: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ D ) @ C )
& ( ( '\'fun_app$a\'' @ A @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ C ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ D ) @ '\'bot$a\'' ) ) )
| ~ ( '\'fun_app$a\'' @ '\'finite$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ C ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ D ) @ '\'bot$a\'' ) ) ) ) ) ) )
=> ~ ( '\'fun_app$a\'' @ '\'finite$\'' @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(494,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ '\'finite$\'' @ A )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ ( '\'fold$\'' @ '\'insert$b\'' ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom637) ).
thf(2843,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ '\'finite$\'' @ A )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ ( '\'fold$\'' @ '\'insert$b\'' ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(379,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
<=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom224) ).
thf(2320,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B )
= B ) )
& ( ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B )
= B )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(94,axiom,
! [A: '\'A_ltln_set_set$\''] :
( ! [B: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ B ) @ A )
=> $false )
=> ( A = '\'bot$\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom157) ).
thf(1052,plain,
! [A: '\'A_ltln_set_set$\''] :
( ! [B: '\'A_ltln_set$\''] :
~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ B ) @ A )
=> ( A = '\'bot$\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(521,axiom,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'bot$a\''
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ B ) ) @ C ) )
<=> ( ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ C )
& ( '\'bot$a\''
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom528) ).
thf(2949,plain,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'bot$a\''
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ B ) ) @ C ) )
=> ( ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ C )
& ( '\'bot$a\''
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C ) ) ) )
& ( ( ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ C )
& ( '\'bot$a\''
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C ) ) )
=> ( '\'bot$a\''
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ B ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(466,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom268) ).
thf(2722,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(500,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C ) )
<=> ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom523) ).
thf(2865,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C ) )
=> ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ C ) ) )
& ( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ C ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(413,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln$\'',C: '\'A_ltln_set$\''] :
( ( '\'bot$a\''
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ C ) ) )
<=> ( ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ B ) @ A )
& ( '\'bot$a\''
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom524) ).
thf(2479,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'bot$a\''
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ C ) ) )
=> ( ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ B ) @ A )
& ( '\'bot$a\''
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ C ) ) ) )
& ( ( ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ B ) @ A )
& ( '\'bot$a\''
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ C ) ) )
=> ( '\'bot$a\''
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(330,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( A = B )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom166) ).
thf(2088,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( A = B )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(319,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ B ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom578) ).
thf(2045,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ B ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(300,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom246) ).
thf(1966,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(70,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\'',D: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ '\'bot$\'' ) )
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ D ) @ '\'bot$\'' ) ) )
<=> ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom426) ).
thf(903,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\'',D: '\'A_ltln_set$\''] :
( ( ( ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ '\'bot$\'' ) )
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ D ) @ '\'bot$\'' ) ) )
=> ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) )
& ( ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) )
=> ( ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ '\'bot$\'' ) )
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ D ) @ '\'bot$\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(348,axiom,
! [A: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ '\'bot$a\'' )
=> ( A = '\'bot$a\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom298) ).
thf(2194,plain,
! [A: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ '\'bot$a\'' )
=> ( A = '\'bot$a\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(229,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'disjnt$\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ C ) @ A ) )
=> ( '\'fun_app$b\'' @ ( '\'disjnt$\'' @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom185) ).
thf(1654,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'disjnt$\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ C ) @ A ) )
=> ( '\'fun_app$b\'' @ ( '\'disjnt$\'' @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(351,axiom,
! [A: '\'A_ltln$\'',B: '\'A_ltln$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ C ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom406) ).
thf(2209,plain,
! [A: '\'A_ltln$\'',B: '\'A_ltln$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ C ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(57,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'bot$\''
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ C ) ) )
<=> ( ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ B ) @ A )
& ( '\'bot$\''
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom525) ).
thf(844,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( '\'bot$\''
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ C ) ) )
=> ( ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ B ) @ A )
& ( '\'bot$\''
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ A ) @ C ) ) ) )
& ( ( ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ B ) @ A )
& ( '\'bot$\''
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ A ) @ C ) ) )
=> ( '\'bot$\''
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(324,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom236) ).
thf(2071,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(402,axiom,
! [A: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ '\'bot$a\'' ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom179) ).
thf(2435,plain,
! [A: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ '\'bot$a\'' ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(598,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom505) ).
thf(3284,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(487,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom591) ).
thf(2818,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(548,axiom,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) )
<=> ( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ B )
| ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom8) ).
thf(3067,plain,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) )
=> ( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ B )
| ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ C ) ) )
& ( ( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ B )
| ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ C ) )
=> ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(327,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom602) ).
thf(2078,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(157,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ C ) @ B ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ C ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom265) ).
thf(1321,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ C ) @ B ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ C ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(415,axiom,
! [A: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ A ) @ A )
<=> ( A = '\'bot$a\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom132) ).
thf(2490,plain,
! [A: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ A ) @ A )
=> ( A = '\'bot$a\'' ) )
& ( ( A = '\'bot$a\'' )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(346,axiom,
! [A: '\'A_ltln_set$\''] :
( ~ ( '\'fun_app$a\'' @ '\'finite$\'' @ A )
=> ( A != '\'bot$a\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom282) ).
thf(2187,plain,
! [A: '\'A_ltln_set$\''] :
( ~ ( '\'fun_app$a\'' @ '\'finite$\'' @ A )
=> ( A != '\'bot$a\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(607,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ B ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ C ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom242) ).
thf(3320,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ B ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ C ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(89,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( B = C ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom307) ).
thf(1010,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( B = C ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(261,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set_bool_fun$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( A != '\'bot$\'' )
& ! [C: '\'A_ltln_set$\''] : ( '\'fun_app$b\'' @ B @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ '\'bot$\'' ) )
& ! [C: '\'A_ltln_set$\'',D: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ D )
& ( D != '\'bot$\'' )
& ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ D )
& ( '\'fun_app$b\'' @ B @ D ) )
=> ( '\'fun_app$b\'' @ B @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ D ) ) ) )
=> ( '\'fun_app$b\'' @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom451) ).
thf(1807,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set_bool_fun$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( A != '\'bot$\'' )
& ! [C: '\'A_ltln_set$\''] : ( '\'fun_app$b\'' @ B @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ '\'bot$\'' ) )
& ! [C: '\'A_ltln_set$\'',D: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ D )
& ( D != '\'bot$\'' )
& ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ D )
& ( '\'fun_app$b\'' @ B @ D ) )
=> ( '\'fun_app$b\'' @ B @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ D ) ) ) )
=> ( '\'fun_app$b\'' @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(37,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B )
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom35) ).
thf(771,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B )
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(510,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
<=> ! [C: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ C ) @ A )
=> ( '\'fun_app$a\'' @ ( '\'member$\'' @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom172) ).
thf(2907,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ! [C: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ C ) @ A )
=> ( '\'fun_app$a\'' @ ( '\'member$\'' @ C ) @ B ) ) )
& ( ! [C: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ C ) @ A )
=> ( '\'fun_app$a\'' @ ( '\'member$\'' @ C ) @ B ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(215,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ! [C: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ A )
=> ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ B ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom100) ).
thf(1590,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ! [C: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ A )
=> ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ B ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(405,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( A != '\'bot$\'' )
& ( '\'fun_app$b\'' @ '\'finite$a\'' @ B )
& ( B != '\'bot$\'' ) )
=> ( ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ A ) ) @ ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom352) ).
thf(2443,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( A != '\'bot$\'' )
& ( '\'fun_app$b\'' @ '\'finite$a\'' @ B )
& ( B != '\'bot$\'' ) )
=> ( ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ A ) ) @ ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(394,axiom,
! [A: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom10) ).
thf(2406,plain,
! [A: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(192,axiom,
! [A: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom9) ).
thf(1481,plain,
! [A: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(11,axiom,
! [A: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ '\'bot$\'' )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom285) ).
thf(652,plain,
! [A: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ '\'bot$\'' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(489,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( A != '\'bot$\'' ) )
=> ( ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ A ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom370) ).
thf(2823,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( A != '\'bot$\'' ) )
=> ( ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ A ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(525,axiom,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ C ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom491) ).
thf(2971,plain,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ C ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(138,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ C ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom177) ).
thf(1244,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ C ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(397,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ~ ( '\'fun_app$a\'' @ '\'finite$\'' @ A )
=> ~ ( '\'fun_app$a\'' @ '\'finite$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom22) ).
thf(2416,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ~ ( '\'fun_app$a\'' @ '\'finite$\'' @ A )
=> ~ ( '\'fun_app$a\'' @ '\'finite$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(173,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
=> ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ A )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom343) ).
thf(1385,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
=> ( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ A )
=> ( B = A ) )
& ( ( B = A )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(241,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ C ) @ B ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ C ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom221) ).
thf(1721,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ C ) @ B ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ C ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(68,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ C ) )
& ( ( A = B )
=> $false )
& ( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ C )
=> $false ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom420) ).
thf(896,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set_set$\''] :
~ ( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ C ) )
& ( A != B )
& ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(333,axiom,
! [A: '\'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ! [D: '\'A_ltln_set$\'',E: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ A @ D ) @ E ) ) @ D )
& ! [D: '\'A_ltln_set$\'',E: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ A @ D ) @ E ) ) @ E )
& ! [D: '\'A_ltln_set$\'',E: '\'A_ltln_set$\'',F: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ D ) @ E )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ D ) @ F ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ D ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ A @ E ) @ F ) ) ) )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom607) ).
thf(2098,plain,
! [A: '\'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ! [D: '\'A_ltln_set$\'',E: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ A @ D ) @ E ) ) @ D )
& ! [D: '\'A_ltln_set$\'',E: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ A @ D ) @ E ) ) @ E )
& ! [D: '\'A_ltln_set$\'',E: '\'A_ltln_set$\'',F: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ D ) @ E )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ D ) @ F ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ D ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ A @ E ) @ F ) ) ) )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(96,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ B )
=> ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom416) ).
thf(1062,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ B )
=> ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(423,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) @ C )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom32) ).
thf(2532,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) @ C )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(328,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( A = B )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom168) ).
thf(2081,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( A = B )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(574,axiom,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ B ) ) @ C )
<=> ( ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ C )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom393) ).
thf(3181,plain,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ B ) ) @ C )
=> ( ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ C )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ B ) @ C ) ) )
& ( ( ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ C )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ B ) @ C ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ B ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(393,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_a_ltln_set_fun$\'',C: '\'A_ltln_set$\'',D: '\'A_ltln_set$\''] :
( ( ( A
= ( '\'fun_app$c\'' @ B @ C ) )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ D )
& ! [E: '\'A_ltln_set$\'',F: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ E ) @ F )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ B @ E ) ) @ ( '\'fun_app$c\'' @ B @ F ) ) ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom338) ).
thf(2399,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_a_ltln_set_fun$\'',C: '\'A_ltln_set$\'',D: '\'A_ltln_set$\''] :
( ( ( A
= ( '\'fun_app$c\'' @ B @ C ) )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ D )
& ! [E: '\'A_ltln_set$\'',F: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ E ) @ F )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ B @ E ) ) @ ( '\'fun_app$c\'' @ B @ F ) ) ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(126,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ '\'finite$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) )
<=> ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( '\'fun_app$b\'' @ '\'finite$a\'' @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom3) ).
thf(1193,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) )
=> ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( '\'fun_app$b\'' @ '\'finite$a\'' @ B ) ) )
& ( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( '\'fun_app$b\'' @ '\'finite$a\'' @ B ) )
=> ( '\'fun_app$b\'' @ '\'finite$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(131,axiom,
! [A: '\'A_ltln_set_set$\''] :
( ? [B: '\'A_ltln_set$\''] : ( '\'fun_app$b\'' @ ( '\'member$a\'' @ B ) @ A )
<=> ( A != '\'bot$\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom170) ).
thf(1212,plain,
! [A: '\'A_ltln_set_set$\''] :
( ( ? [B: '\'A_ltln_set$\''] : ( '\'fun_app$b\'' @ ( '\'member$a\'' @ B ) @ A )
=> ( A != '\'bot$\'' ) )
& ( ( A != '\'bot$\'' )
=> ? [B: '\'A_ltln_set$\''] : ( '\'fun_app$b\'' @ ( '\'member$a\'' @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(34,axiom,
! [A: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'minus$a\'' @ A ) @ A )
= '\'bot$\'' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom550) ).
thf(763,plain,
! [A: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'minus$a\'' @ A ) @ A )
= '\'bot$\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(508,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom46) ).
thf(2902,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(332,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom256) ).
thf(2095,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(46,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ B )
=> ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom59) ).
thf(800,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ B )
=> ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(451,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ B ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ C ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom208) ).
thf(2648,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ B ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ C ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(253,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ~ ( '\'fun_app$b\'' @ '\'finite$a\'' @ A ) )
=> ~ ( '\'fun_app$b\'' @ '\'finite$a\'' @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom259) ).
thf(1777,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ~ ( '\'fun_app$b\'' @ '\'finite$a\'' @ A ) )
=> ~ ( '\'fun_app$b\'' @ '\'finite$a\'' @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(355,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ '\'finite$\'' @ A )
=> ( '\'fun_app$a\'' @ '\'finite$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom432) ).
thf(2230,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ '\'finite$\'' @ A )
=> ( '\'fun_app$a\'' @ '\'finite$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(284,axiom,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ '\'finite$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ B ) )
<=> ( '\'fun_app$a\'' @ '\'finite$\'' @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom384) ).
thf(1893,plain,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ '\'finite$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ B ) )
=> ( '\'fun_app$a\'' @ '\'finite$\'' @ B ) )
& ( ( '\'fun_app$a\'' @ '\'finite$\'' @ B )
=> ( '\'fun_app$a\'' @ '\'finite$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(154,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'disjnt$\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ C ) )
<=> ( ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ B ) @ A )
& ( '\'fun_app$b\'' @ ( '\'disjnt$\'' @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom392) ).
thf(1309,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'disjnt$\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ C ) )
=> ( ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ B ) @ A )
& ( '\'fun_app$b\'' @ ( '\'disjnt$\'' @ A ) @ C ) ) )
& ( ( ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ B ) @ A )
& ( '\'fun_app$b\'' @ ( '\'disjnt$\'' @ A ) @ C ) )
=> ( '\'fun_app$b\'' @ ( '\'disjnt$\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(310,axiom,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom417) ).
thf(2003,plain,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(515,axiom,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ B )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ '\'bot$a\'' ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom460) ).
thf(2930,plain,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ B )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ '\'bot$a\'' ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(165,axiom,
! [A: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ '\'bot$\'' )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom149) ).
thf(1348,plain,
! [A: '\'A_ltln_set$\''] :
~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ '\'bot$\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(197,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ C ) )
= '\'bot$\'' )
<=> ( ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ B ) @ A )
& ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ A ) @ C )
= '\'bot$\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom527) ).
thf(1512,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ C ) )
= '\'bot$\'' )
=> ( ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ B ) @ A )
& ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ A ) @ C )
= '\'bot$\'' ) ) )
& ( ( ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ B ) @ A )
& ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ A ) @ C )
= '\'bot$\'' ) )
=> ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ B ) @ C ) )
= '\'bot$\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(147,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\'',D: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ C ) @ D ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ C ) ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom219) ).
thf(1280,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\'',D: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ C ) @ D ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ C ) ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(234,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] : ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom211) ).
thf(1678,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] : ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(54,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ) @ B )
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom17) ).
thf(833,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ) @ B )
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(205,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set_a_ltln_set_set_fun$\'',D: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$e\'' @ C @ B ) ) @ D )
& ! [E: '\'A_ltln_set_set$\'',F: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ E ) @ F )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$e\'' @ C @ E ) ) @ ( '\'fun_app$e\'' @ C @ F ) ) ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$e\'' @ C @ A ) ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom331) ).
thf(1546,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set_a_ltln_set_set_fun$\'',D: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$e\'' @ C @ B ) ) @ D )
& ! [E: '\'A_ltln_set_set$\'',F: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ E ) @ F )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$e\'' @ C @ E ) ) @ ( '\'fun_app$e\'' @ C @ F ) ) ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$e\'' @ C @ A ) ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(223,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ A ) @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom542) ).
thf(1625,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ A ) @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(200,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom253) ).
thf(1527,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(250,axiom,
! [A: '\'A_ltln_set_set$\''] : ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ '\'bot$\'' ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom128) ).
thf(1757,plain,
! [A: '\'A_ltln_set_set$\''] : ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ '\'bot$\'' ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(570,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom617) ).
thf(3164,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(376,axiom,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ B )
& ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ C ) )
=> ( ( ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ B )
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ C ) )
<=> ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom411) ).
thf(2302,plain,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ B )
& ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ C ) )
=> ( ( ( ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ B )
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ C ) )
=> ( B = C ) )
& ( ( B = C )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ B )
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(460,axiom,
! [A: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ '\'bot$a\'' )
<=> ( A = '\'bot$a\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom300) ).
thf(2683,plain,
! [A: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ '\'bot$a\'' )
=> ( A = '\'bot$a\'' ) )
& ( ( A = '\'bot$a\'' )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ '\'bot$a\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(133,axiom,
! [A: '\'A_ltln_set$\''] :
( ! [B: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ B ) @ A )
=> $false )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ '\'bot$a\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom294) ).
thf(1229,plain,
! [A: '\'A_ltln_set$\''] :
( ! [B: '\'A_ltln$\''] :
~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ B ) @ A )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ '\'bot$a\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(356,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ C ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom611) ).
thf(2233,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ C ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(216,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ A ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom317) ).
thf(1593,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ A ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(439,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ C ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom388) ).
thf(2604,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ C ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ B ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(486,axiom,
! [A: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ '\'bot$a\'' ) @ A )
= '\'bot$a\'' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom532) ).
thf(2815,plain,
! [A: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ '\'bot$a\'' ) @ A )
= '\'bot$a\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(306,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ A ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom318) ).
thf(1986,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ A ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(312,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ B )
= '\'bot$a\'' )
<=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom621) ).
thf(2008,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ B )
= '\'bot$a\'' )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B ) )
& ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ B )
= '\'bot$a\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(153,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ C ) )
& ! [D: '\'A_ltln_set_set$\'',E: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ D ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ E ) @ C )
& ( A
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ D ) @ E ) ) )
=> $false ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom275) ).
thf(1303,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
~ ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ C ) )
& ! [D: '\'A_ltln_set_set$\'',E: '\'A_ltln_set_set$\''] :
~ ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ D ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ E ) @ C )
& ( A
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ D ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(561,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom202) ).
thf(3132,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(44,axiom,
! [A: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ '\'is_empty$a\'' @ A )
<=> ( A = '\'bot$\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom348) ).
thf(790,plain,
! [A: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'is_empty$a\'' @ A )
=> ( A = '\'bot$\'' ) )
& ( ( A = '\'bot$\'' )
=> ( '\'fun_app$b\'' @ '\'is_empty$a\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(565,axiom,
! [A: '\'A_ltln_set_bool_fun$\''] :
( ( '\'bot$\''
= ( '\'collect$\'' @ A ) )
<=> ! [B: '\'A_ltln_set$\''] :
~ ( '\'fun_app$a\'' @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom99) ).
thf(3145,plain,
! [A: '\'A_ltln_set_bool_fun$\''] :
( ( ( '\'bot$\''
= ( '\'collect$\'' @ A ) )
=> ! [B: '\'A_ltln_set$\''] :
~ ( '\'fun_app$a\'' @ A @ B ) )
& ( ! [B: '\'A_ltln_set$\''] :
~ ( '\'fun_app$a\'' @ A @ B )
=> ( '\'bot$\''
= ( '\'collect$\'' @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(274,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'member$a\'' @ B ) @ A ) )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ A ) )
= ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom360) ).
thf(1859,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'member$a\'' @ B ) @ A ) )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ A ) )
= ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(307,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'member$\'' @ C ) @ A ) )
=> ( '\'fun_app$a\'' @ ( '\'member$\'' @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom151) ).
thf(1989,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'member$\'' @ C ) @ A ) )
=> ( '\'fun_app$a\'' @ ( '\'member$\'' @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(168,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) )
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom13) ).
thf(1363,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) )
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(381,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom212) ).
thf(2334,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(613,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom616) ).
thf(3347,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(162,axiom,
! [A: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( A != '\'bot$\'' ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$i\'' @ '\'inf_fin$a\'' @ A ) ) @ ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom350) ).
thf(1335,plain,
! [A: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( A != '\'bot$\'' ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$i\'' @ '\'inf_fin$a\'' @ A ) ) @ ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(463,axiom,
! [A: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ '\'bot$a\'' ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom129) ).
thf(2704,plain,
! [A: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ '\'bot$a\'' ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(95,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set_bool_fun$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ C @ '\'bot$\'' )
& ! [D: '\'A_ltln_set$\'',E: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ E )
& ( '\'fun_app$b\'' @ ( '\'member$a\'' @ D ) @ B )
& ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ D ) @ E )
& ( '\'fun_app$b\'' @ C @ E ) )
=> ( '\'fun_app$b\'' @ C @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ D ) @ E ) ) ) )
=> ( '\'fun_app$b\'' @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom467) ).
thf(1056,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set_bool_fun$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ C @ '\'bot$\'' )
& ! [D: '\'A_ltln_set$\'',E: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ E )
& ( '\'fun_app$b\'' @ ( '\'member$a\'' @ D ) @ B )
& ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ D ) @ E )
& ( '\'fun_app$b\'' @ C @ E ) )
=> ( '\'fun_app$b\'' @ C @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ D ) @ E ) ) ) )
=> ( '\'fun_app$b\'' @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(190,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
=> ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'minus$a\'' @ B ) @ A ) )
<=> ( '\'fun_app$b\'' @ '\'finite$a\'' @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom554) ).
thf(1473,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
=> ( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'minus$a\'' @ B ) @ A ) )
=> ( '\'fun_app$b\'' @ '\'finite$a\'' @ B ) )
& ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ B )
=> ( '\'fun_app$b\'' @ '\'finite$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'minus$a\'' @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(384,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ C ) )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ B ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ C ) @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom569) ).
thf(2340,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ C ) )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ B ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ C ) @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(544,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_bool_fun$\''] :
( ? [D: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ D ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) )
& ( '\'fun_app$\'' @ C @ D ) )
<=> ( ? [D: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ D ) @ A )
& ( '\'fun_app$\'' @ C @ D ) )
| ? [D: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ D ) @ B )
& ( '\'fun_app$\'' @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom56) ).
thf(3045,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_bool_fun$\''] :
( ( ? [D: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ D ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) )
& ( '\'fun_app$\'' @ C @ D ) )
=> ( ? [D: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ D ) @ A )
& ( '\'fun_app$\'' @ C @ D ) )
| ? [D: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ D ) @ B )
& ( '\'fun_app$\'' @ C @ D ) ) ) )
& ( ( ? [D: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ D ) @ A )
& ( '\'fun_app$\'' @ C @ D ) )
| ? [D: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ D ) @ B )
& ( '\'fun_app$\'' @ C @ D ) ) )
=> ? [D: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ D ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) )
& ( '\'fun_app$\'' @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(315,axiom,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ B ) ) @ C )
<=> ( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ C )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom386) ).
thf(2021,plain,
! [A: '\'A_ltln$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ B ) ) @ C )
=> ( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ C )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ C ) ) )
& ( ( ( '\'fun_app$a\'' @ ( '\'member$\'' @ A ) @ C )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ B ) @ C ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ A ) @ B ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(66,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ B )
& ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ C ) )
=> ( ( ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ B )
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ C ) )
<=> ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom412) ).
thf(886,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ B )
& ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ A ) @ C ) )
=> ( ( ( ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ B )
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ C ) )
=> ( B = C ) )
& ( ( B = C )
=> ( ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ B )
= ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(523,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'bot$a\''
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) )
<=> ( ( A = '\'bot$a\'' )
& ( B = '\'bot$a\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom115) ).
thf(2961,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'bot$a\''
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) )
=> ( ( A = '\'bot$a\'' )
& ( B = '\'bot$a\'' ) ) )
& ( ( ( A = '\'bot$a\'' )
& ( B = '\'bot$a\'' ) )
=> ( '\'bot$a\''
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(150,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( A != '\'bot$\'' ) )
=> ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ A ) ) @ B )
<=> ! [C: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ A )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom366) ).
thf(1288,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( A != '\'bot$\'' ) )
=> ( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ A ) ) @ B )
=> ! [C: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ A )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ B ) ) )
& ( ! [C: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ A )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ B ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(444,axiom,
'\'fun_app$a\'' @ '\'finite$\'' @ '\'bot$a\'',
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom280) ).
thf(2619,plain,
'\'fun_app$a\'' @ '\'finite$\'' @ '\'bot$a\'',
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(97,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_bool_fun$\''] :
( ! [D: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ D ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) )
=> ( '\'fun_app$a\'' @ C @ D ) )
<=> ( ! [D: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ D ) @ A )
=> ( '\'fun_app$a\'' @ C @ D ) )
& ! [D: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ D ) @ B )
=> ( '\'fun_app$a\'' @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom53) ).
thf(1065,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_bool_fun$\''] :
( ( ! [D: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ D ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) )
=> ( '\'fun_app$a\'' @ C @ D ) )
=> ( ! [D: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ D ) @ A )
=> ( '\'fun_app$a\'' @ C @ D ) )
& ! [D: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ D ) @ B )
=> ( '\'fun_app$a\'' @ C @ D ) ) ) )
& ( ( ! [D: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ D ) @ A )
=> ( '\'fun_app$a\'' @ C @ D ) )
& ! [D: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ D ) @ B )
=> ( '\'fun_app$a\'' @ C @ D ) ) )
=> ! [D: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ D ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) )
=> ( '\'fun_app$a\'' @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(56,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( A != '\'bot$\'' )
& ! [C: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ A )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ B ) ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ A ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom364) ).
thf(839,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( A != '\'bot$\'' )
& ! [C: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ A )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ C ) @ B ) ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$i\'' @ '\'sup_fin$a\'' @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(418,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ C ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom599) ).
thf(2502,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ C ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(617,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ '\'finite$\'' @ A )
& ~ ( '\'fun_app$a\'' @ '\'finite$\'' @ B ) )
=> ~ ( '\'fun_app$a\'' @ '\'finite$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom568) ).
thf(3362,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ '\'finite$\'' @ A )
& ~ ( '\'fun_app$a\'' @ '\'finite$\'' @ B ) )
=> ~ ( '\'fun_app$a\'' @ '\'finite$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(110,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] : ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom209) ).
thf(1129,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] : ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(145,axiom,
! [A: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ '\'bot$\'' )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom124) ).
thf(1268,plain,
! [A: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ '\'bot$\'' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(202,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ B ) @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom498) ).
thf(1537,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'inf$a\'' @ B ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(92,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'bot$\''
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) )
<=> ( ( A = '\'bot$\'' )
& ( B = '\'bot$\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom114) ).
thf(1019,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( ( '\'bot$\''
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) )
=> ( ( A = '\'bot$\'' )
& ( B = '\'bot$\'' ) ) )
& ( ( ( A = '\'bot$\'' )
& ( B = '\'bot$\'' ) )
=> ( '\'bot$\''
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(303,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ C ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom593) ).
thf(1976,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ C ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(26,axiom,
( '\'bot$\''
= ( '\'collect$\'' @ '\'bot$d\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom302) ).
thf(723,plain,
( '\'bot$\''
= ( '\'collect$\'' @ '\'bot$d\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(280,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom44) ).
thf(1880,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(196,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'disjnt$\'' @ A ) @ B )
<=> ! [C: '\'A_ltln_set$\''] :
~ ( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ A )
& ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom163) ).
thf(1505,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'disjnt$\'' @ A ) @ B )
=> ! [C: '\'A_ltln_set$\''] :
~ ( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ A )
& ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ B ) ) )
& ( ! [C: '\'A_ltln_set$\''] :
~ ( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ A )
& ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ B ) )
=> ( '\'fun_app$b\'' @ ( '\'disjnt$\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(108,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set_bool_fun$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( '\'fun_app$b\'' @ B @ '\'bot$\'' )
& ! [C: '\'A_ltln_set$\'',D: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ D )
& ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ D )
& ( '\'fun_app$b\'' @ B @ D ) )
=> ( '\'fun_app$b\'' @ B @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ D ) ) ) )
=> ( '\'fun_app$b\'' @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom449) ).
thf(1120,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set_bool_fun$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ( '\'fun_app$b\'' @ B @ '\'bot$\'' )
& ! [C: '\'A_ltln_set$\'',D: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ D )
& ~ ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ D )
& ( '\'fun_app$b\'' @ B @ D ) )
=> ( '\'fun_app$b\'' @ B @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ C ) @ D ) ) ) )
=> ( '\'fun_app$b\'' @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(28,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] : ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom267) ).
thf(728,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] : ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(592,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ A ) @ B )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom164) ).
thf(3244,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ A ) @ B )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(539,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) @ C )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom52) ).
thf(3025,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) @ C )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(265,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ '\'finite$a\'' @ B ) )
=> ( '\'fun_app$b\'' @ '\'finite$a\'' @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom257) ).
thf(1827,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ '\'finite$a\'' @ B ) )
=> ( '\'fun_app$b\'' @ '\'finite$a\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(482,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom583) ).
thf(2803,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(495,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom580) ).
thf(2847,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(556,axiom,
! [A: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ '\'bot$a\'' ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom111) ).
thf(3113,plain,
! [A: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ '\'bot$a\'' ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(286,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom14) ).
thf(1902,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(160,axiom,
! [A: '\'A_ltln_set$\''] : ( '\'fun_app$b\'' @ '\'is_singleton$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ '\'bot$\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom472) ).
thf(1331,plain,
! [A: '\'A_ltln_set$\''] : ( '\'fun_app$b\'' @ '\'is_singleton$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$m\'' @ '\'insert$a\'' @ A ) @ '\'bot$\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(47,axiom,
! [A: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ '\'bot$\'' ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom283) ).
thf(803,plain,
! [A: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ '\'bot$\'' ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(76,axiom,
! [A: '\'A_ltln_set_set_a_ltln_set_set_a_ltln_set_set_fun_fun$\'',B: '\'A_ltln_set_set$\'',C: '\'A_ltln_set_set$\''] :
( ( ! [D: '\'A_ltln_set_set$\'',E: '\'A_ltln_set_set$\''] : ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ D ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ A @ D ) @ E ) )
& ! [D: '\'A_ltln_set_set$\'',E: '\'A_ltln_set_set$\''] : ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ E ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ A @ D ) @ E ) )
& ! [D: '\'A_ltln_set_set$\'',E: '\'A_ltln_set_set$\'',F: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ E ) @ D )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ F ) @ D ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ A @ E ) @ F ) ) @ D ) ) )
=> ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ C )
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom229) ).
thf(940,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$\''] : ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ D ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ A @ D ) @ E ) )
& ! [D: '\'A_ltln_set_set$\'',E: '\'A_ltln_set_set$\''] : ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ E ) @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ A @ D ) @ E ) )
& ! [D: '\'A_ltln_set_set$\'',E: '\'A_ltln_set_set$\'',F: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ E ) @ D )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ F ) @ D ) )
=> ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ A @ E ) @ F ) ) @ D ) ) )
=> ( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'sup$a\'' @ B ) @ C )
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(503,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_a_ltln_set_set_fun$\''] :
( ( ( '\'fun_app$a\'' @ '\'finite$\'' @ A )
& ! [C: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ C ) @ A )
=> ( '\'fun_app$b\'' @ '\'finite$a\'' @ ( '\'fun_app$j\'' @ B @ C ) ) ) )
=> ( '\'fun_app$b\'' @ '\'finite$a\'' @ ( '\'bind$\'' @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom86) ).
thf(2881,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_a_ltln_set_set_fun$\''] :
( ( ( '\'fun_app$a\'' @ '\'finite$\'' @ A )
& ! [C: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ C ) @ A )
=> ( '\'fun_app$b\'' @ '\'finite$a\'' @ ( '\'fun_app$j\'' @ B @ C ) ) ) )
=> ( '\'fun_app$b\'' @ '\'finite$a\'' @ ( '\'bind$\'' @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(72,axiom,
! [A: '\'A_ltln_set_set$\''] :
( ~ ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
=> ( A != '\'bot$\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom281) ).
thf(923,plain,
! [A: '\'A_ltln_set_set$\''] :
( ~ ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
=> ( A != '\'bot$\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(321,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ) @ C )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ C ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom572) ).
thf(2059,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ B ) ) @ C )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ C ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(194,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( A = B )
<=> ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ A )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom315) ).
thf(1490,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( ( A = B )
=> ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ A )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B ) ) )
& ( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ A )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(341,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) @ C )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ C ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom577) ).
thf(2170,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) @ C )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ A ) @ C ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(334,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom436) ).
thf(2106,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(411,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set_bool_fun$\''] :
( ( ( '\'fun_app$a\'' @ '\'finite$\'' @ A )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ C @ '\'bot$a\'' )
& ! [D: '\'A_ltln$\'',E: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ '\'finite$\'' @ E )
& ( '\'fun_app$a\'' @ ( '\'member$\'' @ D ) @ B )
& ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ D ) @ E )
& ( '\'fun_app$a\'' @ C @ E ) )
=> ( '\'fun_app$a\'' @ C @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ D ) @ E ) ) ) )
=> ( '\'fun_app$a\'' @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom468) ).
thf(2470,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set_bool_fun$\''] :
( ( ( '\'fun_app$a\'' @ '\'finite$\'' @ A )
& ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B )
& ( '\'fun_app$a\'' @ C @ '\'bot$a\'' )
& ! [D: '\'A_ltln$\'',E: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ '\'finite$\'' @ E )
& ( '\'fun_app$a\'' @ ( '\'member$\'' @ D ) @ B )
& ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ D ) @ E )
& ( '\'fun_app$a\'' @ C @ E ) )
=> ( '\'fun_app$a\'' @ C @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ D ) @ E ) ) ) )
=> ( '\'fun_app$a\'' @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(602,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom541) ).
thf(3296,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(294,axiom,
! [A: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ A ) @ '\'bot$a\'' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom181) ).
thf(1945,plain,
! [A: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'disjnt$a\'' @ A ) @ '\'bot$a\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(581,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom270) ).
thf(3212,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] : ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(603,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B )
= '\'bot$a\'' )
<=> ( ( A = '\'bot$a\'' )
& ( B = '\'bot$a\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom91) ).
thf(3299,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B )
= '\'bot$a\'' )
=> ( ( A = '\'bot$a\'' )
& ( B = '\'bot$a\'' ) ) )
& ( ( ( A = '\'bot$a\'' )
& ( B = '\'bot$a\'' ) )
=> ( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B )
= '\'bot$a\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(123,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'minus$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'minus$a\'' @ A ) @ B ) ) @ B )
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'minus$a\'' @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom518) ).
thf(1184,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'minus$a\'' @ ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'minus$a\'' @ A ) @ B ) ) @ B )
= ( '\'fun_app$e\'' @ ( '\'fun_app$f\'' @ '\'minus$a\'' @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(325,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) @ B )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom18) ).
thf(2074,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) @ B )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(461,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_a_ltln_set_fun$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ! [C: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ A )
=> ( '\'fun_app$a\'' @ '\'finite$\'' @ ( '\'fun_app$c\'' @ B @ C ) ) ) )
=> ( '\'fun_app$a\'' @ '\'finite$\'' @ ( '\'bind$a\'' @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom87) ).
thf(2690,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_a_ltln_set_fun$\''] :
( ( ( '\'fun_app$b\'' @ '\'finite$a\'' @ A )
& ! [C: '\'A_ltln_set$\''] :
( ( '\'fun_app$b\'' @ ( '\'member$a\'' @ C ) @ A )
=> ( '\'fun_app$a\'' @ '\'finite$\'' @ ( '\'fun_app$c\'' @ B @ C ) ) ) )
=> ( '\'fun_app$a\'' @ '\'finite$\'' @ ( '\'bind$a\'' @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(533,axiom,
! [A: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom50) ).
thf(2998,plain,
! [A: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(531,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom24) ).
thf(2993,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ C ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ B ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(578,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln$\'',D: '\'A_ltln_set$\''] :
( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ B ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ D ) ) )
<=> ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ B ) @ D ) )
& ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom622) ).
thf(3200,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln$\'',D: '\'A_ltln_set$\''] :
( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ B ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ D ) ) )
=> ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ B ) @ D ) )
& ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ C ) @ A ) ) )
& ( ( ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ B ) @ D ) )
& ~ ( '\'fun_app$a\'' @ ( '\'member$\'' @ C ) @ A ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'minus$b\'' @ B ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$n\'' @ '\'insert$b\'' @ C ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(347,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ! [C: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ C ) @ A )
=> ( '\'fun_app$a\'' @ ( '\'member$\'' @ C ) @ B ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom101) ).
thf(2191,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\''] :
( ! [C: '\'A_ltln$\''] :
( ( '\'fun_app$a\'' @ ( '\'member$\'' @ C ) @ A )
=> ( '\'fun_app$a\'' @ ( '\'member$\'' @ C ) @ B ) )
=> ( '\'fun_app$a\'' @ ( '\'fun_app$g\'' @ '\'less_eq$\'' @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(90,axiom,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ A ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom102) ).
thf(1014,plain,
! [A: '\'A_ltln_set_set$\'',B: '\'A_ltln_set_set$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'less_eq$a\'' @ B ) @ A ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(278,axiom,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom590) ).
thf(1870,plain,
! [A: '\'A_ltln_set$\'',B: '\'A_ltln_set$\'',C: '\'A_ltln_set$\''] :
( ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ B ) @ C ) )
= ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'inf$\'' @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ B ) ) @ ( '\'fun_app$c\'' @ ( '\'fun_app$d\'' @ '\'sup$\'' @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(3379,plain,
$false,
inference(e,[status(thm)],[1718,2612,2295,1729,2412,1840,2544,1110,2250,645,892,1501,809,1369,1190,2336,2109,2131,1454,1315,1850,2499,666,1818,1950,1549,2077,1158,683,730,2622,2644,2062,3040,2248,741,1205,655,2854,677,1437,861,1750,977,1596,1406,1426,2607,2740,797,2933,3004,2035,1867,2184,2476,2168,698,930,2360,1782,1391,1921,1601,1803,1265,1254,2432,1914,3249,782,1441,973,3088,3308,1935,2173,1366,1628,3275,1298,3116,3342,3061,1907,2217,3125,1577,2488,2571,1323,619,2274,702,1379,1147,3216,1741,1931,1641,1773,1232,1847,638,853,2456,2178,3322,2996,2782,2893,2259,2650,646,1682,1864,2925,937,3152,2017,756,1664,1714,2027,2451,2236,2291,2254,3290,806,3093,766,1843,2437,1886,2137,1351,3327,1521,2884,1564,877,692,1622,774,3243,2809,1345,2799,3097,3229,2204,1691,2574,3169,1199,1153,1338,3318,2737,2660,2905,714,2773,2000,2409,1723,957,746,2541,2596,2277,862,1676,3134,815,2396,2015,1824,1619,1883,1560,3166,1837,2670,1178,1457,2181,2327,3028,2228,974,2769,2653,3282,2958,1968,3090,2565,3137,3349,1210,1656,1089,948,1328,2577,1587,1096,1540,2724,869,3237,1118,2268,3001,874,2840,3122,2946,2990,1794,1017,1856,725,1567,884,1160,1028,1659,2830,2419,3010,2240,1584,2038,2085,2666,1889,1644,1612,2978,3294,1155,1744,2504,2681,1530,1131,2243,1947,1984,3064,2370,2125,1099,1150,1478,2598,3059,2581,2465,3222,2497,2766,1246,1979,779,3074,1759,1393,1333,1434,1202,1779,657,1167,1616,2617,2338,1991,1318,1086,3225,1241,2761,1187,2440,2793,3190,2144,618,1680,3042,824,1747,1927,1631,3158,1959,2556,1301,2734,3187,1833,2727,1125,2393,2514,2806,2827,2970,1007,3234,2048,2938,2791,3240,2525,2657,641,787,3330,2935,1107,1239,2706,919,1464,1356,672,1271,2308,3077,2346,2311,900,2538,3155,2987,2246,1144,2943,1801,2856,2871,2197,1282,3251,2637,2422,3287,1524,2257,2284,3219,811,1471,1821,2446,1862,2923,626,769,2252,2553,1952,2812,2632,2343,2625,964,2874,1112,1688,685,983,1396,2212,827,695,780,2288,3016,2752,2535,1726,1102,2693,2069,1445,2620,3325,3142,2984,1973,1805,2614,663,927,2449,2899,2005,1413,2914,3031,1873,3193,2784,2271,3206,3161,1905,1420,1134,648,1081,749,968,1181,836,1551,776,2715,872,705,1647,3129,2888,2863,3315,3214,971,954,1252,2821,3209,2850,1484,3019,2092,1432,2920,1785,2429,1830,951,1579,643,1220,2354,2569,3246,1262,1235,3359,3174,1285,1738,3095,2675,1543,2838,3356,2975,2511,1372,2266,2584,1898,1257,2357,1955,2843,2320,1052,2949,2722,2865,2479,2088,2045,1966,903,2194,1654,2209,844,2071,2435,3284,2818,3067,2078,1321,2490,2187,3320,1010,1807,771,2907,1590,2443,2406,1481,652,2823,2971,1244,2416,1385,1721,896,2098,1062,2532,2081,3181,2399,1193,1212,763,2902,2095,800,2648,1777,2230,1893,1309,2003,2930,1348,1512,1280,1678,833,1546,1625,1527,1757,3164,2302,2683,1229,2233,1593,2604,2815,1986,2008,1303,3132,790,3145,1859,1989,1363,2334,3347,1335,2704,1056,1473,2340,3045,2021,886,2961,1288,2619,1065,839,2502,3362,1129,1268,1537,1019,1976,723,1880,1505,1120,728,3244,3025,1827,2803,2847,3113,1902,1331,803,940,2881,923,2059,1490,2170,2106,2470,3296,1945,3212,3299,1184,2074,2690,2998,2993,3200,2191,1014,1870]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ITP367_1 : TPTP v8.1.2. Released v8.0.0.
% 0.15/0.16 % Command : run_Leo-III %s %d
% 0.15/0.37 % Computer : n023.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Mon May 6 14:27:54 EDT 2024
% 0.15/0.37 % CPUTime :
% 0.97/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.27/1.21 % [INFO] Parsing done (340ms).
% 2.27/1.22 % [INFO] Running in sequential loop mode.
% 2.71/1.42 % [INFO] eprover registered as external prover.
% 2.71/1.43 % [INFO] cvc4 registered as external prover.
% 2.71/1.43 % [INFO] Scanning for conjecture ...
% 3.19/1.57 % [INFO] Found a conjecture and 639 axioms. Running axiom selection ...
% 3.82/1.71 % [INFO] Axiom selection finished. Selected 615 axioms (removed 24 axioms).
% 4.65/1.98 % [INFO] Problem is typed first-order (TPTP TFF).
% 4.97/2.00 % [INFO] Type checking passed.
% 4.97/2.00 % [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 ...
% 16.08/4.54 % External prover 'e' found a proof!
% 16.08/4.54 % [INFO] Killing All external provers ...
% 16.08/4.54 % Time passed: 4002ms (effective reasoning time: 3318ms)
% 16.08/4.54 % 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)>
% 16.08/4.55 % 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
% 16.08/4.55 % No. of inferences in proof: 1234
% 16.08/4.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4002 ms resp. 3318 ms w/o parsing
% 17.66/4.85 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 17.66/4.86 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------